Journal of Geodynamics 47 (2009) 119–129

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Journal of Geodynamics

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Flexure and seismicity across the ocean–continent transition in theGulf of Cadiz

Maria C. Nevesa,∗, Rui G.M. Nevesb

a CIMA-FCMA, Universidade do Algarve, Campus de Gambelas, 8000 Faro, Portugalb UIED-FCT, Universidade Nova de Lisboa, Monte da Caparica, 2829 Caparica, Portugal

a r t i c l e i n f o

Article history:Received 8 November 2007Received in revised form 30 June 2008Accepted 15 July 2008

Keywords:FlexureStrengthOcean–continent transitionSeismicityGulf of Cadiz

a b s t r a c t

In the Gulf of Cadiz the water/sediment load and the density contrasts between the continental and oceaniclithosphere are sources of vertical loading causing flexure. The main objective of this work is to investi-gate the relation between the bending stresses associated with flexural isostasy and the observed patternof deformation and seismicity. For that we combine a strength analysis and finite element numericalmodelling along a previously studied (Fernandez, M., Marzán, I., Torné, M., 2004. Lithospheric transitionfrom the Variscan Iberian Massif to the Jurassic oceanic crust of the Central Atlantic. Tectonophysics, 386,97–115) vertical section of the lithosphere, approximately perpendicular to the Africa-Eurasia conver-gence. We find that the flexural stresses are focussed in the ocean–continent transition, within a zoneapproximately 150 km wide, between the base of the continental slope and the Horseshoe Abyssal Plain.We show that the flexural stresses are mainly supported by the upper mantle and predict their values fortwo different thermal scenarios. The compositional layering in the crust is shown to play an importantrole in the focussing of the strain energy along the crust/mantle interface. Finally, we observe that there isa correlation between the modelled strain energy and the earthquake distribution. The maximum com-pressive stress difference can be as much as 65% of the strength in compression. The maximum influence

is observed at 10 km depth near the Horseshoe Abyssal Plain. We conclude that flexural stresses aloneare not enough to cause rupture or yielding in the Gulf of Cadiz. However, like plate boundary forces and

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. Introduction

The Gulf of Cadiz, including the Algarve continental margin andhe seaward continuation of the Guadalquivir Basin, frames thefrica-Eurasia plate boundary to the west of the Gibraltar Strait

Fig. 1). Its structure is the result of a complex evolution involvingeveral processes (e.g. Gràcia et al., 2003): (1) extensional processeselated to Pangea rifting and Atlantic opening which led to thereation of a passive margin in the western part of the Gulf; (2)onvergence between the African and Eurasian plates that, sincehe Oligocene, dominates the structural and tectonic setting; and3) the westward movement of the Alboran domain during the

iocene, responsible for the Betics and the Guadalquivir foreland

asin, which caused the emplacement of allochthonous terrains.

In process (1), rifting along the southern Iberian margin startedpproximately in the Early Jurassic (190 Ma) resulting in the break-p of a previously existing large carbonate and clastic shelf (e.g.

∗ Corresponding author. Tel.: +351 289800938; fax: +351 289800069.E-mail address: mcneves@ualg.pt (M.C. Neves).

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264-3707/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.oi:10.1016/j.jog.2008.07.002

ses, they need to be incorporated when assessing seismic hazard in this

© 2008 Elsevier Ltd. All rights reserved.

ndeweg, 2002). Active rifting changed to post-rift during the Lateurassic (160 Ma) with related thermal subsidence lasting untilhe Cretaceous (Vera, 1988 in Andeweg, 2002). The early evolu-ion of the margin and the limits of the oceanic and continentalomains in the Gulf of Cadiz remain unclear. Wide-angle and seis-ic reflection data, as well as gravity data, indicate a continental

omain beneath the central Gulf of Cadiz, with Moho depths vary-ng between ∼30 km near the coastline to ∼20 km offshore, and anceanic domain in the region of the Horseshoe Abyssal Plain, withoho depths of ∼12 km (e.g. Purdy, 1975; González-Fernández et

l., 2001; Fernandez et al., 2004). However, the location of thecean–continent transition is controversial, with some authorsrguing that a portion of oceanic lithosphere, formed during theethys opening, is still present in a presumed fore arc region in theentral part of the Gulf (e.g. Maldonado et al., 1999; Gutscher et al.,002). In the cross-section of the lithosphere we consider in this

tudy, the ocean–continent transition occurs in the contact areaetween transition zones 1 and 2 in Fig. 1.

Process (2), the convergence between the Africa and the Eurasialates, has been one of the most important sources of stress notnly in the Gulf of Cadiz but also all over Iberia (Andeweg, 2002).

120 M.C. Neves, R.G.M. Neves / Journal of Geodynamics 47 (2009) 119–129

Fig. 1. Location map of the study area showing the modelled profile (thick solid line). Shaded relief image of bathymetry and topography from GEBCO dig-ital data (http://www.ngdc.noaa.gov/mgg/gebco/gebco.html), with contour interval at 500 m. Epicenters for the period 1964–2007 taken from the ISC database(http://www.isc.ac.uk) complemented with data from the IM catalogue between 1970 and 2000. Focal mechanisms are from Carrilho (2005) and the CMT Harvard database( sing ga rrinhaS : Gorrt micit

