Slip rates of the Altyn Tagh, Kunlun and Karakorum faults (Tibet) from 3D mechanical modeling

Earth and Planetary Science Letters 274 (2008) 50–58

Contents lists available at ScienceDirect

Earth and Planetary Science Letters j o u r n a l h o m e p a g e : w w w. e l s e v i e r. c o m / l o c a t e / e p s l

Slip rates of the Altyn Tagh, Kunlun and Karakorum faults (Tibet) from 3D mechanical modeling Jiankun He a,⁎, Jean Chéry b a b

Institute of Tibetan Plateau Research, Chinese Academy of Sciences, Beijing, China Geosciences Montpellier, CNRS-Université de Montpellier II, Montpellier, France

A R T I C L E

I N F O

Article history: Received 6 September 2007 Received in revised form 17 June 2008 Accepted 29 June 2008 Available online 9 July 2008 Editor: C.P. Jaupart Keywords: slip rate Altyn Tagh fault Kunlun fault mechanical modeling late Quaternary GPS geodesy Tibetan plateau

A B S T R A C T We use 3-D mechanical modeling representing faults as planar surfaces with frictional properties that obey Coulomb-failure process to explore the long-term slip rates of the Altyn Tagh fault and Kunlun faults in the north Tibetan plateau. Crustal rheology is simplified as an elastoplastic upper crust and a viscoelastic lower crust. Far-field GPS velocities and late Quaternary fault slip rates are used to constrain the model results. Rheological tests show that effective fault friction lower than 0.1–0.08 leads to high slip rates that fit with geologically and geodetically determined slip rates of the Kunlun fault (10–11.7 ± 1.5 mm/yr). Meanwhile, the modeled Altyn Tagh fault reaches slip rates ~ 13.7 mm/yr to ~ 17.8 mm/yr in its central portion, between ranges of the geological slip rates. Associated with high slip rates, our model predicts that central Tibet (~ 84°E–95°E) from the Altyn Tagh fault to the north of the Himalayan arc accommodates north–south shortening and east–west extension rates of ~10–12 mm/yr and ~ 8–10 mm/yr, respectively. We also question the widely accepted idea that interseismic strain is driven at the base of the seismogenic zone by a screw dislocation. If this assumption fails, the presented model implies that interseismic strain around large strikeslip faults could be distributed in a much broader way if the lithosphere deforms as a thin elastic plate rather than an elastic half-space with an embedded dislocation. If this distributed deformation is ignored, and the instantaneous surface deformation field modeled as that resulting from slip on a dislocation below a specified depth embedded in an elastic half-space, the estimated slip rate will inevitably be lower than the true long-term slip rate. This appears to explain why geodetic slip rates proposed for the Altyn Tagh fault (5– 10 mm/yr) are lower than some of the geological slip rates. © 2008 Elsevier B.V. All rights reserved.

1. Introduction The Altyn Tagh fault (ATF) and the Kunlun fault in the north Tibetan plateau are two major active strike-slip faults with length greater than 1000 km (Tapponnier and Molnar, 1977; Molnar and Tapponnier, 1978). The assessment of slip rates of these large faults is important to understand the deformation behavior of the crust and mantle beneath the plateau and to test the predictions of various controversial models (England and Houseman, 1986; Avouac and Tapponnier, 1993; England and Molnar, 1997; Tapponnier et al., 2001; Meade, 2007; Thatcher, 2007). Geological and geodetic studies have documented slip rates on several sites along these major strike-slip faults (Table 1). Along the Kunlun fault, the geological slip rate on its central ~ 800 km displays little scatter over the late Quaternary period (Van der Woerd et al., 2002; Li et al., 2005), and fits GPS-based geodetic rates (Zhang et al., 2004, 2007; Chen et al., 2004). For the

⁎ Corresponding author. E-mail address: [email protected] (J. He). 0012-821X/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.epsl.2008.06.049

Altyn Tagh fault, the geologically determined Quaternary slip rates range from 10 to 30 mm/yr on its central portion (Peltzer et al., 1989; Washburn et al., 2001; Ryerson et al., 2003; Mériaux et al., 2004; Cowgill, 2007), often significantly greater than the geodetic rates (Bendick et al., 2000; Shen et al., 2001a,b; Wright et al., 2004; Wallace et al., 2004; Meade, 2007; Thatcher, 2007). However, it is important to mention that the fastest geological slip rate along the Altyn Tagh fault has been obtained in a zone at ~ 87°E where geodetic motion has not been measured to date. Various explanations have been proposed for the discrepancy between the geological and the geodetic slip rates of the Altyn Tagh fault (Mériaux et al., 2004; Wallace et al., 2004; Cowgill, 2007; IsmailZadeh et al., 2007). One is that geodetic estimates result from a time extrapolation of a short fraction of interseismic motion. Therefore, there is no guarantee that this extrapolation leads to the long-term motion averaged over several seismic cycles of the Altyn Tagh fault (Mériaux et al., 2004). Another one is that the high values of geological slip rates of the ATF contain systematic errors on the fault-related geomorphic observations (Wallace et al., 2004; Cowgill, 2007). Here, we develop a three-dimensional finite element model to investigate the mechanical relation between the far-field loading of south Tibet

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58 Table 1 Slip-rate compilation of the Altyn Tagh fault (ATF), the Kunlun fault (KLF) and the Karakorum fault (KRF) Fault Location

Slip rate

Methods

Ref.

ATF ATF ATF ATF ATF

20–30 5±5 ~9 9.4 ± 2.3 27 ± 7

Offset postglacial Geodetic (InSar) Geodetic (GPS) Offset postglacial 10 Be,26Al,14C

Peltzer et al. (1989) Wright et al. (2004) Shen et al. (2001a,b) Cowgill (2007) Meriaux et al. (2004)

20 ± 3(min.13 ±3)

10

Mériaux et al. (2005)

KLF

78°–96°E ~ 80°E ~ 85°–90°E 87°E 87°E (A1 in Fig. 1) 94°E (A2 in Fig. 1) 94°E 95°E ~ 96°E (A3 in Fig. 1) ~ 92.2°E (B1 in Fig. 1) 94°E (B2 in Fig. 1) ~ 94°E

KLF

94.4°E

12.1 ± 2.6

KLF KLF

94.4°E 99°E (B3 in Fig. 1) 100.5°E (B4 in Fig. 1) ~ 101.4°E ~ 103.1°E ~ 34.6°N (C1 in Fig. 1) ~ 34.6°N (C1 in Fig. 1) ~ 34°N (C2 in Fig. 1) ~ 32°N (C3 in Fig. 1) ~ 79°E

