Crustal structure from gravity signatures in the Iberian Peninsula David Gómez-Ortiz1,†, B.N.P. Agarwal2, Rosa Tejero3, and Javier Ruiz3 1ESCET (Escuela Superior de Ciencias Experimentales y Tecnologia) Área de Geología, Universidad Rey Juan Carlos, 28933 Móstoles, Spain 2Department of Applied Geophysics, Indian School of Mines, Dhanbad 826 004 (Jharkhand), India 3Departamento de Geodinámica, Universidad Complutense de Madrid, Jose Antonio Novais, 3, 28040 Madrid, Spain ABSTRACT Through two-dimensional fi ltering and spectral analysis of gravity data, we infer the density structure of the Iberia Peninsula’s lithosphere (western Europe). The grav- ity anomaly map of the Iberian Peninsula displays long-wavelength anomaly minima related to Alpine ranges. These anomalies are primarily linked to a greater crustal thickness. Low-pass fi ltering of the anomaly map using a cutoff wavelength of 150 km was adequate for effective separation of shallow and deep sources used for computing the three-dimensional (3-D) Moho interface. Tsuboi’s technique (identical to the equiva- lent stratum theorem) is used here to map the 3-D Moho interface by selecting mean source depths from the results of the spectral analysis, and assuming a homogeneous den- sity contrast of 350 kg/m3. The most charac- teristic feature of the 3-D Moho geometry was the presence of several lows associated with mountain ranges created by Alpine tec- tonics. In those areas, the gravity-derived Moho reaches a depth of up to 45 km in the Pyrenees and Cantabrian Mountains and close to 40 km under the Betics, Central Sys- tem, and Iberian Chain. Under the Iberian Massif, the western part of the Iberian Pen- insula composed of a Variscan basement, the Moho was located at a depth of 30–36 km. These results are consistent with existing seismic data and indicate that gravity-based techniques can provide very good estimates of lithosphere structure. INTRODUCTION Measurements of Earth’s gravitational fi eld provide information on anomalous rock masses existing below the plane of observation. The basis for this is that the lithosphere is composed of heterogeneous rock masses that give rise to changes (i.e., anomalies) in gravity fi elds due to the density contrast in a given area. These anom- alies are interpreted in terms of source geome- tries approximating geological structures at dif- ferent depths. The basic problem associated with any gravity data interpretation technique lies in separating the contributions of shallow and deep sources. Such discrimination is accompanied by inherent ambiguity and uncertainty (Roy, 1962; Skeels, 1967) and questions the real validity of a technique for three-dimensional (3-D) Moho mapping. One of several mathematical methods of anomaly separation is based on the frequency contents of the observed data (Fuller, 1967; Zurfl ueh, 1967; Spector and Grant, 1970; Syb- erg, 1972). In general, shallow and deep sources are characterized by high- and low-frequency contents of the anomaly, respectively. Thus, the use of low-pass fi lters would seem to be a reasonably good technique to distinguish the contributions related to the Moho discontinuity/ boundary from the observed anomaly. However, shallow bodies of signifi cant lateral extension, such as sedimentary basins, may not be fully removed by low-pass fi ltering (Chakraborty and Agarwal, 1992). The existence of lateral density variations within the crust introduces further uncertainties for separating anomalies. Spec- tral analysis (Spector and Grant, 1970; Syberg, 1972) has been used to estimate the average depths of sources occurring at different levels, which is required to compute the Moho relief. The inversion techniques available in the litera- ture are suitable for isolated source geometries only (Nabighian et al., 2005). In this study, we used gravity data for the Iberian Peninsula to map the Moho. The Ibe-rian Peninsula features sharp contrasts in crust thickness between its Alpine and Variscan tec-tonic units. The approach used was a simple yet effi cient method proposed by Tsuboi (1979) to invert low-pass-fi ltered anomalies asso- ciated with the gravity Moho discontinuity under the assumption of a layered Earth model. Chakraborty and Agarwal (1992) and Agarwal et al. (1995) successfully demonstrated the utility of long-wavelength anomalies in crustal studies. For example, this technique has been successfully used to map the Moho under com- plex geological structures across France and adjoining regions (Lefort et al., 1998; Lefort and Agarwal, 1999, 2000, 2002). The Moho map produced here shows a relief pattern simi- lar to seismic-derived Moho maps while avoid- ing dubious interpretations due to a lack of seismic data. Effectively, our