Abstract
 Top of page
 Abstract
 1. Introduction
 2. Tectonic Setting
 3. Data
 4. ThreeDimensional PresentDay Load Distribution
 5. Modeling the Basin Evolution
 6. Discussion
 7. Conclusions
 Acknowledgments
 References
[1] Previous quantitative studies dealing with the origin of foreland basins have focused primarily either on the rheological basis of the lithosphere mechanical response or on the relationship between orogenic loading and sediment geometry. To link the evolution of the Guadalquivir foreland basin (South Iberia) with the thermomechanical stratification of the Iberian lithosphere, we combine quantitative approaches to deep and shallow processes: thrust loading, lithospheric flexure, thickness changes of the crust and the lithospheric mantle, and surface mass transport. A planform flexural analysis of the presentday load distribution shows that basement subsidence is related not only to upper crustal thrusting but also to a deepseated additional load. On the basis of the observed gravity and geoid fields, we propose this additional load to be related to a lithospheric mantle thickening larger than the coeval crustal thickening. Further modeling of the evolution of a basin cross section reveals that the architecture of the sedimentary basin is additionally related to the lithosphere rheological response. The quantitative study of the evolution of basement faulting and the forebulge uplift of Sierra Morena leads us to conclude that viscous stress relaxation and/or plastic yielding within the lithosphere are key processes to explain the flexural evolution of the basin.
1. Introduction
 Top of page
 Abstract
 1. Introduction
 2. Tectonic Setting
 3. Data
 4. ThreeDimensional PresentDay Load Distribution
 5. Modeling the Basin Evolution
 6. Discussion
 7. Conclusions
 Acknowledgments
 References
[2] The lithosphere retains finite strength on geological timescales when submitted to external loads, behaving as a rigid thin plate resting on a fluid asthenosphere. Foreland basins have been interpreted as sedimentary accumulations occurring on continental lithosphere when this is tectonically loaded and flexed by an orogenic wedge. Therefore the geometry of the sedimentary infill is expected to be strongly dependent not only on the tectonic evolution of the orogen but also on the rheological behavior of the lithosphere during flexure.
[3] Many authors have studied the evolution of foreland basins by using numerical methods to quantitatively link the processes of orogenic growth, erosion/sedimentation, and flexure. Beaumont [1981] used a viscoelastic plate model to simulate the flexural response of the lithosphere in the Alberta Basin. Flemings and Jordan [1989] incorporated wedgeprogradation gradual loading and sedimentation. Later, Toth et al. [1996] and Ford et al. [1999] explicitly related loading with thrusting in the active margin of the subAndean foreland and the western Alps, respectively. Many among these and other works found that the load derived from the present topography or the thrust kinematics cannot satisfactorily explain the basement deflection. The required additional load [e.g., Royden and Karner, 1984; Bott, 1991], sometimes referred as “hidden load,” is found to be both positive [e.g., Brunet, 1986; Royden, 1988] or negative [LyonCaen and Molnar, 1983, 1985] according to the region of study. This load has been interpreted in diverse ways such as the effect of a relevant paleobathymetry prior to the formation of topography [Stockmal et al., 1986; Van der Beek and Cloetingh, 1992] or the effect of subcrustal forces such as slab pull [Royden and Karner, 1984].
[4] Simultaneously, several authors used synthetic approaches to study the detailed mechanical response of the lithosphere. It has been repeatedly shown that anelastic behavior of the oceanic lithosphere modifies its flexural deflection pattern [e.g., Bodine et al., 1981; GarciaCastellanos et al., 2000]. The equivalent implications of the rheological layering for continental flexure were studied by McNutt et al. [1988] and Burov and Diament [1992, 1995] among others. Waschbusch and Royden [1992] related the episodicity during the evolution of foreland basins to the flexural effects of elasticplastic yielding in the lithosphere. However, there is a lack of modeling studies integrating both surface (erosion/sedimentation) and deep (lithospheric scale) processes to reproduce the evolution of foreland basins.