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71dnf(

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http://www.seismology.harvard.edu/projects/CMT/). Structural domains, in decreand the Oceanic domain taken from Medialdea et al. (2004). Faults traced after TeVF: S. Vicent Fault, MPF: Marquês de Pombal fault, PSF: Pereira de Sousa fault, GBransition 1, transition 2 and continental) according to the crustal structure and seis

arge-scale lithosphere and upper crustal folding distributed acrossberia, with dominant wavelengths of ∼250 km and ∼50 km, haseen shown to have resulted from shortening at both the northernnd southern margins of Iberia (Cloetingh et al., 2002). The plateinematics computed from GPS data shows that present-day Africa-urasia convergence occurs in a NW–SE to WNW–ESE direction atrate of approximately 4–5 mm/year (e.g. Fernandes et al., 2003,007; Nocquet and Calais, 2004). In the Gulf of Cadiz this conver-ence is essentially accommodated by diffuse brittle deformations evidenced by widely developed tectonic structures, with differ-nt orientations and kinematics: predominantly NNE–SSW strikinghrusts and WNW/ESE trending dextral strike-slip faults (e.g. Gràcia

t al., 2003; Sartori et al., 1994; Pinheiro et al., 1996; Hayward et al.,999; Zitellini et al., 2001, 2004; Terrinha et al., 2003; Medialdeat al., 2004). Other evidence of this diffuse brittle deformation ishe seismicity in the area. Earthquake epicentres are mainly lim-ted to an E-W trending area about 150 km wide and ranging from

(ers(

rey intensity from E to W are the Offshore Betic-Rifean domain, the central domainet al. (submitted for publication); GqF: Guadalquivir fault, HsF: Horseshoe fault,

inge Bank, CP: coral patch. The modelled profile is divided in four zones (oceanic,y distribution (in Figs. 2 and 3, respectively).

◦W to 12◦W (Fig. 1). Most earthquakes occur at depths less than50 km (e.g. Bufforn et al., 2004). Large events occur at shallowepths (<30 km) and show thrust and strike-slip faulting mecha-isms consistent with the predominant NNE–SSW and WNW–ESE

ault directions under the observed NW–SE convergence directione.g. Stich et al., 2006).

The dominance of the evidence of compression may explainhy flexural effects have so far been neglected in the offshore

egion. Inland, flexural isostasy plays a major role, particularlyn the Guadalquivir Basin, whose origin is explained by an elas-ic plate model loaded both on top by topography and fromelow by crustal and lithospheric mantle thickness variations

Van Der Beek and Cloetingh, 1992). Further flexural mod-lling of the evolution of this basin emphasized the role ofheological layering and pointed to the importance of viscoustress relaxation and/or plastic yielding within the lithosphereGarcia-Castellanos et al., 2002). Offshore the Algarve margin,

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M.C. Neves, R.G.M. Neves / Journ

exural effects may also arise due to the lateral density varia-ions created by the co-existence of the oceanic and continentalomains.

However, previous numerical models in the Gulf of Cadiz havegnored the strength of the lithosphere and assumed local isostaticquilibrium. This assumption was made in the study by Fernandezt al. (2004) who used a finite element code to solve simultane-usly the geopotential, lithostatic and heat transport equationso estimate the rock parameters and thermal properties of theithosphere along a profile across the ocean–continent transition.t was also made by Jiménez-Munt et al. (2001) and Negredot al. (2002) who used the thin sheet approach to provide first-rder approximations of the strain and strain rate distribution inhe Gulf of Cadiz. These efforts allowed the testing of hypothe-es about kinematic poles and boundary conditions and providedndications on the long-term seismic hazard of faults by estimat-ng their fault slip rates. Nevertheless, this 2D horizontal approachannot resolve vertical variations of strength and neglects flexuraltresses.

In this work we aim to address these issues. Our main goalsre threefold: (1) provide an estimate of the bending stressesnd assess how important flexural isostasy may be in the Gulff Cadiz; for this we model the Fernandez et al. (2004) verti-al profile cutting across the continental and oceanic domains;2) investigate the role of a layered rheology in the stress dis-ribution; for this we use the crustal structure documented byernandez et al. (2004) to infer the vertical strength variationslong the same profile and estimate the mechanical thickness inhis region; and (3) explore the relation between the bendingtresses and the seismicity. Recognising that the bending stressesnduced by flexural loading might be one of the possible causes ofarthquakes (e.g. Watts, 2001), we combine the strength analysisith the numerical modelling to investigate the relation betweenexure and the observed pattern of deformation and seismic-

ty.

. Crustal structure

The lithospheric structure in the Gulf of Cadiz has been the sub-ect of numerous seismic campaigns justified in part by the seismicazard risk in this region. In addition to the seismic reflection pro-les of the oil industry, many near-vertical reflection, refractionnd wide-angle reflection profiles have been acquired in recentears within the scope of projects such as RIFANO92, IAM93,IGSETS98, TASYO-2000, SISMAR2001 and VOLTAIRE2002. Amonghese projects IAM93 was pioneer in revealing the deep structure ofhe crust and mantle (Banda et al., 1995). The combined interpreta-ion of near-vertical reflection and refraction/wide-angle reflectionAM data first suggested that the crust underlying the eastern andentral part of the Gulf of Cadiz is of continental type, with a con-inental basement formed by Precambrian and Palaeozoic rocksGonzález-Fernández et al., 2001). The Moho gradually shallowsrom a depth of 30–32 km in the continental margin of SW Iberia to0–12 km in the Horseshoe Abyssal Plain (HAP), reaching values ofess than 7 km in the Seine Abyssal Plain (SAP) (Purdy, 1975; Sartorit al., 1994; Matias, 1996; González et al., 1998). The oceanic naturef the crust in the HAP, the SAP and in the Gorringe Bank is generallyccepted on the grounds of seismic interpretation, gravity anomalyodelling and bottom sampling (e.g. Purdy, 1975; Hayward et al.,

999; Gràcia et al., 2003). In the region between the continentalomain of the Gulf of Cadiz and the oceanic domain of the HAPhere is no clear evidence of crust type.