6.5 ± 0.9–8.2 ±1.7 ~ 10

ATF ATF ATF ATF KLF KLF

KLF KLF KLF KRF KRF KRF KRF KRF

Be,26Al,14C

5.4 ± 0.7–22.3 ±3.1 Offset postglacial 10 Be,26Al ~ 15 4±2 Offset postglacial

Cowgill (2007) Mériaux et al. (2005) Meyer et al. (1996)

10.0 ± 1.5

Thermoluminescenc Li et al. (2005)

11.7 ± 1.5

10

8–11

Geodetic (GPS) 10

Be,26Al,14C

Be,26Al

Offset postglacial Be,26Al,14C

10

Be,26Al,14C

Van der Woerd et al. (2002) Zhang et al. (2004); Chen et al. (2004) Van der Woerd et al. (1998) Cowgill (2007) Van der Woerd et al. (2002) Van der Woerd et al. (2002) Kirby et al. (2007) Kirby et al. (2007) Brown et al. (2002)

12.5 ± 2.5

10

5.0 ± 1.0 ~ 1,0 4±1

14

10 ± 3.0

U/Pb,

2.7–10.2

U–Pb ID-TIMS

Phillips et al. (2004)

10.7 ± 0.7

10

Chevalier et al. (2005)

1±3

Geodetic (InSar)

C C 10 Be 14

40

Ar/39Ar

Be

Lacassin et al. (2004)

Wright et al. (2004)

and Eurasia and the slip rates along the large faults in north Tibet. We argue that our model may help to understand the slip-rate discrepancy from geological and geodetic determinations especially on the Altyn Tagh fault.

51

2. Model formulation The three-dimensional model covers a wide region surrounding the Altyn Tagh, Kunlun and Karakorum faults (Fig. 1). Due to the large crustal thickness of more than 60 km, the Tibetan plateau is characterized by high surface heat flow and therefore elevated lower crust and uppermost mantle temperatures (Gaudemer et al., 1988). Thus, we assume that only the upper lithosphere (namely upper and middle crust) can support significant deviatoric stress and that the uppermost mantle is part of the asthenosphere. According to this hypothesis, our model of Tibetan lithosphere extends vertically to 30 km depth and is composed of an elastoplastic upper crust (Drucker–Prager's law) and a viscoelastic lower crust. The upper crust is 15-km thick, in agreement with the observed depth of large earthquakes in Tibet (Molnar and Cheng, 1983; Peltzer et al., 1999). The viscoelastic lower crust is modeled as a Maxwell media with a mean viscosity of ~ 1020 Pa s according to mechanical studies of crustal flow and seismic cycle in Tibet (Hilley et al., 2005). To approximate long-term fault motion averaged over several seismic cycles, the Altyn Tagh fault, Kunlun and Karakorum faults are simulated as Coulombtype frictional zones (Bird and Kong, 1994; Provost et al., 2003; Vernant and Chéry, 2006). Thus, the shear stress (τ) needed for fault displacement is controlled by the normal stress (σN) with τ = μ · σN where μ is the effective fault friction. For an easy building of our 3-D mesh and because the faults we model are nearly vertical (Wittlinger et al., 1998), we treat these three faults as vertical planes. Frictional faults are strictly included within the model as the boundary conditions correspond to a continuous velocity field. We acknowledge that this treatment can underestimate modeled slip rates near the fault tips. Also, we do not include, for simplicity purpose, the large strike-slip faults such as the Haiyuan, Xianshuihe and Jiali fault systems. This shortcoming implies that the slip rate that would have occurred on these faults is absorbed by the deformable lithosphere in response to the boundary conditions. The key assumption of our model is that the GPS velocity field at large distance from the faults is not influenced by the seismic cycle and is therefore a proxy of continental long-term surface motion. This hypothesis seems reasonable regarding the fair agreement between geological plate motion on a time scale of ~ 1 Myr and the corresponding geodetic motion (Sella et al., 2002). This assumption

Fig. 1. Model geometry and boundary conditions superimposed on the simplified tectonic map. White line is the model boundary. The south and the east sides are specified with velocities (blue) from GPS data (black) of Zhang et al. (2004); the north side is fixed, and the west side is a symmetric boundary (see text for details). Red lines are main faults; the Altyn Tagh fault, the Kunlun fault and the Karakorum fault are simulated as Coulomb-type frictional zones. Yellow squares are sites with geological slip rates (Table 1) used in Fig. 2. A– B, C–D, and E–F are three profiles. ATF, Altyn Tagh fault; KLF, Kunlun fault; KRF, Karakorum fault; JLF, Jiali fault; XSF, Xianshuihe fault; HYF, Haiyuan fault; QLM, the Qilian mountains; SB, Sichuan basin. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

52

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58

Table 2 Physical parameters for model calculation Parameters

Value

Young's modulus (E) Poisson ratio (ν) Crustal density (ρc) Mantle density (ρm) Low-crust viscosity (η) Cohesion (c) Internal frictional angle (ϕ) Dilatancy (ϕ)a

1011 Pa 0.25 2800 kg/m3 3300 kg/m3 1020 Pa s 10 Mpa 30° 0°

We use ADELI finite element software to solve the mechanical equilibrium (Chéry and Hassani, ADELI user's guide, available at http:// www.gm.univ-montp2.fr/PERSO/chery.html). The three-dimensional model is meshed into 76,320 tetrahedron elements. This resolution corresponds to an element size of ~ 7 km, fine enough to describe accurately gradients of quasi-static deformation. We use a time step as small as 2 yrs for the finite difference scheme. Physical parameters of the model are listed in Table 2. 3. Numerical results

a

Non-dilatant is considered for elastobrittle strain of the upper crust (Chéry and Zoback, 2001; Provost et al., 2003).

