UNIVERSIDAD COMPLUTENSE DE MADRID FACULTAD DE CIENCIAS GEOLÓGICAS TESIS DOCTORAL Modelización estructural de grandes fallas inversas en Marte: implicaciones en el conocimiento de la estructura y contracción de la litosfera MEMORIA PARA OPTAR AL GRADO DE DOCTOR PRESENTADA POR Andrea Herrero Gil Directores Ignacio Romeo Briones Javier Ruiz Pérez Madrid © Andrea Herrero Gil 2020 Directores Ignacio Romeo Briones Javier Ruiz Pérez Andrea Herrero Gil TESIS DOCTORAL MODELIZACIÓN ESTRUCTURAL DE GRANDES FALLAS INVERSAS EN MARTE: IMPLICACIONES EN EL CONOCIMIENTO DE LA ESTRUCTURA y CONTRACCIÓN DE LA LITOSFÉRA Facultad de Ciencias Geológicas 2 UNIVERSIDAD COMPLUTENSE DE MADRID FACULTAD DE CIENCIAS GEOLÓGICAS TESIS DOCTORAL MODELIZACIÓN ESTRUCTURAL DE GRANDES FALLAS INVERSAS EN MARTE: IMPLICACIONES EN EL CONOCIMIENTO DE LA ESTRUCTURA Y CONTRACCIÓN DE LA LITOSFERA MEMORIA PARA OPTAR AL GRADO DE DOCTOR PRESENTADA POR ANDREA HERRERO GIL DIRECTORES Dr. IGNACIO ROMEO BRIONES Dr. JAVIER RUIZ PÉREZ 4 6 7 AGRADECIMIENTOS La presente tesis doctoral recoge el trabajo de más de cuatro años en los que me he formado como investigadora y como persona. Ha sido un camino largo que me ha permitido adentrarme en el mundo de las Ciencias Planetarias y de la Geología Estructural y que, como cuando damos un paseo por la montaña, ha tenido sus momentos gratificantes pero también sus tramos escarpados. Durante este recorrido he coincidido con diferentes personas que me han ayudado, de una forma u otra, a llegar a la cima de este camino, y que merecen una mención en estas páginas. Tengo que agradecer a Ignacio Romeo y Javier Ruiz la confianza que depositaron en mí al darme oportunidad de realizar esta tesis doctoral bajo su dirección. Gracias por todo el tiempo que habéis dedicado en formarme, he aprendido muchísimo a vuestro lado y espero haber estado a la altura. Gracias Ignacio por guiarme durante esta tesis y por haber derrochado horas y paciencia conmigo. Siempre que me he visto al borde de un problema que me parecía un río insalvable me has convencido de que era un charco fácil de saltar. Sin tu optimismo constante no hubiera llegado tan lejos. Gracias Javi por tus consejos inestimables sobre el funcionamiento del mundo de la investigación científica que, indudablemente, me han permitido conocer y avanzar por este camino con paso firme. Quiero dar las gracias a mis compañeros planetarios Alberto, Fede, Isabel, Laura y Samuel, que siempre han estado ahí para ofrecer su ayuda, responder a mis miles de preguntas y darme ánimos, Ha sido un placer compartir con vosotros comidas, viajes y congresos. Laura, parecía que no llegaríamos nunca a la cima y mira, ya lo tenemos. Hemos acumulado muchísimas historias juntas que recordaré con gran cariño. ¿Te has dado cuenta de que nos falta un Océano Pacífico para haber dado la vuelta al mundo hablando de Marte? Durante estos años he sido doctoranda en el Departamento de Geodinámica, Estratigrafía y Paleontología de la Universidad Complutense de Madrid, y tengo que agradecer al personal de este departamento los medios prestados para la realización de esta tesis doctoral. 8 Aunque el Departamento haya sido reorganizado y renombrado en este tiempo, las costumbres en la cuarta planta son inamovibles, y no ha faltado ni un día el café de media mañana en forestales, el que te salva cuando estás a punto de dormirte delante del ordenador. Jorge, Jose Antonio, Josechu, Juanmi, Martín, Rosa, David, Héctor, Emilio, Carol, Meaza, ha sido un placer compartir todos esos desayunos y conversaciones con vosotros. Gracias por acogerme como a una más en el departamento, por vuestros consejos y por el interés que habéis mostrado por la evolución de esta tesis doctoral. Durante estos años he compartido el despacho 20A con dos grandes personas, Paula y Miguel. Ellos han hecho que las horas y horas que hemos pasado encerrados en esos pocos metros cuadrados hayan sido muchísimo más llevaderas y amenas (aunque ello haya bajado ligeramente nuestra productividad). No podría haber tenido mejores compañeros de despacho. En esta etapa he coincidido con un gran grupo de doctorandos que han supuesto una compañía inmejorable. Sonia, Jose Luis, Mercedes, Maialen, Roselis, Paco, Andrea, Violeta, José Alejandro, Sebas, Juncal y muchos otros, con los que he compartido momentos en el día a día en la facultad. Estas pausas han sido imprescindibles para despejarse, coger energía y continuar, mil gracias por ello. Sonia, te tendría que agradecer muchísimas cosas. Fuiste tú la que me mandó la información para solicitar este contrato predoctoral. Gracias por estar siempre pendiente de mí, por intentar transmitirme tu amor por la ciencia y por alegrarte de mis logros más que yo misma. Espero que sigamos coincidiendo en el camino siempre. Jose Luis, gracias por tu amistad y tu confianza, pero sobre todo, por esas conversaciones absurdas, e incluso políticamente incorrectas, que me reseteaban el cerebro cuando me encontraba un poco frustrada. Al margen del mundo académico, tengo una serie de personas a mi alrededor que siempre han tenido una fe absoluta en que terminaría esta tesis doctoral, y les tengo que agradecer todo el apoyo y el ánimo que me han dado estos años. Todos ellos han formado parte de mis altos en el camino, momentos de desconexión imprescindibles para mi durante esta tesis doctoral. Ana, Celia, Cristina, Sandra, gracias por recordarme desde el principio que, aunque la mayoría del tiempo mi cabeza estuviera en otro planeta, hay que mirarse los pies y disfrutar del día a día. Gracias por escucharme siempre atentamente, por preocuparos por mí, y por todas las horas en las que me habéis hecho olvidar que Marte existía. Hay personas a las que me ha ido uniendo la geología a lo largo de los años, ya sea directa o indirectamente. Con ellos parece que el tiempo no pasa y seguimos compartiendo momentos siempre que nos es posible. Yul, Julio, Luis, Elvira, Raúl, Inés, Alejandra, Ane, Marta, Ana Arribas, Julia y Lucía, gracias por vuestro apoyo, por mostrar 9 interés por esta tesis doctoral pero, sobre todo, por preocuparos por mi durante su desarrollo. Tengo que agradecerle a Cristina que me arrastrase a la Academia Espacio Arte, porque si ha habido momentos de desconexión total de la tesis son las tardes que he pasado allí metida. Gracias Elena, porque tu “esto lo solucionamos con barro” es una de las mejores terapias que conozco para un mal día. Quiero agradecer a mi familia la atención, interés y cariño que siempre me muestran. Debo dar las gracias en especial a mi primo Guillermo que ha seguido con atención la evolución de esta tesis y ha tenido la paciencia de leerse los tres artículos que la conforman. Esta tesis doctoral se la debo por completo a mis padres, y a ellos se la dedico. Desde que un día paseando por la playa os dije que quería estudiar geología, me habéis acompañado y me habéis animado en cada una de las decisiones que he tomado. Sin vuestra confianza y apoyo incondicional no habría podido dar ni el primero de todos los pasos que me han llevado hasta aquí. Os lo debo todo. Por último, le tengo que agradecer a Ángel que me haya acompañado durante todo este recorrido. Gracias por disfrutar conmigo cuando el camino ha sido llano y por no parar de animarme cuando ha venido una cuesta arriba. Consigues que las preocupaciones se evaporen con un simple paseo por Madrid o que incluso recuerde con cariño una tarde repasando cálculos en las servilletas de una cafetería. No se por dónde seguirá el camino ahora, pero espero que tengas las zapatillas preparadas. 10 11 ÍNDICE RESUMEN ........................................................................................................................... 15 ABSTRACT ........................................................................................................................... 17 1. Presentación ................................................................................................................. 19 1.1. Formato de la memoria ..................................................................................... 22 1.2. Objetivos ............................................................................................................ 24 2. Introducción general .................................................................................................... 25 2.1. Marco tectónico de Marte ................................................................................. 29 2.1.1 Estructuras tectónicas ............................................................................. 29 2.1.2. El patrón tectónico de Marte .................................................................. 32 2.2. Escarpes lobulados ............................................................................................. 37 3. Análisis estructural y modelización 2D de grandes fallas inversas en Marte .............. 43 3.1. Introducción ....................................................................................................... 45 3.2. Structural modeling of lobate scarps in the NW margin of Argyre impact basin, Mars ................................................................................................................... 47 3.2.1. Introduction ............................................................................................. 48 3.2.2. Geological setting and structural mapping ............................................. 50 3.2.3. Methods .................................................................................................. 53 3.2.3.1. Horizontal shortening of deformed craters ................................ 54 3.2.3.2. Balanced cross sections method. ............................................... 56 3.2.3.3. Forward mechanical dislocation method ................................... 57 3.2.4. Structural analysis and modeling ........................................................... 58 3.2.4.1. Results of the cross-cut craters .................................................. 59 3.2.4.2. Results of the balanced cross sections ....................................... 61 3.2.4.3. Results of the forward mechanical dislocation method ............. 62 3.2.4.4. Displacement-Length relationships ............................................ 64 3.2.5. Heat flow ................................................................................................ 65 3.2.6. Discussion and conclusions .................................................................... 66 3.3. Conclusiones Capítulo 3 ..................................................................................... 73 12 4. Modelización 3D de grandes fallas inversas en Marte ................................................ 75 4.1. Introducción ....................................................................................................... 77 4.2. 3D modeling of planetary lobate scarps: the case of Ogygis Rupes, Mars ........ 79 4.2.1. Introduction ............................................................................................. 80 4.2.2. Ogygis Rupes ........................................................................................... 81 4.2.3. Method .................................................................................................... 84 4.2.3.1. Geometric parameters of fault planes ....................................... 84 4.2.3.2. Trishear parameters.................................................................... 85 4.2.3.3. Modeling workflow ..................................................................... 86 4.2.4. Results of 3D modeling of Ogygis Rupes ................................................. 86 4.2.4.1. 3D Restoration ............................................................................ 86 4.2.4.2. 3D Forward modeling ................................................................ 89 4.2.5. Discussion ................................................................................................ 91 4.2.5.1. Implications for Mars tectonics. ................................................. 95 4.2.6. Conclusions .............................................................................................. 97 4.3. Conclusiones Capítulo 2 ..................................................................................... 98 5. Modelo 3D del sistema de fallas inversas de Amenthes, Marte ................................. 99 5.1. Introducción ..................................................................................................... 101 5.2. Lithospheric contraction on Mars: A 3D model of the Amenthes thrust fault system ............................................................................................................. 103 5.2.1. Introduction ........................................................................................... 104 5.2.1.1. Amenthes Rupes ....................................................................... 105 5.2.2. Data and Method .................................................................................. 107 5.2.3. 3D Structural Analysis Results ............................................................... 110 5.2.3.1. 3D Restoration .......................................................................... 111 5.2.3.2. 3D Forward Modeling ............................................................... 114 5.2.4. Discussion .............................................................................................. 116 5.2.4.1. Structural Modeling .................................................................. 116 5.2.4.2. Tectonic Evolution and Implications for Global Contraction .... 122 5.2.5. Conclusions ............................................................................................ 123 5.3. Conclusiones Capítulo 3 ................................................................................... 125 6. Discusión .................................................................................................................... 127 6.1 Discusión metodológica ................................................................................... 129 6.2. Discusión de los resultados .............................................................................. 131 6.2.1. Profundidad de despegue y estructura mecánica ................................ 131 6.2.2. Buzamientos de las fallas ...................................................................... 134 6.2.3. Geometría de los planos de falla ........................................................... 134 6.2.4. Desplazamiento y acortamiento horizontal .......................................... 135 13 6.3. Implicaciones globales ..................................................................................... 137 6.3.1. Tectónica global .................................................................................... 137 6.3.2. Contracción global ................................................................................. 139 6.4. Perspectiva futura sobre el estudio de escarpes lobulados ............................ 142 7. Conclusiones .............................................................................................................. 145 BIBLIOGRAFÍA ................................................................................................................... 151 ANEXO I ........................................................................................................................... 167 Herrero-Gil, A., Egea-González, I., Ruiz, J., Romeo, I., 2019. Structural modeling of lobate scarps in the NW margin of Argyre impact basin, Mars. Icarus 319, 367–380. ANEXO II .......................................................................................................................... 183 Herrero-Gil, A., Ruiz, J., Romeo, I., 2020. 3D modeling of planetary lobate scarps: The case of Ogygis Rupes, Mars. Earth and Planetary Science Letters 532, 116004. Supplementary material S1 ANEXO III ......................................................................................................................... 199 Herrero-Gil, A., Ruiz, J., Romeo, I., 2020. Lithospheric contraction on Mars: A 3D model of the Amenthes thrust fault system. Journal of Geophysical Research: Planets 125 (3), e2019JE006. Supplementary material S2 14 15 RESUMEN Los escarpes lobulados son relieves que se han descrito en diferentes cuerpos planetarios de tipo terrestre y cuya formación se atribuye al desplazamiento de grandes fallas inversas con rotura en superficie. El estudio de estos relieves en Marte y la caracterización estructural de las fallas que los forman permite ahondar en el estudio de la estructura de la litosfera marciana en el momento de su formación, ya que la profundidad de estas grandes fallas inversas en Marte ha sido relacionada con la profundidad de la transición frágil-dúctil de la época en la que se formaron. Además, conocer cómo se acomoda la contracción en estas grandes fallas inversas permite interpretar regionalmente la deformación que las produjo y el papel de estas estructuras en el patrón tectónico de Marte. En la presente tesis doctoral se han estudiado tres escarpes lobulados localizados en Aonia Terra (Ogygis Rupes, Bosporos Rupes y Phrixi Rupes) y el sistema de fallas de Amenthes Rupes, en la Región de Amenthes. Para ello, se han modelizado un total de doce fallas inversas (incluyendo fallas mayores y menores) relacionadas con la formación de estos relieves. Estas estructuras presentan direcciones concordantes con los campos de esfuerzos que generaron las grandes provincias tectónicas adyacentes, como son la zona de alrededor de la cuenca de impacto de Argyre y los Montes de Thaumasia en el caso de Aonia Terra, o la gran dicotomía en el caso de la Región de Amenthes. Las fallas inversas estudiadas se formaron durante el Noeico Tardío/Hespérico Temprano, junto con otras fallas asociadas a escarpes lobulados distribuidas por las tierras altas de Marte. La modelización de estos relieves permite obtener una aproximación a los parámetros estructurales que definen las grandes fallas inversas subyacentes, atendiendo a que la topografía del escarpe lobulado está relacionada con la geometría de la falla en profundidad. La modelización estructural de las grandes fallas inversas estudiadas se ha llevado a cabo utilizado tres métodos: (1) Cortes compensados por áreas, (2) Método de dislocación mecánica, (3) Combinación de los métodos de fault-parallel flow y trishear en una modelización 3D. La utilización de tres métodos distintos ha dado lugar a un marco de comparación y discusión de los resultados obtenidos, permitiendo obtener conclusiones más robustas sobre la geometría del plano de falla, la profundidad de enraizamiento, el desplazamiento y las variaciones que presentan lateralmente estos parámetros para las fallas estudiadas. 16 Los resultados obtenidos reflejan que las principales fallas inversas analizadas presentan un nivel de despegue profundo situado entre 18 y 36 km, que concuerda con estudios previos en escarpes lobulados que datan de la misma época, apoyando que estas fallas se enraízan en una importante discontinuidad mecánica, atravesando todo el dominio frágil de la parte superior de la corteza. Por otro lado, las fallas menores (secundarias y subsidiarias) modelizadas presentan niveles de despegue someros (entre 2.3 y 13 km) que podrían indicar la existencia de discontinuidades mecánicas menores dentro de este dominio frágil de la corteza. Las morfologías obtenidas mediante la modelización 3D para estas fallas reflejan un buzamiento constante entre 23 y 39° para los primeros kilómetros cerca de la superficie, que disminuye progresivamente en profundidad presentando una geometría lístrica que enraíza en un nivel de despegue subhorizontal. Esto implicaría que el desplazamiento a lo largo del plano de falla de estas fallas inversas es transmitido desde el nivel de despegue, siendo un valor representativo de la contracción horizontal acomodada por la falla. Como consecuencia, el acortamiento regional asociado a cada falla sería entre un ∼6 y un ∼30% mayor usando una falla lístrica que cuando este valor es calculado usando fallas que presentan un buzamiento constante en profundidad. Por otro lado, la modelización del sistema de fallas inversas de Amenthes completo ha permitido obtener valores de acortamiento regional medios para esta zona de entre 2 y 3 km, que en la zona sureste del sistema alcanza los ∼5.5 km. Estos valores suponen un acortamiento en la región entre un 60 y un 200% mayor que el valor calculado previamente modelizando sólo la falla principal del sistema (Amenthes Rupes), lo que refleja la importancia de incluir fallas inversas secundarias y subsidiarias en los cálculos de acortamiento asociados. Atendiendo a estos resultados, el acortamiento horizontal asociado a las fallas inversas que subyacen los escarpes lobulados en una región determinada puede ser constreñido y podría verse sustancialmente incrementado al tener en cuenta la forma lístrica de las mismas en profundidad y la presencia de fallas menores. Esto aumentaría considerablemente las estimaciones de acortamiento global relacionadas con el periodo de contracción que afecta a la litosfera de Marte durante el Noeico Tardío/Hespérico Temprano y que se asocia con la formación de estas estructuras. 17 ABSTRACT Lobate scarps are structural reliefs described on terrestrial planetary surfaces, which formation is related to the displacement of underlying large thrust faults. The study of these reliefs on Mars and the structural analysis of the associated thrust faults allow to improve the knowledge of the lithospheric structure, because the depth of these large thrust faults has been related to the depth of the brittle-ductile transition at the time of formation. Besides, the study of the regional contraction registered on these structures provides information about the causing deformation and the role of these faults in the tectonic pattern of Mars. Three lobate scarps formed by thrust faults located in Aonia Terra (Ogygis Rupes, Phrixi Rupes and Bosporos Rupes) and the Amenthes Rupes thrust fault system, located in the Amenthes Region, have been analyzed in this doctoral dissertation. In order to do that, twelve different thrust faults (including major and minor faults) related to the formation of these reliefs have been modeled. The strike of these structures agrees with the stress fields generated by lateral variations of crustal thickness due to the presence of large tectonic provinces, being parallel to the edge of Thaumasia Montes and concentric to Argyre impact basin in Aonia Terra, and parallel to the dichotomy boundary in the Amenthes Region. The studied thrust faults were formed in the Late Noachian/Early Hesperian, together with other similar faults associated with lobate scarps previously studied in the martian highlands. The modeling of lobate scarp reliefs provides an approximation to the structural parameters defining the underlying large thrust faults, on the basis that the lobate scarp relief is related to the fault plane geometry at depth. The structural modeling of the thrust faults has been performed using three methods: (1) Balanced cross sections, (2) forward mechanical dislocation modeling, and (3) a combination of fault-parallel flow and trishear algorithms in a 3D modeling environment. The use of three different methods create a comparison and discussion framework for the results obtained, providing stronger conclusions about fault plane geometry, depth of faulting, fault slip and lateral variations of these parameters for the studied faults. The results obtained show that the main analyzed faults root into a deep decollement level located between 18 and 36 km of depth, which agrees with previous studies of martian lobate scarps formed in the Late Noachian/Early Hesperian. These 18 results support that these large thrust faults transect the entire brittle domain of the upper crust rooting into a main mechanical threshold. On the other hand, the minor faults modeled (secondary and subsidiary faults) show shallower depths of faulting located between 2.3 and 13 km deep, possibly indicating the presence of mechanical discontinuities inside that brittle domain. The fault morphologies obtained by 3D modeling show a constant dip angle between 23 and 39° for the upper kilometers near the surface that decreases progressively at depth, rooting into a subhorizontal decollement with a listric geometry. This listric morphology implies that the slip on the fault ramp is fully transmitted from the decollement level, being representative of the horizontal contraction accommodated by the thrust fault. Consequently, the regional shortening registered by each fault would be between ∼6 and ∼30% higher than if the shortening is calculated as the heave over a planar fault with a constant dip angle. Furthermore, the modeling of the Amenthes Rupes thrust fault system has provided mean shortening values for the region that range between 2 and 3 km, increasing up to ∼5.5 km in the southeast part of the system. These estimates imply that the regional contraction of the area, registered by these thrust faults, is between a 60 and 200% higher than previous estimates calculated through the modeling of just the main fault of the system (Amenthes Rupes), showing the importance of including secondary and subsidiary faults. The obtained results imply that the horizontal contraction related to the thrust faults that underlain the lobate scarps in a particular region can be better constrained and its value would increase substantially considering the listric morphology of the fault planes at depth and the presence of minor faults. This would increase considerably the global shortening estimates related to the period of contraction affecting the martian lithosphere in the Late Noachian/Early Hesperian that is associated with the formation of these thrust faults. 1 PRESENTACIÓN CAPÍTULO 1 21 La presente tesis doctoral se ha realizado en el Departamento de Geodinámica, Estratigrafía y Paleontología de la Universidad Complutense de Madrid, dentro del Programa de Doctorado de Geología e Ingeniería Geológica. Esta tesis se ha llevado a cabo bajo la dirección y supervisión del Dr. Ignacio Romeo Briones (Universidad Complutense de Madrid) y el Dr. Javier Ruiz Pérez (Universidad Complutense de Madrid), y se ha desarrollado dentro del grupo de investigación de Geodinámica Planetaria, Tectónica Activa y Aplicaciones a Riesgos (UCM-910368). La financiación para la realización de la tesis doctoral ha sido proporcionada por una Ayuda para contratos predoctorales para la formación de doctores 2015 (BES-2015- 073983), contemplada dentro del Programa Estatal de Promoción del Talento y su Empleabilidad en I+D+i perteneciente al actual Ministerio de Ciencia, Innovación y Universidades del Gobierno de España. Esta tesis también ha recibido financiación de los proyectos de investigación AMARTE “Análisis de la tectónica y evolución interna de Marte” (CGL2014-59363-P), AMARTE2 “Análisis de la tectónica y evolución interna de Marte 2: Nuevas perspectivas (PR75/18-21613), y TECTOMARTE “Tectónica, flujo térmico y evolución planetaria de Marte” (PGC2018-095340-B-I00). CAPÍTULO 1 22 1.1. Formato de la memoria La memoria de esta tesis doctoral se presenta en formato de compendio de publicaciones, las cuales cumplen con los objetivos planteados y recogen los resultados obtenidos durante el desarrollo de la misma. Esta memoria sigue la normativa establecida por el R.D. 99/2011 de 28 de enero (BOE 10/02/2011), que regula los estudios de doctorado en la Universidad Complutense de Madrid (BOUC 29/04/2015) y por la normativa del Programa de Doctorado de Geología e Ingeniería Geológica, aprobada por la Junta de la Facultad de Ciencias Geológicas de la Universidad Complutense de Madrid el 16 de noviembre de 2016. Siguiendo esta normativa, después del capítulo de presentación se ha incluido un capítulo de introducción general al tema a tratar en la presente tesis doctoral. Posteriormente se incluyen los tres capítulos centrales que están formados por los tres artículos científicos que componen el cuerpo central de la tesis doctoral, cada uno precedido de una introducción y las correspondientes conclusiones parciales. Este cuerpo central de la tesis está seguido por un sexto capítulo de discusión que integra los tres capítulos principales y, por último, un séptimo capítulo de conclusiones generales de todo el conjunto. Los tres artículos científicos que componen los tres capítulos principales de la tesis se han publicado en revistas incluidas en el Journal Citation Reports (JCR). • El capítulo 3 recoge el análisis estructural realizado en tres grandes fallas inversas localizadas entre los montes de Thaumasia y el NW de la cuenca de impacto de Argyre (Ogygis Rupes, Bosporos Rupes y Phrixi Rupes). Este análisis ha permitido ahondar en las características mecánicas y térmicas de la litosfera de esta región e interpretar la relación entre la formación de estas y los grandes relieves de Thaumasia y Argyre. Herrero-Gil, A., Egea-González, I., Ruiz, J., Romeo, I., 2019. Structural modeling of lobate scarps in the NW margin of Argyre impact basin, Mars. Icarus 319, 367–380. https://doi.org/10.1016/j.icarus.2018.09.027 • El capítulo 4 recoge los resultados obtenidos de una modelización estructural 3D de la falla inversa y dos fallas subsidiarias que forman Ogygis Rupes. Este enfoque expande la información previa de estas estructuras de acortamiento, obteniendo una visión global de la estructura del escarpe lobulado, CAPÍTULO 1 23 identificando variaciones en la geometría del plano de falla y la relación con estructuras subsidiarias. Herrero-Gil, A., Ruiz, J., Romeo, I., 2020. 3D modeling of planetary lobate scarps: The case of Ogygis Rupes, Mars. Earth and Planetary Science Letters 532, 116004. https://doi.org/10.1016/j.epsl.2019.116004 • En el capítulo 5 se utiliza el mismo enfoque que en el capítulo anterior para modelizar un sistema completo de fallas inversas en la región de Amenthes. Mediante el análisis de los parámetros que controlan la geometría de estas fallas inversas, la cinemática de las mismas y la interacción entre las fallas que conforman este sistema de fallas, ha sido posible analizar cómo fue la contracción litosférica en esta región e interpretar su evolución tectónica. Herrero-Gil, A., Ruiz, J., Romeo, I., 2020. Lithospheric contraction on Mars: A 3D model of the Amenthes thrust fault system. Journal of Geophysical Research: Planets 125 (3), e2019JE006. https://doi.org/10.1029/2019JE006201 CAPÍTULO 1 24 1.2. Objetivos El objetivo principal de esta tesis es la caracterización estructural de las grandes fallas inversas que forman los relieves conocidos como escarpes lobulados en la superficie de Marte. La modelización de estas estructuras tectónicas busca avanzar en el conocimiento de la deformación y estructura de la litosfera marciana, entender sus condiciones tectónicas de formación y conocer su papel en el patrón tectónico de Marte, así como ahondar en las posibles implicaciones que esto tiene en la geodinámica y evolución del planeta a lo largo de su historia geológica. Para la consecución de este objetivo principal se establecieron inicialmente una serie de objetivos parciales o específicos. • Estudio de las características estructurales de las grandes fallas inversas que forman los escarpes lobulados en Marte. Análisis del relieve que forma el escarpe lobulado, así como de la dirección de la estructura y vergencia del pliegue. Obtención de la geometría de las fallas en profundidad así como los parámetros que las definen. • Deducción de la evolución temporal de dichas estructuras tectónicas en relación con las formaciones geológicas a las que deforman y con las estructuras adyacentes. Análisis del grado de interacción de las fallas inversas principales con otras fallas secundarias o subsidiarias. • Estudio de las implicaciones que tiene el análisis de las características de estas estructuras en el conocimiento de la estructura de la litosfera y en la evolución geodinámica de Marte, atendiendo a la geometría y profundidad de las fallas, y a la contracción acomodada por su desplazamiento. Interpretación de los procesos tectónicos relacionados con su formación. 2 INTRODUCCIÓN GENERAL CAPÍTULO 2 27 Marte y la Tierra tuvieron unas condiciones de formación similares, por esta razón ambos cuerpos planetarios presentan una composición y estructura interna parecidas. Sin embargo, la historia evolutiva de estos dos cuerpos terrestres ha sido muy distinta, como puede apreciarse en las diferencias que presentan en la actualidad tanto geológica como atmosférica y climáticamente. Esto podría relacionarse con la diferencia de tamaño entre estos dos planetas, siendo el tamaño de Marte mucho menor y presentando una menor intensidad de la gravedad sobre su superficie. En la superficie de Marte hay indicios de que las condiciones ambientales pudieron ser similares a las de la Tierra durante el Noeico, época que va desde la formación del planeta hasta hace ∼3500–3700 Ma (Hartmann y Neukum, 2001; Hartmann, 2005; Werner y Tanaka, 2011), con un ciclo hidrológico importante, una atmósfera densa y una fuerte actividad geológica. Sin embargo, hacia el final de esta época o el inicio del Hespérico, se ha descrito un decrecimiento de la actividad geológica (e.g. Anderson et al., 2001) y un cambio en la composición del vulcanismo, el cual se relaciona con un descenso de la temperatura del manto y/o un cambio en el grado de fusión parcial del manto (e.g. Wilson et al., 2013). Estos cambios en la geodinámica interna del planeta son más o menos coincidentes en el tiempo con variaciones importantes en las condiciones hidrogeológicas, que se reflejan en una disminución drástica de la erosión hídrica y un cambio en la sedimentación (e.g. Golombek y Bridges, 2000; Ehlmann et al., 2011; Mangold et al., 2012); y en las condiciones atmosféricas, pasando a presentar una atmósfera tenue con características más parecidas a las que tiene en la actualidad (e.g. Chassefière et al., 2007). Estos cambios atmosféricos y climáticos se han relacionado con el emplazamiento de la gran provincia volcánica de Tharsis (Phillips et al., 2001) o con el cese del campo magnético global del planeta hace 3700–4000 Ma (e.g. Chassefière et al., 2007; Langlais et al., 2012; Milbury et al., 2012). Otros cambios que se han detectado en esta época en la geodinámica interna de Marte, son cambios en el flujo térmico y en el espesor litósferico hace aproximadamente 3700 Ma (Ruiz et al., 2011; Ruiz, 2014). La relación entre los cambios en la geodinámica interna y externa que presenta un planeta es indiscutible, pero la coincidencia de tantos eventos, tanto ambientales como geológicos, indica que la historia climática de Marte está muy ligada a su evolución interna (Ruiz, 2014), aunque aún se desconozcan las causas exactas. Son estas similitudes y diferencias en la evolución, junto con la cercanía de Marte, los que hacen que este planeta sea el más estudiado del Sistema Solar después de la Tierra. La mejora del conocimiento de este planeta y su evolución geodinámica repercute en la mejora del conocimiento que tenemos de los cuerpos planetarios terrestres, y por lo tanto de la dinámica y evolución de nuestro propio planeta, permitiendo comparar teorías y modelos. En la actualidad los tipos de datos globales disponibles de Marte son muy variados y completos, procedentes de diferentes proyectos de exploración espacial CAPÍTULO 2 28 llevados a cabo por las agencias espaciales. Estos datos suelen ser de libre disposición y accesibles a través de los servidores de la agencia espacial encargada de cada instrumento o misión, e incluyen desde imágenes de diferente resolución en longitudes de onda visibles o infrarrojas, modelos de elevación del terreno obtenidos mediante láser, mapas de anomalías magnéticas en la corteza, mapas de anomalías gravimétricas, e incluso mapas de distribución de algunos elementos químicos. El importante aumento de datos de la superficie de Marte en los últimos años, y la gran mejora de la calidad de los mismos, ha supuesto un importante avance en la cartografía geológica y estructural de la superficie de Marte, y por lo tanto de la comprensión de la geología marciana y de las estructuras y procesos geológicos que han tenido lugar en el planeta. CAPÍTULO 2 29 2.1. Marco tectónico de Marte A nivel geológico y tectónico cabe destacar que Marte carece de un mecanismo eficaz de reciclaje cortical, papel que en la Tierra hace la tectónica de placas. Esto sumado a las bajas tasas de erosión durante el Hespérico y el Amazónico (e.g. Golombek y Bridges, 2000; Golombek y Phillips, 2010), hacen posible que en la superficie de este planeta tengamos un registro de acontecimientos y procesos geológicos bastante completo, encontrando superficies geológicas muy antiguas con edades de datación que llegan hasta el preNoeico (>4100 Ma) (e.g. Tanaka, 1986; Hartmann y Neukum, 2001; Frey et al., 2006; Nyquist et al., 2001). Por ello, existe en Marte un amplio registro de eventos tectónicos, fluviales, glaciares y volcánicos sucedidos a lo largo de prácticamente toda su historia geológica. El estudio de las estructuras de deformación registradas en la superficie de Marte proporciona información sobre la geodinámica interna del planeta y sobre su evolución a lo largo del tiempo. Los principales procesos tectónicos responsables de la formación y distribución de estructuras tectónicas en Marte son la contracción global del planeta debido a su enfriamiento progresivo (e.g. Andrews-Hanna et al., 2008; Nahm y Schultz, 2011), y la flexión de la litosfera debida a la existencia de cargas locales y regionales (causadas, por ejemplo, por el emplazamiento de edificios volcánicos o de llanuras de coladas magmáticas, y por variaciones en el espesor de corteza y la topografía del Moho debido a impactos meteoríticos no compensadas isostáticamente; e.g. Thomson y Head, 2001; Watters y McGovern, 2006; Ruiz et al., 2009) o incluso a escala planetaria (emplazamiento de Tharsis; Phillips et al., 2001). 2.1.1. Estructuras tectónicas En la superficie de Marte es posible identificar diferentes tipos de estructuras de deformación que nos indican que el planeta ha tenido una actividad tectónica importante en el pasado. Las estructuras extensionales y de contracción son muy comunes en este planeta, mientras que las estructuras de desgarre, aunque también presentes en la superficie de Marte, son escasas y en su mayoría son estructuras de acomodación relacionadas con las estructuras de contracción (e.g. Schultz, 1989) o debidas a cambios locales de esfuerzos (e.g. Okubo y Schultz, 2006). Estructuras extensionales Las estructuras extensionales varían en escala pudiendo encontrar desde pequeñas fracturas que apenas presentan desplazamiento (e.g. Okubo, 2010), a grandes fallas con un desplazamiento importante. Estas últimas pueden presentarse como escarpes formados por el desplazamiento de una única falla normal (e.g. Smrekar et al., CAPÍTULO 2 30 2004; Bernhardt et al., 2016), grabens estrechos con formas lineales de cientos de kilómetros de longitud cuya formación ha sido relacionada con la presencia de diques (e.g. Schultz et al., 2004), o grandes rifts de decenas de kilómetros de ancho controlados por el desplazamiento de fallas normales de alto ángulo (e.g. Schultz, 1995; Wilkins y Schultz, 2003). Estructuras de contracción o acortamiento Las estructuras de contracción o acortamiento son estructuras que generan un relieve topográfico positivo y que tradicionalmente se han clasificado según sus dimensiones y criterios geomorfológicos en crestas sinuosas, crestas de relieve alto y escarpes lobulados. Estos términos son una clasificación genérica geomorfológica que se ha venido usando desde el comienzo de las investigaciones planetarias para describir relieves positivos formados por estructuras tectónicas en cuerpos rocosos (Mercurio, Marte y la Luna), y que funciona de forma general, pero no tiene en cuenta las múltiples variaciones geométricas que podemos encontrar, como cambios laterales entre estos tipos de estructuras (e.g. Ruiz et al., 2012), ni los procesos tectónicos asociados a dicha estructura (e.g. Byrne et al., 2018; Klimczak et al., 2019). Debido al aumento de la disponibilidad de datos superficiales de los diferentes cuerpos rocosos del Sistema Solar y el avance de las ciencias planetarias, actualmente se tiene más información sobre estas estructuras y es posible interpretar prácticamente con total seguridad que la formación de la mayoría de las estructuras descritas con estos nombres está relacionada con el resultado de la acomodación de una contracción en una litosfera frágil mediante la formación de fallas inversas y su plegamiento asociado (e.g. Strom et al., 1975; Melosh y McKinnon, 1988; Watters et al., 2004; Watters y Nimmo, 2010). Las crestas sinuosas o wrinkle ridges son las estructuras tectónicas más numerosas sobre la superficie de Marte. Estas estructuras presentan un relieve estrecho que puede llegar a medir cientos de kilómetros de longitud, con una morfología de lineal a curvada o sinuosa (Fig. 2.1). Se encuentran globalmente distribuidas por toda la superficie, aunque son predominantes sobre terrenos volcánicos topográficamente lisos (Watters, 1988). Están formados por una cresta de decenas de kilómetros de anchura que puede llegar a tener varios cientos de metros de alto (ridge), y en la parte superior presentan una forma Figura 2.1 Crestas sinuosas en el Norte de Aonia Terra. El perfil topográfico A-A’ muestra un perfil transversal a la estructura. CAPÍTULO 2 31 crenulada (wrinkle), y a veces discontinua, característica (Schultz, 2000). Estas estructuras son en general asimétricas en sección transversal, con importantes cambios laterales tanto en la anchura como en la altura. Aunque su interpretación es bastante polémica, el análisis detallado de su topografía y la comparación con estructuras terrestres parecen apoyar que estas estructuras se forman por el plegamiento de la superficie asociado al movimiento de una falla inversa ciega (e.g. Schultz, 2000; Golombek et al., 2001; Vidal et al., 2003, Mueller y Golombek, 2004) y la forma crenulada superior (Fig. 2.1) se atribuye al desplazamiento de una falla retrocabalgante antitética que se nuclea en un nivel de debilidad, o a fallas de deslizamiento flexural que facilitan la flexión de los materiales estratificados en los que se forman (e.g. Schultz, 2000; Okubo y Schultz, 2003; Mueller y Golombek, 2004). Las crestas de relieve alto (high-relief ridges) presentan un relieve mayor que las crestas sinuosas, pudiendo exceder el kilómetro de altura (Watters, 1993) y presentando longitudes de cientos de kilómetros (Fig. 2.2). Son las estructuras de contracción menos comunes, siendo escasas en Marte, donde se han descrito algunas en las tierras altas del Noeico (Watters, 2003; Mége y Ernst, 2001). Además de ser estructuras de mayor tamaño, las crestas de relieve alto se diferencian de los escarpes lobulados y las crestas sinuosas por tener una morfología por lo general simétrica en sección transversal (Watters et al., 2001) (Fig 2.2). Lateralmente sus dimensiones pueden variar ligeramente, sin mostrar cambios de tamaño y forma tan fuertes como las crestas sinuosas (Byrne et al., 2018). Estas estructuras son interpretadas como anticlinales simétricos formados por el desplazamiento de fallas inversas de alto ángulo (>45°) (Watters y Nimmo, 2010). Figura 2.2 Crestas de relieve alto al W-SW de la región de Tharsis (Mége y Ernst, 2001). El perfil topográfico B-B’ muestra un perfil transversal a la estructura. Los escarpes lobulados (lobate scarps) son grandes elevaciones topográficas que en superficie presentan una forma de lineal a arqueada, pudiendo llegar a medir cientos de kilómetros de longitud y presentar un relieve de más de 2 kilómetros (e.g. Strom et al., 1975; Melosh y McKinnon, 1988; Watters, 1993). En perfil transversal presentan una morfología marcadamente asimétrica, con una pendiente trasera tendida y una pendiente frontal abrupta (Fig. 2.3). Estas estructuras se interpretan como la expresión en superficie de grandes fallas inversas de bajo ángulo (<45o) (e.g. Strom et al., 1975; Watters, 1993; Watters y Robinson, 1999; Schultz y Watters, 2001). CAPÍTULO 2 32 Las grandes fallas inversas asociadas a la formación de los escarpes lobulados son el objeto de estudio de esta tesis doctoral, por lo que su descripción, formación, distribución e importancia del estudio de estas estructuras será presentada con más detalle en la sección 2.2. 2.1.2. El patrón tectónico de Marte El patrón tectónico de Marte viene marcado por una serie de provincias geológicas con importantes relieves asociados que generan variaciones en la distribución de esfuerzos a su alrededor. Aunque puede haber variaciones locales de esfuerzos que afecten a la dirección de las estructuras, por lo general los grandes relieves rigen la dirección y distribución de las estructuras tectónicas del planeta (Fig. 2.4). La gran dicotomía global de la corteza marciana, cuyo origen es aún muy discutido, es una de las grandes características topográficas del planeta. La dicotomía separa las tierras del norte de las tierras del sur (Fig. 2.4a), las cuales tienen características topográficas y geológicas muy diferentes. Las tierras del norte, también conocidas como tierras bajas, poseen en general un relieve bajo y bastante homogéneo, formado predominantemente por unidades geológicas volcánicas y sedimentarias recientes que generan una superficie bastante suave con una densidad de cráteres baja. La baja densidad de cráteres afectando estas unidades geológicas que tapizan las tierras bajas sugieren una edad de la superficie correspondiente al Hespérico/Amazónico, sin embargo, los cráteres enterrados por estas unidades indican la presencia de un basamento Noeico (e.g. Head et al., 2002; Tanaka et al., 2003; Pan et al., 2019). Las tierras del sur poseen una topografía elevada con respecto a las tierras bajas del norte, por ello son conocidas como tierras altas del sur. Su superficie es abrupta y presenta una alta densidad de cráteres, y en ella se pueden identificar unidades geológicas más antiguas y variadas, que van desde el Noeico Temprano al Amazónico (Tanaka et al., 2014a, 2014b). La dicotomía, como zona Figura 2.3 Escarpe lobulado Ogygis Rupes, localizado en la región de Aonia Terra. El perfil topográfico C-C’ muestra un perfil transversal a la estructura. CAPÍTULO 2 33 de transición entre las tierras altas y las bajas, es un límite especialmente erosionado y afectado por cauces fluviales secos, canales y cráteres (e.g. Howard et al., 2005). Pese a ello, es posible distinguir una serie de estructuras tectónicas extensionales (fallas normales) que forman unos escarpes paralelos a la dicotomía que acomodan el descenso de las tierras del norte con respecto a las del sur (e.g. McGill y Dimitou, 1990; Smrekar et Figura 2.4 Mapa global de Marte hecho mediante superposición del Modelo Digital del Terreno MOLA sobre su modelo de sombras. Sobre él se han representado: (a) Las regiones más importantes del planeta, incluyendo las regiones nombradas en esta tesis. (b) El catálogo de fallas de Marte de Knapmeyer et al. (2006, 2008). CAPÍTULO 2 34 al., 2004) (Fig. 2.4b). Además, se identifican una serie de escarpes lobulados localizados en las tierras altas que son paralelos a la dicotomía en las regiones de Arabia Terra, Amenthes Region y Terra Cimmeria, entre los que se encuentra Amenthes Rupes (e.g. Watters, 2003a; Watters y Robinson, 1999). La provincia volcánica de Tharsis, la región más elevada de Marte, está centrada cerca de la zona ecuatorial del planeta y se extiende entre los hemisferios norte y sur (Fig. 2.4a). En la zona norte de esta región se concentran los grandes edificios volcánicos de Marte, entre los cuales se encuentra Olympus Mons, la mayor elevación conocida en todo el Sistema Solar, con un relieve de 27 km. En la zona sur y sureste de la región de Tharsis se encuentran los Montes de Thaumasia, que incluyen un plateau tectónico formado por una alta planicie volcánica rodeada de zonas montañosas muy afectadas por procesos de deformación, que eran parte de las tierras altas (Dohm y Tanaka, 1999). La actividad tectónica en la región de Tharsis comenzó en el Noeico Temprano (∼4100 Ma), teniendo su mayor actividad o crecimiento durante el Noeico Tardío/Hespérico Temprano (Anderson et al., 2001; Phillips et al., 2001; Viviano-Beck et al., 2017; Bouley et al., 2018), y se extendió hasta el Amazónico Tardío (e.g. Anderson et al., 2001; Head et al., 2002; Bouley et al., 2018). El foco de actividad en esta región ha ido variando a lo largo de todo este tiempo, dando lugar a una compleja historia tectónica. Por ello, las estructuras tectónicas no se encuentran uniformemente distribuidas alrededor de Tharsis (Fig. 2.4b), sino que es posible identificar una tendencia general en su distribución, encontrando que las estructuras extensionales son generalmente radiales a Tharsis mientras que las compresivas presentan una dirección concéntrica (e.g. Dohm y Tanaka, 1999; Mangold et al., 2000; Anderson et al., 2001). Esta tendencia en la distribución de estructuras no sólo se observa en los alrededores de esta región, la carga de Tharsis tiene un efecto importante en la litosfera de Marte que se aprecia en la mayor parte del planeta (Phillips et al., 2001; Ernst, 2004). Dentro de las estructuras radiales a Tharsis se encuentra Valles Marineris (Fig. 2.4a), un gran sistema de cañones con una longitud de más de 2000 km situado al este de la Región de Tharsis, al norte de Thaumasia. Algunos de los cañones que forman esta provincia presentan profundidades de hasta 10 km y anchuras de hasta varios cientos de kilómetros. Su formación está ligada al desplazamiento de fallas normales radiales a Tharsis (Fig. 2.4b) (e.g. Blasius et al., 1977; Schultz, 1991; Lucchitta et al., 1992; Peulvast et al., 2001; Schultz y Lin, 2001; Wilkins y Schultz, 2003). A esta provincia se le ha atribuido un origen tectónico extensional, quizá debido al desarrollo de un rifting pasivo asociado al desarrollo de Tharsis (e.g. Sengör y Burke, 1978; Banerdt et al., 1992; Anderson y Grimm, 1998) y cuya formación comenzó en el Noeico Tardío/Hespérico Temprano, correspondiendo con la fase de mayor crecimiento de Tharsis (e.g. Head et al., 2002; Bouley et al., 2018). CAPÍTULO 2 35 Las grandes cuencas de impacto de Hellas y Argyre, localizadas en las tierras altas del sur, son otras provincias geológicas topográficamente significativas a escala planetaria, con una serie de estructuras tectónicas, canales, planicies volcánicas y unidades sedimentarias a su alrededor controlados por la presencia de estas grandes depresiones (Fig. 2.4a). Hellas Planitia se formó durante el Noeico Temprano (Leonard y Tanaka, 2001), hace ∼4000–4100 Ma (Frey, 2006; Werner, 2008; Fassett y Head, 2011). Esta cuenca de impacto tiene un diámetro de ∼2300 km contando el anillo principal de la cuenca, y el fondo de esta estructura presenta el punto topográficamente más bajo del planeta, aproximadamente 8.2 km por debajo de la media de la superficie (Schultz y Frey, 1990; Smith et al., 1999). Argyre Planitia es una cuenca de impacto multi-anillo muy bien preservada, formada en el Noeico Temprano (Dohm et al., 2015) con una edad estimada de ∼3800–3900 Ma (Werner, 2008; Robbins y Hynek, 2012; Robbins et al., 2013). La depresión asociada a esta cuenca tiene un diámetro de ∼1500 km atendiendo a su anillo principal (Hiesinger y Head, 2002) y 4 km de profundidad (Dohm et al., 2015) aunque los anillos y los depósitos eyectados de su formación tienen un diámetro de hasta 1700–1800 km e incluso se ha definido un posible anillo exterior de 2750 km de diámetro (Hiesinger y Head, 2002). Estas cuencas de impacto presentan una gran cantidad de estructuras de contracción concéntricas a ellas (Fig. 2.4b) entre las que destacan un elevado número de escarpes lobulados, aunque muchas de estas estructuras, las más antiguas posiblemente relacionadas con su formación, se encuentran fuertemente erosionadas. Otras cuencas de impacto grandes, como es el caso de Isidis Planitia, situada sobre la dicotomía y con 1900 km de diámetro (Schultz y Frey, 1990), también muestra esta distribución concéntrica en las estructuras de acortamiento de su alrededor. Las estructuras extensionales tienden a tener una dirección radial a las grandes cuencas de impacto, pero también se han descrito algunos escarpes de falla normal y grabens concéntricos y altamente degradados en la zona interior de las cuencas (e.g. Wichman y Schultz, 1989; Hiesinger y Head, 2002). Utopia Planitia es la mayor cuenca de impacto del planeta con un diámetro de ∼3200 km (Schultz y Frey, 1990; Thomson y Head, 2001), aunque al encontrarse en las tierras bajas del norte su topografía ha sido suavizada por las unidades volcánicas/sedimentarias predominantes en esta zona, por lo tanto su relieve no es tan acusado como el de las grandes cuencas localizadas en las tierras altas. Sin embargo, esta cuenca tiene una gran influencia en el patrón tectónico de las estructuras de contracción de las tierras bajas (Thomson y Head, 2001), que, aunque mayoritariamente presentan una dirección concéntrica a Utopia, también se encuentran en direcciones radiales (Fig. 2.4b) (Searls y Phillips, 2007). Entre estas estructuras predominan las crestas sinuosas, pero también encontramos algunos escarpes lobulados. Es importante remarcar también las diferencias entre la distribución de las estructuras de acortamiento y de extensión desde un punto de vista global. Las estructuras extensionales presentan una distribución más localizada relacionada con las grandes estructuras o relieves geológicos nombrados, que hace pensar que su formación CAPÍTULO 2 36 está estrechamente relacionada. Por el contrario, las estructuras tectónicas de contracción o de acortamiento se encuentran distribuidas globalmente sobre toda la superficie marciana, encontrando estructuras cuya relación con estos grandes relieves no está del todo clara (Fig. 2.4b). CAPÍTULO 2 37 2.2. Escarpes lobulados Los escarpes lobulados son las estructuras de acortamiento más grandes descritas en la superficie de Marte (e.g. Watters y Robinson, 1999; Schultz y Watters, 2001; Grott et al., 2007; Egea-González et al., 2017; Klimczak et al., 2018; Herrero-Gil et al., 2019), pero también han sido descritos en otros cuerpos terrestres del Sistema Solar como Mercurio (e.g. Watters et el., 2002; Egea-González et al., 2012; Galluzzi et al., 2015; Crane y Klimczak, 2019), la Luna (e.g. Williams et al., 2013; Byrne et al., 2015; Watters et al., 2015), Ceres (Ruiz et al., 2019) o el asteroide Eros 433 (Watters et al., 2011). Atendiendo a su estructura, los relieves positivos asimétricos que dan nombre a los escarpes lobulados se consideran pliegues relacionados con el desplazamiento en profundidad de grandes fallas inversas de bajo ángulo (e.g. Strom et al., 1975; Watters y Robinson, 1999; Schultz y Watters, 2001; Anguita et al., 2006; Watters y Nimmo, 2010). Estas elevaciones presentan un flanco trasero tendido (backlimb) y un flanco frontal con una pendiente abrupta (forelimb), formando un anticlinal asimétrico suave con el plano axial inclinado, vergiendo en sentido opuesto al sentido de buzamiento de la falla subyacente. Este anticlinal esta precedido por un sinclinal trasero (trailing syncline), y en la parte frontal presenta un sinclinal delantero (frontal syncline). Estos pliegues son la expresión en superficie del acortamiento acomodado por la falla inversa. El bloque de techo (hanging wall) se desplaza hacia arriba con respecto al bloque de muro (footwall) a medida que la fractura se propaga hacia la superficie (Fig. 2.5a). La deformación en el bloque de techo se acomoda formando un pliegue anticlinal que forma la elevación que vemos en superficie. Estas grandes fallas inversas en ocasiones rompen en superficie por el sinclinal delantero (Fig. 2.5b) creando un escarpe de falla y, en ocasiones, afectando a cráteres en los que queda registrado total o parcialmente el desplazamiento de la falla (e.g. Mueller et al., 2014; Galluzzi et al., 2015; Ruj et al., 2018; Herrero-Gil et al., 2019), lo que evidencia dicha rotura. El escalón de falla colapsa por su propio peso y la fuerza de la gravedad, quedando como una acumulación de material al pie del escarpe (Fig. 2.5c), y siendo difícilmente diferenciable de la pendiente frontal o forelimb. A lo largo de la traza de los escarpes lobulados de Marte se aprecia una variación importante de la altura del relieve, en el que se puede identificar generalmente una tendencia, con una zona central de máxima elevación que disminuye progresivamente hacia los extremos (e.g. Klimczak et al., 2018; Herrero-Gil et al., 2019) (Fig. 2.6). Esta característica está relacionada con la distribución del desplazamiento a lo largo de la falla que subyace el escarpe lobulado y es consistente con los modelos de crecimiento de fallas de la mecánica de rocas (Cowie y Scholz, 1992b; Bürgmann et al., 1994; Fossen, 2010), siendo la altura del escarpe igual a la componente vertical del desplazamiento de la falla (heave). El desplazamiento total a lo largo de la falla, al igual que ocurre con las grandes CAPÍTULO 2 38 fallas en la Tierra, es el resultado acumulado de la deformación acomodada por la falla durante el tiempo que ha durado su actividad tectónica. La propagación de la falla hacia la superficie es proporcional al desplazamiento de la misma y, por lo tanto, es posible que la rotura en superficie no se produzca de forma continua a lo largo de toda la traza. Figura 2.5 Esquema de la evolución de la deformación que forma un escarpe lobulado a medida que aumenta el desplazamiento a lo largo de la falla inversa subyacente (en rojo). (a) La falla aún no ha alcanzado la superficie, el anticlinal de propagación y los sinclinales trasero y delantero ya se han formado, pero la estructura presenta un relieve bajo. (b) El desplazamiento continúa, propagándose la falla hasta la superficie. La rotura en superficie afecta al sinclinal delantero. (c) El desplazamiento del bloque de techo sobre el bloque de muro continúa avanzando, creando un escalón de falla que se desmorona por efecto de la gravedad, tapando el pie del escarpe. La dirección de transporte tectónico de la falla que forma el escarpe lobulado coincide con la dirección del acortamiento. Si esta dirección es completamente perpendicular a la dirección de la falla estaríamos hablando de una falla de dip slip. Sin embargo, esta dirección puede variar, siendo común que en las fallas inversas el desplazamiento sea ligeramente oblicuo con respecto a la traza de la falla. Aunque en muchos casos no es posible medir la componente de desgarre del desplazamiento asociado a un escarpe lobulado, a veces queda registrada en los cráteres cortados por la falla (e.g. Galluzzi et al., 2015; Massironi et al., 2015). CAPÍTULO 2 39 Figura 2.6 Representación de la variación de altura del relieve asociado al desplazamiento de una falla inversa, y de la distribución de desplazamiento a lo largo de la misma. Se aprecia que estas dos características están relacionadas y que los valores máximos coinciden en la zona central de la falla, disminuyendo hacia los límites laterales o tip points (representados con puntos rojos) (basado en Fossen, 2010). La formación de escarpes lobulados se ha relacionado con terrenos masivos sin estratificar (Watters, 1993; Mueller y Golombek, 2004). Además, las grandes dimensiones de las fallas causantes de la formación de escarpes lobulados sugieren que estas estructuras penetran en la litosfera de Marte hasta una gran profundidad, que coincide con un importante cambio reológico en la litosfera (e.g. Schultz y Watters, 2001; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017). Algunos autores han comparado los escarpes lobulados de Marte con relieves en la Tierra que presentan fallas enraizadas en niveles muy profundos de la litosfera como la cordillera Wind River en Wyoming (e.g. Watters y Robinson, 1999; Mueller et al., 2014), el monoclinal East Kaibab en Arizona (Byrne et al., 2017) o las montañas Harz en Alemania (Klimczak et al., 2018). Pese a las similitudes estructurales que presentan, el marco tectónico de las fallas inversas que forman los escarpes lobulados es más simple que el de estos ejemplos terrestres, siendo estructuras bastante aisladas que concentran la mayor parte de la deformación de la zona a lo largo de su estructura. Esta observación, junto con las bajas tasas de deformación (entre 10-17 y 10-19 s-1) calculadas en fallas inversas en Marte (Schultz, 2003) asemeja el ambiente tectónico de formación de los escarpes lobulados a lo que en la Tierra sería un ambiente de intraplaca (e.g. Schultz, 2003; Klimczak et al., 2019). Otra gran diferencia entre los escarpes lobulados en Marte y estos análogos terrestres son las dimensiones, siendo el relieve de los escarpes lobulados por lo general mucho más grande, lo cual puede ser debido no sólo a la diferencia entre las tasas de erosión, sino que puede atribuirse también a diferencias en las propiedades mecánicas de CAPÍTULO 2 40 la litosfera o la aceleración de la gravedad (en Marte es aproximadamente un medio que en la Tierra) (Watters et al., 2000). El estudio de las deformaciones registradas en la superficie de un planeta, que son una respuesta a los esfuerzos a los que está sometida la litosfera, proporciona información sobre cómo son los procesos tectónicos que han tenido lugar y cuál ha sido su evolución a lo largo de la historia geológica. La topografía superficial de los escarpes lobulados es un claro ejemplo de que la geodinámica interna del planeta está relacionada con las características externas que presenta en superficie. Actualmente, la información disponible de la superficie de Marte es extensa y variada, mientras que los datos sub-superficiales son muy limitados. La modelización de la superficie topográfica afectada por fallas inversas permite conocer las características de las fallas que deforman esta superficie, aportando información sobre las propiedades mecánicas y la estructura interna de la litosfera de Marte en el momento de su formación, lo que es indispensable para entender la evolución del planeta y reconstruir así su historia geológica. Los métodos de estudio utilizados para analizar y modelizar tanto fallas como otros aspectos geológicos en Marte son similares a los que se utilizan en la Tierra debido a las similitudes entre estos dos planetas terrestres, pero teniendo en cuenta las características particulares de cada uno. La modelización de escarpes lobulados se realiza bajo la asunción de que la topografía del escarpe lobulado está controlada por la geometría de la falla en profundidad (Schultz y Watters, 2001; Watters et al., 2002). Mediante la modelización se obtiene una aproximación a los parámetros geométricos que definen las grandes fallas inversas que controlan la formación de estos relieves como son el desplazamiento máximo, el buzamiento y la profundidad de despegue de la falla. Es importante remarcar que, debido al tamaño de las fallas inversas asociadas a los escarpes lobulados, a la información disponible de la superficie de Marte o a limitaciones de los métodos, la modelización de estas estructuras se realiza a gran escala, simplificando el plano de falla como una superficie de rotura simple, cuando una estructura de tales dimensiones es común que tenga asociada una zona de deformación compleja (e.g. Kim et al., 2004). Aunque también se han descrito y cartografiado sobre la superficie de Marte escarpes erosionados antiguos que por su localización y dirección podrían corresponder con escarpes lobulados degradados formados durante el Noeico (e.g. Dohm et al., 2015; Bernhardt et al., 2016), la mayoría de los ejemplos estudiados y datados en Marte se encuentran en las tierras altas (e.g. Watters y Robinson, 1999; Grott et al., 2007; Egea- González et al., 2017; Klimczak et al., 2018) y presentan una edad de formación que coincide con el límite Noeico Tardío/Hespérico Temprano (e.g. Watters y Robinson, 1999; Grott et al., 2007; Egea-González et al., 2017). Estos escarpes lobulados presentan por lo general una buena preservación, sin mostrar grandes cambios desde su formación debido a las bajas tasas de erosión que ha habido en Marte desde el Hespérico (e.g. Golombek y CAPÍTULO 2 41 Bridges, 2000; Golombek y Phillips, 2010), lo cual facilita su estudio y modelización. Los escarpes lobulados estudiados en esta tesis se formaron también durante esta época, coincidiendo con los grandes cambios geodinámicos y ambientales que acontecieron en todo el planeta. El valor de desplazamiento máximo obtenido para una falla permite estimar el acortamiento regional registrado en esta estructura (e.g. Schultz y Watters, 2001; Nahm y Schultz, 2011; Herrero-Gil et al., 2020a; 2020b). Estos valores de acortamiento también se han obtenido con estudios que escalan la relación entre el máximo desplazamiento de una falla y la longitud de la misma (D-L relationships) (e.g. Watters y Robinson, 1999; Watters, 2003b; Klimczak et al., 2018). Los valores de los acortamientos regionales acomodados por las fallas inversas de los escarpes lobulados han sido extrapolados a todo el planeta, usando la base de datos de Knapmeyer et al. (2006, 2008) (Fig. 2.4b), para calcular tasas de contracción global durante esta época (Nahm y Schultz, 2011). Por otro lado, el estudio de la profundidad de despegue de estas estructuras de contracción permite identificar grandes discontinuidades mecánicas en la litosfera. Estudios previos que modelizan la superficie de escarpes lobulados formados en el Noeico Tardío/Hespérico Temprano en Marte han reportado profundidades de despegue para las fallas subyacentes que varían generalmente entre 20 y 35 km (Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Egea-González et al., 2017), llegando algunos estudios hasta 45–48 km de profundidad para algunos casos (Mueller et al., 2014; Egea-González et al., 2017). Las altas profundidades de despegue que presentan estas fallas se asocian a un importante cambio reológico, que en Marte se ha relacionado con la transición frágil- dúctil (Brittle-Ductile Transition) del momento en el que se formaron (e.g. Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017). La transición frágil-dúctil se define como el punto donde la resistencia al deslizamiento friccional es igual a la resistencia dúctil (Byerlee, 1978). Esto corresponde con un cambio en el modo de fracturación, por encima de este límite se localiza el régimen frágil, en el cual la deformación se presenta de forma localizada, acomodada predominantemente por fracturación frágil, mientras que por debajo tendríamos el régimen dúctil, en el cual la deformación se encuentra distribuida (e.g. Rutter, 1986; Artemieva, 2011). En este punto es necesario aclarar que la transición frágil-dúctil que se ha relacionado con la profundidad de las grandes fallas inversas se encontraría dentro de la corteza. Aunque “corteza” es un concepto composicional, la diferencia de composición entre la corteza y el manto daría lugar a una estratificación mecánica de la litosfera, por lo que se tendría (bajo las condiciones apropiadas) un dominio frágil en la corteza superior separado del dominio frágil del manto litosférico por una corteza inferior dúctil (e.g. Jiménez-Díaz et al., 2020). CAPÍTULO 2 42 Diversos métodos sugieren que la corteza de Marte es proporcionalmente más gruesa que la terrestre (Wieczorek y Zuber, 2004), con espesores en las tierras altas que pueden ser mayores de 50 o 60 km (e.g. Neumann et al., 2004; Wieczorek et al., 2019). Por consiguiente, se estima que las fallas que forman los escarpes lobulados atraviesan todo el dominio frágil de la corteza (sin alcanzar el manto litosférico), teniendo un despegue (decollement) profundo que coincide con la transición frágil-dúctil. Esta zona de transición entre la deformación frágil y dúctil está controlada en gran medida por la temperatura, por lo que su profundidad es usada para modelizar la estructura térmica de la litosfera y el flujo térmico regional correspondiente a la época en la que se formaron estas estructuras tectónicas en el Noeico Tardío/Hespérico Temprano (e.g. Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008, 2011; Mueller et al., 2014; Egea- González et al., 2017; Herrero-Gil et al., 2019). 3 Análisis estructural y modelización 2D de grandes fallas inversas en Marte Structural modeling of lobate scarps in the NW margin of Argyre impact basin, Mars CAPÍTULO 3 45 3.1. Introducción En este capítulo se han modelizado estructuralmente Ogygis Rupes, Bosporos Rupes y Phrixi Rupes, tres escarpes lobulados localizados en Aonia Terra, una región situada en las tierras altas de Marte. Específicamente, estos escarpes lobulados se encuentran entre los Montes de Thaumasia y la gran cuenca de impacto de Argyre. En esta zona, estas tres estructuras tienen una dirección paralela al borde de Thaumasia, cuya dirección también parece estar condicionada por la cuenca de impacto de Argyre. El análisis y modelización de los relieves de Ogygis Rupes, Bosporos Rupes y Phrixi Rupes, proporciona información sobre los parámetros geométricos de las fallas subyacentes que formaron estas elevaciones, así como de la deformación que los creó. La presencia de algunos cráteres cortados por las fallas que forman los escarpes evidencia la rotura en superficie de estas fallas y permite obtener valores de acortamiento horizontal que han quedado registrados en estos cráteres Dos métodos estructurales diferentes, cortes compensados por áreas y la modelización de dislocaciones mecánicas, han sido utilizados para estudiar estos tres escarpes con el objetivo de constreñir y comparar los parámetros geométricos que definen la morfología de las fallas, así como el desplazamiento a lo largo de ellas. Estos métodos han sido previamente empleados para modelizar escarpes lobulados en Marte (e.g. Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014, Egea-González et al., 2017), Mercurio (e.g. Watters et al., 2002; Egea-González et al., 2012), la Luna (e.g. Williams et al., 2013; Byrne et al., 2015) e incluso en el asteroide Eros 433 (Watters et al., 2011). El método clásico de cortes compensados por áreas (balanced cross sections) (Chamberlin, 1910; 1919), se basa en principios básicos de geología estructural, asumiendo que ha habido conservación de áreas durante el movimiento de la falla. En una sección transversal a la estructura, la superficie elevada por encima del nivel regional por el desplazamiento de la falla se corresponde con el desplazamiento de material en profundidad. Este método proporciona una estimación de la profundidad a la cual se encuentra el nivel de despegue de la falla y del desplazamiento de la misma, usando los valores de acortamiento obtenidos de los cráteres cortados afectados por las fallas analizadas. El segundo método es el método de dislocación mecánica (forward mechanical dislocation), el cual es el más usado a la hora de modelizar escarpes lobulados en cuerpos terrestres. Este método modeliza el efecto, en un perfil topográfico 2D, de una dislocación mecánica en un plano de falla dentro de un medio elástico perfecto con propiedades elásticas isotrópicas y homogéneas (Okada, 1992), utilizando el software Coulomb (Toda et al., 1998). El método de dislocación mecánica permite una buena aproximación a los parámetros estructurales que definen el movimiento a lo largo del plano de falla que forma el escarpe lobulado (Cohen, 1999; Schultz y Watters, 2001), CAPÍTULO 3 46 obteniendo valores de profundidad del plano de falla, buzamiento y desplazamiento. El perfil topográfico modelizado es comparado con el perfil medio resultante de un apilamiento de perfiles transversales a la estructura con el objetivo de disminuir las irregularidades topográficas que pudieran presentar. El ajuste entre estos dos perfiles se ha realizado variando los parámetros del modelo manual e iterativamente dentro de un rango de parámetros coherente con la estructura que estamos modelizando, hasta obtener el resultado visual que mejor encaja con la superficie original. Este resultado se ha alcanzado teniendo en cuenta las partes del pliegue que mayor influencia tienen en la variación de los parámetros de la falla y que es prioritario ajustar. La profundidad de despegue obtenida para las grandes fallas inversas que forman los escarpes lobulados en Marte se ha relacionado con la profundidad de la transición frágil-dúctil. Por lo tanto, el análisis de los datos obtenidos, y el estudio de sus variaciones locales en este área, aportan información sobre la estructura mecánica de la litosfera en esta zona en el momento en que se formaron estos escarpes lobulados en el Noeico Tardío/Hespérico Temprano (Hartmann y Neukum, 2001; Tanaka et al., 2014a) y su relación con las grandes estructuras que limitan este área de estudio por el NW (los Montes de Thaumasia) y el SE (la cuenca de impacto de Argyre). Además, a partir de los datos de profundidad de la transición frágil-dúctil es posible calcular el flujo térmico asociado en esta zona para la que aun no se habían propuesto valores, lo que permite ampliar el conocimiento sobre el estado térmico de Marte en esta época en la que tantos cambios ocurrieron en su dinámica interna (Ruiz et al., 2014). Todo ello permite estudiar la influencia que los grandes relieves de los Montes de Thaumasia y la cuenca de impacto Argyre tienen en la formación de estas grandes fallas inversas localizadas en esta zona intermedia en Aonia Terra. CAPÍTULO 3 47 Structural modeling of lobate scarps in the NW margin of Argyre impact basin, Mars Andrea Herrero-Gil *a, Isabel Egea-González b, Javier Ruiz a, Ignacio Romeo a a Departamento de Geodinámica, Estratigrafía y Paleontología, Facultad de Ciencias Geológicas. Universidad Complutense de Madrid, 28040 Madrid, Spain. b Departamento de Física Aplicada, Escuela Superior de Ingeniería. Universidad de Cádiz, 11519 Puerto Real, Cádiz, Spain. Icarus 319, 367–380 Abstract Martian lobate scarps are prominent tectonic structures interpreted to be the topographic expression of large thrust faults generated under compression. Here, we present a structural modeling performed on three large lobate scarps (Ogygis Rupes, Bosporos Rupes and Phrixi Rupes) located in the heavily cratered highlands of Mars, specifically in Aonia Terra, between Thaumasia Montes and Argyre impact basin. These lobate scarps, formed in the Late Noachian/Early Hesperian, strike parallel to the edge of the Thaumasia Montes, and were generated by ESE-vergent thrust faults. Structural analysis of craters deformed by these lobate scarps gives minimum estimates for the faults slip of ∼1700–3100 m. We applied two structural methods in order to constrain the geometry of these thrust faults at depth, area balanced cross sections and forward mechanical dislocation modeling, obtaining a depth of faulting in this area between ∼18 and ∼45 km, and dip angles between 23° and 35°. These results are consistent with previous studies of lobate scarps on Mars. The depth of faulting gives an estimate of the depth of the brittle-ductile transition at the time of its formation giving a range of depth in which the state of the lithosphere change from brittle to ductile-dominated deformation. The heat flow values calculated from the obtained depths of the brittle– ductile transition range from 25 to 51 mW m−2. We show that the brittle-ductile transition depth in Aonia Terra is set in 18–27 km at a larger distance from the basin center, while it is deeper closer to the Argyre rim (∼33–45 km). This difference seems to indicate a thickening of the brittle domain under Argyre main rim with respect to the external area but, attending to regional geology and heat flow values calculated, this high value (∼33– 45 km) might be an overestimation of the depth of faulting caused by the presence of the crater rim elevation before the formation of the lobate scarps. 3.2. CAPÍTULO 3 48 3. 2. 1. Introduction Lobate scarps are the largest contractional structures described on planetary surfaces (e.g. Strom et al., 1975; Watters, 1993; Schultz and Watters, 2001; Watters et al., 1998, 2015), with lengths of even hundreds of kilometers and reliefs of up to thousands of meters. These structures show a roughly arcuate to linear form in plan view and an asymmetric cross section characterized by a steep frontal scarp and a gently dipping back slope with a trailing depression. This topographic profile have been interpreted as a reverse fault propagation anticline with a trailing syncline, so lobate scarps are considered to be the topographic expression of large thrust faults (e.g. Strom et al., 1975; Watters and Robinson, 1999; Watters and Nimmo, 2010), deforming the crust down to the depth of the brittle-ductile transition (BDT) (e.g. Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017). Several studies on the properties of the thrust faults related to lobate scarps on Mars have been performed. Schultz and Watters (2001) calculated that Amenthes Rupes extends up to 25–30 km of depth using the mechanical dislocation model. The same structure has been studied by Grott et al. (2007) giving a depth of faulting of 35–40 km and by Ruiz et al. (2008) obtaining a depth of faulting between 27 and 35 km, both using an elastic dislocation modeling too. Mueller et al. (2014) calculated a depth of faulting for Amenthes Rupes using the fault-propagation fold theory for a listric fault geometry and, despite that the dip angles obtained by these authors are clearly higher, their depths of faulting range between 33 and 48 km. Attending to other similar studies located in other regions, Grott et al. (2007) used a dislocation model to study two large lobate scarps in the south of Thaumasia, which seem to have characteristics more similar to the scarps studied here, striking parallel the edge of Thaumasia and having a relief slightly higher than a thousand meters. These authors get the best fit model for depths of faulting of 27– 35 and 21–28 km. Egea-González et al. (2017) modelized eight different lobate scarps around Hellas impact basin, including Amenthes Rupes, obtaining for them depths of faulting between 13 and 45 km. Here we present the results of the structural modeling at depth of three large lobate scarps (Ogygis Rupes, Bosporos Rupes and Phrixi Rupes) in Aonia Terra, region located in the southern highlands of Mars, between the Thaumasia Montes and the northwest margin of the Argyre impact basin. The Argyre basin, formed during the Noachian time (Dohm et al., 2015), is one of the largest impact basins on Mars and the best preserved of the multi-ringed impact basins. Hiesinger and Head (2002) defined at least seven rings, with an uncertain eighth ring because of its discontinuity using the criteria of Pike and Spudis (1987). The studied lobate scarps strike parallel to the edge of Thaumasia in this area, like other contractional structures present as wrinkle ridges, which are the surface expression of minor blind thrust faults, reflecting folding and thrust faulting (e.g. Bryan, 1973; Plescia and Golombek, 1986; Mueller and Golombek, 2004; CAPÍTULO 3 49 Watters, 2004), easily recognizable by their uniform spacing and a narrow surface ridge superposed on a broad rise (Golombek et al., 1991). The presence of craters cut by the lobate scarps indicates that the faults underlying these lobate scarps broke the surface. The knowledge of the structural parameters of the faults underlying these lobate scarps, including an estimate of the depth of faulting, will provide constraints on the depth of the BDT and their spatial variation in relation to the lithospheric structure and mechanical state around the Argyre basin in the Late Noachian/Early Hesperian time, when the lobate scarps were formed (Hartmann and Neukum, 2001; Tanaka et al., 2014a). While lobate scarps are considered to be formed by thrust faults extending to the BDT (e.g. Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017), there is no consensus about wrinkle ridges structure and depth of faulting (e.g. Zuber and Aist, 1990; Watters, 1991, 2004; Allemand and Thomas, 1995; Watters and Robinson, 1997; Schultz, 2000; Mueller and Golombek, 2004), consequently, wrinkle ridges are not studied in this work. The BDT is temperature-controlled, and therefore its depth can be used to model the thermal structure of the crust and the heat flow at the time of faulting. Thus, previous works have found Late Noachian/Early Hesperian heat flows to be usually between ∼25 and ∼40 mW m-2 at the the circum-Hellas region (including Amenthes Rupes) and Thaumasia highlands (Ruiz et al., 2008, 2009, 2011; Mueller et al., 2014; Egea-González et al., 2017). This heat flow range is similar to that found for other non-volcanic regions of similar age from the effective elastic thickness of the lithosphere (McGovern et al., 2004; Ruiz et al., 2011). Thus, modeling the thermal structure of the crust and the surface heat flow at the Aonia region serves to enlarge our knowledge of the thermal state of Mars in a time when large changes occurred in its internal dynamics (for a review see Ruiz (2014) and references therein), and permits a first assessment, for that time, of the magnitude of the variation of heat flow through the southern highlands of Mars. Finally, it is worth mentioning in this point that a high depth of faulting is suggestive, but non demonstrative of that the large lobate scarps represent the BDT. In any case, the obtained fault depths represent a consistent lower limit to the BDT, which can be used to obtain mechanical constraint and robust heat flow upper limits for the time of faulting. Moreover, the general consistency of deduced thrust fault depths throughout the martian geography by previous works (and by the present study) does not seem consistent with depths of large faults being controlled for local compositional transitions. Thus, we consider our results as representative of the BDT depth. CAPÍTULO 3 50 3. 2. 2. Geological setting and structural mapping The knowledge of the relations between lobate scarps and other surrounding structures and lithologies is a fundamental issue to understand the structural framework and the geological units affected by contraction associated with lobate scarp formation. Thus, we performed a detailed structural and geological map (Fig. 3.1) of the study area to provide a geological setting of the area where lobate scarps were formed. This geological and structural mapping was performed through the analysis of the Thermal Emission Imaging System (THEMIS, Mars Odyssey mission) daytime infrared (IR) model, which is a 100 meter/pixel mosaic (Christensen et al., 2004) and the Digital Elevation Model (DEM) based on data from the Mars Orbiter Laser Altimeter (MOLA; Zuber et al., 1992; Smith et al., 2001), an instrument on NASA’s Mars Global Surveyor (MGS, Albee et al., 2001) with a 1/128° resolution (about 463 m/pixel). Previous works mapping this area were made for Thaumasia (Dohm and Tanaka, 1999, 2001) and Argyre basin (Dohm et al., 2015), both focused on very large structures compared with the region where the three lobate scarps studied are located. We have analyzed the topographic surface using MOLA model attending to topographic profiles and slope changes. This, together with the high resolution of THEMIS images, allow us to be more accurate delineating geological units and tectonic structures, and as a result, we have created a more detailed map of the studied area according to the map scale. This part of Aonia Terra is considered as the transition zone between the Thaumasia highlands mountain region and the Argyre impact basin. The geological units used and their descriptions are those defined by Dohm et al. (2015) in their study of Argyre basin. Geologically, we can divide the mapped area in two general zones: (1) the highlands where the lobate scarps were formed, and (2) the basin and rim materials associated with the Argyre impact basin. The highlands materials are mostly from Noachian time (Nh1, Nh2, Nhb) and they show a smooth to slightly rough surface. Over these materials, there are others younger, of Noachian-Hesperian age, easily identifiable because they have a smoother surface (HNh3, HNh4). The rim and basin materials (NArsp, NAbr, NAr, NAb1, NAb2, NAb3) of the Argyre basin have a Noachian age, and show irregular roughly surfaces. Impact crater materials (C1, C2, Cfs, Cfr) postdate the Argyre impact deposits (see Dohm et al., 2015 for a detailed description of the units). Contractional structures in Aonia Terra, both wrinkle ridges and lobate scarps, strike roughly parallel to the edge of Thaumasia Montes, but in this transient zone, the Thaumasia edge is slightly parallel to the Argyre structure (Dohm et al., 2015) and the contractional structures at some points also appear to be parallel to Argyre rings. Conversely, the few (∼7) small grabens present in the studied area show a perpendicular strike to the contractional structures, presenting radial patterns with respect to Thaumasia Montes and therefore to Tharsis (Okubo and Schultz, 2003). CAPÍTULO 3 51 Figure 3.1 Geological and tectonic map over THEMIR-IR Day Global Mosaic 100m. Ogygis Rupes, Phrixi Rupes and Bosporos Rupes are shown by light red lines and named as a, b and c respectively. Backthrust faults are shown by dark red lines. Inset globe, colored with the MOLA model, shows the map location. The geological units and their description are from Dohm et al. (2015). Note that the north in the map is rotated. The location of deformed craters from Fig. 3.5 are shown. Our map (Fig. 3.1) and other previous studies (e.g. Watters, 1993; Watters and Robinson, 1999) show that martian lobate scarps occur mainly in intercrater plains in the heavily cratered highlands of the planet. The thrust faults that generated Ogygis Rupes, Bosporos Rupes and Phrixi Rupes in Aonia Terra uplift the oldest formation in the highlands of this CAPÍTULO 3 52 area (Nh1) which seems to be more resistant to erosional agents than the surrounding formations. The asymmetry in the cross sections suggests that the three lobate scarps were generated by ESE-vergent thrust faults. An associated backthrust fault (a subsidiary fault with an opposite vergence to the main thrust fault (McClay, 1992)) appears at the backlimb in some segments of the lobate scarps. Ogygis Rupes (Fig. 3.1, fault a; Table 3.1) is formed a single surface-breaking fault striking N30°E with 190 km in length verging ESE. It has a backthrust verging WNW in the northeastern half of the structure. The slip in this backthrust increases towards the NE in the overlapping zone together with a decrease of the slip of the main fault towards its tip point. Phrixi Rupes (Fig. 3.1, fault b; Table 3.1) which is located southwest of Ogygis Rupes and Bosporos Rupes, strikes N52°E and is 195 km long. It is divided in two segments, showing a right-stepped pattern, the northeast 85 km long and the southwest 140 km long, with an overlapping zone of 30 km where they are separated from each other 12 km. Bosporos Rupes (Fig. 3.1, fault c; Table 3.1) is approximately 590 km long and it is also formed by two segments. In this case both segments are divided into several branches in the overlapping zone, being difficult to separate them. Taking into account a slight change in the direction we have identified the northern segment, which strikes N43°E and is 297 km long, and the second one located south of the first, striking N34°E which is 293 km long. They are arranged showing a left- stepped pattern. There exists a big backthrust throughout most of this structure, located at an average of 100 km from the scarp base and presenting a relief of up to 800 m, which allows to identify a "pop up" structure in some transversal topographic profiles. Wrinkle ridges in our map area are parallel to these lobate scarps and they are mostly in the NNE half of the map, appearing mainly in the younger materials with smooth surface (HNh3, HNh4). Wrinkle ridges are more numerous and frequent than lobate scarps and sometimes intersect between them. Despite this, their direction is readily identifiable because of their high density in these smooth materials, striking parallel to the edge of Thaumasia Montes. Table 3.1 Lobate scarps locations and surface characteristics Location Length (km) Max. relief (m) Ogygis Rupes N 54.5°W 33.1°S 190 2115 Phrixi Rupes N 66.8°W 44.6°S 195 1250 Bosporos Rupes N 56.4°W 41.5°S 590 1570 The terrain on which these lobate scarps were formed is modified and partially eroded by different surface-shaping agents like runoffs and landslides. This is especially evident in Bosporos Rupes, where further surface modifications can be identified, complicating the structural analysis. The cross-cutting relationships between the tectonic CAPÍTULO 3 53 structures and the geological units are evident in spite of those surface processes. The three lobate scarps studied only cut or affect directly the Noachian materials Nh1 and Nh2. The lobate scarps and the associated backthrusts are not directly affecting Nhb and HNh4 units although they are in contact with them covering in some places the scarp base. So, according to these observations, the scarp formation is subsequent to the deposition of Noachian materials Nh1 and Nh2. Wrinkle ridges appear in the Noachian materials Nhb and Nh2, and in the Hesperian/Noachian smooth materials HNh3 and HNh4, so they were formed after the deposition of these geological units. The grabens present in the area deform Nh2 and HNh4 materials, so they were formed after these materials. Attending to the five main stages of geological activity (Anderson et al., 2001; Dohm et al., 2001) in the Thaumasia region and surroundings, which correspond to the martian stratigraphic scheme of Tanaka (1986), these lobate scarps studied in Aonia Terra, together with the wrinkle ridges of this area, were formed during the stages 2 and 3, in the Late Noachian/Early Hesperian (Dohm and Tanaka, 1999; Anderson et al., 2001; Dohm et al., 2001), equivalent to an age of ∼3.8–3.6 Gyr (Hartmann and Neukum, 2001; Werner and Tanaka, 2011). The small radial grabens present in this area could have been formed also in the stage 2, like most of the extensional structures radial to Thaumasia (Anderson et al., 2001). The geological relation between the lobate scarps and the Noachian highlands affected by them (Fig. 3.1) is consistent with their formation after the emplacement of these Noachian units. 3. 2. 3. Methods The structural analysis of lobate scarps has been done using two different methods in order to compare the respective results and better constrain the structural parameters, especially the depth of faulting but also the fault slip and the dip of faulting. Furthermore, we have measured the deformation of craters cross-cut by lobate scarps, which has provided an estimate of minimum horizontal slip. The first method, the analysis of balanced cross sections (Chamberlin, 1910), is based on basic tenets of structural geology assuming mass conservation in a thrust fault-propagation folding model (Suppe, 1983; Seeber and Sorlien, 2000). This analysis, together with the horizontal shortening measured on cross-cut craters, allow us to obtain the fault displacement and the depth of faulting. For the second method, we have used the forward mechanical dislocation software Coulomb (Toda et al., 1998) which generates an output profile for a specific fault parameters allowing us to compare it with the real topography. This method models the surface topography by the deformation of a perfectly elastic media when a displacement is imposed on the fault, providing a good approach to the fault parameters when the fault properties are unknown. CAPÍTULO 3 54 The stacking of several topographic profiles for each lobate scarp, perpendicular to its strike and equidistant between them, has been made to reduce the errors related to differences in the topography, such as lithology changes or erosion, when performing structural analysis. Other differences between specific profiles, such as impact craters, were removed prior to calculate a mean topographic profile through stacking for each lobate scarp. We selected similar contiguous profiles, representative for the general structure of the lobate scarp coinciding with the highest elevation of each scarp. Visualization, mapping and data processing were carried out using the Geographical Information System (GIS) software ArcGIS® (ESRI, 2014). 3.2.3.1. Horizontal shortening of deformed craters When a fault cuts or affects other structures or a geoform of known initial geometry formed previously or during the fault activity period, the offset can register the fault displacement totally or partially. On planetary surfaces, craters have been found to be a good deformation marker due to their generally circular initial geometry. When a crater is cut by a fault, the strike of shortening and the horizontal and/or vertical components of movement can be estimated (e.g. Golombek et al., 1996; Strom et al., 1975; Watters et al., 1998; Watters et al., 2009; Galluzzi et al., 2015; Mueller et al., 2014). We have measured the horizontal fault displacement (Δx) of some craters cross- cut by lobate scarps. To quantify the shortening, we assumed that the craters had an almost perfect circular morphology before the deformation (e.g. Galluzzi et al., 2015). Although there are unusual exceptions of craters with non-circular shape (Thomas and Allemand, 1993), all the analyzed craters in this study show highly circular shapes in the sectors undeformed by the fault and we do not have criteria that make us think otherwise. The timing between impact crater generation and fault activity has different possible configurations: (1) the crater was formed before the onset of fault activity, in this case it registers the total deformation; (2) the crater was formed after the onset but before the end of fault activity, in this case the slip estimate is minimum, and (3) the crater was formed after the end of fault activity, so it did not register any deformation. Moreover, two geometrical scenarios are possible when a fault transects a crater: (1) the fault cuts the crater across the inner depression separating the rim in two arcs, each one located on each fault block (Fig. 3.2a); or (2) the fault cuts the crater close to its edge destroying part of the rim, in this case only one rim arc remains on one fault block (Fig. 3.2b). The first scenario registers the horizontal displacement (Δx) of the fault since the generation of the crater and allows to calculate the direction of that displacement, which vector is obtained by locating the center of both arc rims. It also allows to obtain the fault vertical component of slip (Δy). The second scenario is less constrained, but allows to calculate a minimum amount of horizontal slip by measuring the loss of crater CAPÍTULO 3 55 radius due to the fault onlap. Even considering a crater formed before the onset of fault rupture, the second scenario provides a minimum horizontal fault slip for two reasons: (a) the fault rupture on surface is initially located at an unknown distance to the crater rim and (b) the strike of the fault horizontal slip vector is unconstrained, so if the fault has a strike-slip component again the estimate of horizontal slip is a minimum. Figure 3.2 Two possible scenarios of a fault cutting a crater are shown in plant view and cross section. (a) The fault cuts the crater separating the rim in two identifiable arcs. The red cross indicates the crater center location before deformation. The orange cross indicates the crater center location obtained from the displaced rim arc. The distance between both centers (yellow arrow) is the horizontal displacement (Δx). The elevation difference between the two arc rims is the vertical displacement (Δy). (b) The fault cuts the crater close to its edge destroying part of the rim. The red cross shows the crater center. The displacement measured is a minimum (Δx’) because the initial location of the fault surface rupture (gray dashed lines) and the strike of the fault horizontal slip vector are unknown (some displacement possibilities are shown by orange arrows). The center of each crater sector has been calculated by fitting a circumference to the crater rim. To do this we created a grid of points at the bottom of the crater. For each grid point we radially measure distances to the crater rim (without the rim sectors affected by landslides) and we calculated an average radius (the arithmetic mean of the measured distances to the crater rim) and a measure of the data dispersion by the mean squared error. The best circumference fit is provided by the grid point with minimum error. Once the circumference was adjusted to the crater rim, we measured its deformation. For each crater analysis, we have used a stereographic projection centered on the crater to avoid a distortion of the shape and get reliable distance measures. The accuracy of the measurements is limited by the MOLA resolution whose slope changes have been used to delimit the crater rim, together with THEMIS images. CAPÍTULO 3 56 3.2.3.2. Balanced cross sections method. The balanced cross sections method (Chamberlin, 1910, 1919), also known as Chamberlin approach, consists in the application of geometric relations to geological structures analysis assuming plane deformation so the displaced area in a cross section is preserved during the deformation process, existing a balance of areas between the state prior to deformation and the deformed state. In this way, in a compressional scenario, the material uplifted above the regional level in a cross section (A) has to equal the amount of material laterally displaced on the decollement at depth, assuming volume conservation (Fig. 3.3) and it can be obtained by A = dh, where d is the horizontal displacement on the decollement and h is the depth of faulting (depth of the decollement where the thrust faults root). Therefore, we can calculate the depth of faulting (h) knowing the uplifted area (A) and the horizontal displacement (d). The difference between the initial state and the deformed state of the topographic surface, assuming that it has been only modified by tectonics, can be used to measure the horizontal displacement (Dahlstrom, 1969; Moretti and Carrot, 2012). The total horizontal displacement of the thrust on the decollement is accommodated by a fold and the rupture of the fault on the surface (Δx). The horizontal displacement accommodated by the fold is given by Lf – W (Fig. 3.3), where Lf is the longitude of the fold measured along the topographic surface and W is its horizontal projection. Thus, the horizontal displacement on the decollement can be estimated by d = Δx + (Lf – W). The horizontal component of slip on the fault at the surface (Δx) has been estimated by structural analysis of cross-cut craters (providing a minimum estimate, see Section 3.2.3.1). Since the topographic profile for each cross section studied and the deformed craters do not occur at the same position on the fault trace, a proportional escalation of Δx has been done using the relief of the lobate scarp (Δz) given by the vertical component of the fault offset (Fig. 3.4). The same proportional escalation has been done to estimate the horizontal slip component on the fault at surface in the segments where there are no cross-cut craters, assuming that the relief and the horizontal slip are directly related. Figure 3.3 Representation of the balanced cross section method (based on Groshong, 2006). The excess area above the regional level corresponds to the displaced area at depth (both in gray) and it is directly related to the displacement and the depth of faulting by A = dh. The displacement (d) can be estimated by adding the horizontal fault slip (Δx) to the shortening generated by the fold (Lf – W), d = Δx + (Lf – W). CAPÍTULO 3 57 3.2.3.3. Forward mechanical dislocation method This method is based on the modeling of a fault that reproduces the observed topography across the lobate scarp, and it has been previously used to analyze thrust faults on Mars (Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Egea- Gonzalez et al., 2017), as well as on other planetary bodies including Mercury (Watters et al., 2002; Egea-Gonzalez et al., 2012), the Moon (Williams et al., 2013), and asteroid 433 Eros (Watters et al., 2011). Here, we use the forward mechanical dislocation modeling software Coulomb (Toda et al., 1998; Lin and Stein, 2004; Toda et al., 2005) to model displacements on the surface caused by thrust faulting. The fault is idealized as a rectangular plane with a specific length, dip angle and vertical depth of faulting. The program estimates the surface deformation caused by the fault movement following Okada (1992) for an elastic halfspace with uniform isotropic elastic properties. This method provides good fits for the topography above a fault for a limited range of parameters (Cohen, 1999; Schultz and Lin, 2001). Non-planar fault geometries such as positive listric faults have been previously proposed to be the cause of lobate scarps formation (Watters and Nimmo, 2010), but elastic dislocation modeling of listric thrust faults does not provide model fits as good as planar geometries in this case (Schultz and Watters, 2001; Watters et al., 2002). We set a crustal elastic modulus of 80 GPa and Poisson’s ratio of 0.25 (Schultz and Watters, 2001). The coefficient of friction was 0.7, corresponding to the value for reverse faults. We have kept these parameters fixed since these values are comparable to those used in modeling the deformation associated with fault offset in the continental crust on Earth (e.g. Freed and Lin, 1998; Schultz and Watters, 2001) and reasonable variations in these parameters do not produce significant variations in the results (Watters et al., 2002; Grott et al., 2007; Ritzer et al., 2010; Egea-González et al., 2017). There are four principal variables that can be adjusted to fit the model output profile with the stacked MOLA topographic profiles: the offset value, the fault dip angle, the depth of faulting and the displacement distribution along the fault plane. These parameters are interrelated, but it is roughly possible to determine how the variation of each of them affects the output profile. An increase in the fault slip entails a higher relief. A deeper depth of faulting results in a wider and bulkier crest, while a shallower depth produces a narrower structure in the surface and a trailing syncline topographically below the scarp base. Lower dip angles provide a bulkier backlimb and a wider ridge, similar to an increasing in depth but less pronounced, while higher dips entail a steeper backlimb. The distribution of the displacement along the fault also influences the fit. A displacement distribution decreasing towards the edges of the fault plane generally improves the fit in our studied cases, generating more rounded shapes in the output profile, which are more similar to what we see in the topographic profiles than the result of a regular distribution, which generates profiles with angular and abrupt shapes (Schultz and Watters, 2001). CAPÍTULO 3 58 Best fit adjustments between predicted topography and stacked topographic profiles of the lobate scarp have been obtained varying systematically and iteratively these parameters until getting the best visual fit for each fault. The forward mechanical dislocation modeling provides more than one possible solution, (Egea-González et al., 2017) so we have chosen those values within reasonable ranges for a thrust fault, which fit fairly well with real topography. The main limitation of this method is that it does not take into account the fault- propagation folding including plastic deformation and distributed brittle deformation so there can exist differences between the topographic and the modeled profile, but it has been demonstrated to be a good approximation while modeling a topographic elevation caused by long-term deformation due to cumulative fault offsets (e.g. King et al., 1988; Taboada et al., 1993; Cohen, 1999). Other limitation of this modeling procedure is that fault slip decrease at the bottom of the fault plane and it is not transmitted from a horizontal decollement. The volume loss due to erosion and subsequent sedimentation might modify surface topography, being another factor that could cause differences in the adjustments. However, erosion in Mars is considered to have a very low rate (e.g. Golombek and Bridges, 2000; Golombek and Phillips, 2010). The studied lobate scarps present a good state of preservation lacking significant evidence of topographic degradation, which leads us to assume that the erosional rates in this area of Aonia Terra have remained low since lobate scarps formation. 3.2.4. Structural analysis and modeling Variations of vertical fault displacement along lobate scarps can be obtained from lengthwise topographic profiles (Fig. 3.4) in which there are represented the maximum scarp elevations (z') corresponding to the fault-propagation fold crest, and the scarp base elevations (z). The elevations of the scarp face (sharp plane defined by the highest slope) are also shown, which may or may not coincide with the scarp crest. When a lobate scarp is characterized by different fault segments and these segments overlapped, we represent the scarp crest of the highest segment and the scarp base of the segment located SE. The elevation values plotted along the fault length provide a frontal view of the lobate scarp relief (Δz = z’ – z), which is a minimum estimate of the vertical component of fault displacement. If we ignore the material deposited from the scarp face and the possible erosion by the engagement of surface runoff in the scarp base, the scarp base (z) should correspond with the regional level. Ogygis Rupes has the maximum scarp relief almost in the center of the structure (Δz ≈ 2115 m), decreasing towards the edges. Phrixi Rupes, which is divided in two segments, has the maximum vertical displacement in the center of its northeastern segment (Δz ≈ 1250 m) while the southwest segment has a small relief throughout its CAPÍTULO 3 59 entire length. Bosporos Rupes is a long structure with an irregular surface also divided in two segments. Its topography is heavily modified and we cannot identify a clear trend in the scarp relief although there is a slight decrease towards the edges. When removing the crater depressions at the base of the scarp (Fig. 3.4), the maximum scarp relief belongs to the northeastern segment (Δz ≈ 1570 m). The vertical fault displacement distribution shown by each segment of the studied lobate scarps, corresponds with a displacement in the fault plane greater in the center and decreasing towards the lateral fault tips (Fossen, 2010). Displacement-Length relationships of the faults underlying the lobate scarps have also been calculated attending to these observations. Figure 3.4 Lengthwise profiles for each lobate scarp showing the vertical displacement distribution (vertical exaggeration x5) along the fault. The dashed black line shows the highest elevation of the lobate scarp (z') (corresponding to the fault-propagation fold crest), while the solid black line is the scarp base (z). The gray area (Δz) is the difference between the scarp base and the highest elevation of the lobate scarp. The solid yellow line indicates the top of the scarp face. Vertical red lines mark the points of maximum relief for each segment. 3.2.4.1. Results of the cross-cut craters There are three craters affected by the studied lobate scarps. The diameters of the examined craters are between 17 and 28 kilometers. The resolution of the MOLA model (463 m/pixel) limits the use of this data set for determining the deformation of craters when the horizontal fault slip is under this spatial resolution. The first one (Fig. 3.5a) is located approximately in the center of Ogygis Rupes. The upper fault block appears thrusting on the edge of the crater rim (case shown in Fig. 3.2b). The side of the crater affected by the lobate scarp shows an arched geometry concave towards the center of the crater. First, we adjusted a circumference to the undeformed part of the crater rim and another one to the arched line of the deformed side of the rim, and then we measured the distance between their centers, providing measure of the horizontal shortening (Δx’1 = 1310 m). An equivalent procedure was followed using the same centers to adjust two more circumferences to the bottom line of the crater to verify that the shortening value is similar (1330 m). The same procedure was used with the second crater (Fig. 3.5b) which is located in the backlimb of the northern part of Ogygis Rupes lobate scarp. In this case the crater is not cut by the main lobate scarp but it is affect by a backthrust verging NW which continues northwards (Fig. 3.2a). The horizontal shortening measured (Δx’2) is 970 m. This CAPÍTULO 3 60 result seems to indicate that this backthrust of Ogygis Rupes acts as a relay fault of the main lobate scarp as the structural map shows (Fig. 3.1). The mean elevation difference between the two rim arcs (Δy) is 700 m, allowing to estimate a dip of faulting of approximate 36° for the Ogygis backthrust given that tg θ = Δy / Δx. Figure 3.5 Analysis of cross-cut craters. Red circumferences represent the best fit for the undeformed crater rim. Color grids show the mean squared error of the distance from each grid point to the crater rim. The location of the minimum value of the mean squared error is the best estimate of the crater center. Orange lines are adjusted to the crater rim of the deformed side. (a) Crater deformed by Ogygis Rupes. (b) Crater deformed by a backthrust on the norther termination of Ogygis Rupes. (c) Crater deformed by Bosporos Rupes northern segment, in this case the orange circumference fit the arc of the crater rim on the hanging wall and grids for calculating both circle centers are shown. The yellow arrows indicate the horizontal components of slip (Δx). The third crater (Fig. 3.5c), which is over Bosporos Rupes, could be an example of scenario 2 (Fig. 3.2a) but, in this case, the crater modifies the lobate scarp topography and it is also affected by the fault that forms the lobate scarp, dividing the crater in half. Because of that, we interpret it to be synchronous with the fault movement, in a way that the impact took place after the first stages of formation of Bosporos Rupes but before the last fault activity. We calculated the center of the circumferences that best fit each of the two sectors in which is divided the crater rim in order to analyze the dislocation of this crater. The horizontal slip (Δx3) is estimated to be the distance between the two circumference centers and it is 580 m. If we broadly compare the relief of the lobate scarp at this point (Δz ≈ 1000 m), with the elevation difference between the two halves of the crater (∼300 m) it can be deduced that the total thrust fault movement is approximately CAPÍTULO 3 61 three times larger than the last movements registered by the crater. Furthermore, the displacement vector obtained is almost parallel to the direction of the scarp, which would imply a strike sinistral kinematics at least for the last movements of the fault, highly contradictory with the thrust fault characteristics shown by Bosporos Rupes. But, it is also necessary to take into account that the measured horizontal shortening is small compared with the pixel size of the THEMIS and MOLA (100 meter/pixel and ∼463 m/pixel respectively) that we have used to measure it. For these reasons, we cannot use this horizontal slip measure in the balanced cross section analysis. The vertical component associated with the horizontal displacement was not registered in the crater rim because half of the crater rim was formed over a previously elevated fault block. The measure of the vertical displacement associated with the last fault displacement in the bottom of the crater cannot be performed because this surface is highly irregular due to surface runoff modifications. 3.2.4.2. Results of the balanced cross sections Applying the balanced cross section method (Fig. 3.3) to the mean profile of the stacking topographic profiles for each lobate scarp, represented in Fig. 3.6, we have calculated the fault parameters (Table 3.2). Final length (Lf) and the length of the structure at regional level (W) can be measured in each mean profile, allowing to calculate the uplifted area (A) and the horizontal displacement accommodated by the fold (Lf – W). The horizontal fault slip has been calculated using d = Δx + (Lf – W). For the fault slip calculation of Bosporos Rupes and Phrixi Rupes there are not cross-cut craters measurements so we have made a proportional escalation with the horizontal slip measured in the first crater (Fig. 3.5a), assuming that the relief of the lobate scarp and the horizontal slip are directly related and there exists the same proportion in the three lobate scarps. The horizontal slip (d) associated with the formation of Ogygis Rupes is calculated in 2300 m with a depth of faulting (h) of 18 km. Using this horizontal slip value, the total fault slip based on the relief of the lobate scarp is 2900 m. The horizontal slip (d) associated with the fault underlying Phrixi Rupes is 1580 m and the depth of the fault decollement (h) obtained is 24.5 km. Accordingly, the total fault slip calculated is 2000 m. The horizontal slip (d) obtained for Bosporos Rupes is 1330 m corresponding with a depth of faulting (h) of 45 km. The total fault slip calculated is 1700 m. We have to take into account that the surface of this lobate scarp is heavily altered, so originally, the excess area (A) and the lobate scarp relief (Δz) were probably greater. CAPÍTULO 3 62 Table 3.2 Fault parameters and calculated surface heat flows intervals Balanced cross section Forward mechanical dislocation Heat Flow Fault slip (m) Depth of faulting (km) Fault slip (m) Dip angle (°) Depth of faulting (km) FS (Diabasa) mW/m2 Ogygis Rupes 2900 18 2500-3100 35 27-20 30-51 Phrixi Rupes 2000 24.5 1700-1850 33 36-25 26-40 Bosporos Rupes 1700 45 2650-2750 23 41-33 25-33 3.2.4.3. Results of the forward mechanical dislocation method The maximum relief of Ogygis Rupes coincides with the central zone of the structure (Fig. 3.4). This area was selected to apply this method, performing a topographic profile stacking in a band of ≈30 km (Fig. 3.6a). The best fit corresponds with fault slips that range between 2500 and 3100 m, according with the maximum relief of the scarp, a dip angle of 35° and a depth of faulting of 27 km (Table 3.2). The topographic profile stacking for Phrixi Rupes was performed in the central part of the northern segment coinciding with the higher scarp relief of the structure (Fig. 3.6b), in a band of ≈25 km. The proximity of Phrixi Rupes to the Thaumasia southeast edge seems the cause of a regional slope that affects this lobate scarp. This regional slope is calculated to be 0.18° SE. We have tilted the model output 0.18° in order to get the best fit with the real topography because the software model does not allow to set an initial tilted surface. The best fit for Phrixi Rupes stacking was obtained with a fault slip between 1700 and 1850 m, a dip angle of 33° and a depth of faulting of 36 km (Table 3.2). Despite of being a long structure, Bosporos Rupes area is heavily eroded and cratered, which hinders the selection of the area with representative topographic profiles for stacking. The selected topographic profiles are in a band of ≈35 km approximately in the center of the northern fault segment that is characterized by the presence of a backthrust (Fig. 3.6c). Although the stacking is done in an area where the backthrust does not have a significant topographic expression, the best fit corresponds to a model with two faults with an opposite vergence, the main thrust fault and a backthrust. The best fit model provides a main fault slip between 2200 and 2300 m, a dip angle of 23° to the NW and 41 km of depth of faulting and a backthrust slip of 450 m, a dip angle of 17° to the SE and 24 km of depth of faulting (Table 3.2). The regional slope observed in Phrixi Rupes decreases gradually towards the southeast and cannot be detected in Bosporos Rupes area which is further away from Thaumasia. The local modification of the topography due to erosion and sedimentation avoid the detection of a regional slope in this area. Bosporos Rupes is adjacent to the Argyre basin rim, for this reason there exists an abrupt slope CAPÍTULO 3 63 descending towards the southeast in front of the scarp face, which avoids a properly fit of the output model in this part. This slope corresponds to the outcrop of the Argyre basin materials, which are topographically below the highlands materials where these lobate scarps are formed. Figure 3.6 Forward mechanical dislocation method best fit models compared with MOLA stacked topographic profiles (gray area) for each lobate scarp. The mean topographic profiles, calculated after removing craters, are also shown. THEMIS model images attached to each graphic show the location of the area where the topographic profile stacking was performed. We established a tapered slip in the models, implying a slip concentration in the center of the fault plane decreasing toward the edges, vertically and horizontally to reproduce the observed fault displacement (Fig. 3.4) (Fossen, 2010). In our models (Fig. 3.6), we have set a displacement distribution which decreases horizontally in the last 10 km near the edges to minimize the boundary effects, and vertically in the last 7, 11 and 8 CAPÍTULO 3 64 km, respectively, for Ogygis Rupes, Phrixi Rupes and Bosporos Rupes. The modeled scarp face is steeper when the vertical distance of decreasing is minor. 