results indicate that gravity-based methods are powerful tools to determine the structure of the continental crust. GEOLOGICAL SETTING AND CRUSTAL THICKNESS Continental Iberia can be divided into a west-ern part consisting of Paleozoic and Proterozoic rocks and an eastern part in which Mesozoic and Cenozoic sediments predominate (Fig. 1). The western part, or Iberian Massif, is a fragment of the Variscan orogen composed of metamorphic and igneous rocks. The Iberian Massif features several tectono- stratigraphic zones, some of which are bounded by sutures that represent the diverse microcontinents involved in the oblique collision among Gondwana, Laurentia, and Baltica in the Paleozoic (Matte, 1991). Once the Variscan cycle was over, the geodynamic evolution of the Iberian plate was controlled by the Tethys cycle and opening of the North Atlantic (Capote et al., 2002; Ribeiro, 2006). In the early Mesozoic, the Iberian plate was deformed by large-scale stretching, which gave rise to extensional basins at the Iberian plate margins and within the intraplate domain. The present geology of the Iberian Peninsula was shaped from the Late Cretaceous to late Ceno- zoic when the European and African plates con- verged. Intense crustal deformation took place at the Iberian plate margins. At the northern boundary, an E-W mountain chain—the Pyre- nean belt—developed as a collisional orogen verging both to the N and S and extending from the Mediterranean Sea to the Atlantic Ocean. Within this belt, there are two ranges, the Pyr- enees to the east and the Cantabrian Mountains to the west (Fig. 1). The southern margin of the belt is defi ned by two foreland basins, the Duero and the Ebro Basins, which formed by infi lling sediments as a result of erosion related to the uplifted orogen. At the southern margin of the Iberian plate, convergence of the African and Iberian plates formed the Betics. The fl exural response of the lithosphere created the Gua- dalquivir Basin, which has been infi lled with Neogene to Quaternary rocks, at the northern margin of the Betics. Since the middle-late Mio- cene, the orogen has undergone severe exten- sional deformation inducing crustal thinning (Comas et al., 1992; Torné and Banda, 1992). Within the Iberia intraplate domain, two mountain chains, the Iberian Chain and Central System, developed in the Cenozoic. The Iberian Chain in the east consists of thick sequences of Upper Permian to Mesozoic sediments. The Central System trends NE-SW along the cen- tral part of continental Iberia. It consists of an uplifted crustal block bounded by two main reverse faults determining that basement rocks overlie Tertiary sediments of the Duero and Tajo Basins. Crustal Thickness A Bouguer anomaly map of the Iberian Pen- insula (Mezcua et al., 1996) refl ects crustal thickness differences and negative anoma- lies related to crustal roots. The gravity Moho map of De Vicente (2004; Fig. 7b) assumed an Airy-Heiskanen model of isostatic equilibrium, and also displayed a thickened crust under the Alpine chains, but in general depths were lower than those estimated from the seismic studies mentioned next. On the Mediterranean coast, the Moho has been located at 24 km (e.g., Dañobeitia et al., 1992; Gallart et al., 1994) and reaches a depth of ~28 km at the Atlantic margin (e.g., Córdoba et al., 1987; González et al., 1998; Díaz et al., 2003). The Pyrenees, in the Alpine Ranges, exhibit among the larg- est crust thicknesses. Beneath its axial zone, the Moho deepens to 45–50 km (Daignieres et al., 1998; Choukroune and ECORS Team, 1989), while to the east, toward the Mediterranean coast, the Moho rises to ~24 km. The thickened crust extends to the west beneath the Cantabrian Mountains, where the Moho attains a depth of 46–48 km (Pulgar et al., 1996; Fernández-Viejo et al., 1998, 2000; Díaz et al., 2003). Seismic data for the other major Alpine chains, i.e., the Betics, reveal a crust of ~32 km at the mar- gins, increasing further toward the central zone to ~36–38 km. The crust progressively thins toward the southern margin of the Betics, and the Moho rises to a depth of ~15 km in the Albo- ran Sea (Fig. 1) (Hatzfeld and Ben Sari, 1977; Working Group for DSS in the Alboran Sea, 1974, 1978). For the Iberian Chain, a crustal thickness of 40 km derived from gravity stud- ies (Salas and Casas, 1993) is consistent with the seismic profi le interpretation (Zeyen et al., 1985; Gallart et al., 2004). The Moho has been attributed a maximum depth of 35 km under the Central System, shallowing to ~30 km under the Duero and Tajo Basins (Suriñach and Vegas, 1988; ILIHA DSS Group, 1993). In the west- ern and central parts of the Iberian Peninsula, Moho depth varies from 30 to 34 km under the