3D mechanical modeling of the GPS velocity ¢eldalong the North Anatolian fault

Ann-Sophie Provost a;�, Jean Che¤ry a, Riad Hassani b

a Laboratoire Dynamique de la Lithosphe're, Universite¤ Montpellier 2, cc060, Place E. Bataillon, 34095 Montpellier Cedex 5, Franceb Laboratoire d’Instrumentation Ge¤ophysique, Universite¤ de Savoie, Le Chablais, 73376 Le Bourget-du-lac, France

Received 14 November 2002; received in revised form 17 February 2003; accepted 20 February 2003

Abstract

The North Anatolian fault (NAF) extends over 1500 km in a complex tectonic setting. In this region of the easternMediterranean, collision of the Arabian, African and Eurasian plates resulted in creation of mountain ranges (i.e.Zagros, Caucasus) and the westward extrusion of the Anatolian block. In this study we investigate the effects ofcrustal rheology on the long-term displacement rate along the NAF. Heat flow and geodetic data are used toconstrain our mechanical model, built with the three-dimensional finite element code ADELI. The fault motion occurson a material discontinuity of the model which is controlled by a Coulomb-type friction. The rheology of thelithosphere is composed of a frictional upper crust and a viscoelastic lower crust. The lithosphere is supported by ahydrostatic pressure at its base (representing the asthenospheric mantle). We model the long-term deformation of thesurroundings of the NAF by adjusting the effective fault friction and also the geometry of the surface fault trace. Todo so, we used a frictional range of 0.0^0.2 for the fault, and a viscosity varying between 1019 and 1021 Pa s. One ofthe most striking results of our rheological tests is that the upper part of the fault is locked if the friction exceeds 0.2.By comparing our results with geodetic measurements [McClusky et al., J. Geophys. Res. B 105 (2000) 5695^5719]and tectonic observations, we have defined a realistic model in which the displacement rate on the NAF reaches V17mm/yr for a viscosity of 1019 Pa s and a fault friction of 0.05. This strongly suggests that the NAF is a weak fault likethe San Andreas fault in California. Adding topography with its corresponding crustal root does not induce gravityflow of Anatolia. Rather, it has the counter-intuitive effect of decreasing the westward Anatolian escape. We find apoor agreement between our calculated velocity field and what is observed with GPS in the Marmara and the Aegeanregions. We suspect that the simple lithosphere model is responsible for this discrepancy. Taking into account theweaknesses of these deforming regions should allow us to build a more realistic model that would match groundobservations more appropriately. On the other hand, our results fit well GPS measurements in central Anatolia,setting the basis of modeling crustal strain in Turkey.B 2003 Elsevier Science B.V. All rights reserved.

Keywords: North Anatolian fault; mechanical modeling; ¢nite element; fault friction; lithospheric rheology; GPS; Turkey

0012-821X / 03 / $ ^ see front matter B 2003 Elsevier Science B.V. All rights reserved.doi:10.1016/S0012-821X(03)00099-2

* Corresponding author. Tel. : +33-4-67-14-36-85; Fax: +33-4-67-52-39-08.E-mail addresses: provost@dstu.univ-montp2.fr (A.-S. Provost), jean@dstu.univ-montp2.fr (J. Che¤ry), riad.hassani@univ-savoie.fr

(R. Hassani).

EPSL 6591 2-4-03

Earth and Planetary Science Letters 209 (2003) 361^377

www.elsevier.com/locate/epsl

1. Introduction

The North Anatolian fault (NAF) system delin-eates the northern boundary of the Anatolianplate and is characterized by a right-lateral strike-slip motion [2,3]. In this complex tectonic envi-ronment the collision of the Arabian, Africanand Eurasian plates leads to a compressive regimeto the east of the Anatolian block (creation ofmountain ranges like the Zagros and the Cauca-sus), a right-lateral strike-slip fault zone to thenorth (which accommodates the westward escapeof the Anatolian block [2,4]), and a subductionzone, associated with back arc spreading in theAegean sea [2,3] to the southwestern boundaryof the Anatolian block (Fig. 1). Due to the intensetectonic activity of this region, the NAF systemhas been the locus of large seismic events in past

centuries, which presents a major risk for the pop-ulation. Improving our knowledge of mechanicalproperties of the crust in which they take placewill contribute to a better understanding of theoverall tectonics of this region and the occurrenceof these earthquakes. In this study we investigatethe interactions between rheological properties ofthe Anatolian crust and the displacement rate onthe NAF, constrained by heat £ow and geodeticdata, and using a three-dimensional (3D) mechan-ical model.

1.1. Velocity ¢eld in Anatolia

The NAF, as it is known today, extends over1500 km from the Karliova triple junction (KTJ),on the east side of the Anatolian block, to main-land Greece [5] (Fig. 1). The fault mainly consists

Fig. 1. Simpli¢ed tectonic map of the studied area, from the Aegean Sea to the Karliova triple junction (KTJ). The black arrowsshow the relative plate velocity’s directions, and the thick black line shows the location of the right-lateral strike-slip NAF zone.The dashed-contour rectangle shows the boundaries of our model presented in Fig. 2. Abbreviations are: (NAF) North Anato-lian fault; (K) Karliova triple junction; (Er) Erzincan; (Mu) Mudurnu Valley; (IzF) Izmit fault; (GF) Ganos fault. For this mapwe used the UTM projection with zone 36.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377362

of one strand from east to west, but when reach-ing the Mudurnu Valley it splits into threebranches traversing the Sea of Marmara and theAegean. Recent studies have focused on the faultgeometry and tectonic evolution of the sea ofMarmara region. In their analysis of the basinlocated between the Izmit and Ganos faults, Ar-mijo et al. [6] have revealed no evidence fora continuous purely strike-slip fault, but rathersuggest the presence of a tensional tectonic re-gime (pull-apart basin). However, this interpreta-tion is not unique, and Le Pichon et al. [7]have proposed that a single, dextral strike-slipfault system cuts the entire trough. West of Mar-mara, the northern part of the fault system isthe most active and accommodates most of theslip.

Major historical earthquakes occurred on thefault system with a westward migrating pattern,from the KTJ to the region of Marmara, in series,every 200^400 yr [8,9]. The latest one started in1939, in eastern Turkey, with the Mw 7.9 Erzincanearthquake, rupturing the crust over 360 km andwith a maximum right-lateral o¡set of 7.5 m. Itthen progressed along the fault with 10 Ms 6events and reached Mudurnu Valley with the re-cent 1999, Mw 7.4; 7.2 Izmit and Du«zce earth-quakes [8,10].

As a result of the accumulation of this seismicactivity, the NAF system accommodates the dis-placement of the Anatolian plate relative to thestable Eurasian plate, at a geological rate of 16^25mm/yr [4,5,11,12], compatible with the value of24 S 1 mm/yr obtained by GPS [1]. However, thetotal displacement on the fault system is not ashomogeneous and is the subject of present con-troversies. According to o¡sets of geological fea-tures and late Miocene sediments [5] it is about 40km near Erzincan in the east and about 25 kmnear Mudurnu on the west side, giving slip ratesof 10 and 5 mm/yr, respectively. To constrain ourmodel we used global velocities from GPS as thegoal is not the resolve the controversies aboutlocal slip rate determination.