3.2.4.4. Displacement-Length relationships There is a scaling relationship between the maximum displacement of the fault (D) and the fault length (L), for planetary faults as well as for terrestrial faults. D and L are related by D = cLn where c is a constant related to material properties and n is the power- law exponent (Walsh and Watterson, 1988). The relation between D and L for fault populations located in uniform rocks is represented as a lineal function D = γL being γ the critical shear stress for fault propagation, related to the tectonic setting and the mechanical properties of the material, and it ranges between 100 and 10-3 (Cowie and Scholz, 1992b). Figure 3.7 Plot of maximum fault displacement (D) in function of fault length (L) (modified from Schultz et al., 2006). The data for the three studied lobate scarps is shown in blue: Ogygis Rupes is shown by a square, Phrixi Rupes segments by circles, and Bosporos Rupes segments by triangles. The error bars indicate the displacement range for fault plane dips between 20° and 35°, corresponding with the range for planar thrust faults. Earth data for thrust faults is shown by black squares (Elliott, 1976) and triangles (Mége and Riedel, 2001). Mercury and Mars data are shown by gray diamonds and white circles respectively (Watters et al., 2000, 2002; Watters, 2003b). Using the maximum relief of the lobate scarp (Δz) and the dip angle of the fault plane (θ), we can estimate the maximum displacement necessary to restore the surface by D = Δz / sinθ (Wojtal, 1996; Watters et al., 2000; Watters, 2003b). We have calculated D for each segment of our three lobate scarps using the dip angles resulting of the forward mechanical modeling method (Table 3.2). These values are within the common range of dip angle for planar thrust faults, which ranges between 20° and 35° (e.g. Jaeger and Cook, 1979; Brewer et al., 1980; Stone, 1985). These data are included together with the results in Fig. 3.7 where it is also calculated the value of γ for this small population of lobate scarps, which is ∼1.7 x 10-2. Despite not being a very representative population, if we compare this value with those calculated for other locations (Fig. 3.7) including terrestrial trust fault populations (∼8.0 x 10-2) (Watters et al., 2000), Mercurian lobate scarps (∼6.5 x 10-3) (Watters et al., 2000) or martian dichotomy boundary thrust faults (∼6.2 x 10-3) CAPÍTULO 3 65 (Watters, 2003b), all of them calculated for θ = 30°; our result is an intermediate value, closer to those calculated for lobate scarps in Mercury and in the martian dichotomy. The segment with less displacement, which is part of Phrixi Rupes, matches perfectly with the observations for Mars and Mercury, while the rest data of the analyzed segments remain above due to the high displacement, which exceeds the thousand meters, with respect to the segment longitude. 3.2.5. Heat flow The depth of the BDT can be used in order to calculate the surface heat flow at the time of faulting. Thus, here we calculate heat flows from our results on fault depths at the Aonia Region following the methodology detailed in Ruiz et al. (2011) and Egea-González et al. (2017). This methodology calculates the heat flow from the temperature at the BDT depth (TBDT), which in turn is derived from equating the brittle and ductile strength at the BDT. Assuming homogeneously distributed crustal heat sources, the surface heat flow can be calculated from TBDT from 𝐹𝐹𝐹𝐹 = 𝑘𝑘(𝑇𝑇𝐵𝐵𝐵𝐵𝐵𝐵−𝑇𝑇𝑠𝑠) 𝑧𝑧𝐵𝐵𝐵𝐵𝐵𝐵 + 𝑧𝑧𝐵𝐵𝐵𝐵𝐵𝐵𝐻𝐻 2 , (1) where k is the thermal conductivity of the crust, TS is the temperature at the surface, ZBDT is the BDT depth, and H is the volumetric heat production rate. We have used k = 2 W m-1 K-1, which is appropriated for intact non-porous basaltic rocks (Beardsmore and Cull, 2001), and TS = 220 K, the present mean surface temperature on Mars (e.g., Kieffer et al., 1977). The radioactive heat production rate depends on the abundance of heat-producing elements (HPEs) in the crust. Near surface K and Th abundances were measured by Mars Odyssey GRS (Boynton et al., 2007; Hahn et al., 2011). Because the comparatively homogeneous HPEs distribution in the southern highlands, and that the martian crust is considered to be much less geochemically varied than the Earth’s crust (Taylor et al., 2006), we use as representative of the crust the average abundances, measure by GRS, of K and Th, respectively 3652 and 0.69 ppm (Hahn et al., 2011), whereas for estimating U abundance a Th/U ratio of 3.8 was assumed (e.g., Meyer, 2003). Heat dissipation rates are calculated for decay constants from Van Schmus (1995) and a time range of 3.6 to 3.8 Ma. Because ductile deformation is temperature-dependent, TBDT can be derived from equating the brittle and ductile strength at the BDT, and therefore 𝑇𝑇𝐵𝐵𝐵𝐵𝑇𝑇 = 𝑄𝑄 𝑛𝑛𝑛𝑛 �𝑙𝑙𝑙𝑙 �(1−𝜆𝜆)𝛼𝛼𝛼𝛼𝛼𝛼𝑧𝑧𝐵𝐵𝐵𝐵𝐵𝐵 (έ 𝐴𝐴⁄ )1 2⁄ �� −1 , (2) CAPÍTULO 3 66 where Q is the activation energy of creep, n and A are laboratory-determined constants for creep deformation, R is the gas constant (8.3145 J mol-1 K-1), λ is the pore fluid pressure, ρ is the density, α is a coefficient that depends on the stress regime (which takes a value of 3 in the case of thrust faulting; e.g., Ranalli, 1997), g is the acceleration due to the gravity (3.72 m s-2 for Mars), and έ is the strain rate. Here we take λ values between 0 and 0.35 (which is valid for dry and hydrostatic conditions), strain rates between 10-16 s-1 and 10-19 s-1, and for creep parameters we use the flow law of wet diabase of Caristan (1982), appropriate for a basaltic crust. [For a complete discussion on the parameters used in the calculation see Ruiz et al. (2011) and Egea-González et al. (2017)]. The results are shown in Table 3.2. Heat flows derived for Bosporos Rupes and Phrixi Rupes, which have been calculated to be 25-33 mW m-2 and 26-40 mW m-2 respectively, are similar to those usually found in the Thaumasia and circum-Hellas regions (Ruiz et al., 2008, 2009, 2011; Mueller et al., 2014; Egea-González et al., 2017), but heat flow obtained for Ogygis Rupes, which is 30-51 mW m-2, is comparatively higher, as a consequence of the lower BDT depth estimated for this lobate scarp. 3.2.6. Discussion and conclusions The structural modeling of three lobate scarps located between Thaumasia Montes and Argyre impact basin by two different methods allow us to constrain the depth where the underlying thrust faults root. Understanding the limitations of each method used is fundamental issue when comparing the respective results. On the one hand, the displacement used in the balanced cross sections method is the fault slip measured in cross-cut craters, which is a minimum estimate because, even assuming that the crater was formed before the beginning of the fault rupture, we do not know the initial distance between the surface fault rupture and the crater rim and the strike of the horizontal slip vector is unconstrained (Fig. 3.2b). If the real fault displacement value was larger, the depth of faulting calculated would be shallower, otherwise if there is volume loss due to erosion or loss of porosity by compaction the real depth of faulting would be deeper than our estimate. The erosion in Mars is considered to have a very low rate (Golombek and Bridges, 2000; Golombek and Phillips, 2010) but, together along with compaction, they could have a slight influence in the obtained depth. On the other hand, the forward mechanical modeling method also does not take into account these volume variations and, additionally, ignores fault-propagation fold deformation. Both methods, despite its limitations, have been demonstrated to be a good approximation to the fault parameters and applying both we constrain a more reliable range of parameters for the faults underlying the three lobate scarps located in Aonia Terra. Dip angles were obtained from the forward mechanical dislocation method, while the balanced cross section method does not provide information on the fault dip. The dip CAPÍTULO 3 67 angles for the faults underlying the three lobate scarps, 35° for Ogygis Rupes, 33° for Phrixi Rupes and 23° for Bosporos Rupes, are inside the range of dip angles for thrust faults in terrestrial planets, typically ranging between 20° and 35° (e.g., Jaeger and Cook, 1979; Brewer et al., 1980; Stone, 1985; Watters and Nimmo, 2010). The differences between both methods, both in depth and fault slip (Table 3.2; Fig. 3.8), are probably related to limitations in the models and also by the distribution of the volume and the width of the structure, conditioned by the appearance of backthrusts (Ogygis Rupes and Bosporos Rupes) and fault segmentation (Phrixi Rupes and Bosporos Rupes) which modify the distribution of displacement in the structure and hinder its analysis and understanding. Ogygis Rupes, despite having a backthrust which only affects the north part of the lobate scarp, seems to be the simplest structure. In addition, it is the lobate scarp that seems less affected by processes of sedimentation and erosion of the three lobate scarps analyzed, which is visible by comparing the results obtained by the two methods, which are quite similar (Fig. 3.8a). In this way, the fault slip in Ogygis Rupes is set between 2500–3100 m, extending to depth of faulting of 18–27 km. Phrixi Rupes is divided in two segments, which have the same direction and are quite close to each other, but its interaction in depth is unknown. The surface of its southern segment seems very altered and modified but it does not appear to be so in the zone of maximum lobate scarp relief used for the analysis located in the northern segment. Even so, the results of the two methods do not show a great difference (Fig. 3.8b) and the fault slip for Phrixi Rupes is set between 1700 and 2000 m and the depth of faulting is 24.5–36 km. Bosporos Rupes is the longest and most complex structure here analyzed. It is divided in two segments and has a backthrust fault along most of its length, showing a significant displacement with respect to these two segments. Its surface is quite affected by craters, and by erosion and sedimentation processes. The fault slip value obtained by the balanced cross section method (1700 m) is quite small compared with the forward mechanical modeling result (2650–2750 m). This difference in the result, together with the high shortening accommodated by the backthrust, seems to indicate that the total displacement in this lobate scarp is significantly larger than the one deduced from the cross-cut craters analysis and used for the balanced cross section method. In spite of this, the depth of faulting obtained by the two methods has a similar range of 33–45 km (Fig. 3.8c). Considering the observed lengthwise profiles (Fig. 3.4), in which the displacement will be larger in the center of the fault plane, we have selected an elliptical displacement distribution for the forward mechanical method, which fits the results reasonably well. This distribution also agrees with a triangular distribution, providing similar results except for a reduction in the displacement value (Ma and Kusznir, 1992) due to the influence of the edges. Given that the displacement results would differ greatly using a triangular distribution from those obtained using the balanced cross section method, we select an elliptical distribution in which the center of the structure is not affected by the distance CAPÍTULO 3 68 to the edges, aiming to avoid this effect and simplifying the model. Anyway, this reduction in the displacement would not significantly change our conclusions since the dip angle and depth of faulting results remain unchanged. The decreasing displacement in the shallower meters of the fault plane could be justified by the fault-propagation fold model in which the shortening at the beginning of the contraction is accommodated by early folding followed by the formation of a thrust fault that accommodates the displacement propagating upward from depth (Allmendinger and Shaw, 2000). In the same way, the displacement decreases in the deeper part of the fault plane (Fig. 3.8) which can be interpreted as a gradual BDT where the fault displacement decreases until reaching ductile domain. This interpretation, considering the decollement associated with the large thrust faults underlying large lobate scarps to be a main rheological change reflecting the start of ductile flow as dominant deformation mechanism, has been assumed by multiple authors previously (e.g. Schultz and Watters, 2001; Ruiz et al., 2008; Egea-González et al., 2017). Figure 3.8 General cross sections of the three lobate scarps showing the results of the depth of faulting estimated by both methods. The gray area corresponds to the displaced volume (i.e. the hanging wall). Balanced cross section results are shown by a striped dark red line. Forward mechanical dislocation model results are shown by dotted lines and the displacement decrease in the last kilometers at depth is indicated by a red to yellow gradient. CAPÍTULO 3 69 The formation of the Argyre impact basin during the Noachian time, which has a calculated absolute age of ∼3.93 Gyr (Robbins and Hynek, 2012; Robbins et al., 2013), produces impact-related deformation up to 2000 km away from the basin rim in the form of different structures such as concentric ring scarps or radial structurally-controlled valleys (Dohm et al., 2015). Eight concentric rings have been described associated with Argyre impact basin (Hiesinger and Head, 2002) (Fig. 3.9). The ring 6, defined as the closest approximation to the transient crater rim, could be defined as the main Argyre ring showing steep slopes facing towards the basin interior. Bosporos Rupes scarp base is located on ring 6 with its backlimb extending between rings 6 and 7 (Fig. 3.9). Bosporos Rupes strikes concentric to the impact basin, leading to suggest that its strike might be structurally controlled by the presence of Argyre basin. However, Ogygis Rupes and Phrixi Rupes which are located between the rings 7 (formed by the main topographic elevations around the impact basin) and 8 (the most external and uncertain), do not strike concentric to the Argyre basin, but conversely, they strike parallel to the edge of Thaumasia, being concentric to Tharsis, together with the wrinkle ridges present in this area (Fig. 3.1), suggesting a causal relationship (Wise et al., 1979; Watters et al., 1993; Anderson et al., 2001). This difference in the orientation of the contractional structures corroborates that this part of Aonia Terra in the northwestern margin of Argyre basin is more influenced by the proximity of Thaumasia than by the Argyre impact basin, although the presence of the Argyre rings could have a certain influence (Dohm et al., 2015). Figure 3.9 Radial MOLA topographic profiles from the center of Argyre basin (O) to the outside (A, B, C) across the three lobate scarps studied. The eight rings of Argyre defined by Hiesinger and Head (2002) are shown. The Argyre image, colored from MOLA elevation model overlaying THEMIS, shows the location of the three topographic profiles and impact basin rings in black, and the lobate scarps in red. Attending to the Late Noachian/Early Hesperian age (∼3.8–3.6 Gyr) (Dohm et al., 2001, Hartmann and Neukum, 2001), established for these lobate scarps and consistent with their emplacement in Noachian units (Fig. 3.1), we can compare our results for the three lobate scarps on Aonia Terra with previous thrust fault studies on lobate scarps on Mars (Table 3.3) formed approximately in the same age (Schultz and Watters, 2001; Ruiz CAPÍTULO 3 70 et al., 2008; Mueller et al., 2014; Grott et al., 2007; Egea-González et al., 2017), whose calculated fault parameters are comparable to those obtained in this study. Considering that almost all the previous studied lobate scarps have reliefs of the order of a few hundred meters while the three lobate scarps analyzed in this study have maximum reliefs over 1200 m, even exceeding 2000 m in the case of Ogygis Rupes, it is a reasonable result that the fault slips calculated for the lobate scarps in Aonia Terra are considerably higher than those calculated for Amenthes Rupes (Schultz and Watters, 2001; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017), for lobate scarps in the south of Thaumasia (Grott et al., 2007) and for lobate scarps in the circum-Hellas region (Egea- González et al., 2017). The dip angles calculated in all the studies, including our value of 23–35°, are very similar and they are within the typical dip range for reverse faults (20– 35°) (e.g., Jaeger and Cook, 1979; Brewer et al., 1980; Stone, 1985; Watters and Nimmo, 2010) or very close to it, except the dip angle obtained by Mueller et al. (2014) for Amenthes Rupes which is quite higher (42–54°). Accordingly, the depth of faulting obtained for the three lobate scarps of Aonia Terra (18–45 km) is a perfectly reasonable value if we compared it to other lobate scarps studied, whose depths of faulting range between 13 and 48 km. Table 3.3 Comparison with fault parameters from previous studies. Displacement (m) Dip angle (°) Depth of faulting (m) Amenthes Rupes (Schultz and Watters, 2001) 1500 25–30 25–30 Amenthes Rupes (Ruiz et al., 2008) 1900–2300 19–24 27–35 Amenthes Rupes (Mueller et al., 2014) 1170–1440 41.5–56.1 33–48 Amenthes Rupes (Egea-González et al., 2017) 1500–2000 20–35 27–33 South of Thaumasia (Grott et al., 2007) 2100 30 21–35 Circum-Hellas Region (Egea-Gonzalez et al., 2017) 400–2000 13–40 13–45 Aonia Terra (This study) 1700–3100 23–35 18–45 The shallower depth of the BDT at the time of faulting in this area of Aonia Terra between Thaumasia and Argyre impact basin is found closer to the edge of Thaumasia (18–36 km) than near the Argyre basin rim (33–45 km). Ogygis Rupes and Phrixi Rupes have depths of faulting (18–36 km) similar to the values obtained by Grott et al. (2007) in the south edge of Thaumasia (21–35 km) which are located close to our study area. CAPÍTULO 3 71 However, the depth of faulting calculated for Bosporos Rupes is higher. Although this value matches the range of depths previously calculated for lobate scarps on Mars (Table 3.3), if we consider that the three lobate scarps were formed in the same restricted age (Late Noachian/Early Hesperian) in a relatively small area, the observed variation needs an explanation. Attending to its location over the main crater rim (ring 6), our results seem to suggest a thicker brittle domain under Bosporos Rupes (and ring 6) with respect to the external area probably associated with the impact basin structure. A significant difference in heat flow, being lower under Bosporos Rupes, seems to contradict the thickened crust with more radiogenic elements under the Argyre main rim in this area. A high variation in such a restricted area of the depth of faulting and, consequently, of the BDT seems to be unrealistic, especially considering that the three lobate scarps are similar in age according to regional geology. Alternatively, the BDT depth also depends on the strain rate (Dragoni, 1993). A deeper BDT such as the obtained for Bosporos Rupes would correspond with a faster deformation compared with Ogygis Rupes and Phrixi Rupes. But the origin of such difference would be unknown. A simple explanation for the discrepancy in the obtained depth of faulting comes from the presence of the main Argyre rim at the same location where Bosporos Rupes was generated. The match between part of Argyre ring 6 and Bosporos Rupes in location and strike strongly suggests that this ring acted as a mechanical anisotropy conditioning the nucleation of Bosporos Rupes on it, which makes very difficult to evaluate the contribution of each structure to the current topography. Thus, the modeled topography might not correspond only to the topography uplifted by the movement of the fault underlying Bosporos Rupes, which would result in inaccurate calculated fault parameters. This could explain the difference of depth of faulting as a consequence of the crater rim topographic contribution. The area uplifted by the thrust fault movement has been overestimated, providing a deeper depth of faulting under Bosporos Rupes than the real value. The orientation of the contractional strain field that generated these lobate scarps, and also the wrinkle ridges of the area, is mainly controlled by the gravitational field originated by Tharsis topographic elevation and, in less degree, by the presence of Argyre impact basin and the global contraction of the planet. Concentric contractional structures are predicted by lithospheric deformation models of Tharsis (Golombek and Phillips, 2010). Dimitrova et al. (2006) defined a deviatoric stress field associated with horizontal gradients of gravitational potential energy (GPE) to explain the formation of concentric contractional structures and radial extensional structures with respect to Tharsis. Argyre basin, due to its low topography and thin crust, produces deviatoric extension in GPE models, generating a decay of the compression stress field near the basin. The heat flows derived from the BDT depth for the Aonia Terra region (Table 3.2) suggest, when putted together with the previous results for Thaumasia and circum-Hellas CAPÍTULO 3 72 regions (Ruiz et al., 2008, 2009, 2011; Mueller et al., 2014; Egea-González et al., 2017), a roughly constant heat flow during the Late Noachian/Early Hesperian time in, at least, much of the southern highlands of Mars. Because the contribution of radioactive crustal heat sources supposes a substantial component to the total surface heat flow related to crustal thickness (Parro et al., 2017), the relatively similar surface heat flow and high crustal thicknesses in these regions suggest that both the crustal and mantle heat flow must also be similar across the southern highlands. A relatively uniform mantle heat flow in such an extensive area could support some previous expectations (e.g., Ruiz, 2014) suggesting relatively inefficient convective heat transfer, and low surface heat flow beyond volcanic areas. CAPÍTULO 3 73 3.3. Conclusiones Capítulo 3 El análisis estructural de los tres escarpes lobulados localizados en Aonia Terra, entre los Montes de Thaumasia y la cuenca de impacto de Argyre, proporciona estimaciones de los principales parámetros estructurales para las grandes fallas que son causantes de estos relieves. La cartografía geológica y estructural detallada de este área proporciona una edad estimada para estas estructuras de ∼3800–3600 Ma (Noeico Tardío/Hespérico Temprano). La orientación de las estructuras de acortamiento de la zona, tanto los escarpes lobulados estudiados, como las crestas sinuosas, corrobora que esta parte de Aonia Terra está estructuralmente más controlada por la proximidad de los Montes Thaumasia que por la cuenca de impacto de Argyre, dado que los escarpes lobulados son subparalelos al borde de Thaumasia. Así pues, podemos interpretar que la orientación del campo de esfuerzos compresivos que generó las estructuras de contracción de esta zona está principalmente controlado por el campo de esfuerzos originado por la elevación de la provincia de Tharsis (de la cual Thaumasia representa su relieve situado al SE) y, en menor medida, por la cuenca de impacto de Argyre. Alrededor de las cuencas de impacto pueden existir zonas concéntricas alternas de corteza engrosada y adelgazada por efecto del impacto comúnmente conocidas como “anillos”. La presencia de los anillos de la cuenca de Argyre también genera control estructural en este área dado que Bosporos Rupes, que se encuentra situado más al SE, presenta una dirección claramente concéntrica a Argyre, situándose además sobre uno de estos anillos. Los resultados obtenidos por los dos métodos para estos tres escarpes lobulados se encuentran dentro de los rangos obtenidos en estudios previos de escarpes lobulados en Marte. Sin embargo, al comparar más detalladamente los resultados de desplazamiento y profundidad de los dos métodos usados, y teniendo el cuenta la proximidad entre las fallas, podemos apreciar algunas diferencias. Los valores de buzamiento para estas tres fallas varían entre 23° y 35° lo que concuerda con los valores de fallas inversas en la Tierra y con resultados obtenidos en diferentes estudios en escarpes lobulados en Marte. Ogygis Rupes, el cual se encuentra más cerca de Thaumasia, presenta el mayor desplazamiento (2500–3100 m), acorde con su mayor relieve. Mientras que Phrixi Rupes y Bosporos Rupes registran desplazamientos de entre 1700 y 2750 metros. El desplazamiento sobre el plano de falla del método de dislocación de falla, decrece en profundidad en los últimos metros antes de llegar al nivel de despegue, lo que puede interpretarse como la entrada en la transición frágil-dúctil, mientras que los resultados obtenidos de los cortes compensados por áreas estarían indicando el inicio de la transición frágil-dúctil como puede verse en el caso de Ogygis CAPÍTULO 3 74 Rupes y Phrixi Rupes (Fig. 3.8). Atendiendo a los resultados obtenidos de profundidad de las fallas, la mayor profundidad corresponde con Bosporos Rupes (33–43 km), el cual está situado más próximo a la cuenca de Argyre. Esta profundidad decrece al alejarnos de la cuenca, de modo que Phrixi Rupes presenta una profundidad de 24.5–36 km, mientras que Ogygis Rupes, que se encuentra más cerca del borde de Thaumasia, presentaría una profundidad menor (18–27 km). Asumiendo que las profundidades obtenidas para los escarpes lobulados corresponden con la profundidad de la transición frágil-dúctil del momento de su formación (Noeico Tardío/Hespérico Temprano), nuestros resultados sugieren un dominio frágil engrosado debajo del anillo principal de Argyre, con respecto a la zona más alejada de la cuenca. Esta es una variación de profundidad bastante brusca en un área tan pequeña para la misma época. Además, los valores de flujo térmico bajos obtenidos para Bosporos Rupes contradicen esta corteza engrosada bajo el anillo principal de Argyre. La explicación más simple para estos resultados anómalos en Bosporos Rupes puede ser la presencia del anillo antes de que el relieve de Bosporos Rupes se formase, el cual actuó como zona de anisotropía mecánica favoreciendo la formación de esta estructura, por lo que al modelizar este relieve estaríamos modelizando el relieve del anillo como parte de la elevación asociada al movimiento de la falla. Esta sobreestimación de la topografía elevada por el desplazamiento de la falla durante la contracción tectónica conllevaría una sobreestimación de la profundidad del nivel de despegue. Los valores de flujo térmico obtenidos para esta zona de Aonia Terra, analizados conjuntamente con los obtenidos en zonas cercanas en trabajos previos (Ruiz et al., 2008, 2009, 2011; Mueller et al., 2014; Egea-González et al., 2017), sugieren un flujo térmico bastante constante durante el Noeico Tardío/Hespérico Temprano en las tierras altas del sur de Marte. 4 Modelización 3D de grandes fallas inversas en Marte 3D modeling of planetary lobate scarps: the case of Ogygis Rupes, Mars CAPÍTULO 4 77 4.1. Introducción La modelización 3D de un escarpe lobulado proporciona una visión completa de la dinámica de las grandes fallas inversas que controlan la formación de estas estructuras. La expresión topográfica de estas estructuras varía lateralmente, lo que refleja que existen cambios laterales en la geometría de las fallas subyacentes y en las tasas de desplazamiento a lo largo de una misma estructura (e.g. Klimczak et al., 2018; Herrero-Gil et al., 2019). La modelización 3D permite reproducir la topografía del escarpe lobulado incluyendo estas variaciones laterales, así como interacciones con estructuras secundarias o subsidiarias, lo que supone un gran avance respecto a métodos previos. El mecanismo de plegamiento asociado al desplazamiento de la falla inversa que forma el escarpe lobulado ha sido considerado, en este trabajo, como un pliegue de propagación de falla (fault-propagation fold), ya que otros mecanismos de plegamiento como los pliegues de flexión de falla (fault-bend folds) o los pliegues de detachment no concuerdan con las características topográficas que presenta la estructura (Jamison, 1987). En este trabajo hemos utilizado un mecanismo simple de pliegue de propagación de falla en el que la falla se propaga hacia la superficie para simplificar el proceso de modelización. Este tipo de deformación es un caso especial de pliegues de gradiente de desplazamiento (displacement-gradient folds) (Wickham, 1995) en el que la línea de “fault tip” se desplaza hacia la superficie, en lugar de permanecer estacionaria o descender. El marco tridimensional utilizado combina los algoritmos de fault-parallel flow (Egan et al., 1997; Ziesch et al., 2014) con los algoritmos de trishear (Erslev, 1991; Allmendinger, 1998) asumiendo la conservación de volúmenes durante la modelización (Cristallini y Allmendinger, 2001; Cardozo, 2008; Ziesch et al., 2014). Los algoritmos de fault-parallel flow modelizan el desplazamiento del bloque de techo sobre el bloque de muro, donde el material del bloque de techo se desplaza en la dirección del movimiento de la falla siguiendo líneas de flujo paralelas al plano de falla, mientras que el método de trishear permite modelizar el plegamiento que ocurre delante de la falla al propagarse. El proceso de modelización incluye una restitución 3D de la superficie topográfica original deformada por el movimiento de las fallas y un posterior modelado directo a partir de una superficie topográfica de la cual se ha eliminado la estructura tectónica, con el objetivo de obtener la geometría de la falla a partir de la cual se recrea con mayor precisión la superficie original. El objetivo final es la obtención de los parámetros que definen la geometría y desplazamiento de la falla, y los parámetros de trishear, que controlan el plegamiento asociado, así como las variaciones de estos valores a lo largo de la estructura. CAPÍTULO 4 78 La interpretación de estos parámetros amplía de manera sustancial la información previa que se obtenía al modelizar estas estructuras con métodos 2D (e.g. Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Egea-González et al., 2017; Herrero-Gil et al., 2019), permitiendo una mejora del entendimiento de la cinemática de las grandes fallas que forman los escapes lobulados y de la estructura mecánica de la litosfera en el momento en que se formaron. Las variaciones de dirección y buzamiento permiten usar morfologías de falla complejas más realistas que concuerdan con la forma del trazado de las fallas en superficie. La profundidad del nivel de despegue (decollement) donde se enraíza cada falla nos da indicios sobre el tipo de discontinuidad mecánica en el que se nuclea la estructura, y si esta se mantiene constante a lo largo de la misma. Además, la distribución del desplazamiento a lo largo de la superficie de la falla permite interpretar como ha sido el acortamiento regional de la zona. En este capítulo se presentan los resultados obtenidos al modelizar el escarpe lobulado Ogygis Rupes, localizado en el margen NW de la cuenca de impacto de Argyre. Esta estructura, con más de 2000 metros de altura y ∼220 kilómetros de longitud (Klimczak et al., 2018; Herrero-Gil et al., 2019), es uno de los escarpes lobulados con mayor relieve descrito en Marte, formado durante el Noeico Tardío/Hespérico Temprano (Dohm y Tanaka, 1999; Anderson et al., 2001). Ogygis Rupes es una estructura continua, aislada y en general muy bien preservada, su signatura topográfica es fácilmente identificable de la topografía regional lo que la convierte en un candidato idóneo para la modelización de su superficie. Su relieve asimétrico, y su estructura continua y sin grandes cambios de dirección indican que su relieve principal ha sido formado por el desplazamiento de una única falla principal con vergencia hacia el ESE (Herrero-Gil et al., 2019). Además, este escarpe lobulado presenta dos fallas subsidiarias retrocabalgantes (backthrusts) de pequeñas dimensiones afectando su pendiente trasera (backlimb) en la zona norte de la estructura. Estas fallas subsidiarias han sido incluidas en la modelización, y su relación con la falla principal proporciona indicios sobre la presencia de posibles discontinuidades mecánicas menores dentro del dominio frágil de la corteza. CAPÍTULO 4 79 3D modeling of planetary lobate scarps: the case of Ogygis Rupes, Mars Andrea Herrero-Gil *a, Javier Ruiz a, Ignacio Romeo a a Departamento de Geodinámica, Estratigrafía y Paleontología, Facultad de Ciencias Geológicas. Universidad Complutense de Madrid, 28040 Madrid, Spain. Earth and Planetary Science Letters 532, 116004 Abstract Lobate scarps are the topographic expression of the largest thrust faults observed on the surfaces of terrestrial planets and their study provides information on the mechanical characteristics of the lithosphere at the time of formation. Here we show the results of 3D modeling of Ogygis Rupes, located in Aonia Terra, which is one of the most topographically pronounced lobate scarps described in the cratered martian highlands. The observed relief of Ogygis Rupes has been modeled by a combination of trishear and fault-parallel flow algorithms, providing a successful reproduction of the observed topography through a 3D modeling that includes the main thrust fault, forming the lobate scarp relief, and two subsidiary backthrusts. This recreation allows us to interpret Ogygis Rupes relief, modeling the fault-propagation folding, and constraining fault parameters and their variations along strike. The detailed slip distribution along the three faults reflects a general decay from the center to the edges for each fault, with the maximum slip value (2850 m) located approximately at the center of the main fault. The fault surfaces obtained for the main thrust fault and the two backthrusts show listric geometries at depth. The decollement where the main fault roots is set at ∼17–18 km deep, related to a main rheological threshold that on Mars is interpreted to be the depth of the Brittle-Ductile Transition at the time of the lobate scarp formation (Late Noachian/Early Hesperian). The listric morphology of the main fault implies that the total slip associated with this thrust fault is transmitted from the decollement, being representative of the regional shortening associated with the lobate scarp formation. Otherwise, the modeled backthrusts are subsidiary listric faults rooting at shallower depths (2.3–5.6 km), probably indicating the presence of mechanical discontinuities in the brittle domain of the martian lithosphere. 4.2. CAPÍTULO 4 80 4. 2. 1. Introduction Lobate scarps are common contractional tectonic structures present on the surfaces of terrestrial planetary bodies (e.g., Strom et al., 1975; Watters, 1993; Schultz and Watters, 2001). These large structures are interpreted to be the topographic expression of large surface-breaking thrust faults (e.g., Strom et al., 1975; Watters and Robinson, 1999; Watters and Nimmo, 2010). Lobate scarps show surface strikes from linear to slightly sinuous, with lengths of up to hundreds of kilometers and maximum reliefs of up to thousands of meters. These structures present a characteristic asymmetry in cross section, with a frontal steep slope (the scarp front) and a gentle back slope. These morphological characteristics correspond to a thrust fault propagation anticline followed by a trailing syncline. The large thrust faults underlying lobate scarps are considered to cut the brittle domain of the lithosphere, being rooted at the Brittle-Ductile Transition (BDT) of the time when they were formed (e.g., Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017). Previous studies on martian lobate scarps have been performed using 2D structural modeling methods with the aim of knowing the properties of the large faults that formed these structures, assuming that lobate scarp topography is controlled by fault geometry (Schultz and Watters, 2001; Watters et al., 2002). The depth of faulting, the dip angle and the fault slip are the structural parameters usually derived from these studies. The generally accepted interpretation that faults underlying lobate scarps root at the BDT provides information on the state of the lithosphere at the time of their formation (Schultz and Watters, 2001; Watters et al., 2002; Ruiz et al., 2008), and allows to calculate local or regional heat flow values (e.g. Ruiz et al., 2008, 2011; Grott et al., 2007; Mueller et al., 2014; Egea-González et al., 2017; Herrero-Gil et al., 2019). Several studies have been performed in 2D cross sections of Amenthes Rupes using a forward mechanical dislocation method (FMD) for an elastic halfspace with uniform isotropic elastic properties (Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Egea-González et al., 2017). The same method has also been applied to study two lobate scarps in the southern Thaumasia region (Grott et al., 2007), eight lobate scarps in the circum-Hellas region (Egea-González et al., 2017) and three lobate scarps in the northwest margin of Argyre impact basin (Herrero-Gil et al., 2019). The elastic dislocation method has also been applied to lobate scarps on other terrestrial bodies like Mercury (e.g., Watters et al., 2002; Egea-González et al., 2012; Watters et al., 2016), the Moon (e.g. Byrne et al., 2015) and the asteroid 433 Eros (Watters et al., 2011). The balanced cross section (BCS) method (Chamberlin, 1910), which attends to fault-propagation fold theory (Suppe, 1983; Seeber and Sorlien, 2000) assuming mass conservation during the deformation process, has also been used to analyze lobate scarps on Mars. Using this method, Mueller et al. (2014) calculated Amenthes Rupes fault parameters on 2D profiles and Herrero-Gil et al. (2019) also analyzed the three lobate scarps near Argyre basin. These two methods provide a first approach to the structural characterization of lobate scarps, but the results offered by 2D CAPÍTULO 4 81 modeling may be limited by the selection of specific cross sections. These cross sections provide a limited view of the structure because they do not take into account the whole geometry of the lobate scarp, the variations of fault parameters along strike, and the 3D spatial interaction with other subsidiary structures. The 3D modeling of a lobate scarp extends the information obtained from 2D modeling, providing a more complete vision of the dynamics of these large tectonic structures. The topographic expression of lobate scarps changes laterally, reflecting fault geometry and slip variation along their strikes. Our 3D modeling successfully reproduces the observed topography characterized by a fault-propagation fold including the interaction with other subsidiary structures. The 3D approach allows us to constrain the slip distribution on the fault surface, the variations of dip at depth and along strike (allowing non-planar realistic fault geometries according to the mapped fault traces), the depth of the decollement where the fault roots, and the degree of interaction between different nearby structures. The formation of subsidiary thrust faults with an opposite vergence to the main fault, known as backthrusts, is common in large mountain ranges on Earth (e.g., Jayangondaperumal et al., 2015). Backthrusts associated with large thrust faults forming lobate scarps have also been identified on Mars (e.g., Herrero-Gil et al., 2019; Klimczak et al., 2019). The relation between the main thrust fault and these subsidiary backthrusts provides insights on the existence of crustal mechanical discontinuities at the depth where these subsidiary faults root. Here we present the results of a 3D model of Ogygis Rupes, which is one of the most topographically pronounced lobate scarps described on Mars, providing an improvement on the understanding of lobate scarps kinematics and lithospheric structure at the time of formation. The results provide advances on the geometry and kinematics of the underlying faults (including positive listric geometries), the interaction of the main fault with subsidiary backthrusts and a constraint on the thickness of the brittle lithospheric domain. The main thrust fault of Ogygis Rupes together with two subsidiary backthrusts form an isolated structure whose topographic signature can be easily identified from the regional topographic trend (Fig. 4.1). The erosion rate that has affected this lobate scarp since its formation seems to be low resulting in a broadly well-preserved structure (Herrero-Gil et al., 2019), although some fluvial channels have shaped Ogygis Rupes backlimb in the southern half of the structure (Klimczak et al., 2018). These particularities make Ogygis Rupes a successful candidate for 3D modeling. 4. 2. 2. Ogygis Rupes Ogygis Rupes is located in Aonia Terra, in the transition zone between the Argyre basin and the Thaumasia Montes, in the southern highlands of Mars (Fig. 4.1). This lobate scarp is apparently formed by a main single fault striking N30°E and verging ESE (Herrero- CAPÍTULO 4 82 Gil et al., 2019) that has a length of 220 km. The maximum scarp relief is ∼2200 m, corresponding to the crest of the fault-propagation fold, and it is located near the center of the structure, at ∼100 km from the southern fault tip. Figure 4.1 Tectonic map of Ogygis Rupes area over an image combining colored MOLA elevation model overlaying THEMIS-IR Day Global Mosaic 100m. The main fault is shown in red color, while Backthrust 1 and Backthrust 2 are the thrust faults shown in black color (minor thrust faults). The inset globe, colored with MOLA model, shows the map location. Ogygis Rupes presents two associated subsidiary backthrusts, verging WNW, which are located in the northeastern half of the structure (Fig. 4.1, Fig. 4.2a) cutting the backlimb of the propagation anticline of the main fault. The main fault and Backthrust 1 cut two different craters providing strong evidence of surface rupture by faulting (Herrero-Gil et al., 2019). Backthrust 1 strikes N10°E and is ∼60 km long. This fault is laterally spaced about 20 km from the main fault, generating a "pop up" structure in the northern part of Ogygis (Fig. 4.2a, b). The maximum relief of Backthrust 1 is ∼450 m (measured at ∼16 km from the southern tip (Fig. 4.2b) avoiding the transected crater where this measurement would be overestimated due to the elevation difference between the crater rim and the bottom of the crater). CAPÍTULO 4 83 Figure 4.2 (a) Mosaic made of CTX images showing in detail the northern part of the Ogygis Rupes structure, where the Backthrust 1 and 2 are shown. Cross sections A-A’ and B-B’ are marked in white. (b) Cross section A-A’ where the asterisks indicate the location of the mapped thrust faults on image a (10x vertical exaggeration). (c) Cross section B-B’ where the asterisks indicate the location of mapped thrust faults and the black arrow indicate the northwestern rim of the double crater rim where a wrinkle ridge is mapped on figure a (10x vertical exaggeration). Backthrust 2 is 65 km long and is spaced about 50 km from the main fault, overlapping just half of its length with the northern part of the main fault and, consequently, also with Backthrust 1. The trace of this backthrust seems to be structurally controlled by the southeastern rim of two ancient superposed craters, following a curved morphology with an average strike of N27°E. A cross section through Backthrust 2 (Fig. 4.2c) shows that this fault uplifts a large relief with the characteristic asymmetric profile of a fault-propagation fold. The rest of the rim barely presents relief, even though a wrinkle ridge deforms the northwestern rim (Fig. 4.2c). Reverse faults structurally controlled by preexisting structures related to impact craters have been described on Mercury (Crane and Klimczak, 2019), the Moon (Byrne et al., 2015) and possibly Ceres (Ruiz et al., 2019). The maximum relief associated with Backthrust 2 (∼850 m between fold crest and scarp base) is located at the center of this structure. The main fault of Ogygis Rupes and both subsidiary backthrusts show a gradual decrease of relief from the point with maximum relief towards the lateral fault tips. Regional studies on the geological history of the area where Ogygis Rupes is located indicate that this structure was formed during the Late Noachian/Early Hesperian (Dohm and Tanaka, 1999; Anderson et al., 2001), which is equivalent to an age of ∼3.8– 3.6 Gyr (see Hartmann and Neukum, 2001; Werner and Tanaka, 2011). This age is CAPÍTULO 4 84 consistent with the cross-cutting relationships between the faults forming the lobate scarp and the geological units affected by their slip (Herrero-Gil et al., 2019). 4. 2. 3 . Method The 3D modeling of Ogygis Rupes has been performed combining trishear algorithms (Erslev, 1991; Allmendinger, 1998) to recreate the fault-propagation folding ahead of the fault and fault-parallel flow algorithms (Egan et al., 1997; Ziesch et al., 2014) to define the movement of the hanging wall over the footwall, assuming volume conservation (Cristallini and Allmendinger, 2001; Cardozo, 2008; Ziesch et al., 2014). This combination provides the best fit between the 3D model output and the original lobate scarp topography. The modeling was performed using the software MOVETM (Midland Valley), in which trishear and fault-parallel flow algorithms are implemented in 3D (Cardozo, 2008; Ziesch et al., 2014) with the possibility of including complex fault geometries as listric propagating thrust faults (Brandenburg, 2013; Cardozo and Brandenburg, 2014). This tool was successfully used in 3D modeling of thrust faults on Earth (e.g., Cristallini and Allmendinger, 2001; Maesano et al., 2013; Watkins et al., 2015). The Digital Elevation Model (DEM) used was obtained from Mars Orbiter Laser Altimeter (MOLA, Mars Global Surveyor mission) data (Smith et al., 2001) whose horizontal resolution is ∼463 m/px and the vertical resolution is ±3 m. The Thermal Emission Imaging System (THEMIS, Mars Odyssey mission) daytime infrared (IR) mosaic was used as a base image because its resolution of 100 m/px (Christensen et al., 2004) allows to accurately identify the structures in the area, providing the support for a detailed structural map (Fig. 4.1). Context Camera (CTX, Mars Reconnaissance Orbiter) images (Malin et al., 2007) were used to characterize small features. 4.2.3.1. Geometric parameters of fault planes The principal variables that define the kinematic properties of a fault are depth of faulting, dip of the fault plane, and fault slip. These parameters have a strong influence in the topographic expression of the structure and they control width (horizontal distance between the scarp base and trailing syncline) and topographical relief (elevation difference between the scarp base and anticline crest) of the lobate scarp (Schultz and Watters, 2001; Watters et al., 2002). An increase of the depth of faulting (keeping the rest of parameters constant) results in a larger volume of uplifted material providing a wider anticline with the same relief, while shallower depths of faulting entail a narrower structure. An increase of the fault dip angle (keeping the rest of parameters constant) provides a narrower structure CAPÍTULO 4 85 with greater relief and a steeper backlimb. A gradual decrease of the fault dip with depth until reaching a horizontal decollement (positive listric fault geometry) controls the slope and width of the backlimb, and, as a consequence, the shape of the trailing syncline. A larger listric zone, characterized by a gradual dip change at depth, provides a wider and gentler backlimb and a wider trailing syncline. Otherwise, an abrupt dip change, where the fault reaches the decollement level, entails a narrower and steeper backlimb. Fault slip changes exclusively affect the relief of the structure. 4.2.3.2. Trishear parameters Trishear parameters control the shape of the fault-propagation fold. The hanging wall slips over a fixed footwall under a contractional tectonic setting characterized by a thrust fault that propagates upwards from a decollement level (Fig. 4.3). The triangular zone where the fault-propagation fold is developed, defined by the trishear angle (θ), moves forward from a certain depth (fault tip depth) as the fault propagates upwards with a propagation to slip ratio (P/S) (Hardy and Ford, 1997). A small trishear angle increases the deformation ahead of the fault tip, producing a narrow fold with a steep forelimb, while a large angle involves that the deformation is distributed in a bigger area generating a broad anticline (Allmendinger, 1998). Figure 4.3 Representation of trishear method (based on Hardy and Ford, 1997; and Zehnder and Allmendinger, 2000). Trishear area is colored in grey. Trishear angle (θ) is shown in red, while its divisions depending on whether it affects the hanging wall (θ1) or the footwall (θ2) are shown in orange. Fault tip is marked with a big red dot. The distribution of the velocity of the hanging wall relative to the footwall in the trishear area is marked with grey slip vectors, varying from top (where they are parallel and equal to the one that defines the movement of the hanging wall) to bottom (where these vectors decrease in magnitude turning its orientation to be parallel to the lower boundary of the trishear zone until being zero). The orientation of the trishear zone with respect to the fault (θ1, θ2) also affects the geometry of the fault-propagation fold (Fig. 4.3). The deformation caused by fault propagation can be symmetrically distributed between the hanging wall and footwall (θ1 = θ2), larger in the hanging wall than in the footwall (θ1 > θ2) or the opposite (θ1 < θ2). CAPÍTULO 4 86 The P/S ratio describes how rapidly the fault tip propagates with respect to the fault slip and it is associated with the degree of development of the fault-propagation fold (Hardy and Ford, 1997). Low values of P/S (below 2) cause more intense deformation of the forelimb (especially at depth) because the material spends more time within the trishear zone. 4.2.3.3. Modeling workflow The modeling procedure consists of three steps: (1) 2D restitution and forward modeling along selected cross sections that provide a first order approximation to the fault geometries and the displacement distribution, (2) 3D restoration where the fault geometries and displacements were checked and refined, and finally (3) 3D forward modeling to constrain the trishear parameters that best reproduce the observed topography. The displacement vector of the main fault and the backthrusts that formed Ogygis Rupes was assumed to be perpendicular to the fault strike (pure dip-slip reverse faulting), according to the observations of cross-cut craters (Herrero-Gil et al., 2019). The footwall was considered to remain static during modeling. The 3D fault surfaces were built interpolating between the 2D cross sections modeled, and they were used as an initial setup for 3D modeling. In the 3D restoration process fault displacements were restored, unfolding the fault propagation anticline to reconstruct the original topographic surface. This procedure provides a refinement of the fault geometry and the displacement distribution along the strike. Finally, the 3D forward modeling allows to constrain the propagation-slip ratio and the parameters of the trishear zone. The forward modeling was performed starting from a topographic base surface obtained by removing the craters and Ogygis Rupes relief from MOLA model. This surface was forward deformed starting with the fault surfaces and the parameters obtained from the 3D restoration of the main fault and the two backthrusts. 4.2.4. Results of 3D modeling of Ogygis Rupes 4.2.4.1. 3D Restoration The topographic surface deformed by the tectonic structures forming Ogygis Rupes (Fig. 4.4a) is restored using the 3D fault surfaces, obtaining an undeformed topographic surface as plain and homogeneous as possible (Fig. 4.4b). CAPÍTULO 4 87 Figure 4.4 (a) Ogygis Rupes original surface colored from MOLA elevation model overlaying THEMIS-IR Day Global Mosaic 100m. (b) Topographic surface of Ogygis Rupes restored from the original MOLA model of the area. The 3D restoration process highlighted that the movement backwards of the main fault does not restore all the observed uplifted topography, consequently, the restoration of both backthrusts is needed to completely remove Ogygis Rupes relief. Both the main fault and the backthrusts, do not show large variations of dip angle and depth of faulting along their strike. Conversely, fault slip values clearly decrease towards the edges in the three faults that form the lobate scarp structure. The geometry of the fault surfaces and displacements were iteratively modified until restoration was as complete as possible (Fig. 4.4b). A successful restoration was obtained when planar geometries for the first kilometers were combined with positive listric (a decay of the dip angle at depth) morphologies at depth (Fig. 4.5). Otherwise, completely planar fault geometries that keep a constant dip until the decollement depth cannot restore the backlimb geometry of the fault propagation anticline, producing a steep and narrow backlimb that does not match the observed topography (see Supplementary material, Fig. S1). The dip angle obtained for the main fault is 39° towards the NW for the first ∼11 km of the fault plane measured from the topographic surface (until a depth of ∼5.5 km). From this depth, the dip angle gradually decreases with a positive listric geometry rooting into a horizontal decollement at 17.2–17.8 km deep (Table 4.1). Backthrust 1 dips towards the opposite direction (SE) than the main fault, with an angle of 22° (constant for the first ∼9 km of the fault plane measured from the topographic surface, until a depth of ∼1.2 km), that flattens downwards until a depth of faulting of 2.3–2.9 km. Backthrust 2 dips 23° to the SE for the first ∼12 km of the fault CAPÍTULO 4 88 measured from the topographic surface (until a depth of ∼3 km), gradually decreasing to a subhorizontal dip at 5.5–5.6 km of depth (Table 4.1). Figure 4.5 3D model of Ogygis Rupes area with an inclined perspective from the north in which it can be observed part of the topographic surface. The other part of the topography has been hidden allowing to observe the three fault surfaces underlying the lobate scarp. Three SE-NW cross sections perpendicular to the lobate scarp, located in the north (A-A’), center (B-B’) and south (C-C’) of the structure, are shown. The main fault, Backthrust 1 and Backthrust 2 are also shown in these cross sections. Table 4.1 Fault and trishear parameters calculated for Ogygis Rupes Length (km) Depth (km) Dip angle (°) Max. fault slip (m) Trishear angle (°) Fault tip depth (m) P/S ratio Main fault 220 17.2–17.8 39 2850 76 (center), 70 (edges) -4700 3 Backfault 1 60 2.3–2.9 22 1200 70 -750 2 Backfault 2 65 5.5–5.6 23 1800 36 -1200 2 CAPÍTULO 4 89 4.2.4.2. 3D Forward modeling The Ogygis Rupes anticline does not present constant characteristics along strike (Fig. 4.5), reflecting a slight variation of the trishear parameters between the center and the edges of the structure. The initial topographic surface used for the forward modeling (Fig. 4.6a) is iteratively deformed using the fault surfaces from 3D restoration until obtaining a model as similar as possible to the original observed surface (Fig. 4.4a). The most accurate fit between the forward modeled surface of Ogygis Rupes and MOLA surface (Fig. 4.6b) for the main fault is provided by a trishear angle of 76° at the center of the structure and 70° at the edges. The trishear zone distribution is asymmetrical at the center of the structure with the fault-propagation folding developed in the hanging wall (θ1 = θ, θ2 = 0), resulting in a quite wide anticline and a narrow front syncline with the forelimb presenting a gentle slope. However, the trishear zone at the fault tips is symmetrically distributed between the hanging wall and the footwall (θ1 = θ2), so that the anticline is slightly narrower, the front syncline is wider and the forelimb is steeper than at the center of the structure. The P/S ratio is 3, remaining constant throughout the entire main fault. The propagating fault tip is initially located at 4.7 km deep. The trishear area of Backthrust 1 is defined by a trishear angle of 70° asymmetrically oriented (θ2 = 1.5θ1) presenting a narrow anticline and a broad frontal syncline resulting in a forelimb with a slight slope. The P/S ratio obtained for Backthrust 1 is 2 and the fault tip is initially located at 0.75 km of depth. Backthrust 2 was modeled with a trishear angle smaller (36°) asymmetrically distributed (θ2 = 4θ1) presenting a folding mostly developed in the footwall, where the front syncline is very wide comparing with the narrow anticline and the forelimb slope is very gentle. The propagating fault tip for Backthrust 2 was initially located at 1.2 km of depth. The P/S ratios obtained reflect that the development of the folding ahead of the main fault is minor compared with the folding development associated with backthrusts, because the main fault presents a larger P/S ratio which entails a narrowing of the deformation zone (Hardy and Ford, 1997). These P/S ratios and fault tip depths obtained for the main fault and both backthrusts allow these fault ruptures to reach the surface as it is demonstrated by the presence of craters cut by the main fault and the Backthrust 1 (Herrero-Gil et al., 2019). The 3D forward model provides a good estimate for the distribution of the cumulative fault displacement on each fault. The largest fault slips were generally found at the central zone of each fault and decay to zero towards the lateral tips, although the shape of the slip distribution is different for each fault (Fig. 4.7). The maximum displacement of the main fault corresponds to a fault slip of 2850 m, with its maximum offset located in the zone of maximum elevation of the whole structure, decreasing towards the lateral fault tips. A secondary slip peak of 2200 m occurs at ∼50 km from the northern fault tip. The relief associated with Backthrust 1 was modeled by a symmetric plateau slip distribution with a maximum flat top of 1200 m. The relief produced by CAPÍTULO 4 90 Backthrust 2 was obtained by an asymmetric peak slip distribution with its maximum (1800 m) located at 25 km from the southern tip. Figure 4.6 (a) Colored topographic surface of Ogygis Rupes area where the lobate scarp relief has been removed together with the craters. (b) Recreation of Ogygis Rupes topographic surface made from the topographic model 6.a using the fault surfaces shown in Fig. 4.5. Figure 4.7 Lengthwise profiles of Ogygis Rupes showing the fault slip distribution of the main thrust fault, Backthrust 1 and Backthrust 2 along their strike. The model that best fits the topographic surface of Ogygis Rupes was determined by minimizing the elevation difference between the forward modeled topography and MOLA observed topography (Fig. 4.8). The interquartile range associated with the elevation difference data of the best fit model chosen with respect to the MOLA surface is set in ∼36 m, representing the data dispersion around a median value set in ∼7 m. CAPÍTULO 4 91 Figure 4.8 Absolute elevation difference between the best fit topographic surface obtained in the 3D forward modeling and Ogygis Rupes original surface (MOLA). Zero values represent a perfect match between our model and observed topography. 