The section of the lithosphere considered in this study is rep-esented in Fig. 2. Between the eastern end of the HAP and Cape

SfBtt

eodynamics 47 (2009) 119–129 121

an Vincent (CSV) it coincides with seismic reflection profile IAM3,lready studied in great detail by several authors (e.g. Gonzálezt al., 1996; Tortella et al., 1997). In the SAP the crustal structures based on the work of Purdy (1975), Sartori et al. (1994) and

edialdea et al. (2004). Inland of CSV, in the South Portugueseone, it is based on the interpretation of seismic wide-angle andefraction data by Matias (1996) and González et al. (1998). Ratherhan strictly following the seismically defined interfaces, we incor-orate the results of the modelling of Fernandez et al. (2004) toefine the geometry and physical properties of the different lay-rs.

Regarding the basement, four main zones can be identifiedlong the section of Fig. 2. From SW to NE: (1) an oceanic domainround the SAP where the crust, about 7 km thick, is divided inton upper part with P-wave velocities in the range 4.1–5.6 km/s andlower part with velocities of about 6.3 km/s; (2) a transitional

omain spanning from around km-300 to km-150 where the crustas an intermediate composition/density between that of oceanicrust/2840 kg/m3 and that of upper continental crust/2740 kg/m3;3) a second transitional domain ranging from km-150 km to km-50onsisting of stretched continental lithosphere. This domain con-ists of two layers with seismic velocities analogous to the uppernd middle continental crust; and (4) a continental crust char-cterized by three layers that thickens to 30 km within 50 km ofSV. Here P-wave velocities are 5.2–6.1 km/s in the upper crust,.2–6.4 km/s in the middle crust, 6.7–6.9 km/s in the lower crustnd 8.1–8.2 km/s in the mantle. We call the ocean–continent tran-ition the region near km-150 lying between transitional zones 1nd 2.

The sedimentary cover is continuous from the SAP to CSV hav-ng a variable thickness that reaches its maximum (∼2 s TWT) inhe eastern HAP. It consists of five stratigraphic units, spanningn age from upper Jurassic-lower Aptian at the base to Miocene-uaternary at the top (Tortella et al., 1997; Medialdea et al., 2004).mong these units the allochthonous body of the Gulf of Cadiz,bout 400–500 ms TWT thick in the HAP, is particularly relevantor its chaotic character and role in the geodynamic evolution ofhis region. P-wave velocities in the depositional sequence rangerom 2.0 km/s in the post-Miocene marine sediments at the top to.7 km/s in what is interpreted as the Mesozoic carbonate succes-ion also found in the Algarve margin outcrops.

The SAP and the HAP are characterised by active thrust tectonics,ith a northwestward verging thrust system trending NNE-SSW

ffecting both the sediment cover and the basement. Some ofhese thrust faults are observed as internal crustal reflectors thatole out developing seafloor elevations (e.g. Terrinha et al., 2003;edialdea et al., 2004). Shortening in the region is also expressed

s large amplitude (up to 800 m) and intermediate wavelength10–60 km) folds of the sediments and basement (Hayward et al.,999; Medialdea et al., 2004). Similar intermediate wavelengtholds are also observed within the Iberia Peninsula (Cloetingh etl., 2002). The NNE–SSW thrust system is crosscut by lineamentsrending WNW–ESE that have been interpreted as seafloor man-festations of deep right-lateral strike-slip faults (Terrinha et al.,ubmitted for publication).

. Seismicity

The seismicity data used in this study is taken from the IM

eismic Catalogue of Continental Portugal and adjacent regionor 1970–2000, and from the ISC catalogue (http://www.isc.ac.uk/ulletin) for the period from 1964 to the present. As shown in Fig. 1he seismicity from 12◦W to 7◦W is distributed in an E-W direc-ion within a band of approximately 150 km. Within this band three

122 M.C. Neves, R.G.M. Neves / Journal of Geodynamics 47 (2009) 119–129

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ig. 2. Structure of the crust along the profile studied by Fernandez et al. (2004) shg/m3. OC: oceanic crust, TC: transitional crust, UC: upper continental crust, MC: mccording to the seismicity distribution (in Fig. 3).

egions of concentrated events, which seem to be SW–NE oriented,an be recognised: the region of the Gorringe Bank, the region thatuns from CSV along the S. Vicente Canyon to the HAP, and theegion of the Guadalquivir Bank. The largest events concentrate inhe HAP (29.2.1969, Ms = 8 and 12.2.2007, Mw = 6.1) but the majorityave small to moderate magnitudes (Ms < 5).

Earthquakes are observed up to 140 km depth both in theceanic and continental domains (e.g. Bufforn et al., 2004). In theceanic lithosphere the brittle–ductile transition often occurs in theantle so the depths of the events recorded to the west of 10◦ W

re considered normal. In the region to the east of this longitudehe explanation for the observed intermediate-depth seismicity is

ore controversial since the continental mantle is generally aseis-ic at these depths.Focal mechanisms show essentially thrust and strike-slip fault-

ng, with thrusting motion dominating (e.g. Udías et al., 1976;rimison and Chen, 1986; Borges et al., 2001; Bufforn et al., 2004).he strike-slip solutions have predominantly E-W striking planesith right-lateral motion. The seismicity studies are unanimous in

onsidering that both thrust and strike-slip events are compatibleith a NNW–SSE direction of horizontal maximum of compression

�1), close to the direction of the plate convergence between Africand Eurasia. Furthermore, both the shallow and deep earthquakeshow the same direction of maximum compression, supporting theypothesis of mechanical crust–mantle coupling (Stich et al., 2006).here is nonetheless some evidence that the least compressivetress is steeper at the surface and more sub-horizontal at depth,uggesting a transition in the faulting regime from reverse fault-ng at shallow depths to strike-slip faulting at intermediate depthsStich et al., 2006).

