Large-scale crustal deformation of the Tibetan Plateau

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106, NO. B4, PAGES , APRIL 10, 2001 Large-scale crustal deformation of the Tibetan Plateau Feng Shen Department of Geology, Peking University, Beijing, China Leigh H. Royden and B. Clark Burchfiel Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology Cambridge, Massachusetts Abstract. The topography, velocity, and strain fields calculated from a three-dimensional Newtonian viscous model for large-scale crustal deformation are generally in good agreement with results from geological, geodetic and earthquake studies in and around the Tibetan Plateau, provided that the model rheology incorporates a weak zone within the deep crust beneath the plateau (equivalent to a viscosity of 10 TM Pa s within a 250-mthick channel or 1018 Pa s within a 15-km-thick channel). Model studies and observations show a plateau at -- 5 km elevation with steep topographic gradients across the southern and northern plateau margins and more gentle gradients across the southeastern and northeastern margins. Rapid shortening strain is concentrated along the lower portions of the northern and southern plateau margins (at rates mm/yr). Model results show north-south shortening (---10 mm/yr) in reasonable agreement with GPS data (5-8 mm/yr of north-south shortening across the northern two thirds of the plateau) and east-west stretching (10-15 mm/yr) across the eastern half of the high plateau, in reasonable agreement with seismic, geologic, and GPS data. Upper crustal material moves eastward from the plateau proper into a lobe of elevated topography that extends to the south and east. Clockwise rotation of material around the east Himalayan syntaxis (at rates up to mm/yr) occurs partly as a result of dextral shear between Indian and Asian mantle at depth and partly as a result of gravitational spreading from the high plateau to the south and east. There is little difference in model surface deformation for assumptions of moderately weak or extremely weak lower crust, except in southern and northern Tibet where margin-perpendicular extension occurs only for the case of an extremely weak lower crust. Our results suggesthat the Tibetan Plateau is likely to have gone through a twostage development. The first stage produced a long, narrow, high orogen whose height may have been comparable to the modern plateau. The second stage produced a plateau that grew progressively to the north and east. East-west stretching, eastward plateau growth and dextral rotation around the east Himalayan syntaxis probably did not begin until well into the second stage of plateau growth, perhaps becoming significant after m.y. of convergence. 1. Introduction Increasingly, earth scientists are coming to recognize that deformation and topography are inextricably linked. For example, the large-scale topographic expression of actively deforming regions is strongly controlled by the crustal rheology and the deformation mechanisms that operate at local to regional scales. Conversely, topographic gradients averaged over distances longer than the flexural length scale of the lithosphere also appear to exert a first-order control on crustal deformation because of the large lateral pressure gradients that they induce within the crust. The second point has been illustrated for several actively deforming regions, including the Himalayan-Tibetan region, Formerly at Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachu- setts. Copyright 2001 by the American Geophysical Union. Paper number 2000JB /01/2000JB by studies that compare gradients in potential energy (which are closely linked to topographic gradients) with active deformation rates inferred from earthquake data. These studies conclude that the modern topography of this region is capable of explaining most of the active crustal deformation using a vertically averaged rheology to describe the deformation of the entire lithosphere [Holt et al., 1991; Holt and Haines, 1993; Holt, 2000; England and Molnar, 1997]. However, such models of lithospheric deformation have been less successful in explaining how applied forces act on the lithosphere to produce the topography and morphology of the modern Tibetan Plateau. For example, early thin sheet models were able to produce broadly uplifted regions that had some first-order similarities with the Tibetan Plateau, but these models have generally been unable to reproduce smaller-scale topographic and deformational features of the plateau [England and McKenzie, 1982; England and Houseman, 1986, 1988]. Other two-dimensional models that examine how depth-dependent crustal rheology controls the morphology of mountain belts have shown that the low topographic relief of the high Tibetan Plateau is consistent with the presence of weak crust beneath

2 6794 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 5 o 100 I ø 1 5 o --40ø ß DHS1 East Tarim Basin CSD4 ß MZZ4 GLMIß LI -35 ø -- MDX1 SBPIß : 35 \ P2 ß East Qinling BTX4ß TJP2 ß JSP4 Sichuan _ 30 ø ß LHASA Basin THZ4 SLW2 ß SWB1 East Himalayan Syntaxis THZ4 _25 ø 3sc2 ø LSC1 [ 25 ø ø Figure 1. Map showing major active faults in eastern Tibet and surrounding regions and locations of GPS stations [modified from Chen et al., 2000]. I 105 ø the plateau and stronger crust beneath the plateau margins sional convergence between India and Asia has been accom- [Willett al., 1993; Royden, 1996]. This paper investigates how modated by thrusting of Indian continental lithosphere bethe three-dimensional topography, morphology and strain par- neath Asia, by deformation of Asian lithosphere, and by lateral titioning of the Himalayan-Tibetan region may be related to extrusion of Asian lithosphere, although there is little agreeand controlled by differences in rheology between the upper ment on the relative importance of these mechanisms [e.g., and lower crust. Dewey et al., 1988; Barazangi and Ni, 1982; Zhao and Morgan, 1985; Houseman and England, 1996; Avouac and Tapponnier, 2. The Himalayan-Tibetan Region 1993]. Earthquakepicenters and reflection seismic profiling The Tibetan Plateau is the largest and highest plateau on show clear evidence for under thrusting of India beneath the Earth and is the result of the collision and postcollisional Himalaya [Molnar and Chen, 1978; Nelson et al., 1996; Hauck et convergence of India and Asia at 50 Ma (Figures 1 and al., 1998], while paleomagnetic [Achache et al., 1984] and geo- 2 and Plate 1; see recent review by Rowley [ 996]). Postcolli- logic data [Coward et al., 1988; Tapponnier et al., 1990] show

3 .. - SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU ø 25 ø 7 øo 75 ø 80 ø 85 ø 90 ø 95 ø 00 ø 't '000 3 f ) TOPOGRAPHY Plate 1. Topography of Tibet and surrounding regions. White lines show location of profiles in Figure 3. 40' 35' 30' 25' 20 ø [10 ø [t5 ø 100 ø 105' 110 ø Figure 2. GPS velocities for Tibet and surrounding regions relative to southeast China [from Chen et al., 2000]. Station names are given in Figure 1.