[5] The work presented here intends to show that integrating the quantitative modeling of the lithosphere anelastic behavior and the thrust load evolution and incorporating simple approaches of noninstantaneous erosion/sedimentation can provide new insights into the system as a whole. In particular, we propose a selfconsistent quantitative model for the evolution of the Guadalquivir Basin (southern Spain) linking the emplacement of the Betic Range, the subcrustal mass redistribution, and the rheology of the flexed lithosphere. For this purpose, we apply a numerical code based on GarciaCastellanos et al. [1997] that allows the calculation of the flexural subsidence of a multilayered lithosphere (in a similar way to Waschbusch and Royden [1992] and Burov and Diament [1992, 1995]) when loaded by noninstantaneous thrusting and erosion/sedimentation processes (similar to Toth et al. [1996]).
[6] Previous flexural modeling of the Guadalquivir foreland basin [Van der Beek and Cloetingh, 1992] showed that the presentday basement depth is explained by loading of an elastic plate only if an extra load is added to the topographic load. Subsequently, the flexural origin of the basin has been adopted to interpret various observations such as stress measurements [Herraiz et al., 1996] or refraction seismics [González et al., 1998]. Recent seismic, oil well, heat flow, palaeontological, and field data compilations and interpretations by Fernàndez et al. [1998a], Berástegui et al. [1998], and Sierro et al. [1996] provide the keys to model the basin evolution, linking it with the structure and mechanical behavior of the south Iberian lithosphere and permitting identification of the different loads and evaluation of their timing.
2. Tectonic Setting
 Top of page
 Abstract
 1. Introduction
 2. Tectonic Setting
 3. Data
 4. ThreeDimensional PresentDay Load Distribution
 5. Modeling the Basin Evolution
 6. Discussion
 7. Conclusions
 Acknowledgments
 References
[7] The Neogene Guadalquivir foreland basin is located in the southern part of the Iberian Peninsula, limited by the Iberian Massif to the north and the Betic mountain chain to the south (Figure 1). The Betic Range is the northern segment of a strongly arcuate orogen that continues in the Rif Chain (northern Africa) across the Gibraltar Strait. The Alborán Sea extensional basin occupies at present the inner part of this orogen. The tectonic evolution of the whole area, which constitutes the westernmost part of the Alpine Chain, was controlled by the postCretaceous relative movement between the African and Eurasian plates. Plate motion studies from Dewey et al. [1989] suggest that this part of the plate boundary experienced ∼200 km of roughly NS convergence between midOligocene and late Miocene, followed by ∼50 km of WNW directed oblique convergence from late Miocene to Recent time.
[8] The major paleogeographic elements forming the BeticsGuadalquivir system correspond to three tectonic domains that were well delimited by the beginning of the Neogene [Balanyá and GaríaDueñas, 1987]: (1) the External Zones of the Betic chain corresponding to the inverted Mesozoic continental margin of the Iberian plate; (2) the Flysch Units, which are made up of allochthonous sediments; and (3) the Internal Zones of the Betic chain, composed of a polyphase thrust stack that includes three highpressure lowtemperature metamorphic nappe complexes [e.g. Bakker et al., 1989; Tubia and GilIbarguchi, 1991].
[9] The tectonic evolution of the Betic Range is relatively poorly constrained, and its study has lead to significant discrepancies between authors. For instance, Platt [1998] requires only two tectonic events (compressive and extensive) to explain the metamorphic record and other geological evidence, whereas Balanyá et al. [1997] define four tectonic events of successive compression and extension. There are also discrepancies on the depth of the contact between External and Internal Betics, varying from midcrustal [Banks and Warburton, 1991] to the base of crust [Sanz de Galdeano, 1990] and the base of lithosphere [Montenat and D'Estevou, 1996]. Similar disagreements arise regarding the age of the sedimentary infill of the Guadalquivir Basin, where the oldest Neogene sediments have been dated either as Helvetian [Perconig, 1962, 1971], Tortonian [Sierro et al., 1996], or very late Langhian [Berástegui et al., 1998; Fernàndez et al., 1998a]. The basin infill records progradation toward the WSW after the Messinian [Sierro et al., 1996], reflecting the present direction of sediment transport, whereas before this period the sedimentary units show small lateral variations along the strike of the basin [Berástegui et al., 1998].