1.2. Heat £ow

Because rock viscosity is chie£y controlled by

temperature [13], knowing the heat £ow densityvalues for Anatolia’s lithosphere is of great im-portance to constrain its rheological propertiesin the construction of a thermo-mechanical mod-el. As previously mentioned, the northwesternpart of Turkey marks the transition from purelystrike-slip motion on the NAF to a transtensionalregime in the Aegean. This region, the most seis-mically active part of our study zone, is associatedwith numerous hot springs for which the totalthermal energy output adds up to 60^130mW/m2 [14]. This geothermal activity forms a lo-cal anomaly compared to the global heat £ow ofthe Anatolian block. Tezcan [15] found that theheat £ow density distribution of Turkey rangesfrom 40 to 140 mW/m2. The highest values corre-spond to the very high geothermal activity in thenorthwest, other somewhat high values seem to belinked to metamorphic massifs and large graniticintrusions. On the other hand, no heat £owanomalies were detected near the NAF system.According to heat £ow estimates deduced fromsilica temperature measurements [16] the crustalcontribution of the heat £ow density is about50^60 mW/m2 in the regions south of Marmara.To our knowledge, no direct heat £ow measure-ments (i.e. borehole temperature data) have beenpublished on central and eastern Anatolia. In thefollowing, we consider the lithosphere as relativelyhot and homogeneous. The corresponding rheo-logical model consists of a frictional upper crustdown to 15 km depth and of a ductile lower crustbetween 15 km and the Moho depth. We considerhere that the uppermost mantle has a negligiblestrength compared to the crust.

2. Model

2.1. Previous work

Mechanical modeling is a key tool to inferrheological properties of the lithosphere in vari-ous regions of the globe. It has been extensivelyused either in two dimensions (e.g. [17^21]) orthree dimensions (e.g. [22^24]). Furthermore,some researchers have focused on the complexkinematics of the eastern Mediterranean and de-

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 363

veloped ¢nite element models to constrain rheo-logical parameters of the crust in this area [25^27]. Kasapoglu and Toksoz [28] built a two-di-mensional, plane stress, ¢nite element scheme tomodel the interaction between the Arabian, Afri-can, Anatolian and Eurasian plates. They foundthat the deformation observed in the ¢eld cannotbe explained by considering only a push from theArabian and the African plates, but a supplemen-tary driving force (gravitational push or shearforces) was necessary to produce observed move-ment along major faults that were modeled asrelatively weak zones having a friction coe⁄cientof 0.4^0.5. In another ¢nite element approach,Cianetti et al. [29] found that a northward motionof Arabia at 30 mm/yr and a suction force of 40MPa at the Hellenic trench were necessary in or-der to explain the velocity and stress ¢elds ob-served. They also noticed that lateral variationof crustal rheology was necessary to reproducethe partitioning of the deformation from central

Anatolia to central Aegean [30]. More recently,Jimenez-Munt et al. [21] have studied deformationin the whole Mediterranean and suggest that theAfrican^Arabian vs. Eurasian collision and thesubduction in the Aegean Sea are the main tec-tonic factors responsible for the deformationpresent in these regions.

Recently, extensive geodetic studies of Aegeanand Anatolia have provided a precise picture ofthe present-day, interseismic, continental defor-mation [1,31]. Even if these studies do not capturethe strain localization along the fault, the inter-seismic far ¢eld velocity is generally thought asrepresentative of the long-term fault motion [32].Therefore, there is a strong interest to comparethe steady-state velocity ¢eld, given by 3D numer-ical modeling, to this dense array of velocity mea-surements. By doing such a comparison, weshould be able to ¢nd out which rheology andfault geometry corresponds most closely to theobserved velocity ¢eld.

Fig. 2. Geometry of the model superimposed on the geographical map. The model extends over 1800 km and the NAF is ap-proximated by a small circle. The dashed line represents the location of the north branch geometry used further in the experi-ment. The velocity boundary conditions are shown by black arrows along the faces of the model. Only the northern face is ¢xed,corresponding to the stable Eurasian plate. The white arrows represent the reference ground velocities deduced from GPS mea-surements [1], the names of the corresponding stations are plotted next to them. Abbreviations are: (P) Peloponnesus; (Cr) Crete;(Cy) Cyprus.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377364

2.2. Geometry and boundary conditions

The geometry and boundary conditions of ourmodel have been superimposed on the topo-graphic map of our study zone for a better visual-ization (Fig. 2). Our model is 1800 km long and900 km wide (along the X and Y axes, respec-tively). It extends from the Peloponnesus (west)to the lesser Caucasus (east), and from the BlackSea (north) to the Island of Crete (south). Wehave used simple geometries for the NAF basedon di¡erent models [6,7,10]. The NAF is ¢rst rep-resented by a small circle extending from the KTJto mainland Greece. Our crust is 30 km thick(with bc = 2800 kg/m3) and its base is submittedto hydrostatic forces in order to simulate the in-teraction with a £uid asthenosphere (with ba =3300 kg/m3). We do not account for Earth spher-icity and our model corresponds to a £at litho-sphere. Our model is submitted to gravity forcesand in a ¢rst step no initial topography is as-sumed. Also we did not include in this modelthe East Anatolian fault as our main goal is tostudy the strain localization along the NAF andits distribution in the fault’s surroundings.

At the boundary of our model we have appliedvelocity gradients corresponding to horizontal ve-locities compiled from GPS observations [1]. Thusto simulate the plate tectonics of the area we haveused horizontal velocities of (Vx, Vy) = (314.0,12.5) mm/yr on the southeast face, correspondingto the impact of the Arabian push together with

the fault slip rate of the East Anatolian fault inEastern Anatolia. Velocities of (Vx, Vy) = (315.0,325.0) mm/yr on the southwest face correspondto the pull of the Aegean subduction zone. Thenorthern boundary is ¢xed (Eurasian plate), andthe velocities on faces connecting these vary be-tween these values (see Fig. 2). On all of the facesthe vertical velocity Vz is free.

In order to compare our results with groundobservations we have used 21 reference pointscorresponding to GPS stations from McCluskyet al. [1]. They are designated by their four-letternames and their corresponding velocity vectorsare shown next to them.

2.3. Numerical formulation and constitutive laws

The crustal rheology is modeled according topressure and temperature variations within thecrust (see Fig. 3). At low P^T, the frictional crus-tal behavior involves a plastic yield stress that ismainly pressure-dependent. Therefore, we modelthe upper crust with a Drucker^Prager model [33].We use a friction angle of 15‡ consistent with ahigh internal friction (0.6) and a hydrostatic porepressure for the upper crust [23]. Because the fric-tional strain may be considered as non-dilatantat the modeled scale, we set the dilatancy angleto zero. At high P^T, a viscoelastic behavior isassumed and a linear Maxwell model is used.Although the rock viscosity is strongly tempera-ture-dependent, we choose to use a constant vis-cosity for the lower crust in order to simplify theforthcoming discussion. As previously mentioned,we set the rheological change between the friction-al upper crust and the viscous lower crust at 15 kmdepth, which is consistent with the earthquakefocal depth usually observed in the Anatolian re-gion. The NAF is represented by a small circle atthe surface of the model, where the e¡ective faultfriction W is modeled using Signorini and Cou-lomb laws ([18] and references therein). Therefore,the shear stress d is limited by:

MdM ¼ W effc n

where cn is the stress normal to the fault. Contactforces are computed between all nodes belongingto the discontinuity of the NAF between the sur-

Fig. 3. Crustal rheology used in the model. See text for de-tails.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 365

face and the Moho. These forces are added to theinternal and external forces in order to computethe acceleration of the mesh nodes. Velocities anddisplacements are computed using the dynamicrelaxation method [18,34]. A mesh resolution of20 000 elements has been used.