Iberian Massif and the Tertiary basins (Banda 2°W 4°E6°W10°W 42°N 40°N 38°N 0 100 km 2°W 4°E6°W10°W 40°N 42°N EUROPE Ib er ia n M as si f PyreneesPyreneesPyrenees Betics Guadalquivi Guadalquivir Basin Basin Guadalquivir Basin CentraCentral System System Central System Iberia Iberian Chain Chain Iberian Chain Duero Basin Tajo Basin Pyrenees Betics Iberian Chain Cenozoic basins Mesozoic outcrops Iberian Massif Ebro Basin Figure 1. Geological map of the Iberian Peninsula. et al., 1981; Córdoba et al., 1987; ILIHA DSS Group, 1993; Téllez et al., 1993; Gallart et al., 1994; Pulgar et al., 1996; González et al., 1996, 1998; Flecha et al., 2009). ANALYSIS OF THE GRAVITY ANOMALIES Gravity Data Three different sets of gravity data were combined to construct a fi nal anomaly map. The fi rst data set, obtained by the present authors, includes data from 2892 gravity sta- tions covering an area of ~23,657 km2 in central Spain (Fig. 2). All gravity measurements were corrected for Earth-tide, free-air, and Bouguer effects. Terrain correction up to 166.7 km was also applied. Terrain correction was applied by considering topography variation up to a radius of 166.7 km from the point of observa- tion. In addition, we used 28,202 data points from the Bouguer anomaly map of the Iberian Peninsula (Mezcua et al., 1996), and data from the Bureau Gravimetrique Internationale (BGI) for France (141,223 stations) to the north, and Morocco and Algeria (8613 stations) to the south. A comparison of 469 duplicate gravity measurements revealed a root mean squares error of ±0.88 mGal. This is an acceptable error for a regional study, and thus the different data sets were merged. A standard density value of 2670 kg/m3 was used in the reduction of the data. For gravity values in marine areas, the most detailed bathymetric data available were used to compute the Bouguer anomalies from the free- air gravity anomalies (GEODAS database from the National Geophysical Data Center, http:// www.ngdc.noaa.gov/mgg/ geodas/geodas .html). This was done by replacing the sea- water with a slab of density 2670 kg/m3 and thickness equal to the bathymetric depth deter- mined using the GEBCO Digital Atlas data (IOC, IHO, and BODC, 2003) available for the area. The last of the three data sets used, -400 0 400 800 1200 3600 3800 4000 4200 4400 4600 4800 5000 5200 5400 -200 mGal -160 mGal -120 mGal -80 mGal 0 mGal 0 200 400 km Gravity anomaly (mGal) -40 mGal 40 mGal 80 mGal 120 mGal 160 mGal 200 mGal 240 mGal 280 mGal 320 mGal 360 DB EB B CM CS TB I M IC GB PY Figure 2. Bouguer gravity anomaly map of the Iberian Peninsula and surrounding areas. UTM coordinates in kilometers, zone 30N. Inset shows the central area retained after data processing and analysis. The abbreviations used are: CM— Cantabrian Mountains; PY—Pyrenees; DB—Duero Basin; EB—Ebro Basin; CS—Central System; TB—Tajo Basin; IC— Iberian Chain; GB—Guadalquivir Basin; B—Betics; IM—Iberian Massif. corresponding to an offshore area, included data recorded at 9400 stations. The station data were interpolated by krig- ing with a spacing of 5 km and a total length of 2000 km both in x and y directions (grid size: 401 rows by 401 columns) to generate a Bou- guer anomaly map (Fig. 2), which was then subjected to spectral analysis, low-pass fi lter- ing, and inversion. After this processing, only the central core corresponding to the Iberian Peninsula (1500 km × 1140 km) was retained and displayed for minimization of artifacts due to Fourier transform–based data process- ing techniques. Figure 2 shows that the gravity fi eld over the entire area varies from −200 to +378 mGal, and over the Iberian Peninsula, it varies from −140 to +220 mGal. Relatively large negative anomalies may be observed across the con- tinental areas of the Iberian Peninsula. The marine part of this peninsula displays positive anomalies associated with crustal thinning in a seaward direction from the coast. Figure 2 gen- erally exhibits good correlation with geologi- cal units. The Alpine chains are associated with gravity anomaly minima. Prior gravity and seismic studies indicate that the main cause of these anomalies is a thickened crust (e.g., Salas and Casas, 1993; Suriñach and Chavez, 1996; Casas et al., 1997; Gómez-Ortiz, 2001; Rivero et al., 2002; Gómez-Ortiz et al., 2005). Gravity anomaly minima have also been linked to the Tertiary Duero and Tajo Basins. Positive anomalies observed in SW Iberia are due to increased crustal density toward the SW part of the Iberian Massif (Fig. 1); this density peaks in the Sub-Portuguese zone (e.g., Sánchez Jiménez, 2003). Data Processing Techniques The observed gravity anomaly is the sum of the contributions due to lateral variations in density within several