3.1. Fault slip rates

seems also valid across the Himalaya for which the geological convergence rate of 21 ± 1.5 mm/yr (Lavé and Avouac, 2000) is close to the GPS rate of 18 ± 2–19 ± 2.5 mm/yr (Larson et al., 1999; Bettinelli et al., 2006). Also, the strain rate between India and Eurasia appears to be similar for both geodetic and geological time scales (England and Molnar, 2005). Therefore, we are confident that the GPS velocities around the Tibetan plateau coincide with its long-term average as postulated by other mechanical studies (Provost et al., 2003; Meade and Hager, 2005). In our model (Fig. 1), the displacement rates of the south and east edges are specified with present-day velocities deduced from numerous GPS data (Zhang et al., 2004). Motion of the north edge of the model in the northern Tien-Shan and in the Gobi-Alashan is assumed negligible in the Eurasian reference frame (Holt et al., 2000; Wang et al., 2001). The western edge crosses approximately through the center of the Pamir Syntaxis. GPS data show that the Pamir moves northward at ~23± 3 mm/yr with almost no east–west motion (Reigber et al., 2001). Because of north–south shortening of the Pamir, we specified a maximum northward velocity of ~25 mm/yr on the southern part of this edge. We submit the model to gravitational forces and the model base to a hydrostatic pressure boundary with assumed densities of 2800 kg/m3 and 3300 kg/m3 representative of, respectively, average crustal and mantle values for the continental lithosphere. Using a combination of an elastoviscoplastic rheology for the lithosphere continuum and a Coulomb friction condition for fault motion allows us to study the mechanical processes controlling fault slip rate and deformation of the bounding crust.

To show whether the contemporary far-field motion of the India– Asia convergence could result in the long-term fault slip rates averaged over several seismic cycles fitting the geological rates, we run series of models with effective fault friction coefficients from 0.02 to 0.6. The wide range of friction coefficient exploration is needed because no consensus has been reached so far on the effective friction occurring on active faults. Indeed, as laboratory experiments provides friction coefficient of 0.6–0.8 for most rock types (Byerlee, 1967), geophysical interpretation of stress and heat flow and also some modeling approaches indicate that some fault zones may be almost frictionless (Zoback et al., 1987;Wang et al., 1994; Scholz, 1996; Hassani et al., 1997) with friction coefficient lower than 0.1. We first compare modeled and geological slip rates along the Kunlun fault (Fig. 2a), since there its geological and geodetic slip rates are similar (Van der Woerd et al., 1998, 2002; Chen et al., 2004; Zhang et al., 2004; Li et al., 2005). Results show that for an effective fault friction greater than 0.2, the slip rate along the Kunlun fault remains lower than ~1.5 mm/yr, significantly less than the average geological slip rate of ~10 mm/yr (Table 1). With an effective fault friction less than 0.1, the modeled slip rates tend to reach the geological rates on the central part of the fault. Towards the east (~100.5°E), the modeled slip rate (~ 8 mm/yr) remains smaller than the mean geological rate of 12.5 ± 2.5 mm/yr (Van der Woerd et al., 2002), but within errors when the full range of the geological displacement (180 ± 20 km) averaged over 20–11 ka is considered. Thus, only with a very low fault friction (b0.06) do we obtain agreement between modeled and geological slip rates for the Kunlun fault.

Fig. 2. Comparison of the modeled and the observed slip rates on different sites along the Kunlun fault (a), Karakorum fault (b), and the Altyn Tagh fault (c), showing that a low effective fault friction (b 0.1) is needed to fit the geological slip rates. The site locations and the origin of the geological slip rates are shown in Fig. 1.

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58

A similar fault friction–fault slip rate relation also exists along the Karakorum fault (Fig. 2b). Only for one site near ~34.6°N is a fault friction larger than 0.1 needed to match the geological estimate of 4 ± 1 mm/yr (Brown et al., 2002). Based on the same experiments, we then compare modeled and geological slip rates along the Altyn Tagh fault. In the central portion of the fault, several Quaternary slip rates that are well constrained with radiocarbon and cosmogenic dating of displaced Quaternary landforms − 87°E (Mériaux et al., 2004) and 94°E (Mériaux et al., 2005) although some of these rates have been questioned (Cowgill, 2007). The effective friction–slip rate relation of the Altyn Tagh fault is similar to the one found for the Kunlun and Karakorum faults, showing that an effective fault friction greater than 0.2 predicts slip rates lower than ~ 1.5 mm/yr, significantly smaller than geological rates (Fig. 2c). This suggests that these large-scale active faults sustain a shear stress much smaller than expected from rock mechanics as already proposed for other large faults like the San Andreas fault (Zoback and Beroza, 1993) and the North Anatolian fault (Provost et al., 2003). With an effective fault friction less than 0.08, the modeled slip rate (~ 3– 5 mm/yr) near the eastern end of the fault (~ 96°E) fits the geological rate of 4 ± 2 mm/yr (Meyer et al., 1996); towards the west near 94°E, the modeled slip rate reaches 10–12 mm/yr, less than the geological rate of 20 ± 3 mm/yr, but close to its low bound of 13

53

± 3 mm/yr (Ryerson et al., 2003); further to the west near 87°E, the modeled slip rate increases to ~ 13.3–17.8 mm/yr, again being less than the geological rate of 27 ± 7 mm/yr (Mériaux et al., 2004), but higher than its lower bound of ~ 10 mm/yr (Cowgill, 2007). We plot the modeled slip rates along the entire length of the faults for the effective fault friction of 0.2 (Fig. 3a) and 0.02 (Fig. 3b), respectively. For an effective fault friction of 0.2, modeled slip rates are negligible both for the Altyn Tagh and Kunlun faults (b1.5 mm/yr). An important clue is that the western portion of the Altyn Tagh fault displays a dextral motion for such a friction (Fig. 3a), while geodetic and geologic observations show a sinistral motion (Peltzer et al., 1989; Wright et al., 2004). Modeled slip rate obtained with a fault friction of 0.02 are much higher and the western portion of the Altyn Tagh fault turns to slip with a sinistral motion (Fig. 3b). If we exclude slip rates near the model boundaries because of the fault tip effect, the low friction model leads to slip rates from ~ 8.3 mm/yr to ~ 12.4 mm/yr along the central ~800–1000 km of the Kunlun fault, from ~ 8.6 mm/yr to ~13.3 mm/yr for the Karakorum fault at its central ~ 600–800 km, and from ~ 13.7 mm/yr to ~17.8 mm/yr along the Altyn Tagh fault in its central ~ 1000 km (Fig. 3b). For the Kunlun fault, the modeled slip rate for lower fault friction is consistent with the geological late Quaternary slip rates along its central portion. To the east around ~104°E, the slip rate is decreases gradually as indicated by geological studies (Kirby et al., 2007). The slip rate of the Altyn Tagh fault on its

Fig. 3. Spatial variations of the modeled slip rates along the Altyn Tagh fault, the Kunlun fault and the Karakorum fault with effective frictions of the faults of respectively 0.2 (a) and 0.02 (b).