4 6796 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU that some of the convergence between India and Asia has been accommodated by shortening localized within Asian crust. Geologic structures that lie north of the Indian subcontinent, including those of the Himalaya, the central Tibetan Plateau, and mountain ranges to the north, suggesthat deformation in this area has been largely the result of north-south convergence, consistent with recent GPS results [Larson et al., 1999; Freymuller et al., 1996; King et al., 1997; Chen et al., 2000]. East-west extension of the central plateau may have begun in middle Miocene time [Coleman and Hodges, 1995] with an estimated mm/yr of extension now occurring across the eastern half of the plateau [Armijo et al., 1986; Larson et al., 1999]. East of the east Himalayan syntaxis, east-west structures of the plateau curve to the southeast. Young geologic structures developed in this region and GPS data indicate that this region of the eastern plateau forms a broad zone of right-lateral shear between the (relatively) northward moving Tibetan Plateau to the west and southeast China to the east [Dewey et al., 1988; King et al., 1997; Wang and Burchfiel, 1997; Chen et al., 2000]. Geologic studies, earthquake data, and recently collected GPS data indicate that for Pliocene-Quaternary time, the eastern margin of the Tibetan Plateau can be divided into three distinct subregions [Burchfiel et al., 1996; Royden et al., 1997; King e! al., 1997; Chen e! al., 2000]. In northeastern Tibet (north of Xian at ---35øN), approximately margin-perpendicular shortening occurs along thrust faults at the plateau margins and within the Qilian Shan and Qaidam basin region, with shortening rates of---13 mm/yr [Chen e! al., 2000]. South of Xian and north of the Xianshuihe-Xiaojiang fault system ( øN in the Longmen Shan region), there is little to no young shortening deformation across the plateau margin despite an increase in elevation of more than 4 km from the foreland to the plateau [Burchfiel et al., 1996]. Here, crustal material contained within the plateau is nearly stationary with respect to southeast China [King et al., 1997; Chen et al., 2000]. South of the Xianshuihe- Xiaojiang fault system (Yunnan region south of 30øN) and east of the east Himalayan syntaxis, crustal material of the plateau moves southeastward to southwestward at up to mm/yr with respect to southeast China [King et al., 1997; Chen et al., 2000] as crustal material of the southeastern plateau rotates clockwise around the syntaxis [Wang et al., 1998]. The abrupt changes in topographic elevation across the plateau margin (Figures 2 and 3) and the abrupt transitions in deformational style and rate between subregions of the eastern plateau (Figure 1) suggesthat partitioning of strain at horizontal scales < km is controlled by heterogeneity and anisotropy within the crust of the plateau and its foreland. However, it is not clear if crustal inhomogeneities are important in influencing the deformation at greater spatial scales or if they function only as local controls that produce abrupt transitions and second-order differences in deformation style. Many of the faults active within Tibet today appear to have a history that goes back only as far as Pliocene to late Miocene time [Burchfiel and Royden, 1991; Mdtivier et al., 1998; Wang et al., 1998]. Prior to Miocene time the history of much of the plateau remains largely unknown. In addition, data to indicate the time(s) of uplift of the plateau and the distribution of uplift in space and time are largely lacking, with proposed timing of uplift ranging from late Eocene to Oligocene time (southern and central Tibet) to Pliocene time (northeasternmost Tibet), with some authors suggesting that a lower and less extensive plateau may have been present prior to the India-Eurasia col- o loo Topography Figure 3. Topographic profiles across the Himalaya and southern Tibetan Plateau (locations in Figure 2). Topography on each profile is mean topography averaged across a 200 km wide swath. Smooth lines show model topography after 40 m.y. of convergence at 50 mm/yr (model 1, Table 1). lision [Murphy et al., 1997] or that rapid uplift of most of the plateau is Pliocene-Quaternary in age [Che, 1986; Pan et al., 1990; Li, 1996]. In section 3 we describe a quantitative approach that we have developed to model the evolution of orogenic systems in three dimensions. Using this approach, we seek to understand how much of the topography, active deformation, and deformation history of the Tibetan Plateau and surrounding regions can be described as a first-orderesult of continental convergence. 3. Modeling of Deformation and Topography 3.1. Computational Method Analytic equations that govern the large-scale threedimensional deformation of a viscous crust are derived by Royden [1996]. In this approach, an idealized, incompressible Newtonjan-viscous crust is assumed to consist of two layers, an upper layer with a uniform viscosity (/ o) and a lower layer with viscosity decreasing exponentially with depth (/ oe- / ), where z - 0 corresponds to the interface between the upper and lower layers (Figure 4). In order to provide tractable solutions the viscosity of the crust is assumed to depend only on depth below the surface. Although we will not repeat the derivation of Royden [1996], in essence, her approach consists of expressing the flow velocity (u, v, w) within the crust in terms of a stream function,, where (u, w)= v x,p and substitution of ß into the Stokes equation with depthdependent viscosity tz(z) to yield 11, 74 tl x -}- 2( Ozl ) ( OzV2 ttx) + (Ozz)(Ozz%- Oxx'Px- %%)= o + + (Oz)Oz,Pz] = 0, (2) A B D

5 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 6797 z=-lz VISCOSITY b asal velocity ß u mmayr "ASIA" velocity 50 mm/yr basal velocity "INDIA" Figure 4. (a) Viscosity versus depth for model crust used in this paper (/x, viscosity;/xo, viscosity of upper (uniform viscosity) crust; b, maximum thickness of upper (uniform viscosity) crust; h o, initial thickness of lower crust; h max, maximum thickness of lower crust; a, viscosity decay coefficient for lower crust). (b) Map view of mantle "plates" and assigned velocities for "Indian" and "Asian" mantle and the intervening mantle suture (models i and 2, Table 1). Indian mantle is 2000 km in width and moves northward relative to Asian mantle at 50 mm/yr. Mantle suture between India and Asia moves northward relative to Asian mantle at 10 mm/yr. Side boundary conditions (at infinity, dashed line) require zero topographic elevation and crustal velocity that is depth-independent and equal to the velocity of the underlying mantle. V(X, y, Z) : V i -- (b + a)a(e z/ - 1)(4Oyyvi + OxxV i q- 3Oxybli) +(OyT)(pcg/lxo)[(e / - 1)a(b - a) + aze / ] O _< z _< h, where/,/i is the flow velocity in the x-direction evaluated at z = O, vi is the flow velocity in the y direction evaluated at z = 0, T is topographic elevation, Pc is crustal density, # is gravitational acceleration, and Ox denotes differentiation with respect to x, etc. Crustal flow is determined at each time step using the functional representation for flow with depth as given by (3) and (4), coupled with two-dimensional numerical solution for u i, vi, and T using a finite difference scheme applied to (3) and (4) and implemented over a two-dimensional surface grid with node positions that remain fixed through time. Basal boundary conditions can be applied either as velocities u and v at the Moho (at z = h) or by differentiating and integrating (3) and (4) appropriately to rewrite in terms of basal shear stress. The net crustal flux in the x and y directions at each node can then be obtained by integrating (3) and (4) with respect to z. The change in crustal thickness with respect to time and the z component of velocity, w, are Oh Ifi x) h(y) d-b Ot Ox u(x, y, z) dz Oy v(x y z) dz w = -Ox u(x, y, z) dz - Oy v(x, y, z) dz. b b (4b) (6) where x is the x component of, etc. If the crust is assumed to be Airy compensated with a stress-free upper boundary, then crustal flow is uniquely determined by the viscosity-depth profile of the crust and the velocity (or shear stress) boundary conditions applied at the Moho and at the side boundaries of the model. For an upper layer with uniform viscosity/x o and a lower layer with exponentially decreasing viscosity (/Xo e-z/") this yields flow velocities in the x and y directions: bl(x, y, Z) -- bl i q- (OxT)(pc#/IXo) [(z + b) 2 - b (3a) -b _< z _< O, u(x, y, z) = ui- (b + a)a(e / - 1)(4OxxU i + OyyU i + 3OxyVi) +(Oxr)(pcg/lxo)[(e / - 1)a(b- a) + aze / ] V(X, y, Z) ---' V i q- (OyT)(pcg/Ixo) [(z 1 + b )2- b 2] O <_z <_h, (4a) -b _< z _< O, By using the functional representations for u and v in (5), crustal thickening can be numerically computed over a twodimensional surface grid without solving explicitly for veloci- ties within the crust (except for u i and vi), although velocity as a function of depth can easily be computed at any time from (3), (4), and (6). Side boundary conditions are applied at infinity where we require that crustal velocity be independent of depth and equal to the Moho velocity Rheological Considerations In this paper we specify velocity at the Moho (z = h) and assume that the mantle lithosphere beneath Tibet behaves in a "plate-like" fashion, where each mantle plate moves with uniform and constant velocity (Table 1). Relative motions be- (31t een mantle plates are assumed to occur across narrow man- tle sutures, typically less than several tens of kilometers in width. This is equivalent to prescribing a mantle lithosphere that is very much stronger than the crust and in which defor- mation is localized along the plate boundaries (but allowing the mantle to flex easily to produce Airy compensation of the Table 1. Parameters for Modeling Indian Mantle Mantle Suture Velocity a Velocity a Viscosity Decay Upper Crustal Upper Crustal Initial Crustal Viscous (Northward), (Northward), Coefficient c, Viscosity/ 0, Thickness b, Thickness b + h0, Model mm/yr mm/yr km X 1021 Pa s km km awith respect to Asia.