lithological units, from the plane of observation to deep inside Earth. It is, therefore, essential to identify contributions due to lateral variations in density occurring at different depths. As a rule of thumb, high- frequency components of the observed anoma- lies are attributed to shallow depths, and low- frequency components are attributed to deep depths. Zurfl ueh (1967) suggested the use of appropriate low-pass fi lters to separate effects due to deep and shallow sources. A certain amount of uncertainty in achieving the anomaly contribution associated with a particular layered structure is likely to exist by the use of low-pass fi lters. We tackled this problem by extending the survey area by several hundred kilometers all along the area of interest. Design of the Low-Pass Filter A two-dimensional low-pass fi lter with a cir- cularly symmetric frequency response having a prespecifi ed low cutoff frequency was designed using the fi lter coeffi cients computed for a one-dimensional (1-D) data set. Martin (1962) described an excellent approach to computing digital fi lter coeffi cients of a low-pass fi lter with a prespecifi ed cutoff frequency using a closed mathematical equation involving a prespecifi ed roll off (transition zone) over which the ampli- tude response decreases as per the assumed mathematical function. These 1-D fi lter coef- fi cients were then used in the space domain to yield coeffi cients for a 2-D fi lter by McCllelan transformation (McCllelan, 1973). Thus, we can easily compute a 2-D fi lter coeffi cient cor- responding to any prespecifi ed cutoff frequency and roll off. Energy Spectrum Analysis Spector and Grant (1970) proposed a statisti- cal technique based on the ensemble average of the random distribution of anomalous sources below the plane of observation by computing the energy density of the observed data. These authors observed that a plot of the natural logarithm of the energy of the anomaly versus angular frequency exhibits a decay in energy produced with increasing angular frequency. Syberg (1972) mathematically proved that the decay process is predominantly controlled by the ensemble average depth of the random dis- tribution of sources, which can be approximated by straight lines (e.g., corresponding to regional and residual anomalies). Thus, the power spec- trum may be expressed in terms of straight-line segments characterizing the sources at different depth levels. When this study is performed over a large area, the averaged depths will be related to the main density discontinuities of the litho- sphere. Because there is a relationship between density and P-wave velocity, we can correlate the lithospheric P-wave velocity discontinuities with the Moho. Computing the Mass Distribution and Relief of an Interface We used Tsuboi’s (1979) technique to com- pute mass distribution, which was then con- verted into Moho relief. The details of the math- ematical formulation used can be found in the Appendix. The basic assumptions considered for computing the relief in Moho depth are: (1) the gravity effect (anomaly) is entirely due to the relief at the interface formed by two isotropic and homogeneous rocks of different densities, and (2) the density contrast and mean depth to the horizontal interface are known. Processing of Gravity Data The gravity anomaly map (Fig. 2) reveals high-frequency “noises” superimposed on the main anomaly trends. These noises represent an unwanted signature to be removed before any discussion of the data. To remove the high- frequency component, the observed data matrix (401 × 401 points) was low-pass fi ltered to allow the passage of only those anomalies associated with a wavelength of 40 km and above. Such an approach minimizes aliasing, and computation of the energy spectrum becomes more reliable. The fi ltered map (not shown here) after removal of the noise was used as the base map for further data processing and analysis. To study the probable depths of the sources, the entire matrix of observed data (Fig. 2) was subjected to the 2-D Fast Fourier Transform algorithm to plot the logarithm of the energy of anomalies versus angular radial frequency (Fig. 3). Three linear segments were distin- guished in this plot, each of which is associ- ated with a range of frequencies, providing an indication of their average depth. The depths of the anomalous horizons are: 134, 25.6, and 10.9 km. From other independent geophysi- cal information, we can relate these horizons to main crustal discontinuities. Several recent publications (e.g., Piromallo and Morelli, 2003; Boschi et al., 2004; Panza et al., 2007; Fullea et al., 2010) dealing with mantle structure in the Iberian Peninsula inferred from shear-wave tomography and