Fig. 3 shows a cross-section of the seismicity along the profileonsidered in this study. All projected earthquakes lie in a 150 kmide band centred on the profile thus excluding events in theorringe Bank and in the Guadalquivir Bank. Alignments of earth-uakes at 10 and 30 km depth have been filtered out from the IMatabase as these correspond to poorly constrained hypocenters (F.arrilho, personal communication). The geometry of the crust ishown in the background for reference, but note that the verticalxis in Fig. 3 represents depth below the seafloor and not depthelow sea level as in Fig. 2.

Looking at Fig. 3 we can divide the seismicity into four mainones: (1) a practically aseismic oceanic domain; (2) a transitionalomain called “transition 2” dominated by the cluster of relatively

arger earthquakes in the HAP extending from km-250 to km-150;3) another transition zone called “transition 1”, from km-150 to

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also the extent of the IAM3 profile. P-wave velocities are in km/s and densities incontinental crust, LC: lower continental crust. The profile is divided in four zones

m-50, marked by the cluster of small magnitude events near thease of the crust running along San Vincent Canyon. Their align-ent suggests the presence of a fault plane sub-parallel to the base

f the crust; and finally (4) a continental domain characterised bymall magnitude earthquakes mostly confined within the crust.he presence of a local short-period seismic network since 1996ear Monchique contributed to the high density of recorded eventsear km-50 (Carrilho et al., 2004). Relatively larger events (ML > 4)ccur at the top of the crust and in the upper mantle beneath theontinental shelf. These events have known fault plane solutionshowing a dominant strike-slip faulting regime. Extension paral-el to the steepest topography due to lateral density variations canacilitate the strike-slip regime here, i.e. modify pure compressiono strike-slip (Andeweg, 2002).

. Rheology

.1. Deformation laws

To constrain the mechanical structure of the lithosphere in theulf of Cadiz we use the concept of yield strength envelope. Thisoncept is based on the assumption that at low confining pressuresnd temperatures fracturing is predominant, while at high temper-tures creep deformation mechanisms dominate in the lithosphere.or the brittle regime the critical stress difference at failure (theield strength) is given by the Coulomb frictional law, assumingaults of favourable orientation and negligible cohesion (Sibson,974),

1 − �3 = ˛ � g z(1 − �) (1)

here �1 − �3 is the maximum stress difference, ˛ is a constantelated to the fault type and frictional coefficient, � is the aver-ge density of rocks above depth z, and � is the pore fluid factor.n the absence of information regarding the pore fluid factor wessume hydrostatic conditions (� = 0.4). A friction coefficient of 0.75ommon for most rock types gives ˛ = 3.0 in compression (thrustaulting) and ˛ = 0.75 in extension (normal faulting).

In the ductile regime, deformation is assumed to follow a power-aw dislocation creep equation (Ranalli, 1995),

(ε)1/n (

A)

1 − �3 =B

expnRT

(2)

here ε is the strain rate (s−1), R is the universal ideal gas constant, Ts the absolute temperature, A is the creep activation enthalpy and Bnd n are material creep parameters. The yield strength envelope is

M.C. Neves, R.G.M. Neves / Journal of Geodynamics 47 (2009) 119–129 123

Fig. 3. Cross-section showing the vertical seismicity distribution along the modelled profile. The light grey region displays the crustal geometry, without sediments, after thes hin a 7E ferentd n zona of Cap

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ubtraction of the seawater-depth. The focal depths of the earthquakes that fall witvents with magnitude greater than 4 are displayed as larger grey circles. Four difominated by large earthquakes in the Horseshoe Abyssal Plain (see Fig. 1), transitiond the continental domain characterised by an essentially aseismic mantle inland

uilt assuming that at each depth the maximum stress differences given by the minimum of Eqs. (1) and (2). We further assume,s a first-order approximation, that the brittle–ductile transition isharp.

We also assume that the present-day bulk strain rate is 10−16 s−1.his is an average value consistent with measurements of present-ay shortening rates of 4–5 mm/year (e.g. Fernandes et al., 2003)veraged over an area of horizontal deformation of about 150 km,nd also with numerical modelling results in the Gulf of Cadiz thatnclude the contribution of both fault slip and inelastic deformationJiménez-Munt et al., 2001; Negredo et al., 2002).

The rheological structure along the profile was derived fromhe density and seismic velocity model (Fig. 2) following studieshat correlate seismic velocities measured in the laboratory and theominant lithology (e.g. Christensen and Mooney, 1995; Okaya etl., 1996). Although a unique correlation does not exist, a first-orderetrological classification derived from seismic P-wave velocitiesnd densities is listed in Table 1. Creep parameters for the severalheologies were taken from Afonso and Ranalli (2004).

The main lithologic units in the continent are quartzite inhe upper crust, felsic granulite in the middle crust, mafic gran-lite in the lower crust and peridotite in the mantle. We havedopted hydrated rheologies because these seem to be appropri-te in most continental environments affected by post-Paleozoicectono-thermal events (Afonso and Ranalli, 2004). For the oceanicrust we assumed the wet diabase deformation law.