[12] In summary, the Guadalquivir Basin formed in an overall environment of plate convergence as the late foreland basin of the Betics, but this convergence is not reflected in the extensional Neogene kinematics of either the Internal Betic zones or the Alborán Basin. The presentday Guadalquivir Basin only correlates with the late stages (Langhian to Recent) of the Betic tectonic history that began during Late Cretaceous.
4. ThreeDimensional PresentDay Load Distribution
 Top of page
 Abstract
 1. Introduction
 2. Tectonic Setting
 3. Data
 4. ThreeDimensional PresentDay Load Distribution
 5. Modeling the Basin Evolution
 6. Discussion
 7. Conclusions
 Acknowledgments
 References
[20] Before addressing the relationship between the sediment infill geometry and the lithosphere thermomechanical behavior, we need first to evaluate the origin and relative importance of the different loads responsible for the basin formation. For this purpose, we study the regional isostatic equilibrium using as the main constraint the geometry of the preCenozoic basement of the basin. Flexural calculations have been performed using an elastic thinplate model with elastic thickness varying from 13 km in the western limit of the basin to 7 km in the east, as constrained by Van der Beek and Cloetingh [1992] and the present work. The twodimensional (2D) differential equation relating flexural deflection, load distribution, and elastic plate thickness [Van Wees and Cloetingh, 1994] is solved by the method of finite differences assuming null derivative and null curvature of the deflection in the boundaries.
[21] As shown by Van der Beek and Cloetingh [1992], the flexural formation of the Guadalquivir Basin cannot be explained only by the presentday topographic load, which is a frequent situation in continental settings [e.g., Brunet, 1986; Royden, 1988; Buiter et al., 1998; Bott, 1991]. To estimate the presentday 3Dload distribution acting in the BeticsGuadalquivir region, we consider that apart from the topographic load, loading is related to crustal and lithospheric thickness variations along time (Figure 4). Because of the lower density of the crust relative to the upper mantle, a thickening of the lower crust would imply buoyant loading. Similarly, a thickening of the lithospheric mantle (denser than the asthenosphere) implies a downward load.
[22] The topographic load is defined as the weight of the column between the presentday topography and the paleotopography at basin initiation minus the weight of the initial water column. Therefore, at the southern margin of the Guadalquivir Basin the topographic load will correspond to the difference between the initial submarine relief and the present relief of the External Betics. At the passive margin of the basin, which corresponds to the Palaeozoic Iberian Massif, we assume an initial plate altitude equal to the mean present topography (350 m), and thus the topographic load is considered to be zero in this area. Prior to the formation of the basin, paleogeographic reconstructions show an inherited Mesozoic passive margin where the relief related to the Palaeogene Internal Betic thrusting was still low and located far from the present basin [Sanz de Galdeano and Rod íguezFernández, 1996]. The shoreline did not change much since the end of Mesozoic until Langhian [GaríaHernández et al., 1980; Sanz de Galdeano and RodíguezFernández, 1996]. Although turbidites are reported in earlier marine deposits [Sanz de Galdeano and RodíguezFernández, 1996], the first sediments of the present basin (Langhian basal calcarenite) indicate very shallow coastal environments [Berástegui et al., 1998]. On the basis of these studies, we use an initial paleotopography consisting of a shoreline parallel to the present Palaeozoic outcrop, 60 km southward from it, dividing the 350 m altitude in the Iberian Massif from water depths down to 800 m in the present location of the Internal Betics (Figure 4a). Although the paleobathymetry is poorly constrained in the present area of Internal Betics, it will be shown later in this section that its isostatic effect on the model is minor.
[23] The crustal load (related to crustal thickness variation) is calculated as the difference between the present Moho depth and the Moho depth at the beginning of basin evolution, measuring both depths relative to the basin basement. The initial base of the crust is calculated by isostatically compensating (local isostasy) the initial topography (see Figure 4a). Hence the amount of crustal thickness change (CT) excluding the topography component can be written as the difference between the present Moho depth (MD) and the deflected initial Moho, i.e.,
assuming that the deflection is positive downward. Finally, the subcrustal load is an unknown that will be deduced from the modeling and then translated in terms of lithospheric thickening/thinning during the formation of the basin.