P-wave velocity data have located the lithosphere-asthenosphere boundary (LAB) at a depth of 110–140 km. Our deep- est depth is fairly consistent with this estimate, suggesting it could correspond to the base of the lithosphere. Our intermediate-depth value represents a mean Moho depth for the study area, taking into account marine and continen- tal areas (see section on geological setting and crustal thickness). The shallowest depth could be located within the crust and could represent a major crust discontinuity like the upper crust– lower crust boundary (e.g., ILIHA DSS Group, 1993; Suriñach and Vegas, 1988; González et al., 1998; Simancas et al., 2003). Through several studies (Lefort and Agarwal, 1996, 1999, 2000, 2002) using small and large data sets, it has been observed that a low-pass- fi ltered anomaly map with a cutoff wavelength around 150 km will effectively correspond to Moho anomalies. Though this cutoff wavelength may vary from area to area with variations in the geological setup, the computed Moho depth needs to be compared with seismic data to assess Crustal structure in the Iberian Peninsula Geological Society of America Bulletin, July/August 2011 1251 the quality of the outcome. The low-pass-fi ltered anomaly map (Fig. 4) obtained from the data in Figure 2 for wavelengths greater than 150 km is quite smooth, and it is likely to refl ect anomalies associated with the Moho discontinuity. We further computed the topographic relief of the Moho discontinuity (Fig. 5) in Figure 4 using Tsuboi’s (1979) method, by assuming a mean depth to a horizontal interface of 25 km, obtained from the spectral analysis (h2, Fig. 3). From published crustal layer velocities and the P-wave velocity–density empirical relationship (Christensen and Mooney, 1995), a mean den- sity contrast of 350 kg/m3 between crust and mantle is estimated. GRAVITY MOHO MAP OF THE IBERIAN PENINSULA The two largest Moho lows occur along the Pyrenees and Cantabrian Mountains, and the Betics. The fi rst one runs parallel to the moun- tain belt, along the northern margin of the Ibe- rian Peninsula trending E-W with deepening of the Moho to 45 km (Figs. 5 and 6, profi les 1 and 2). The second one trends ENE-WSW beneath the Betics. In the peninsula interior, two further Moho lows are respectively related to the Cen- tral System, trending NE-SW, and the Iberian Chain, trending NW-SE (Figs. 1 and 5). In the latter, the Moho reaches a depth of ~40 km. Far from the Alpine ranges, the gravity Moho shows a mean depth of 34 km, which decreases to 28–30 km toward the coast. A relief map of seismic Moho depths aver- aged over a large area (0.5° × 0.5°) prepared by Díaz and Gallart (2009) reveals the existence of deep crustal roots under the Pyrenean Belt, as well as thickening of the crust under the Ibe- rian Chain, Central System, and Betics (Fig. 6). Thus, due to averaging, the seismic Moho is much smoother than the computed gravity Moho. For a more detailed comparison between seismic Moho data and our gravity Moho, we constructed three profi les by integrating geo- logical, seismic, and gravity data (Fig. 7). The northern part of profi le 1 was close to the ECORS Central Pyrenees cross section (Chouk- roune and ECORS Team, 1989; Muñoz, 1992), and the Moho depths beneath the Iberian Chain were provided mainly by Zeyen et al. (1985) and Gallart et al. (2004). Profi les 2 and 3 were constructed by integrating the ESCIN-2 data in profi le 2 and refraction and wide-angle refl ec- tion profi les in profi les 2 and 3 (Pulgar et al., 1996; Fernández-Viejo et al., 2000; Pedreira et 6.04.02.00 Angular Frequency, radian/km 10 15 20 25 30 35 Ln en er gy h3=10.9 km h2=25.6 km h1=134 km WN Radial angular frequency (radian/km) Figure 3. Plot of the logarithm of the power of Bouguer anomaly versus radial angular frequency. Three linear segments, corresponding to causative sources located at mean depths of 134, 25.6, and 10.9 km, are matched. WN—white noise. al., 2003). In the southern areas of these profi les, seismic Moho depths under the Betics were taken from a deep seismic-refl ection, seismic- refraction, and wide-angle refl ection survey undertaken close to profi le 3 (García-Dueñas et al., 1994; Banda et al., 1993). Moho depths under the Iberian Massif were compiled from seismic- refraction studies (ILIHA DSS Group, 1993; González et al., 1998) and seismic-refl ection profi ling (Simancas et al., 2003; Carbonell et al., 2007; Tejero et al., 2008). Seismic Moho depths beneath the Central System are those reported by Suriñach and Vegas (1988). Profi le 1 (Fig. 7) reveals a good match between the seismic and gravity Moho in the Pyrenees and Iberian Chain. Both are characterized by well-defi ned gravity lows produced