54

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58

central segment (87°E) is between the lower and upper bounds of geological late Quaternary slip rates (Mériaux et al., 2004; Cowgill, 2007). Toward the two ends of the Altyn Tagh fault, the modeled slip rates decrease gradually, suggesting that the western segment of the Altyn Tagh fault may bear a lower slip rate than previous estimates (Peltzer et al., 1989). 3.2. Strain rate and long-term velocity field

Fig. 4. Modeled strain rate intensity at depth of 10 km, and surface velocity field for fault frictions of 0.2 (a), and 0.02 (b). The strain rate is expressed as the quadratic invariant of the strain rate tensor.

In our model, effective friction largely affects fault slip rate because of the plastic character of the lithosphere. Indeed, a high fault friction allows high deviatoric stress throughout both faults and lithosphere. Such high stress leads the continuum lithosphere to deform at a higher strain rate, thus changing the kinematic balance between localized strain (across faults) and diffusive strain. Conversely, a low friction concentrates the strain on faults and the strain intensity within the lithosphere accordingly decreases. Fig. 4 shows this interplay between fault strength and crustal deformation. With an effective friction of 0.2, the Altyn Tagh and the Kunlun fault slip rates remain small (Figs. 3a and 4a). The deformation is larger in south Tibet than in north Tibet (Fig. 4a) probably due to the specific velocity field along the southern boundary north of the Himalayan arc. Also, one can think that this continuous strain would be lesser if large faults such as the Jiali fault and the Xianshuihe fault in south Tibet have been taken into account as frictional discontinuities. Decreasing the effective friction to 0.02 leads the strain rate in north Tibet and inside the Tarim to decay dramatically (Fig. 4b). However, the strain rate in the south Tibetan plateau remains almost unchanged for high fault friction (Fig. 4a) and low fault friction (Fig. 4b), highlighting again the strong influence of the southern boundary condition. Assigning a low fault friction to the Altyn Tagh fault and the Kunlun fault allows to obtain slip rates in agreement with their geological rates (Fig. 2). This does not mean that the crust surrounding the two faults does not deform as shown by the strain rate patterns of Fig. 4. We analyze the corresponding velocity field on three profiles (Fig. 1), and we compare it to the GPS velocity field in the profile vicinity. Along profiles

Fig. 5. Modeled velocities along three profiles in Fig. 1 with fault frictions of 0.2 (red lines) and 0.02 (cyan lines). To show the difference of the modeled results, GPS velocities observed within ~ 300 km of the profiles are also plotted. WTB, western Tibet; CTB, Central Tibet; ETB, Eastern Tibet; for other abbreviations, see Fig. 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58

A–B and C–D crossing the Altyn Tagh and Kunlun faults, profile-normal velocities (parallel to the fault strike-slip motion) are very sensitive to fault friction (Fig. 5a, c), suggesting that locked (high friction) and unlocked (low friction) fault behavior affects the averaged velocity field over very long distances. On the profile-parallel (compression) directions, the modeled velocity field is less sensitive to fault friction (Fig. 5b, d), meaning that the shortening rate across Tibet cannot be easily used to discriminate among different fault frictions. The effect of the fault friction on north–south velocities is small around the central Tibet (Fig. 5 e), but increasingly affects the east– west velocity component (Fig. 5f). West of ~93°E, the east–west extension rate (~ 8 mm/yr) corresponding to a lower fault friction fits the long-term estimate of ~ 7 mm/yr (Molnar and Deng, 1984), while the higher fault friction leads to a rate of ~ 14 mm/yr having less discrepancy with the GPS rate of ~17 mm/yr (Zhang et al., 2004). However, as both high and low frictions for the Altyn Tagh fault lead to east–west extension of western and central Tibet, this persistent tectonic feature is clearly due to the eastward Indian motion relative to the Pamir (Fig. 1). East of ~ 93°E, the east–west velocity shows ~8 mm/yr compression both for lower and higher fault frictions (Fig. 5f), which may also represent the block rotations (Meade, 2007; Thatcher, 2007), since profile E–F may extend over different geological blocks as assumed by some studies (Chen et al., 2004; Meade, 2007; Thatcher, 2007). 4. Discussion During the last two decades, the debate of the long-term behavior of the Tibetan plateau and the kinematic of large faults has been obscured by the lack of a common mechanical viewpoint. As summarized by Thatcher (2007), the lithosphere can be viewed as two end-member models. One behavior consists of rigid blocks separated by major faults as in the global tectonic plate model (block model). This model allows in principle to accumulate all the motion provided by the boundary conditions on a few faults. Although this model has a kinematical origin, it corresponds to a mechanical view in which weak faults are surrounded by strong lithospheric blocks. Alternatively, continuous strain may also occur in the lithosphere according to a fluid-like behavior of a viscous material (continuum model). In this case, the strain in the brittle crust is distributed on many faults and is therefore close to a continuous behavior. In this view, most of the lithospheric strength is taken by ductile layers in the lower crust and the uppermost mantle. Being too thin to generate significant strength, the upper crust follows passively the overall lithospheric motion (Bourne et al., 1998). The model we use in this paper has rheological properties of both block model and continuum model. First, the use of faults with an a-priori fault strength using an effective friction allows to create a discontinuous motion if the friction is low (block model behavior). Conversely, a high friction will lead the fault to remain inactive, the strain being kept inside the continuum medium (continuum model behavior). At depth, the use of a flow law contributes to a viscous stress which promotes strain diffusion as it occurs in the continuum model. One result of our modeling is that for each value of the effective friction on the Kunlun, the Altyn Tagh and the Karakorum faults, we observe a specific fault–slip rate ratio. If a low friction is used, the maximum Altyn Tagh fault slip rate is ~17.8 mm/yr, compared to ~ 12.4 mm/yr for the Kunlun fault and ~13.3 mm/yr for the Karakorum fault (Fig. 3a). The high friction case leads to slip rates of ~1.3 mm/yr, ~ 1 mm/yr and ~ 3.6 mm/yr respectively for the Altyn Tagh, Kunlun and Karakorum faults (Fig. 3b). Interestingly, the maximum slip rate of the Altyn Tagh fault is ~ 30–50% faster than the corresponding slip rate of the Kunlun fault for all the experiments we made. This is likely to be due to the relative position of these two faults with respect to the boundary condition of southern Tibet. Indeed, the highest rate of the Altyn Tagh fault in our model occurs in its central part at ~87°E west to