[24] To determine the presentday load distribution acting on the study region, we must first calculate the distance at which these loads can contribute to the deflection of the Guadalquivir Basin. Figure 5 shows the relative changes induced on the plate deflection W_{0} produced in front of a rectangular load of finite length L relative to a load of infinite length. Calculations have been performed assuming an infinite 1D thin elastic plate approach with constant elastic thickness (T_{e}). Results indicate that for T_{e} = 10 km (a maximum estimate for the Guadalquivir Basin according to Van der Beek and Cloetingh [1992]), a load length of 50 km accounts for more than 90% of the deflection produced by an infinite load. Therefore, in terms of flexural analysis the study region is limited to the south by the External Betics, since the loads associated with the Internal Betics and the Alborán Basin are too far from the presentday Guadalquivir Basin to noticeably contribute to its subsidence.
[25] Using the parameter values given in Table 1. and bearing in mind the above considerations, we first calculate the deflection produced by the loads related to topography and crustal deformation. Figure 6a shows the basement depth (i.e., deflection plus paleotopography) resulting from applying the mass difference between the paleotopography and the presentday topography (topographic load). Paleobathymetry is a relevant factor increasing the topographic load and all materials above the initial paleosurface have been considered as topographic load. In fact, an important part of the deflection shown in Figure 6a is related to the initial paleobathymetry rather than to the presentday relief above sea level. However, the predicted basement depth is insufficient to explain the observations in Figure 2a.
Table 1. Parameters Used for the Elastic 2D (Planform) Model of PresentDay Load Distribution  Value 

T_{e}  7–13 km 
Density of topography  2700 kg m^{−3} 
Density of water  1013 kg m^{−3} 
Density of infill  2700 kg m^{−3} 
Density of crust  2800 kg m^{−3} 
Density of mantle  3300 kg m^{−3} 
Density of asthenosphere  3250 kg m^{−3} 
Gridding  6 × 6 km 
Maximum initial altitude  350 m 
[26] The subsidence obtained when including the load related to crustal thickness changes is shown in Figure 6b. In this case, the predicted basement depth is closer to that observed, but still a positive (downward) additional load is required to reproduce the deflection of the Iberian plate. This additional load is calculated by using a forward modeling technique to fit the observed basement depth shown in Figure 2a. The resulting load distribution is shown in Figure 7 in terms of lithospheric thickening using a meandensity contrast between the lithospheric mantle and the asthenosphere of 50 kg m^{−3}. According to these results, the thickening of the lithospheric mantle increases to ∼30 km beneath the External Betics showing small variations along strike and vanishing progressively toward the northern limit of the basin. The amount of thickness variation is subjected to the uncertainty of the initial topography, which in turn constrains the initial crustal configuration. Overestimating the paleobathymetry at the present basin domain in 200 m (i.e., considering that the Langhian coastal basal calcarenites were deposited 200 m deep) produces a 25% reduction of the predicted lithospheric thickening. Although the uncertainty in the paleobathymetry farther to the south (present Betics) is higher, its isostatic effect is reduced because of the larger distance to the present basin location. Thus, although keeping in mind this uncertainty in the lithospheric thickening distribution, the effect of paleobathymetry [Van der Beek and Cloetingh, 1992] reveals insufficient to explain the hidden load associated with the Guadalquivir Basin.
[27] Thickening of the lithospheric mantle beneath the Guadalquivir Basin region is also supported by gravity and geoid data. The coincidence of Bouguer and geoid minima in the Guadalquivir region [Fernàndez et al., 1998a] is a rather unusual feature in crustal thickening areas. An interpretation of this feature in terms of crustal and lithospheric geometry is undertaken below based on 2D gravity field calculations based on the algorithms by Talwani et al. [1959] and Chapman [1979]. Figures 8a and 8b show the calculated gravity and geoid anomalies for three lithospheric geometries under isostatic compensation generating a topographic elevation of 800 m (representing the mean value of the Betics relative to the Iberian foreland). The results show that a simple crustal or homogeneous crust/mantle thickening (cases 1 and 2 in Figure 8a) do not predict a geoid low. Instead, to reproduce the geoid and Bouguer anomalies of similar magnitude to that observed in the BeticGuadalquivir system (Figure 8c), it is necessary that the lithospheric mantle thickens twice as much as the crust (case 3 in Figures 8a and 8b). In case 3, the crust and the mantle thickening have been mutually shifted 50 km to simulate the thickening geometry derived in this work.