.2. Temperature and strength

Estimates of surface heat flow in SW Iberia are scarce. In theouth Portuguese Zone the few measurements available rangeetween 60 and 70 mW/m2 (Fernandez et al., 1998), so we assumedcontinental surface heat flow of 64 mW/m2. Offshore the heat

ow is even less constrained with very few available heat floweasurements in the region of the Horseshoe Abyssal Plain (HAP)

ndicating an average value of 57 ± 15 mW/m2 (Fernandez et al.,998; Verzhbitsky and Zolotarev, 1989). The Fernandez et al. (2004)odelling yielded a value of about 40 mW/m2 in the HAP but this

alue is not consistent with the asymptotic geotherm for oceanicithosphere more than 120 Ma old. (Hayward et al. (1999) suggestedn age of ∼152 Ma for the oceanic lithosphere in the nearby Gor-inge Bank.)

Given the scarcity of surface heat flow measurements we recon-

tructed the temperature structure along the modelled profiley fixing five geotherms (GT1 to GT5) and linearly interpolatingetween then (Fig. 4a). GT4 (=GT5) is the asymptotic geothermor oceanic lithosphere 120 Ma old, computed according to thelate Cooling Model (mantle temperature = 1330 ◦C and plate thick-

atrNr

5 km wide window in either side of the profile are projected on the cross-section.zones are distinguished: a practically aseismic oceanic domain, transition zone 2e 1 dominated by small magnitude earthquakes clustering at the base of the crust,e St. Vincent (at km 0).

ess = 125 km). In the transition zones and in the continentalargin the geotherms were computed by solving the steady state

D heat conduction equation with radiogenic heat production forhree-layer lithospheric models of varying thickness and composi-ion. For GT3 at km-150 the three layers considered were sediments,rust (UC + MC average, see Fig. 2) and mantle. For GT2 and GT1 wesed the upper crust, the combined mid- and lower crust (MC + LC),nd mantle. Note that the sediments are included in the ther-al structure computation for their blanketing effect but they are

tripped off the numerical model (Section 5). The heat productionates and thermal conductivities for the several rock compositionsre listed in Table 1 and were taken from Afonso and Ranalli (2004).

The present-day strength envelopes for different sites alonghe profile are shown in Fig. 4a. We only show the envelopesor compression because this is the dominant regime in theulf of Cadiz. An extensional regime, which can exist locally,ould produce slightly deeper cut-off depths of brittle strength.

n the continent there is mechanical layering with ductile lay-rs in the crust, particularly at the bottom of the middlefelsic granulite) and lower (mafic granulite) crust. In con-rast, there are no ductile interleaved layers in the transitionnd oceanic zones. There, the upper crust strength is essen-ially in the brittle domain with a slight deepening of therittle–ductile transition oceanwards. However, most of thetrength resides in the mantle and there are no pronounced lat-ral strength variations. These are general features that remainnchanged when other sensible composition options are consid-red.

The rheological structure adopted to construct the strengthnvelope is not free from ambiguities (e.g. Ranalli, 2003; Burov,003). To address the effect of another temperature structure on thetrength-depth distribution we considered the hypothetical sce-ario shown in Fig. 4b. A cosine bell function was used to interpolateetween geotherms T1 and T2 (Fig. 4b), inspired on the work ofowie et al. (2005) who used a similar procedure. T1 is the con-inental geotherm computed as in Fig. 4a assuming a continentalurface heat flow of 64 mW/m2 and a surface temperature of 15 ◦C.2 is the geotherm for oceanic lithosphere 10 Ma old computedccording to the Plate Cooling Model. Taking into account that thege of the oceanic lithosphere at the end of the rifting in the westernart of the Gulf of Cadiz was 30 Ma, the thermal structure in Fig. 4bay perhaps resemble that of the active rifting stage. To isolate the

ffect of the temperature we assumed a present-day composition

nd strain rate. In this hypothetical scenario the cut-off depth ofhe brittle strength shallows oceanwards producing a significanteduction of strength in the transition and oceanic zones (Fig. 4b).evertheless, the strength in the transitional and oceanic zones still

esides mostly in the mantle.

124 M.C. Neves, R.G.M. Neves / Journal of Geodynamics 47 (2009) 119–129

Table 1Thermal and mechanical material parameters

Sediments UCC (wet quartzite) MCC (wet felsic granulite) LCC (wet mafic granulite) OC (wet diabase) TC (wet quartzite) Mantle (wet peridotite)

Q (�W m−3) 1.2 1.4 0.4 0.4 – 0.4 0.006K (W m−1 K−1) 2.3 2.5 2.1 2.1 – 2.1 3.0� (kg m−3) 2400 2740 2800 2950 2840 2800 3300A (MPa−n s−1) – 3.2 × 10−4 8.0 × 10−3 1.4 × 104 2.0 × 10−4 3.2 × 10−4 2.0 × 103

B (kJ mol−1) – 154 243 445 260 154 471n – 2.3 3.1 4.2 3.4 2.3 4.0E (Pa) – 0.7 × 1011 0.7 × 1011 0.7 × 1011 0.7 × 1011 0.7 × 1011 0.7 × 1011

� 0.25

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5

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5

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– 0.25 0.25

, volumetric heat production rate; K, thermal conductivity; �, density; A, E and n,analli (2004) and Fernandez et al. (2004).

. Flexural modelling

Vertical loads in isostatic equilibrium produce flexure and bend-ng when the lithosphere has non-zero strength. However, themportance of flexural isostasy to the overall deformation has noteen duly emphasized in previous studies of the Gulf of Cadiz. Toddress this problem we used an elasto-visco-plastic 2D finite ele-ent modelling approach and analysed the deformation in terms

f stress and strain distribution with depth.