55

the end of the Kunlun fault. If one believes that the slip rate ratio observed in our model holds in nature, it is then tempting to use the well constrained Kunlun fault slip rate to infer the Altyn Tagh fault slip rate. Indeed, geologic rates of the Kunlun fault agree well with the geodetic rates, and a maximum slip rate of 10–12 mm/yr seems to be well constrained. Assuming that the Altyn Tagh fault may slip ~30– 50% faster at 87°E than the Kunlun fault, a maximum slip rate of ~ 13– 18 mm/yr is found. Despite the fact that the maximum fault slip rate of the Altyn Tagh fault is a subject of much debate, only the studies of Mériaux et al. (2004) and Cowgill (2007) document this value at about 87°E. The latter study proposes a rate of 7.1–11.7 mm/yr, and the former a rate of 15.1–31.3 mm/yr if extreme values are considered. These two studies are not mutually compatible and only the lowest rate of Mériaux et al. (2004) may be adjusted by our modeling. We therefore propose a value of ~ 15–17 mm/yr for the maximum slip rate of the Altyn Tagh fault. However, our approach does not allow to rule out lower values that would correspond to a slightly higher effective friction of the Altyn Tagh fault. We acknowledge that several model's assumptions may influence the fault slip rate we obtained. One specific point concerns the Tarim motion that does not display a perfect rigid behavior as it is suggested by the GPS velocity field. However, the weak fault model of Fig. 4b leads to a northward motion of the basin at ~10 mm/yr with a regular decrease to the east in agreement with the measured velocity field (Fig. 1). Accounting for a stronger lithosphere beneath the Tarim and introducing the Tien-Shan as a weak zone would probably allow to obtain a rigid block motion for the Tarim as it has been already done in continuum models (England and Molnar, 2005). However, we do not believe that it would change much our model's results as the southern part of the Tarim displays a motion in fair agreement with the observed block motion. Another important point is that we obtain a maximum fault slip rate of 15–17 mm/yr for the Altyn Tagh fault at 87°E, strikingly smaller than the preferred value of ~27 mm/yr given by Mériaux et al., (2004). However, our estimate remains significantly higher than the slip rate provided by the analysis of GPS data using a continuum approach (England and Molnar, 2005) or a block model analysis (Bendick et al., 2000; Wallace et al., 2004; Meade, 2007; Thatcher, 2007) that are within the range of −10 mm/yr. Three lines of evidence could explain this discrepancy: Low slip rates found by the continuum approach (England and Molnar, 2005) are directly linked to the use of a thin viscous sheet model. As England and Molnar quote, most of the velocity field within Tibet can be easily explained with a smooth strain. However, geologic fault slip rates used by these authors in order to obtain the purely continuous velocity field do not include high values of fault slip rate listed in Table 1. Also, the thin viscous sheet model does not allow to distinguish the long-term motion from the present-day motion corresponding to an interseismic period during which the faults are locked. Therefore, these two shortcomings may lead to underestimate the geologic fault slip rate of the Altyn Tagh fault. Contrary to the continuum approach, the block model explicitly uses the interseismic velocity field to reconstruct the long-term slip rate (Meade, 2007). Also, geodetic sites far enough from the fault location should display a motion close to the long-term average (Thatcher, 2007). Both studies of Meade (2007) and Thatcher (2007) propose fault slip rate of the central Altyn Tagh fault in fair agreement with values of respectively 7 and 9 mm/yr. However, examining the spatial GPS coverage used for these two studies reveals that sites constraining the central Tibet motion are few and far between (as quoted by the authors themselves, see for example Fig. 3 of Thatcher, 2007). In fact, no geodetic measurements have been published to date south of the Altyn Tagh fault between ~ 84°E–88°E. Only at ~ 90°E, does a dense GPS profile crosses the Altyn Tagh fault, yielding a geodetic inferred slip rate of 5–13 mm/yr (Bendick et al., 2000; Wallace et al., 2004). Given that the maximum slip rate at ~ 87°E is located 350 km to the west to the GPS profile, a ~5 mm/yr increase of fault slip rate over

56

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58

this distance appears plausible. This increase could in turn be linked to a westward decrease of slip rate of the Kunlun fault as predicted by our modeling (Fig. 3b). Another aspect that may plague the determination of fault slip rate using the block model concept is the way in which interseismic strain is interpretated in order to obtain the long-term motion. As originally proposed by Savage and Burford (1973), interseismic velocity is generally viewed as an elastic strain induced by fault creep at depth. This model corresponds to a screw dislocation in an elastic half-space and generates a surface velocity (v) described by v = v0 arctan (x/d) where x is the distance to the fault, d is the depth of the buried dislocation and v0 is the fault slip rate. Adjusting the locking depth leads for most of continental strike-slip faults to values of 10–20 km, often in agreement with the maximum coseismic depth. Also, this model predicts that interseismic velocity field corresponds to 80% of the long-term velocity at a distance of 3d, i.e., 30–60 km. At a larger distance, the velocity field becomes close to a rigid block motion. In such a model, fault slip rate can be simply determined using the differential velocity between the two blocks. This model prediction appears to be correct for most of large strike-slip intracontinental faults such as the San Andreas fault (Lisowski et al., 1991), the North Anatolian fault (McClusky et al., 2000) and the Dead Sea fault (Reilinger et al., 2006). However, the relation between interseismic and long-term velocity field provided by the Savage and Burford model may not be valid for Tibet as already pointed out by some authors (Zhang et al., 2004; England and Molnar, 2005; Jolivet et al., 2008). For example, the GPS velocity field across the Kunlun fault varies on distances as large as 400–600 km as indicated in Fig. 5c. This large-scale variation could be interpreted as the consequence of a large value of the locking depth d (N ~100 km) in the Savage and Burford model. But this explanation would not be compatible with the small seismogenic thickness of Tibet that is thought to be 10–20 km (Molnar and Cheng, 1983; Peltzer et al., 1999; Jordan and Watts, 2005). Rather, we suggest that an appropriate interseismic strain model of Tibet is closer to a thin elastic plate than a thick elastic lithosphere as in the Savage and Burford model. If we conjecture the behavior of our long-term model during interseismic time, this suggests that the relation between the far-field velocity field and the Tibetan fault slip rate may not be emulated correctly by the Savage and Burford model. Indeed, if the lower crust of Tibet below the seismogenic zone (~ 10–20 km) deforms mainly at low stress by viscous flow (Royden et al., 1997; Shen et al., 2001a,b; Hilley et al., 2005), no elastic screw dislocation below ~ 10–20 km depth of the fault is likely to drive the upper crust. Because of its elastic nature, the Savage and Burford model predicts a unique relation between the far-field velocity field and the fault slip rate. Our mechanical model demonstrates that fault slip rate varies with effective friction for a given far-field velocity field. At low fault friction, a low deviatoric stress is transmitted to the lithosphere, which in turn deforms moderately. Consequently, most of the remote velocity is transmitted to the fault (Fig. 5a, cyan line). At higher friction, a higher deviatoric stress and therefore a higher plastic strain occur in the continuum lithosphere (Fig. 5a, thick red line). In this case, most of the remote velocity damps in the lithosphere and the fault slips at a low slip rate. Clearly, the ability of the crust to plastically deform (i.e., the occurrence of small earthquakes or other evidences of anelastic strain) will make more difficult to assess fault slip rates from interseismic geodetic strain. In order to clarify the relation between the rheological model and the velocity field, we use a simplified tectonic setting corresponding to an infinitely long strike-slip fault as in the Savage and Burford model (Fig. 6). We then consider two endmember models. The first one (Fig. 6a) corresponds to the elastic halfspace driven by fault slip at depth (Savage and Burford, 1973). For such a model, the long-term velocity field appears to be a step function as shown on Fig. 6c while the interseismic strain corresponds to the arctan curve (Fig. 6d). We now consider an alternative model provided