6 6798 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU Table 2. Parameters for Two-Dimensional Profiles Viscous Case Indian Mantle Mantle Suture Velocity a Velocity a Viscosity Decay Upper Crustal Upper Crustal Initial Crustal (Northward), (Northward), Coefficient a, Viscosity/z0, Thickness b, Thickness b + h 0, mm/yr mm/yr km x 102 Pa s km km whole crust awith respect to Asia. crust). Thus, although the crust is treated as a linearly viscous medium, there is a strong nonlinearity built into the model in the form of the prescribed velocity conditions at the top of the mantle. To first order, the behavior of such a viscous crust, underlain by a plate-like mantle, should be approximately analogous to that of a more rheologically realistic lithosphere. For example, Brace and Kohlstedt [1980] divided the continentalithosphere into three regions: a relatively strong upper crust that fails by faulting and obeys Byerlee's law, a relatively weak ductile middle to lower crust (present only where temperatures are high enough to induce ductile flow) whose properties may be governed by steady state creep of quartz, and a (usually) strong upper mantle whose strength is governed by the laboratorydetermined properties of dry olivine [Goetze and Evans, 1979]. The obvious shortcomings of the purely viscous rheology assumed here are the lack of an explicit temperature dependence in the ductilely deforming regions of the lower crust, the fact that viscous model results may produce slow upper crustal strain at stresses too low to be consistent with frictional sliding in a purely brittle regime, and the lack of distributed deformation in the mantle lithosphere. We note that the strength of crustal material undergoing ductile deformation is critically dependent on temperature, shear stress, rock type, and water content, of which we have little knowledge within the middle to lower crust, and is extrapolated over many orders of magnitude in strain rate from laboratory data. Moreover, weakening of the crust at high temperatures may not be due solely to thermal softening but may also be related to production of small amounts of partial melt due directly to elevated temperatures in the crust or resulting from metamorphic reactions in the deep crust. If so, then crustal weakening might occur abruptly at some threshold temperature that depends critically on lithology. For these reasons we believe that computation of effective viscosities based on model values of temperature are highly uncertain for the deeper crust. Specifying crustal viscosities in the relatively ad hoc manner of this paper is, we believe, no less uncertain than computing effective viscosities from model temperatures, and has the virtue of simplicity in that the "rheology" of the model crust is straightforward and its effects easy to interpret. In general, however, it is probably correct that thicker crust experiences higher maximum temperatures than does thinner crust. This occurs partly because for a fixed geotherm, temperatures near the base of a thick crust will be higher than those near the base of a thin crust. If radiogenic heat production occurs throughout much of the deeper crust, as would be expected in crust subjected to recent tectonic thickening, then geotherms may also be much higher for thick crust because crustal heat production produces a large contribution to crustal temperatures and because maximum temperatures due to crustal heat production increase as the square of the thickness of the heat producing layer. Thus we have chosen to represent the crust as a uniformly viscous material except where the crust becomes very thick. Then the crust may develop a low-viscosity zone. As we shall see in section 3.3, the general topography of the Tibetan Plateau will require that the Tibetan crust be relatively strong until it reaches a thickness of around km, but that crust which is thicker than this value must contain a crustal layer which is very much weaker than thinner crust. In a sense, we are using the large-scale topography of Tibet to calibrate our viscosities rather than computation of viscosity from model temperatures. We stress that in assuming a Newtonian viscosity for the crust our intention is not to replicate the deformation history of the Himalayan-Tibetan region but rather to understand the basic crustal processes that control the evolution of this region at large to intermediate scales and to understand how features like topography, surface velocity, strain partitioning, and finite strain result from and can be used to constrain the relative strength of upper and lower crust and the degree of coupling between crust and mantle Coupled and Decoupled Crustal Flow The viscosity-depth profile of the crust plays an important role in continental deformation and is a dominant factor in controlling the mode of crustal deformation. For example, Royden [1996] has shown that viscous crustal deformation can be characterized by two end-member flow modes: coupled flow and decoupled flow. Where the lower crust is of similar strength (has a similar viscosity) to the upper crust, crustal flow is strongly coupled to mantle motions by shear stresses transmitted through the strong lower crust. For convergence at moderate or fast rates, crustal shortening takes place in a narrow zone above the mantle suture (at early times) or at the foot of the mountain belt (at later times). The topography of the orogenic belt that develops is approximately triangular in cross section (assuming no erosion, Figure 5a and Table 2). This represents the coupled flow mode between upper crust and mantle because large shear stresses can be supported within the strong lower crust and total shear stress transmission from mantle to upper crust can occur across a narrow zone. Where the lower crust is very much weaker (has a lower viscosity) than the upper crust, crustal flow is weakly coupled to mantle motions because large shear stresses cannot be transmitted through the weak lower crust. Thus the total shear stress transmission from mantle to upper crust is spread across a wide zone within the lower crust; upper crustal shortening takes place across a wide zone even in the early stages of convergence (Figure 5c). Large topographic gradients, which correspond to large lateral pressure gradients, cannot develop because even gentle gradients induce rapid crustal

7 _ SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 6799 N-S section at 20 m.y. i i i i i, o I I I I I I I km5øø N-S section at 20 m.y. i i i i I (a) I I I I I I -5oo 0 km5øø N-S section at 20 m.y. i i i i i i 2500 (b) -20 E -4o -6O -80 I I I I I I I I km Figure 5. Examples of different mountain belt styles (topography and Moho depth are plotted) after 20 m.y. of convergence at a rate of 50 mm/yr (parameters given in Table 2). (a) case 1, strong lower crust; (b) case 2, strong lower crust for crust thinner than 55 km, otherwise weak lower crust below 55 km depth; (c) case 3, weak lower crust below 25 km depth. Mantle suture is located at x = 200 km (north is to the left) (c) flow within the weak lower crust, and the maximum topographic relief remains low. For extremely weak lower crust, upper crustal deformation can become so weakly coupled to motions of the underlying mantle that the upper crust is effectively decoupled from the mantle on all but the longest length scales. Development of a plateau requires that the lower and midcrust beneath the topographically steep margins of the plateau be strong (high viscosity) in order to support the large horizontal pressure gradients that are present beneath the steep marginal slopes of the plateau and that the lower or midcrust be weak (low viscosity) beneath the plateau proper in order to inhibit the development of steep regional topographic gradients on the plateau (Figure 5b). This implies that the plateau margins will be strongly coupled to the underlying mantle, while the upper crust of the high plateau will be weakly coupled to the underlying mantle. When the lower or midcrust is so weak that crustal defor- mation becomes very strongly decoupled from mantle motions, crustal deformation within the weak crustal layer can occur as "channel flow," where flow velocities within the weak channel may be much faster than and/or in a different direction from the velocities at the base of the crust and at the surface (Figure 6). When channel flow occurs beneath a plateau, it disappears abruptly at the edge of the plateau, at the transition from weak to strong lower crust. Although channel flow in the lower crust is not essential for development of a plateau, it indicates a very weak lower crust and upper crustal deformation that is essentially decoupled from local motions of the underlying mantle. In each of these cases it is important to emphasize that the local behavior (velocity) of the mantle lithosphere is mainly important for surface deformation where the deep crust is strong and has a sufficiently high viscosity to transmit large shear stresses from the upper mantle to the upper crust. Where the deep crust becomes very weak (has a low viscosity), the local behavior of the upper mantle is not important because little shear stress can be transmitted upward through the weak crust. Instead, upper crustal deformation above zones of weak crust is controlled largely by horizontal transmission of stress through the upper crust and produces deformation only over large horizontal length scales. We illustrate this point later in the paper by showing that the model topography and deformation fields for "Tibet" do not change very much if the mantle lithosphere beneath the weak crust parts of Tibet is considered (1) to be "Indian" and move north- ward at 50 mm/yr relative to Asia or (2) "Asian" and fixed relative to Asia.