4.2.5. Discussion The resulting topographic surface obtained through the 3D modeling of Ogygis Rupes demonstrates that this is a good approach to recreate lobate scarp morphologies, providing a general view of the whole structure and the parameters that define it. However, some limitations might condition our results, and previous studies must be taken into account when analyzing the validity of the results obtained. Impact craters and associated ejecta were removed in the topographical surface used as a base for the forward modeling (Fig. 4.6a). This causes that when comparing the surface obtained from the forward modeling (Fig. 4.6b) with the original one (Fig. 4.4a), the greater elevation differences match with the location of the craters and not with the relief of the lobate scarp (Fig. 4.8). Thus, the main contribution to the misfit between the 3D forward model and MOLA topography observed in Fig. 4.8 corresponds to the craters and not to the modeling of the tectonic structure. In order to avoid this effect, the topographic data from craters were filtered when calculating the model-MOLA topography misfit. The median value of the elevation difference obtained when comparing the best fit modeled surface with the original MOLA surface is ∼7 m. The interquartile range reflects that half of the data is concentrated between -8 m and 28 m. Although the structure of Ogygis Rupes is well preserved, and the erosional rates on Mars are estimated to have been low (e.g., Golombek and Bridges, 2000; Golombek and Phillips, 2010), specifically in Aonia Terra since lobate scarp formation (Herrero-Gil et al., 2019), some erosive agents have slightly modified the relief. There is a small depression in the CAPÍTULO 4 92 southern half of Ogygis Rupes anticline caused by the presence of channels (Klimczak et al., 2018) which has not been taken into consideration during modeling, consequently the forward modeled surface presents a slightly higher elevation than the observed MOLA topography in this area. Another small misfit between modeled and original surfaces is observed at the scarp base, which can be partially covered by sediments from the scarp front, including rockfalls and alluvial deposits. Some assumptions needed to simplify the model might affect the results obtained. The main thrust fault underlying Ogygis Rupes was assumed to have dip-slip kinematics, excluding the possibility of any strike-slip component for which no evidence was found. The large trace of the main fault suggests that it could be formed by more than one segment (Klimczak et al., 2018), but this is not clearly appreciable on the surface since the scarp base seems to be continuous and there are not remarkable strike changes. If the main fault were composed of several segments, they would be hard-linked (Klimczak et al., 2018) as evidenced by the results obtained by modeling the main fault as a single fault surface. There are other limitations of the method itself that may influence the uplifted relief, including the end of the fold formation when the fault rupture reaches the surface or errors associated with the building of 3D surfaces where the faults were idealized as smooth surfaces without irregularities (Watkins et al., 2015). Previous works about lobate scarps on Mars and other planetary bodies using the elastic dislocation approach generally modeled the faults underlying lobate scarps using planar geometries (e.g., Schultz and Watters, 2001; Watters et al., 2002; Grott et al., 2007; Egea-González et al., 2012; Byrne et al., 2015; Watters et al., 2016; Egea-González et al., 2017; Herrero-Gil et al., 2019). Some non-planar geometries were proposed for lobate scarps using elastic dislocation modeling (Schultz and Watters, 2001; Watters et al., 2002) but they did not provide fits as good as planar geometries. Mueller et al. (2014), using structural techniques based on area balanced cross sections, presented a curved listric geometry for the fault underlying Amenthes attending to the surface characteristics of the uplifted topography, showing a fault-propagation fold similar to those developed in terrestrial continental crust. Studies of listric thrust faults on Earth allow to establish a relationship between fault-propagation fold and fault geometry (e.g. Erslev, 1986; Seeber and Sorlien, 2000; Amos et al., 2007), defining a broad gentle backlimb and an abrupt forelimb, which is exactly the surface geometry of lobate scarps. The gentle backlimb corresponds to the surface manifestation of a differential tilt between the hanging wall and footwall blocks as a result of the displacement over a positive listric fault (e.g., Erslev, 1986; Johnson and Johnson, 2002; Amos et al., 2007). The fault surfaces modeled in the present work for the main thrust fault and the two backthrusts show planar geometries in the upper kilometers while they present a decreasing dip angle at depth (Fig. 4.5), with a curved listric shape, according to the morphology of the backlimb and the trailing syncline, which is consistent with the knowledge of thrust fault propagation across the terrestrial brittle lithosphere (e.g., Amos et al., 2007; Cardozo and Brandenburg, 2014; CAPÍTULO 4 93 Jayangondaperumal et al., 2015), with numerical models (e.g., Ellis et al., 2004, Cardozo and Brandenburg, 2014; Pei et al., 2014) and with analog models (e.g., Ellis et al., 2004). An abrupt dip change when reaching the decollement depth entails a very steep backlimb leading to an angular and narrow trailing syncline that does not reflect what is observed in the lobate scarp topography (see Supplementary Fig. S1). The trishear parameters obtained from 3D modeling define the fault-propagation folding. In the main fault, trishear parameters vary along the structure affecting the distribution of the folding between hanging wall and footwall. In the center of the main fault the folding affects the hanging wall, while it is equally distributed between the hanging wall and the footwall towards the lateral fault tips. The variation of trishear angle along strike, together with the variation of slip distribution, can involve a slight volume change due to 3D formulation that in nature is solved by different processes as subordinated folding or faulting, compaction or dissolution (Cardozo, 2008). Pei et al. (2014) analyzed 13 natural examples previously modeled by trishear algorithms (e.g., Allmendinger, 1998; Hardy and Ford, 1997; Cardozo, 2005) to set a range of best-fit parameters when analyzed natural structures by trishear, with P/S ratios of 2–3, trishear angles between 30° and 100°, and fault dips from 25° to 45°. The resulting parameters obtained for the main fault and the backthrusts forming Ogygis Rupes (Table 4.1), are within these ranges. Ogygis Rupes was previously studied by Herrero-Gil et al. (2019), using BCS and FMD methods to get an approximation to the parameters of the main fault underlying the structure. The fault parameters obtained in the present study agree with the ones obtained by BCS. The depth of faulting resulting from BCS method (18 km) is very similar than the depth of faulting obtained in the present study (17.2–17.8 km), as well as the fault slip value (2900 m). These similar results were expected because the fault-parallel flow and the trishear algorithms applied in a 3D approach conserve volume within reasonable limits (∼2% volume loss; Cardozo, 2008). However, some variation of the derived parameters is appreciated if we compare our results with those obtained by the FMD method. The maximum fault slip value obtained in this study (2850 m) is in the range obtained by the FMD method (2500–3100 m). The dip angle obtained here (39°) is slightly larger than the one obtained with the FMD method (35°); although it is somewhat high for thrust faults (e.g., Jaeger and Cook, 1979; Watters and Nimmo, 2010), it is included in the range (20–40°) obtained from several modelings of martian lobate scarps (Fig. 4.9). The depth of faulting calculated in the present study (∼17–18 km) is shallower than the range obtained by FMD method (20–27 km) (Herrero-Gil et al., 2019). The range of depths obtained by FMD corresponds to the depths where the modeled fault slip decreases from the total slip at 20 km to zero slip at 27 km, which has been interpreted to correspond to the propagation of the fault into the BDT (Herrero-Gil et al., 2019). The algorithms used in the 3D models of our study were designed for deformations in the brittle lithospheric domain characterized by faulting and folding with volume conservation (Cristallini and CAPÍTULO 4 94 Allmendinger, 2001; Cardozo, 2008; Ziesch et al., 2014). Thus, the level at which the modeled fault roots (with a listric geometry that transmits the total fault slip from the decollement level due to tectonic regional shortening), can be interpreted to be the lower limit of the lithospheric brittle domain (the upper boundary of the BDT zone). Consequently, the comparison between both methods should contrast the upper limit of FMD (20 km) with the depth of faulting obtained in this study (∼17–18 km). The more realistic 3D model provides for Ogygis Rupes a result 2–3 km shallower for the upper boundary of the BDT. Figure 4.9 Dip angle (°) as function of depth of faulting (km) from the different studies performed in Late Noachian/Early Hesperian lobate scarps on Mars. The represented dip angle from the studies that modeled listric fault morphologies (Mueller et al., 2014; and the present study) is the fault dip near the surface. The data has been represented as points, lines or rectangles depending on the range of the value. Previous heat flow calculations (giving 30–51 mW m-2) for Ogygis Rupes used the entire range of 18–27 km for the BDT obtained from both BCS and FMD methods by CAPÍTULO 4 95 Herrero-Gil et al. (2019); therefore the results here obtained support the upper values of the calculated range, but would not substantially modify them. The fault slip distribution of the main thrust fault of Ogygis Rupes, being roughly greater at the center of the structure and decreasing towards the lateral fault tips, was previously observed by Klimczak et al. (2018) and Herrero-Gil et al. (2019), and it is consistent with fault growth models of fracture mechanics (Cowie and Scholz, 1992b; Bürgmann et al., 1994). The modeled slip distribution of the main fault presents a secondary plateau located NE of the main peak (Fig. 4.7) in agreement with the relief profile of Ogygis Rupes (Klimczak et al., 2018; Herrero-Gil et al., 2019). Our modeling of Ogygis Rupes backthrusts shows that these faults present low dip angles (22–23°) compared with the main fault, which can be explained by a passive transportation of the backthrusts over the main listric thrust fault causing a decrease of their dip angles with the evolution of the structure (Ellis et al., 2004). The backthrusts reach the main fault surface at 2.3–2.9 and 5.5–5.6 km deep, which are much shallower depths than the depth where the main fault roots. The listric geometries of both subsidiary faults, together with the fact that they do not root at the same depth than the main thrust fault, provide evidence of internal mechanical discontinuities inside the brittle domain of the lithosphere. 4.2.5.1. Implications for Mars tectonics. A comparison of dip and depth of faulting between our results and previous studies of lobate scarps formed in the Late Noachian/Early Hesperian (Fig. 4.9) shows that the results obtained here for Ogygis Rupes are well defined and close to the left edge of the data distribution of previous estimates as shown in the figure. The depth of faulting calculated for Ogygis Rupes (17–18 km) is a bit lower than the values usually estimated by previous works but agrees with the low depths of faulting obtained by Egea-González et al. (2017) for Chalcophoros and Thyles Rupis (although as noted by those authors, the topography near both structures is affected by other structures, which could have affected the modeling). The combination of trishear and fault-parallel flow algorithms in a 3D modeling allows to model, for the first time, the fault-propagation fold of a lobate scarp using a listric fault geometry, which is a significant advance with respect to previous methods. Although we have analyzed by 3D modeling only one lobate scarp (Ogygis Rupes), the results provide shallower depths of faulting than those obtained by Herrero-Gil et al. (2019) with FMD (Fig. 4.9). If this difference is confirmed in the future for other lobate scarps, it would suggest that BDT was slightly shallower, likely requiring a higher global thermal flow at the time of formation. CAPÍTULO 4 96 The listric geometry obtained for the main fault at depth, suggests that the fault slip on the fault ramp was entirely transmitted from the decollement in which the fault is rooted. This interpretation is in good agreement with the well-known mechanics of formation and propagation of large thrust fault systems (e.g. Amos et al., 2007; Cardozo and Brandenburg, 2014; Ellis et al., 2004; Pei et al., 2014). Large thrust faults on Earth usually nucleate from a subhorizontal decollement and propagate with ramps towards the surface. The good fit of the fault-propagation fold of Ogygis Rupes 3D model confirms that the fault propagates upwards and consequently the amount of accumulated fault slip decreases upwards. Therefore shortening calculations should consider that the fault slip on the ramps was entirely transmitted from the decollement level, so the shortened distance equals the fault slip at the ramp. This interpretation, supported by the 3D models, provides larger shortening estimates than when shortening is obtained from the horizontal component of the fault slip at the ramp (heave). For a given fault slip (S) on the ramp, the heave (Sh) is S · cos β, being β the dip angle of the ramp. Therefore, the total slip value considered to be the shortened distance transmitted from the decollement, provides an estimate between ∼6 and ∼30% (for 20°–40° dips) larger than the heave value (Sh) calculated on the fault ramp. Global shortening estimates for lobate scarps will be hence increased up to ∼30% under the assumption that the fault slips of these large faults on Mars are completely transmitted from the BDT. A larger shortening associated with lobate scarps than previously thought (if confirmed for other cases) could have important implications for the thermal history of Mars. Indeed, Nahm and Schultz (2011) estimated that the shortening related to lobate scarps and wrinkle ridges implied a lower amount of time-cumulated global contraction than expected from thermal history models (Andrews-Hanna al., 2008). This would be consistent with limited secular cooling of the martian interior, at least during some phases of their thermal history (Ruiz et al., 2011), because reduced mantle cooling limits the thermal contraction that can drive surface contraction. Subsequently, Klimczak (2015) proposed that elastic deformation of the lithosphere could accommodate a certain level of contraction previously to the beginning of thrust faulting, adding a substantial amount of potential contraction, up to ∼40% more, with respect to Nahm and Schultz (2011) estimate. By increasing the shortening associated with thrust faults due to a listric morphology, the total amount of contraction recorded by martian thrust faults could be up to 70% higher than previously thought. This continues to be lower than theoretical expectations (Andrews-Hanna al., 2008; Nahm and Schultz, 2011), but would confirm that substantial contraction occurred in the Late Noachian/Early Hesperian time. CAPÍTULO 4 97 4.2.6. Conclusions The 3D forward modeling of Ogygis Rupes through the combination of trishear fault-propagation folding and fault-parallel flow algorithms shows that this method is a consistent and accurate approach to recreate lobate scarp structures, expanding the information about their geometry and kinematics. The three modeled faults, including the main thrust fault and two backthrusts, show listric geometries at depth, according to analog and numerical models, and studies of large thrust faults on Earth. The main thrust fault roots into a horizontal decollement at ∼17–18 km deep, which is assumed to be the BDT at the time of formation (Late Noachian/Early Hesperian). The listric morphology where the main fault roots into the BDT implies that the total fault slip was transmitted from the decollement to the fault ramp, leading to a larger regional shortening estimate related to the lobate scarp formation than if the shortening is interpreted to be only the heave of a planar fault. The two backthrusts of Ogygis Rupes show shallower depths of faulting estimated at ∼2.5 km and ∼5.5 km, probably indicating the presence of mechanical discontinuities in the martian brittle lithosphere. CAPÍTULO 4 98 4.3. Conclusiones Capítulo 4 La modelización 3D de Ogygis Rupes combinando los métodos de trishear y fault- parallel flow ha demostrado tener un gran potencial para modelizar escarpes lobulados y mejorar así el conocimiento que tenemos sobre la geometría y cinemática de estas estructuras. La falla principal de Ogygis Rupes y las dos fallas subsidiarias retrocabalgantes han sido incluidas en el modelo 3D. Los resultados muestran que estas fallas tienen un buzamiento constante durante los primeros kilómetros que va disminuyendo en profundidad hasta enraizarse en un nivel subhorizontal, dando lugar a una morfología lístrica en profundidad. La falla principal presenta un buzamiento de 39o y su nivel de despegue está situado a ∼17–18 km de profundidad, lo que concuerda en general con cálculos previos de profundidad en esta y otras fallas que subyacen escarpes lobulados. Esta profundidad es asumida como el inicio de la transición frágil-dúctil de la época en la que se formó la estructura (Noeico Tardío/Hespérico Temprano). La morfología lístrica con la que la falla principal enraíza en el inicio de la transición frágil-dúctil implica que el desplazamiento máximo de la falla, calculado en 2850 metros, es transmitido íntegramente desde el nivel de despegue a la rampa de la falla. De este modo el acortamiento regional acomodado por esta falla sería igual al desplazamiento total sobre el plano de falla. Esto supone un cambio respecto a cálculos previos en los que las fallas eran modelizadas como estructuras planares y el acortamiento regional asociado era calculado con la componente horizontal del desplazamiento sobre esta falla planar, lo que incrementa la estimación del acortamiento asociado a la falla entre un ∼6% y un ∼30% más dependiendo del ángulo de la misma. Esto supondría un aumento en las estimaciones de acortamiento global del planeta calculadas en escarpes lobulados de hasta un ∼30% si se confirmase que el desplazamiento horizontal de la falla es transmitido íntegramente desde el nivel de despegue. Las dos fallas subsidiarias retrocabalgantes de Ogygis Rupes presentan valores de desplazamiento, buzamientos y profundidades de enraizamiento mucho menores que los de la falla principal. Los ángulos de buzamiento menores (22o –23o) pueden explicarse por un transporte pasivo de estas fallas por la falla principal, cuya forma en profundidad genera una inclinación en el bloque de techo al desplazarse sobre el bloque de muro, lo que reflejaría que su formación ha sido sintectónica a la de la falla principal. Las profundidades de enraizamiento han sido calculadas en ∼2.5 km y ∼5.5 km, lo que puede indicar la probable existencia de discontinuidades mecánicas dentro del dominio frágil de la corteza de Marte. 5 Modelo 3D del sistema de fallas inversas de Amenthes, Marte Lithospheric contraction on Mars: A 3D model of the Amenthes thrust fault system CAPÍTULO 5 101 5.1. Introducción Amenthes Rupes es el escarpe lobulado más estudiado de la superficie de Marte debido a sus grandes dimensiones, a su proximidad a la dicotomía y a su orientación paralela a este límite (e.g. Schultz & Watters, 2001; Watters, 2003b). Esto hace que su estudio sea indispensable a la hora de analizar las propiedades mecánicas y térmicas, así como la evolución de la litosfera de Marte (e.g. Schultz & Watters, 2001; Ruiz et al., 2011; Egea-González et al., 2017) en el Noeico Tardío/Hespérico Temprano, edad en la que se formó (e.g. Watters & Robinson, 1999; Schultz & Watters, 2001; Egea-González et al., 2017). Esta estructura que se localiza en las tierras altas del sur (Schultz & Watters, 2001; Schultz, 2003a; Caprarelli et al., 2007; Erkeling et al., 2011), concretamente en la Región de Amenthes, ha sido estudiada y modelizada por lo general como una estructura aislada (e.g. Watters et al., 2000; Schultz & Watters, 2001; Schultz, 2003a; Watters, 2003b; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017). Sin embargo, Amenthes Rupes es la expresión topográfica de la falla principal de un sistema de fallas inversas más extenso (Schultz, 2003a). A su vez, este conjunto de fallas forma parte de una serie de escarpes lobulados paralelos a la dicotomía y situados al suroeste de ella, a distancias de entre 100 y 500 km, en las tierras altas de Arabia Terra, Amenthes Region y Terra Cimmeria (Watters, 2003b). En este capítulo se ha modelizado en conjunto el sistema de fallas inversas de Amenthes utilizando los algoritmos de fault-parallel flow (Egan et al., 1997; Ziesch et al., 2014) y trishear (Erslev, 1991; Allmendinger, 1998) implementados en un marco tridimensional (Cardozo, 2008; Ziesch et al., 2014), asumiendo que las características topográficas de estos relieves concuerdan con la morfología de pliegues asociados a la existencia de una falla que se propaga hacia la superficie (fault-propagation fold). El objetivo de este trabajo es constreñir los parámetros que controlan la geometría de las fallas en profundidad y los parámetros estructurales que controlan la formación de los pliegues de propagación de falla, así como conocer cómo es la interacción entre estas fallas y como se acomoda el acortamiento horizontal de esta región a lo largo del sistema de fallas. Las profundidades de enraizamiento obtenidas para las fallas mayores proporcionan estimaciones sobre la profundidad de la transición frágil-dúctil (Schultz y Watters, 2001; Watters et al., 2002; Ruiz et al., 2008) en esta zona hace 3600–3700 Ma (Egea-González et al., 2017), mientras que la profundidad de fallas secundarias y subsidiarias aporta información acerca de la posible presencia de discontinuidades mecánicas en la corteza (Herrero-Gil et al., 2020a). Además, el análisis conjunto de la distribución del desplazamiento a lo largo del sistema de fallas y la geometría de cada falla en profundidad permite cuantificar el acortamiento regional registrado por estas CAPÍTULO 5 102 estructuras y compararlo con estimaciones previas, que a su vez han sido usadas en cálculos de la contracción global del planeta. De este modo, la interpretación de los resultados obtenidos para cada falla, junto con el análisis de cómo es la interacción entre ellas, proporciona una detallada visión 3D del marco tectónico del área y proporciona un esquema general de cómo ha sido la evolución de la de la contracción que generó estas estructuras paralelas a la dicotomía CAPÍTULO 5 103 Lithospheric contraction on Mars: A 3D model of the Amenthes thrust fault system Andrea Herrero-Gil *a, Javier Ruiz a, Ignacio Romeo a a Departamento de Geodinámica, Estratigrafía y Paleontología, Facultad de Ciencias Geológicas. Universidad Complutense de Madrid, 28040 Madrid, Spain. Journal of Geophysical Research: Planets 125 (3), e2019JE006 Abstract Amenthes Rupes is the topographic expression of a main fault belonging to a thrust fault system located parallel to the martian dichotomy boundary. A 3D forward model has been applied to the Amenthes thrust fault system, constraining fault geometries at depth, variations of slip along strike, and structural parameters controlling the formation of fault- propagation folds. Our results provide a complex 3D view of the tectonic framework of the area, with implications for tectonic evolution, regional shortening distribution, and the main mechanical discontinuities in the lithosphere. The modeled fault surfaces show planar morphologies combined with listric geometries at depth. The obtained depths of faulting for the major faults of this fault system suggest a depth of the brittle-ductile transition (at the time of formation) of 20–24 km, somewhat shallower than previous estimates for this area. A possible mechanical discontinuity located at 9.5–13 km deep can be deduced from the faulting depths of the secondary faults. The listric geometries at depth imply that slip is transmitted from the decollement, which, together with the inclusion in the model of secondary and subsidiary faults, allow us to estimate the horizontal shortening recorded in this area ranging from 2–3 km up to ∼5.5 km in the southeastern part of the fault system. This range increases the previous shortening estimates in this area between ∼60% and ∼200%. Consequently, global shortening estimates based on global fault maps are biased by the detail of mapping, and shortening would substantially increase if secondary faults were included. 5.2. CAPÍTULO 5 104 5. 2. 1. Introduction Lobate scarps are positive structural reliefs observed on terrestrial planetary surfaces, assumed to be the expression of large thrust faults (e.g., Anguita et al., 2006; Schultz & Watters, 2001; Strom et al., 1975; Watters & Nimmo, 2010; Watters & Robinson, 1999). These structures present an asymmetric relief that shows the characteristic morphology of a fault-related fold caused by the displacement of a low angle thrust fault breaking the topographic surface. The lobate scarp uplift is formed by an anticline with a gentle trailing flank (backlimb) and a frontal abrupt flank forming the scarp face (forelimb). A trailing syncline and a frontal syncline are usually present on each side of the anticline (e.g., Grott et al., 2007; Herrero-Gil et al., 2019, 2020; Schultz, 2000; Schultz & Watters, 2001). The large thrust faults underlying lobate scarps have been studied and modeled by several authors on different terrestrial bodies like Mars (e.g., Egea-González et al., 2017; Grott et al., 2007; Herrero-Gil et al., 2019, 2020; Klimczak et al., 2018; Mueller et al., 2014; Ruiz et al., 2008; Ruj et al., 2018; Schultz & Watters, 2001), Mercury (e.g., Crane & Klimczak, 2019; Egea-González et al., 2012; Galluzzi et al., 2015, 2019; Giacomini et al., 2019; Semenzato et al., 2018; Watters et al., 2002), the Moon (e.g., Byrne et al., 2015; Williams et al., 2013), Ceres (Ruiz et al., 2019), and asteroid 433 Eros (Watters et al., 2011). These works usually include the study of the timing of faulting and the analysis of the structural parameters that define the fault morphology and kinematics (depth of faulting, dip angle and fault slip), with the final aim of advancing on the knowledge of the tectonic and thermal evolution of these terrestrial bodies. The modeling of the structural parameters is performed assuming that fault geometry and fault slip control lobate scarp topography (Schultz & Watters, 2001; Watters et al., 2002). The study of martian lobate scarps provides insights on the rheology of the martian lithosphere at the time of formation (Ruiz et al., 2008). The depth of faulting of the large underlying faults has been related to a main rheological discontinuity, that on Mars is considered to represent the brittle-ductile transition (BDT) at the time of lobate scarp formation (e.g., Grott et al., 2007; Ruiz et al., 2008, 2009; Schultz & Watters, 2001). The most studied lobate scarp on Mars is Amenthes Rupes (e.g., Egea-González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008; Schultz, 2003; Schultz & Watters, 2001; Watters et al., 2000), due to its large dimensions and its location near the dichotomy boundary (Watters, 2003b) (Fig. 5.1), which makes its study essential when analyzing the mechanical and thermal properties and the evolution of the lithosphere of Mars (e.g., Egea-González et al., 2017; Ruiz et al., 2011; Schultz & Watters, 2001). The Amenthes Rupes lobate scarp, as well as most of the lobate scarps modeled on Mars, has been modeled through 2D cross sections analysis (e.g., Egea-González et al., 2017; Grott et al., 2007; Herrero-Gil et al., 2019; Mueller et al., 2014; Ruiz et al., 2008; Schultz & Watters, 2001). This 2D modeling applied to lobate scarps restricts the results obtained to the chosen cross sections of structures that are hundreds of kilometers long and present significant variations along their length (e.g., Herrero-Gil et al., 2020; Klimczak et al., CAPÍTULO 5 105 2018). Besides, Amenthes Rupes is not formed by an isolated fault. This is the largest structure belonging to a structural set of surface breaking thrust faults (Schultz, 2003; Watters & Robinson, 1999) located in the Amenthes Region (Fig. 5.1). The complexity of the interaction between these faults and the main Amenthes thrust fault controls the topographic expression of lobate scarps in this area. The 3D modeling of lobate scarps allows expansion of our knowledge of fault geometries at depth, fault kinematics and the mechanical structure of the lithosphere at the time of formation (Herrero-Gil et al., 2020). Here we show the results of a detailed 3D modeling of the Amenthes thrust fault system providing information about the fault geometries and fault related folding, together with the variations of the structural parameters along their strike and with depth, and the interaction between faults, resulting in a complex tectonic framework. This 3D procedure provides a step forward in the understanding of thrust fault systems on Mars compared with previous 2D approaches. The depth of faulting of the main modeled faults provides estimates of the BDT depth at the time of formation. In addition, the study of the secondary and subsidiary faults provides information about the presence of mechanical discontinuities in the crust. This analysis also provides insights about the nature of the deformation in this region close to the martian dichotomy boundary, as well as about the general processes that formed martian lobate scarps and the amount of horizontal contraction implied (the terms “contraction” and “contractional structures” are used through the text in the sense of structures generated by linear horizontal contractional deformation, i.e., shortening), which in turn has implications for the tectonic and thermal evolution of Mars. 5.2.1.1. Amenthes Rupes Amenthes Rupes is located in the heavily cratered highlands of Mars (e.g., Caprarelli et al., 2007; Erkeling et al., 2011; Mueller et al., 2014; Schultz, 2003; Schultz & Watters, 2001; Watters, 2003b), specifically in the northeast of the Amenthes Region. This topographic structure is the morphological expression of the displacement on a large thrust fault with surface rupture (e.g., Mueller et al., 2014; Schultz & Watters, 2001). The main thrust fault that forms Amenthes Rupes is part of an array of five thrust faults underlying a set of lobate scarps (Schultz, 2003; Watters & Robinson, 1999), striking 120– 140°E (Fig. 5.1), parallel to the NE margin of Amenthes Planum (Caprarelli et al., 2007), which is located southwest. The Amenthes Rupes lobate scarp was formed in the Late Noachian/Early Hesperian (e.g., Schultz & Watters, 2001; Watters & Robinson, 1999), around 3.7 Ga ago (Egea-González et al., 2017). The Late Noachian highland crust, where lobate scarps formed, is expected to be formed by nonlayered rocks with more isotropic character than the Amazonian-Hesperian units that postdate them (e.g., Mueller et al., 2014; Schultz, CAPÍTULO 5 106 2000). Martian erosion rates have remained very low from Hesperian to the present (e.g., Golombek & Bridges, 2000; Golombek & Phillips, 2010), and this area does not show significant signs of erosion affecting the lobate scarps. However, the structural relief related to this fault system was modified by several impact craters, some of them clearly postdating its formation. A geological unit of Amazonian-Hesperian age postdates the Late Noachian cratered terrains, forming smooth plains in the areas of low topographic relief, as well as infilling most of the craters (Erkeling et al., 2011). Figure 5.1 Structural map of the study area of Amenthes Region. The base map is made by combining a MOLA model (DEM) over a THEMIS-IR Day image. The thrust faults included in the modeling are colored in red. The inset globe shows the location of the study area. Amenthes Rupes has aroused great interest due to its proximity to the dichotomy boundary. This is the largest of a series of lobate scarps located between 100 and 500 km southwest of the dichotomy boundary, in the highlands of Arabia Terra, Amenthes Region and Terra Cimmeria. These lobate scarps are roughly parallel to the dichotomy boundary and record a contractional strain perpendicular to this boundary (e.g., McGill & Dimitriou, 1990; Nimmo, 2005; Watters, 2003a, 2003b; Watters et al., 2007; Watters & Robinson, 1999). The deformation along the dichotomy boundary in these areas occurred during the Late Noachian and Early Hesperian (McGill & Dimitriou, 1990; Nimmo, 2005; Ruiz et al., 2008; Watters & Robinson, 1999), postdating the formation of the dichotomy boundary but being important in the shaping of its current relief. These observations suggest that the formation of the lobate scarps in these areas is related to the dichotomy boundary (Watters & Robinson, 1999), which has been associated with lithospheric flexure (Watters, 2003a; Watters & McGovern, 2006). The formation of Amenthes Rupes has CAPÍTULO 5 107 been also related to the Isidis basin due to its radial orientation with respect to the basin center (Wichman & Schultz, 1989). Egea-González et al. (2017) included Amenthes Rupes in their circum-Hellas study since it presents a concentric orientation to Hellas basin, being orthogonal to a compressive stress associated with this large impact basin. Similar contractional structures parallel to Amenthes Rupes can be found closer to Hellas basin (Cerberus Dorsa). Previous studies focused on modeling Amenthes Rupes had as a main objective the calculation of the depth of faulting of the underlying fault, which on Mars is assumed to coincide with the BDT at the time of faulting. This BDT depth has been used to model the thermal structure of the early martian lithosphere and to calculate the heat flow values during the Late Noachian/Early Hesperian (Egea-González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008, 2011; Schultz & Watters, 2001). The forward mechanical dislocation (FMD) method (Toda et al., 1998, 2005) that models the surface as an elastic halfspace and the balanced cross sections (BCS) method (Chamberlin, 1910, 1919; Dahlstrom, 1969) based on mass conservation are the two approaches previously applied to model 2D topographic profiles across Amenthes Rupes. Although non-planar fault morphologies (listric fault geometries) have been proposed to explain lobate scarp formation (Mueller et al., 2014; Watters & Nimmo, 2010), previous works that have modeled Amenthes Rupes with FMD method present the fault plane as a planar surface with a constant dip, because the results obtained using non-planar geometries did not provide satisfactory results (Schultz & Watters, 2001). Schultz and Watters (2001) modeled two cross sections of Amenthes Rupes with FMD method to obtain a depth of faulting of 25–30 km. The same method was later applied by Ruiz et al. (2008) to a perpendicular cross section obtaining a depth of faulting of 27–35 km, and by Egea-González et al. (2017) to obtain a depth of faulting of 27–33 km. The BCS method was used by Mueller et al. (2014) proposing a listric fault, due to the topographic characteristics of the lobate scarp, obtaining a depth of faulting of 33–48 km. 5.2.2. Data and Method The objective of the 3D modeling of lobate scarps is to obtain fault geometries, slip distribution, and trishear parameters that best replicate the topographic surface uplifted by each fault with the smallest misfit with the observed topography. A detail mapping of the studied structures is necessary before the modeling process to identify the fault structures of the area. The topographic base used for the mapping and modeling of Amenthes thrust fault system is the Mars Orbiter Laser Altimeter data (MOLA, Mars Global Surveyor) with a ∼463 m/pixel resolution (Smith et al., 2001; Zuber et al., 1992). The main base image used during mapping is the Thermal Emission Imaging System (THEMIS, Mars Odyssey mission) daytime infrared (IR) model with a 100 m/pixel resolution (Christensen et al., 2004). The Context Camera images (CTX, Mars Reconnaissance Orbiter) (Malin et al., 2007) have been consulted occasionally. The CAPÍTULO 5 108 analysis of the MOLA topography, together with THEMIS and CTX images, allowed us to make a detailed structural map of the area (Fig. 5.1). The identification of the tectonic structures in the area was performed by analyzing several profiles, attending to slope changes to identify the reliefs that may be related to tectonic deformation. THEMIS images (or CTX images when more resolution was needed) were used to verify their tectonic origin and to trace them in the map. The five large thrust faults underlying the reliefs that meet the description of lobate scarp, together with their associated fold structures, were mapped following this procedure. Other minor contractional structures have been identified in the area. The minor thrust faults have been distinguish from wrinkle ridges because it was possible to identify the vergence of the structure due to the uplift of the hanging wall. Nevertheless, wrinkle ridges present a lower relief and a complex structure that requires an exhaustive analysis to identify the vergence of the underlying thrust faults, which is not the objective of this work, so we have kept this morphological term in the structural map. The folding associated with thrust fault generation has been considered, in this study, to be caused by fault-propagation folding since the morphologies of other fault- related folds, like fault-bend folds and detachment folds, do not match the observations (Jamison, 1987). Displacement-gradient folds (Wickham, 1995) have been proposed to play a role in the folding process of lobate scarps (e.g., Klimczak et al., 2018), but a simple fault-propagation folding mechanism has been chosen for modeling simplification purposes. The role of fault-propagation folding is strongly supported by the evidence of surface rupture. The fault-propagation fold of each lobate scarp forming the Amenthes Rupes fault system has been modeled using the fault-parallel flow (Egan et al., 1997; Kane et al., 1997; Wheeler, 1987) and trishear (Allmendinger, 1998; Erslev, 1991) algorithms applied in a 3D modeling framework (Cardozo, 2008; Cristallini & Allmendinger, 2001) using MOVETM software (Midland Valley). The fault-parallel flow algorithm determines the deformation of the hanging wall caused by the displacement over a complex fault geometry, while the trishear method defines the deformation distributed ahead of a propagating tip point. The combination of both algorithms is a pure geometric approach, which was designed for modeling strain in the brittle lithosphere, characterized by faulting and folding assuming volume conservation (e.g., Cristallini & Allmendinger, 2001; Ziesch et al., 2014). This combination has been proven useful in the modeling of thrust belts on Earth (e.g., Cardozo, 2008; Cardozo & Brandenburg, 2014; Cristallini & Allmendinger, 2001; Li et al., 2020; Maesano et al., 2013; Watkins et al., 2015) to constrain the tectonic scenarios at depth due to the possibility of varying the parameters that define faulting and folding along the structure. It has also been applied to model Ogygis Rupes lobate scarp together with two subsidiary backthrusts (Herrero-Gil et al., 2020) on Mars. The topographic surface of Amenthes Region has been modeled attending to the premise that the erosion rates on Mars have remained low since lobate scarps formation (e.g., Golombek & Phillips, 2010). We have assumed that no other mechanisms has substantially CAPÍTULO 5 109 altered the slopes of the structural reliefs identified as the result of the displacement of the underlying thrust fault system, although some gravitational deposits at the scarps bases can be observed at some scarce locations. Fault-parallel flow algorithms constrain the movement of the hanging wall over the footwall through the assumption of volume conservation (Ziesch et al., 2014). The deformation is defined by a fault-parallel shear, where the material of the hanging wall moves in the direction of the fault slip along flow paths parallel to the fault surface. The geometry of the fault plane controls the topography of the lobate scarp (Schultz & Watters, 2001; Watters et al., 2002); specifically, the dip and depth of the fault plane mostly define the width of the associated lobate scarp (distance between the trailing syncline and the scarp base), and the fault slip controls the relief of the structure. The depth of faulting influences the amount of uplifted material, defining the location of the syncline and consequently the width of the anticline, while the dip angle of the fault is directly related to the slope of the backlimb. Accordingly, variations in fault dip at depth modify the backlimb slope. A gradual decrease of the dip angle at depth, flattening downwards into the decollement (resulting in listric fault geometries), creates a gentle and wider backlimb, due to a tilting of the hanging wall with respect to the footwall (e.g., Amos et al., 2007; Erslev, 1986; Johnson & Johnson, 2002; Ziesch et al., 2014). If the decrease of the dip angle at depth is abrupt, it generates a steeper and narrower backlimb (e.g., Amos et al., 2007; Ziesch et al., 2014). The absence of rooting level, using a fault that ends abruptly, would result in a lack of backlimb development and non-generation of a trailing syncline. The effect in the topography caused by the variation of these fault parameters is explained in Text S1 in the supporting information. Trishear algorithms (Allmendinger, 1998; Erslev, 1991) successfully replicate the folding ahead of a propagating thrust fault (Fig. 5.2). In cross section, the folding occurs in a triangular shear zone (trishear zone) defined by a variable angle (θ) (Allmendinger, 1998), where a distributed shear deforms the material ahead of a propagating fault tip. The trishear parameters define the shape of the main anticline and the frontal syncline, through the distribution of the trishear zone between the hanging wall and the footwall (θ1, θ2) with respect to the fault (Zehnder & Allmendinger, 2000), the depth of the initial fault tip, and the fault propagation to fault slip ratio (P/S) (Hardy & Ford, 1997). A small trishear area implies that the deformation is more concentrated, creating a narrower syncline (with a steeper forelimb) than if the deformation is distributed in a larger trishear area (Allmendinger, 1998). The P/S ratio (Hardy and Ford, 1997) is directly related to the degree of fold development. Low P/S values (below 2) imply that the material spends more time in the trishear zone, undergoing more deformation of the forelimb before faulting. The effect that the variation of trishear parameters has on the uplifted topography is explained in Text S1. CAPÍTULO 5 110 Figure 5.2 Schematic representation of trishear method (based on Hardy & Ford, 1997; Zehnder & Allmendinger, 2000). The area colored in grey is the trishear area and it is defined by the trishear angle (θ) and its distribution between the hanging wall and the footwall (θ1, θ2). The propagating fault tip is marked in blue. The velocity of the hanging wall relative to the footwall is marked by a grey slip vector, decreasing from top to bottom inside the trishear area. The modeling workflow comprises from the construction of the fault surfaces to the reproduction of the observed topographic surface through the forward slip of the thrust faults with propagating fault tips and associated trishear folding (Herrero-Gil et al., 2020). First, a preliminary 2D restoration of the topographic surface and forward modeling were performed for several cross sections made along each fault, to get a first-order approximation of the fault geometries. The 3D fault surfaces used during the modeling were built by interpolation between these cross sections. Second, the created 3D fault surfaces were validated thought a 3D restoration of the MOLA-observed topographic surface. These 3D fault geometries serve as a starting point for the restoration, and their shapes were modeled until generating the best surface restoration, through the iterative variation of dip and depth along the structure paying attention to the resulting topographic surface modifications (see Text S1). This restoration process shows the subsurface interaction between nearby structures and provides an approximation for fault slip values and trishear parameters. Finally, the 3D fault geometries resulting from the 3D restoration have been used in the 3D forward modeling. Fault slip and trishear parameters have been adjusted in this last step of the process, comparing the resulting modeled surface to the original MOLA topography until the best possible fit is achieved. The initial topographic surface used during the 3D forward modeling was obtained from the original MOLA topography, from which crater depressions, rims, ejecta and structural reliefs related to lobate scarps were removed (Herrero-Gil et al., 2020), taking the grid points that are outside these structures and interpolating the surface using the kriging geostatistical procedure. 5.2.3. 3D Structural Analysis Results The area of study includes Amenthes Rupes (main fault) and other four major thrust faults forming the largest structural reliefs (Fig. 5.1, Table 5.1). The general vergence of these lobate scarps is toward the SW, except for Fault 3, which is a backthrust verging NE. The main fault and Faults 2, 3 and 4 are interrelated, their traces intersect or CAPÍTULO 5 111 their associated topographies interfere with each other. Otherwise, Fault 5 is located northern to the main fault, striking parallel to it. Table 5.1 Compilation of structural parameters calculated for the studied Amenthes Region faults. Name Length (km) Max. relief (m) Strike (°) Fault parameters Trishear parameters Dip angle (°) Depth of faulting (km) Max. Slip (m) Trishear angle (°) Trishear distribution P/S ratio Fault tip depth (m) θ1 θ2 Main fault (Amenthes Rupes) 470 1050 N131E 27–28 NE 20–24 2100 86 72 14 3 -2050 Fault 2 (splay) 180 570 N120E 29.5 NE 23.5–24 1300 85 71.5 13.5 2 -1180 Fault 3 (backthrust) 220 900 N138E 31–33 SW 21.5– 22.5 1600 80 40 40 3 -2100 Fault 4 126 800 N125E 23 NE 13 1720 44 28.5 15.5 2 -2700 Fault 5 Segment NW 180 600 N122E 28 NE 10.5– 11.5 1100 85 33 52 2 -940 Fault 5 Segment SE 160 480 N131E 27–27.5 NE 9.5–11 1000 60 42 18 2 -1800 5.2.3.1. 3D Restoration The restoration of the lobate scarp reliefs present on the observed MOLA topographic surface (Fig. 5.3a) has been made by reversing the thrust slip of the underlying 3D fault surfaces in order to obtain a surface without any relief associated with thrust faults, which is representative of the topographic surface prior to contractional deformation (Fig. 5.3b). The modeled fault surfaces reflect a planar geometry in the upper kilometers with a gradual decrease of the dip at depth, until it flattens when reaching the decollement level, resulting in listric morphologies constrained by the shape of the structural relief. The presence of a decollement level is supported by the presence of a trailing syncline associated with all the thrust faults modeled (Fig. 5.1). Subsurface relationships between faults appear when trying to restore MOLA topography, which allows us to group the five studied faults. Each thrust fault has been assumed to present dip-slip reverse faulting with the slip vector of each fault perpendicular to the fault strike, since no evidence of a strike- slip component of deformation was observed. CAPÍTULO 5 112 Figure 5.3 (a) Original MOLA surface over a THEMIS-IR Day image of the studied area. (b) Restored topographic surface where the uplifts present in the original MOLA model, which are related to the studied thrust faults, have been removed. Main Fault and Fault 2 The Amenthes Rupes lobate scarp is generated by a 470 km long thrust fault. The largest relief (∼1,050 m) of Amenthes Rupes is located near the center of the structure and corresponds with the crest of the fault propagation anticline. The surface rupture of this thrust fault is denoted by a cross-cut crater located approximately in the middle of the structure (Mueller et al., 2014). The modeled dip angle of the main thrust fault is 27– 28°NE for the first ∼30–32 km (measured on the fault plane from the surface) until a depth of ∼14–15 km, where the dip angle begins a gradual decrease with a listric geometry. The main fault roots into a decollement at 20 km of depth in the northwestern part of the structure, deepening up to 24 km in the southeastern part (Fig. 5.4b, c). Fault 2 is a 180 km long thrust fault that entirely overlaps the southern part of the main fault, being mostly parallel to it. It is located on the hanging wall of the main thrust fault, with a spacing value of ∼10 km, although it increases up to 20 km near the southeast fault tip. The maximum relief associated with this fault is ∼570 m. Fault 2 is modeled as a splay fault that roots with a listric geometry at the same decollement than the main fault (Fig. 5.4b). However, it presents a slightly higher dip angle than the main fault (29.5°NE) for the upper ∼31 km measured on the fault plane from the surface (until ∼15 km deep). CAPÍTULO 5 113 Figure 5.4 (a) Perspective of the 3D model of the studied area where MOLA topographic surface has been hidden southeastern from the profile A-A’ to show the underlying fault planes of the main fault, Fault 2, Fault 3 and Fault 4. (b) Cross section A-A’ perpendicular to the mean strike of the faults. (c) Perspective of the 3D model where the MOLA surface has been hidden southeastern from the profile B-B’. All the fault planes of the 3D modeling are visible. (d) Rose diagram representing the dip azimuth of the 3D fault planes included in the modeling. The mean dip azimuth (N36.6°E) is shown with a black arrow. (e) Cross section B- B’, perpendicular to the mean strike of the studied faults. Fault 3 and Fault 4 Fault 3 is a 220 km long thrust fault verging NE, opposite to the main fault vergence (i.e., Fault 3 is a backthrust), which presents an arcuate form in map view. Fault 3 intersects at the present topographic level with the main fault at 130 km from its southern tip point, forming a 40 km long pop-up elevation located north of the intersection point. The main fault and Fault 3 form a pop-down structure southwards from this intersection point (Fig. 5.4a, b). The lobate scarp associated with Fault 3 presents a maximum relief of 900 m in its central part. The dip angle of this backthrust is estimated to be 31–33°SW for CAPÍTULO 5 114 the first ∼29 km (measured along the fault from the surface) until ∼15 km of depth, where the dip angle decreases gradually in a listric geometry. The depth of faulting has been set at 21.5–22.5 km. Two minor faults, not included in the modeling due to their small dimensions (Fig. 5.1), seem to distribute the displacement of this fault to the southeast. Fault 4 is a SW verging thrust fault separated 70 km southeast from Fault 3, striking parallel to it. It is a 126 km long thrust fault that overlaps along all its length with Fault 3, generating a pop-up structure (Fig. 5.4a, b). The backlimb of its associated lobate scarp presents two big craters that mask the morphology of the uplifted relief, which has been measured to be 800 m. The fault surface underlying this structure presents an estimated dip angle of 23°NE for the first ∼22 km (measured along fault from the surface) that decreases gradually at ∼9 km of depth until rooting at 13 km deep into the subhorizontal decollement (Fig. 5.4b). Fault 5 Faults 5 is located ∼85 km northeast from the main fault and parallel to it, and it is formed by two linked fault segments. The NW Segment presents a linear trace 180 km long. The topography of the anticline forming the lobate scarp was modified by impact craters, but its maximum relief has been measured to be 600 m. The SE Segment is 160 km long, and it is separated ∼15 km south from NW Segment, overlapping 25 km. Its trace reflects two lobes in map view, with a maximum relief peak in each lobe of approximately 500 m. Both fault segments present similar modeled dip angles (27–28°NE) near the surface (the first ∼15–16 km measured on the fault plane), decreasing from ∼7–8 km of depth. The depth of faulting of Segment NW is calculated to be 10.5–11.5 km (Fig. 5.4e), while the SE Segment roots at 9.5–11 km. 5.2.3.2. 3D Forward Modeling The 3D forward modeling reproduces the original topographic surface (Fig. 5.3a) starting with the fault surfaces obtained from the 3D restoration to deform an initial surface in which the uplifted topography related to the displacement of the thrust faults have been removed (Fig. 5.5a). The best fit model (Fig. 5.5b) is obtained modeling the fault-propagation fold for each thrust fault along its strike, by adjusting the trishear parameters that define the folding ahead of the propagating fault tip (Table 5.1) and the distribution of the fault slip (Fig. 5.6). Main thrust fault, Fault 2, the backthrust (Fault 3), and the NW Segment of Fault 5 present large modeled trishear angles (80–86°), while Fault 4 and the SE Segment of Fault 5 present moderate trishear angles (44–60°). The P/S ratios for the main fault and Fault 3 have been estimated to be 3, however, the P/S ratios obtained for the other faults included in the model are 2. CAPÍTULO 5 115 Figure 5.5 (a) Colored topographic surface used as a base for the forward modeling procedure where the uplifts associated with the slip of the thrust faults have been removed together with the craters in the area. (b) Topographic surface resulting from the 3D forward modeling, where the original MOLA surface is reproduced from the 5.a. surface. Figure 5.6 Modeled slip distribution along lengthwise profiles of the five studied faults. The distribution of the cumulative fault slip (Fig. 5.6) calculated for each analyzed thrust fault reflects a decay of the slip toward the lateral tip points. The maximum slip is located in the center of the main fault, with an estimated value of ∼2,100 m. This maximum slip decays to zero towards the northwestern tip point, while it flattens out at ∼1,050 m to the southeast, before decaying until reaching the zero value at the tip point. Fault 2 presents a symmetric peak type slip distribution (Fossen, 2010) with a maximum modeled slip of ∼1,300 m in the center that coincides with the secondary flat top of the main fault. The maximum fault slip of Fault 3 is estimated to be ∼1,600 m, and it is located approximately 75 km from its southern tip point leading to an asymmetric slip distribution. This fault presents a constant decrease to zero slip toward the south, while to the northern tip point the slip decreasing plummets when it intersects with the main fault. Fault 4 presents a symmetric plateau type slip distribution (Fossen, 2010) with a maximum flat top corresponding with an estimated slip of ∼1,720 m. The maximum modeled slip of Fault 5 NW Segment is ∼1,100 m, which is located at 30 km from the southeastern tip CAPÍTULO 5 116 point. The modeling of the SE Segment of Fault 5 reflects two peaks in the slip distribution of ∼1,000 and ∼920 m corresponding with the two lobes identified in plan view (Fig. 5.1). The accuracy of the best fit model obtained has been probed by comparison with the observed MOLA topography (Fig. 5.7), trying to minimize the elevation difference between them. The study area is characterized by the presence of a large number of impact craters that modify the topography. The greatest differences in elevation are due to these impact craters that we have removed from the initial modeling surface when removing the lobate scarp reliefs, thus the calculation of the difference between the observed topography (Fig. 5.3a) and the forward modeled topography (Fig. 5.5b) has been made excluding crater values. The median value calculated for the elevation difference between the MOLA model and the modeled topographic surface is ∼3 m. The quartile deviation associated with this median value, which is indicative of the average fit of the model, is ∼29 m, indicating that half of the values obtained when comparing these two surfaces are concentrated between 32 and −26 m. Figure 5.7 Absolute elevation difference between the original MOLA topographic surface and the model obtained from the 3D forward modeling. Perfect fit between the model and the observed topography is represented by zero values. 