Fig. 6. Seismic cycle models and velocity fields. (a) Elastic half-space (Savage and Burford model). (b) thin elastoplastic plate (this paper). (c) long-term velocity field associated with elastic half-space and thin elastoplastic plate. (d) interseismic velocity associated to the same models.

by a thin elastoplastic plate above a low viscosity ductile crust (Fig. 6b) as used in our mechanical modeling. For such a case, the long-term velocity field is similar to the one given by the Savage and Burford model if the fault friction is low enough to prevent the seismogenic crust to deform (meaning that no earthquakes should occur except on the main fault). The fault slip rate is then maximum and equal to v. A friction increase leads to an increase of the anelastic strain in the crust, therefore a slip rate decrease. The key feature of the thin elastoplastic plate model is that different long- term velocity fields (i.e. low friction and high slip rate or high friction and low slip rate) could have the same interseismic strain signature. Indeed, the interseismic strain of the model in Fig. 6b always corresponds to a linear trend if we consider that the fault is locked in the seismogenic zone and that postseismic strain becomes negligible after a short fraction of the interseismic time (meaning that the deviatoric stress in the ductile layer becomes much smaller than the one in the seismogenic crust). To summarize, if the rheological model of Tibet is formed by a thin elastoplastic plate (the seismogenic crust) above a low viscosity channel (the ductile middle and lower crust) (Royden et al., 1997; Shen et al., 2001a,b), then the long-term slip rate of major faults like the Altyn Tagh, Kunlun and Karakorum faults cannot be calculated from the interseismic surface velocity field. This interpretation thus questions the validity of determining the long-term velocity of the Altyn Tagh fault based solely on interseismic velocity field using an elastic half-space and more generally the relation between interseismic strain and geological fault motion (Chéry, 2008). In the same vein, the GPS-based claim that geological deformation in Tibet is mainly continuous (Zhang et al., 2004) could be incorrect as a

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58

continuous interseismic velocity field can be compatible with a discontinuous, long-term velocity field. 5. Conclusion Loaded with the present-day far-field velocity, our model for Tibet predicts maximum sinistral slip rates of the Altyn Tagh fault and the Kunlun fault on their central segments of about 13.7– 17.8 mm/yr and 8.3–12.4 mm/yr, respectively. This suggests that geological slip rates of the Altyn Tagh faults higher than 18 mm/yr are not compatible with the far-field GPS velocity field of the India–Eurasia collision given our current understanding of the rheology of Tibet. Model results also show that across central Tibet (~ 84°E–95°E) from the Altyn Tagh fault to the Himalayan arc, north–south shortening and east–west extension rates reach ~ 10– 12 mm/yr and ~ 8–10 mm/y, respectively. As for other large intracontinental faults like the San Andreas fault and the North Anatolian fault, low effective friction coefficient (b0.1) must be used for these large faults in order to obtain slip rates in agreement with geological rates. An important clue is that low and high fault slip rates given by our model may have similar interseismic deformation patterns. This suggests that low values (5–10 mm/yr) for geodetically-based fault slip rate rates of Tibetan faults could be unreliable. We point out that these incorrect fault slip rates estimates are not due to geodetic measurements themselves but rather to the way they are extrapolated in time in order to provide long-term slip rates. Indeed, it could be flawed to use a screw dislocation embedded in a thick elastic lithosphere to compute slip rates of large Tibetan faults. A more appropriate rheological model is likely to be a thin elastic or elastoplastic plate lying on top of a viscoelastic lithosphere below. Acknowledgements J. He is grateful to the French CNRS that supported this study with providing a visiting researcher position. This work was also supported by National Science Foundation of China (NSFC) NO.40774050. The original manuscript has been largely improved by three anonymous reviewers and the review of J. Van der Woerd who provided thoughtful comments. Most of the figures were prepared with GMT software (Wessel and Smith, 1995). References Avouac, J.P., Tapponnier, P., 1993. Kinematic model of active deformation in central Asia. Geophys. Res. Lett. 20, 895–898. Bendick, R., Bilham, R., Freymueller, J., Larson, K., Yin, G., 2000. Geodetic evidence for a low slip rate in the Altyn Tagh fault system. Nature 404, 69–72. Bettinelli, P., Avouac, J.P., Flouzat, M., Jouanne, F., Bollinger, L., et al., 2006. Plate motion of India and interseismic strain in the Nepal Himalaya from GPS and DORIS measurements. J. Geodesy 80, 567–589. Bird, P., Kong, X., 1994. Computer simulations of California tectonics confirm very low strength of major faults. Geol. Soc. Amer. Bull. 106, 159–174. Bourne, S.J., England, P.C., et al., 1998. The motion of crustal blocks driven by flow of the lower lithosphere: implications for slip rates of faults in the south island of New Zealand and Southern California. Nature 391, 655–659. Brown, E., Bendick, R., Bourles, D., Gaur, V., Molnar, P., et al., 2002. Slip rates of the Karakorum fault, Ladakh, India, determined using cosmic ray exposure dating of debris flows and moraines. J. Geophys. Res. 107, 2192. doi:10.1029/2000JB000100. Byerlee, J.D., 1967. Frictional characteristics of granite under high confining pressure. J. Geophys. Res. 72, 3639–3648. Chen, Q., Freymueller, J.T., Wang, Q., Yang, Z., Xu, C., Liu, J., 2004. A deforming block model for the present-day tectonics of Tibet. J. Geophys. Res. 109, B01403. doi:10.1029/2002JB002151. Chéry, J., Zoback, M.D., 2001. A integrated mechanical model of the San Andreas fault in central and northern California. J. Geophys. Res. 106, 22051–22066. Chéry, J., 2008. Geodetic strain across the San Andreas fault reflects elastic plate thickness variations (rather than fault slip rate). Earth and planet. Sci. Lett 269, 351–364. Chevalier, M.L., Ryerson, F.J., Tapponnier, P., Finkel, R.C., Van Der Woerd, J., Li, H., Liu, Q., 2005. Slip-rate measurements on the Karakorum fault may imply secular variations in fault motion. Science 307, 411–414.