5. Modeling the Basin Evolution
 Top of page
 Abstract
 1. Introduction
 2. Tectonic Setting
 3. Data
 4. ThreeDimensional PresentDay Load Distribution
 5. Modeling the Basin Evolution
 6. Discussion
 7. Conclusions
 Acknowledgments
 References
[28] The presentday load distribution acting on the Guadalquivir Basin region shows that despite the topography (and hence the topographic load) having important variations along strike (higher in the Central Betics than in the Western Betics), the total load has an acceptable 2D (cross section) symmetry. This is reflected in the small lateral variations along strike of the flexural subsidence (Figure 2a) and suggests that the evolution of the basin can be addressed by modeling a representative cross section (located in Figure 1). The objective of this modeling is to quantitatively link the basin infill evolution with the lithosphere rheology using a simple kinematic model of the emplacement of the External Betics and the subcrustal loads determined in the previous section. Although the model is mainly constrained by the presentday basement depth and the geometry and timing of the sedimentary basin infill, additional observations such as the reactivation of basement faults and the uplift of Sierra Morena will be also considered. In order to fit those constraints, forward modeling is performed varying the parameters controlling the lithospheric, tectonic, and erosion/sedimentation processes.
[29] The crosssectional models below are based on a finite difference code that links the load associated with the emplacement of thrust sheets with the surface mass transport and the mechanical behavior of the flexed lithosphere [GarciaCastellanos et al., 1997; GarciaCastellanos, 1998]. Thrust sheet kinematics are calculated by vertical shear, i.e., preserving the vertical thickness of every thrusting unit during their movement and assuming that thrusting propagates toward the foreland. The thickness of the thrusting units (5 km) is constrained by the geological cross sections of Berástegui et al. [1998] and Fernàndez et al. [1998a], whereas the shortening velocity has been arbitrarily defined to fit the final basin volume. The timing of shortening applied (4 km Ma^{−1} before 10.5 Ma; 2.5 km Ma^{−1} between 10.5 and 6.5 Ma and 0 km Ma^{−1} after 6.5 Ma) is constrained with the end of compressional deformation of the frontal sediment imbricates observed in seismic profiles [Berástegui et al., 1998]. The total amount of shortening in the last 18 Myr is 40 km, which implies a total volume of thrustgenerated relief of 200 km^{2} (cubic kilometer volume per kilometer length along the strike). It must be noted that the initial time of the model does not correspond to the first shortening episodes recorded in the External Betics but to those that produced basement deflection in the region occupied by the presentday Guadalquivir Basin.
[30] The sedimentary record of the Guadalquivir Basin (see Figure 3 and Berástegui et al. [1998]) shows that the southern margin of the basin consists of a lateral diapir of Triassic evaporites and a frontal north verging imbricate wedge involving Tortonian sediments. Our modeling does not intend to reproduce either the emplacement of the Triassic evaporites or the deformation of the frontal Miocene imbricates. Nevertheless, for loading purposes we have considered that Triassic evaporites contribute to basement deflection, whereas the Miocene imbricates form part of the sedimentary infill disregarding its internal structure. In consequence, the frontal thrusts resulting from our models (e.g., Figure 9) must be geometrically interpreted as the frontal part of the lateral Triassic diapirs. The sedimentation rate was higher during the Messinian, when a similar sediment thickness to the other units was deposited in a shorter time [Berástegui et al., 1998]. This leads us to incorporate to the model the subcrustal loads derived in the previous section at the time t = 6 Ma (as an instantaneous load), although this choice depends on the approaches used in the sedimentation model.