3. Results

3.1. E¡ect of friction and viscosity

In order to de¢ne a realistic rheological modelwe ¢rst tested the in£uence of viscosity and faultfriction on the long-term velocity. Viscosity valuesbetween 1019 and 1021 Pa s were tested for thelower crust. To simulate a lower crust with noviscosity, we also ran numerical models wherethe lower crust is not involved by limiting themesh at 15 km depth. Although this end-membercase is not realistic, it allows us to evaluate theimportance of the upper crustal forces and of theNAF fault friction alone. These experiments arereferred to as zero-viscosity cases. Because of thelack of principal stress inversion along the NAF,it is not possible to precisely bound the e¡ectivefriction of this fault as has been done on the SanAndreas fault [35]. Therefore, we tested valuesbetween 0.0 (very weak fault) and 0.6 (strongfault). Fig. 4 shows the east component of thevelocity di¡erence between the IKAN and TEBA

points (Fig. 2). The GPS value is 17.5 mm/yr,presumably due to the localized motion on theNAF. For lower crustal viscosities between 1019

and 1021 Pa s, the friction leading to the observeddi¡erential velocity ranges between 0.05 and 0.1.By contrast, a friction coe⁄cient larger than 0.2leads to velocity values lower than 6 mm/yr. Anorth^south velocity pro¢le across the fault(Fig. 4b) clearly shows that the non-zero velocitydi¡erence between these two stations is not due toslip on the fault itself but rather to deformation ofthe crust alone. Therefore, it is possible to con-clude that the fault slip rate falls to zero if thee¡ective fault friction is larger than 0.2. The com-parison with the case with zero viscosity showsthat the rapid decrease of the slip rate with in-creasing friction is largely enhanced by the cou-pling of the lower crust. For example, the velocitydi¡erence is 17.5 mm/yr for the zero-viscosity casewith W= 0.2, and falls to 4^6 mm/yr for othercases. We explain in Section 4 why none of thetested cases reaches the velocity of 24 mm/yr pro-posed by McClusky as an upper bound for theNAF velocity (see Section 4.1).

Because the coupling between the frictional partof the model and the viscous part may be depen-dent on the mesh size, we tested the discretizationof our model and used 12 layers of elements in-stead of six for our 30 km thick crust. The resultsobtained for this case with a viscosity of 1019 Pa sare displayed in Fig. 4 with open diamonds. They

Table 1Relative east^west velocities on the NAF at x = 800 km, Vnaf = (VTEBA3VIKAN) = 17.50 mm/yr with McClusky’s data

Case # Model (viscosity, fault friction) Vnaf RMS Mean NvVN Max NvVN Name of station(mm/yr) (mm/yr) (mm/yr) (mm/yr)

1 no topo (1019, 0.05) 19.80 5.06 4.28 11.78 NSKR2 no topo (1019, 0.1) 15.74 5.39 4.70 10.48 NSKR3 no topo (1019, 0.15) 8.91 6.69 6.08 11.52 HIOS4 no topo (1019, 0.2) 3.05 7.93 7.31 13.38 GIRE5 no topo (1020, 0.05) 17.44 5.27 4.52 10.81 NSKR6 no topo (1021, 0.05) 18.25 5.26 4.45 11.85 NSKR7 no topo, no viscosity 22.33 5.31 4.22 14.35 NSKR8 topo (1019, 0.05) 16.03 5.20 4.38 8.46 ASKT9 #8 with north branch 13.47 4.71 4.30 7.54 GIRE10 #8 real-fault-trace 12.09 5.05 4.66 8.13 ASKT11 #9 northwestern BC 13.96 4.54 4.14 7.44 BODR

RMS and mean NvVN between McClusky’s velocity vectors and the ones estimated by our model (for 21 reference points shownin Fig. 2). The maximum value of NvVN is also mentioned along with the name of the corresponding station (see Fig. 2).

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377366

slightly di¡er from the ones obtained with the six-layer case, with a positive o¡set of 2^4 mm/yr.However, they lead to the same conclusion aboutthe e¡ect of friction on the velocity.

According to these rheological tests, it is clearthat there is a trade-o¡ between friction and vis-cosity and that di¡erent couples are leading to thesame di¡erential velocity. Because a viscosity of1019 Pa s for the lower crust has often been pro-posed as appropriate in order to model the seis-mic cycle (e.g. [36]), we use this value for ourfurther experiments. Therefore the preferred fric-tion coe⁄cient should be 0.05 or 0.1. In order toevaluate the friction e¡ect at the scale of Anatolia,we performed a direct comparison of our results

with horizontal velocities deduced from GPS mea-surements [1]. We show these map views for twocases, fault friction 0.05 and 0.2 (Fig. 5a,b, respec-tively). Velocity vectors (black for our model andwhite for McClusky’s GPS data) and strain ratecontours are shown for both cases. A friction of0.05 (case 1) leads to deformation concentrated inthe Lesser Caucasus to the east and the Aegeanregion to the west, while the Anatolia does notdeform. Also, the velocities of points south ofthe fault trace are in good agreement with theGPS data. On the other hand, relatively pooragreement occurs in the Aegean (point NSKR).O¡set estimations between the data and the modelare summarized in Table 1. A friction of 0.2 (case4) leads to largely underestimated velocities for

Fig. 4. (a) East component of the velocity di¡erence betweenIKAN and TEBA points obtained for di¡erent viscositiesand fault friction. Two reference lines were added, one atV =17.5 mm/yr deduced from our reference GPS measure-ment shown in Fig. 2 [1], and one at V =24 mm/yr represent-ing the upper bound velocity across the fault [1]. (b) North^south velocity pro¢le across the fault at x =800 km for case4 with W= 0.2.

Fig. 5. Map views of the distribution of strain rate as well asvelocity vectors (black arrows) deduced from the model, fortwo tests: fault friction of 0.05 (panel a) and 0.02 (panel b).Here the viscosity is 1019 Pa s. Strain rate is expressed as thequadratic invariant of the strain rate tensor. The white ar-rows are velocity vectors from the GPS reference pointsshown in Fig. 2 [1]. See text for details.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 367

most Anatolian points (Fig. 5b), together with thelow slip rate of the NAF (see Table 1). Moreover,the deformation is distributed evenly throughoutthe model and central Anatolia signi¢cantly de-forms at a rate of 0.5U10315 s31. These remarkscon¢rm the statement, made in the last para-graph, that for a friction of 0.2 or more, ourmodel cannot ¢t ¢eld observations. A preliminaryconclusion is that NAF slips for only very smallvalues of fault friction, similar to those proposedfor the San Andreas fault in central California[35,37].