5.2.4. Discussion 5.2.4.1. Structural Modeling The general agreement of the forward modeled topographic surface and the MOLA-observed surface (Fig. 5.7) is evidenced by the low median value (∼3) and the dispersion of the data around it (quartile deviation of ∼29 m). This quartile deviation represents 2.8% of the maximum relief associated with the main fault (1,050 m), while it CAPÍTULO 5 117 represents 6% of the maximum relief associated with the smallest modeled fault (Fault 5 Segment SE, 480 m). The uncertainties in the fault slip estimate that can cause the obtained quartile deviation of the modeled topography (29 m) are +/−74 m for the minimum modeled dip angle (23°) and +/−53 m for the maximum modeled dip angle (33°) (the slip uncertainty can be obtained by the quartile deviation/sin β, β being the dip angle). These values show that our 3D model is a good approximation to the geometry and kinematics of thrust faults in the study area, which closely reproduces lobate scarp structural reliefs. Nevertheless, this model is a simplification, and some minor local differences can be observed due to modeling limitations and non-modeled geological processes. The modeling method presents some limitations when the propagating fault reaches the topographic surface (surface rupture). The trishear fault propagating folding ends at this point and the hanging wall continues its displacement over the footwall following a fault-parallel flow movement. This, together with the presence of landslides and rockfalls due to the steep slope of the forelimb, hinders the fitting of the forelimb and the scarp base throughout the entire length of the structure, generating small misfits between the model and the original surface especially at the scarp bases. The building of the 3D fault planes has been performed idealizing them as a smooth surfaces, therefore the presence of probable irregularities along fault surfaces, which would influence the topography (Watkins et al., 2015), have not been taken into account. From this point of view, our model can be considered a first-order approximation to the general 3D faulting framework. The tectonic transport direction has been set perpendicular to each fault strike, although Mueller et al. (2014) obtained a slip vector direction for Amenthes Rupes that deviates 16° from pure dip-slip, by measuring the dislocation of a crater cut by the main fault, which would reflect a small strike-slip component of deformation. However, these authors claim that this estimate presents a significant error, because the half of the crater located on the hanging wall is affected by a subsequent crater, significantly reducing the amount of data involved in the calculation. Besides, an oblique slip generates surface geometries similar to those generated by dip-slip (Cristallini & Allmendinger, 2001), and an obliquity of the slip as low as 16° only results in a very slight changes in slip and trishear angle needed to fit the model. A pure dip-slip fault kinematics has been assumed for all the modeled faults with the slip vectors perpendicular to the average strike of fault traces, because the high sinuosity of the mapped lobate scarps (Fig. 5.1) and the lack of en-echelon patterns do not indicate an evident strike-slip component of deformation. The fault surfaces obtained in this study for the five analyzed faults show positive listric morphologies at depth (a decay of dip angle with depth, McClay & Ellis, 1987). Previous studies using the FMD method modeled the underlying fault of Amenthes Rupes, as well as other lobate scarps in Mars, as a rectangular planar fault (Egea-González et al., 2017; Herrero-Gil et al., 2019; Grott et al., 2007; Ruiz et al., 2008; Schultz & Watters, CAPÍTULO 5 118 2001), because this method does not provide results as good as when the model is made using non-planar morphologies (Schultz & Watters, 2001; Watters & Nimmo, 2010). A positive listric fault morphology was obtained by Mueller et al. (2014) for Amenthes Rupes and by Herrero-Gil et al. (2020) for Ogygis Rupes and its backthrusts, based on the relation between the fault propagation anticline topography and the fault plane characteristics (e.g., Amos et al., 2007; Cardozo & Brandemburg, 2014; Ellis et al., 2004; Erslev, 1986; Seeber & Sorlien, 2000). On the contrary, a planar fault morphology that keeps its dip constant until the horizontal decollement would generate a backlimb with the same dip as the fault and abrupt limits (e.g., Amos et al., 2007; Brandemburg, 2013; Hardy & Ford, 1997), which is not the case for any of the studied faults (Fig. S1). The dip angles obtained for the first kilometers of depth for the analyzed faults range between 27° and 33° (Table 5.1), except Fault 4, which presents a lower dip angle of 23°. These dip values are within the typical range calculated for reverse faults (20–35°) (e.g., Jaeger & Cook, 1979; Stone, 1985; Watters & Nimmo, 2010). The lower dip of Fault 4 can be explained by considering its relation with Fault 3 (Fig. 5.4). Both faults form a “pop-up” structure in which Fault 4 roots at a shallower depth indicating that it is subsidiary. Fault 4 can be passively transported by Fault 3 with a slight tilting due to its listric fault morphology at depth, causing the decreasing of its dip angle as Fault 3 slips (Ellis et al., 2004). The estimated slip distribution (Fig. 5.6) of the studied fault set allows us to obtain an approximate value of the horizontal shortening in the area (Fig. 5.8) as a result of the NE-SW compressive stress that generated these structures. The listric geometry obtained for these faults at depth suggests that the slip on the fault ramps near the surface was transmitted by a horizontal slip of the same value along the decollement (Herrero-Gil et al., 2020). Thereby, the regional shortening related to Amenthes Rupes thrust fault system can be estimated by stacking the slips of the contractional faults in the area (Fig. 5.8). This value has been measured in the direction N36.6°E, the mean dip azimuth of the studied faults (Fig. 5.4d), which is orthogonal to the mean strike value. The horizontal displacement presents a multimodal asymmetrical distribution characterized by three peaks of different value increasing notably toward the southeast. The northwestern peak is due to the contraction accommodated by the NW part of the main fault and the NW Segment of Fault 5. The horizontal slip corresponding to the central peak is due to the shortening generated by the slip of the central part of the main fault and the SE Segment of Fault 5. The southeastern peak shows the largest shortening value of the total distribution (∼5,450 m) due to the combining of the slip values generated by Faults 2, 3, 4, and the southern part of the main fault, which are mostly parallel in this area (Fig. 5.1). The analysis of the shortening distribution (Fig. 5.8) shows a main change in the amount of shortening at ∼360 km from the NE. This point marks an abrupt increase of shortening toward the SE associated with the third described peak. The structural map (Fig. 5.1) reveals that Faults 2, 3, and 4 appear to the SE of this diffuse limit, where Fault 5 ends. CAPÍTULO 5 119 The largest shortening value abruptly decays to the southeast. In this area, there are two minor faults (Fig. 5.1) not included in the modeling that distribute the slip of the Fault 3 to the south. These minor faults seem to have a shorter length due to the presence of a heavily cratered area affecting their traces (southeast corner Fig. 5.1); nevertheless, these structures continue to the S-SE outside the study area with associated high relief, which reflects that the shortening continues along these faults although they are not included in this study. Figure 5.8 Representation of the total horizontal shortening estimate in a lengthwise profile orthogonal to the general shortening direction, which corresponds with the mean strike of the fault system (N126.6°E). Therefore, the shortening associated with each fault is equal to the fault slip under the assumption that the slip is transmitted from the decollement due to the listric fault morphology at depth. This interpretation requires that the shortening estimates calculated using listric fault morphologies be larger than when the shortening is obtained from the horizontal component of the slip (heave) over a planar fault (from ∼6% for a dip angle of 20°, up to ∼30% for 40°) (Herrero-Gil et al., 2020). Consequently, the horizontal contraction that generated lobate scarps implies a shortening value up to ∼30% larger than the estimates calculated from modeling the slip over a planar fault. The analysis of the calculated faulting depths presents a bimodal distribution; so, the obtained results can be grouped into two different depths (Table 5.1). The major faults of the area (the main fault, its splay Fault 2, and Fault 3), which are the longest and uplift the widest and highest reliefs, root into a deep decollement level, that ranges in depth from 20–24 km. This depth value is within the range of depths of faulting calculated previously for the large faults underlying different lobate scarps formed in the Late Noachian/Early Hesperian spread across the highlands of Mars (Egea-González et al., 2017; Grott et al., 2007; Herrero-Gil et al., 2019, 2020; Mueller et al., 2014; Ruiz et al., 2008; Schultz & Watters, 2001), supporting that this rooting level is not a regional rheological threshold. The depth of faulting of these large thrust faults has been considered as the BDT depth at the time of its formation (e.g., Ruiz et al., 2008, 2009, 2011; Schultz & Watters, 2001), which corresponds to a change from localized failure to distributed failure (Byerlee, 1967, 1968; Rutter, 1986). On the other hand, Fault 4 and the two segments corresponding to Fault 5 present a modeled depth of faulting of 9.5–13 km, CAPÍTULO 5 120 much shallower than the BDT where the large faults root. This bimodal distribution of depths shows the mechanical complexity of the crustal layers affected by faulting, indicating that the lithospheric brittle domain is not a homogeneous medium, but it probably presents heterogeneities such as mechanical discontinuities where subsidiary faults root. Table 5.2 Fault parameters obtained in different studies performed on Amenthes Rupes. Maximum slip (m) Dip angle (°) Depth of faulting (km) Amenthes Rupes (Schultz & Watters, 2001) 1500 25–30 25–30 Amenthes Rupes (Ruiz et al., 2008) 1900–2300 19–24 27–35 Amenthes Rupes (Mueller et al., 2014) 1170–1440 41.5–56.1 33–48 Amenthes Rupes (Egea-González et al., 2017) 1500–2000 20–35 27–33 Amenthes Rupes (This study) 2100 27–28 20–24 Amenthes Rupes-Fault 2 (This study) 1300 29.5 23.5–24 Amenthes Rupes-Fault 3 (This study) 1600 31–33 21.5–22.5 The results obtained in this study for the major faults in the area that root into a deep decollement (main fault forming Amenthes Rupes, Fault 2, and Fault 3) can be compared with the fault parameter estimates of previous works in Amenthes Rupes, which are focused in the main fault (Egea-González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008; Schultz & Watters, 2001) (Table 5.2). The slip value calculated for the main fault is within the range calculated by Ruiz et al. (2008) while is quite higher than the values calculated by other authors (Egea-González et al., 2017; Mueller et al., 2014; Schultz & Watters, 2001). Fault 2 and Fault 3 are expected to present different slip values since they are different structures than the main fault. However, the depth of faulting of these faults in the area can be compared because it is expected that the BDT does not present large variations in such a small area during the same period of time. When we compare the depths of faulting of these three faults with those of previous works (Egea- González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008; Schultz & Watters, 2001), our estimates provide shallower values. The BDT is temperature and strain rate dependent (e.g., Artemieva, 2011; Ruiz et al., 2011). The shallower depth of the BDT deduced from CAPÍTULO 5 121 our results suggests that the associated heat flow of the Amenthes Region at the time of lobate scarps formation could be somewhat higher than previous estimates. Faster deformation deepens the brittle domain of the crust. The strain rates calculated for the Amenthes thrust fault system (Schultz, 2003) are small (between 10−17 and 10−19 s−1) and comparable to intraplate tectonic settings on Earth; accordingly, large variations in the strain rate, affecting significantly the depth of the BDT, are not expected in this area. The dip values obtained are in the range of those previously calculated for Amenthes Rupes (19–35°) (Egea-González et al., 2017; Ruiz et al., 2008; Schultz & Watters, 2001), but away from the highest values obtained by Mueller et al. (2014). The trishear parameters obtained for the modeled faults (Table 5.1) are within the best-fit ranges calculated by Pei et al. (2014) through the analysis by trishear of several real structures on Earth. They stablished a P/S ratios ranging between 2 and 3 and trishear angles between 30° and 100°. The main fault and Fault 3 present a P/S ratio of 3, coinciding with their larger dimensions and deeper depths of faulting. They also have in common a large trishear angle (80–86°) showing that the folding occurs in a wide area that in main fault affects mainly the hanging wall, while in Fault 3 equally affects the hanging wall and the footwall. Fault 2 presents a trishear angle and its distribution similar to the main fault (Fault 2 is a splay of the main fault), with a P/S ratio of 2. Fault 4 and both segments of Fault 5 also have P/S ratios of 2 and variable trishear angles between 40° and 85°. The initial fault tip depth of the SE Segment of Fault 5, comparing to its maximum slip, reflects that this fault does not break the topographic surface at the end of the forward modeling. The fault propagation is strongly linked with the fault slip distribution. This may imply that the surface rupture does not occur along the structure (blind thrust) or that it occurs at specific locations that usually match with the location of maxima in the slip distribution. The modeling of Fault 4 presented several challenges. The propagating fault tip of this fault at the end of the forward modeling does not reach the topographic surface, suggesting that this could be a blind fault. However, the large original topographic dimensions of this fault and its net scarp base observed in the MOLA topography and THEMIS images suggest a surface rupture at least in its central part. The scarp base and frontal syncline generated by Fault 4 displacement are completely covered by a deposit of Amazonian-Hesperian smooth plains (Erkeling et al., 2011). Caprarelli et al. (2007) estimated the thickness of this geological unit by calculating the depth of the craters before the infilling. The high thickness of this resurfacing material (1–1.5 km) suggests that the relief uplifted by Fault 4 was initially much higher than the relief currently observed. Moreover, the backlimb Fault 4 propagation anticline is affected by two big impact craters postdating the fault displacement and by the presence of some wrinkle ridges (Fig. 5.1) parallel to Faults 3 and 4, which also affect the modeling results. These two large craters were also infilled by the same resurfacing unit. Therefore, the obtained CAPÍTULO 5 122 slip for this fault is a minimum value, and due to these observations, other parameters of Fault 4 may also present additional uncertainties. 5.2.4.2. Tectonic Evolution and Implications for Global Contraction Since Amenthes Rupes and its companion thrust faults are located in the highlands near the dichotomy boundary, their characteristics can give us information on the evolution of the boundary, at least locally. The faults forming the Amenthes Region thrust fault system all show similar strikes and kinematics (pure reverse faults) and thus can be interpreted to be formed under the same compressive stress field with a shortening direction (N36.6°E) perpendicular to their average strike (Fig. 5.4d). This agrees with the direction of the dichotomy boundary and with other lobate scarps in the adjoining Arabia Terra and Terra Cimmeria (Nimmo, 2005; Watters, 2003a; Watters et al., 2007; Watters & Robinson, 1999). Watters and Robinson (1999) calculated the horizontal shortening across Amenthes Rupes using the fault throw (lobate scarp relief), obtaining 1,800–3,400 m (corresponding with the heave on a planar fault), depending on the dip angle (assumed to be 20–35°). The fault parameters obtained in the present 3D modeling also allow a constraint on the maximum shortening registered by Amenthes Rupes main fault, which is ∼2,100 m, assuming that the slip is transmitted from the decollement. The regional shortening distribution associated with the whole fault system (Fig. 5.8) suggests a maximum value in the southeastern of the thrust system of ∼5,450 m, which is well above the previously calculated range for this area (1,800–3,400 m), increasing the shortening estimates of the area between ∼60% and ∼200%. This difference in the shortening values is mainly due to the inclusion of secondary and subsidiary faults in our model that were not previously considered, and yet they accommodate ∼62% of the maximum shortening in this area. Besides, there are other minor contractional structures identified in the area (Fig. 5.1), including minor thrust faults and wrinkle ridges, that have not been included in the model, and they would increase this shortening calculation, especially in the southeastern half of the thrust fault system. Whereby the regional shortening estimated by our model (Fig. 5.8) is a minimum value. Previous global shortening estimates based on thrust faults (Nahm & Schultz, 2011) were performed using the dataset of faults of Knapmeyer et al. (2006). Although this structural mapping is quite exhaustive and extensive, the number of structures considered were significantly biased by the global scale of mapping, so the database did not contain all the subsidiary and minor faults present on Mars surface. Our study shows that the consideration of subsidiary faults, including backthrusts and fault splays, and independent secondary and minor faults in global calculations of contraction would provide a significant increase of the global planetary shortening accommodated by thrust faulting. Although all the faults were generated during the same epoch, some relative time relationships can be deduced from structural cross-cut evidence, providing information CAPÍTULO 5 123 on the evolution of the fault system. Fault 2 is a splay of the main fault, indicating that the slip of main fault is progressively accommodated by Fault 2 toward the SE. This kinematic link between both faults, which root at the same decollement, suggests that they could have been active at the same time. The main fault and Fault 2 traces are slightly displaced by Fault 3 slip, indicating that, although the activity of these faults could be contemporary, the last movement belongs to Fault 3 (backthrust). Fault 4 is a subsidiary antithetic fault with respect to Fault 3; consequently, both faults are probably contemporary. Fault 5 does not intersect other faults, so it is not possible to deduce its place in the formation order. A general tectonic evolution of the contraction that generated the lobate scarps in the Amenthes Region can be outlined according to the described cross-cutting constraints and the horizontal slip distribution of figure 5.8. Initially, the compressional stress field generated a homogeneous shortening in the area associated with the main fault, Fault 2, and probably Fault 5. Later, the contraction continued in the SE region of the study area with the generation of Fault 3 and its subsidiary Fault 4, which significantly increases the total shortening in this sector (maximum peak shown in Fig. 5.8), propagating deformation toward the SW with respect to the main fault and its splay (Fig. 5.1). This assumption that the deformation shifts and continues to the southeast agrees with previous observations that the lobate scarps on Terra Cimmeria, located ∼500 km southeast of the studied fault system, deform geological units from the early Hesperian, which indicates that their formation continued during that age (Greeley & Guest, 1987; Watters et al., 2007; Watters & Robinson, 1999). These observations can be representative of the evolution pattern of the deformation that modified this part of the dichotomy boundary in the Late Noachian/Early Hesperian, which implies a shortening recorded by thrust faults that is more than double of previous estimates if the calculation includes subsidiary and secondary faults. 5.2.5. Conclusions Five thrust faults forming the Amenthes thrust fault system, which is located in the Amenthes Region, have been modeled by 3D forward modeling through a combination of trishear and fault-parallel flow methods. All the modeled fault surfaces show listric geometries at depth constrained by the low slopes of the fault propagation anticline backlimbs and by the width of the trailing syncline. The obtained depths of faulting of the major faults present in the fault system suggest a depth of the BDT of 20–24 km at the time of formation in the Late Noachian/Early Hesperian, a value shallower than previous estimates. A possible mechanical discontinuity in the lithosphere located at 9.5–13 km of depth can be deduced from the depths of faulting of secondary faults. The estimated horizontal shortening accumulated by the thrust system ranges between 2,000 and 3,000 m, increasing toward the SE part of the study area to a maximum shortening value of ∼5,450 m. This value represents an increase in the maximum regional shortening CAPÍTULO 5 124 registered by thrust faults of between 60% and 200% higher than previous estimates, due to the consideration of subsidiary and secondary faults. The contribution of minor, secondary, and subsidiary faults to the planetary contraction could provide a significant increase of martian global shortening. CAPÍTULO 5 125 5.3. Conclusiones Capítulo 5 Cinco grandes fallas inversas han sido incluidas en la modelización 3D del sistema de fallas de Amenthes usando la combinación de los algoritmos de trishear y fault-parallel flow. Todas las fallas muestran una disminución del ángulo de buzamiento en profundidad, presentando geometrías lístricas que están constreñidas por la pendiente tendida que presenta el flanco trasero de sus anticlinales asociados (backlimb) y por la forma abierta de los sinclinales traseros. Las profundidades de enraizamiento obtenidas permiten agrupar estas fallas en dos grupos. La fallas mayores del sistema de fallas, incluyendo la principal (Amenthes Rupes), su splay (Falla 2) y la falla retrocabalgante (Falla 3), tienen su profundidad de despegue entre 20 y 24 km. Esta profundidad, pese a ser ligeramente más somera que valores previos de profundidad calculados para la falla que forma Amenthes Rupes, concuerda con valores de la profundidad de la transición frágil-dúctil asociados a diferentes escarpes lobulados estudiados en Marte para la edad de formación en el Noeico Tardío/Hespérico Temprano (e.g. Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Egea-Gonzalez et al., 2017; Herrero-Gil et al., 2019; 2020a). Las fallas menores incluidas en el modelo (Falla 4 y los dos segmentos que conforman la Falla 5) tienen una profundidad de enraizamiento menor, localizada a 9.5–13 km de profundidad, indicando la presencia de una posible discontinuidad mecánica dentro del dominio frágil en la corteza. El acortamiento horizontal acumulado por este sistema de fallas inversas presenta un valor medio entre 2000 y 3000 m, incrementando hacia la mitad SE de la estructura, donde la superposición de las falla principal y las fallas 2, 3 y 4 hace que el valor de acortamiento incremente hasta un máximo de ∼5450 m. Este valor de acortamiento supone un incremento respecto al valor de acortamiento regional calculado previamente de entre el 60 y el 200%, debido principalmente a la inclusión de las fallas secundarias y subsidiarias en el modelo. La presencia de otras fallas menores, así como crestas sinuosas, que acomodan deformación en la zona y no han sido modelizadas, supone que este valor de acortamiento sea, aún así, un valor mínimo. Esta observación nos lleva a pensar que las estimaciones de acortamiento global acomodado por las grandes fallas inversas (Nahm y Schultz, 2011) están sesgadas por el detalle de la cartografía estructural que se ha usado en el cálculo (Knapmeyer et al., 2006; 2008), que a su vez es directamente dependiente de la resolución de los datos planetarios disponibles. Por lo tanto, podemos afirmar que tener en consideración fallas secundarias y menores a nivel global, y su incorporación a los cálculos de acortamiento, supondría un aumento significativo en los cálculos de contracción global de Marte. CAPÍTULO 5 126 Es posible identificar una evolución temporal de la actividad tectónica que generó este sistema de fallas. El análisis de las relaciones de corte y cruce de las fallas, junto con la distribución de acortamiento que registran, parece reflejar que la contracción afectó inicialmente a la falla principal, la Falla 2 y probablemente la Falla 5, y que posteriormente continuó hacia el SE del sistema de fallas con la generación de las fallas 3 y 4, lo que incrementó el acortamiento en esta zona. 6 DISCUSIÓN CAPÍTULO 6 129 El interés en conocer las características de las fallas que forman los escarpes lobulados radica en la información sobre la estructura mecánica de la litosfera de Marte y sobre la contracción litosférica en dicho planeta que podemos obtener al analizar los datos resultantes de modelizar la superficie topográfica de estos relieves. Los resultados obtenidos en esta tesis concuerdan con los resultados de trabajos previos que apoyan un nivel de despegue profundo para las grandes fallas inversas en Marte, que indica la presencia de una importante discontinuidad mecánica en la litosfera que ha sido relacionada con la transición frágil-dúctil en la corteza (e.g. Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008, 2011; Egea-González et al., 2017). Además, la profundidad de fallas secundarias o subsidiarias proporciona indicios sobre la presencia de otras discontinuidades mecánicas dentro del dominio frágil de la corteza. La morfología de los planos de falla, junto con el análisis de cómo es el desplazamiento a lo largo ellas, proporciona información sobre la contracción regional que las generó. También es posible establecer una relación entre las grandes estructuras que forman los relieves principales de Marte y la distribución y orientación de las fallas estudiadas. 6.1. Discusión metodológica En esta tesis se han utilizado tres métodos para modelizar la superficie de los escarpes lobulados desde diferentes enfoques con el objetivo de conocer la geometría de las fallas inversas que los forman y los parámetros estructurales que controlan su desplazamiento: (1) Método de cortes compensados por áreas (balanced cross sections) (Chamberlin, 1910), (2) Método de dislocación mecánica (forward mechanical dislocation) (Toda et al., 1998), (3) Métodos de trishear (Erslev, 1991; Allmendinger, 1998) y fault- parallel flow (Egan et al., 1997; Ziesch et al., 2014) combinados en un marco 3D (Cardozo, 2008; Ziesch et al., 2014). La utilización de tres métodos distintos, algunos de los cuales llevan aplicándose desde los primeros trabajos de modelización de escarpes lobulados en Marte, permite crear un marco de comparación y discusión de los resultados obtenidos, algo necesario debido a los cambios en la disponibilidad de los datos, y a la evolución de la metodología aplicable, así como la aparición de nuevos programas de modelización. La mayor diferencia técnica entre los métodos aplicados es que el método de dislocación mecánica modeliza la superficie como un medio deformado elásticamente tras la imposición de un desplazamiento determinado en un plano de falla, mientras que el método de los cortes compensados por áreas y la combinación de trishear y fault- parallel flow se basan en la conservación del materia (área o volumen) teniendo en cuenta que se genera una deformación permanente por plegamiento al propagarse la rotura en CAPÍTULO 6 130 el dominio frágil de corteza. A la hora de caracterizar la deformación registrada en las fallas y el plegamiento asociado a ellas, consideramos que el enfoque de deformación permanente es más adecuado y realista que el enfoque de una deformación en un medio puramente elástico. Estudios de deformación de rocas en laboratorio reflejan que, en escalas de tiempo geológicas, la litosfera de un cuerpo planetario rocoso no es puramente elástica, sino que su estructura incluye los regímenes frágil y dúctil, en los cuales la deformación se traduce en fracturación y flujo dúctil respectivamente (Kohlstedt et al., 1995). El régimen frágil suele dominar en la parte superior de la corteza, pero puede extenderse a toda ella, y también puede estar presente en la parte superior del manto litosférico. El régimen dúctil puede estar presente en la parte inferior de la corteza y define, al menos, la parte inferior del manto litosférico. En regiones de flujo térmico elevado la litosfera puede verse limitada a la corteza. Un modelo puramente elástico requiere flexiones de la litosfera poco realistas y conlleva la ausencia de ruptura en superficie (e.g. Goetze y Evans, 1979), lo cual contradice las observaciones que se pueden apreciar en superficie asociados a los escarpes lobulados, incluyendo la evidencia de cráteres cortados por la falla. Pese a ello, el método de dislocación mecánica ha demostrado ser una buena aproximación a la hora de modelizar la superficie topográfica elevada por una falla inversa para obtener el buzamiento, profundidad y desplazamiento de la misma dentro de unos rangos conocidos (e.g. Cohen, 1999; Schultz y Watters, 2001; Watters et al., 2002). Al haber aplicado los tres métodos en la falla principal de Ogygis Rupes, es posible comparar y analizar los resultados obtenidos para esta. La profundidad de despegue obtenida por el método de cortes compensados por áreas (18 km) es similar a la obtenida aplicando los algoritmos de trishear y fault-parallel flow (17.2–17.8 km). Es de esperar que estos dos métodos proporcionen resultados similares al basarse ambos en la conservación del material. Esta profundidad de despegue indicaría la presencia de una gran discontinuidad mecánica que puede relacionarse con la base del dominio frágil de la corteza. La base del dominio frágil se define como la profundidad de la transición frágil- dúctil (e.g. Byerlee, 1967, 1968; Artemieva, 2011). La profundidad obtenida mediante el método de dislocación mecánica (20–27 km) refleja un decrecimiento del desplazamiento en los últimos 7 km, lo que podría estar relacionado con la entrada en la transición frágil- dúctil. Así pues, los resultados obtenidos con este método sitúan el inicio de la transición a 20 km de profundidad, indicando una profundidad ∼2 km mayor que la obtenida por los dos métodos anteriores para esta discontinuidad. Los valores de buzamiento y de desplazamiento obtenidos para esta falla mediante el método de dislocación mecánica (35° y 2500–3100 m) son muy próximos a los obtenidos mediante la combinación de trishear y fault-parallel flow (39° y ∼2850 m), al igual que ocurre con el valor de desplazamiento del método de cortes compensados por áreas (∼2900 m). CAPÍTULO 6 131 Si atendemos a los resultados obtenidos para la falla principal de Amenthes Rupes mediante trishear y fault-parallel flow, y su comparación con estudios previos que utilizan los otros métodos (Tabla 5.2), se observa que los resultados de los diferentes métodos son en general concordantes, pero si se aprecian algunas diferencias que pueden ser debidas a la elección de diferentes secciones transversales o a los criterios de ajuste seguidos por los diferentes autores. La profundidad obtenida mediante la combinación de trishear y fault-parallel flow es de aproximadamente 20 km en el norte de la estructura, aumentando progresivamente hasta 24 km en la zona central-sur de la misma. Estos valores son ligeramente menores que las profundidades calculadas por el método de dislocación mecánica en secciones transversales en la zona central de Amenthes Rupes, que se concentran en su mayoría en el rango 25–35 km (Schultz y Watters, 2001, Ruiz et al., 2008; Egea-González et al., 2017), si atendemos a que este rango de profundidad indicaría la zona en la que decrece el desplazamiento. Al igual que ocurre en Ogygis Rupes, este valor menor de profundidad podría explicarse por la diferencia entre la localización de la base del dominio frágil y la entrada de la falla en la transición frágil-dúctil. El valor de desplazamiento máximo calculado en nuestro estudio para la falla principal de Amenthes (2100 m) está dentro del rango de 1500–2300 m en el que se concentran la mayoría de los resultados de estudios previos (Schultz y Watters, 2001, Ruiz et al., 2008; Egea-González et al., 2017). Lo mismo sucede con los valores de buzamiento para esta falla, que en el presente estudio es de 27°–28° y estudios previos sitúan en 19°–35° (Schultz y Watters, 2001, Ruiz et al., 2008; Egea-González et al., 2017). 6.2. Discusión de los resultados Gracias a esta comparación de los resultados obtenidos podemos afirmar que los tres métodos proporcionan resultados concordantes para los parámetros geométricos que definen las fallas estudiadas, pudiendo analizar los resultados conjuntamente. 6.2.1. Profundidad de despegue y estructura mecánica Atendiendo a la interpretación de que el rango de profundidad obtenida por el método de dislocación mecánica, en el que se produce la disminución de desplazamiento en profundidad, indicaría la entrada en la transición frágil-dúctil, tomaremos el dato de profundidad superior, que indicaría el inicio de la misma, para compararlo con los obtenidos por los otros dos métodos. Así, las profundidades obtenidas para el inicio de la transición frágil-dúctil para las fallas situadas entre la cuenca de impacto de Argyre y los Montes de Thaumasia serían de 17.2–20 km para Ogygis Rupes, 24.5–25 km para Phrixi CAPÍTULO 6 132 Rupes y 33–45 km para Bosporos Rupes (Tabla 6.1). Estos valores reflejan un dominio frágil profundo cerca de la cuenca de Argyre que va disminuyendo con la distancia a esta. Se aprecia una diferencia importante en los valores de profundidad obtenidos mediante los dos métodos para la falla que forma Bosporos Rupes. Además, este valor de profundidad es alto comparado con los de Ogygis y Phrixi Rupis, lo que conllevaría una variación lateral de la profundidad de la transición frágil-dúctil demasiado grande para el área en el que se encuentran estas fallas. La presencia del anillo principal de la cuenca, sobre el que se sitúa Bosporos Rupes, parece condicionar los resultados obtenidos al haber modelizado el relieve del anillo como parte de la elevación producida por el desplazamiento de la falla, por lo que la profundidad obtenida para esta falla parece ser una sobreestimación. La falla principal, la Falla 2 y la Falla 3 del sistema de fallas de Amenthes (Tabla 6.1) presentan un nivel de despegue profundo que, junto con sus grandes dimensiones, nos permite clasificarlas como fallas mayores, considerando que atraviesan todo el dominio frágil de la corteza. La profundidad de estas fallas, que correspondería con la profundidad de la transición frágil-dúctil en esta región, varía entre 20 y 24 km, teniendo su profundidad menor en la zona noroeste, y aumentando hacia el sur-sureste. Tabla 6.1 Resumen de los principales parámetros obtenidos para las fallas mayores estudiadas. Desplazamiento (m) Buzamiento (°) Profundidad inicio BDT (km) Ogygis Rupes 2500–3100 35–39 17.2–20 Phrixi Rupes 1700–2000 33 24.5–25 Bosporos Rupes 1700–2750 23 33–45 (?) Amenthes Rupes (Falla principal) 2100 27–28 20–24 Amenthes Rupes (Falla 2 splay) 1300 29.5 23.5–24 Amenthes Rupes (Falla 3 backthrust) 1600 31–33 21.5–22.5 Las altas profundidades de despegue obtenidas para las grandes fallas inversas que subyacen los escarpes lobulados estudiados en esta tesis doctoral (Tabla 6.1), y en estudios previos realizados en escarpes lobulados distribuidos por todo el planeta (Fig. 4.9; Tabla 3.3, Tabla 5.2), sugieren que estas estructuras se enraízan en un límite global existente en el Noeico Tardío/Hespérico Temprano, y no en una profundidad correspondiente con un límite regional. De ser una profundidad controlada por características reológicas o composicionales locales se esperarían profundidades menores que presentarían mayores variaciones entre diferentes áreas al localizarse en sitios tan alejados. La transición frágil-dúctil es un límite cuya profundidad es fuertemente dependiente de la temperatura, pero también de la tasa de deformación (e.g. Artemieva, CAPÍTULO 6 133 2011; Ruiz et al., 2011). Sin embargo, los valores de tasas de deformación obtenidos para fallas inversas en Marte presentan unos valores tan bajos (comparables a un ambiente de tectónica de intraplaca) (Schultz, 2003) que no se esperan grandes variaciones de la tasa de deformación que afecten sustancialmente a la profundidad de la transición frágil-dúctil en las áreas estudiadas en esta tesis doctoral, siendo las profundidades obtenidas dependientes principalmente de la temperatura. Consecuentemente, los valores de profundidad ligeramente menores que se han obtenido para la Región de Amenthes en comparación con trabajos previos (Schultz y Watters, 2001; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017) (Tabla 5.2), sugieren que el flujo térmico asociado en esta zona en el momento de formación de las grandes fallas inversas (3600–3700 Ma) podría ser algo más elevado que lo que se había calculado con anterioridad. Estas altas profundidades que presentan las fallas mayores estudiadas tanto en el noroeste de la cuenca de Argyre como en la Región de Amenthes contrastan con las profundidades someras obtenidas para las fallas secundarias o subsidiarias incluidas en los modelos. Los niveles de despegue obtenidos al modelizar los backthrusts 1 y 2 de Ogygis Rupes se encuentran a 2.3–2.9 y 5.5–5.6 km de profundidad respectivamente (Fig. 4.5; Tabla 6.2). En el sistema de fallas inversas de Amenthes, el nivel de despegue obtenido para la Falla 4 se encuentra a 13 km de profundidad, mientras que la profundidad modelizada para los dos segmentos que forman la Falla 5 es de 9.5–11.5 km (Fig. 5.4; Tabla 6.2). Estos niveles de despegue indican la posible presencia de discontinuidades mecánicas regionales dentro del dominio frágil en la corteza de Marte. Aunque darle una explicación a estas discontinuidades es altamente especulativo debido a la falta de información disponible de la sub-superficie de Marte, estos resultados sugieren que las litologías masivas a las que se atribuye la formación de los escarpes lobulados (Watters, 1993; Mueller y Golombek, 2004) podrían presentar variaciones en profundidad de sus propiedades reológicas que pueden estar relacionados con cambios regionales en la estructura o composición de las rocas. Tabla 6.2 Resumen de los principales parámetros obtenidos para las fallas menores estudiadas. Desplazamiento (m) Buzamiento (°) Profundidad despegue (km) Ogygis Rupes (Backthrust 1) 1200 22 2.3–2.9 Ogygis Rupes (Backthrust 2) 1800 23 5.5–5.6 Amenthes Rupes (Falla 4) 1720 23 13 Amenthes Rupes (Falla 5 Segmento NW) 1100 28 10.5–11.5 Amenthes Rupes (Falla 5 Segmento SE) 1000 27–27.5 9.5–11 CAPÍTULO 6 134 6.2.2. Buzamientos de las fallas Los valores de buzamiento obtenidos para la mayoría de las fallas inversas estudiadas en la presente tesis doctoral, tanto mayores como secundarias o subsidiarias, varían en general entre 22° y 33° (Tablas 6.1, Tabla 6.2), estando dentro del rango de buzamientos observado en fallas inversas terrestres (20°–35°) (Fig. 6.1) (e.g., Jaeger y Cook, 1979; Brewer et al., 1980; Stone, 1985; Watters y Nimmo, 2010). Los valores de buzamiento obtenidos para Ogygis Rupes (35°–39°) a pesar de estar ligeramente por encima de este rango, están dentro del rango obtenido en estudios previos en fallas inversas en Marte (20°–40°) (Fig. 6.1). Figura 6.1 Representación de los datos de buzamiento (°) obtenidos en diferentes estudios realizados en Marte. La zona gris representa el rango de buzamientos típico observado en fallas inversas terrestres (20°– 35°). Los datos obtenidos en esta tesis doctoral están representados en rojo. 6.2.3. Geometría de los planos de falla La morfología del plano de falla condiciona la forma del anticlinal que forma el relieve del escarpe lobulado en superficie (e.g. Schultz & Watters, 2001; Watters et al., 2002; Li et al., 2020). El uso de los algoritmos de trishear y fault-parallel flow en un marco 3D permite modelizar el plano de falla tanto en profundidad como lateralmente, usando morfologías complejas (Brandenburg, 2013; Cardozo y Brandenburg, 2014) más realistas que las formas planares rectangulares que se obtienen al modelizar mediante el método de dislocación mecánica. Las morfologías resultantes para las fallas principales modelizadas por esta combinación (falla principal de Ogygis Rupes, y fallas principal, 2 y 3 del sistema de fallas Amenthes) presentan un buzamiento constante para los primeros kilómetros cercanos a la superficie, que va disminuyendo en profundidad, con una CAPÍTULO 6 135 morfología lístrica que se enraíza en un nivel de despegue profundo (Fig. 4.5; Fig. 5.4). Esta morfología concuerda con la pendiente tendida que presenta el flanco trasero de las estructuras analizadas, así como con la forma del sinclinal trasero (e.g. Mueller et al., 2014; Herrero-Gil et al., 2020a, 2020b), y es consistente con el conocimiento de fallas inversas que afectan al dominio frágil en la Tierra (e.g., Amos et al., 2007; Cardozo y Brandemburg, 2014; Jayangondaperumal et al., 2015; Li et al., 2020), con modelos numéricos (e.g. Ellis et al., 2004, Cardozo y Brandemburg, 2014; Pei et al., 2014) y con estudios de modelos análogos (e.g., Ellis et al., 2004). Esta disminución del buzamiento con la profundidad se ha descrito en la Tierra en fallas enraizadas en niveles profundos que se han relacionado con la transición frágil-dúctil (e.g. Lynn et al., 1983; Yonkee y Weil, 2015; Pfiffner, 2017; Groshong y Porter, 2019). Las fallas subsidiarias y secundarias modelizadas también presentan dicha disminución del buzamiento en profundidad, pero por lo general esta disminución es más gradual. Las fallas subsidiarias modelizadas en Ogygis Rupes (Backthrust 1 y Backthrust 2) que se generan sobre el franco trasero del pliegue asociado al desplazamiento de la falla principal, presentan un buzamiento bajo (22° y 23°, Tabla 6.2) que se ha atribuido al transporte pasivo de estas fallas sobre la falla principal al encontrarse sobre el bloque de techo, y al basculamiento de este bloque al desplazarse sobre el bloque de muro debido a la morfología lístrica de la falla principal (Ellis et al., 2004) (Fig. 4.5). La misma razón podría atribuirse al buzamiento de 23° obtenido para la Falla 4 del sistema de fallas de Amenthes (Tabla 6.2), que presenta una relación similar con la Falla 3, desplazándose con el movimiento del bloque de techo de esta (Fig. 5.4). 6.2.4. Desplazamiento y acortamiento horizontal La distribución de desplazamiento a lo largo de las fallas estudiadas no es homogénea, sino que está directamente relacionada con la altura de la estructura. Por lo general el desplazamiento de la falla es mayor en la zona de máximo relieve de la estructura, que suele estar próxima a la zona central de cada falla, y va disminuyendo hacia los límites laterales de la falla (tip points), donde el desplazamiento es cero (Fig. 2.6; Fig. 4.7; Fig. 5.6). Las morfologías lístricas obtenidas en profundidad para los planos de las fallas principales modelizadas mediante el método conjunto de trishear y fault-parallel flow sugieren que el desplazamiento a lo largo del plano de falla es transmitido enteramente desde el nivel de despegue a la rampa, siendo el acortamiento acomodado por la falla igual al desplazamiento de la falla a lo largo de la rampa. Esto concuerda con la mecánica de formación y propagación de grandes sistemas de fallas en la Tierra (e.g. Amos et al., 2007; Cardozo y Brandenburg, 2014; Pei et al., 2014; Li et al., 2020) y con modelos análogos (e.g. Ellis et al., 2004), en los que las fallas se nuclean en un nivel de despegue y se propagan hacia la superficie mediante rampas. Esta interpretación proporciona CAPÍTULO 6 136 mayores estimaciones del acortamiento asociado al desplazamiento de la falla inversa que las obtenidas cuando este valor es calculado como la componente horizontal del desplazamiento (Sh) a lo largo de una falla plana. Para buzamientos de entre 20° y 40°, que es el rango obtenido para modelizaciones de fallas inversas en Marte, esta consideración de que el desplazamiento es igual al acortamiento transmitido desde el despegue mediante una falla lístrica, proporciona un valor de acortamiento asociado a la misma de entre un ∼6 y un ∼30% mayor que si consideramos que el acortamiento es el valor horizontal del desplazamiento a lo largo de una falla plana. Por otro lado, la modelización del sistema de fallas de Amenthes nos ha permitido comparar el valor de acortamiento horizontal acumulado obtenido para todo el sistema de fallas en este estudio, con el valor de acortamiento previamente calculado en esta zona. El resultado de desplazamiento que hemos obtenido para la falla principal de Amenthes Rupes (∼2100 m) considerando el pliegue de propagación de falla y que el desplazamiento se transmite desde el nivel de despegue, está dentro del rango de 1800– 3400 m obtenido por Watters y Robinson (1999), calculado como el desplazamiento horizontal sobre una falla plana para un rango de buzamientos entre 20o y 35o, teniendo en cuenta la altura del escarpe. La altura de la estructura está directamente relacionada con el desplazamiento a lo largo de la falla por lo que es un buen criterio para obtener una aproximación a este parámetro cuando no se tiene información del valor de buzamiento. Sin embargo, al modelizar la superficie de la estructura podemos obtener una aproximación a la geometría del plano de falla, lo que permite constreñir mejor el desplazamiento asociado. Además, al incluir en el cálculo las fallas secundarias y subsidiarias que se han modelizado como parte del sistema de fallas inversas de Amenthes, el resultado del cálculo del acortamiento regional acomodado por las fallas aumenta hasta un valor de ∼5450 m en la zona sureste del área de estudio de la Región de Amenthes (Fig. 5.8), valor que está muy por encima del rango calculado por Watters y Robinson (1999) para esta zona (1800–3400 m). Este valor de acortamiento regional, que aumenta el acortamiento calculado en la zona entre un ∼60 y un ∼200% respecto al cálculo previo, es, aún así, un valor mínimo para este área teniendo en cuenta que en la zona hay fallas menores y crestas sinuosas que no hemos modelizado y que también acomodan acortamiento. CAPÍTULO 6 137 6.3. Implicaciones globales 6.3.1. Tectónica global El mapa de distribución de estructuras de contracción en Marte (Fig. 2.4b) presenta una distribución global homogénea tanto por las tierras bajas como por las altas, que contrasta con la distribución localizada de las estructuras de extensión a favor de grandes relieves geológicos. Si atendemos exclusivamente a los escarpes lobulados estudiados y modelizados en Marte (Fig. 6.2), estos presentan una distribución uniforme en las tierras altas. Las tierras bajas, presentan también una alta densidad de estructuras de acortamiento (Fig. 2.4b), pero estas se encuentran en muchas ocasiones tapadas por las unidades litológicas hespéricas y amazónicas que tapizan su superficie, lo que dificulta su identificación, clasificación y estudio, siendo esta la razón de la escasez de estudios de modelización de grandes fallas en esta zona hasta la fecha. Figura 6.2 Distribución de grandes fallas inversas asociadas a escarpes lobulados. Los puntos blancos señalan estructuras descritas y/o analizadas como grandes fallas inversas (e.g. Watters y Robinson, 1999; Klimczak et al., 2018; Atkins et al., 2020). Los puntos negros indican cuáles de estas estructuras han sido modelizadas para conocer más en detalle los parámetros que definen la geometría y movimiento de estas fallas (e.g. Schultz y Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Egea-González et al., 2017), de estas, las estructuras estudiadas en esta tesis doctoral están señaladas (Herrero-Gil et al., 2019; 2020a; 2020b). CAPÍTULO 6 138 Los escarpes lobulados modelizados en las tierras altas se encuentran en el sur de Thaumasia (Grott et al., 2007), noroeste de la cuenca de Argyre (Herrero-Gil et al., 2019, 2020a), región circum-Hellas (Egea-González et al., 2017) y en la región de Amenthes (Schultz y Watters, 2001; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017; Herrero-Gil et al., 2020b) (Fig. 6.2). Pese a estar muy alejados los unos de los otros, estas estructuras de contracción, así como otros escarpes lobulados y crestas sinuosas datadas, presentan edades similares que difieren de las de los grandes relieves cercanos, habiéndose formado con posterioridad, la mayoría datados con una edad entre 3900 y 3600 Ma (e.g. Grott et al., 2007; Egea-González et al., 2017) correspondiendo con el Noeico Tardío/Hespérico Temprano. Las estructuras tectónicas en superficies planetarias son comúnmente usadas para determinar el estado de los esfuerzos litosféricos en el momento de su formación. Se ha descrito que las direcciones de los escarpes lobulados modelizados, al igual que otras estructuras de acortamiento cercanas, guardan una relación con los grandes relieves cercanos, pese a tener edades más modernas, siendo paralelas al borde de Thaumasia (Grott et al., 2007; Herrero-Gil et al., 2019) o a la dicotomía (e.g. Watters y Robinson, 1999; Herrero-Gil et al., 2020b), o concéntricas a las cuencas de impacto de Hellas (Egea- González et al., 2017) y Argyre (Herrero-Gil et al., 2019). La orientación de las grandes fallas inversas estudiadas entre los Montes de Thaumasia y la cuenca de impacto de Argyre (Ogygis Rupes, Bosporos Rupes y Phrixi Rupes), y de otras estructuras de contracción presentes en la zona de estudio (crestas sinuosas) (Fig. 3.1), parece responder a un campo de esfuerzos compresivo controlado por el campo gravitacional de Tharsis y, en menor medida, por la presencia de la cuenca de impacto de Argyre. Otro ejemplo de que la presencia de estos grandes relieves condicionan la orientación de las estructuras tectónicas formadas posteriormente es el sistema de fallas de Amenthes, así como otras fallas asociadas a escarpes lobulados localizadas en las tierras altas de Arabia Terra y Terra Cimmeria (Nimmo, 2005; Watters, 2003a; Watters & Robinson, 1999; Watters et al., 2007), que presentan una dirección paralela a la dicotomía pese a ser posteriores a la formación de esta. Las fallas que forman el sistema de fallas inversas de Amenthes se han modelizado atendiendo a una cinemática de falla inversa pura, con una dirección de acortamiento (N36.6°E) (Fig. 5.4d) perpendicular a su orientación general. La dirección de los esfuerzos compresivos que generan este desplazamiento en las fallas es perpendicular a la dirección de la dicotomía, lo que sugiere que existen variaciones de las propiedades litosféricas asociados a esta que condicionarían la orientación del campo de esfuerzos regional de la época en la que se formó el sistema de fallas hace 3600–3700 Ma. De acuerdo a estas observaciones, y a trabajos previos (e.g. Watters, 1993; Mège y Masson, 1996; Dimitrova et al., 2006; Nahm y Schultz, 2011), la presencia de estos grandes relieves distribuidos por la superficie de Marte genera grandes variaciones laterales de espesor cortical y de las propiedades litosféricas, condicionando la orientación de los campos de esfuerzos locales o regionales bajo los que se formaron las CAPÍTULO 6 139 estructuras de contracción (e.g. Banerdt, 1982; Mangold et al., 2000, Beuthe, 2010) del Noeico Tardío/Hespérico Temprano. Esto rige principalmente la dirección que presentan en superficie las estructuras de contracción, pero también puede influir en otras propiedades como la tasa de deformación, algo que se ha descrito alrededor de Tharsis (e.g. Andrews-Hanna et al., 2008; Nahm y Schultz, 2011), sin dejar de mantener valores bajos. Como consecuencia, la presencia de estos grandes relieves puede afectar a los resultados obtenidos, como sucede con Bosporos Rupes debido a su localización sobre el anillo principal de la cuenca de impacto de Argyre (Herrero-Gil et al., 2019). 6.3.2. Contracción global De los principales procesos tectónicos responsables de generar procesos de deformación en la superficie de Marte, un periodo de contracción global asociado a enfriamiento planetario parece ser el único mecanismo capaz de producir la distribución global observada de grandes fallas inversas identificadas en Marte (Fig. 6.2) con las características que presentan estas estructuras (e.g. Golombek y Phillips, 2010; Nahm y Schultz, 2011). Un periodo de enfriamiento del interior del planeta daría lugar a un esfuerzo compresivo horizontal global y a una deformación contraccional cerca de la superficie (e.g. Turcotte, 1983; Schubert et al., 1992; Hauck et al., 2004). Los modelos térmicos de Marte predicen que el planeta se ha ido enfriando a lo largo del tiempo geológico, con una tasa de enfriamiento que no tiene por qué haber sido constante a lo largo del tiempo (e.g. Schubert y Spoon, 1990; Schubert et al., 1992; Ruiz et al., 2011). El pico de contracción global relacionado con este periodo de enfriamiento planetario se ha estimado que tuvo lugar durante el Noeico Tardío y el Hespérico Temprano (3800–3600 Ma; Hartmann y Neukum, 2001; Nahm y Schultz, 2011). El conjunto de fallas inversas analizadas en esta tesis doctoral, junto con otras estructuras de contracción presentes en las tierras altas y cuyas edades y orientaciones son similares y concordantes, parecen registrar en la superficie del planeta esta fase de contracción global que se ha atribuido a enfriamiento planetario (e.g. Anderson et al., 2001; Andrews-Hanna et al., 2008; Nahm y Schultz, 2011; Ruiz et al., 2011; Ruj et al., 2019). La contracción continuó durante el Hespérico Tardío (3600–3500 Ma), basado en la presencia de crestas sinuosas sobre los terrenos lisos del Hespérico que tapizan en algunas zonas las tierras altas del Noeico, y en sus correspondientes dataciones por conteo de cráteres (e.g. Mangold et al., 2000; Ruj et al., 2019). En algunas zonas en las tierras altas se han observado escarpes lobulados en terrenos del Noeico cuya morfología cambia a crestas sinuosas (e.g. Ruiz et al., 2012) al extenderse por estos terrenos Hespéricos, presentando un menor relieve, lo que puede indicar que algunas de estas grandes fallas inversas que se formaron y tuvieron su mayor desarrollo durante el periodo de contracción del Noeico Tardío/Hespérico Temprano, siguieron teniendo actividad o se reactivaron durante el Hespérico Tardío. CAPÍTULO 6 140 El pico de contracción global coincide temporalmente con las etapas 2 (Noeico Tardío) y 3 (Hespérico Temprano) de formación de Tharsis, cuando esta provincia tuvo su máximo crecimiento (e.g. Anderson et al., 2001; Phillips et al., 2001) y se estima que se formaron el 61% de estructuras de contracción asociadas a ella (Bouley et al., 2018). El pico de crecimiento se sitúa en la etapa 3, durante el Hespérico Temprano. Aunque el número de estructuras extensionales asociadas a Tharsis es homogéneo a lo largo del tiempo, la evolución de la tasa de deformación extensional es mayor durante el Noeico Tardío, teniendo su máximo también en el Hespérico Temprano (Bouley et al., 2018). Estas deformaciones están relacionadas con crecimiento cortical en respuesta a un levantamiento isostático y/o carga flexural de Tharsis. Sin embargo, la coetaneidad del periodo de máximo crecimiento de las estructuras de contracción en Tharsis y del periodo de contracción global lleva a pensar que algunas de las estructuras de contracción relacionadas con el periodo de contracción global, contribuyen a este pico de formación de estructuras de contracción en Tharsis durante el Hespérico Temprano (Bouley et al., 2018), como puede ser el caso de las fallas inversas estudiadas entre la cuenca de Argyre y los Montes de Thaumasia. Nahm y Schultz (2011) cuantificaron la contracción registrada en la superficie de Marte acomodada por las fallas inversas, utilizando la base de datos de fallas de Knapmeyer et al., 2006, 2008) (Fig. 2.4b). Esta extensa cartografía incluye alrededor de 15000 fallas clasificadas por edades, de las cuales algo menos de la mitad son fallas inversas, sin diferenciar entre fallas asociadas a escarpes lobulados o a crestas sinuosas. Las fallas asociadas a los escarpes lobulados pueden llegar a acomodar gran cantidad de acortamiento horizontal en la superficie de Marte, como se puede ver en los resultados de acortamiento calculados para la región de Amenthes, mientras que las crestas sinuosas, acumulan acortamientos del orden de decenas o centenas de metros (e.g. Plescia, 1993; Golombek et al., 2001; Schultz, 2000; Watters, 2004) pero son mucho más numerosas. Por ello, Nahm y Schultz (2011) calcularon un valor de contracción mínimo acomodado por todas las fallas inversas identificadas de -0.011%, considerando que todas las estructuras eran crestas sinuosas, y un valor máximo de -0.22%, considerando todas las estructuras como escarpes lobulados. Estos valores corresponden con una disminución del radio del planeta entre 0.19 y 3.77 km. Los valores superiores calculados suponiendo que todas las fallas son escarpes lobulados son una sobreestimación, ya que la mayoría de las fallas en la superficie de Marte son crestas sinuosas (Tanaka et al., 1991; Watters, 2004). Aún así, los valores de contracción y disminución del radio asociado obtenidos eran varias veces menores que los calculados mediante modelos térmicos (-0.4% y 1.33–27.9 km, Hauck y Phillips, 2002; Andrews-Hanna et al., 2008; Nahm y Schultz, 2011), llegando a la conclusión de que los modelos térmicos existentes sobreestiman la cantidad de acortamiento acomodada por las estructuras contraccionales. Posteriormente, Klimczak (2015) calculó la deformación asociada a la contracción global que puede acomodar la litosfera antes de la formación de fallas inversas atendiendo a la resistencia de la misma, CAPÍTULO 6 141 duplicando la cantidad de acortamiento global calculado por Nahm y Schultz (2011) hasta un valor de disminución total del radio de Marte de 0.4–6 km. Aún así, el valor de contracción global, y el subsecuente valor de decrecimiento del radio del planeta, sigue siendo varias veces menor que el calculado por los modelos de evolución térmica. El valor de contracción asociado a las grandes fallas inversas que forman escarpes lobulados podría constreñirse teniendo en cuenta el pliegue asociado con el desplazamiento de estas fallas y que el acortamiento que acomodan se transmite desde el nivel de despegue debido a la morfología lístrica, pero lo que más influiría en este cálculo sería incluir fallas subsidiarias, secundarias y menores, atendiendo a los resultados obtenidos en la Región de Amenthes. El cálculo de acortamiento asociado a las fallas inversas de Nahm y Schultz (2011) está sesgado por la resolución de 1km/px del modelo digital usado por Knapmeyer et al. (2006, 2008) para realizar esta cartografía (Fig. 2.4a), como ya observó Klimczak (2015). Actualmente, atendiendo a la mejora de la resolución de los datos disponibles, es posible identificar estructuras de menor tamaño asociadas a las fallas principales como fallas subsidiarias, o fallas secundarias o menores, lo que aumentaría considerablemente el número de estructuras a tener en cuenta en el cálculo de contracción del planeta. Esto supondría un aumento sustancial del valor de acortamiento global del planeta registrado por las fallas inversas, como se confirma en la modelización del conjunto de fallas inversas de la Región de Amenthes. Por otro lado, el cálculo de la disminución del radio asociado a los valores de contracción de las fallas de Nahm y Schultz (2011) tiene en cuenta el valor de profundidad de falla de 30 km calculado para Amenthes Rupes por Schultz y Watters (2001), que es un valor ligeramente superior al obtenido en esta tesis para la misma falla (20–24 km). Un mayor acortamiento asociado al desplazamiento de las grandes fallas inversas que forman los escarpes lobulados, como indican los resultados obtenidos en esta tesis, podría tener importantes implicaciones para la historia térmica de Marte, conllevando que la contracción que el planeta sufrió durante el periodo de enfriamiento del Noeico Tardío/Hespérico Temprano, y la disminución asociada del radio del planeta, son mayores de lo que se pensaba, generando un acercamiento a las estimaciones de contracción procedentes de los modelos de evolución térmica. CAPÍTULO 6 142 6.4. Perspectiva futura sobre el estudio de escarpes lobulados Los resultados de esta tesis están basados en los datos de las misiones Mars Global Surveyor (Albee et al., 2001), Mars Odyssey (Saunders et al., 2004) y Mars Reconnaissance Orbiter (Zurek y Smrekar, 2007). La información planetaria disponible va aumentando y mejorando con el envío de nuevas misiones espaciales, lo que implica la necesidad de estar al tanto de los datos disponibles en cada momento. Los datos de instrumentos enviados a analizar la superficie o sub-superficie, pertenecientes a misiones más recientes y aún no disponibles, podrían mejorar la comprensión que tenemos sobre estas fallas inversas en un futuro cercano. El análisis de los datos obtenidos por el radar MARSIS, enviado a bordo de Mars Express (Picardi et al., 2004) podría aportar información importante sobre la distribución de la deformación en las zonas más superficiales de las fallas inversas analizadas. Del mismo modo podría ser clave en el estudio de las fallas inversas localizadas en las tierras bajas del norte, permitiendo identificar la potencia de las unidades que las tapan y arrojando luz sobre estas estructuras enterradas. Por otro lado, el sismógrafo SEIS, recientemente enviado a Marte en la misión Insight (Lognonné et al., 2019), ha reportado datos de actividad sísmica en el presente. La transición frágil- dúctil define la profundidad potencial máxima a la que pueden llegar las fallas en la parte superior competente de la litosfera, por lo que es clave para entender los registros de actividad sísmica en Marte (e.g. Watts y Burov, 2003). Estos parecen indicar la presencia de actividad tectónica actual asociada a fallas extensionales que forman grabens en la región de Elysium Mons (Giardini et al., 2020), cuya formación ha sido relacionada con la existencia de diques (Rivas-Dorado et al., 2019). El aumento del registro de actividad sísmica en Marte permitirá conocer si alguna de estas estructuras de contracción repartidas por el planeta aún presenta actividad tectónica. Además, este aumento del registro y su análisis detallado también permitirá interpretar cómo están estructuradas internamente la corteza y la litosfera basándose en la atenuación de las ondas sísmicas en profundidad (Lognonné et al., 2020). Del mismo modo, el desarrollo de softwares de modelización que implementan métodos estructurales ya aplicados en la Tierra, puede ser un gran avance en el estudio de otros planetas si los enfocamos y adecuamos a las características e información disponible del cuerpo planetario en concreto. Los tres métodos aplicados en esta tesis son el reflejo de esta evolución y se aprecia una mejora en la cantidad de información que podemos obtener de la utilización de cada uno. Realizar estudios estructurales de este tipo en otras fallas o sistemas de fallas en diferentes regiones de Marte ampliaría la información que tenemos sobre las propiedades y características de estas estructuras, permitiendo comparar resultados y sacar conclusiones más fiables a escala global de los mismos. CAPÍTULO 6 143 El periodo de contracción global al que se asocia la formación de estas estructuras suscita interés y crea polémica en cuanto a su duración y causa. La mejora de la cartografía de estructuras a nivel global es un trabajo extenso que además debería completarse con un estudio detallado de las edades de formación de las grandes fallas inversas. Esto podría confirmar que su formación está ligada y relacionada con un periodo de contracción global y, por lo tanto, mejorar la comprensión de dicho evento. 