[31] The sedimentation rate varies laterally according to the available space below sea level, and it is limited with a maximum value (Tables 2 and 3). The subaerial erosion rate is proportional to altitude above sea level except for the PlioQuaternary period, during which the level dividing erosion and sedimentation has been raised 100 m above sea level to reproduce the complete infill of the basin with continental sediments. Sedimentation and erosion constants were modified to fit the observed sedimentary unit thickness as displayed in Figure 3 and the presentday topography and basement depth. No mass conservation is considered between erosion and sedimentation, since transport in the strike direction has been dominant during the basin history. At each time step, a new increment in flexural deflection is calculated from the load redistribution produced by thrusting and erosion/sedimentation. The model numerical domain 400 km long.
Table 2. Parameters Used for the Viscoelastic 1D (Cross Section) Model  Value 

T_{e}  15 km 
Relaxation time τ  1.2 Myr 
Initial time  18 Ma 
Final time  0 Ma 
Shortening velocity before t = 10.5 Ma  4 km Myr^{−1} 
Shortening velocity from t = 10.5 to t = 6.5 Ma  2.5 km Myr^{−1} 
Sediment density  2300 kg m^{−3} 
Horizontal tectonic compressional force F_{x}  0 N m^{−1} 
Basement and crust density  2700 kg m^{−3} 
Erosion rate K_{EC}  0.09 m m^{−1} Myr^{−1} 
Maximum sedimentation rate K_{SM}  160 m Myr^{−1} 
Gridding dx  0.5 km 
Maximum initial altitude  350 m 
Table 3. Parameters Used for the ElasticPlastic 2D (Cross Section) Model^{a}  Value 


Thermal lithosphere thickness  93 km 
Mechanical lithosphere thickness  53 km 
Crustal thickness  32 km 
Upper crust thickness  21 km 
Initial time  22 Ma 
Final time  0 Ma 
Shortening velocity before t = 10.5 Ma  4 km Myr^{−1} 
Shortening velocity from t = 10.5 to t = 6.5 Ma  2.5 km Myr^{−1} 
Sediment density  2300 kg m^{−3} 
Basement and crust density  2700 kg m^{−3} 
Erosion rate K_{EC}  0.12 m m^{−1} Myr^{−1} 
Maximum sedimentation rate K_{SM}  200 m Myr^{−1} 
Gridding dx, dz  0.5, 0.6 km 
Horizontal tectonic compressional force F_{x}  −0.3 TN m^{−1} 
[32] First tentative models have shown that it is not possible to reproduce the Tortonian basinward shift of the position of the onlap (Figure 3) by using a pureelastic plate model and a thrusting propagation toward the foreland, since this predicts a continuous onlap of sequences as found also by Flemings and Jordan [1989]. On the other hand, incorporation of eustatic curves [Haq et al., 1987] to these models showed that sea level variations are insufficient to explain the strong Tortonian basinward shift of the pinchout observed in the Guadalquivir Basin. Because of the important basement dip reached at Tortonian, the migration of the pinchout in this period would require an unreasonable eustatic sea level change of 300–500 m. Therefore we investigate two complementary mechanisms that may cooperate with eustasy to explain the shift of the pinchout during the Tortonian: viscous relaxation of the lithospheric stresses, and elasticplastic yielding within the lithosphere.
5.1. Viscoelastic Model
[33] According to the viscoelastic model of lithospheric flexure [e.g., Nadai, 1963; Beaumont, 1981], after responding elastically to a load, the lithosphere presents a timedependent deflection related to the viscous relaxation of the stress within the plate. This viscous relaxation reduces the wavelength of the deflection pattern through time, producing a basin narrowing similar to that caused by a reduction in elastic thickness. The velocity of this viscous deformation is controlled by the relaxation time parameter τ, related to the viscosity of the plate. We solve via the finite difference method the equation governing a viscoelastic plate. This equation relates the deflection profile to the external acting loads and plate parameters (elastic thickness and relaxation time), and is based on the standard thinplate approach [e.g., Beaumont, 1981]. At each time step of the numerical model a new deflection increment is calculated and added in terms of subsidence/uplift to the basin profile. Further details on the applied technique are given by GarciaCastellanos et al. [1997].