3.2. E¡ect of topography

A signi¢cant part of the crustal stress maycome from di¡erential topography [38]. Becauseit can a¡ect the deformation ¢eld, we performeda numerical experiment including topography (fora viscosity of 1019 Pa s and a friction of 0.05, case8). Our model contains only the long-wavelengthpart of the topography as shown in Fig. 6a. Acrustal root which isostatically compensates thetopography is assumed according to crustal andmantle density. Therefore the minimum crustalthickness is in the Aegean and Black seas (24km) and the maximum appears in the Lesser Cau-casus (44 km). In order to check the e¡ect of thetopography separately from the e¡ect of lateral-velocity boundary conditions, we ¢rst ran a modelwhere all velocity boundary conditions were set tozero, (i.e. no displacement occurs on the modelboundaries). The di¡erential topography inducesa transient gravitational £ow, which progressivelydecreases and ¢nally ceases. The surface velocitygoes to zero. The corresponding displacement¢eld has an orientation perpendicular to the topo-graphic contours (Fig. 6a). The maximum ampli-tude of this gravitational motion is V200 m,which occurs between the eastern Anatolian pla-teau and the Black Sea where the di¡erential to-pography is the highest. We then ran a modelincluding the lateral boundary conditions as incase 1, but with topography (case 8), and we com-pared the results with the ones previously ob-tained in case 1. For this case, and the followingones, a short transient phase due to topographicloading is followed by a long enough stationary

phase so that the contribution of the transientphase to total displacement is very small. Fig.6b displays the ¢nal velocity for the two experi-ments. The added topography has little e¡ect onthe velocity pattern. The overall e¡ect is to de-crease the velocity of 2^4 mm/yr on the sites southof the NAF (GIRE, TEBA, KKIR, KMAH). Bycontrast, the ASKT velocity (northern Greece)increases by 4 mm/yr. The velocity changes canbe more precisely evaluated on three pro¢les (Fig.

Fig. 6. Comparison of cases 1 and 8, no topography vs. to-pography. (a) Displacement vectors (m) due to the sole e¡ectof topography (km) on our model. (b) Velocity vectors forcase 1, without topography (white arrows) and case 8, withtopography (black arrows) superimposed on the deformationdistribution calculated for case 8. Small black circles show thereference points used to make the pro¢le in panel c. (c) Pro¢leacross the fault, at x =800 km, of the long-term velocity re-sulting from the two cases mentioned above, with (open dia-monds) and without (plusses) topography. Here we used afault friction of 0.05 and a viscosity of 1019 Pa s. The refer-ence line [1] is highlighted by closed circles.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377368

6c); one for the case without topography (case 1,crosses), one with topography (case 8, open dia-monds) and one estimated from McClusky’s ve-locity vectors (closed circles) [1]. Our pro¢les werecomputed starting at (x,y) = (800,200) km (seeFig. 2) over 600 km northward and correspondto the points AFYO, DMIR, GIRE, IKAN, andthe points shown as solid circles in Fig. 6b. Thetwo solutions given by cases 1 and 8 underesti-mate the velocity of Anatolia by about 1^5 mm/yr. A di¡erence between the two cases (1 and 8)only occurs south of the fault. The velocitychange between GIRE and IKAN is 19.8 mm/yrfor the case without topography, and 16 mm/yrfor the case with topography (see Table 1). Be-cause the velocity ¢elds of the cases 1 and 8 areroughly similar, and because the meshes related tothese two cases have di¡erent discretizations, onemay ask if the di¡erence has a numerical origin.In an attempt to answer this question, we com-puted the solutions of 12-layer models, for cases 1and 8. Because a trend similar to the one observedfor the six-layer models is observed, we concludethat the reduced motion observed in case 8 is nota numerical artifact.

Therefore, our modeling predicts a decreasingvelocity of northern Anatolia when gravitationalforces of the topography are included. At ¢rstglance, this behavior seems puzzling becausebody forces induce a northwest directed motionassociated with the topographic gradient (Fig.6a). This e¡ect should therefore increase the west-ward Anatolian velocity. However, we recall thatthe long-term velocity due to the gravitationale¡ect alone goes to zero. This means that thegenerated di¡erential stresses do not overcomethe strength of the Anatolian lithosphere. Thus,the simple idea that topography induces litho-spheric £ow, as has been proposed by numerousauthors [39,40], is not supported by our modeling.Nevertheless, it still remains puzzling that whentopographic forces are included, the escape ofthe Anatolian plateau is slowed down. We thinkthat this behavior is directly linked to the Cou-lomb law used to control the NAF shear stress.Indeed, the shear stress scales with W and cn. Be-cause the weight of Anatolian topography on thesides of the NAF fault increases its normal stress

by several MPa, this makes the fault plane a littlemore resistant and less prone to slide.

3.3. E¡ect of geometry and boundary conditions

Considering the complex geometry of the west-ern part of the NAF compared to the easternNAF (see Fig. 1), we tested two new fault geom-etries to see their in£uence on stress and strain inAnatolia. The ¢rst geometry concerns the regionof the Sea of Marmara where the NAF splits intothree branches, with one more north than theothers. In this area, GPS and geological informa-tion suggest that the north NAF is more activethan the south branch [1,6,41,42]. We thus de-signed the western portion of the fault so that itwould match the trace of the north branch in thisarea (case 9, see Fig. 7a for a map view). Thisgeometrical change has a clear e¡ect on the west-ern and northern parts of the model. The regionwhich corresponds to northern Greece deformssigni¢cantly. This does not seem to be consistentwith the motion at the SOXO and ASKT sites.Also, a deforming zone is present 300 km south-west of the Marmara region, indicating that Ana-tolia does not behave rigidly there. This is consis-tent with observations of McClusky et al. [1] thatshow considerable strain in western Turkey. Onecan also notice that the region of the Sea of Mar-mara, which has been described as an activelydeforming pull-apart basin [6], does not su¡er alarge deformation in our model. A positive con-sequence of this change of fault geometry is thatvelocities in the Aegean are more consistent withGPS motions, e.g. for the NSKR site. Overall, thenorth branch case seems more satisfactory andindicates that the fully circular approximationmade for the NAF for cases 1^8 causes a signi¢-cant deformation mismatch in the Aegean.

The second geometry ¢ts as closely as possiblethe real trace of the fault from the KTJ to theAegean Sea (case 10, see Fig. 7b for a mapview). It is composed of ¢ve connected segments,all with the same fault friction of 0.05 (Table 1).The deformation distribution on the Anatolianblock is not very di¡erent from that for the pre-vious case. The most noticeable di¡erence occurssouth of the sharp NAF bend in central Anatolia

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 369

(at x = 1200 km), where the strain rate reaches2U10315 s31. However, it must be pointed outthat the motion of the corresponding GPS siteKKIR is not signi¢cantly a¡ected by the bend.As for case 9, the velocity of points of northernGreece is overestimated by 5^8 mm/yr.