7 CONCLUSIONES CAPÍTULO 7 147 Un total de ocho grandes fallas inversas localizadas en la superficie de Marte, en las regiones de Aonia Terra y Amenthes Region, han sido analizadas y modelizadas en esta tesis doctoral. Para estudiar los relieves topográficos asociados a estas fallas inversas, conocidos como escarpes lobulados, se han aplicado tres métodos de modelización diferentes, que han demostrado ser individualmente un buen enfoque a la hora de estudiar las fallas que subyacen los escarpes lobulados, proporcionando un marco de comparación que ha permitido discutir y constreñir los resultados obtenidos. Las estructuras analizadas son reflejo de una actividad litosférica dinámica en el Noeico Tardío/Hespérico Temprano, y los resultados obtenidos han permitido interpretar aspectos relacionados con su formación que mejoran la comprensión de la geodinámica del planeta; proporcionando ideas sobre el evento de contracción y los procesos tectónicos asociados, o la estructura interna de la litosfera. Conclusiones sobre las características geométricas de las fallas. El análisis y la modelización de la superficie topográfica elevada por el desplazamiento de las fallas inversas han permitido obtener una aproximación a las características geométricas que definen los planos de las fallas en profundidad. Marte es un planeta de tipo terrestre, y como tal sus propiedades no varían sustancialmente de las de la Tierra, pudiendo observar que las grandes estructuras de contracción estudiadas presentan características similares a algunas fallas inversas terrestres. • Los perfiles longitudinales que reflejan la variación de altura de los escarpes lobulados, y los perfiles de distribución lateral del desplazamiento obtenidos en los modelos 3D, representan que el desplazamiento es generalmente mayor en la zona central de las fallas, disminuyendo de forma progresiva hacia los bordes laterales de las mismas. • Los valores de buzamiento obtenidos para la mayoría de las fallas inversas modelizadas varían entre 23° y 33°, estando dentro del rango de buzamientos observado para fallas inversas en la Tierra (20°–35°) (e.g., Jaeger y Cook, 1979; Brewer et al., 1980; Stone, 1985; Watters y Nimmo, 2010). Ogygis Rupes presenta un buzamiento ligeramente mayor (35°–39°) correspondiendo con valores obtenidos en estudios previos en escarpes lobulados (20°–40°) (e.g. Egea-González et al., 2017). • Los resultados de los modelos 3D muestran que estas fallas tienen un buzamiento constante durante los primeros kilómetros que va disminuyendo en profundidad hasta enraizarse en un nivel subhorizontal, dando lugar a una morfología lístrica CAPÍTULO 7 148 en profundidad, que responde a la forma que presentan el flanco trasero y el sinclinal trasero de dichas estructuras. Conclusiones sobre la estructura mecánica de la litosfera en el Noeico Tardío/Hespérico Temprano. Las profundidades de despegue de las fallas que subyacen los escarpes lobulados modelizados permiten interpretar aspectos de la estructura mecánica que presentaba la parte superior competente de la litosfera en el momento de formación de estas estructuras. • Los resultados de profundidad obtenidos para las grandes fallas modelizadas concuerdan con resultados previos obtenidos al modelizar fallas inversas en Marte, apoyando un nivel de despegue profundo que sugiere la presencia de una importante discontinuidad mecánica global en la litosfera. Esta discontinuidad mecánica ha sido relacionada con la profundidad de la transición frágil-dúctil en el Noeico Tardío/Hespérico Temprano. El dominio frágil en la corteza se extiende hasta una profundidad de 17.2–25 km en la zona de Aonia Terra y hasta 20–24 km de profundidad en la región de Amenthes • Las fallas subsidiarias y secundarias modelizadas presentan profundidades de 2.3– 5.6 km en la zona de Aonia Terra, y 9.5–13 km en la región de Amenthes, lo cual refleja la posible presencia de discontinuidades mecánicas regionales dentro del dominio frágil en la corteza. Conclusiones sobre la influencia de las grandes provincias tectónicas en la formación de las fallas inversas estudiadas. Las grandes provincias tectónicas presentes en la superficie de Marte crean una serie de variaciones laterales de espesor cortical que condicionan los campos de esfuerzos presentes cuando se formaron las grandes fallas inversas que forman los escarpes lobulados estudiados en el Noeico Tardío/Hespérico Temprano. La presencia de estas grandes provincias condiciona la orientación de estas estructuras de contracción y, aunque aparentemente no son la causa de su formación, sí pueden influir en los resultados obtenidos. • La orientación de las grandes fallas inversas estudiadas entre los Montes de Thaumasia y la cuenca de impacto de Argyre, y de otras estructuras de contracción paralelas presentes en la zona, parece responder a un campo de esfuerzos compresivo que formó estas estructuras en el Noeico Tardío/Hespérico Temprano, cuya orientación estaba controlada por el campo gravitacional de Tharsis, y, en menor medida, por la presencia de la cuenca de impacto de Argyre. CAPÍTULO 7 149 • Las profundidades de las grandes fallas estudiadas entre los Montes de Thaumasia y la cuenca de impacto de Argyre sugieren que el dominio frágil se encuentra engrosado bajo el anillo principal de la cuenca de Argyre. Sin embargo los valores de flujo térmico obtenidos no apoyan este engrosamiento y parece ser la presencia del relieve del anillo previo a la deformación que formó las grandes fallas inversas estudiadas, el que condiciona los resultados de profundidad altos obtenidos para Bosporos Rupes. • El sistema de fallas inversas de Amenthes presenta una orientación paralela a la dicotomía que también se observa en otras fallas localizadas en áreas adyacentes. Este sistema de fallas se ha modelizado siguiendo una dirección media de acortamiento N36.6°E, perpendicular a la orientación general del sistema de fallas, lo que sugiere que existen variaciones laterales de las propiedades litosféricas asociadas a la dicotomía que condicionaron la orientación del campo de esfuerzos regional de la época en la que se formó el sistema de fallas hace 3600–3700 Ma. Conclusiones respecto al episodio de contracción global que generó estas estructuras. La distribución global de las grandes fallas inversas sobre la superficie de Marte junto con las características topográficas similares que presentan y las dataciones realizadas en trabajos previos, que sitúan la formación de estas grandes estructuras de contracción en el Noeico Tardío/Hespérico Temprano, sugieren que su génesis está relacionada. La formación de estas estructuras se ha relacionado con un evento de contracción global, relacionado con un pulso de enfriamiento del planeta en esta época, por lo que el análisis de cómo se acomoda esta contracción en las grandes fallas inversas nos ayuda a entender este evento de deformación. • La forma lístrica que presentan los planos de falla al llegar al nivel de despegue implica que el acortamiento regional acomodado por esta falla es transmitido por completo desde el nivel de despegue, siendo su valor igual al desplazamiento total sobre el plano de falla. Esto incrementa la estimación del acortamiento asociado a estas grandes fallas entre un ∼6% y un ∼30% más (dependiendo del ángulo de buzamiento de la misma) con respecto a cálculos previos en los que las fallas eran modelizadas como estructuras que presentan un buzamiento constante en profundidad. Esto supondría un aumento importante en las estimaciones de acortamiento acomodadas por las fallas que subyacen los escarpes lobulados si se confirmase que el acortamiento asociado a la falla es transmitido desde el nivel de despegue. • Al modelizar el sistema de fallas de Amenthes en conjunto se ha obtenido un valor medio del acortamiento regional de entre 2000 y 3000 m, que aumenta hasta un CAPÍTULO 7 150 máximo de ∼5450 m en la zona sur. Este valor de acortamiento supone un incremento respecto al valor de acortamiento regional calculado previamente de entre un 60% y un 200%, debido principalmente a que en el cálculo se han incluido fallas secundarias y menores. 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Journal of Geophysical Research 112 (E5), E05S01. ANEXO I Herrero-Gil, A., Egea-González, I., Ruiz, J., Romeo, I., 2019. Structural modeling of lobate scarps in the NW margin of Argyre impact basin, Mars. ICARUS 319, 367–380 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Structural modeling of lobate scarps in the NW margin of Argyre impact basin, Mars Andrea Herrero-Gila, ⁎ , Isabel Egea-Gonzálezb, Javier Ruiza, Ignacio Romeoa a Departamento de Geodinámica, Estratigrafía y Paleontología, Facultad de Ciencias Geológicas. Universidad Complutense de Madrid, 28040 Madrid, Spain bDepartamento de Física Aplicada, Escuela Superior de Ingeniería. Universidad de Cádiz, 11519 Puerto Real, Cádiz, Spain A R T I C L E I N F O Keywords: Lobate scarp Mars thrust fault depth of faulting heat flow A B S T R A C T Martian lobate scarps are prominent tectonic structures interpreted to be the topographic expression of large thrust faults generated under compression. Here, we present a structural modeling performed on three large lobate scarps (Ogygis Rupes, Bosporos Rupes and Phrixi Rupes) located in the heavily cratered highlands of Mars, specifically in Aonia Terra, between Thaumasia Montes and Argyre impact basin. These lobate scarps, formed in the Late Noachian/Early Hesperian, strike parallel to the edge of the Thaumasia Montes, and were generated by ESE-vergent thrust faults. Structural analysis of craters deformed by these lobate scarps gives minimum estimates for the faults slip of ∼1700–3100m. We applied two structural methods in order to con- strain the geometry of these thrust faults at depth, area balanced cross sections and forward mechanical dis- location modeling, obtaining a depth of faulting in this area between ∼18 and ∼45 km, and dip angles between 23° and 35°. These results are consistent with previous studies of lobate scarps on Mars. The depth of faulting gives an estimation of the depth of the brittle-ductile transition at the time of its formation giving a range of depth in which the state of the lithosphere change from brittle to ductile-dominated deformation. The heat flow values calculated from the obtained depths of the brittle–ductile transition range from 25 to 51mW m−2. We show that the brittle-ductile transition depth in Aonia Terra is set in 18–27 km at a larger distance from the basin center, while it is deeper closer to the Argyre rim (∼33–45 km). This difference seems to indicate a thickening of the brittle domain under Argyre main rim with respect to the external area but, attending to regional geology and heat flow values calculated, this high value (∼33–45 km) might be an overestimation of the depth of faulting caused by the presence of the crater rim elevation before the formation of the lobate scarps. 1. Introduction Lobate scarps are the largest compressive structures described on planetary surfaces (e.g. Strom et al., 1975; Watters, 1993; Schultz and Watters, 2001; Watters et al., 1998, 2015), with lengths of even hun- dreds of kilometers and elevations of up to thousands of meters. These structures show a roughly arcuate to linear form in plan view and an asymmetric cross section characterized by a steep frontal scarp and a gently dipping back slope with a trailing depression. This topographic profile have been interpreted as a reverse fault propagation anticline with a trailing syncline, so lobate scarps are considered to be the to- pographic expression of large thrust faults (e.g. Strom et al., 1975; Watters and Robbinson, 1999; Watters and Nimmo, 2010), deforming the crust down to the depth of the brittle-ductile transition (BDT) (e.g. Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017). Several studies on the properties of the thrust faults related to lobate scarps on Mars have been performed. Schultz and Watters (2001) calcu- lated that Amenthes Rupes extends up to 25–30 km depth using the me- chanical dislocation model. The same structure has been studied by Grott et al. (2007) giving a depth of faulting of 35–40 km and by Ruiz et al. (2008) obtaining a depth of faulting between 27 and 35 km, both using an elastic dislocation modeling too. Mueller et al. (2014) calculated a depth of faulting for Amenthes Rupes using a fault propagation fold theory for a listric fault geometry and, despite that the dip angles obtained by these authors are clearly higher, their depths of faulting range between 33 and 48 km. Attending to other similar studies located in other regions, Grott et al. (2007) used a dislocation model to study two large lobate scarps in the south of Thaumasia, which seem to have characteristics more similar to the scarps studied here, striking parallel the edge of Thaumasia and having a relief slightly higher than a thousand meters. These authors get the best fit model for depths of faulting of 27–35 and 21–28 km. Egea- https://doi.org/10.1016/j.icarus.2018.09.027 Received 26 February 2018; Received in revised form 11 September 2018; Accepted 22 September 2018 ⁎ Corresponding author. E-mail address: andreaherrero@ucm.es (A. Herrero-Gil). ANEXO I 169 González et al. (2017) modelized eight different lobate scarps around Hellas impact basin, including Amenthes Rupes, obtaining for them depths of faulting between 13 and 45 km. Here we present the results of the structural modeling at depth of three large lobate scarps (Ogygis Rupes, Bosporos Rupes and a third unnamed one) in Aonia Terra, region located in the southern highlands of Mars, between the Thaumasia Montes and the northwest margin of the Argyre impact basin. The Argyre basin, formed during the Noachian time (Dohm et al., 2015), is one of the largest impact basins on Mars and the best preserved of the multi-ringed impact basins. Hiesinger and Head (2002) defined at least seven rings, with an uncertain eighth ring because of its discontinuity, using the criteria of Pike and Spudis (1987). The studied lobate scarps strike parallel to the edge of Thaumasia in this area, like other compressive structures present as wrinkle ridges, which are the surface expression of minor blind thrust faults, reflecting folding and thrust faulting (e.g. Bryan, 1973; Plescia and Golombek, 1986; Mueller and Golombek, 2004; Watters, 2004), easily recognizable by their uniform spacing and a narrow surface ridge superposed on a broad rise (Golombek et al., 1991). The presence of craters cut by the lobate scarps indicates that the faults underlying these lobate scarps broke the surface. The knowledge of the structural parameters of the faults underlying these lobate scarps, including an estimation of the depth of faulting, will provide constraints on the depth of the BDT and their spatial variation in relation to the lithospheric structure and mechanical state around the Argyre basin in the late Noachian/Early Hesperian time, when the lobate scarps were formed (Hartmann and Neukum, 2001; Tanaka et al., 2014). While lobate scarps are considered to be formed by thrust faults extending to the BDT (e.g. Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017), there is no consensus about wrinkle ridges structure and depth of faulting (e.g. Zuber and Aist, 1990; Watters, 1991, 2004; Allemand and Thomas, 1995; Watters and Robinson, 1997; Schultz, 2000; Mueller and Golombek, 2004), conse- quently, wrinkle ridges are not studied in this work. The BDT is temperature-controlled, and therefore its depth can be used to model the thermal structure of the crust and the heat flow at the time of faulting. Thus, previous works have found Late Noachian/Early Hesperian heat flows to be usually between ∼25 and ∼40mW m−2 at the circum-Hellas region (including Amenthes Rupes) and Thaumasia highlands (Ruiz et al., 2008, 2009, 2011; Mueller et al., 2014; Egea- González et al., 2017). This heat flow range is similar to that found for other non-volcanic regions of similar age from the effective elastic thickness of the lithosphere (McGovern et al., 2004; Ruiz et al., 2011). Thus, modeling the thermal structure of the crust and the surface heat flow at the Aonia region serves to enlarge our knowledge of the thermal state of Mars in a time when large changes occurred in its internal dynamics (for a review see Ruiz, 2014 and references therein), and permits a first assessment, for that time, of the magnitude of the var- iation of heat flow through the southern highlands of Mars. Finally, it is worth mentioning in this point that a high depth of faulting is suggestive, but non demonstrative of that the large lobate scarps represent the BDT. In any case, the obtained fault depths re- present a consistent lower limit to the BDT, which can be used to obtain mechanical constraint and robust heat flow upper limits for the time of faulting. Moreover, the general consistency of deduced thrust fault depths throughout the Martian geography by the previous works (and by the present study) does not seem consistent with depths of large faults being controlled for local compositional transitions. Thus, we consider our results as representative of the BDT depth. 2. Geological setting and structural mapping The knowledge of the relations between lobate scarps and other surrounding structures and lithologies is a fundamental issue to un- derstand the structural framework and the geological units affected by contraction associated with lobate scarps formation. Thus, we per- formed a detailed structural and geological map (Fig. 1) of the study area to provide a geological setting of the area where lobate scarps were formed. This geological and structural mapping was performed through the analysis of the Thermal Emission Imaging System (THEMIS, Mars Odyssey mission) daytime infrared (IR) model, which is a 100 m/pixel mosaic (Christensen et al., 2004) and the Digital Elevation Model (DEM) based on data from the Mars Orbiter Laser Altimeter (MOLA; Zuber et al. 1992; Smith et al., 2001), an instrument on NASA's Mars Global Surveyor (MGS, Albee et al., 2001) with a 1/128° resolution (about 463m/pixel). Previous works mapping this area were made for Thaumasia (Dohm and Tanaka, 1999; Dohm et al., 2001) and Argyre basin (Dohm et al., 2015), both focused on very large structures com- pared with the region where the three lobate scarps studied are located. We have analyzed the topography surface using MOLA model attending to topographic profiles and slope changes. This, together with the high resolution of THEMIS images, allow us to be more accurate delineating geological units and tectonic structures, and as a result, we have created a more detailed map of the studied area according to the map scale. This part of Aonia Terra is considered as the transition zone between the Thaumasia highlands mountain region and the Argyre impact basin. The geological units used and their descriptions are those defined by Dohm et al. (2015) in their study of Argyre basin. Geologically, we can divide the mapped area in two general zones: (1) the highlands where the lobate scarps were formed, and (2) the basin and rim materials associated with the Argyre impact basin. The highlands materials are mostly from Noachian time (Nh1, Nh2, Nhb) and they show a smooth to slightly rough surface. Over these materials, there are others younger, of Noachian-Hesperian age, easily identifiable because they have a smoother surface (HNh3, HNh4). The rim and basin materials (NArsp, NAbr, NAr, NAb1, NAb2, NAb3) of the Argyre basin have a Noachian age, and show irregular roughly surfaces. Impact crater materials (C1, C2, Cfs, Cfr) postdate the Argyre impact deposits (see Dohm et al., 2015 for a detailed description of the units). Compressive structures in Aonia Terra, both wrinkle ridges and lo- bate scarps, strike roughly parallel to the edge of Thaumasia Montes, but in this transient zone, the Thaumasia edge is slightly parallel to the Argyre structure (Dohm et al., 2015) and the compressive structures at some points also appear to be parallel to Argyre rings. Conversely, the few (∼7) small grabens present in the studied area show a perpendi- cular strike to the compressive structures, presenting radial patterns with respect to Thaumasia Montes and therefore to Tharsis (Okubo and Schultz, 2003). Our map (Fig. 1) and other previous studies (e.g. Watters, 1993; Watters and Robinson, 1999) show that Martian lobate scarps occur mainly in intercrater plains in the heavily cratered highlands of the planet. The thrust faults that generated Ogygis Rupes, Bosporos Rupes and Phrixi Rupes in Aonia Terra uplift the oldest formation in the highlands of this area (Nh1) which seems to be more resistant to ero- sional agents than the surrounding formations. The asymmetry in the cross sections suggests that the three lobate scarps were generated by ESE-vergent thrust faults. An associated backthrust fault (a subsidiary fault with an opposite vergence to the main thrust fault (McClay, 1992)) appears at the backlimb in some segments of the lobate scarps. Ogygis Rupes (Fig. 1(a); Table 1) is a single surface breaking scarp striking N30°E with 190 km in length verging ESE. It has a backthrust fault verging WNW in the northeastern half. The slip in this backthrust increases towards the NE in the overlapping zone together with a decrease of the slip of the main fault towards its tip point. Phrixi Rupes (Fig. 1(b); Table 1) which is located southwest of Ogygis Rupes and Bosporos Rupes, strikes N52°E and is 195 km long. It is divided in two segments, showing a right-stepped pattern, the northeast 85 km long and the southwest 140 km long, with an overlapping zone of 30 km where they are separated from each other 12 km. Bosporos Rupes (Fig. 1(c); Table 1) is approximately 590 km long and it is also formed by two segments. In this case both segments are divided into several branches in the overlapping zone, being difficult to separate them. Taking into account a slight change in the direction we have identified A. Herrero-Gil et al. ANEXO I 170 the northern segment, which strikes N43°E and is 297 km long, and the second one located south of the first, striking N34°E which is 293 km long. They are arranged showing a left-stepped pattern. There exists a big backthrust throughout most of this structure, located at an average of 100 km from the scarp base and reaching elevations of up to 800m, which allows to identify a "pop up" structure in some transversal to- pographic profiles. Wrinkle ridges in our map area are parallel to these lobate scarps and they are mostly in the NNE half of the map, appearing mainly in the younger materials with smooth surface (HNh3, HNh4). Wrinkle ridges are more numerous and frequent than lobate scarps and Fig. 1.. Geological and tectonic map over THEMIR-IR Day Global Mosaic 100m. Ogygis Rupes, Phrixi Rupes and Bosporos Rupes are shown by light red lines and named as a, b and c, respectively. Backthrust faults are shown by dark red lines. Inset globe, colored with the MOLA model, shows the map location. The geological units and their description are from Dohm et al. (2015). Note that the north in the map is rotated. The location of deformed craters from Fig. 5 are shown. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) A. Herrero-Gil et al. ANEXO I 171 ANEXO I 172 3.2. Balanced cross sections method The balanced cross sections method (Chamberlin, 1910, 1919), also known as Chamberlin approach, consists in the application of geometric relations to geological structures analysis assuming plane deformation so the displaced area in a cross-section is preserved during the deformation process, existing a balance of areas between the state prior to deformation and the deformed state. In this way, in a compressional scenario, the material uplifted above the regional level in a cross-sec- tion (A) has to equal the amount of material laterally displaced on the decollement at depth, assuming volume conservation (Fig. 3) and it can be obtained by A=dh, where d is the horizontal displacement on the Fig. 2.. Two possible scenarios of a fault cutting a crater are shown in plant view and cross-section. (a) The fault cuts the crater separating the rim in two identifiable arcs. The red cross indicates the crater center location before deformation. The orange cross indicates the crater center location obtained from the displaced rim arc. The distance between both centers (yellow arrow) is the horizontal displacement (Δx). The elevation difference between the two arc rims is the vertical displacement (Δy). (b) The fault cuts the crater close to its edge destroying part of the rim. The red cross shows the crater center. The displacement measured is a minimum (Δx’) because the initial location of the fault surface rupture (gray dashed lines) and the strike of the fault horizontal slip vector are unknown (some displacement possibilities are shown by orange arrows). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 3.. Representation of the balanced cross section method (based on Groshong, 2006). The excess area above the regional level corresponds to the displaced area at depth (both in gray) and it is directly related to the displacement and the depth of faulting by A=dh. The displacement (d) can be estimated by adding the horizontal fault slip (Δx) to the shortening generated by the fold (Lf – W), d= Δx+ (Lf – W). Fig. 4.. Lengthwise profiles for each lobate scarp showing the vertical displacement distribution (vertical exaggeration x5) along the fault. The dashed black line shows the highest elevation of the lobate scarp (z') (corresponding to the fault propagation fold crest), while the solid black line is the scarp base (z). The gray area (Δz) is the difference between the scarp base and the highest elevation of the lobate scarp. The solid yellow line indicates the top of the scarp face. Vertical red lines mark the points of maximum elevation for each segment. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) A. Herrero-Gil et al. ANEXO I 173 decollement and h is the depth of faulting (depth of the decollement where the thrust faults root). Therefore, we can calculate the depth of faulting (h) knowing the uplifted area (A) and the horizontal dis- placement (d). The difference between the initial state and the de- formed state of the topographic surface, assuming that it has been only modified by tectonics, can be used to measure the horizontal dis- placement (Dahlstrom, 1969; Moretti and Carrot, 2012). The total horizontal displacement of the thrust on the decollement is accom- modated by a fold and the rupture of the fault on the surface (Δx). The horizontal displacement accommodated by the fold is given by Lf – W (Fig. 3), where Lf is the longitude of the fold measured along the to- pographic surface and W is its horizontal projection. Thus, the hor- izontal displacement on the decollement can be estimated by d = Δx + (Lf – W). The horizontal component of slip on the fault at the surface (Δx) has been estimated by structural analysis of cross-cut craters (providing a minimum estimation, see Section 3.1). Since the topographic profile for each cross section studied and the deformed craters do not occur at the same position on the fault trace, a propor- tional escalation of Δx has been done using the elevation of the lobate scarp (Δz) given by the vertical component of the fault offset (Fig. 4). The same proportional escalation has been done to estimate the hor- izontal slip component on the fault at surface in the segments where there are no cross-cut craters, assuming that the vertical elevation and the horizontal slip are directly related. 3.3. Forward mechanical dislocation method This method is based on the modeling of a fault that reproduces the observed topography across the lobate scarp, and it has been previously used to analyze thrust faults on Mars (Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Egea-Gonzalez et al., 2017), as well as on other planetary bodies including Mercury (Watters et al., 2002; Egea- Gonzalez et al., 2012), the Moon (Williams et al., 2013), and asteroid 433 Eros (Watters et al., 2011). Here, we use the forward mechanical dis- location modeling software Coulomb (Toda et al., 1998; Lin and Stein 2004; Toda et al., 2005) to model displacements on the surface caused by thrust faulting. The fault is idealized as a rectangular plane with a spe- cific length, dip angle and vertical depth of faulting. The program esti- mates the surface deformation caused by the fault movement following Okada (1992) for an elastic halfspace with uniform isotropic elastic properties. This method provides good fits for the topography above a fault for a limited range of parameters (Cohen, 1999; Schultz and Lin, 2001). Non-planar fault geometries such as positive listric faults have been previously proposed to be the cause of lobate scarps formation (Watters and Nimmo, 2010), but elastic dislocation modeling of listric thrust faults does not provide model fits as good as planar geometries in this case (Schultz and Watters, 2001; Watters et al., 2002). We set a crustal elastic modulus of 80 GPa and Poisson's ratio of 0.25 (Schultz and Watters, 2001). The coefficient of friction was 0.7, corresponding to the value for reverse faults. We have kept these parameters fixed since these values are comparable to those used when modeling the deformation associated with fault offset in the continental crust on Earth (e.g. Freed and Lin, 1998; Schultz and Watters, 2001) and reasonable variations in these parameters do not produce sig- nificant variations in the results (Watters et al., 2002; Grott et al., 2007; Ritzer et al., 2010; Egea-González et al., 2017). There are four principal variables that can be adjusted to fit the model output profile with the stacked MOLA topographic profiles: the offset value, the fault dip angle, the depth of faulting and the dis- placement distribution along the fault plane. These parameters are in- terrelated, but it is roughly possible to determine how the variation of each of them affects the output profile. An increase in the fault slip entails a higher elevation. A deeper depth of faulting results in a wider and bulkier crest, while a shallower depth produces a narrower struc- ture in the surface and a trailing syncline topographically below the scarp base. Lower dip angles provide a bulkier backlimb and a wider ridge, similar to an increasing in depth but less accused, while higher dips entail a steeper backlimb. The distribution of the displacement along the fault also influences the fit. A displacement distribution de- creasing towards the edges of the fault plane generally improves the fit in our studied cases, generating more rounded shapes in the output profile, which are more similar to what we see in the topographic profiles than the result of a regular distribution, which generates pro- files with angular and abrupt shapes (Schultz and Watters, 2001). Best fit adjustments between predicted topography and stacked to- pographic profiles of the lobate scarp have been obtained varying sys- tematically and iteratively these parameters until getting the best visual fit for each fault. The forward mechanical dislocation modeling pro- vides more than one possible solution, (Egea-González et al., 2017) so we have chosen those values within reasonable ranges for a thrust fault, which fit fairly well with real topography. The main limitation of this method is that it does not take into ac- count the fault propagation folding including plastic deformation and distributed brittle deformation so there can exist differences between the topographic and the modeled profile, but it has been demonstrated to be a good approximation while modeling a topographic elevation caused by long-term deformation due to cumulative fault offsets (e.g. King et al., 1988; Taboada et al., 1993; Cohen, 1999). Other limitation of this modeling procedure is that fault slip decreases at the bottom of the fault plane and it is not transmitted from a horizontal decollement. The volume loss due to erosion and subsequent sedimentation might modify surface topography, being another factor that could cause dif- ferences in the adjustments. However, erosion in Mars is considered to have a very low rate (e.g. Golombek and Bridges, 2000; Golombek and Phillips, 2010). The studied lobate scarps present a good state of pre- servation lacking significant evidence of topographic degradation, which leads us to assume that the erosional rates in this area of Aonia Terra have remained low since lobate scarps formation. 4. Structural analysis and modeling Variations of vertical fault displacement along lobate scarps can be obtained from lengthwise topographic profiles (Fig. 4) in which there are represented the maximum scarp heights (z') corresponding to the fault propagation fold crest, and the scarp base heights (z). The heights of the scarp face (sharp plane defined by the highest slope) are also shown, which may or may not coincide with the scarp crest. When a lobate scarp is characterized by different fault segments and these segments overlapped, we represent the scarp crest of the highest seg- ment and the scarp base of the segment located SE. The height values plotted along the fault length provide a frontal view of the lobate scarp elevation (Δz = z′ – z), which is a minimum estimation of the vertical component of fault displacement. If we ignore the material deposited from the scarp face and the possible erosion by the engagement of surface runoff in the scarp base, the scarp base (z) should correspond with the regional level. Ogygis Rupes has the maximum scarp relief almost in the center of the structure (Δz≈2115m), decreasing towards the edges. Phrixi Rupes, which is divided in two segments, has the maximum vertical displacement in the center of its northeastern segment (Δz≈1250m) while the southwest segment has a very small scarp relief throughout its length. Bosporos Rupes is a long structure with an irregular surface also divided in two segments. Its topography is heavily modified and we cannot identify a clear trend in the scarp heights distribution although there is a slight decrease towards the edges. When removing the crater depressions at the base of the scarp (Fig. 4), the maximum scarp relief belongs to the northeastern segment (Δz≈1570m). The vertical fault displacement distribution shown by each segment of the studied lobate scarps, corresponds with a displacement in the fault plane greater in the center and smaller towards the edges (Fossen, 2010) in the fault plane. Displacement–Length relationships of the faults underlying the lobate scarps have also been calculated attending to these observations. A. Herrero-Gil et al. ANEXO I 174 4.1. Results of the cross-cut craters There are three craters affected by the studied lobate scarps. The diameters of the examined craters are between 17 and 28 km. The re- solution of the MOLA model (463m/pixel) limits the use of this data set for determining the deformation of craters when the horizontal fault slip is under this spatial resolution. The first one (Fig. 5(a)) is located ap- proximately in the center of Ogygis Rupes. The upper fault block appears thrusting on the edge of the crater rim (case shown in Fig. 2(b)). The side of the crater affected by the lobate scarp shows an arched geometry concave towards the center of the crater. First, we adjusted a cir- cumference to the undeformed part of the crater rim and another one to the arched line of the deformed side of the rim, and then we measured the distance between their centers, providing measure of the horizontal shortening (Δx′1=1310m). An equivalent procedure was followed using the same centers to adjust two more circumferences to the bottom line of the crater to verify that the shortening value is similar (1330m). The same procedure was used with the second crater (Fig. 5(b)) which is located in the backlimb of the northern part of Ogygis Rupes lobate scarp. In this case the crater is not cut by the main lobate scarp but it is affect by a backthrust verging NW which continues northwards (Fig. 2(a)). The horizontal shortening measured (Δx′2) is 970m. This result seems to indicate that this backthrust of Ogygis Rupes acts as a relay fault of the main lobate scarp as the structural map shows (Fig. 1). The mean elevation difference between the two rim arcs (Δy) is 700m, allowing to estimate a dip of faulting of approximate 36° for Ogygis backthrust given that tg θ = Δy/Δx. The third crater (Fig. 5(c)), which is over Bosporos Rupes, could be an example of scenario 2 (Fig. 2(a)) but, in this case, the crater modifies the lobate scarp topography and it is also affected by the fault that forms the lobate scarp, dividing the crater in half. Because of that, we interpret it to be synchronous with the fault movement, in a way that the impact took place after the first stages of formation of Bosporos Rupes but before the last fault activity. We calculated the center of the circumferences that best fit each of the two sectors in which is divided the crater rim in order to analyze the dislocation of this crater. The horizontal slip (Δx3) is estimated to be the distance between the two circumference centers and it is 580m. If we broadly compare the elevation of the lobate scarp in this point (Δz≈1000m), with the height difference between the two halves of the crater (∼300m) it can be deduced that the total thrust fault movement is approximately three times larger than the last movements registered by the crater. Furthermore, the displacement vector obtained is almost par- allel to the direction of the scarp, which would imply a strike sinistral kinematics at least for the last movements of the fault, highly contra- dictory with the thrust fault characteristics shown by Bosporos Rupes. But, it is also necessary to take into account that the measured horizontal shortening is small compared to the pixel size of the THEMIS and MOLA (100 m/pixel and ∼463m/pixel, respectively) that we have used to Fig. 5.. Analysis of cross-cut craters. Red circumferences represent the best fit for the undeformed crater rim. Color grids show the mean squared error of the distance from each grid point to the crater rim. The location of the minimum value of the mean squared error is the best estimation of the crater center. Orange lines are adjusted to the crater rim of the deformed side. (a) Crater deformed by Ogygis Rupes. (b) Crater deformed by a backthrust on the norther termination of Ogygis Rupes. (c) Crater deformed by Bosporos Rupes northern segment, in this case the orange circumference fit the arc of the crater rim on the hanging wall and grids for calculating both circle centers are shown. The yellow arrows indicate the horizontal components of slip (Δx). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) A. Herrero-Gil et al. ANEXO I 175 measure it. For these reasons, we cannot use this horizontal slip measure in the balanced cross section analysis. The vertical component associated with the horizontal displacement was not registered in the crater rim be- cause half of the crater rim was formed over a previously elevated fault block. The measure of the vertical displacement associated to the last fault displacement in the bottom of the crater cannot be performed because this surface is highly irregular due to surface runoff modifications. 4.2. Results of the balanced cross sections Applying the balanced cross section method (Fig. 3) to the mean profile of the stacking topographic profiles for each lobate scarp, re- presented in Fig. 6, we have calculated the fault parameters (Table 2). Final length (Lf) and the length of the structure at regional level (W) can Fig. 6.. Forward mechanical dislocation method best fit models compared with MOLA stacked topographic profiles (gray area) for each lobate scarp. The mean topographic profiles, calculated after removing craters, are also shown. THEMIS model images attached to each graphic show the location of the area where the topographic profile stacking was performed. Table 2. Fault parameters and calculated surface heat flows intervals. Balanced cross section Forward mechanical dislocation Heat flow Fault slip (m) Depth of faulting (km) Fault slip (m) Dip angle (°) Depth of faulting (km) FS (Diabasa) mW/m2 Ogygis Rupes 2900 18 2500–3100 35 27–20 30–51 Phrixi Rupes 2000 24.5 1700–1850 33 36–25 26–40 Bosporos Rupes 1700 45 2650–2750 23 41–33 25–33 A. Herrero-Gil et al. ANEXO I 176 be measured in each mean profile, allowing to calculate the uplifted area (A) and the horizontal displacement accommodated by the fold (Lf – W). The horizontal fault slip has been calculated using d= Δx+ (Lf – W). For the fault slip calculation of Bosporos Rupes and Phrixi Rupes there are not cross-cut craters measurements so we have made a pro- portional escalation with the horizontal slip measured in the first crater (Fig. 5(a)), assuming that the vertical elevation of the lobate scarp and the horizontal slip are directly related and there exists the same pro- portion in the three lobate scarps. The horizontal slip (d) associated with the formation of Ogygis Rupes is calculated in 2300m with a depth of faulting (h) of 18 km. Using this horizontal slip value, the total fault slip based on the elevation of the lobate scarp is 2900m. The horizontal slip (d) associated with the fault underlying Phrixi Rupes is 1580m and the depth of the fault detachment (h) obtained is 24.5 km. Accordingly, the total fault slip calculated is 2000m. The horizontal slip (d) obtained for Bosporos Rupes is 1330m corresponding with a depth of faulting (h) of 45 km. The total fault slip calculated is 1700m. We have to take into account that the surface of this lobate scarp is heavily altered, so originally, the excess area (A) and the lobate scarp height (Δz) were probably greater. 4.3. Results of the forward mechanical dislocation method The maximum height of Ogygis Rupes scarp relief coincides with the central zone of the structure (Fig. 4). This area was selected to apply this method, performing a topographic profile stacking in a band of≈30 km (Fig. 6(a)). The best fit corresponds with fault slips that range between 2500 and 3100m, according with the maximum elevation of the scarp, a dip angle of 35° and a depth of faulting of 27 km (Table 2). The topographic profile stacking for Phrixi Rupes was performed in the central part of the northern segment coinciding with the higher scarp relief of the structure (Fig. 6(b)), in a band of≈25 km. The proximity of Phrixi Rupes to the Thaumasia southeast edge seems the cause of a regional slope that affects this lobate scarp. This regional slope is calculated to be 0.18° SE. We have tilted the model output 0.18° in order to get the best fit with the real topography because the soft- ware model does not allow to set an initial tilted surface. The best fit for Phrixi Rupes stacking was obtained with a fault slip between 1700 and 1850m, a dip angle of 33° and a depth of faulting of 36 km (Table 2). Despite of being a long structure, Bosporos Rupes area is heavily eroded and cratered, which hinders the selection of the area with re- presentative topographic profiles for stacking. The selected topographic profiles are in a band of≈ 35 km approximately in the center of the northern fault segment that is characterized by the presence of a backthrust (Fig. 6(c)). Although the stacking is done in an area where the backthrust does not have a significant topographic expression, the best fit corresponds to a model with two faults with an opposite ver- gence, the main thrust fault and a backthrust. The best fit model pro- vides a main fault slip between 2200 and 2300m, a dip angle of 23° to the NW and 41 km of depth of faulting and a backthrust slip of 450m, a dip angle of 17° to the SE and 24 km of depth of faulting (Table 2). The regional slope observed in Phrixi Rupes decreases gradually towards the southeast and cannot be detected in Bosporos Rupes area which is further away from Thaumasia. The local modification of the topography due to erosion and sedimentation avoid the detection of a regional slope in this area. Bosporos Rupes is adjacent to the Argyre basin rim, for this reason there exists an abrupt slope descending towards the southeast in front of the scarp face, which avoids a properly fit of the output model in this part. This slope corresponds to the outcrop of the Argyre basin materials, which are topographically below the highlands materials where these lobate scarps are formed. We established a tapered slip in the models, implying a displace- ment concentration in the center of the fault plane falling toward the edges, vertically and horizontally to reproduce the observed fault dis- placement (Fig. 4) (Fossen, 2010). In our models (Fig. 6), we have set a displacement distribution which decreases horizontally in the last 10 km near the edges to minimize the boundary effects, and vertically in the last 7, 11 and 8 km, respectively, for Ogygis Rupes, Phrixi Rupes and Bosporos Rupes. The modeled scarp face is steeper when the ver- tical distance of decreasing is minor. 4.4. Displacement-Length relationships There is a scaling relationship between the maximum displacement of the fault (D) and the fault length (L), for planetary faults as well as for terrestrial faults. D and L are related by D= cLn where c is a constant related to material properties and n is the power-law exponent (Walsh and Watterson, 1988). The relation between D and L for fault populations located in uniform rocks is represented as a lineal function D= γL being γ the critical shear stress for fault propagation, related to the tectonic setting and the mechanical properties of the material, and it ranges between 100 and 10−3 (Cowie and Scholz, 1992b). Using the maximum relief of the lobate scarp (Δz) and the dip angle of the fault plane (θ), we can estimate the maximum displacement necessary to restore the surface by D= Δz/sinθ (Wotjtal, 1996; Watters et al., 2000; Watters, 2003). We have calculated D for each segment of our three lobate scarps using the dip angles resulting from the forward mechanical modeling method (Table 2). These values are within the common range of dip angle for planar thrust faults, which ranges be- tween 20° and 35° (e.g. Jaeger and Cook, 1979; Brewer et al., 1980; Stone, 1985). These data are included together with the results in Fig. 7, where it is also calculated the value of γ for this small population of lobate scarps, which is ∼1.7× 10−2. Despite not being a very re- presentative population, if we compare this value with those calculated for other locations (Fig. 7) including terrestrial trust fault populations (∼8.0×10−2) (Watters et al., 2000), Mercurian lobate scarps (∼6.5×10−3) (Watters et al., 2000) or Martian dichotomy boundary thrust faults (∼6.2× 10−3) (Watters, 2003), all of them calculated for θ=30°; our result is an intermediate value, closer to those calculated for lobate scarps in Mercury and in the Martian dichotomy. The seg- ment with less displacement, which is part of Phrixi Rupes, matches perfectly with the observations for Mars and Mercury, while the rest data of the analyzed segments remain above due to the high displace- ment, which exceeds the thousand meters, with respect to the segment longitude. 5. Heat flow The depth of the BDT can be used in order to calculate the surface heat flow at the time of faulting. Thus, here we calculate heat flows from our results on fault depths at the Aonia Region following the methodology detailed in Ruiz et al. (2011) and Egea-González et al. (2017). This methodology calculates the heat flow from the tempera- ture at the BDT depth (TBDT), which in turn is derived from equating the brittle and ductile strength at the BDT. Assuming homogeneously distributed crustal heat sources, the sur- face heat flow can be calculated from TBDT from Fs k T T z z H( ) 2 ,BDT s BDT BDT = + (1) where k is the thermal conductivity of the crust, TS is the temperature at the surface, ZBDT is the BDT depth, and H is the volumetric heat pro- duction rate. We have used k=2W m−1 K−1, which is appropriated for intact non-porous basaltic rocks (Beardsmore and Cull, 2001), and TS=220 K, the present mean surface temperature on Mars (e.g., Kieffer et al., 1977). The radioactive heat production rate depends on the abundance of heat-producing elements (HPEs) in the crust. Near surface K and Th abundances were measured by Mars Odyssey GRS (Boynton et al., 2007; Hahn et al., 2011). Because the comparatively homogeneous HPEs distribution in the southern highlands, and that the Martian crust is considered to be much less geochemically varied than the Earth's crust (Taylor et al., 2006), we use as representative of the A. Herrero-Gil et al. ANEXO I 177 crust the average abundances, measure by GRS, of K and Th, respec- tively, 3652 and 0.69 ppm (Hahn et al., 2011), whereas for estimating U abundance a Th/U ratio of 3.8 was assumed (e.g., Meyer, 2003). Heat dissipation rates are calculated for decay constants from Van Schmus (1995) and a time range of 3.6–3.8 Ma. Because ductile deformation is temperature-dependent, TBDT can be derived from equating the brittle and ductile strength at the BDT, and therefore T Q nR ln gz A (1 ) ( ´ / ) ,BDT BDT 1/2 1 = (2) where Q is the activation energy of creep, n and A are laboratory-de- termined constants for creep deformation, R is the gas constant (8.3145 J mol−1 K−1), λ is the pore fluid pressure, ρ is the density, α is a coefficient that depends on the stress regime (which takes a value of 3 in the case of thrust faulting; e.g., Ranalli, 1997), g is the acceleration due to the gravity (3.72m s−2 for Mars), and έ is the strain rate. Here we take λ values between 0 and 0.35 (which is valid for dry and hy- drostatic conditions), strain rates between 10−16 s−1 and 10−19 s−1, and for creep parameters we use the flow law of wet diabase of Caristan (1982), appropriate for a basaltic crust. (For a complete dis- cussion on the parameters used in the calculation see Ruiz et al., 2011 and Egea-González et al., 2017.) The results are shown in Table 2. Heat flows derived for Bosporos Rupes and Phrixi Rupes, which have been calculated to be 25–33mW m−2 and 26–40mW m−2, respectively, are similar to those usually found in the Thaumasia and circum-Hellas regions (Ruiz et al., 2008, 2009, 2011; Mueller et al., 2014; Egea-González et al., 2017), but heat flow obtained for Ogygis Rupes, which is 30–51mW m−2, is comparatively higher, as a consequence of the lower BDT depth esti- mated for this lobate scarp. 6. Discussion and conclusions The structural modeling of three lobate scarps located between Thaumasia Montes and Argyre impact basin by two different methods allow us to constrain the depth where the underlying thrust faults root. Understanding the limitations of each method used is fundamental issue when comparing the respective results. On the one hand, the dis- placement used in the balanced cross sections method is the fault slip measured in cross-cut craters, which is a minimum estimation because, even assuming that the crater was formed before the beginning of the fault rupture, we do not know the initial distance between the surface fault rupture and the crater rim, and the strike of the horizontal slip vector is unconstrained (Fig. 2(b)). If the real fault displacement value was larger, the depth of faulting calculated would be shallower, otherwise if there is volume loss due to erosion or loss of porosity by compaction the real depth of faulting would be deeper than our esti- mation. The erosion in Mars is considered to have a very low rate (Golombek and Bridges, 2000; Golombek and Phillips, 2010) but, to- gether along with compaction, they could have a slight influence in the obtained depth. On the other hand, the forward mechanical modeling method also does not take into account these volume variations and, additionally, ignores fault propagation fold deformation. Both methods, despite its limitations, have been demonstrated to be a good approx- imation to the fault parameters and applying both we constrain a more reliable range of parameters for the faults underlying the three lobate scarps located in Aonia Terra. Dip angles were obtained from the forward mechanical dislocation method, while the balanced cross section method does not provide in- formation on the fault dip. The dip angles for the faults underlying the three lobate scarps, 35° for Ogygis Rupes, 33° for Phrixi Rupes and 23° for Bosporos Rupes, are inside the range of dip angles for thrust faults in terrestrial planets, typically ranging between 20° and 35° (e.g., Jaeger and Cook, 1979; Brewer et al., 1980; Stone, 1985; Watters and Nimmo, 2010). The differences between both methods, both in depth and fault slip (Table 2; Fig. 8), are probably related to limitations in the models and also by the distribution of the volume and the width of the struc- ture, conditioned by the appearance of backthrusts (Ogygis Rupes and Bosporos Rupes) and fault segmentation (Phrixi Rupes and Bosporos Rupes) which modify the distribution of displacement in the structure and hinder its analysis and understanding. Ogygis Rupes, despite having a backthrust which only affects the north part of the lobate scarp, seems to be the simplest structure. In addition, it is the lobate scarp that seems less affected by processes of sedimentation and erosion of the three lobate scarps analyzed, which is visible by comparing the results obtained by the two methods, which are quite similar (Fig. 8(a)). Fig. 7.. Plot of maximum fault displacement (D) in function of fault length (L) (modified from Schultz et al., 2006). The data for the three studied lobate scarps is shown in blue: Ogygis Rupes is shown by a square, Phrixi Rupes segments by circles, and Bosporos Rupes segments by triangles. The error bars indicate the displacement range for fault plane dips between 20° and 35°, corresponding with the range for planar thrust faults. Earth data for thrust faults is shown by black squares (Elliott, 1976) and triangles (Mége and Riedel, 2001). Mercury and Mars data are shown by gray diamonds and white circles, respectively (Watters et al., 2000, 2002; Watters, 2003). (For inter- pretation of the references to color in this figure legend, the reader is referred to the web version of this article.) A. Herrero-Gil et al. ANEXO I 178 In this way, the fault slip in Ogygis Rupes is set between 2500–3100m, extending to depth of faulting of 18–27 km. Phrixi Rupes is divided in two segments, which have the same direction and are quite close to each other, but its interaction in depth is unknown. The surface of its southern segment seems very altered and modified but it does not ap- pear to be so in the zone of maximum lobate scarp elevation used for the analysis located in the northern segment. Even so, the results of the two methods do not show a great difference (Fig. 8(b)) and the fault slip for Phrixi Rupes is set between 1700 and 2000m and the depth of faulting is 24.5–36 km. Bosporos Rupes is the longest and most complex structure here analyzed. It is divided into two segments and has a backthrust fault along most of its length, showing a significant displacement with re- spect to these two segments. Its surface is quite affected by craters, and by erosion and sedimentation processes. The fault slip value obtained by the balanced cross section method (1700m) is quite small compared with the forward mechanical modeling result (2650–2750m). This difference in the result, together with the high shortening accom- modated by the backthrust, seems to indicate that the total displace- ment in this lobate scarp is significantly larger than the one deduced from the cross-cut craters analysis and used for the balanced cross section method. In spite of this, the depth of faulting obtained by the two methods has a similar range of 33–45 km (Fig. 8(c)). Considering the observed lengthwise profiles (Fig. 4), in which the displacement will be larger in the center of the fault plane, we have selected an elliptical displacement distribution for the forward me- chanical method, which fits the results reasonably well. This distribu- tion also agrees with a triangular distribution, providing similar results except for a reduction in the displacement value (Ma and Kusznir, 1992) due to the influence of the edges. Given that the dis- placement results would differ greatly using a triangular distribution from those obtained using the balanced cross section method, we se- lected an elliptical distribution in which the center of the structure is not affected by the distance to the edges, aiming to avoid this effect and simplifying the model. Anyway, this reduction in the displacement would not significantly change our conclusions since dip angle and depth of faulting results remain unchanged. The decreasing displace- ment in the shallower meters of the fault plane could be justified by the fault propagation fold model in which the shortening at the beginning of the compression is accommodated by early folding followed by the formation of a thrust fault that accommodates the displacement pro- pagating upward from depth (Allmendinger and Shaw, 2000). In the same way, the displacement decreases in the deeper part of the fault plane (Fig. 8) which can be interpreted as a gradual BDT where the fault displacement decreases until reaching ductile domain. This interpreta- tion, considering the decollement associated with the large thrust faults Fig. 8.. General cross sections of the three lobate scarps showing the results of the depth of faulting estimated by both methods. The gray area corresponds to the displaced volume (i.e. the hanging wall). Balanced cross section results are shown by a striped dark red line. Forward mechanical dislocation model results are shown by dotted lines and the displacement decrease in the last kilometers at depth is indicated by a red to yellow gradient. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) A. Herrero-Gil et al. ANEXO I 179 underlying large lobate scarps to be a main rheological change re- flecting the start of ductile flow as dominant deformation mechanism, has been assumed by multiple authors previously (e.g. Schultz and Watters, 2001; Ruiz et al., 2008; Egea-González et al., 2017). The formation of the Argyre impact basin during the Noachian time, which has a calculated absolute age of ∼3.93 Gyr (Robbins and Hynek, 2012; Robbins et al., 2013), produces impact-related deformation up to 2000 km away from the basin rim in the form of different structures such as concentric ring scarps or radial structurally-controlled valleys (Dohm et al., 2015). Eight concentric rings have been described asso- ciated with Argyre impact basin (Hiesinger and Head, 2002) (Fig. 9). The ring 6, defined as the closest approximation to the transient crater rim, could be defined as the main Argyre ring showing steep slopes facing towards the basin interior. Bosporos Rupes scarp base is located on ring 6 with its backlimb extending between rings 6 and 7 (Fig. 9). Bosporos Rupes strikes concentric to the impact basin, leading to sug- gest that its strike might be structurally controlled by the presence of Argyre basin. However, Ogygis Rupes and Phrixi Rupes which are lo- cated between the rings 7 (formed by the main topographic elevations around the impact basin) and 8 (the most external and uncertain), do not strike concentric to the Argyre basin, but conversely, they strike parallel to the edge of Thaumasia, being concentric to Tharsis, together with the wrinkle ridges present in this area (Fig. 1), suggesting a causal relationship (Wise et al., 1979; Watters et al., 1993; Anderson et al., 2001). This difference in the orientation of the compressional structures corroborates that this part of Aonia Terra in the northwestern margin of Argyre basin is more influenced by the proximity of Thaumasia than by the Argyre impact basin, although the presence of the Argyre rings could have a certain influence (Dohm et al., 2015). Attending to the Late Noachian/Early Hesperian age (∼3.8–3.6 Gyr) (Dohm et al., 2001; Hartmann and Neukum, 2001), established for these lobate scarps and consistent with their emplace- ment in Noachian units (Fig. 1), we can compare our results for the three lobate scarps on Aonia Terra with previous thrust fault studies on lobate scarps on Mars (Table 3) formed approximately in the same age (Schultz and Watters, 2001; Ruiz et al., 2008; Mueller et al., 2014; Grott et al., 2007; Egea-González et al., 2017), whose calculated fault para- meters are comparable to those obtained in this study. Considering that almost all the previous studied lobate scarps have reliefs of the order of a few hundred meters while the three lobate scarps analyzed in this study have maximum elevations over 1200m, even exceeding 2000m in the case of Ogygis Rupes, it is a reasonable result that the fault slips calculated for the lobate scarps in Aonia Terra are considerably higher than those calculated for Amenthes Rupes (Schultz and Watters, 2001; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017), for lobate scarps in the south of Thaumasia (Grott et al., 2007) and for lobate scarps in the circum-Hellas region (Egea-González et al., 2017). The dip angles calculated in all the studies, including our value of 23–35°, are very similar and they are within the typical dip range for reverse faults (20–35°) (e.g., Jaeger and Cook, 1979; Brewer et al., 1980; Stone, 1985; Watters and Nimmo, 2010) or very close to it, ex- cept the dip angle obtained by Mueller et al. (2014) for Amenthes Rupes which is quite higher (42–54°). Accordingly, the depth of faulting ob- tained for the three lobate scarps of Aonia Terra (18–45 km) is a per- fectly reasonable value if we compared it to other lobate scarps studied, whose depths of faulting range between 13 and 48 km. The shallower depth of the BDT at the time of faulting in this area of Aonia Terra between Thaumasia and Argyre impact basin is found closer to the edge of Thaumasia (18–36 km) than near the Argyre basin rim (33–45 km). Ogygis Rupes and Phrixi Rupes have depths of faulting (18–36 km) similar to the values obtained by Grott et al. (2007) in the south edge of Thaumasia (21–35 km) which are located near our study area. However, the depth of faulting calculated for Bosporos Rupes is higher. Although this value matches the range of depths previously cal- culated for lobate scarps on Mars (Table 3), if we consider that the three lobate scarps were formed in the same restricted age (Late Noachian/Early Hesperian) in a relatively small area, the observed variation needs an explanation. Attending to its location over the main crater rim (ring 6), our results seem to suggest a thicker brittle domain under Bosporos Rupes (and ring 6) with respect to the external area probably associated with the impact basin structure. A significant difference in heat flow, being lower under Bosporos Rupes, seems to contradict the thickened crust with more radiogenic elements under the Argyre main rim in this area. A high var- iation in such a restricted area of the depth of faulting and, consequently, of the BDT seems to be unrealistic, especially considering that the three lobate scarps are similar in age according to regional geology. Alter- natively, the BDT depth also depends on the strain rate (Dragoni, 1993). A deeper BDT such as the obtained for Bosporos Rupes would correspond with a faster deformation compared to Ogygis Rupes and Phrixi Rupes. But the origin of such difference would be unknown. A simple explanation for the discrepancy in the obtained depth of faulting comes from the presence of the main Argyre rim at the same location where Bosporos Rupes was generated. The match between part of Argyre ring 6 and Bosporos Rupes in location and strike strongly suggests that this ring acted as a mechanical anisotropy conditioning the nucleation of Bosporos Rupes on it, which makes very difficult to Fig. 9.. Radial MOLA topographic profiles from the center of Argyre basin (O) to the outside (A, B, C) across the three lobate scarps studied. The eight rings of Argyre defined by Hiesinger and Head (2002) are shown. The Argyre image, colored from MOLA elevation model overlaying THEMIS, shows the location of the three topographic profiles and impact basin rings in black, and the lobate scarps in red. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) A. Herrero-Gil et al. ANEXO I 180 evaluate the contribution of each structure to the current topography. Thus, the modeled topography might not correspond only to the to- pography uplifted by the movement of the fault underlying Bosporos Rupes, which would result in inaccurate calculated fault parameters. This could explain the difference of depth of faulting as a consequence of the crater rim topographic contribution. The area uplifted by the thrust fault movement has been overestimated, providing a deeper depth of faulting under Bosporos Rupes than the real value. The orientation of the compressional strain field that generated these lobate scarps, and also the wrinkle ridges of the area, is mainly controlled by the gravitational field originated by Tharsis topographic elevation and, in less degree, by the presence of Argyre impact basin and the global contraction of the planet. Concentric compressional structures are predicted by lithospheric deformation models of Tharsis (Golombek and Phillips, 2010). Dimitrova et al. (2006) defined a de- viatoric stress field associated with horizontal gradients of gravitational potential energy (GPE) to explain the formation of concentric com- pressional structures and radial extensional structures with respect to Tharsis. Argyre basin, due to its low topography and thin crust, pro- duces deviatoric extension in GPE models, generating a decay of the compression stress field near the basin. The heat flows derived from the BDT depth for the Aonia Terra region (Table 2) suggest, when putted together with the previous results for Thaumasia and circum-Hellas regions (Ruiz et al., 2008, 2009, 2011; Mueller et al., 2014; Egea-González et al., 2017), a roughly constant heat flow during the Late Noachian/Early Hesperian time in, at least, much of the southern highlands of Mars. Because the con- tribution of radioactive crustal heat sources supposes a substantial component to the total surface heat flow related to crustal thickness (Parro et al., 2017), the relatively similar surface heat flow and high crustal thicknesses in these regions suggest that both the crustal and mantle heat flow must also be similar across the southern highlands. A relatively uniform mantle heat flow in such an extensive area could support some previous expectations (e.g., Ruiz, 2014) suggesting rela- tively inefficient convective heat transfer, and low surface heat flow beyond volcanic areas. Acknowledgments This research has been supported by the project AMARTE CGL2014- 59363-P and A. Herrero-Gil work has been supported by a FPI 2015 grant BES-2015-073983, both funded by the Spanish Ministry of Economy and Competitiveness (MINECO). I. Egea-González is grateful to the Universidad de Cádiz for supporting this work through the pro- ject PR2017-074. We thank the comments and suggestions from two anonymous reviewers that helped to improve the manuscript quality. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.icarus.2018.09.027. References Albee, A.L., Arvidson, R.E., Palluconi, F., Thomas, T., 2001. Overview of the Mars Global Surveyor mission. J. Geophys. Res. 106 (E10), 23291–23316. Allemand, P., Thomas, P.G., 1995. Localization of Martian ridges by impact craters: mechanical and chronological implications. J. Geophys. Res. 100, 3251–3262. Allmendinger, R.W., Shaw, J.H., 2000. 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Earth and Planetary Science Letters 532, 116004 Supplementary material S1 Earth and Planetary Science Letters 532 (2020) 116004 Contents lists available at ScienceDirect Earth and Planetary Science Letters www.elsevier.com/locate/epsl 3D modeling of planetary lobate scarps: The case of Ogygis Rupes, Mars Andrea Herrero-Gil ∗, Javier Ruiz, Ignacio Romeo Departamento de Geodinámica, Estratigrafía y Paleontología, Facultad de Ciencias Geológicas, Universidad Complutense de Madrid, 28040 Madrid, Spain a r t i c l e i n f o a b s t r a c t Article history: Received 15 February 2019 Received in revised form 2 December 2019 Accepted 3 December 2019 Available online 12 December 2019 Editor: W.B. McKinnon Keywords: lobate scarps Mars thrust fault Brittle-Ductile Transition 3D modeling Lobate scarps are the topographic expression of the largest thrust faults observed on the surfaces of terrestrial planets and their study provides information on the mechanical characteristics of the lithosphere at the time of formation. Here we show the results of 3D modeling of Ogygis Rupes, located in Aonia Terra, which is one of the most topographically pronounced lobate scarps described in the cratered martian highlands. The observed relief of Ogygis Rupes has been modeled by a combination of Trishear and Fault Parallel Flow algorithms, providing a successful reproduction of the observed topography through a 3D modeling that includes the main thrust fault, forming the lobate scarp relief, and two subsidiary backthrusts. This recreation allows us to interpret Ogygis Rupes relief, modeling the fault propagation folding, and constraining fault parameters and their variations along strike. The detailed slip distribution along the three faults reflects a general decay from the center to the edges for each fault, with the maximum slip value (2850 m) located approximately at the center of the main fault. The fault surfaces obtained for the main thrust fault and the two backthrusts show listric geometries at depth. The decollement where the main fault roots is set at ∼17–18 km deep, related to a main rheological threshold that on Mars is interpreted to be the depth of the Brittle-Ductile Transition at the time of the lobate scarp formation (Late Noachian/Early Hesperian). The listric morphology of the main fault implies that the total slip associated with this thrust fault is transmitted from the decollement, being representative of the regional shortening associated with the lobate scarp formation. Otherwise, the modeled backthrusts are subsidiary listric faults rooting at shallower depths (2.3–5.6 km), probably indicating the presence of mechanical discontinuities in the brittle domain of the martian lithosphere. © 2019 Elsevier B.V. All rights reserved. 1. Introduction Lobate scarps are common contractional tectonic structures present on the surfaces of terrestrial planetary bodies (e.g., Strom et al., 1975; Watters, 1993; Schultz and Watters, 2001). These large structures are interpreted to be the topographic expression of large surface-breaking thrust faults (e.g., Strom et al., 1975; Watters and Robinson, 1999; Watters and Nimmo, 2010). Lobate scarps show surface strikes from linear to slightly sinuous, with lengths of up to hundreds of kilometers and maximum reliefs of up to thousands of meters. These structures present a characteristic asymmetry in cross section, with a frontal steep slope (the scarp front) and a gentle back slope. These morphological characteristics correspond to a thrust fault propagation anticline followed by a trailing syn- cline. The large thrust faults underlying lobate scarps are consid- ered to cut the brittle domain of the lithosphere, being rooted at * Corresponding author. E-mail address: andreaherrero@ucm.es (A. Herrero-Gil). the Brittle-Ductile Transition (BDT) of the time when they were formed (e.g., Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; Mueller et al., 2014; Egea-González et al., 2017). Previous studies on martian lobate scarps have been performed using 2D structural modeling methods with the aim of knowing the properties of the large faults that formed these structures, assuming that lobate scarp topography is controlled by fault geom- etry (Schultz and Watters, 2001; Watters et al., 2002). The depth of faulting, the dip angle and the fault slip are the structural param- eters usually derived from these studies. The generally accepted interpretation that faults underlying lobate scarps root at the BDT provides information on the state of the lithosphere at the time of their formation (Schultz and Watters, 2001; Watters et al., 2002; Ruiz et al., 2008), and allows to calculate local or regional heat flow values (e.g. Ruiz et al., 2008; 2011; Grott et al., 2007; Mueller et al., 2014; Egea-González et al., 2017; Herrero-Gil et al., 2019). Several studies have been performed in 2D cross sections of Amen- thes Rupes using a Forward Mechanical Dislocation method (FMD) for an elastic halfspace with uniform isotropic elastic properties (Schultz and Watters, 2001; Grott et al., 2007; Ruiz et al., 2008; https://doi.org/10.1016/j.epsl.2019.116004 0012-821X/© 2019 Elsevier B.V. All rights reserved. ANEXO II 185 2 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 Egea-González et al., 2017). The same method has also been ap- plied to study two lobate scarps in the southern Thaumasia region (Grott et al., 2007), eight lobate scarps in the circum-Hellas re- gion (Egea-González et al., 2017) and three lobate scarps in the northwest margin of Argyre impact basin (Herrero-Gil et al., 2019). The elastic dislocation method has also been applied to lobate scarps on other terrestrial bodies like Mercury (e.g., Watters et al., 2002, 2016; Egea-González et al., 2012), the Moon (e.g. Byrne et al., 2015) and the asteroid 433 Eros (Watters et al., 2011). The Balanced Cross Section (BCS) method (Chamberlin, 1910), which attends to fault propagation fold theory (Suppe, 1983; Seeber and Sorlien, 2000) assuming mass conservation during the deforma- tion process, has also been used to analyze lobate scarps on Mars. Using this method, Mueller et al. (2014) calculated Amenthes Ru- pes fault parameters on 2D profiles and Herrero-Gil et al. (2019) also analyzed the three lobate scarps near Argyre basin. These two methods provide a first approach to the structural characteriza- tion of lobate scarps, but the results offered by 2D modeling may be limited by the selection of specific cross sections. These cross sections provide a limited view of the structure because they do not take into account the whole geometry of the lobate scarp, the variations of fault parameters along strike, and the 3D spatial in- teraction with other subsidiary structures. The 3D modeling of a lobate scarp extends the information ob- tained from 2D modeling, providing a more complete vision of the dynamics of these large tectonic structures. The topographic ex- pression of lobate scarps changes laterally, reflecting fault geome- try and slip variation along their strikes. Our 3D modeling success- fully reproduces the observed topography characterized by a fault propagation fold including the interaction with other subsidiary structures. The 3D approach allows us to constrain the slip distri- bution on the fault surface, the variations of dip at depth and along strike (allowing non-planar realistic fault geometries according to the mapped fault traces), the depth of the decollement where the fault roots, and the degree of interaction between different nearby structures. The formation of subsidiary thrust faults with an oppo- site vergence to the main fault, known as backthrusts, is common in large mountain ranges on Earth (e.g., Jayangondaperumal et al., 2015). Backthrusts associated with large thrust faults forming lo- bate scarps have also been identified on Mars (e.g., Herrero-Gil et al., 2019; Klimczak et al., 2018). The relation between the main thrust fault and these subsidiary backthrusts provides insights on the existence of crustal mechanical discontinuities at the depth where these subsidiary faults root. Here we present the results of a 3D model of Ogygis Rupes, which is one of the most topographically pronounced lobate scarps described on Mars, providing an improvement on the understand- ing of lobate scarps kinematics and lithospheric structure at the time of formation. The results provide advances on the geom- etry and kinematics of the underlying faults (including positive listric geometries), the interaction of the main fault with sub- sidiary backthrusts and a constraint on the thickness of the brittle lithospheric domain. The main thrust fault of Ogygis Rupes to- gether with two subsidiary backthrusts form an isolated structure whose topographic signature can be easily identified from the re- gional topographic trend (Fig. 1). The erosion rate that has affected this lobate scarp since its formation seems to be low resulting in a broadly well-preserved structure (Herrero-Gil et al., 2019), al- though some fluvial channels have shaped Ogygis Rupes backlimb in the southern half of the structure (Klimczak et al., 2018). These particularities make Ogygis Rupes a successful candidate for 3D modeling. Fig. 1. Tectonic map of Ogygis Rupes area over an image combining colored MOLA elevation model overlaying THEMIS-IR Day Global Mosaic 100 m. Main fault, Backthrust 1 and Backthrust 2 are the thrust faults shown in red color. The inset globe, colored with MOLA model, shows the map location. (The reader is referred to the web version of this article for color interpretation.) ANEXO II 186 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 3 2. Ogygis Rupes Ogygis Rupes is located in Aonia Terra, in the transition zone between the Argyre basin and the Thaumasia Montes, in the south- ern highlands of Mars (Fig. 1). This lobate scarp is apparently formed by a main single fault striking N30◦E and verging ESE (Herrero-Gil et al., 2019) that has a length of 220 km. The max- imum scarp relief is ∼2200 m, corresponding to the crest of the fault propagation fold, and it is located near the center of the structure, at ∼100 km from the southern fault tip. Ogygis Rupes presents two associated subsidiary backthrusts, verging WNW, which are located in the northeastern half of the structure (Fig. 1, Fig. 2a) cutting the backlimb of the propagation anticline of the main fault. The main fault and Backthrust 1 cut two different craters providing strong evidence of surface rupture by faulting (Herrero-Gil et al., 2019). Backthrust 1 strikes N10◦E and is ∼60 km long. This fault is laterally spaced about 20 km from the main fault, generating a “pop up” structure in the north- ern part of Ogygis (Fig. 2a, b). The maximum relief of Backthrust 1 is ∼450 m (measured at ∼16 km from the southern tip (Fig. 2b) avoiding the transected crater where this measurement would be overestimated due to the elevation difference between the crater rim and the bottom of the crater). Fig. 2. a. Mosaic made of CTX images showing in detail the northern part of the Ogygis Rupes structure, where the Backthrust 1 and 2 are shown. Cross sections X- X′ and Y-Y′ are marked in white. b. Cross section X-X′ where the asterisks indicate the location of the mapped thrust faults on image c (10× vertical exaggeration). c. Cross section Y-Y′ where the asterisks indicate the location of mapped thrust faults and the black arrow indicate the northwestern rim of the double crater rim where a wrinkle ridge is mapped on figure c (10× vertical exaggeration). (The reader is referred to the web version of this article for color interpretation.) Backthrust 2 is 65 km long and is spaced about 50 km from the main fault, overlapping just half of its length with the north- ern part of the main fault and, consequently, also with Backthrust 1. The trace of this backthrust seems to be structurally controlled by the southeastern rim of two ancient superposed craters, fol- lowing a curved morphology with an average strike of N27◦E. A cross section through Backthrust 2 (Fig. 2c) shows that this fault uplifts a large relief with the characteristic asymmetric profile of a fault propagation fold. The rest of the rim barely presents re- lief, even though a wrinkle ridge deforms the northwestern rim (Fig. 2c). Reverse faults structurally controlled by preexisting struc- tures related to impact craters have been described on Mercury (Crane and Klimczak, 2019), the Moon (Byrne et al., 2015) and possibly Ceres (Ruiz et al., 2019). The maximum relief associated with Backthrust 2 (∼850 m between fold crest and scarp base) is located at the center of this structure. The main fault of Ogygis Rupes and both subsidiary backthrusts show a gradual decrease of relief from the point with maximum relief towards the lateral fault tips. Regional studies on the geological history of the area where Ogygis Rupes is located indicate that this structure was formed during the Late Noachian/Early Hesperian (Dohm and Tanaka, 1999; Anderson et al., 2001), which is equivalent to an age of ∼3.8–3.6 Gyr (see Hartmann and Neukum, 2001; Werner and Tanaka, 2011). This age is consistent with the cross-cutting re- lationships between the faults forming the lobate scarp and the geological units affected by their slip (Herrero-Gil et al., 2019). 3. Method The 3D modeling of Ogygis Rupes has been performed com- bining Trishear algorithms (Erslev, 1991; Allmendinger, 1998) to recreate the fault propagation folding ahead of the fault and Fault Parallel Flow algorithms (Egan et al., 1997; Ziesch et al., 2014) to define the movement of the hanging wall over the footwall, as- suming volume conservation (Cristallini and Allmendinger, 2001; Cardozo, 2008; Ziesch et al., 2014). This combination provides the best fit between the 3D model output and the original lobate scarp topography. The modeling was performed using the software MOVETM (Mid- land Valley), in which Trishear and Fault Parallel Flow algorithms are implemented in 3D (Cardozo, 2008; Ziesch et al., 2014) with the possibility of including complex fault geometries as listric propagating thrust faults (Brandenburg, 2013; Cardozo and Bran- denburg, 2014). This tool was successfully used in 3D modeling of thrust faults on Earth (e.g., Cristallini and Allmendinger, 2001; Maesano et al., 2013; Watkins et al., 2015). The Digital Elevation Model (DEM) used was obtained from Mars Orbiter Laser Altimeter (MOLA, Mars Global Surveyor mis- sion) data (Smith et al., 2001) whose horizontal resolution is ∼463 m/px and the vertical resolution is ±3 m. The Thermal Emission Imaging System (THEMIS, Mars Odyssey mission) daytime infrared (IR) mosaic was used as a base image because its resolution of 100 m/px (Christensen et al., 2004) allows to accurately identify the structures in the area, providing the support for a detailed structural map (Fig. 1). Context Camera (CTX, Mars Reconnaissance Orbiter) images (Malin et al., 2007) were used to characterize small features. 3.1. Geometric parameters of fault planes The principal variables that define the kinematic properties of a fault are depth of faulting, dip of the fault plane, and fault slip. These parameters have a strong influence in the topographic expression of the structure and they control width (horizontal distance between the scarp base and trailing syncline) and topo- graphical relief (elevation difference between the scarp base and anticline crest) of the lobate scarp (Schultz and Watters, 2001; Watters et al., 2002). ANEXO II 187 4 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 An increase of the depth of faulting (keeping the rest of pa- rameters constant) results in a larger volume of uplifted material providing a wider anticline with the same relief, while shallower depths of faulting entail a narrower structure. An increase of the fault dip angle (keeping the rest of parameters constant) provides a narrower structure with greater relief and a steeper backlimb. A gradual decrease of the fault dip with depth until reaching a horizontal decollement (positive listric fault geometry) controls the slope and width of the backlimb, and, as a consequence, the shape of the trailing syncline. A larger listric zone, characterized by a gradual dip change at depth, provides a wider and gentler backlimb and a wider trailing syncline. Otherwise, an abrupt dip change, where the fault reaches the decollement level, entails a narrower and steeper backlimb. Fault slip changes exclusively af- fect the relief of the structure. 3.2. Trishear parameters Trishear parameters control the shape of the fault propagation fold. The hanging wall slips over a fixed footwall under a contrac- tional tectonic setting characterized by a thrust fault that prop- agates upwards from a decollement level (Fig. 3). The triangular zone where the fault propagation fold is developed, defined by the trishear angle (θ ), moves forward from a certain depth (fault tip depth) as the fault propagates upwards with a propagation to slip ratio (P/S) (Hardy and Ford, 1997). A small trishear angle increases the deformation ahead of the fault tip, producing a narrow fold with a steep forelimb, while a large angle involves that the defor- mation is distributed in a bigger area generating a broad anticline (Allmendinger, 1998). The orientation of the trishear zone with respect to the fault (θ1, θ2) also affects the geometry of the fault propagation fold (Fig. 3). The deformation caused by fault propagation can be sym- metrically distributed between the hanging wall and footwall (θ1 = θ2), larger in the hanging wall than in the footwall (θ1 > θ2) or the opposite (θ1 < θ2). Fig. 3. Representation of Trishear method (based on Hardly and Ford, 1997; and Zehnder and Allmendinger, 2000). Trishear area is colored in grey. Trishear angle (θ ) is shown in red, while its divisions depending on whether it affects the hanging wall (θ1) or the footwall (θ2) are shown in orange. Fault tip is marked with a big red dot. The distribution of the velocity of the hanging wall relative to the footwall in the trishear area is marked with grey slip vectors, varying from top (where they are parallel and equal to the one that defines the movement of the hanging wall) to bottom (where these vectors decrease in magnitude turning its orientation to be parallel to the lower boundary of the trishear zone until being zero). (The reader is referred to the web version of this article for color interpretation.) The P/S ratio describes how rapidly the fault tip propagates with respect to the fault slip and it is associated with the degree of development of the fault propagation fold (Hardly and Ford, 1997). Low values of P/S (below 2) cause more intense deformation of the forelimb (especially at depth) because the material spends more time within the trishear zone. 3.3. Modeling workflow The modeling procedure consists of three steps: (1) 2D resti- tution and forward modeling along selected cross sections that provide a first order approximation to the fault geometries and the displacement distribution, (2) 3D restoration where the fault ge- ometries and displacements were checked and refined, and finally (3) 3D forward modeling to constrain the trishear parameters that best reproduce the observed topography. The displacement vector of the main fault and the backthrusts that formed Ogygis Rupes was assumed to be perpendicular to the fault strike (pure dip-slip reverse faulting), according to the obser- vations of cross-cut craters (Herrero-Gil et al., 2019). The footwall was considered to remain static during modeling. The 3D fault surfaces were built interpolating between the 2D cross sections modeled, and they were used as an initial setup for 3D modeling. In the 3D restoration process fault displacements were restored, unfolding the fault propagation anticline to recon- struct the original topographic surface. This procedure provides a refinement of the fault geometry and the displacement distribution along the strike. Finally, the 3D forward modeling allows to con- strain the propagation-slip ratio and the parameters of the trishear zone. The forward modeling was performed starting from a topo- graphic base surface obtained by removing the craters and Ogygis Rupes relief from MOLA model. This surface was forward deformed starting with the fault surfaces and the parameters obtained from the 3D restoration of the main fault and the two backthrusts. 4. Results of 3D modeling of Ogygis Rupes 4.1. 3D restoration The topographic surface deformed by the tectonic structures forming Ogygis Rupes (Fig. 4a) is restored using the 3D fault sur- faces, obtaining an undeformed topographic surface as plain and homogeneous as possible (Fig. 4b). The 3D restoration process highlighted that the movement backwards of the main fault does not restore all the observed up- lifted topography, consequently, the restoration of both backthrusts is needed to completely remove Ogygis Rupes relief. Both the main fault and the backthrusts, do not show large variations of dip an- gle and depth of faulting along their strike. Conversely, fault slip values clearly decrease towards the edges in the three faults that form the lobate scarp structure. The geometry of the fault surfaces and displacements were iteratively modified until restoration was as complete as possi- ble (Fig. 4b). A successful restoration was obtained when planar geometries for the first kilometers were combined with positive listric (a decay of the dip angle at depth) morphologies at depth (Fig. 5). Otherwise, completely planar fault geometries that keep a constant dip until the decollement depth cannot restore the back- limb geometry of the fault propagation anticline, producing a steep and narrow backlimb that does not match the observed topogra- phy (see Supplementary material, Fig. S1). The dip angle obtained for the main fault is 39◦ towards the NW for the first ∼11 km of the fault plane measured from the topographic surface (until a depth of ∼5.5 km). From this depth, the dip angle gradually decreases with a positive listric geometry rooting into a horizon- tal decollement at 17.2–17.8 km deep (Table 1). Backthrust 1 dips towards the opposite direction (SE) than the main fault, with an angle of 22◦ (constant for the first ∼9 km of the fault plane mea- sured from the topographic surface, until a depth of ∼1.2 km), that flattens downwards until a depth of faulting of 2.3–2.9 km. ANEXO II 188 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 5 Fig. 4. a. Ogygis Rupes original surface colored from MOLA elevation model overlaying THEMIS-IR Day Global Mosaic 100 m. b. Topographic surface of Ogygis Rupes restored from the original MOLA model of the area. (The reader is referred to the web version of this article for color interpretation.) Fig. 5. 3D model of Ogygis Rupes area with an inclined perspective from the north in which it can be observed part of the topographic surface. The other part of the topography has been hidden allowing to observe the three fault surfaces underlying the lobate scarp. Three SE-NW cross sections perpendicular to the lobate scarp, located in the north (A-A′), center (B-B′) and south (C-C′) of the structure, are shown. The main fault, Backthrust 1 and Backthrust 2 are also shown in these cross sections. (The reader is referred to the web version of this article for color interpretation.) ANEXO II 189 6 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 Table 1 Fault and trishear parameters calculated for Ogygis Rupes. Length (km) Depth (km) Dip angle (◦) Max. fault slip (m) Trishear angle (◦) Fault tip depth (m) P/S ratio Main fault 220 17.2–17.8 39 2850 76 (center), 70 (edges) −4700 3 Backfault 1 60 2.3–2.9 22 1200 70 −750 2 Backfault 2 65 5.5–5.6 23 1800 36 −1200 2 Backthrust 2 dips 23◦ to the SE for the first ∼12 km of the fault measured from the topographic surface (until a depth of ∼3 km), gradually decreasing to a subhorizontal dip at 5.5–5.6 km of depth (Table 1). 4.2. 3D forward modeling The Ogygis Rupes anticline does not present constant charac- teristics along strike (Fig. 5), reflecting a slight variation of the trishear parameters between the center and the edges of the struc- ture. The initial topographic surface used for the forward modeling (Fig. 6a) is iteratively deformed using the fault surfaces from 3D restoration until obtaining a model as similar as possible to the original observed surface (Fig. 4a). The most accurate fit between the forward modeled surface of Ogygis Rupes and MOLA surface (Fig. 6b) for the main fault is provided by a trishear angle of 76◦ at the center of the structure and 70◦ at the edges. The trishear zone distribution is asymmetrical at the center of the structure with the fault propagation folding developed in the hanging wall (θ1 = θ , θ2 = 0), resulting in a quite wide anticline and a narrow front syncline with the forelimb presenting a gentle slope. How- ever, the trishear zone at the fault tips is symmetrically distributed between the hanging wall and the footwall (θ1 = θ2), so that the anticline is slightly narrower, the front syncline is wider and the forelimb is steeper than at the center of the structure. The P/S ratio is 3, remaining constant throughout the entire main fault. The propagating fault tip is initially located at 4.7 km deep. The trishear area of Backthrust 1 is defined by a trishear angle of 70◦ asymmetrically oriented (θ2 = 1.5θ1) presenting a narrow anticline and a broad frontal syncline resulting in a forelimb with a slight slope. The P/S ratio obtained for Backthrust 1 is 2 and the fault tip is initially located at 0.75 km of depth. Backthrust 2 was mod- eled with a trishear angle smaller (36◦) asymmetrically distributed (θ2 = 4θ1) presenting a folding mostly developed in the footwall, where the front syncline is very wide comparing with the narrow anticline and the forelimb slope is very gentle. The propagating fault tip for Backthrust 2 was initially located at 1.2 km of depth. The P/S ratios obtained reflect that the development of the fold- ing ahead of the main fault is minor compared with the folding development associated with backthrusts, because the main fault presents a larger P/S ratio which entails a narrowing of the defor- mation zone (Hardly and Ford, 1997). These P/S ratios and fault tip depths obtained for the main fault and both backthrusts allow these fault ruptures to reach the surface as it is demonstrated by the presence of craters cut by the main fault and the Backthrust 1 (Herrero-Gil et al., 2019). The 3D forward model provides a good estimate for the dis- tribution of the cumulative fault displacement on each fault. The largest fault slips were generally found at the central zone of each fault and decay to zero towards the lateral tips, although the shape of the slip distribution is different for each fault (Fig. 7). Fig. 6. a. Colored topographic surface of Ogygis Rupes area where the lobate scarp relief has been removed together with the craters. b. Recreation of Ogygis Rupes topographic surface made from the topographic model a. using the fault surfaces shown in Fig. 5. (The reader is referred to the web version of this article for color interpretation.) ANEXO II 190 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 7 Fig. 7. Lengthwise profiles of Ogygis Rupes showing the fault slip distribution of the main thrust fault, Backthrust 1 and Backthrust 2 along their strike. (The reader is referred to the web version of this article for color interpretation.) The maximum displacement of the main fault corresponds to a fault slip of 2850 m, with its maximum offset located in the zone of maximum elevation of the whole structure, decreasing towards the lateral fault tips. A secondary slip peak of 2200 m occurs at ∼50 km from the northern fault tip. The relief associated with Backthrust 1 was modeled by a symmetric plateau slip distribu- tion with a maximum flat top of 1200 m. The relief produced by Backthrust 2 was obtained by an asymmetric peak slip distribution with its maximum (1800 m) located at 25 km from the southern tip. The model that best fits the topographic surface of Ogygis Ru- pes was determined by minimizing the elevation difference be- tween the forward modeled topography and MOLA observed to- pography (Fig. 8). The interquartile range associated with the ele- vation difference data of the best fit model chosen with respect to the MOLA surface is set in ∼36 m, representing the data disper- sion around a median value set in ∼7 m. Fig. 8. Absolute elevation difference between the best fit topographic surface ob- tained in the 3D forward modeling and Ogygis Rupes original surface (MOLA). Zero values represent a perfect match between our model and observed topography. (The reader is referred to the web version of this article for color interpretation.) 5. Discussion The resulting topographic surface obtained through the 3D modeling of Ogygis Rupes demonstrates that this is a good ap- proach to recreate lobate scarp morphologies, providing a general view of the whole structure and the parameters that define it. However, some limitations might condition our results, and previ- ous studies must be taken into account when analyzing the validity of the results obtained. Impact craters and associated ejecta were removed in the topo- graphical surface used as a base for the forward modeling (Fig. 6a). This causes that when comparing the surface obtained from the forward modeling (Fig. 6b) with the original one (Fig. 4a), the greater elevation differences match with the location of the craters and not with the relief of the lobate scarp (Fig. 8). Thus, the main contribution to the misfit between the 3D forward model and MOLA topography observed in Fig. 8 corresponds to the craters and not to the modeling of the tectonic structure. In order to avoid this effect, the topographic data from craters were filtered when calculating the model-MOLA topography misfit. The median value of the elevation difference obtained when comparing the best fit modeled surface with the original MOLA surface is ∼7 m. The interquartile range reflects that half of the data is concentrated be- tween −8 m and 28 m. Although the structure of Ogygis Rupes is well preserved, and the erosional rates on Mars are estimated to have been low (e.g., Golombek and Bridges, 2000; Golombek and Phillips, 2010), specifically in Aonia Terra since lobate scarp for- mation (Herrero-Gil et al., 2019), some erosive agents have slightly modified the relief. There is a small depression in the southern half of Ogygis Rupes anticline caused by the presence of channels (Klimczak et al., 2018) which has not been taken into considera- tion during modeling, consequently the forward modeled surface presents a slightly higher elevation than the observed MOLA to- pography in this area. Another small misfit between modeled and original surfaces is observed at the scarp base, which can be par- tially covered by sediments from the scarp front, including rock- falls and alluvial deposits. Some assumptions needed to simplify the model might affect the results obtained. The main thrust fault underlying Ogygis Ru- pes was assumed to have a dip-slip kinematics, excluding the pos- sibility of any strike-slip component for which no evidence was found. The large trace of the main fault suggests that it could be formed by more than one segment (Klimczak et al., 2018), but this is not clearly appreciable on the surface since the scarp base seems to be continuous and there are not remarkable strike changes. If the main fault were composed of several segments, they would be hard-linked (Klimczak et al., 2018) as evidenced by the re- sults obtained by modeling the main fault as a single fault surface. There are other limitations of the method itself that may influence the uplifted relief, including the end of the fold formation when ANEXO II 191 8 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 the fault rupture reaches the surface or errors associated with the building of 3D surfaces where the faults were idealized as smooth surfaces without irregularities (Watkins et al., 2015). Previous works about lobate scarps on Mars and other plane- tary bodies using the elastic dislocation approach generally mod- eled the faults underlying lobate scarps using planar geometries (e.g., Schultz and Watters, 2001; Watters et al., 2002, 2016; Grott et al., 2007; Egea-González et al., 2012, 2017; Byrne et al., 2015; Herrero-Gil et al., 2019). Some non-planar geometries were pro- posed for lobate scarps using elastic dislocation modeling (Schultz and Watters, 2001; Watters et al., 2002) but they did not provide fits as good as planar geometries. Mueller et al. (2014), using struc- tural techniques based on area balanced cross sections, presented a curved listric geometry for the fault underlying Amenthes attend- ing to the surface characteristics of the uplifted topography, show- ing a fault propagation fold similar to those developed in terrestrial continental crust. Studies of listric thrust faults on Earth allow to establish a relationship between fault propagation fold and fault geometry (e.g. Erslev, 1986; Seeber and Sorlien, 2000; Amos et al., 2007), defining a broad gentle backlimb and an abrupt forelimb, which is exactly the surface geometry of lobate scarps. The gentle backlimb corresponds to the surface manifestation of a differen- tial tilt between the hanging wall and footwall blocks as a result of the displacement over a positive listric fault (e.g., Erslev, 1986; Johnson and Johnson, 2002; Amos et al., 2007). The fault surfaces modeled in the present work for the main thrust fault and the two backthrusts show planar geometries in the upper kilometers while they present a decreasing dip angle at depth (Fig. 5), with a curved listric shape, according to the morphology of the backlimb and the trailing syncline, which is consistent with the knowledge of thrust fault propagation across the terrestrial brittle lithosphere (e.g., Amos et al., 2007; Cardozo and Brandenburg, 2014; Jayan- gondaperumal et al., 2015), with numerical models (e.g., Ellis et al., 2004; Cardozo and Brandenburg, 2014; Pei et al., 2014) and with analog models (e.g., Ellis et al., 2004). An abrupt dip change when reaching the decollement depth entails a very steep back- limb leading to an angular and narrow trailing syncline that does not reflect what is observed in the lobate scarp topography (see Supplementary Fig. S1). The trishear parameters obtained from 3D modeling define the fault propagation folding. In the main fault, trishear parameters vary along the structure affecting the distribution of the folding between hanging wall and footwall. In the center of the main fault the folding affects the hanging wall, while it is equally dis- tributed between the hanging wall and the footwall towards the lateral fault tips. The variation of trishear angle along strike, to- gether with the variation of slip distribution, can involve a slight volume change due to 3D formulation that in nature is solved by different processes as subordinated folding or faulting, com- paction or dissolution (Cardozo, 2008). Pei et al. (2014) analyzed 13 natural examples previously modeled by Trishear algorithms (e.g., Allmendinger, 1998; Hardly and Ford, 1997; Cardozo, 2005) to set a range of best-fit parameters when analyzed natural struc- tures by Trishear, with P/S ratios of 2–3, trishear angles between 30◦ and 100◦ , and fault dips from 25◦ to 45◦ . The resulting pa- rameters obtained for the main fault and the backthrusts forming Ogygis Rupes (Table 1), are within these ranges. Ogygis Rupes was previously studied by Herrero-Gil et al. (2019), using BCS and FMD methods to get an approximation to the parameters of the main fault underlying the structure. The fault parameters obtained in the present study agree with the ones ob- tained by BCS. The depth of faulting resulting from BCS method (18 km) is very similar than the depth of faulting obtained in the present study (17.2–17.8 km), as well as the fault slip value (2900 m). These similar results were expected because the Fault Parallel Flow and the Trishear algorithms applied in a 3D approach con- serve volume within reasonable limits (∼2% volume loss; Cardozo, 2008). However, some variation of the derived parameters is ap- preciated if we compare our results with those obtained by the FMD method. The maximum fault slip value obtained in this study (2850 m) is in the range obtained by the FMD method (2500–3100 m). The dip angle obtained here (39◦) is slightly larger than the one obtained with the FMD method (35◦); although it is somewhat high for thrust faults (e.g., Jaeger and Cook, 1979; Watters and Nimmo, 2010), it is included in the range (20–40◦) obtained from several modelings of martian lobate scarps (Fig. 9). The depth of faulting calculated in the present study (∼17–18 km) is shallower than the range obtained by FMD method (20–27 km) (Herrero-Gil et al., 2019). The range of depths obtained by FMD corresponds to the depths where the modeled fault slip decreases from the total slip at 20 km to zero slip at 27 km, which has been inter- preted to correspond to the propagation of the fault into the BDT (Herrero-Gil et al., 2019). The algorithms used in the 3D models of our study were designed for deformations in the brittle litho- spheric domain characterized by faulting and folding with volume conservation (Cristallini and Allmendinger, 2001; Cardozo, 2008; Ziesch et al., 2014). Thus, the level at which the modeled fault roots (with a listric geometry that transmits the total fault slip from the decollement level due to tectonic regional shortening), can be interpreted to be the lower limit of the lithospheric brit- tle domain (the upper boundary of the BDT zone). Consequently, the comparison between both methods should contrast the upper limit of FMD (20 km) with the depth of faulting obtained in this study (∼17–18 km). The more realistic 3D model provides for Ogy- gis Rupes a result 2–3 km shallower for the upper boundary of the BDT. Previous heat flow calculations (giving 30–51 mWm−2) for Ogygis Rupes used the entire range of 18–27 km for the BDT obtained from both BCS and FMD methods by Herrero-Gil et al. (2019); therefore the results here obtained support the upper val- ues of the calculated range, but would not substantially modify them. The fault slip distribution of the main thrust fault of Ogygis Rupes, being roughly greater at the center of the structure and de- creasing towards the lateral fault tips, was previously observed by Klimczak et al. (2018) and Herrero-Gil et al. (2019), and it is con- sistent with fault growth models of fracture mechanics (Cowie and Scholz, 1992b; Bürgmann et al., 1994). The modeled slip distribu- tion of the main fault presents a secondary plateau located NE of the main peak (Fig. 7) in agreement with the relief profile of Ogy- gis Rupes (Klimczak et al., 2018; Herrero-Gil et al., 2019). Our modeling of Ogygis Rupes backthrusts shows that these faults present low dip angles (22–23◦) compared with the main fault, which can be explained by a passive transportation of the backthrusts over the main listric thrust fault causing a de- crease of their dip angles with the evolution of the structure (Ellis et al., 2004). The backthrusts reach the main fault surface at 2.3–2.9 and 5.5–5.6 km deep, which are much shallower depths than the depth where the main fault roots. The listric geometries of both subsidiary faults, together with the fact that they root at different depth than the main thrust fault, provide evidence of in- ternal mechanical discontinuities inside the brittle domain of the lithosphere. 5.1. Implications for Mars tectonics A comparison of dip and depth of faulting between our re- sults and previous studies of lobate scarps formed in the Late Noachian/Early Hesperian (Fig. 9) shows that the results obtained here for Ogygis Rupes are well defined and close to the left edge of the data distribution of previous estimates as shown in the figure. The depth of faulting calculated for Ogygis Rupes (17–18 km) is a ANEXO II 192 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 9 Fig. 9. Dip angle (◦) as function of depth of faulting (km) from the different studies performed in Late Noachian/Early Hesperian lobate scarps on Mars. The represented dip angle from the studies that modeled listric fault morphologies (Mueller et al., 2014; and the present study) is the fault dip near the surface. The data has been represented as points, lines or rectangles depending on the range of the value. (The reader is referred to the web version of this article for color interpretation.) bit lower than the values usually estimated by previous works but agrees with the low depths of faulting obtained by Egea-González et al. (2017) for Chalcophoros and Thyles Rupis (although as noted by those authors, the topography near both structures is affected by other structures, which could have affected the modeling). The combination of Trishear and Fault Parallel Flow algorithms in a 3D modeling allows to model, for the first time, the fault propagation fold of a lobate scarp using a listric fault geometry, which is a significant advance with respect to previous methods. Although we have analyzed by 3D modeling only one lobate scarp (Ogygis Rupes), the results provide shallower depths of faulting than those obtained by Herrero-Gil et al. (2019) with FMD (Fig. 9). If this difference is confirmed in the future for other lobate scarps, it would suggest that BDT was slightly shallower, likely requiring a higher global thermal flow at the time of formation. The listric geometry obtained for the main fault at depth, sug- gests that the fault slip on the fault ramp was entirely transmitted from the decollement in which the fault is rooted. This interpre- tation is in good agreement with the well-known mechanics of formation and propagation of large thrust fault systems (e.g. Amos et al., 2007; Cardozo and Brandenburg, 2014; Ellis et al., 2004; Pei et al., 2014). Large thrust faults on Earth usually nucleate from a subhorizontal decollement and propagate with ramps towards the surface. The good fit of the fault propagation fold of Ogygis Rupes 3D model confirms that the fault propagates upwards and conse- quently the amount of accumulated fault slip decreases upwards. Therefore shortening calculations should consider that the fault slip on the ramps was entirely transmitted from the decollement level, so the shortened distance equals the fault slip at the ramp. This interpretation, supported by the 3D models, provides larger shortening estimates than when shortening is obtained from the horizontal component of the fault slip at the ramp (heave). For a given fault slip (S) on the ramp, the heave (Sh) is S · cosβ , being β the dip angle of the ramp. Therefore, the total slip value considered to be the shortened distance transmitted from the decollement, provides an estimate between ∼6 and ∼30% (for 20◦–40◦ dips) larger than the heave value (Sh) calculated on the fault ramp. Global shortening estimates for lobate scarps will be hence in- creased up to ∼30% under the assumption that the fault slips of these large faults on Mars are completely transmitted from the BDT. A larger shortening associated with lobate scarps than previ- ously thought (if confirmed for other cases) could have impor- tant implications for the thermal history of Mars. Indeed, Nahm and Schultz (2011) estimated that the shortening related to lo- bate scarps and wrinkle ridges implied a lower amount of time- cumulated global contraction than expected from thermal history models (Andrews-Hanna et al., 2008). This would be consistent with limited secular cooling of the martian interior, at least during some phases of their thermal history (Ruiz et al., 2011), because reduced mantle cooling limits the thermal contraction that can drive surface contraction. Subsequently, Klimczak (2015) proposed that elastic deformation of the lithosphere could accommodate a certain level of contraction previously to the beginning of thrust faulting, adding a substantial amount of potential contraction, up to ∼40% more, with respect to Nahm and Schultz (2011) estimate. By increasing the shortening associated with thrust faults due to a listric morphology, the total amount of contraction recorded by martian thrust faults could be up to 70% higher than previ- ously thought. This continues to be lower than theoretical expec- tations (Andrews-Hanna et al., 2008; Nahm and Schultz, 2011), but ANEXO II 193 10 A. Herrero-Gil et al. / Earth and Planetary Science Letters 532 (2020) 116004 would confirm that substantial contraction occurred in the Late Noachian/Early Hesperian time. 6. Conclusions The 3D forward modeling of Ogygis Rupes through the com- bination of Trishear fault propagation folding and Fault Parallel Flow algorithms shows that this method is a consistent and ac- curate approach to recreate lobate scarp structures, expanding the information about their geometry and kinematics. The three mod- eled faults, including the main thrust fault and two backthrusts, show listric geometries at depth, according to analog and numeri- cal models, and studies of large thrust faults on Earth. The main thrust fault roots into a horizontal decollement at ∼17–18 km deep, which is assumed to be the BDT at the time of formation (Late Noachian/Early Hesperian). The listric morphology where the main fault roots into the BDT implies that the total fault slip was transmitted from the decollement to the fault ramp, leading to a larger regional shortening estimate related to the lobate scarp for- mation than if the shortening is interpreted to be only the heave of a planar fault. The two backthrusts of Ogygis Rupes show shallower depths of faulting estimated at ∼2.5 km and ∼5.5 km, probably in- dicating the presence of mechanical discontinuities in the martian brittle lithosphere. Declaration of competing interest The authors declare that they have no known competing finan- cial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements This research has been supported by the project PR75/18-21613 funded by the research program Santander-UCM, and TECTOMARS (PGC2018-095340-B-I00), funded by the Spanish Ministry of Sci- ence, Innovation and Universities. A. Herrero-Gil work has been supported by a FPI2015 grant BES-2015-073983, funded by the Spanish Ministry of Economy and Competitiveness (MINECO). The software MOVETM 2018.2 was provided by Petroleum Experts Ltd. through the donation of an Academic license to the Department of Geodynamics, Stratigraphy and Paleontology of the Universi- dad Complutense de Madrid. We appreciate the constructive com- ments of the editor W. B. McKinnon, C. Klimczak and an anony- mous reviewer, which substantially improved the quality of the manuscript. We also thank P. 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Icarus 215, 603–607. Zehnder, A.T., Allmendinger, R.W., 2000. Velocity field for the trishear model. J. Struct. Geol. 22, 1009–1014. Ziesch, J., Tanner, D.C., Krawczyk, C.M., 2014. Strain associated with the Fault-Parallel Flow algorithm during kinematic fault displacement. Math. Geosci. 46, 59–73. ANEXO II 195 3D modeling of planetary lobate scarps: the case of Ogygis Rupes, Mars Andrea Herrero-Gila*, Javier Ruiza, Ignacio Romeoa SUPPLEMENTARY MATERIAL A forward 3D model of Ogygis Rupes with planar fault geometries (constant dip angle) for the main fault and the two backthrusts (Fig. S1. b) has been performed in order to check if it can reproduce the observed topographic surface (Fig. S1. a). The parameters used during the modeling for each fault are summarized in Table S1. Fig.S1. (a) Original topographic surface (MOLA) of Ogygis Rupes overlaying THEMIS-IR Day. The main fault and the two backthrusts are mapped. (b) Modeled surface obtained using planar fault surfaces, keeping a constant dip angle at depth. (c) Elevation misfit between the original MOLA topography and the modeled surface. (d) Cross section D-D’ (marked in a and b) in which the model profile (green line) is superposed on the topographic profile (black line). The planar main fault is shown in red. ANEXO II Supplmentary material 197 The resulting modeled surface reflects a planar and wide scarp crest and a narrow and steep backlimb (Fig. S1. b) with a slope angle equal to the fault dip angle, limited by neat margins (Fig S1. d), due to the use of planar fault surfaces (e.g. Amos et al. 2007; Ziesch et al., 2014). This model does not match the original topography of the backlimb. This is caused by the sharp dip change when the fault reaches the detachment level. The surface elevation misfit (Fig S1. c) between the original MOLA topography and the model, shows a large misfit between this narrow and steep backlimb and the real gentle backlimb that the lobate scarp presents. This effect is also present in the backlimbs of the backthrusts, but the misfit in this case is less pronounced due to the minor relief associated with these structures. The fault propagation fold is controlled by the trishear parameters, which have remained unchanged (Table S1). That is the reason why no changes are observed in the modeling of the forelimb of the fault propagation fold with respect to Fig. 5b. Table S1 Fault and trishear parameters calculated for Ogygis Rupes using planar fault planes. Length (km) Depth (km) Dip angle(°) Max. fault slip (m) Trishear angle (°) Fault tip depth (m) P/S ratio Main fault 220 17.2–17.8 39 2850 76 (center), 70 (edges) -4700 3 Backfault 1 66 2.3–2.9 22 1200 70 -750 2 Backfault 2 65 5.5–5.6 23 1800 36 -1200 2 References: Amos, C.B., Burbank, D.W., Nobes, D.C., Read, S.A.L., 2007. Geomorphic constraints on listric thrust faulting: Implications for active deformation in the Mackenzie Basin, South Island, New Zealand. Journal of Geophysical Research 112, B03S11. Ziesch, J., Tanner, D.C., Krawczyk, C.M., 2014. Strain associated with the Fault-Parallel Flow algorithm during kinematic fault displacement. Mathematical Geosciences 46, 59–73. ANEXO II Supplmentary material 198 ANEXO III Herrero-Gil, A., Ruiz, J., Romeo, I., 2020. Lithospheric contraction on Mars: A 3D model of the Amenthes thrust fault system. Journal of Geophysical Research: Planets 125 (3), e2019JE006 Supplementary material S2 Lithospheric Contraction on Mars: A 3D Model of the Amenthes Thrust Fault System A. Herrero‐Gil1 , J. Ruiz1 , and I. Romeo1 1Departamento de Geodinámica, Estratigrafía y Paleontología, Universidad Complutense de Madrid, Madrid, Spain Abstract Amenthes Rupes is the topographic expression of a main fault belonging to a thrust fault system located parallel to the martian dichotomy boundary. A 3D forward model has been applied to the Amenthes thrust fault system, constraining fault geometries at depth, variations of slip along strike, and structural parameters controlling the formation of fault propagation folds. Our results provide a complex 3D view of the tectonic framework of the area, with implications for tectonic evolution, regional shortening distribution, and the main mechanical discontinuities in the lithosphere. The modeled fault surfaces show planar morphologies combined with listric geometries at depth. The obtained depths of faulting for the major faults of this fault system suggest a depth of the brittle‐ductile transition (at the time of formation) of 20–24 km, somewhat shallower than previous estimates for this area. A possible mechanical discontinuity located at 9.5–13 km deep can be deduced from the faulting depths of the secondary faults. The listric geometries at depth imply that slip is transmitted from the decollement, which, together with the inclusion in the model of secondary and subsidiary faults, allow us to estimate the horizontal shortening recorded in this area ranging from 2–3 km up to ~5.5 km in the southeastern part of the fault system. This range increases the previous shortening estimates in this area between ~60% and ~200%. Consequently, global shortening estimates based on global fault maps are biased by the detail of mapping, and shortening would substantially increase if secondary faults were included. Plain Language Summary Amenthes Rupes is a large topographic relief known as a lobate scarp, formed by the displacement of a contractional fault belonging to a fault system located in the Amenthes Region, Mars. The study of the faults forming these reliefs provides insights on the faulting and folding processes, which are related to the state of the lithosphere at the time of formation. A 3D modeling has been applied to Amenthes fault system, modeling fault geometries at depth, interaction between faults, associated slip values, depth of faulting, and other parameters that control the formation of the relief. These results provide a complex 3D view of how the area contracted. The obtained fault surfaces show curved geometries at depth. The major faults in the fault system root at a depth where ductile deformation in the lithosphere begins, estimated to be at 20–24 km. The estimated regional horizontal shortening accommodated by the fault system range between 2 and ~5.5 km, which increases the shortening in this area between 60% and 200% compared with previous estimates. This recognizes that the inclusion of secondary faults in global contraction models would increase substantially the global shortening estimates. 