[34] Figure 9 shows the evolution of the best fitting viscoelastic model of the Guadalquivir Basin using a viscoelastic plate. The parameter values required during the forward modeling are summarized in Table 2. The last stage in Figure 9 (t = 0) shows that the viscoelastic approach satisfactorily reproduces the presentday basement geometry, the sedimentary infill geometry, and the mean topography. In agreement with the observed sedimentary record (Figure 3), the Tortonian and PlioQuaternary depocenters migrate basinward relative to the Latest LanghianSerravallian and Messinian units, respectively. The basin geometry is here a result of the competition (at each time step of the model) between the instantaneous elastic response to thrusting (that shifts the basin depocenter toward the foreland) and the speed of viscous relaxation (that narrows the basin and uplifts it distal margin). During the syntectonic phase, thrust loading and its associated elastic flexural response are the leading processes, prevailing over the erosion unloading and the viscous relaxation and generating a foreland basin together with the subcrustal load acting at 6 Ma. In the posttectonic period (after 6 Ma), only the viscous relaxation takes place, reducing the basin width and uplifting its sediment infill (particularly in the distal part). The incorporation of the subcrustal load derived from the planform modeling produces an increase in bathymetry in the basin and a reduction of the topography in the orogen. The calculated maximum bathymetry is 350 m, coinciding with the emplacement of the subcrustal load (Figure 9), but it depends on the sedimentation rate, which is in turn poorly constrained. Finally, the erosion and sedimentation processes lead to the present low topography and overfilled basin.
[35] The flexural forebulge at the final stage is centered between x = 20 km and x = 45 km. The maximum rebound there is 174 m, though most of this relief has been eroded (dotted line in Figure 9). The predicted location of the forebulge coincides with Sierra Morena, the mountain range bounding the basin to the north and acting as water divide between the Guadalquivir drainage basin and the Iberian Massif. The predicted amount of uplift is smaller but comparable to the mean height of this range relative to the Iberian Massif (∼300 m), suggesting that forebulge uplift could be a firstorder process contributing to the formation of Sierra Morena. Incorporation of horizontal compression throughout the evolution (reflecting the overall convergence between Iberia and Africa) and minor parameter changes with respect to the model shown in Figure 9 enhances the forebulge uplift by buckling the lithosphere, while preserving a good fit of the basin geometry. However, rather than finding the horizontal force by fitting a poorly constrained forebulge uplift, the calculation of this force is addressed in section 5.2 by means of an elasticplastic model that attempts to account for the stress evolution in the plate.
5.2. ElasticPlastic Model
[36] A second lithosphere mechanical behavior that can explain the characteristics of the sedimentary infill geometry of the Guadalquivir Basin is plastic yielding. According to this plate model, the lithosphere behaves elastically below a certain yield stress that varies in depth. When this yield stress is reached, anelastic deformation takes place and the apparent rigidity of the plate is reduced. Waschbusch and Royden [1992] demonstrated that the elasticplastic stratification of the lithosphere could induce a nonlinear flexural response that generates sedimentary unconformities. Following these authors, we use similar approaches to model the evolution of the basin geometry. We refer to GarciaCastellanos et al. [1997] and GarciaCastellanos [1998] for a detailed description of the elasticplastic multilayered plate model used in this work. A significant improvement has been made to their model: Instead of calculating the stress distribution in the elasticplastic plate as a function of the plate curvature at every time step, here we add stress increments to the cumulated stress distribution (similar to Waschbusch and Royden [1992]).
[37] The main differences between the viscoelastic and the elasticplastic models (compare Tables 2 and 3) are (1) the rheological behavior of the lithosphere; (2) in order to reach the earlier stages of basin evolution with a quasi steady state stress accumulation in the plate, the modeling initiates at t = 22 Ma instead of t = 18 Ma, and an additional thrust unit is active during this new period; and (3) a constant horizontal tectonic force of F_{x} = −0.3 TN m^{−1} causing an overall compressive regime is incorporated throughout the model evolution to increase the tilting of the basement without further weakening of the thermal structure of the lithosphere. This force reflects qualitatively the overall collisional regime between Iberia and Africa during the formation of the basin and the present NNWSSE compressional regime in Iberia.