A possible cause of the mismatch of the mod-eled velocities in northern Greece is tied to thewestern boundary condition of the model. Indeed,we simply impose a linear variation from zerovelocity (Eurasia) to 30 mm/yr to the southwest(south Peloponnesus). Detailed GPS and tectonicstudies in Greece have demonstrated that a largepart of extensive strain is concentrated within theCorinth Gulf (14 mm/yr in its western part) andwithin the adjacent part of continental Greece. Toaccount for this strain localization, the northwest-ern boundary of our case 11 was changed to ¢tthe non-deforming northern Greece one and alocalized velocity gradient of 15 mm/yr aroundthe Corinth Gulf (Fig. 7c). As a result, the defor-mation remains unchanged in most parts of themodel with respect to case 9, with a signi¢cantdecrease in the northwestern part only. Velocitiesat stations SOXO and ASKT are reduced by 30%compared to the ones in case 9, without reachingthe observed values.

4. Discussion

None of the 10 numerical experiments summa-rized in Table 1 provides very good agreementwith the GPS velocity ¢eld. The RMS errors be-tween the 21 inner control points vary from 7.93mm/yr for case 4 (W= 0.2) to 4.71 mm/yr for case9 (the north branch, W= 0.05), supporting ourchoice of 0.05 for fault friction. This result is con-sistent with the early work of Kasapoglu andTokso«z [28] that found the NAF is locked witha friction coe⁄cient of 0.4. This is also in closeagreement with the thin-shell ¢nite element tec-tonic model of the whole Mediterranean proposedby Jimenez-Munt and Sabadini [43]. Their predic-tions revealed that a very low friction (0.05) isnecessary on the NAF to observe the Anatolianblock rotation illustrated by GPS measurements.On the other hand, their results favor a hard lith-

Fig. 7. Map views of the distribution of the deformation aswell as velocity vectors (black arrows) deduced from themodel, for two geometrical tests: northern branch geometryin the region of Marmara (case 9; panel a) and the real faulttrace geometry over the whole of Anatolia (case 10; panelb), and for a boundary condition test: northern Greeceboundary condition changed (case 11; panel c). The whitearrows are velocity vectors from the GPS reference pointsshown in Fig. 2 [1]. See text for details.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377370

ospheric rheology, while according to their com-putations we use a soft or medium rheology inour model.

Concerning the fault geometry, the northbranch cases (9 and 11), and to a lesser extentthe real fault trace case (10), display better agree-ment with velocity data than the other cases. Wenow evaluate in more detail how our modelsmatch the long-term slip rate of the NAF andhow the predicted stress ¢eld ¢ts with availablestress data in Anatolia.

4.1. Fault slip rate of the NAF

A good measure of the quality of these modelsis provided by the fault slip rate of the NAF,which can be assessed by geodetic and geologicalmeasurements. The east velocity di¡erence be-tween TEBA and IKAN is 17.5 mm/yr and pro-vides an estimate of the NAF velocity (Table 1).This value is signi¢cantly smaller than the valueof 24 mm/yr proposed by McClusky et al. [1]when considering that Anatolia rotates rigidlyrelative to Eurasia around a pole located nearthe Sinai. The reason for this discrepancy is theprogressive decrease of the site velocities whenapproaching the fault. Indeed, the sites thatare within 100 km south of the fault (GIRE,HMZA, GEML; see Fig. 6c) see their velocitydecreasing from 24 to 19 mm/yr with increasinglatitude. This velocity decrease can be interpretedin two ways. First, this may correspond to a per-manent deformation of the crust by wrenching inthe NAF vicinity. To our knowledge this has notbeen directly documented. However, it is remark-able that long-term slip rates given by geologicalstudies [11] are systematically smaller than 24mm/yr. Another hypothesis is that velocity de-crease may correspond to an interseismic transi-ent, i.e. the elastic strain accumulation during theseismic cycle, as suggested by McClusky et al. [1].Indeed, large earthquakes (Ms 7) occurred onthe whole length of the NAF during the 20thcentury and a post-seismic e¡ect may still occuraway from the fault [44^46]. Therefore, the ve-locity of GPS sites within 100 km of the faultmay not be representative of the long-term veloc-ity.

In order to precisely evaluate the data^modelagreement around the NAF, we compare theGPS site velocities of ¢ve sites in Anatolia andGreece (Fig. 8) with the velocities predicted forcases 1, 8, 9, and 10. Because GPS sites northof the fault move slightly to the west (0^4 mm/yr), the values of Fig. 8 represent an upper boundof the di¡erential velocity between Anatolia andEurasia. However, the data re£ect that the Ana-tolian motion and probably the NAF slip rate arenot constant with distance along the fault. TheGPS velocity is 22 mm/yr to the east (KMAH),decreases to 17 mm/yr in central Anatolia(KKIR), then increases to 20, 24 and 27 mm/yr(TEBA, GIRE and NSKR, respectively). We ac-knowledge that the velocity di¡erences along thefault could also be due to other factors, such asdistance from the fault or fault branches. Never-theless, it is signi¢cant that cases 1 and 8 com-pletely fail to mimic the NSKR motion (15 mm/yr). This is clearly due to the position of the west-ern end of our fault, which is east of this point.Cases 9 and 10, which are geometrically morerealistic, predict velocities of 24 and 23 mm/yr,respectively.

Fig. 8. Velocities at ¢ve reference points along the fault,NSKR GIRE TEBA KKIR and KMAH, for various experi-ments: without topography (case 1; plusses), with topogra-phy (case 8; open diamonds), with the new branch to thenorth (case 9; open triangles), and with the real fault tracegeometry (case 10; open squares). McClusky’s [1] referenceline is represented by closed circles.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 371

All the models fail to reproduce the velocitytransition observed south of the Marmara region.The predicted velocity of GIRE and TEBA isunderestimated by 4^8 mm/yr for cases 9 and10. These low velocities are probably due to thebend associated to these cases. Indeed, cases 9 and10 force the slip to be restricted to the north NAFonly. In nature, the deformation of the Marmarazone is accommodated by di¡erent faults (northMarmara fault system, south NAF), which prob-ably allow an easier accommodation of the mo-tion between Anatolia and Eurasia. It has beenproposed that most of this motion occurs on thenorth NAF, while no more than 20% occurs onthe south NAF [6,42]. We are not reaching thislevel of complexity here, but it can be conjecturedthat the introduction of the di¡erent NAF strandsand of the deformable Marmara region, in themodel, could allow a better ¢t of neighboringGPS site velocities. Using a dislocation model inan elastic half-space, Flerit et al. [47] built aninterseismic model of the Marmara pull-apart.They started with a one-branch fault geometryfor the NAF west of Marmara and then addedmore complexity to the model with two branchesfor the NAF and extensional structures in westernTurkey. Even though the velocity vectors com-puted by their model have amplitudes similar tothe GPS ones, their azimuths di¡er by 11^18‡,especially in the region just south of the sea ofMarmara (site GIRE). According to this, evenusing a speci¢c fault geometry for this regiondoes not allow one to reproduce the velocity ¢elddeduced from GPS measurements. It would prob-ably be necessary to introduce a weak rheology inthe Marmara trough or in western Turkey to lo-calize the deformation and reduce the thickness ofthe crust in this area.

Central Anatolia motion given by KKIR is wellmodeled by cases 8^10. To the east the KMAHvelocity is systematically underestimated by 4mm/yr. This low value is clearly due to the termi-nation of the fault in our model at x = 1700 km.This induces a deformation zone around the faulttip that reaches the point KMAH and decreasesits velocity. Modeling the KTJ with a slippingfault to the east should improve the velocity ¢tand correct this model artifact.