8 6800 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU al a2 o flow velocity (a) 0 0 flow velocity Figure 6. Schematic diagram showing how crustal flow velocity varies as a function of depth with the development of a weak crustal layer at the base (a) or middle part (b) of the crust. Outside of the shaded region the crustal viscosity is strong and uniform. Flow velocities are shown for assumed viscosity of shaded region being the same as the rest of the crust (a and b ); significantly less than the rest of the crust but not weak enough to accommodate channel flow (a 2 and b2); and very much weaker than the rest of the crust such that channel flow occurs in the weak layer (a3 and b3). Boundary conditions are zero flow velocity at the base of the crust and a stress-free upper surface. 4. Application to the Tibetan Plateau: Model Results 4.1. Two-Dimensional Constraints on Crustal Properties In this paper we assume a two-plate mantle (Figure 4) with the velocity at the top of the mantle being uniform throughout each plate. Although the behavior of the mantle lithosphere beneath the high plateau is largely unknown, the velocity of the mantle lithosphere immediately outside of the region of deformation that surrounds the plateau is probably similar to the modern surface velocities. These velocities, which can be equated with the motion of India relative to Eurasia, are fairly well constrained over the past 40 m.y., at -50 mm/yr. It is also likely that the mantle velocities beneath the margins of the plateau are similar to those adjacent to the foreland. Here we assume that Indian mantle lithosphere moves northward with respect to Asian mantle at 50 mm/yr, with a northward velocity of the convergent mantle "suture" that varies between 10 and 40 mm/yr (Table 1). For simplicity, we also assume that the component of mantle velocity parallel to the convergent suture (eastward) is zero; for a discussion of the effects of suture- Crustal deformation within the India-Eurasia convergent boundary is fundamentally three-dimensional, especially along the eastern margin of the plateau and near the eastern Himalayan syntaxis. However, before moving to a full threedimensional analysis of plateau deformation it will be useful to use some simple two-dimensional results, applied to northsouth cross section(s) across the central Tibetan Plateau, in order to constrain the various crustal parameters that characterize the current state of the plateau. We can then use these constraints to make predictions about the nature of the deformation along the eastern plateau margin and about the development of the plateau through time. There are three rheologic variables in the equations that constrain the two-dimensional evolution of the model viscous crust (Figure 4): (1) the thickness b (2) the viscosity/ of the parallel mantle motion, see Royden [1996]. upper uniform-viscosity layer (upper crust); and (3) the decay The initial crustal thicknesses are not well known (e.g., see coefficient a, which describes the exponential decay of viscosity discussions of Murphy et al. [1997] and Zhang et al. [1998]), but with depth within the lower layer (lower crust). The only other much of the area of Tibet experienced nonmarine to shallow free variables are the initial crustal thickness (ho + b, where marine depositional conditions around the time of collision, h o is the initial thickness of the lower crustal layer; wherever h suggesting an initial crustal thickness of perhaps km (in is negative, we assume that the crust has a uniform viscosity this paper we use an initial crustal thickness of 30 km throughthroughout) and the velocity imposed at the base of the crust, out). This leaves only the three rheological parameters,/x o, a, which has an x and y component. Thus the number of free and b, which can be constrained by requiring the resulting variables in the model is small. model plateau to have a height and topographic gradients on

9 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU b f / -- ' mantll suture ß , km 600- mantl ture,, - ' 400- o 200- I: _ ß krn (0) 00_. _ m tle suture o 200-1, ' ' (c) Figure 7. Two-dimensional model topography after 40 m.y. of convergence. Dots show location of underlying mantle suture for each profile; mantle left of the mantle suture moves to the right at 50 mm/yr; mantle to the right of the mantle suture is ed. Dark lines shows results from case 1 (Table 2; for comparison to obse ations see Figure 3). (a) Results for va ing only the m imum thickness of upper, uniform viscosi, crust (b = 45, 55 and 60 km for o = 1 x 10 : Pa s and a = 1 km); (b) results for va ing only the viscosi of the upper, uniform viscosi, crust ( o = 1 x 10 gø, 5 x 10 gø, 1 x 10 g, 2.5 x 10 g Pa s for b = 55 km and a = 1 km); (c) results for va ing only the viscosi decay coefficient for lower crust (a = 0.01, 0.25, 1.0, 2.0, and 5.0 km for o = 1 x 10 g Pa s and b = 55 km). the plateau and plateau margins that are generally consistent Assuming that a is -<1 km, b is constrained to be between 50 with observations from the Himalayan-Tibetan region. Figure 3 shows several north-south profiles across the Himalayan-Tibetan region, showing that the maximum plateau and 60 km. Values for any one of these three parameters that fall much outside the ranges described here will not produce a plateau with the same general topographic signature as the height is around km, the slopes on the southern margin Tibetan Plateau. of the plateau (in the Himalayas) are _ 0.01, and the average slopes across the plateau are less than (less than half a kilometer over 1000 km). Assuming that the convergence rate and initial crustal thickness can be fixed at 50 mm/yr and 30 km, respectively, Figures 7 and 8 show how slope For the remainder of this paper we will use b - 55 km, /a, o = 102 Pa s, and a = 1 km or a = 0.25 km (Table 1, models 1 and 3). As we shall show, these two different values of a produce generally similar patterns of crustal deformation at the surface but have very different implications for the and plateau height depend on o, a, and b after 40 m.y. of behavior of the lower crust. convergence. (Where not specified, the default values of the parameters used in Figures 7 and 8 are o = 102 Pa s, a = 1 km, and b = 55 km.) At the margins of the model plateau, where the viscosity of the crust is uniform with depth and equal to o, the topo- (Note that in this paper we have chosen to allow viscosity to vary only as a function of depth in order to preserve the simplicity of the analytic solution given by Royden [1996]. For this reason, lateral variation of viscosity is not allowed except insofar as differences in crustal thickness produce different graphic slope is effectively independent of b and a but strongly viscosities at the base of the crust. Because plateaus form only dependent on o. Comparing Figures 3, 7, and 8 suggests that o should fall somewhere in the range of 0.5 x 102 and 3 x when the weakest crust beneath the plateau is very much weaker than that beneath the marginal slopes, the weakest part 1021 Pa s. Conversely, the topographic slope developed across of the model crust beneath high plateaus is forced to be within the top of the model plateau is highly sensitive to the exponential decay of viscosity with depth, a. For o = 102 Pa s, a must be < 1 km in order to produce no more than m of regional elevation difference across the high plateau. The maximum height of the plateau depends strongly on b and on a. the lowermost crust. If lateral variation of crustal viscosity were allowed, then the weak crustal layer beneath the plateau could be located at any depth. Regardless of where the weak crustal layer is located, at a fixed convergence rate the topographic slope developed above the plateau is approximately linearly