mainly by a thickened crust (Zeyen et al., 1985; Salas and Casas, 1993; Gallart et al., 2004). The greatest mismatches are found in the Cantabrian Mountains and the Betics. Under the Cantabrian Mountains, the gravity Moho shallows to 38 km, while seismic data indicate a depth of 45 km (Fig. 7, profi les 2 and 3). In this region, the gravity anomaly is characterized by a smooth gravity low bounded by the positive anomalies extending eastward far from the coast (Fig. 2). These discrepan- cies in Moho depths correspond to an area of crustal doubling due to convergence processes. In the south of the Iberia margin, under the Bet- ics, the gravity Moho is ~5 km deeper than the seismic Moho (~36 km) (Figs. 1 and 7, profi les 2 and 3). In this Alpine chain, even different seismic methods have yielded different Moho depths. Seismic tomographic imaging suggests a 34–36-km-thick crust, in contrast to seismic- refl ection estimates of 28–30 km beneath the topographic highs (García-Dueñas et al., 1994; Carbonell et al., 1998). Magnetotelluric studies have suggested the presence of a large conduc- tive layer interpreted as a zone of partial melt- ing within the lithosphere (e.g., Carbonell et al., 1998). This would decrease the density of the lithospheric mantle, increasing the gravity mini- mum associated with the Betics and deepening the calculated gravity Moho. The gravity Moho indicates a thicker crust than the seismic Moho (40 km versus 34 km) under the Central System. This discrepancy may be due to superimposi- tion of gravity effects of low-density Tertiary sediments of the Duero and Tajo Basins on the effects of the crustal root of the Central System. Both these factors are considered to be respon- sible for the gravity minimum in the central part of the Iberian Peninsula. The gravity Moho varies from 28 to 36 km in the Iberian Massif, where seismic surveys have indicated a depth of 30–35 km (ILIHA DSS Group, 1993; Díaz and Gallart, 2009; Pal- omeras et al., 2009) and a decrease in crustal Gómez-Ortiz 1252 Geological Society of America Bulletin, July/August 2011 thickness of only ~3 km southwestward in the Sub- Portuguese zone (Matias, 1996). Seis- mic surveys in the SW Iberian Peninsula have revealed that the seismic signature of the crust changes laterally (ILIHA DSS Group, 1993; González et al., 1996). Recently, Flecha et al. (2009) took into account the heterogeneous character of the crust and obtained more real- istic average velocity models considering a high-velocity layer at midcrustal depth, a highly refl ective lower crust, and a relatively horizontal Moho. The resulting model exhibits a layered mafi c intrusion in the middle crust, which had been previously identifi ed through seismic- refl ection profi ling (Simancas et al., 2003; Car- bonell et al., 2007), and a strongly laminated lower crust with a Moho depth of ~33 km. DISCUSSION AND CONCLUSIONS The previous comparisons indicate maximum differences in depth between seismic and grav- ity Moho estimates ranging from 5 to 10 km, and they are concentrated in areas of crustal doubling, where the short wavelength of the Moho crustal root cannot be recovered by the fi ltering technique applied to the gravity data. Apart from this, the discrepancies between both Moho maps are not signifi cant due to the fact that they fall into the uncertainty values inher- ent to both methods (Fig. 7). Indeed, seismic- derived Moho depths also have several uncer- tainties in interpretation leading to variations from ±2 to ±10 km in depth (e.g., Grad et al., 2009), which are associated with determination of velocities in different horizons and type of the seismic method used to estimate the depth (e.g., modern seismic-refraction profi les, surface wave tomography, refl ection surveys, broad- band stations, etc.). Signifi cant numbers of refraction and refl ection lines have sampled the crust of the Iberian Peninsula lithosphere and have reported crustal thicknesses and P-wave velocities. Published results for the same area present Moho depth variations close to ±3 km (Díaz and Gallart, 2009, and references therein). For example, the Moho depth map of Figure 6 displays a Moho located 2 km shallower in the central Iberian Peninsula in comparison to data profi ling (Suriñach and Vegas, 1988). This effect corresponds to gridding smooth- ing. Thicknesses estimated from Vp/Vs ratio 12008004000-400 3600 3800 4000 4200 4400 4600 4800 5000 5200 5400 0 200 400 km Gravity anomaly (mGal) 380 340 mGal 300 mGal 260 mGal 220 mGal 180 mGal 140 mGal 100 mGal 60 mGal 20 mGal -20 mGal -60 mGal -100 mGal -140 mGal -180 mGal -220 mGal DB EB CS TB B CM I M IC GB PY Figure 4. Filtered gravity anomaly map created to retain wavelengths greater than 150 km