1. Introduction Lobate scarps are positive structural reliefs observed on terrestrial planetary surfaces, assumed to be the expression of large thrust faults (e.g., Anguita et al., 2006; Schultz & Watters, 2001; Strom et al., 1975; Watters & Nimmo, 2010; Watters & Robinson, 1999). These structures present an asymmetric relief that shows the characteristic morphology of a fault‐related fold caused by the displacement of a low angle thrust fault breaking the topographic surface. The lobate scarp uplift is formed by an anticline with a gentle trailing flank (backlimb) and a frontal abrupt flank forming the scarp face (forelimb). A trailing syncline and a fron- tal syncline are usually present on each side of the anticline (e.g., Grott et al., 2007; Herrero‐Gil et al., 2019, 2020; Schultz, 2000; Schultz & Watters, 2001). The large thrust faults underlying lobate scarps have been studied and modeled by several authors on different terrestrial bodies like Mars (e.g., Egea‐González et al., 2017; Grott et al., 2007; Herrero‐Gil et al., 2019, 2020; Klimczak et al., 2018; Mueller et al., 2014; Ruiz et al., 2008; Ruj et al., 2018; Schultz & Watters, 2001), Mercury (e.g., Crane & Klimczak, 2019; Egea‐ González et al., 2012; Galluzzi et al., 2015, 2019; Giacomini et al., 2019; Semenzato et al., 2018; Watters et al., ©2020. American Geophysical Union. All Rights Reserved. RESEARCH ARTICLE 10.1029/2019JE006201 Key Points: • A 3D forward model combining fault‐parallel flow and trishear gives listric fault geometries at depth for the Amenthes thrust fault system • Major faults root at 20–24 km deep, interpreted to be the brittle‐ductile transition, while secondary faults root at 9.5–13 km • Considering secondary faults increases regional shortening by 60% to 200%, implying higher global contraction than previously estimated Supporting Information: • Supporting Information Data S1 Correspondence to: A. Herrero‐Gil, andreaherrero@ucm.es Citation: Herrero‐Gil, A., Ruiz, J., & Romeo, I. (2020). Lithospheric contraction on Mars: A 3D model of the Amenthes thrust fault system. Journal of Geophysical Research: Planets, 125, e2019JE006201. https://doi.org/ 10.1029/2019JE006201 Received 9 SEP 2019 Accepted 15 FEB 2020 Accepted article online 3 MAR 2020 Corrected 12 JUNE 2020 This article was corrected on 12 JUNE 2020. See the end of the full text for details. HERRERO‐GIL ET AL. 1 of 17 ANEXO III 201 2002), the Moon (e.g., Byrne et al., 2015; Williams et al., 2013), Ceres (Ruiz et al., 2019), and asteroid 433 Eros (Watters et al., 2011). These works usually include the study of the timing of faulting and the analysis of the structural parameters that define the fault morphology and kinematics (depth of faulting, dip angle and fault slip), with the final aim of advancing on the knowledge of the tectonic and thermal evolution of these terrestrial bodies. The modeling of the structural parameters is performed assuming that fault geometry and fault slip control lobate scarp topography (Schultz & Watters, 2001; Watters et al., 2002). The study of martian lobate scarps provides insights on the rheology of the martian lithosphere at the time of formation (Ruiz et al., 2008). The depth of faulting of the large underlying faults has been related to a main rheological discontinuity, that on Mars is considered to represent the brittle‐ductile transition (BDT) at the time of lobate scarp formation (e.g., Grott et al., 2007; Ruiz et al., 2008, 2009; Schultz & Watters, 2001). The most studied lobate scarp on Mars is Amenthes Rupes (e.g., Egea‐González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008; Schultz, 2003; Schultz & Watters, 2001; Watters et al., 2000), due to its large dimen- sions and its location near the dichotomy boundary (Watters, 2003b) (Figure 1), which makes its study essential when analyzing the mechanical and thermal properties and the evolution of the lithosphere of Mars (e.g., Egea‐González et al., 2017; Ruiz et al., 2011; Schultz & Watters, 2001). The Amenthes Rupes lobate scarp, as well as most of the lobate scarps modeled on Mars, has been modeled through 2D cross sec- tions analysis (e.g., Egea‐González et al., 2017; Grott et al., 2007; Herrero‐Gil et al., 2019; Mueller et al., 2014; Ruiz et al., 2008; Schultz & Watters, 2001). This 2D modeling applied to lobate scarps restricts the results obtained to the chosen cross sections of structures that are hundreds of kilometers long and present signifi- cant variations along their length (e.g., Herrero‐Gil et al., 2020; Klimczak et al., 2018). Besides, Amenthes Rupes is not formed by an isolated fault. This is the largest structure belonging to a structural set of surface breaking thrust faults (Schultz, 2003; Watters & Robinson, 1999) located in the Amenthes Region (Figure 1). The complexity of the interaction between these faults and the main Amenthes thrust fault controls the topographic expression of lobate scarps in this area. Figure 1. Structural map of the study area of Amenthes Region. The base map is made by combining a MOLA model (DEM) over a THEMIS‐IR Day image. The thrust faults included in the modeling are colored in red. The inset globe shows the location of the study area. 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 2 of 17 ANEXO III 202 The 3D modeling of lobate scarps allows expansion of our knowledge of fault geometries at depth, fault kinematics and the mechanical structure of the lithosphere at the time of formation (Herrero‐Gil et al., 2020). Here we show the results of a detailed 3D modeling of the Amenthes thrust fault system providing information about the fault geometries and fault related folding, together with the variations of the struc- tural parameters along their strike and with depth, and the interaction between faults, resulting in a complex tectonic framework. This 3D procedure provides a step forward in the understanding of thrust fault systems on Mars compared with previous 2D approaches. The depth of faulting of the main modeled faults provides estimates of the BDT depth at the time of formation. In addition, the study of the secondary and subsidiary faults provides information about the presence of mechanical discontinuities in the crust. This analysis also provides insights about the nature of the deformation in this region close to the martian dichotomy bound- ary, as well as about the general processes that formed martian lobate scarps and the amount of horizontal contraction implied (the terms “contraction” and “contractional structures” are used through the text in the sense of structures generated by linear horizontal contractional deformation, i.e., shortening), which in turn has implications for the tectonic and thermal evolution of Mars. 1.1. Amenthes Rupes Amenthes Rupes is located in the heavily cratered highlands of Mars (e.g., Caprarelli et al., 2007; Erkeling et al., 2011; Mueller et al., 2014; Schultz, 2003; Schultz & Watters, 2001; Watters, 2003b), specifically in the northeast of the Amenthes Region. This topographic structure is the morphological expression of the dis- placement on a large thrust fault with surface rupture (e.g., Mueller et al., 2014; Schultz & Watters, 2001). The main thrust fault that forms Amenthes Rupes is part of an array of five thrust faults underlying a set of lobate scarps (Schultz, 2003; Watters & Robinson, 1999), striking 120–140°E (Figure 1), parallel to the NE margin of Amenthes Planum (Caprarelli et al., 2007), which is located southwest. The Amenthes Rupes lobate scarp was formed in the Late Noachian/Early Hesperian (e.g., Schultz & Watters, 2001; Watters & Robinson, 1999), around 3.7 Ga ago (Egea‐González et al., 2017). The Late Noachian highland crust, where lobate scarps formed, is expected to be formed by nonlayered rocks with more isotropic character than the Amazonian‐Hesperian units that postdate them (e.g., Mueller et al., 2014; Schultz, 2000). Martian erosion rates have remained very low from Hesperian to the present (e.g., Golombek & Bridges, 2000; Golombek & Phillips, 2010), and this area does not show significant signs of ero- sion affecting the lobate scarps. However, the structural relief related to this fault system was modified by several impact craters, some of them clearly postdating its formation. A geological unit of Amazonian‐Hesperian age postdates the Late Noachian cratered terrains, forming smooth plains in the areas of low topographic relief, as well as infilling most of the craters (Erkeling et al., 2011). Amenthes Rupes has aroused great interest due to its proximity to the dichotomy boundary. This is the lar- gest of a series of lobate scarps located between 100 and 500 km southwest of the dichotomy boundary, in the highlands of Arabia Terra, Amenthes Region and Terra Cimmeria. These lobate scarps are roughly parallel to the dichotomy boundary and record a contractional strain perpendicular to this boundary (e.g., McGill & Dimitriou, 1990; Nimmo, 2005; Watters, 2003a, 2003b; Watters et al., 2007; Watters & Robinson, 1999). The deformation along the dichotomy boundary in these areas occurred during the Late Noachian and Early Hesperian (McGill & Dimitriou, 1990; Nimmo, 2005; Ruiz et al., 2008; Watters & Robinson, 1999), postdat- ing the formation of the dichotomy boundary but being important in the shaping of its current relief. These observations suggest that the formation of the lobate scarps in these areas is related to the dichotomy bound- ary (Watters & Robinson, 1999), which has been associated with lithospheric flexure (Watters, 2003a; Watters & McGovern, 2006). The formation of Amenthes Rupes has been also related to the Isidis basin due to its radial orientation with respect to the basin center (Wichman & Schultz, 1989). Egea‐González et al. (2017) included Amenthes Rupes in their circum‐Hellas study since it presents a concentric orientation to Hellas basin, being orthogonal to a compressive stress associated with this large impact basin. Similar con- tractional structures parallel to Amenthes Rupes can be found closer to Hellas basin (Cerberus Dorsa). Previous studies focused on modeling Amenthes Rupes had as a main objective the calculation of the depth of faulting of the underlying fault, which on Mars is assumed to coincide with the BDT at the time of fault- ing. This BDT depth has been used to model the thermal structure of the early martian lithosphere and to calculate the heat flow values during the Late Noachian/Early Hesperian (Egea‐González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008, 2011; Schultz & Watters, 2001). 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 3 of 17 ANEXO III 203 The forward mechanical dislocation (FMD) method (Toda et al., 1998, 2005) that models the surface as an elastic halfspace and the balanced cross sections (BCS) method (Chamberlin, 1910, 1919; Dahlstrom, 1969) based on mass conservation are the two approaches previously applied to model 2D topographic pro- files across Amenthes Rupes. Although non‐planar fault morphologies (listric fault geometries) have been proposed to explain lobate scarp formation (Mueller et al., 2014; Watters & Nimmo, 2010), previous works that have modeled Amenthes Rupes with FMD method present the fault plane as a planar surface with a constant dip, because the results obtained using non‐planar geometries did not provide satisfactory results (Schultz & Watters, 2001). Schultz and Watters (2001) modeled two cross sections of Amenthes Rupes with FMD method to obtain a depth of faulting of 25–30 km. The same method was later applied by Ruiz et al. (2008) to a perpendicular cross section obtaining a depth of faulting of 27–35 km, and by Egea‐González et al. (2017) to obtain a depth of faulting of 27–33 km. The BCS method was used by Mueller et al. (2014) proposing a listric fault, due to the topographic characteristics of the lobate scarp, obtaining a depth of fault- ing of 33–48 km. 2. Data and Method The objective of the 3D modeling of lobate scarps is to obtain fault geometries, slip distribution, and trishear parameters that best replicate the topographic surface uplifted by each fault with the smallest misfit with the observed topography. A detail mapping of the studied structures is necessary before the modeling process to identify the fault structures of the area. The topographic base used for the mapping and modeling of Amenthes thrust fault system is the Mars Orbiter Laser Altimeter data (MOLA, Mars Global Surveyor) with a ~463 m/pixel resolution (Smith et al., 2001; Zuber et al., 1992). The main base image used during mapping is the Thermal Emission Imaging System (THEMIS, Mars Odyssey mission) daytime infrared (IR) model with a 100 m/pixel resolution (Christensen et al., 2004). The Context Camera images (CTX, Mars Reconnaissance Orbiter) (Malin et al., 2007) have been consulted occasionally. The analysis of the MOLA topography, together with THEMIS and CTX images, allowed us to make a detailed structural map of the area (Figure 1). The identification of the tectonic structures in the area was performed by analyzing several profiles, attending to slope changes to identify the reliefs that may be related to tectonic deformation. THEMIS images (or CTX images when more resolution was needed) were used to verify their tectonic origin and to trace them in the map. The five large thrust faults underlying the reliefs that meet the description of lobate scarp, together with their associated fold structures, were mapped following this procedure. Other minor contractional structures have been identified in the area. The minor thrust faults have been distin- guish from wrinkle ridges because it was possible to identify the vergence of the structure due to the uplift of the hanging wall. Nevertheless, wrinkle ridges present a lower relief and a complex structure that requires an exhaustive analysis to identify the vergence of the underlying thrust faults, which is not the objective of this work, so we have kept this morphological term in the structural map. The folding associated with thrust fault generation has been considered, in this study, to be caused by fault propagation folding since the morphologies of other fault‐related folds, like fault‐bend folds and detachment folds, do not match the observations (Jamison, 1987). Displacement‐gradient folds (Wickham, 1995) have been proposed to play a role in the folding process of lobate scarps (e.g., Klimczak et al., 2018), but a simple fault propagation foldingmechanism has been chosen for modeling simplification purposes. The role of fault propagation folding is strongly supported by the evidence of surface rupture. The fault propagation fold of each lobate scarp forming the Amenthes Rupes fault system has been modeled using the fault‐parallel flow (Egan et al., 1997; Kane et al., 1997; Wheeler, 1987) and trishear (Allmendinger, 1998; Erslev, 1991) algo- rithms applied in a 3D modeling framework (Cardozo, 2008; Cristallini & Allmendinger, 2001) using MOVETM software (Midland Valley). The fault‐parallel flow algorithm determines the deformation of the hanging wall caused by the displacement over a complex fault geometry, while the trishear method defines the deformation distributed ahead of a propagating tip point. The combination of both algorithms is a pure geometric approach, which was designed for modeling strain in the brittle lithosphere, characterized by faulting and folding assuming volume conservation (e.g., Cristallini & Allmendinger, 2001; Ziesch et al., 2014). This combination has been proven useful in the modeling of thrust belts on Earth (e.g., Cardozo, 2008; Cardozo & Brandenburg, 2014; Cristallini & Allmendinger, 2001; Li et al., 2020; Maesano et al., 2013; Watkins et al., 2015) to constrain the tectonic scenarios at depth due to the possibility of varying the parameters that define faulting and folding along the structure. It has also been applied to model Ogygis 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 4 of 17 ANEXO III 204 Rupes lobate scarp together with two subsidiary backthrusts (Herrero‐Gil et al., 2020) on Mars. The topographic surface of Amenthes Region has been modeled attending to the premise that the erosion rates on Mars have remained low since lobate scarps formation (e.g., Golombek & Phillips, 2010). We have assumed that no other mechanisms has substan- tially altered the slopes of the structural reliefs identified as the result of the displacement of the underlying thrust fault system, although some gravitational deposits at the scarps bases can be observed at some scarce locations. Fault‐parallel flow algorithms constrain the movement of the hanging wall over the footwall through the assumption of volume conservation (Ziesch et al., 2014). The deformation is defined by a fault‐parallel shear, where the material of the hanging wall moves in the direction of the fault slip along flow paths parallel to the fault surface. The geometry of the fault plane controls the topography of the lobate scarp (Schultz & Watters, 2001; Watters et al., 2002); specifically, the dip and depth of the fault plane mostly define the width of the associated lobate scarp (distance between the trailing syncline and the scarp base), and the fault slip controls the relief of the structure. The depth of faulting influences the amount of uplifted material, defining the location of the syncline and consequently the width of the anticline, while the dip angle of the fault is directly related to the slope of the backlimb. Accordingly, variations in fault dip at depth modify the backlimb slope. A gra- dual decrease of the dip angle at depth, flattening downwards into the decollement (resulting in listric fault geometries), creates a gentle and wider backlimb, due to a tilting of the hanging wall with respect to the foot- wall (e.g., Amos et al., 2007; Erslev, 1986; Johnson & Johnson, 2002; Ziesch et al., 2014). If the decrease of the dip angle at depth is abrupt, it generates a steeper and narrower backlimb (e.g., Amos et al., 2007; Ziesch et al., 2014). The absence of rooting level, using a fault that ends abruptly, would result in a lack of backlimb development and non‐generation of a trailing syncline. The effect in the topography caused by the variation of these fault parameters is explained in Text S1 in the supporting information. Trishear algorithms (Allmendinger, 1998; Erslev, 1991) successfully replicate the folding ahead of a propa- gating thrust fault (Figure 2). In cross section, the folding occurs in a triangular shear zone (trishear zone) defined by a variable angle (θ) (Allmendinger, 1998), where a distributed shear deforms the material ahead of a propagating fault tip. The trishear parameters define the shape of the main anticline and the frontal syn- cline, through the distribution of the trishear zone between the hanging wall and the footwall (θ1, θ2) with respect to the fault (Zehnder & Allmendinger, 2000), the depth of the initial fault tip, and the fault propaga- tion to fault slip ratio (P/S) (Hardy & Ford, 1997). A small trishear area implies that the deformation is more concentrated, creating a narrower syncline (with a steeper forelimb) than if the deformation is distributed in a larger trishear area (Allmendinger, 1998). The P/S ratio (Hardly and Ford, 1997) is directly related to the degree of fold development. Low P/S values (below 2) imply that the material spends more time in the trishear zone, undergoing more deformation of the forelimb before faulting. The effect that the variation of trishear parameters has on the uplifted topography is explained in Text S1. The modeling workflow comprises from the construction of the fault surfaces to the reproduction of the observed topographic surface through the forward slip of the thrust faults with propagating fault tips and associated trishear folding (Herrero‐Gil et al., 2020). First, a preliminary 2D restoration of the topographic surface and forward modeling were performed for several cross sections made along each fault, to get a first‐order approximation of the fault geometries. The 3D fault surfaces used during the modeling were built by interpolation between these cross sections. Second, the created 3D fault surfaces were validated thought a 3D restoration of the MOLA‐observed topographic surface. These 3D fault geometries serve as a starting point for the restoration, and their shapes were modeled until generating the best surface restoration, through the iterative variation of dip and depth along the structure paying attention to the resulting topo- graphic surface modifications (see Text S1). This restoration process shows the subsurface interaction between nearby structures and provides an approximation for fault slip values and trishear parameters. Finally, the 3D fault geometries resulting from the 3D restoration have been used in the 3D forward Figure 2. Schematic representation of trishear method (based on Hardy & Ford, 1997; Zehnder & Allmendinger, 2000). The area colored in gray is the trishear area, and it is defined by the trishear angle (θ) and its distribu- tion between the hanging wall and the footwall (θ1, θ2). The propagating fault tip is marked in blue. The velocity of the hanging wall relative to the footwall is marked by a gray slip vector, decreasing from top to bottom inside the trishear area. 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 5 of 17 ANEXO III 205 modeling. Fault slip and trishear parameters have been adjusted in this last step of the process, comparing the resulting modeled surface to the original MOLA topography until the best possible fit is achieved. The initial topographic surface used during the 3D forward modeling was obtained from the original MOLA topography, from which crater depressions, rims, ejecta and structural reliefs related to lobate scarps were removed (Herrero‐Gil et al., 2020), taking the grid points that are outside these structures and interpolating the surface using the kriging geostatistical procedure. 3. 3D Structural Analysis Results The area of study includes Amenthes Rupes (main fault) and other four major thrust faults forming the lar- gest structural reliefs (Figure 1, Table 1). The general vergence of these lobate scarps is toward the SW, except for Fault 3, which is a backthrust verging NE. The main fault and Faults 2, 3 and 4 are interrelated, their traces intersect or their associated topographies interfere with each other. Otherwise, Fault 5 is located northern to the main fault, striking parallel to it. 3.1. 3D Restoration The restoration of the lobate scarp reliefs present on the observedMOLA topographic surface (Figure 3a) has beenmade by reversing the thrust slip of the underlying 3D fault surfaces in order to obtain a surface without any relief associated with thrust faults, which is representative of the topographic surface prior to contrac- tional deformation (Figure 3b). The modeled fault surfaces reflect a planar geometry in the upper kilometers with a gradual decrease of the dip at depth, until it flattens when reaching the decollement level, resulting in listric morphologies con- strained by the shape of the structural relief. The presence of a decollement level is supported by the presence of a trailing syncline associated with all the thrust faults modeled (Figure 1). Subsurface relationships between faults appear when trying to restore MOLA topography, which allows us to group the five studied faults. Each thrust fault has been assumed to present dip‐slip reverse faulting with the slip vector of each fault perpendicular to the fault strike, since no evidence of a strike‐slip component of deformation was observed. 3.1.1. Main Fault and Fault 2 The Amenthes Rupes lobate scarp is generated by a 470 km long thrust fault. The largest relief (~1,050 m) of Amenthes Rupes is located near the center of the structure and corresponds with the crest of the fault pro- pagation anticline. The surface rupture of this thrust fault is denoted by a cross‐cut crater located approxi- mately in the middle of the structure (Mueller et al., 2014). The modeled dip angle of the main thrust fault is 27–28°NE for the first ~30–32 km (measured on the fault plane from the surface) until a depth of ~14–15 km, where the dip angle begins a gradual decrease with a listric geometry. The main fault roots into a decollement at 20 km of depth in the northwestern part of the structure, deepening up to 24 km in the southeastern part (Figures 4b and 4c). Fault 2 is a 180 km long thrust fault that entirely overlaps the southern part of the main fault, being mostly parallel to it. It is located on the hanging wall of the main thrust fault, with a spacing value of ~10 km, Table 1 Compilation of Structural Parameters Calculated for the Studied Amenthes Region Faults Name Length (km) Max. relief (m) Fault parameters Trishear parameters Strike (°) Dip angle (°) Depth of faulting (km) Max. Slip (m) Trishear angle (°) Trishear distribution P/S ratio Fault tip depth (m)θ1 θ2 Main fault (Amenthes Rupes) 470 1,050 N131E 27–28 NE 20–24 2,100 86 72 14 3 −2,050 Fault 2 (splay) 180 570 N120E 29.5 NE 23.5–24 1,300 85 71.5 13.5 2 −1,180 Fault 3 (backthrust) 220 900 N138E 31–33 SW 21.5–22.5 1,600 80 40 40 3 −2,100 Fault 4 126 800 N125E 23 NE 13 1,720 44 28.5 15.5 2 −2,700 Fault 5 Segment NW 180 600 N122E 28 NE 10.5–11.5 1,100 85 33 52 2 −940 Fault 5 Segment SE 160 480 N131E 27–27.5 NE 9.5–11 1,000 60 42 18 2 −1,800 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 6 of 17 ANEXO III 206 although it increases up to 20 km near the southeast fault tip. The maximum relief associated with this fault is ~570 m. Fault 2 is modeled as a splay fault that roots with a listric geometry at the same decollement than the main fault (Figure 4b). However, it presents a slightly higher dip angle than the main fault (29.5°NE) for the upper ~31 km measured on the fault plane from the surface (until ~15 km deep). 3.1.2. Fault 3 and Fault 4 Fault 3 is a 220 km long thrust fault verging NE, opposite to the main fault vergence (i.e., Fault 3 is a back- thrust), which presents an arcuate form in map view. Fault 3 intersects at the present topographic level with the main fault at 130 km from its southern tip point, forming a 40 km long pop‐up elevation located north of the intersection point. The main fault and Fault 3 form a pop‐down structure southwards from this intersec- tion point (Figures 4a and 4b). The lobate scarp associated with Fault 3 presents a maximum relief of 900 m in its central part. The dip angle of this backthrust is estimated to be 31–33°SW for the first ~29 km (mea- sured along the fault from the surface) until ~15 km of depth, where the dip angle decreases gradually in a listric geometry. The depth of faulting has been set at 21.5–22.5 km. Two minor faults, not included in the modeling due to their small dimensions (Figure 1), seem to distribute the displacement of this fault to the southeast. Fault 4 is a SW verging thrust fault separated 70 km southeast from Fault 3, striking parallel to it. It is a 126 km long thrust fault that overlaps along all its length with Fault 3, generating a pop‐up structure (Figures 4a and 4b). The backlimb of its associated lobate scarp presents two big craters that mask the morphology of the uplifted relief, which has been measured to be 800 m. The fault surface underlying this structure presents an estimated dip angle of 23°NE for the first ~22 km (measured along fault from the surface) that decreases gra- dually at ~9 km of depth until rooting at 13 km deep into the subhorizontal decollement (Figure 4b). 3.1.3. Fault 5 Faults 5 is located ~85 km northeast from themain fault and parallel to it, and it is formed by two linked fault segments. The NW Segment presents a linear trace 180 km long. The topography of the anticline forming the lobate scarp was modified by impact craters, but its maximum relief has been measured to be 600 m. The SE Segment is 160 km long, and it is separated ~15 km south from NW Segment, overlapping 25 km. Its trace Figure 3. (a) Original MOLA surface over a THEMIS‐IR Day image of the studied area. (b) Restored topographic surface where the uplifts present in the original MOLA model, which are related to the studied thrust faults, have been removed. 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 7 of 17 ANEXO III 207 reflects two lobes in map view, with a maximum relief peak in each lobe of approximately 500 m. Both fault segments present similar modeled dip angles (27–28°NE) near the surface (the first ~15–16 kmmeasured on the fault plane), decreasing from ~7–8 km of depth. The depth of faulting of Segment NW is calculated to be 10.5–11.5 km (Figure 4e), while the SE Segment roots at 9.5–11 km. 3.2. 3D Forward Modeling The 3D forward modeling reproduces the original topographic surface (Figure 3a) starting with the fault sur- faces obtained from the 3D restoration to deform an initial surface in which the uplifted topography related to the displacement of the thrust faults have been removed (Figure 5a). The best fit model (Figure 5b) is obtained modeling the fault propagation fold for each thrust fault along its strike, by adjusting the trishear parameters that define the folding ahead of the propagating fault tip (Table 1) and the distribution of the fault slip (Figure 6). Figure 4. (a) Perspective of the 3D model of the studied area where MOLA topographic surface has been hidden southeastern from the profile A‐A′ to show the underlying fault planes of the main fault, Fault 2, Fault 3, and Fault 4. (b) Cross section A‐A′ perpendicular to the mean strike of the faults. (c) Perspective of the 3D model where the MOLA surface has been hidden southeastern from the profile B‐B′. All the fault planes of the 3D modeling are visible. (d) Rose diagram representing the dip azimuth of the 3D fault planes included in the modeling. The mean dip azimuth (N36.6°E) is shown with a black arrow. (e) Cross section B‐B′, perpendicular to the mean strike of the studied faults. 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 8 of 17 ANEXO III 208 Main thrust fault, Fault 2, the backthrust (Fault 3), and the NW Segment of Fault 5 present large modeled trishear angles (80–86°), while Fault 4 and the SE Segment of Fault 5 present moderate trishear angles (44–60°). The P/S ratios for the main fault and Fault 3 have been estimated to be 3. however, the P/S ratios obtained for the other faults included in the model are 2. The distribution of the cumulative fault slip (Figure 6) calculated for each analyzed thrust fault reflects a decay of the slip toward the lateral tip points. The maximum slip is located in the center of the main fault, with an estimated value of ~2,100 m. This maximum slip decays to zero towards the northwestern tip point, while it flattens out at ~1,050 m to the southeast, before decaying until reaching the zero value at the tip point. Fault 2 presents a symmetric peak type slip distribution (Fossen, 2010) with a maximum modeled slip of ~1,300 m in the center that coincides with the secondary flat top of the main fault. The max- imum fault slip of Fault 3 is estimated to be ~1,600 m, and it is located approximately 75 km from its south- ern tip point leading to an asymmetric slip distribution. This fault presents a constant decrease to zero slip toward the south, while to the northern tip point the slip decreasing plummets when it intersects with the main fault. Fault 4 presents a symmetric plateau type slip distribution (Fossen, 2010) with a maximum flat Figure 5. (a) Colored topographic surface used as a base for the forwardmodeling procedure where the uplifts associated with the slip of the thrust faults have been removed together with the craters in the area. (b) Topographic surface resulting from the 3D forward modeling, where the original MOLA surface is reproduced from the 5(a) surface. Figure 6. Lengthwise profile of the Amenthes thrust fault system showing the slip distribution obtained for each of the five faults included in the modeling. 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 9 of 17 ANEXO III 209 top corresponding with an estimated slip of ~1,720 m. The maximummodeled slip of Fault 5 NW Segment is ~1,100 m, which is located at 30 km from the southeastern tip point. The modeling of the SE Segment of Fault 5 reflects two peaks in the slip distribution of ~1,000 and ~920 m corresponding with the two lobes identified in plan view (Figure 1). The accuracy of the best fit model obtained has been probed by comparison with the observed MOLA topo- graphy (Figure 7), trying to minimize the elevation difference between them. The study area is characterized by the presence of a large number of impact craters that modify the topography. The greatest differences in elevation are due to these impact craters that we have removed from the initial modeling surface when removing the lobate scarp reliefs, thus the calculation of the difference between the observed topography (Figure 3a) and the forward modeled topography (Figure 5b) has been made excluding crater values. The median value calculated for the elevation difference between the MOLA model and the modeled topo- graphic surface is ~3 m. The quartile deviation associated with this median value, which is indicative of the average fit of the model, is ~29 m, indicating that half of the values obtained when comparing these two surfaces are concentrated between 32 and −26 m. 4. Discussion 4.1. Structural Modeling The general agreement of the forward modeled topographic surface and the MOLA‐observed surface (Figure 7) is evidenced by the lowmedian value (~3) and the dispersion of the data around it (quartile devia- tion of ~29 m). This quartile deviation represents 2.8% of the maximum relief associated with the main fault (1,050 m), while it represents 6% of the maximum relief associated with the smallest modeled fault (Fault 5 Figure 7. Absolute elevation difference between the original MOLA topographic surface and the model obtained from the 3D forward modeling. Perfect fit between the model and the observed topography is represented by zero values. 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 10 of 17 ANEXO III 210 Segment SE, 480 m). The uncertainties in the fault slip estimate that can cause the obtained quartile devia- tion of the modeled topography (29 m) are +/−74 m for a the minimummodeled dip angle (23°) and +/−53 m for the maximum modeled dip angle (33°) (the slip uncertainty can be obtained by the quartile deviation/sin β, β being the dip angle). These values show that our 3D model is a good approximation to the geometry and kinematics of thrust faults in the study area, which closely reproduces lobate scarp struc- tural reliefs. Nevertheless, this model is a simplification, and some minor local differences can be observed due to modeling limitations and non‐modeled geological processes. Themodeling method presents some limitations when the propagating fault reaches the topographic surface (surface rupture). The trishear fault propagating folding ends at this point and the hanging wall continues its displacement over the footwall following a fault‐parallel flowmovement. This, together with the presence of landslides and rockfalls due to the steep slope of the forelimb, hinders the fitting of the forelimb and the scarp base throughout the entire length of the structure, generating small misfits between the model and the original surface especially at the scarp bases. The building of the 3D fault planes has been performed idealizing them as a smooth surfaces, therefore the presence of probable irregularities along fault surfaces, which would influence the topography (Watkins et al., 2015), have not been taken into account. From this point of view, our model can be considered a first‐order approximation to the general 3D faulting frame- work. The tectonic transport direction has been set perpendicular to each fault strike, although Mueller et al. (2014) obtained a slip vector direction for Amenthes Rupes that deviates 16° from pure dip‐slip, by measuring the dislocation of a crater cut by the main fault, which would reflect a small strike‐slip component of deformation. However, these authors claim that this estimate presents a significant error, because the half of the crater located on the hanging wall is affected by a subsequent crater, significantly reducing the amount of data involved in the calculation. Besides, an oblique slip generates surface geometries similar to those generated by dip‐slip (Cristallini & Allmendinger, 2001), and an obliquity of the slip as low as 16° only results in a very slight changes in slip and trishear angle needed to fit the model. A pure dip‐slip fault kinematics has been assumed for all the modeled faults with the slip vectors perpendi- cular to the average strike of fault traces, because the high sinuosity of the mapped lobate scarps (Figure 1) and the lack of en‐echelon patterns do not indicate an evident strike‐slip component of deformation. The fault surfaces obtained in this study for the five analyzed faults show positive listric morphologies at depth (a decay of dip angle with depth, McClay & Ellis, 1987). Previous studies using the FMDmethod mod- eled the underlying fault of Amenthes Rupes, as well as other lobate scarps in Mars, as a rectangular planar fault (Egea‐González et al., 2017; Herrero‐Gil et al., 2019; Grott et al., 2007; Ruiz et al., 2008; Schultz & Watters, 2001), because this method does not provide results as good as when the model is made using non‐planar morphologies (Schultz & Watters, 2001; Watters & Nimmo, 2010). A positive listric fault mor- phology was obtained by Mueller et al., (2014) for Amenthes Rupes and by Herrero‐Gil et al., (2020) for Ogygis Rupes and its backthrusts, based on the relation between the fault propagation anticline topography and the fault plane characteristics (e.g., Amos et al., 2007; Cardozo & Brandemburg, 2014; Ellis et al., 2004; Erslev, 1986; Seeber & Sorlien, 2000). On the contrary, a planar fault morphology that keeps its dip constant until the horizontal decollement would generate a backlimb with the same dip as the fault and abrupt limits (e.g., Amos et al., 2007; Brandemburg, 2013; Hardy & Ford, 1997), which is not the case for any of the studied faults (Figure S1). The dip angles obtained for the first kilometers of depth for the analyzed faults range between 27° and 33° (Table 1), except Fault 4, which presents a lower dip angle of 23°. These dip values are within the typical range calculated for reverse faults (20–35°) (e.g., Jaeger & Cook, 1979; Stone, 1985; Watters & Nimmo, 2010). The lower dip of Fault 4 can be explained by considering its relation with Fault 3 (Figure 4). Both faults form a “pop‐up” structure in which Fault 4 roots at a shallower depth indicating that it is subsidiary. Fault 4 can be passively transported by Fault 3 with a slight tilting due to its listric fault morphology at depth, causing the decreasing of its dip angle as Fault 3 slips (Ellis et al., 2004). The estimated slip distribution (Figure 6) of the studied fault set allows us to obtain an approximate value of the horizontal shortening in the area (Figure 8) as a result of the NE‐SW compressive stress that generated these structures. The listric geometry obtained for these faults at depth suggests that the slip on the fault ramps near the surface was transmitted by a horizontal slip of the same value along the decollement (Herrero‐Gil et al., 2020). Thereby, the regional shortening related to Amenthes Rupes thrust fault system 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 11 of 17 ANEXO III 211 can be estimated by stacking the slips of the contractional faults in the area (Figure 8). This value has been measured in the direction N36.6°E, the mean dip azimuth of the studied faults (Figure 4d), which is orthogonal to the mean strike value. The horizontal displacement presents a multimodal asymmetrical distribution characterized by three peaks of different value increasing notably toward the southeast. The northwestern peak is due to the contraction accommodated by the NW part of the main fault and the NW Segment of Fault 5. The horizontal slip corresponding to the central peak is due to the shortening generated by the slip of the central part of the main fault and the SE Segment of Fault 5. The southeastern peak shows the largest shortening value of the total distribution (~5,450 m) due to the combining of the slip values generated by Faults 2, 3, 4, and the southern part of the main fault, which are mostly parallel in this area (Figure 1). The analysis of the shortening distribution (Figure 8) shows a main change in the amount of shortening at ~360 km from the NE. This point marks an abrupt increase of shortening toward the SE associated with the third described peak. The structural map (Figure 1) reveals that Faults 2, 3, and 4 appear to the SE of this diffuse limit, where Fault 5 ends. The largest shortening value abruptly decays to the southeast. In this area, there are two minor faults (Figure 1) not included in the modeling that distribute the slip of the Fault 3 to the south. These minor faults seem to have a shorter length due to the presence of a heavily cratered area affecting their traces (southeast corner Figure 1); nevertheless, these structures continue to the S‐SE outside the study area with associated high relief, which reflects that the shortening continues along these faults although they are not included in this study. Therefore, the shortening associated with each fault is equal to the fault slip under the assumption that the slip is transmitted from the decollement due to the listric fault morphology at depth. This interpretation requires that the shortening estimates calculated using listric fault morphologies be larger than when the shortening is obtained from the horizontal component of the slip (heave) over a planar fault (from ~6% for a dip angle of 20°, up to ~30% for 40°) (Herrero‐Gil et al., 2020). Consequently, the horizontal contraction that generated lobate scarps implies a shortening value up to ~30% larger than the estimates calculated from modeling the slip over a planar fault. The analysis of the calculated faulting depths presents a bimodal distribution; so, the obtained results can be grouped into two different depths (Table 1). Themajor faults of the area (the main fault, its splay Fault 2, and Fault 3), which are the longest and uplift the widest and highest reliefs, root in a deep decollement level, that ranges in depth from 20–24 km. This depth value is within the range of depths of faulting calculated pre- viously for the large faults underlying different lobate scarps formed in the Late Noachian/Early Hesperian spread across the highlands of Mars (Egea‐González et al., 2017; Grott et al., 2007; Herrero‐Gil et al., 2019, 2020; Mueller et al., 2014; Ruiz et al., 2008; Schultz &Watters, 2001), supporting that this rooting level is not a regional rheological threshold. The depth of faulting of these large thrust faults has been con- sidered as the BDT depth at the time of its formation (e.g., Ruiz et al., 2008, 2009, 2011; Schultz & Watters, 2001), which corresponds to a change from localized failure to distributed failure (Byerlee, 1967, 1968; Rutter, 1986). On the other hand, Fault 4 and the two segments corresponding to Fault 5 present a modeled depth of faulting of 9.5–13 km, much shallower than the BDT where the large faults root. This bimodal dis- tribution of depths shows themechanical complexity of the crustal layers affected by faulting, indicating that the lithospheric brittle domain is not a homogeneous medium, but it probably presents heterogeneities such as mechanical discontinuities where subsidiary faults root. Figure 8. Representation of the total horizontal shortening estimate in a lengthwise profile orthogonal to the general shortening direction, which corresponds with the mean strike of the fault system (N126.6°E). 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 12 of 17 ANEXO III 212 The results obtained in this study for the major faults in the area that root in a deep decollement (main fault forming Amenthes Rupes, Fault 2, and Fault 3) can be compared with the fault parameter estimates of pre- vious works in Amenthes Rupes, which are focused in the main fault (Egea‐González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008; Schultz & Watters, 2001) (Table 2). The slip value calculated for the main fault is within the range calculated by Ruiz et al., (2008) while is quite higher than the values calculated by other authors (Egea‐González et al., 2017; Mueller et al., 2014; Schultz & Watters, 2001). Fault 2 and Fault 3 are expected to present different slip values since they are different structures than the main fault. However, the depth of faulting of these faults in the area can be compared because it is expected that the BDT does not present large variations in such a small area during the same period of time. When we compare the depths of faulting of these three faults with those of previous works (Egea‐González et al., 2017; Mueller et al., 2014; Ruiz et al., 2008; Schultz & Watters, 2001), our estimates provide shallower values. The BDT is temperature and strain rate dependent (e.g., Artemieva, 2011; Ruiz et al., 2011). The shallower depth of the BDT deduced from our results suggests that the associated heat flow of the Amenthes Region at the time of lobate scarps formation could be somewhat higher than previous estimates. Faster deformation deepens the brittle domain of the crust. The strain rates calculated for the Amenthes thrust fault system (Schultz, 2003) are small (between 10−17 and 10−19 s−1) and comparable to intraplate tectonic settings on Earth; accordingly, large variations in the strain rate, affecting significantly the depth of the BDT, are not expected in this area. The dip values obtained are in the range of those previously calculated for Amenthes Rupes (19– 35°) (Egea‐González et al., 2017; Ruiz et al., 2008; Schultz &Watters, 2001), but away from the highest values obtained by Mueller et al. (2014). The trishear parameters obtained for the modeled faults (Table 1) are within the best‐fit ranges calculated by Pei et al. (2014) through the analysis by trishear of several real structures on Earth. They stablished a P/S ratios ranging between 2 and 3 and trishear angles between 30° and 100°. The main fault and Fault 3 present a P/S ratio of 3, coinciding with their larger dimensions and deeper depths of faulting. They also have in common a large trishear angle (80–86°) showing that the folding occurs in a wide area that in main fault affects mainly the hanging wall, while in Fault 3 equally affects the hanging wall and the footwall. Fault 2 presents a trishear angle and its distribution similar to the main fault (Fault 2 is a splay of the main fault), with a P/S ratio of 2. Fault 4 and both segments of Fault 5 also have P/S ratios of 2 and variable trishear angles between 40° and 85°. The initial fault tip depth of the SE Segment of Fault 5, comparing to its max- imum slip, reflects that this fault does not break the topographic surface at the end of the forward modeling. The fault propagation is strongly linked with the fault slip distribution. This may imply that the surface rup- ture does not occur along the structure (blind thrust) or that it occurs at specific locations that usually match with the location of maxima in the slip distribution. The modeling of Fault 4 presented several challenges. The propagating fault tip of this fault at the end of the forward modeling does not reach the topographic surface, suggesting that this could be a blind fault. However, the large original topographic dimensions of this fault and its net scarp base observed in the MOLA topography and THEMIS images suggest a surface rupture at least in its central part. The scarp base and frontal syncline generated by Fault 4 displacement are completely covered by a deposit of Amazonian‐Hesperian smooth plains (Erkeling et al., 2011). Caprarelli et al. (2007) estimated the thickness of this geological unit by calculating the depth of the craters before the infilling. The high thickness of this resurfacing material (1–1.5 km) suggests that the relief uplifted by Fault 4 was initially much higher than the relief currently observed. Moreover, the backlimb Fault 4 propagation anticline is affected by two big impact Table 2 Fault Parameters Obtained in Different Studies Performed on Amenthes Rupes Maximum slip (m) Dip angle (°) Depth of faulting (km) Amenthes Rupes (Schultz & Watters, 2001) 1,500 25–30 25–30 Amenthes Rupes (Ruiz et al., 2008) 1,900–2,300 19–24 27–35 Amenthes Rupes (Mueller et al., 2014) 1,170–1,440 41.5–56.1 33–48 Amenthes Rupes (Egea‐González et al., 2017) 1,500–2,000 20–35 27–33 Amenthes Rupes (This study) 2,100 27–28 20–24 Amenthes Region‐Fault 2 (This study) 1,300 29.5 23.5–24 Amenthes Region‐ Fault 3 (This study) 1,600 31–33 21.5–22.5 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 13 of 17 ANEXO III 213 craters postdating the fault displacement and by the presence of some wrinkle ridges (Figure 1) parallel to Faults 3 and 4, which also affect the modeling results. These two large craters were also infilled by the same resurfacing unit. Therefore, the obtained slip for this fault is a minimum value, and due to these observa- tions, other parameters of Fault 4 may also present additional uncertainties. 4.2. Tectonic Evolution and Implications for Global Contraction Since Amenthes Rupes and its companion thrust faults are located in the highlands near the dichotomy boundary, their characteristics can give us information on the evolution of the boundary, at least locally. The faults forming the Amenthes Region thrust fault system all show similar strikes and kinematics (pure reverse faults) and thus can be interpreted to be formed under the same compressive stress field with a short- ening direction (N36.6°E) perpendicular to their average strike (Figure 4d). This agrees with the direction of the dichotomy boundary and with other lobate scarps in the adjoining Arabia Terra and Terra Cimmeria (Nimmo, 2005; Watters, 2003a; Watters et al., 2007; Watters & Robinson, 1999). Watters and Robinson (1999) calculated the horizontal shortening across Amenthes Rupes using the fault throw (lobate scarp relief), obtaining 1,800–3,400 m (corresponding with the heave on a planar fault), depending on the dip angle (assumed to be 20–35°). The fault parameters obtained in the present 3D mod- eling also allow a constraint on the maximum shortening registered by Amenthes Rupesmain fault, which is ~2,100 m, assuming that the slip is transmitted from the decollement. The regional shortening distribution associated with the whole fault system (Figure 8) suggests amaximum value in the southeastern of the thrust system of ~5,450 m, which is well above the previously calculated range for this area (1,800–3,400 m), increasing the shortening estimates of the area between ~60% and ~200%. This difference in the shortening values is mainly due to the inclusion of secondary and subsidiary faults in our model that were not pre- viously considered, and yet they accommodate ~62% of the maximum shortening in this area. Besides, there are other minor contractional structures identified in the area (Figure 1), including minor thrust faults and wrinkle ridges, that have not been included in the model, and they would increase this shortening calcula- tion, especially in the southeastern half of the thrust fault system. Whereby the regional shortening esti- mated by our model (Figure 8) is a minimum value. Previous global shortening estimates based on thrust faults (Nahm & Schultz, 2011) were performed using the dataset of faults of Knapmeyer et al. (2006). Although this structural mapping is quite exhaustive and extensive, the number of structures considered were significantly biased by the global scale of mapping, so the database did not contain all the subsidiary and minor faults present on Mars surface. Our study shows that the consideration of subsidiary faults, including backthrusts and fault splays, and independent secondary and minor faults in global calculations of contraction would provide a significant increase of the global planetary shortening accommodated by thrust faulting. Although all the faults were generated during the same epoch, some relative time relationships can be deduced from structural cross‐cut evidence, providing information on the evolution of the fault system. Fault 2 is a splay of the main fault, indicating that the slip of main fault is progressively accommodated by Fault 2 toward the SE. This kinematic link between both faults, which root at the same decollement, sug- gests that they could have been active at the same time. The main fault and Fault 2 traces are slightly dis- placed by Fault 3 slip, indicating that, although the activity of these faults could be contemporary, the last movement belongs to Fault 3 (backthrust). Fault 4 is a subsidiary antithetic fault with respect to Fault 3; con- sequently, both faults are probably contemporary. Fault 5 does not intersect other faults, so it is not possible to deduce its place in the formation order. A general tectonic evolution of the contraction that generated the lobate scarps in the Amenthes Region can be outlined according to the described cross‐cutting constraints and the horizontal slip distribution of Figure 8. Initially, the compressional stress field generated a homogeneous shortening in the area associated with the main fault, Fault 2, and probably Fault 5. Later, the contraction continued in the SE region of the study area with the generation of Fault 3 and its subsidiary Fault 4, which significantly increases the total shortening in this sector (maximum peak shown in Figure 8), propagating deformation toward the SW with respect to the main fault and its splay (Figure 1). This assumption that the deformation shifts and continues to the southeast agrees with previous observations that the lobate scarps on Terra Cimmeria, located ~500 km southeast of the studied fault system, deform geological units from the early Hesperian, which indicates that their formation continued during that age (Greeley & Guest, 1987; Watters et al., 2007; Watters & 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 14 of 17 ANEXO III 214 Robinson, 1999). These observations can be representative of the evolution pattern of the deformation that modified this part of the dichotomy boundary in the Late Noachian/Early Hesperian, which implies a short- ening recorded by thrust faults that is more than double of previous estimates if the calculation includes sub- sidiary and secondary faults. 5. Conclusions Five thrust faults forming the Amenthes thrust fault system, which is located in the Amenthes Region, have been modeled by 3D forward modeling through a combination of trishear and fault‐parallel flow methods. All the modeled fault surfaces show listric geometries at depth constrained by the low slopes of the fault pro- pagation anticline backlimbs and by the width of the trailing syncline. The obtained depths of faulting of the major faults present in the fault system suggest a depth of the BDT of 20–24 km at the time of formation in the Late Noachian/Early Hesperian, a value shallower than previous estimates. A possible mechanical dis- continuity in the lithosphere located at 9.5–13 km of depth can be deduced from the depths of faulting of secondary faults. The estimated horizontal shortening accumulated by the thrust system ranges between 2,000 and 3,000 m, increasing toward the SE part of the study area to a maximum shortening value of ~5,450 m. This value represents an increase in the maximum regional shortening registered by thrust faults of between 60% and 200% higher than previous estimates, due to the consideration of subsidiary and second- ary faults. The contribution of minor, secondary, and subsidiary faults to the planetary contraction could provide a significant increase of martian global shortening. References Allmendinger, R. (1998). Inverse and forward numerical modeling of trishear fault‐propagation folds. Tectonics, 17(4), 640–656. Amos, C. B., Burbank, D. W., Nobes, D. C., & Read, S. A. (2007). 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The error has since been corrected and this version may be considered the authoritative version of record. 10.1029/2019JE006201Journal of Geophysical Research: Planets HERRERO‐GIL ET AL. 17 of 17 ANEXO III 217 Journal of Geophysical Research: Planets ANEXO III Supplementary Material 219 ANEXO III Supplementary Material 220 ANEXO III Supplementary Material 221 ANEXO III Supplementary Material 222 Departamento de Geodinámica, Estratigrafía y Paleontología Tesis Andrea Herrero Gil PORTADA INDICE RESUMEN ABSTRACT 1. PRESENTACIÓN 2. INTRODUCCIÓN GENERAL 3. ANÁLISIS ESTRUCTURAL Y MODELIZACIÓN 2D DE GRANDES FALLAS INVERSAS EN MARTE 4. MODELIZACIÓN 3D DE GRANDES FALLAS INVERSAS EN MARTE 5. MODELO 3D DEL SISTEMA DE FALLAS INVERSAS DE AMENTHES, MARTE 6. DISCUSIÓN 7. CONCLUSIONES BIBLIOGRAFÍA ANEXO I ANEXO II ANEXO III