10 6802 SHEN ET AL.' CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU x frontal slope frontal slope o o ß 0 0.5! plateau slope x lo upper crustal thickness b (krn) Figure 8. Graphical constraints on the viscosity decay coefficient for lower crust (a = 0.01 to 5.0 km), plotted against observed (a) frontal and (b) plateau topographic slopes (see Figures 2 and 3 for cros sections); (c) the viscosity of the upper, uniform viscosity, crust (/x o = 1020 to 1022 Pa s) plotted against observed frontal topographic slope; and (d) dependence of plateau height on the maximum thickness of the upper, uniformviscosity crust (b = 45 to 65 km) and the viscosity decay coefficient (a) (contour lines denoting maximum plateau height, in km). Dark lines with shading show observed range for the Himalaya and the Tibetan Plateau. Except as denoted on the plot, all parameters are the same as those given in Table 1, model 1. proportional to the total integrated flux within the weak crustal layer, which is in turn proportional to the ratio (c3// ), where c is the thickness of the weak crustalayer and/ is its viscosity. For a viscosity profile with an exponential decay constant a, the effective thickness of the weak crustal layer is approximately c = a, same computations for grid spacings from 10 to 100 km; results were effectively independent of spacing except for the expected smoothing of topography at the larger grid spacing. The time step used for the implicit finite difference computations was 0.01 m.y., which gave the same results as for time steps of m.y. and the effective viscosity of this layer is the viscosity at the base For the first 5 to 10 m.y. after the initiation of convergence, of the crust,/ = i o e-h/'. Thus plateau geometries very similar to crustal deformation produces a long, linear mountain belt that those shown in Figure 7 could be produced by using a uniform is approximately triangular in cross section (erosion is not viscosity/ o everywher except within a weak crustalayer that is considered in these models). After 5 m.y. of convergence the present only beneath the high part of the plateau, such that mountain belt is 4.5 km high and km in width; a zone of (c3//x) = (a3eh/ //Xo). Also, the lateral transition from strong to low viscosity has begun to develop in the lower crust. By weak crust beneath the edge of the high plateau must occur across 10 m.y. this zone of low-viscosity crust has become wider and a zone that is no wider than the transition zone from steep to flat thicker, by which time the mountains have reached their maxtopographic gradients across the edge of the plateau. Thus an imum height of 5.3 km with a width of km. abrupt transition in viscosity will yield a well-defined plateau edge, This early stage of deformation can be thought of as the while a gradual transition in viscosity will yield a gradual transition from steep to flat topographic slopes.) "linear mountain belt" stage, which begins with the beginning of continental collision and ends with development of a signif Model Geometry and Evolution of the Tibetan Plateau icant low viscosity zone in the lower crust. During the linear Figure 9 and Plate 2 show the geometric evolution of a model "Tibetan" plateau in three dimensions, plotted relative to a stable "Eurasia"(for a = 1 km and assuming that the convergent mantle suture between "India" and "Eurasia" moves northward at 10 mm/yr relative to Eurasia, Figure 4 and mountain belt stage the mountain belt becomes higher and wider with time, with its maximum height being controlled mainly by the maximum thickness of the strong crustal layer. During this time, there is little to no motion of material parallel to the mantle suture (in an east-west direction) and little Table 1). Model results were computed over a horizontal grid rotation of crustal rocks about a vertical axis. with a spacing between grid points of 25 km. We performed the Throughout most of this stage, crustal flow is strongly cou-

11 SHEN ET AL.' CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 6803 I I s:tolomoi s o omoi

12 6804 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 10 S I I I I I o m.y. alpha = 1.0 I I I I s lo N o -lo o 40 m.y. alpha = 1.Okm looo I I I I Figure 10a. North-south cross-sections from 3-D model (taken at x = 0 on Figures 9 and 12) showing position of passive crustal markers originally at 15 and 27 km depth, after 10 and 40 m.y. of convergence. Results are from Figure 9, model 1 in Table 1, with a moderately weak lower crustal layer. pied to mantle motions. At the base of the crust, crustal material is carried toward the suture by movement of the mantle, while gravitational body forces carry upper crustal material downhill and away from the mantle suture. Although the net thickness of the crust is increasing everywhere, a north-south cross section through the center of the model plateau at 10 m.y. shows that above the mantle suture, crustal thinning occurs in the upper part of the crust due to north-south extension and crustal thickening occurs in the lower part of the crust due to north-south shortening (Figure 10). The maximum rates of crustal shortening at the surface occur at the foot of mountains where the second spatial derivative of topography is most positive. After a significant low-viscosity zone develops in the lower crust, a steep-sided flat-topped plateau begins to form. This stage of deformation can be thought of as the "plateau" stage, where the plateau increases in width without a significant increase in height. The average topographic slope across the high part of the plateau depends mainly on the thickness and rheologic properties of the weakest crustal layer. The maximum elevation occurs at the end of the linear mountain belt stage and the beginning of the plateau stage. The maximum elevation of the plateau decreaseslightly throughouthe plateau stage, largely because of the effects of lateral (east-west) crustal flow within the plateau and lateral growth of the plateau. Throughout the plateau stage of development, the central portion of the plateau moves northward at a velocity that is approximately half the northward velocity of the Indian plate. East-west motions of crustal material are mainly lacking during the early stages of plateau development, but as the area of the plateau increases, the portion of the plateau that experiences an east-west component of surface motions also increases. Over the same time period, rotation of material within the southeastern and southwestern portions of the plateau becomes more pronounced (Figure 9 and Plate 2). For example, after 10 m.y. of convergence, significant clockwise rotation of crust occurs only within a very small area near the southeastern corner of the plateau (and similarly in the southwest). However, by 40 m.y., a much larger area within the southeastern portion of the plateau shows clockwise rotation by more than 90 ø. Similarly, there is little east-west stretching of the plateau before -20 m.y., but by 40 m.y. the east-west stretching across much of the plateau is -50% (with the largest magnitudes occurring near the surface expression of the crustal suture). As the area of high topography grows, the plateau spreads by flow of crustal material from areas of high topography to areas of low topography. For example, a region of high topography develops southeast of the eastern "Himalayan" syntaxis (and similarly in the west). Here, surface motions are eastward and southward by up to -10 mm/yr, in contrast to northward velocities of mm/yr modeled for the central part of the plateau. At high elevations the southeastern corner of the plateau undergoes rapid clockwise rotation around the syntaxis. This rapid clockwise rotation is largely the surface expression of dextral shear along the north-south trending "transform" fault within the underlying mantle (at x = 1000 km). Below elevations of m, the dextral shear in the mantle is expressed at the surface by a narrowly defined northsouth trending zone of right-lateral shear at the surface, but at high elevations this zone of dextral shear in the crust broadens to encompass a region -500 km wide. This broadening of the surface deformation zone is due to the presence of the lowviscosity layer beneath the high plateau, which acts to decrease the maximum shear stress that can be transmitted upward through the crust and instead distributes the transmitted stress across a wide area. Thus the clockwise rotation within the high plateau is partly a manifestation of distributed dextral shear