corresponding to Moho undula- tions in the Iberian Peninsula and surrounding areas. UTM coordinates in kilometers, zone 30N. Abbreviations are as in Figure 2. Crustal structure in the Iberian Peninsula Geological Society of America Bulletin, July/August 2011 1253 Depth (km) 1000800600400200-200 4000 0 4200 4400 4600 4800 5000 48 44 Km 40 Km 36 Km 32 Km 28 Km 24 Km 20 Km 16 Km 12 Km 8 Km 4 Km 0 Km DB EB CS TB B CM I M IC PY GB Figure 5. Gravity Moho depth map obtained by inverting the fi ltered gravity anomaly of Figure 4 using Tsuboi’s (1979) method. UTM coordinates in kilometers, zone 30N. Abbreviations are as in Figure 2. DeptDepth (h (km)km) Figure 6. Interpolated seismic crustal depth model for the Iberian Peninsula. Crustal thickness isolines represented every 2 km. Figure is reprinted with permission from Elsevier from Diaz and Gallart, “Crustal structure beneath the Iberian Peninsula and surrounding waters: a new compilation of deep seismic sounding results,” Physics of the Earth and Planetary Interiors, v. 173, p. 181–190, copyright 2009. Gómez-Ortiz 1254 Geological Society of America Bulletin, July/August 2011 A C D E B Figure 7. (A) Topography of continental Iberia and (B) gravity Moho depth contours showing the location of three profi les (C, D, and E) used to illustrate the relationship between seismic and gravity Moho depths. UTM coordinates in kilometers, zone 30N. Large Moho depths are associated with Alpine ranges. Abbreviations are as in Figure 2. Error bars represent the uncer- tainty value estimated for the Moho gravity data. Crustal structure in the Iberian Peninsula Geological Society of America Bulletin, July/August 2011 1255 APPENDIX THEORY ON COMPUTATION OF MASS DISTRIBUTION Let us assume a Cartesian system of coordinates with z-axis positive vertical downward. Let f(x, y) be a certain quantity measured on the horizontal plane (x, y). We can express f(x, y) by a double Fourier series of the form (Tsuboi, 1979) ∑∑= m n nymxmnyxf cos sin cos sin),( α . (A1) Suppose a distribution of f(x, y) is given within a square 0 ≤ x ≤ 2π, 0 ≤ y ≤ 2π. The distribution of the value of f(x, y) in the direction of x along a certain value of y can be expressed by a single Fourier series of x such as ∑= m mxymyxf cos sin)(),( β . (A2) The coeffi cient β m changes according to y, so that it can be expressed by a single Fourier series of y such as ∑= m mxnym cos sin)( γβ . (A3) Then as a whole, f(x, y) is ∑∑= m n nymxnmyxf cos sin cos sin),( γβ . (A4) If β m γ n is written as α mn , then ∑∑= m n nymxmnyxf cos sin cos sin),( α . (A5) Using this double Fourier series, if a distribution of gravity values g(x, y) is ∑∑= m n nymxmnByxg cos sin cos sin),( , (A6) then the underground mass M at a depth d that will produce this g(x, y) is given by ∑∑ += m n nmd mn B G yxM })22(exp{ 2 1 ),( π nymx cos sin cos sin . (A7) variations show uncertainties ranging from ±0.5 to ±2.5 km (Julià and Mejía, 2004). These values are similar to those obtained from other seismic methods. Thus, we can conclude that an uncertainty of seismic Moho depth of ±3–4 km can be assumed in the Moho depth data for this area. In contrast, errors in computed grav- ity Moho depths are mainly the consequence of inadequate separation between shallow and deep sources, uncertainties on prespecifi ed cut- off wavelength, density contrast, and assumed mean depth of the interface. Also, long wave- lengths due to shallow sources such as Tertiary basins may affect the computed depth of the anomalous horizon. Gómez-Ortiz et al. (2005) argued that if the effect of shallow sources is removed, the mean depth regional source is better defi ned. This could be very important when the study area is relatively small and long- wavelength shallow sources are suffi ciently large to mask the effect of deep sources. The density contrast value used here is derived from seismic velocities and the cutoff wavelength can be determined from the gravity power spectrum or can be assumed from previous works. Here, we assumed a cutoff wavelength of 150 km, which was successfully applied to analyze the gravity data over a crust with characteristics close to those of the Iberian Peninsula. In order to visualize the uncertainty involved in com- putation of Moho depth from gravity data, we obtained different Moho depth maps by varying density contrast and Moho mean depth values. The density contrast and mean depth data values were 350 ± 30 kg/m3 and 25 ± 2 km, respec- tively, which are considered representative for the studied area. Using all the maps generated, the root mean square (RMS) error was obtained as an estimation of the uncertainty in Moho depth due to variations in the two key param- eters used during the inversion of gravity data. The