4.2. Stress ¢eld in Anatolia and Aegean

4.2.1. Stress dataIn order to compare the stress results obtained

with our model with known stress regimes in Ana-tolia we have collected stress data from the liter-ature. We have superimposed the results on stressregimes and orientation maps calculated with ourmodels (Fig. 9). White arrows represent thesedata, while black ones represent our results.

In general, slip on the NAF is dominated byright-lateral strike-slip motion, but some thrustingis detected east of KTJ after the intersection withthe East Anatolian fault, and some normal fault-ing is present on the western end of the faultsystem before it connects with the Aegean [48].P and T axes deduced from fault-plane solutionsof major earthquakes on the central NAF showcompression oriented at about 50‡ from the traceof major faults in a mostly right-lateral strike-slipregime, while further to the east, near the KTJ,fault-plane solutions show some thrusting compo-nent associated with right-lateral strike-slip [48].Some evidence of active thrust faulting, awayfrom the fault, at the southern Black Sea marginwas revealed by the Mw 6.6 Bartin earthquake of1968 [49]. Several small to moderate events haveoccurred in this area, and most of them show areverse fault-plane solution with one of their no-dal planes roughly parallel to the margin. Thisindicates the presence of compressional stressesoriented approximately perpendicular to the mar-gin. In central western Anatolia, Zanchi and An-gelier [50] were able to invert about 66 fault-planesolutions and obtained a stress tensor showing aNNE^SSW extension, with the azimuth of theleast principal stress c3 at N25‡E. In the Sea ofMarmara area, geological evidence has been inter-preted as a combination of strike-slip and normalfaults [6]. Compilation of stress data [51] showsa north^south extension in the northwestern partof the Aegean and Anatolia with SH (maximumhorizontal compression) oriented N85‡E. In theregion of the Marmara Sea stress data show amore heterogeneous stress ¢eld, correspondingto the transition to a purely strike-slip regime incentral Anatolia [51].

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377372

4.2.2. Stress modelStress orientation and stress regime distribu-

tions of the four cases 1, 8, 9 and 10 are repre-sented in Fig. 9. This stress map has been drawnat a mean depth of 7 km, and is representative ofthe state of deviatoric stress in the seismogeniccrust with the orientation of minimum and max-imum horizontal stress. The amplitudes of theorientations are based on the following ratio:c13c3/ c , where c1 and c3 are the absolute mag-nitude of the maximum and least principal stress-es, respectively, and c is the mean stress. We em-phasize that these values do not provide anyinformation on the strain rate which has beenpreviously discussed. The three tectonic states ofstress are present on this map. The overall picturegiven by cases 1, 8, 9 and 10 is an extensional

domain to the west (Aegean and western Anato-lia), a strike-slip domain (Black sea and easternAnatolia) and a compressional domain to the east(Caucasus). This is in agreement with the datacollected and mentioned above, showing the pres-ence of normal faults in the Aegean [51], mostlyright-lateral strike-slip earthquakes along theNAF [48], and a strong thrust component in thefault-plane solutions of events occurring in theEast [48]. In our model this pattern is mainlydue to the lateral boundary conditions that evolvefrom compressive to extensional between east andwest. Most of the di¡erences between the fourcases occur in central Anatolia. For example,the normal to strike-slip transition occurs atx = 1100 km for case 1 (no topography). On theother hand, the extensional domain invades the

(4)

(1)(1)(2)(3)

Fig. 9. Map views of the stress regimes and orientations deduced from the model for four cases, without topography (a), with to-pography (b), with the new branch to the north (c), and with the real fault trace geometry (d). Black arrows represent the resultsobtained with our modeling, their length scales with (c13c3)/ c , while white arrows refer to data taken from the literature: (1)[48], (2) [50], (3) [51], and (4) [49]. For a better viewing the white arrows were enlarged, the scale does not apply for these data.See text for details.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 373

whole Anatolian plateau for case 8 (with topog-raphy). This change is easily understandable, as ahigh plateau can be under extension due to itsown weight [38]. However, not only lateralboundary conditions and topographic weight areresponsible for the stress state: the normal tostrike-slip limit in case 9 (north branch case)moves to the west, due to the deviation of theNAF. Unfortunately, the di¡erences observed be-tween these four cases mainly occur in centralAnatolia, where the seismic strain is very low,i.e. smaller than 10315 s31 for W= 0.05, which isin agreement with observations and data (seeFigs. 5^7). It is therefore di⁄cult to discriminateamong these models on the base of stress data.The GPS-based velocity ¢eld and the geologicalslip rate of the NAF provide better constraints onthe mechanical behavior of the Aegean^Anatoliansystem.

4.3. Cause for disparity between model and data

Most of the discrepancy between GPS velocitiesand those predicted by our models occurs in thewestern part of the model (Greece and westernAnatolia). If we choose cases 9^11 (north branchand real fault trace; see Fig. 7) for the purpose ofdiscussion, three zones of the model do not pro-vide a good ¢t to the GPS velocities.

The ¢rst zone is the Marmara region. The siteGIRE has a velocity underestimated by 7.5 mm/yr. It is probable that adding the south branch ofthe NAF, as well as east^west grabens in westernTurkey highlighted by historical seismicity, wouldlead to a velocity gain for the GIRE site.

The second zone is the Aegean (NSKR, HIOS,BODR and MILO). Only MILO, which is closeto the boundary condition imposed along theCrete island, has a correct velocity. The otherthree sites have velocities underestimated byabout 5 mm/yr. Therefore, a N40‡ extension Ae-gean is predicted at 5 mm/yr, in disagreement withGPS data, which do not show a signi¢cant defor-mation. Di¡erent causes can be responsible forsuch a discrepancy: (1) the Aegean lithosphere ismore rigid than expected in the model ; (2) a vis-cous £ow with a N220‡ direction at the base ofthe lithosphere forces the Aegean crust to move

southwest; (3) the ill-modeled adjacent zones ofMarmara and western Turkey have an impact onthe motion of the Aegean.

The third zone is northern Greece (SOXO andASKT). Case 9 displays a velocity of 8 mm/yr forthese two sites. Corresponding GPS velocities donot exceed 3 mm/yr. In this area, the cause forsuch a mis¢t is the lack of deformation occurringin active grabens such as the Corinth Gulf, theEvvia graben and the North Aegean trough. Forexample, the Corinth Gulf is opening at a rate of11^14 mm/yr in a narrow zone of 15 km [31]. Thecontinent north of the gulf is not deformed. Onthe contrary, our model shows that northernGreece deforms rather homogeneously, and activedeformation reaches the northwest corner of themodel. This is clearly due to the northwest bound-ary condition of our model, which imposes alinearly decreasing viscosity from southwest tonortheast on the edge. Modifying this boundarycondition, as is done in case 11, reduces the veloc-ities of the two GPS stations considered and local-izes the deformation in the region of the grabens.Thus modeling the Corinth Gulf as a strain local-ization zone is needed to reproduce the velocitypattern of northern Greece.