57

Cowgill, E., 2007. Impact of riser reconstructions on estimation of secular variation in rates of strike-slip faulting: revisiting the Cherchen River site along the Altyn Tagh Fault, NW China. Earth Planet. Sci. Lett. 254, 239–255. England, P., Houseman, G., 1986. Finite strain calculations of continental deformation: 2. Comparison with the India–Asia collision zone. J. Geophys. Res. 91, 3664–3676. England, P., Molnar, P., 1997. The field of crustal velocity in Asia calculated from Quaternary rates of slip on faults. Geophys. J. Inter. 130, 551–582. England, P., Molnar, P., 2005. Late Quaternary to decadal velocity fields in Asia. J. Geophys. Res. 110. doi:10.1029/2004JB003541. Gaudemer, Y., Jaupart, C., et al., 1988. Thermal control on post orogenic extension in collision belts. Earth and Planet. Sci. Lett. 89, 48–62. Hassani, R., Jongmans, D., et al., 1997. Study of plate deformation and stress in subduction processes using two-dimensional numerical models. J. Geophys. Res. 102, 17951–17965. Hilley, G.E., Burgmann, R., Zhang, P., Molnar, P., 2005. Bayesian inference of plastosphere viscosities near the Kunlun fault, northern Tibet. Geophys. Res. Lett. 32, L01302. doi:10.1029/2004GL021658. Holt, W.E., Chamot-Rooke, N., Le Pichon, X., Haines, A.J., et al., 2000. Velocity field in Asia inferred from Quaternary fault slip rates and Global Positioning System observations. J. Geophys. Res. 105, 19185–19209. Ismail-Zadeh, A., Le Mouel, J.L., Soloviev, A., Tapponnier, P., Vorovieva, I., 2007. Numerical modeling of crustal block-and-fault dynamics, earthquakes and slip rates in the Tibet–Himalayan region. Earth Planet. Sci. Letts. 258. doi:10.1016/j. epsl.2007.04.006. Jolivet, R., Cattin, R., et al., 2008. Thin-plate modeling of interseismic deformation and asymmetry across the Altyn Tagh fault zone. Geoph. Res. Lett. 35, L02309. Jordan, T.A., Watts, A.B., 2005. Gravity anomalies, flexure and the elastic thickness structure of the India–Eurasia collisional system. Earth Planet. Sci. Lett. 236, 737–750. Kirby, E., Harkins, N., Wang, E.Q., Shi, X.H., Fan, C., Burbank, D., 2007. Slip rate gradients along the eastern Kunlun fault. Tectonics 26. doi:10.1029/2006TC002033. Lacassin, R., Valli, F., Arnaud, N., Leloup, P., et al., 2004. Large-scale geometry, offset and kinematic evolution of the Karakorum fault, Tibet. Earth Planet. Sci. Lett. 219, 255–269. Larson, K.M., Burgmann, R., Bilham, R., Freymueller, J.T., 1999. Kinematics of the India– Eurasia collision zone from GPS measurements. J. Geophys. Res. 104, 1077–1093. Lavé, J., Avouac, J.P., 2000. Active folding of fluvial terraces across the Siwaliks Hills, Himalayas of central Nepal. J. Geophys. Res. 105, 5735–5770. Li, H., Van der Woerd, J., Tapponnier, P., Klinger, Y., Qi, X., Yang, J., Zhu, Y., 2005. Slip rate on the Kunlun fault at Hongshui Gou, and recurrence time of great events comparable to the 14/11/2001, Mw ~ 7.9 Kokoxili earthquake. Earth Planet. Sci. Lett. 237, 285–299. Lisowski, M., Savage, J.C., Prescott, W.H., 1991. The velocity field along the San Andreas fault in central and southern California. J. Geophys. Res. 96, 8369–8389. McClusky, S., Balassanian, S., Barka, A., Demir, C., et al., 2000. Global Positioning System constrains on plate kinematics and dynamics in the eastern Mediterranean and Caucasus. J. Geophys. Res. 105, 5695–5719. Meade, B.J., 2007. Present-day kinematics at the India–Asia collision zone. Geology 35, 81–84. Meade, B.J., Hager, B.H., 2005. Block models of crustal motion in southern California constrained by GPS measurements. J. Geophys. Res. 110. doi:10.1029/ 2004JB003209. Mériaux, A., Ryerson, F.J., Tapponnier, P., Van der Woerd, J., et al., 2004. Rapid slip along the central Altyn Tagh Fault: morphochronologic evidence from the Cherchen He and Sulamu Tagh. J. Geophys. Res. 109, B06401. doi:10.1029/2003JB002558. Mériaux, A.S., Tapponnier, P., et al., 2005. The Aksai segment of the northern Altyn–Tagh fault: tectonic geomorphology, landscape evolution, and Holocene slip rate. J. Geoph. Res. 110 (B04404). doi:10.1029/2004JB003210. Meyer, B., Tapponnier, P., Gaudemer, Y., Peltzer, G., Shunmin, G., Zhitai, C., 1996. Rate of left lateral movement along the easternmost segment of the Altyn Tagh fault, east of 96oE (China). Geophys. J. Inter. 124, 29–44. Molnar, P., Tapponnier, P., 1978. Active tectonics of Tibet. J. Geophys. Res. 83, 5361–5375. Molnar, P., Cheng, W., 1983. Focal depths and fault solutions of earthquakes under the Tibetan plateau. J. Geophys. Res. 88, 1180–1196. Molnar, P., Deng, Q., 1984. Faulting associated with large earthquakes and the average rate of deformation in central and eastern Asia. J. Geophys. Res. 89, 6203–6227. Peltzer, G., Tapponnier, P., Armijo, R., 1989. Magnitude of Late Quaternary left-lateral displacement along the north edge of Tibet. Science 246, 1285–1289. Peltzer, G., Crampe, F., King, G., 1999. Evidence of nonlinear elasticity of the crust from the Mw7.6 Manyi (Tibet) earthquake. Science 286, 272–276. Phillips, R., Parrish, R., Searle, M., 2004. Age constraints on ductile deformation and long-term slip rates along the Karakoram fault zone, Ladakh. Earth Planet. Sci. Lett. 226, 305–319. Provost, A.S., Chéry, J., Hassani, R., 2003. 3D mechanical modeling of the GPS velocity field along the North Anatolian fault. Earth Planet. Sci. Lett. 209, 361–377. Reigber, C., Michel, G.W., Galas, R., Angermann, D., Klotz, J., et al., 2001. New space geodetic constraints on the distribution of deformation in Central Asia. Earth Planet. Sci. Lett. 191, 157–165. Reilinger, R., McClusky, S., Vernant, P., Lawrence, S., et al., 2006. GPS constraints on continental deformation in the Africa–Arabia–Eurasia continental collision zone and implications for the dynamics of plate interactions. J. Geophys. Res. 111, B05411. doi:10.1029/2005JB004051. Royden, L.H., Burchfiel, B.C., King, R.W., Wang, E., et al., 1997. Surface deformation and lower crustal flow in eastern Tibet. Science 276, 788–790. Ryerson, J., Meriaux, A., Tapponnier, P., Van der Woerd, J., et al., 2003. Northeastwards decrease in the late Pleistocene–Holocene slip rate of the Altyn Tagh fault (China). Geophys. Res. Abstracts 5, 08070.