13 SHEN ET AL.' CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 6805 lo i i i i i o- -lo - -2o - -3o o - 10 m.y. alpha = 0.25km -60 -looo I 2000 lo o s I -lo - -2o - -3o -4o- -5o - 40 m.y. alpha = 0.25km -60 -looo Figure 10b. Same as Figure 10a except results are from Figure 12, model 2 in Table 1, with a very weak lower crustal layer. above a north-south trending zone of strike-slip and partly a gravitational spreading of the high plateau toward lower regions to the east and south. Throughout the plateau stage of deformation, crustal flow is strongly coupled to mantle motions beneath the lower slopes of the plateau but only weakly coupled to mantle motions beneath the high plateau. Beneath the lower slopes of the plateau, lower crustal material is carried toward the plateau by movement of the mantle. However, at the surface, gravitational body forces carry upper crustal material away from the edge of the plateau, resulting in minor amounts of upper crustal thinning at the northern and southern edges of the plateau. Although the net deformation of the crust is thickening everywhere, the north-south cross section through the model plateau at 40 m.y. shows that above the edges of the plateau a small amount of crustal thinning occurs in the upper part of the crust while crustal thickening occurs in the underlying lower crust (Figure 10a; note that the narrow region of thinned upper crust in the central plateau is related to crustal thinning that occurre during the first 10 m.y. of convergence). In order to characterize the active deformation fields of the model plateau after 40 m.y. of convergence we computed surface strain and rotation fields from the velocity field using the technique described by Dong [1993]. Strain computations involve assuming a uniform strain field at each location and solving for the velocity gradient tensor. We then calculated strain and rotation rates for the various subregions defined in our numerical model (Figures 11a and 11b). The principal components of the strain field show that different parts of the model plateau undergo strain at different rates and in different directions. Within the central plateau the strain field is fairly uniform, showing slow north-south shortening (at -5 x l0-6 s - ) and east-west stretching (also at ---5 x S-1). Along the lower margins of the plateau the axes of maximum com- pressive strain are aligned approximately perpendicular to the trend of the margin and to the regional topographic contours. These compressive strain rates are a maximum along the northern and southern plateau margins and intermediate along the northeastern (and northwestern) parts of the plateau margin. In contrast, compressional strain rates are very much slower along the eastern and southeastern portions of the plateau margin. In addition to the slow east-west stretching within the central plateau, only very minor amounts of stretching occur near the northern and southern margins of the high plateau (near the 5000 km contour in Figure 11a). Within the eastern part of the plateau, somewhat more rapid stretching occurs in a northeastsouthwesto north-south direction, with progressive clockwise rotation of the extensional strain axes from the central plateau to its eastern edge. Large extensional strains occur only near the location of the eastern Himalayan syntaxis, where extensional strain rates are of the order 3 x 10 -ls s -1 above 3000 m elevation (near x = 1000 kin). Below 3000 m elevation, northwest trending extensional strain axes accompany northeast trending compressional strain axes of approximately equal magnitude, consistent with rapid right-slip along north-south trending faults. Between and 5000 m elevation, eastsoutheast directed extensional strain is accompanied only by minor amounts of compressional strain, suggesting rapid thinning of upper crustal rocks in this well localized region near the syntaxis. Figure lib shows the instantaneous rotation field (after 40 m.y. of convergence) relative to south China. Clockwise rotation rates in excess of lø/m.y. occur over a large portion of southeastern Tibet, confined mainly to elevations above 5000 m. The maximum rates of rotation exceed 6ø/m.y. near the eastern syntaxis proper, at elevations between 2000 and 4000 m. Before comparing these results to geodetic and geologic

14 6806 SHEN ET AL.' CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU / / alpha=l.0 (km) x x x ;000, km E-07/yr (a) OO E-08/yr (2.85ø/m.y) Figure 11. Model strain rates (showing principle axes of the strain rate tensors) and rotation rates after 40 m.y. of convergence. Rates are instantaneous, computed at the surface. (a, b) Results correspond to Figure 9 and Plate 2, model 1 in Table 1, with a moderately weak lower crustal layer; (c, d) results correspond to Figure 12 and Plate 3, model 2 in Table 1, with a very weak lower crustal layer. (b) observations within the Tibetan region, we briefly discuss the sensitivity of these model results to the strength of the lower (or weakest part of the) crust and to assumptions about the rate of motion of the mantle beneath the high plateau Dependence on lower crustal strength. Whenever the lower crust is sufficiently weak, surface deformation will be largely decoupled from motions within the underlying mantle, at least at short length scales. However, when the lower crust becomes very weak, flow within the lower crust occurs within a weak crustal channel. This channel flow can occur in a direc- tion different from and even opposite to the direction of motion in the underlying mantle or at the surface. This can be

15 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 6807 / ' alpha=0.25 (km),/ /,/ /, ' / /,/ t O0 km E-07/yr (c) E-08/yr (2.85ø/m.y) Figure 11. (continued) 1800 illustrated by computing model results using the same parameters as before, but using a km, so that the strength of the lower crust falls off much more rapidly with increasing crustal thickness. Figure 12 and Plate 3 show the topography, surface velocity pattern and cumulative strain field after 40 m.y. of convergence for a = 0.25 km. The minimum viscosity beneath the plateau is x 10 TM Pa s at the base of a lower crustal channel effectively 250 m thick. This is equivalent to a viscosity of 10 8 Pa s in a channel 15 km thick, which might seem more physically realistic. However, we note that if weakening occurs due to the presence of small amounts of partial melt at high temperatures, the effective thickness of the weak crustal layer at any time might be extremely small. In any case, model results depend only on the net flux of material in the channel, which goes as (c3//x), where c is channel thickness and/x is channel

16 6808 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU i ] I I 0 I -500 I i [ 0-40 m.y., alpha=0.25km kilometers looo 15oo O ß Plate 3. Model topography through time for the case of a very weak lower crust beneath the plateau with cumulative surface deformation (mesh originally with 100 x 100 km grid spacing). White lines show position of surface suture between Indian and Asian crust, and dark lines show position of mantle suture between India and Asia. All parameters are for model 2, Table 1; basel velocity boundary conditions are as shown in Figure 4b. viscosity. Thus the model does not distinguish between different viscosity structures for the lower crust if they produce the same value for (c3/kt). Comparison of topography, surface velocities and strain field for a = 1.0 km and a = 0.25 km shows qualitatively similar results for the two cases except for the presence of north-south margin-perpendicular extension in the a = 0.25 km case. In this case, well localized, north-south directed extensional strains occur along the northern and southern plateau edges above 4000 m elevation, at strain rates of -- 3 x 10 -is s -l. The rate of margin-perpendicular extension at the plateau edge decreases southeastward from the northern Tibetan margin and is effectively absent in southeastern Tibet, east of the Himalayan syntaxis. Thus the main difference between the two cases (a = 1 km and a = 0.25 km) that can be observed from surface motions and deformation is the presence or absence of margin-perpendicular extension in northern and southern Tibet. Comparison of north-south cross sections through the central plateau shows that for the case of the weaker lower crust (a = 0.25 km), upper crustal material being incorporated into the plateau by thrusting and shortening at the base of the plateau margin subsequently undergoes -- 30% extension as it passes across the high edge of the plateau (and over the transition from strong to weak lower crust, Figure 10b) ! I 40 m.y., alpha=0.25km _ i )oo 'f Is œ z 1 z, I s z i I i kilometers Figure 12. Model topography and instantaneousurface velocities corresponding to Plate 3 (very weak lower crust beneath the plateau, model 2, Table 1). For reference, India moves 50 mm/yr to the north.