[38] The mechanical response of an elasticplastic plate is determined by means of the yield stress envelope (YSE) concept [e.g., Lynch and Morgan, 1987]. We have constructed an YSE for the Iberian lithospheric plate based on the measured surface heat flow [Fernàndez et al., 1998b] and using standard rheological parameters (Table 4). To calculate the geotherm shown in Figure 10a we use three layers of constant thermal conductivity k and radiogenic heat production H_{RP}, with a surface heat flow of 66 mW m^{−2} [Marzán et al., 1996; Fernàndez et al., 1998b]. The resulting base of the thermal lithosphere (1330°C isotherm) is located at 93 km depth. To derive the yield stress at each depth from the temperature profile, we use a deformation rate of = 10^{−16} s^{−1}. The vertical discretization interval of the plate is dz = 0.6 km. The resulting YSE (Figure 10a) shows a mechanical thickness (depth above which strength >10 MPa) of 53 km and a very low strength at the base of the crust, indicating a probable mechanical decoupling between crust and mantle. The integrated lithospheric strength is 5.4 × 10^{12} N m^{−1} (compression) and 4.6 × 10^{12} N m^{−1} (extension). The equivalent elastic thickness of this elasticplastic plate is not assumed a priori, but it is a result of the YSE and the history of the deflection profile curvature. The predicted values of T_{e} at the last stage vary laterally from 25.1 km in the areas distant from the basin down to 6.7 km below the basin, where the deflection has a higher curvature.
Table 4. Parameters Used to Calculate the Geotherm and the Yield Stress Envelope of the South Iberian Lithosphere (Figure 10)^{a}  Thickness, km  k, W m^{−1} K^{−1}  H_{RP}, μW m^{−3}  _{o}, M Pa^{−n}s^{−1}  Q*, KJ mol^{−1} 


Upper crust  21  2.5  1.4  2.5 × 10^{−8}  140 
Lower crust  11  2.1  0.2  3.2 × 10^{−3}  250 
Lithospheric mantle  93^{b}  3.1  0  10^{3}  523 
[39] A major factor controlling the final stress distribution is the irreversibility of plastic deformation and the cumulative stress history [Mueller et al., 1996a, 1996b]. If this process is dismissed (i.e., stress distribution is calculated only as a function of the present curvature; Figure 10b), then the inversion of stresses at the top of the plate is predicted at an inflexion point of the deflection profile, where curvature changes in sign. Instead, in our modeling the inversion occurs over a maximum curvature point (Figure 10c). The reader is referred to the work by Mueller et al. [1996a, 1996b] for further details on this subject.
[40] The resulting basin geometry (Figure 11) is in good agreement with the observed sediment units (Figure 3) and the basinward migration of the onlap during Tortonian is satisfactorily reproduced. This geometry is here the result of the competition between the thrusting toward the foreland and the reduction in equivalent elastic thickness related to the increase in plate curvature (which induces a basin narrowing similar to the viscous relaxation in the previous model), explaining the Tortonian depocenter migration toward the wedge. The Messinian progradation of the onlap is due to the subcrustal loading at 6 Ma. The main parameter controlling the final basin geometry is the surface heat flow, which determines the geotherm and the strength distribution. The best fitting value (66 mW m^{−2}) is within the range of observations derived from oil and water well measurements [Fernàndez et al., 1998b].
[41] The other best fitting parameter values (Table 3) do not differ substantially from those found in the viscoelastic model. The most significant result from the elasticplastic model is that it predicts the change in the lithospheric stress regime recorded by nearvertical faults affecting the basement [Berástegui et al., 1998]. Figure 11 shows the calculated stress distribution at different time steps showing that the top of the presentday basin (from x = −40 to x = 0 km) changes from an extensional regime at t = −15.5 Ma to a compressional regime at present. Thus the elasticplastic model provides a selfconsistent explanation for the reactivation of normal faults as inverse faults in the basement as based on the thermomechanical structure of the South Iberian lithosphere.