58

J. He, J. Chéry / Earth and Planetary Science Letters 274 (2008) 50–58

Savage, J.C., Burford, R.O., 1973. Geodetic determination of relative plate motion in central California. J. Geophys. Res. 78, 832–845. Scholz, C.H., 1996. Faults without friction? Nature 381, 556–557. Sella, G.F., Dixon, T.H., Mao, A., 2002. REVEL: a model for recent plate velocities from space geodesy. J. Geophys. Res. 107. doi:10.1029/2000JB000033. Shen, F., Royden, L.H., Burchfiel, B.C., 2001a. Large-scale crustal deformation of the Tibetan plateau. J. Geophys. Res. 106, 6793–6816. Shen, Z., Wang, M., Li, Y., Jackson, D., Yin, A., Dong, D., Peng, F., 2001b. Crustal deformation along the Altyn Tagh fault system, western China, from GPS. J. Geophys. Res. 106, 30607–30621. Tapponnier, P., Molnar, P., 1977. Active faulting and tectonics in China. J. Geophys. Res. 82, 2905–2930. Tapponnier, P., Xu, Z., Roger, F., Meyer, B., Arnaud, N., Wittlinger, G., Yang, Y., 2001. Oblique stepwise rise and growth of the Tibetan plateau. Science 294, 1671–1677. Thatcher, W., 2007. Microplate model for the present-day deformation of Tibet. J. Geophys. Res. 112, B01401. doi:10.1029/2005JB004244. Van der Woerd, J., Ryerson, J., Tapponnier, P., Gaudemer, Y., Finkel, R., et al., 1998. Holocene left-slip rate determined by cosmogenic surface dating on the Xidatan segment of the Kunlun Fault (Qinghai, China). Geology 26, 695–698. Van der Woerd, J., Tapponnier, P., Ryerson, F.J., Meriaux, A.S., Meyer, B., et al., 2002. Uniform postglacial slip-rate along the central 600 km of the Kunlun Fault (Tibet), from 26Al, 10Be, and 14C dating of riser offsets, and climatic origin of the regional morphology. Geophys. J. Inter. 148, 356–388. Vernant, P., Chéry, J., 2006. Low fault friction in Iran implies localized deformation for the Arabia–Eurasia collision zone. Earth Planet. Sci. Lett. 246, 197–206. Wallace, K., Yin, G., Bilham, R., 2004. Inescapable slow slip on the Altyn Tagh fault. Geophys. Res. Lett. 31, L09613. doi:10.1029/2004GL019724.

Wang, K., Dragert, H., et al., 1994. Finite element study of uplift strain across Vancouver Island. J. Struct. Geol.Can. 31, 1510–1522. Wang, Q., Zhang, P., Freymueller, J.T., Bilham, R., et al., 2001. Present-day crustal deformation in China constrained by Global Positioning System measurements. Science 294, 574–577. Washburn, Z., Arrowsmith, J.R., Forman, S.L., Cowgill, E., et al., 2001. Late Holocene earthquake history of the central Altyn Tagh Fault, China. Geology 29, 1051–1054. Wessel, P., Smith, W.H.F., 1995. New version of the generic mapping tools released. EOS Trans., AGU F76, 329. Wittlinger, G., Tapponnier, P., Poupinet, G., Jiang, M., et al., 1998. Tomographic evidence for localized lithospheric shear along the Altyn Tagh fault. Science 282, 74–76. Wright, T., Parsons, B., England, P., Fielding, E., 2004. InSar observations of low slip rates on the major faults of western Tibet. Science 305, 236–239. Zhang, P., Shen, Z., Wang, M., Gan, W., Burgmann, R., Molnar, P., et al., 2004. Continuous deformation of the Tibetan plateau from global positioning system data. Geology 32, 809–812. Zhang, P.Z., Molnar, P., et al., 2007. Late Quaternary and present-day rates of slip along the Altyn Tagh Fault, northern margin of the Tibetan plateau. Tectonics 26. doi:10.1029/2006TC002014. Zoback, M.D., Zoback, M.L., et al., 1987. New evidence on the state of stress of the San Andreas fault system. Science 238, 1105–1111. Zoback, M.D., Beroza, G., 1993. Evidence for near-frictionless faulting in the 1989(M6.9) Loma Prieta, California earthquake and its aftershocks. Geology 21, 181–185.