.1. Numerical procedure

To perform the elasto-plastic simulations we used a modifiedersion of the FEVPLIB finite element program that was describedn detail by Bott (1997). This package incorporates elasto-plasticeformation with a finite yield strength using the viscoplasticethod and has been used to model stress and displacements

roduced by anomalous density in a variety of tectonic settingse.g. Bott, 1997; Zhang and Bott, 2000; Neves et al., 2004). The

ield strength is computed at each depth assuming brittle andower-law creep deformation depending on temperature. Theemperature structure is specified as input and the thermal evo-ution is not modelled. When the yield strength is exceeded,he excess stress is removed using a time stepping scheme. The

b

dau

ig. 4. Cross-section showing the calculated strength envelops in compression for selectesotherm interval. (A) Present-day strength and temperature distribution. The GT1 to GT5see text). (B) An hypothetical thermal scenario and the corresponding strength profiles us

ay represent an early stage of the Algarve’s margin rifting. A cosine bell function was usend T2 (present-day continental geotherm).

0.25 0.25 0.25

ial creep parameters; E, Young’s modulus; �, Poisson’s ratio. Data from Afonso and

ondition for plastic yielding obeys the Mohr–Coulomb crite-ion.

The finite element grid that represents the vertical section ofhe lithosphere is 600 km long and 140 km deep. Quadrilaterallements with eight nodes form a regular grid with maximum res-lution of 1 km × 0.5 km in the topmost 30 km. The plane strainypothesis, suitable to study flexure in two dimensions, is assumed.s boundary conditions we fix the SW end of the model in theorizontal direction, but let it be free to move in the vertical direc-ion. Other boundaries are free to move in both directions. Isostaticoundary conditions are applied at the surface to simulate isostaticestoring forces.

.2. Applied loads

The development of topography is the flexural isostatic responsef the model to the vertical loads. The vertical loads are separatedn two parts: (1) the weight of the sediments and water and (2) theravitational body forces due to the lateral density contrasts caused

y continental stretching.

The sediment and water load is applied instantaneously asirect nodal forces (Fig. 5a). The seawater and sediment layersre removed and all density interfaces lying underneath shiftedpwards, so that the top of the basement is initially at the sur-

d sites along the profile and the estimated temperature field contoured at a 400 ◦Cindicate the location of the geotherms used to estimate the temperature structureed to evaluate the effect of the temperature on the modelling results. This scenariod to interpolate the temperature between geotherm T1 (10 Ma oceanic lithosphere)

M.C. Neves, R.G.M. Neves / Journal of Geodynamics 47 (2009) 119–129 125

F eigha line cru re obts

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ig. 5. Loads applied to the numerical model. (A) The dashed line represents the wpplied at the surface as direct nodal forces. (B) Restored cross-section of the crystalpwards. (C) The density anomalies that generate internal gravitational body forces atructure shown above.

ace of the finite element model (Fig. 5b). The gravitational bodyorces are incorporated as density anomalies relative to a referenceensity–depth profile at the SW end of the model. The referenceensity–depth profile comprises two layers: normal oceanic crustkm thick and uniform mantle below, with densities of 2840 and300 kg/m3, respectively. The density anomalies are obtained byubtracting the reference depth–density profile from the densitytructure (Fig. 5c). Negative density anomalies generate buoyancyorces and uplift, while positive anomalies generate downwardorces and subsidence. While the sediment and water load produceoncave upward flexure, buoyancy of the continental crust rela-ive to the oceanic crust/mantle causes the uplift of the continental

argin relative to the ocean basin (Fig. 6).

.3. Modelling results

The loads in Fig. 5 have been applied to the two strength-depthistributions shown in Fig. 4. The resulting flexural response of the

ithosphere is now examined in terms of the patterns of differen-ial stress and strain energy. The relation of these with the observed

eismicity is discussed in the next section. The differential stress ishe difference between the horizontal and vertical stress in the ver-ical plane of the model. The conditions for failure can be describedsing this difference. According to Anderson’s theory of faultingnd following Sibson (1974) the faulting regimes can be classified

trfltb

ig. 6. The deflection of the top surface of the model in response to the topographic and iathymetry supported by flexure (grey solid line). The solid dark grey line is the actual ba

t of the sediment layer. The solid line is the sum of the water and sediment loadsust. The water and sediment layers were removed and all density interfaces shiftedained by subtracting the reference depth–density profile (see text) from the density

s normal or as thrust if the maximum compressive stress is ver-ical or horizontal, respectively. Since the plane strain formulationmplies that the out-of-plane stress is the intermediate stress, our

odels foresee a normal or thrust fault regime depending on theign and magnitude of the differential stress. We use the conven-ion that a negative differential stress corresponds to compressionthrust fault regime) and a positive differential stress to an exten-ion (normal fault regime). The density of the strain energy (strainnergy per unit of volume hereafter shortly called strain energy) ishe energy contained in a material as a consequence of its elasticeformation (Ranalli, 1995). The strain energy state, and its vari-tions with time, reflect the intensity of crustal activity and is anmportant index of earthquake potential.