5. Conclusion

Our numerical modeling of the Anatolian pla-teau allowed us to integrate the forces acting onthe lithospheric system in terms of velocityboundary conditions and body forces due to thetopography. According to borehole stress dataand rock mechanics experiments (i.e. an e¡ectivefriction of 0.6), we made the assumption that thelithospheric crust can sustain a high stress. Underthis condition, our numerical modeling indicatesthat the NAF must be a very weak material het-erogeneity of the lithosphere. Indeed, we need toassign a very low e¡ective friction on the NAF(0.05) to reproduce the ¢rst-order character ofthe velocity ¢eld. Because the velocity ¢eldaround and inside the Anatolian plateau is wellknown, the modeling is accurate enough to pre-dict that the upper bound of the e¡ective frictionshould not be higher than 0.1. This value is sim-

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377374

ilar to that proposed for the SAF using stress data[35,37,52]. The e¡ective fault velocity is here re-vealed using GPS velocity data alone. Stress dataappear here as a secondary data set that do notcontradict the conclusion previously drawn. Usedin conjunction with dense GPS data, 3D numeri-cal modeling appears to be an e⁄cient tool toconstrain the rheological properties of the litho-sphere. However, the present study displays in-triguing discrepancies between modeled velocitieswith respect to the GPS. This probably meansthat some limitations of the present study needto be tackled in order to step beyond. The mainone is that the lithosphere is not homogeneous. Amore accurate modeling should therefore accountfor the lateral strength variations across the east-ern Mediterranean as well as the presence of theuppermost mantle as a mechanical layer. A sec-ond problem relies on the systematic use of thekinematically prescribed boundary conditions (ve-locities), which overlooks the lithospheric system.The use of a stress boundary condition on thesouthern part of the Aegean and Anatolia wouldallow one to reproduce more closely the true ef-fect of the African subduction. Adding such adegree of freedom could also lead to a better eval-uation of the impact of the di¡erential topogra-phy on the predicted velocity ¢eld.

Acknowledgements

We are grateful to the reviewers Peter Bird andRobert Reilinger whose helpful comments sub-stantially improved the manuscript. This workhas been supported by the research program‘ACI Pre¤vention des catastrophes naturelles’ ofthe French Ministry of Research.[AC]

References

[1] S. McClusky, S. Balassanian, A.A. Barka, C. Demir, S.Ergintav, I. Georgiev, O. Gurkan, M. Hamburger, K.Hurst, H. Kahle, K. Kastens, G. Kekelidze, R. King, V.Kotzev, O. Lenk, S. Mahmoud, M. Nadariya, A. Ouzou-nis, D. Paradissis, Y. Peter, M. Prilepin, R. Reilinger, I.Sanli, H. Seeger, A. Tealeb, M.N. Toksoz, G. Veis, Glob-

al positioning system constraints on plate kinematics anddynamics in the eastern mediterranean and Caucasus,J. Geophys. Res. 105 (2000) 5695^5719.

[2] D. McKenzie, Active tectonics of the Mediterranean re-gion, Geophys. J. R. Astron. Soc. 30 (1972) 109^185.

[3] A.A. Barka, L. Gu«len, New contraints on age and totalo¡set of the North Anatolian fault zone: implications fortectonics of the Eastern Mediterranean region, in: MelihTokay Symposium, Spec. Publ. Middel-east Techn. Univ.,Ankara, 1988, pp. 39^65.

[4] A.M.C. Sengo«r, The North Anatolian transform fault itsage, o¡set and tectonic signi¢cance, J. Geol. Soc. London136 (1979) 269^282.

[5] A.A. Barka, The North Anatolian fault zone, Ann. Tec-ton. VI (Special Issue) (1992) 164^195.

[6] R. Armijo, B. Meyer, S. Navarro, G. King, A.A. Barka,Asymmetric slip partitioning in the Sea of Marmara pull-apart: a clue to propagation processes of the North An-atolian fault?, Terra Nova 14 (2002) 80^86.

[7] X. Le Pichon, A.M.C. Sengo«r, E. Demirbag, C. Rangin,C. Imren, R. Armijo, N. Gorur, N. Cagatay, B. Mercierde Lepinay, B. Meyer, R. Saatc\ilar, B. Tok, The activemain Marmara fault, Earth Planet. Sci. Lett. 192 (2001)595^616.

[8] A.A. Barka, Slip distribution along the North Anatolianfault associated with the large earthquakes of the period1939 to 1967, Bull. Seismol. Soc. Am. 86 (1996) 1238^1254.

[9] N.N. Ambraseys, The seismic activity of the Marmara searegion over the last 2000 years, Bull. Seismol. Soc. Am. 92(2002) 1^18.

[10] A.A. Barka, H.S. Akyu«z, E. Altunnel, G. Sunal, Z. Cakir,A. Dikbas, B. Yerli, R. Armijo, B. Meyer, J.B. de Chaba-lier, T. Rockwell, J.R. Dolan, R. Hartleb, T. Dawson, S.Christo¡erson, A. Tucker, T. Fumal, R. Langridge, H.Stenner, W. Lettis, J. Bachhuber, W. Page, The surfacerupture and slip distribution of the 17 August 1999 Izmitearthquake (M 7.4), North Anatolian Fault, Bull. Seis-mol. Soc. Am. 92 (2002) 43^60.

[11] R. Armijo, B. Meyer, A. Hubert, A.A. Barka, Westwardpropagation of the North Anatolian fault into the north-ern Aegean: Timing and kinematics, Geology 27 (1999)267^270.

[12] R. Westaway, Present-day kinematics of the Middle Eastand eastern Mediterranean, J. Geophys. Res. 99 (1994)12,071^12,090.

[13] S.H. Kirby, A.K. Kronenberg, Rheology of the litho-sphere: selected topics, Rev. Geophys. 25 (1987) 1219^1244.

[14] M. P¢ster, L. Rybach, S. Simsek, Geothermal reconnais-sance of the Marmara Sea region (NW Turkey): surfaceheat £ow density in an area of active continental exten-sion, Tectonophysics 291 (1998) 77^89.

[15] A.K. Tezcan, Geothermal explorations and heat £ow inTurkey, in: M. Yamano (Ed.), Terrestrial Heat Flow andGeothermal Energy in Asia, A.A. Balkema, Rotterdam,1995, pp. 23^42.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 375

[16] M.O. Ilkisik, Regional heat £ow in western Anatolianusing silica temperature estimates from thermal springs,Tectonophysics 244 (1995) 175^184.

[17] P. Bird, J. Baumgardner, Fault friction, regional stress,and crust-mantle coupling in souther California from ¢-nite element methods, J. Geophys. Res. 89 (1984) 1932^1944.

[18] R. Hassani, D. Jongmans, J. Che¤ry, Study of plate defor-mation and stress in subduction processes using two-di-mensional numerical models, J. Geophys. Res. 102 (1997)17951^17965.

[19] P. Bird, Testing hypothese on plate-driving mechanismswith global lithosphere models including, topography,thermal structure, and faults, J. Geophys. Res. 103(1998) 10115^10129.

[20] M. Roy, L.H. Royden, Crustal rheology and faulting atstrike-slip boundaries 2. E¡ects of lower crustal £ow,J. Geophys. Res. 105 (2000) 5599^5613.

[21] I. Jimenez-Munt, M. Marnoni, R. Sabadini, R. Devoti, V.Luceri, C. Ferraro, G. Bianco, Geophysical and geodeticdeformation patterns in the Mediterranean, Geophys.Res. Abstracts 4 (27) (2002) EGS02-A-01182.