17 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU OO 1500 lo00 o,,,,,, m.y. i!! i kilometers 6O9O -'l Plate 4. Model topography through time for the case of a moderately weak lower crust beneath the plateau and where the mantle suture moves northward at 40 mm/yr with respect to Asia; cumulative surface deformation (mesh originally with 100 x 100 km grid spacing). White lines show position of surface suture between Indian and Asian crust, and dark lines show position of mantle suture between India and Asia. All parameters are for model 3, Table 1. Closely related to the magnitude of extensional deformation along the plateau edge is the presence or absence of channel flow within the lower crust. Figure 13 shows the velocities of lower crustal flow within the weakest part of the crust (measured at a distance a above the base of the crust). For the case of the weaker lower crust (a = 0.25 km), lower crustal material is carried by channel flow away from the central plateau and toward its edges. Channel flow terminates abruptly at the edge of the plateau, where the lower crust changes from weak (beneath the plateau) to strong (beneath the plateau margins). Upwelling of lower crust beneath the plateau edge creates significanthickening of the lower crust in concert with marginperpendicular extension of the upper crust at the plateau edge. In the case of a stronger lower crust, a = 1.0 km, both channel flow and margin-perpendicular extension are largely lacking Dependence on mantle velocities beneath the high plateau. We can examine the sensitivity of results to the assumed velocity of the mantle beneath the high parts of the plateau by increasing the northward velocity of the mantle "suture" from 10 to 40 mm/yr. Geologically, this could correspond to southward subduction of Asian mantle lithosphere, to shortening and thickening of Asian mantle lithosphere north of the suture, or to indentation of a weak Asian mantle lithosphere by a more rigid Indian mantle. Figure 14 and Plate 4 show model plateau topography, instantaneousurface velocity field and cumulative surface strain under the assumption that the mantle suture has moved northward with respect to Eurasia at 40 mm/yr (Table 1). All other parameters are the same as those used in Figure 9 and Plate 2. Qualitatively, the topography, surface velocity field, and cumulative surface strain rates are fairly insensitive to the motion of the mantle suture with respec to Eurasia. The most obvious difference between the two cases is the location of the mantle suture beneath the plateau: For a mantle suture velocity of 10 mm/yr the mantle suture is located beneath the southern part of the plateau (at position y = 400 km, Figure 9 and Plate 2), while for a mantle suture velocity of 40 mm/yr the mantle suture is located beneath the northern part of the plateau (aty = 1600 km, Figure 14 and Plate 4). Thus in the first instance, most of the high plateau is underlain by mantle lithosphere that is fixed with respect to Asia, while in the second instance most of the high plateau is underlain by mantle lithosphere that moves northward at 50 mm/yr with respect to Asia. Although reality is probably somewhere in between these two extreme end-members, these results indicate that the deformation field and plateau topography are relatively insensitive to the details of mantle deformation beneath the high, weak portions of the plateau and indicate that a broad diffuse zone of mantle convergence would produce similar results at the surface. Hence it is probably impossible to determine much about the nature and location of the mantle interaction zone beneath Tibet from observations of surface ve- locity, deformation history, or topography. 5. Comparison of Model Results With Observations The model results presented in section 4 show a good correlation with a variety of different observations from Tibet and the surrounding regions. In particular, it is probably best to compare the model results to observations from the eastern half of the plateau because deformation of the northwestern part of the plateau appears to have been more affected by lateral differences in crustal strength within the foreland. For example, the Tarim basin is less deformed than the adjacent Tien Shan and Tibetan Plateau (Figures 1 and 2 and Plate 1), suggesting that it is underlain by a relatively strong lithosphere, although geophysical studies of the basin have been interpreted to indicate that it is either strong [Grand and Helm-

18 6810 SHEN ET AL.' CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU OO kilometers 1 ooo (a) 40 m.y. alpha=0.25km / _ kilometers (b) Figure 13. Instantaneous flow velocities in the lower crust (arrows) computed at a height a above the crust-mantle interface. (a) Results correspond to Figure 9 and Plate 2, model 1, with a moderately weak lower crustal layer. Arrow in upper right-hand corner denotes 50 mm/yr; (b) results correspond Figure 12 and Plate 3, model 2, with a very weak lower crustal layer. Arrow in upper right-hand corner denotes 500 mm/yr. Note scale difference in velocities in Figures 13a and 13b. berger, 1985] or weak [Roecker et al., 1993]. Nevertheless, in a qualitative sense, many of the model results appear to be compatible with observations taken from the whole plateau region. Model topography after 40 m.y. of convergence is qualitatively similar to the overall topography of the Tibetan Plateau and surrounding regions (compare Figures 2, 3, and 9 and Plates 1 and 2) with a region of high topography extending eastward beyond the projection of the north-south trending dextral shear zone that separates the northward moving Indian plate from the Asian plate. East of this dextral shear zone a lobe of elevated topography extends south and east from the plateau proper, with elevations that decrease gradually from plateau elevations in the northwest to foreland elevations in the south and east. Regional slopes across this topographic lobe are much gentler than across the northern and southern margins of the plateau. Direct comparison of model surface velocities with GPS data is slightly problematic because the model supposes that the mantle is stationary beneath the entire foreland region outside of the plateau. In contrast, GPS results show that the regions north and east of the Tibetan Plateau are not stationary relative to one another (Figures 1 and 2 and Plate 1) as the stations north of the plateau (DHS1 and HCY1) move north at mm/yr relative to stations in southeast China (CHDU and SLW2). Thus the "foreland" region is also subjecto deforma- tion [King et al., 1997; Chen et al., 2000]. Below we compare model results to GPS data viewed in a frame of reference that is stationary with respecto the eastern foreland of the plateau in order to best image the rotations of the southeastern plateau around the east Himalayan syntaxis. We can also compare surface strain rates inferred from GPS data and from young geological structures that accommodate active deformation with the surface strain field computed directly from the model velocities (computed on a grid with a 25-km interval between grid points but shown only at 200 km