The differential stress and strain energy due to flexure are shownn Fig. 7 for the actual and hypothetical scenarios. The pattern of dif-erential stress reflects the downward deflection of the lithospherend is typical of concave elastic bending: negative stresses occurt relatively shallow levels due to contraction and positive valuesccur at the bottom due to extension. Vertically, the largest stressesoncentrate at a depth of approximately 10–40 km in the hypo-

hetical scenario and at 10–50 km in the actual state. This depthange corresponds to the elastic core that is capable of supportingexural stresses on a long time scale. Laterally, the largest differen-ial stresses occur where the plate curvature reaches its maximum,etween km-200 and km-50. Moreover, there is no significant prop-

nternal gravitational loads (dotted black line) fits the wavelengths (>150 km) of thethymetry referenced to the depth of the ocean basin at the SW end of the profile.

126 M.C. Neves, R.G.M. Neves / Journal of G

Fig. 7. Close up of the modelling results in the ocean–continent transition zone andatcp

absttdl

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6

f

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ture. These events may be due to other local processes and/or maybe related to the 3D nature of the deformation. For instance, the lat-eral density variations associated with the changing trend of steeptopographic slopes, from nearly EW along the Algarve coast to NS

djacent region. Top two panels: stress difference distribution predicted for hypo-hetical (Fig. 4b) and the present-day (Fig. 4a) thermal states. Bottom two panels:orresponding density of strain energy. The focal depths of the earthquakes are alsolotted for the actual state.

gation of stresses seawards or landwards, that is, the effect ofending is rather localized in the transition zone. The compres-ive stresses focus just below the base of the crust regardless of theemperature structure, although they spread over a wider area inhe actual state. In contrast, the trend of the region of extension,ipping to the NE in the hypothetical scenario, is controlled by the

ateral temperature gradient.The pattern of strain energy is very similar to that of the dif-

erential stress being distributed into approximately two mainreas. Comparing the two scenarios the upper area, adjacent to theoho, remains nearly stationary, while the lower area is deduced

o deepen and rotate towards the horizontal in the actual state. Theelease of the strain energy in the form of earthquakes is more likelyo occur in regions where the strain energy accumulates. The strainnergy accumulates in the upper mantle and not in the crust. Thus,he Moho limits the upper strain accumulation region. This strongependence of strain energy on composition is even more evident

n Fig. 8. The strain pattern produced by a uniform crust model (top)s quite different from that produced by a more realistic model thatncludes compositional layering in the crust (bottom). This resulthows that a layered rheology seems to be more at its place in thisituation.

. Discussion

.1. Flexure and earthquakes

The time scale of seismic energy release is certainly differentrom the time scale of elastic plate flexure. So, it is extraordinary to

Fpci

eodynamics 47 (2009) 119–129

bserve a correlation between estimates of elastic plate thicknessnd estimates of seismogenic layer thickness. Indeed, in the Pacificcean the earthquakes show a distribution and a focal mechanismattern that seems to be directly connected to the up-warping ofhe oceanic lithosphere seaward deep-sea trenchs (e.g. Watts, 2001;assara et al., 2007). In the continents this relation is harder to provend has been strongly debated (e.g. Maggi et al., 2000; Watts andurov, 2003; Handy and Brun, 2004). One of the reasons for such dif-culty is that the continents have been subjected to more complexvolution histories than the oceans. In addition, the lithosphere’smemory” justifies the existence of earthquakes which are relatedith the sequence of geological processes and not with the actualeformation state (e.g. Muller et al., 1996).

It is obvious that flexure is not the only source of stress in theulf of Cadiz. Geological, geodetic and focal mechanism data show

hat the region is dominated by NW–SE compression associatedith the Africa-Eurasia convergence. Moreover, inherited mechani-

al weaknesses are certainly a key factor in the distribution of stress.t is therefore expected that the earthquakes are releasing energyf deformation associated with the plate convergence, focussed atnherited mechanical weaknesses. So the question is whether or notexure contributes to the actual state of stress. In our opinion Fig. 7hows that there is a clear correlation between strain energy asso-iated with flexure and the earthquake distribution. Furthermore,t shows that there is a relation between seismicity and mechanicaliscontinuities connecting zones of contrasting density and rhe-logy. This relation is particularly visible in the upper mantle justelow the Moho between km-110 and km-70. Another correlationetween the modelling results and the seismicity is the apparentipping trend to the NE of the distributions along the transitionone. This trend is not only suggested by the cluster of small mag-itude events below the Moho but also by the larger magnitudearthquakes with known focal mechanism solutions which becomeeeper towards the NE (e.g. between km-200 and km-100). Thisuggests that the strain energy induced by flexure in the past mayave created preferential regions of weakness, which are now beingeactivated in the actual state of compression.

It is evident that there are other clusters of events, particularly inhe continental region, which do not show any correlation with flex-

ig. 8. Dependence of the strain energy distribution on composition. Top: the com-osition of the crust is uniform (wet quartzite). Bottom: the crust has a layeredomposition (as in Fig. 2 and Table 1). The present-day thermal structure is assumedn both cases. The strain energy (U) scale is the same as in Fig. 7.

M.C. Neves, R.G.M. Neves / Journal of Geodynamics 47 (2009) 119–129 127

F transid 150 an∼

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ig. 9. Estimates of the integrated strength (solid line) along the ocean–continentepth distribution of the modelled stress-difference in the actual state (track at km-30 km depth the stress difference is compressive and below is tensile.

orth of the Gorringe Bank, can lead to extensional and strike-slipeformation under predominantly pure compressional deforma-ion (Andeweg, 2002). These hypotheses need further investigationsing a full 3D modelling approach that is currently under way. 3Dodelling will also allow us to explore the relation between the

ocal mechanisms and the strain/stress-depth distribution.