[22] J. Braun, Three-dimensional numerical simulations ofcrustal-scale wrenching using a non-linear failure criteri-on, J. Struct. Geol. 16 (1994) 1173^1186.

[23] J. Che¤ry, M.D. Zoback, R. Hassani, An integrated me-chanical model of the San Andreas Fault in central andnorthern California, J. Geophys. Res. 106 (2001) 22051^22066.

[24] J.C. Lynch, M.A. Richards, Finite element models ofstress orientations in well-developed strike-slip faultzones: Implications for the distribution of lower crustalstrain, J. Geophys. Res. 106 (2001) 26707^26729.

[25] J.-C. Bremaecker, P. Hucon, X. LePichon, The deforma-tion of Aegean: a ¢nite element study, Tectonophysics 86(1982) 197^221.

[26] P.T. Meijer, M.J.R. Wortel, Temporal variation in thestress ¢eld of the Aegean region, Geophys. Res. Lett. 23(1996) 439^442.

[27] P. Lundgren, D. Giardini, R. Russo, A geodynamicframework for eastern Mediterranean kinematics, Geo-phys. Res. Lett. 25 (1998) 4007^4010.

[28] K.E. Kasapoglu, M.N. Toksoz, Tectonic consequencesof the collision of the Arabian and Eurasian plates:¢nite element models, Tectonophysics 100 (1983) 71^95.

[29] S. Cianetti, P. Gasperini, M. Boccaletti, C. Giunchi, Re-producing the velocity and stress ¢elds in the Aegeanregion, Geophys. Res. Lett. 24 (1997) 2087^2090.

[30] S. Cianetti, P. Gasperini, C. Giunchi, E. Boschi, Numer-ical modelling of the Aegean-Anatolian region: geody-namical constraints from observed rheological heteroge-neities, Geophys. J. Int. 146 (2001) 760^780.

[31] P. Briole, A. Rigo, H. Lyon-Caen, J.C. Ruegg, K. Papa-zissi, C. Mitsakaki, A. Balodimou, G. Veis, D. Hatzfeld,A. Deschamps, Active deformation of the Corinth rift,Greece: Results from repeated Global Positioning System

surveys between 1990 and 1995, J. Geophys. Res. 105(2000) 25605^25625.

[32] W.R. Thatcher, Microplate versus continuum descriptionsof active tectonic deformation, J. Geophys. Res. 100(1995) 3885^3894.

[33] Y. Leroy, M. Ortiz, Finite element analysis of strain local-ization in frictional materials, Int. J. Numer. Anal. Meth-ods Geomech. 13 (1989) 53^74.

[34] P.A. Cundall, M. Board, A microcomputer program formodelling large-strain plasticity problems, in: G. Swobo-da (Ed.), International Conference on Numerical Meth-ods in Geomechanics, A.A. Balkema, Brook¢eld, VT,1988, pp. 2101^2108.

[35] M.D. Zoback, M.L. Zoback, V.S. Mount, J. Suppe, J.P.Eaton, J.H. Healy, D. Oppenheimer, P. Reasenberg, L.M.Jones, B.C. Raleigh, I.G. Wong, O. Scotti, C. Wentworth,New evidence on the state of stress of the San Andreasfault system, Science 238 (1987) 1105^1111.

[36] W. Thatcher, Present-day crustal movements and the me-chanics of cyclic deformation, in: R.E. Wallace (Ed.), TheSan Andreas Fault system, California, Geological SurveyProfessional Paper 1515, Washington, DC, 1990, pp. 189^205.

[37] V.S. Mount, J. Suppe, State of stress near the San An-dreas fault: Implications for wrench tectonics, Geology 15(1987) 1143^1146.

[38] L. Fleitout, C. Froidevaux, Tectonics and topography fora lithosphere containing density heterogeneities, Tectonics1 (1982) 21^56.

[39] J.F. Dewey, Extensional collapse of orogens, Tectonics 7(1988) 1123^1139.

[40] S. Willet, C. Beaumont, P. Fullsack, Mechanical modelfor the tectonics of doubly vergent compressional oro-gens, Geology 21 (1993) 371^374.

[41] C. Straud, H.-G. Kahle, C. Schindler, GPS and geologicalestimates of tectonic activity in the Marmara Sea region,NW Anatolia, J. Geophys. Res. 102 (1997) 27,587^27,601.

[42] B.J. Meade, B.H. Hager, S.C. Mcclusky, R.E. Reilinger,S. Ergintav, O. Lenk, A.A. Barka, H. Ozener, Estimatesof seismic potential in the Marmara Sea region fromblock models of secular deformation constrained byGlobal Positioning System measurements, Bull. Seismol.Soc. Am. 92 (2002) 208^215.

[43] I. Jimenez-Munt, R. Sabadini, The block-like behavior ofAnatolia envisaged in the modeled and geodetic strainrates, J. Geophys. Res. 29, in press.

[44] J. Che¤ry, S. Merkel, S. Bouisson, A physical basis for timeclustering of large earthquakes, Bull. Seismol. Soc. Am.91 (2001) 1685^1693.

[45] E. Mantovani, M. Viti, N. Cenni, D. Albarello, D. Bab-bucci, Short and long term deformation patterns in theAegean-Anatolian systems: insights from space geodeticdata (GPS), Geophys. Res. Lett. 28 (2001) 2325^2328.

[46] E.H. Hearn, B.H. Hager, R. Reilinger, Viscoelastic defor-mation from North Anatolian fault zone earthquakes andthe eastern Mediterranean GPS velocity ¢eld, Geophys.Res. Lett. 29 (2002) 1549.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377376

[47] F. Flerit, R. Armijo, G. King, B. Meyer, A.A. Barka, Slippartitioning in the Sea of Marmara pull-apart determinedfrom GPS velocity vectors, Geophys. J. Int. (2002), sub-mitted.

[48] J. Jackson, D. McKenzie, Active tectonics of the Alpine-Himalayan belt between Turkey and Pakistan, Geophys.J. R. Astron. Soc. 77 (1984) 185^264.

[49] O. Alptekin, J.L. Nabeleck, M.N. Toksoz, Source mech-anism of the Bartin earthquake of September 3, 1968 inNorthwestern Turkey: Evidence for active thrust faultingat the southern Black sea margin, Tectonophysics 122(1986) 73^88.

[50] A. Zanchi, J. Angelier, Seismotectonics of western Ana-tolia: regional stress orientation from geophysical andgeological data, Tectonophysics 222 (1993) 259^274.

[51] B. Mu«ller, M.L. Zoback, K. Fuchs, L. Mastin, S. Gre-gersen, N. Pavoni, O. Stephansson, C. Ljunggren, Re-gional pattern of tectonic stress in Europe, J. Geophys.Res. 97 (1992) 11783^11803.

[52] A.-S. Provost, H. Houston, Orientation of the stress ¢eldsurrounding the creeping section of the San Andreasfault: Evidence for a narrow mechanically-weak faultzone, J. Geophys. Res. 106 (2001) 11373^11386.

EPSL 6591 2-4-03

A.-S. Provost et al. / Earth and Planetary Science Letters 209 (2003) 361^377 377