resulting uncertainty is ±3.1 km, similar to the seismic uncertainty previously mentioned. This value has been incorporated into the Moho profi les (Fig. 7) in the form of error bars for comparison with the corresponding seismic Moho data. Thus, we consider that the generated gravity Moho map adequately represents the relief of the base of the Iberian crust and that the techniques used demonstrate their robustness to estimate main density discontinuity depths and topography. The following main conclusions may be drawn from our study. Through two-dimensional fi ltering and spectral analysis of available gravity data for continental Iberia, we were able to identify three main anoma- lous horizons within the lithosphere at depths of 134, 25.4, and 10.9 km. Geophysical data sug- gest that these correspond to the lithosphere- asthenosphere boundary, Moho discontinuity, and the upper-lower crust limit, respectively. (1) The major characteristic feature of the gravity derived 3-D Moho geometry is the presence of several lows associated with moun- tain ranges created during Alpine tectonics. In these areas, the gravity Moho reaches a depth of up to 45 km in the Pyrenees and Cantabrian Mountains and close to 40 km under the Betic Ranges, Central System, and Iberian Chain. Under the Iberian Massif, the western part of the Iberian Peninsula composed of a Variscan basement, the Moho was located at a depth of 30–36 km. (2) Our results are similar to seismic data, suggesting that the present technique can pro- vide a reasonable estimate on depths of the lithospheric discontinuities. ACKNOWLEDGMENTS Agarwal acknowledges the Department of Sci- ence and Technology, Government of India, New Delhi, for funding several projects having objec- tives to improve the computational facilities used in the present work. Ruiz was supported by a Ramon y Cajal contract, cofi nanced by the European Social Fund. We also thank Shalivahan Srivastava for revis- ing the manuscript and for useful comments. We greatly appreciate the comments and suggestions of the associate editor (Donald White), Andrew Hynes, and an anonymous reviewer, that have considerably improved the original manuscript. We wish to thank Ana Burton for linguistic assistance. This research was supported by Ministerio de Ciencia e Innovación, Project CGL2008-03463. Gómez-Ortiz 1256 Geological Society of America Bulletin, July/August 2011 In the two-dimensional cases, the coeffi cients are 4 mn in number. For instance, if 2π is divided into six both in x- and y-directions, the number of coeffi cients will be 4 × 6 × 6 = 144, instead of 6 in one-dimensional case. If 2π is divided into 18, the number of coeffi cients needed are as many as 4 × 18 × 18 = 1296. The factor four is needed because there are four different combinations: cos mx·cos ny, cos mx·sin ny, sin mx·cos ny, and sin mx·sin ny. The (sin x)/x method can also be extended to two-dimensional cases. In these cases, the integral, ∫ ∫ += 1 0 })22(exp{coscos 1 0 ' dndmnmdnymxφ , (A8) has to be evaluated numerically for different values of x and y. It may be worth mentioning here that the coeffi cient φ′ exhibits eightfold symmetry as observed in a downward-continuation fi ltering operation. There are several tables that give the values of φ′ (Tsuboi et al., 1958; Kanamori, 1963; Takeuchi and Saito, 1964; all taken from Tsuboi, 1979) for various values of d. To apply this method to two- dimensional gravity interpretations, gravity values g mn at square grid points and φ′ mn values at the corresponding points are multiplied, and the products g mn φ′ mn at all the grid points are added. When the sum of all the products is divided by 2πG, this will give the mass right beneath the point corresponding to m = n = 0. Here, G is univer- sal gravitational constant. The relief in the interface at the point of computation can be obtained by dividing the computed mass by the density contrast Δρ between the upper and the lower formations. The previous technique for computation of relief due to a single interface is exactly the same as proposed by Grant and West (1965) using the equivalent stra- tum theorem in the gravity fi eld. Grant and West (1965, p. 250, their Equation 9.9 and fi g. 9.7) have proved an equation for equivalent stratum theorem as ),(2),,( yxhGdyxg ρπ Δ= , (A9) where g(x, y, d) is the downward-continued gravity anomaly at a depth d, and h(x, y) is the vertical departure of the interface at any point from its mean depth d. Thus, by continuing the residual (fi ltered) gravity anomaly on the plane of measurement downward to an assumed depth, d, one can construct an equivalent topographic surface provided the density contrast is known. 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