.2. The strength of the ocean–continent transition

It has long been recognised that ocean–continent transitionones are often weak relative to normal oceanic and continentalithosphere. This is expressed by low values of elastic plate thick-ess in extended continental lithosphere, reflecting a long-termechanical weakness (e.g. Watts and Stewart, 1998). The reasons

ehind such a weak behaviour on long-time scales are still unclear.hen the beta stretching factor is greater than 3, models of exten-

ion at the West Iberia margin predict embrittlement of the wholerust with development of crustal penetrating faults which canct as fluid conduits, allowing serpentinization of the upper man-le peridotites (Pérez-Gussinyé and Reston, 2001). The coefficientf friction of serpentinite (∼0.3) is considerably lower than thatredicted by Byerlee’s law (Escartín et al., 1997). Moreover, ser-entinites may favour the confinement of fluids within fault zones,ontributing to an increase in the pore fluid factor and to a strengtheduction of the whole crust. This would partially explain theoncentration of deformation and seismicity in ocean–continentransition zones subjected to large present-day tectonic stresses.

In this study we have not incorporated any weakness in the tran-ition zone, since we have used a constant coefficient of frictionf 0.75 to build the brittle part of the strength envelope. Con-equently, the integrated strength is predicted to increase gentlylong the profile, from 3.2 × 1013 N/m in the continent (km-50) to.4 × 1013 N/m in the ocean (km-250) (Fig. 9). The mechanical thick-ess of the lithosphere (depth above which the strength > 10 MPa)

s 48 and 45 km in the oceanic and transition zones, respectively.Only in the case of a single-layer elastic rheology, high flexu-

al rigidity and small curvatures will the elastic thickness approachhe mechanical thickness (Watts and Burov, 2003). Otherwise, the

echanical thickness provides an upper bound limit for the elas-ic thickness. Thus, in the oceanic lithosphere of the Gorringe Bank,ayward et al. (1999) found that the gravity anomaly is explained bydiscontinuous (broken) elastic plate model 35 km thick at the timef loading (the lithosphere would have been 140 Ma old when it was

oaded 12 Ma ago). Flexural modelling results in the Western Iberia

argin also indicate a present-day elastic layer thickness in excessf 35 km (T. Cunha, personal communication). Yielding related tohe Africa-Eurasia convergence and the presence of mechanicaleaknesses not considered in this study may therefore explain the

•

tion, based on the strength envelopes in compression shown at selected sites. Thed km-50) is shown in dark grey for comparison with the strength envelopes. Above

iscrepancy between the elastic thickness and mechanical thick-ess estimates in this region.

According to our results the flexural bending stresses are notnough to cause yielding and reduce the effective elastic thickness.e compare the stress difference in the actual state (Fig. 7) and the

trength envelope at km-150 and km-50 in Fig. 9. The maximumompressive stress difference generated by flexure, which occurs athe base of the crust at km-150, attains 65% of the strength in com-ression at the same depth (∼10 km). Unless there is a reductionf the brittle strength in the ocean–continent transition, flexurelone is not sufficient to produce brittle failure and earthquakes inhe crust and upper mantle. However, its contribution to the overalltress in the Gulf of Cadiz cannot be disregarded.

. Conclusions

In the Gulf of Cadiz the density contrast between oceanicnd continental crust is a source of vertical loading at thecean–continent transition. Vertical loads in isostatic equilibriumroduce flexure when the lithosphere has non-zero strength. Weodelled the flexure on a vertical section of the lithosphere approx-

mately perpendicular to the Africa-Eurasia convergence. Althoughhis approach does not incorporate out-of-plane displacement of

aterial, it allowed us to analyse the contribution of the flexure sep-rately from other sources of stress such as the dominant NW–SEompression. Our main objective was to explore how the bend-ng stresses were related to the observed deformation, especiallys regards the actual release of strain energy in the form of earth-uakes. Since the strength is an input of the modelling, we have alsolaced constraints on the mechanical structure of the lithosphere.he main conclusions of our study are thus the following:

The flexural stresses are focussed in the ocean–continent transi-tion, within a ∼150 km wide zone between km-250 and km-50of the modelled profile.The focussing of bending stresses on the transition zone is pre-dicted for different thermal scenarios so this result is relativelyindependent of temperature.The bending stresses are mainly supported by the upper man-tle and show a bipolar distribution. The compressive stressesconcentrate just below the Moho (at ∼10 km depth in theocean–continent transition). The tensile stresses underneath (at∼40 km depth) show a dipping trend that is controlled by the

lateral temperature gradient.The strain energy due to flexure also resides in the upper man-tle. The largest accumulation of strain energy occurs below thestretched continental lithosphere underneath the Moho. Nearkm-100 the strain energy concentration coincides with an impor-

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28 M.C. Neves, R.G.M. Neves / Journ

tant cluster of earthquakes located between the S. Vincent faultand the Horseshoe fault.The observed correlation between the strain energy and theearthquake distribution shows that lithospheric flexure exerts asignificant control on the seismicity pattern.The compositional layering in the crust plays an important rolein the focussing of the strain energy along the crust/mantle inter-face.Flexural stresses alone are not enough to cause rupture or yield-ing in the Gulf of Cadiz. However, like plate boundary forces andinherited mechanical weaknesses, they need to be taken intoaccount in the seismic hazard assessment.

cknowledgements

We would like to thank Luís Matias, Mourad Bezzeghoud, Fer-ando Carrilho, Tiago Cunha and Filipe Rosas for useful discussions.e also acknowledge work on free software GMT (Wessel and

mith, 1998) and MIRONE (Luis, 2007). This work is a contributiono the ALMOND project PTDC/CTE-GIN/71862/2006.

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