19 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU I I 40 m.y m kilometers Figure 14. Model topography and instantaneousurface velocities corresponding to Plate 3 (moderately weak lower crust beneath the plateau with northward suture motion at 40 mm/yr, model 3, Table 1). For reference, India moves 50 mm/yr to the north. intervals, Figure 11). Last, our model results can be compared with studies of earthquake focal mechanism in the region of the eastern Himalayan syntaxis [Holt et al., 1991; Holt and Haines, 1993; Holt, 2000; Molnar and Deng, 1984] Crustal Shortening: Plateau Margins and High Plateau Model results indicate -20 mm/yr of north-south shortening across the southern margin of the plateau, concentrated mainly at low elevations at the foot of the plateau. This is similar to estimates of mm/yr shortening across the Himalayan thrust front from studies of seismicity and migration rates for the Ganges foreland basin [Molnar and Deng, 1984; Lyon Caen and Molnar, 1985; Holt and Haines, 1993] and GPS studies across the Himalaya in Nepal [Bilham et al., 1997]. Within the east-central plateau, observed and model velocities show north-northeastward motion at rates of mm/yr relative to southeast China (22 mm/yr measured at LHAS [Larson et al., 1999; Chen et al., 2000]). Slow north-south to northnortheast shortening is distributed across the high plateau at model rates of -10 mm/yr across the entire plateau and observed rates of -6-8 mm/yr for the northern two thirds of the plateau (LHAS to GLM1, DQD4, and XRH1). Marginperpendicular shortening is concentrated along the northern to northeastern plateau margin at model rates of mm/yr and observed rates of 9-12 mm/yr (GLM1 to DHS1 and CSD4). The observed left-lateral strike-slip motion along the Altyn Tagh fault is not predicted in the model and probably results from preexisting lithospheric anisotropy along the southern margin of the Tarim basin. Moving southeastward around the plateau margin, marginperpendicularates of shortening decrease from model rates of -20 mm/yr on the northern plateau margin to -10 mm/yr where the eastern plateau margin trends north-south, and even slower rates to the south. GPS data also show a decrease in margin-perpendicular shortening rates but with an abrupt transition from rapid shortening along the northeastern margin (9-12 mm/yr) to a nearly complete absence of marginperpendicular shortening along the eastern and southeastern plateau margins (south of the latitude of Xian [King et al., 1997]). Geologic data are consistent with the GPS results, as shortening structures of late Cenozoic age are generally absent or of small magnitude south along the plateau margin south of Xian at 35øN [Burchfiel et al., 1996; Wang et al., 1998]. Most probably, many of these differences between model results and observations along the eastern plateau margin result from our assumption of a completely viscous model crust versus the reality of brittle behavior for upper crustal material. For example, at low stresses a viscous crust will continue to deform at slow strain rates, whereas deformation within a brittle crust may be inhibited below some critical stress level. Thus, if a brittle upper crustal layer were added to the model that inhibits deformation for stress differences <5 MPa (equivalent to strain rates <1.5 x 10 - s s-l), the model results would probably be similar to the observed deformation along the eastern plateau margin, dropping abruptly to zero in regions of low stress Clockwise Rotations in Eastern Tibet Eastward from the central plateau, model velocity vectors are rotated clockwise so that toward the east the northward component of velocity decreases and the eastward component increases. At a location -100 km north of the east Himalayan syntaxis, model velocities are -12 mm/yr to the east (relative to southeast China), while at a location -500 km north of the syntaxis model velocities are -20 mm/yr to the northeast. Geodetically observed motions are similar: 9 mm/yr to the east at station BMZ1 and 19 mm/yr to the east-northeast at station BTX4. Particularly striking is the clockwise rotation of upper crustal material around the Himalayan syntaxis, with observed velocities to the southeast, south and southwest, relative to southeast China, at rates of 7-13 mm/yr (at stations THZ4, DLH3, SXD3, TAC3, and SZS2). (An anomalously high value of 17 mm/yr at BHC2 appears to be the result of an earthquake that occurred in 1996 near this station between GPS campaigns.) Model velocities in the same general region are to the southeast and south at 7-10 mm/yr. (It is noteworthy that GPS velocity vectors rotate clockwise around the eastern Himalayan

20 6812 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU syntaxis until they trend southwest or even west-southwest in the southernmost part of the plateau (e.g., stations OLZ3 and QLQ1), while the model velocities are rotated only to a southward trend in the same general area. We suspect that the westward component in the observed vectors is probably reeast Himalayan syntaxis. This extension is related to the transition from motion along the well-defined north trending rightslip fault zone, which accommodates northward motion of India, to crustal motions within the broad zone of clockwise rotation, and to dextral shear that accommodates the northlated to active eastward subduction and possible rollback of ward motion of the Tibetan Plateau relative to southeast this part of the Indian plate beneath the Indo-Burman ranges China. Field observations indicate that rapid unroofing of deep that lie to the west and southwest of the Sagaing fault in Figure crustal material has occurred at both the western and eastern 1 [Guzman-Speziale and Ni, 1996], inducing slow westward syntaxes [Zeitler et al., 1993; Burg et al., 1998]. Although extenmotion of crust located east of this subduction boundary. (This sional structures have been described from the area immedizone of probable slow mantle convergence was not included in the model configuration, thus accounting for the lack of a westward component in the model velocities. In our opinion this discrepancy between observed and model motions is a second-order effect that could be eliminated by prescribing somewhat more complex mantle velocities within the model.) ately north of the western Himalayan syntaxis (Nanga Parbat region [Hubbard et al., 1995]), they have not been recognized in the poorly explored area that lies immediately north of the east Himalayan syntaxis (Namche Barwa region). Most workers in these regions have favored compressional deformation accompanied by erosion to exhume these rocks [e.g., Schneider et al., The area of clockwise rotation of crust in southeastern Tibet 1999; Burg et al., 1998; Burg and Podladchikov, 1999]. Nevercorresponds geologically to a region of left-slip faults that form approximately circular arcs around an approximate pole located near the east Himalayan syntaxis. Here, numerous leftslip faults appear to have accommodated clockwise rotation for at least the past 2-4 m.y. and possibly the past 6-8 m.y. (Faults include the Ganzi, Xianshuihe-Xiaojiang, Litang, Zhongdian, and Dien Bien Phu fault zones [Wang et al., 1998]. Geological theless, localized east-west extension occurring near the Himalayan syntaxe seems to be a fundamental feature of the model in the development of the Tibetan Plateau, and we suggest that it may be found to play a role in accommodating rotation of upper crustal material around the syntaxis and in the recent rapid unroofing of deep crustal material near both syntaxes. Another important type of extensional deformation has relations also indicate that clockwise rotation occurred here at been observed within the Tibetan region; north-south marginearlier times but must have been accommodated along different faults [Wang and Burchfiel, 1997]). Although the details of the observed strain field in this area cannot be reproduced by our model, which lacks discrete faults, the overall clockwise rotations in this region are similar. perpendicular extension has occurred at the southern edge of the high plateau during several episodes of extension over the last 20 m.y. (along the South Tibetan Detachment and related structures [Burchfiel et al., 1992]). Margin-perpendicular extension along the South Tibetan Detachment is at least locally Model results also show that the transition from fast short- active today [Hurtado et al., 2001]. No such zone of extension is observed in the model results when the lower crust beneath ening rates along the southern plateau margin to slow shortening rates along the southeastern plateau margin occurs abruptly in the area of the east Himalayan syntaxis and that these two regions are separated by a zone of fast right-slip faulting along the north trending shear zone that separates India from southeast China. This approximately coincides with the location of the right-slip Sagiang fault, which currently accommodates the much of the northward motion of India with respect to southeast China [Guzman-Speziale and Ni, 1996]. In neither observations nor model results does this localized zone of rapid right slip extend northward into the high plateau. Instead, right slip appears to be accommodated by thrusting at the Himalayan mountain front and, within the high plateau, by the clockwise rotations described above Extension and Stretching Within the Plateau The model strain field computed for the central plateau region is consistent with a component of slow east-west stretching across the plateau, although the model strain field suggests strike-slip rather than pure extensional motion (Figure 11). The total rate of east-west stretching shown by the model is mm/yr measured from the center to the eastern part of the plateau. This is approximately consistent with the observed -10 mm/yr of east-west stretching calculated from GPS data [Larson et al., 1999] and geological data [Armijo et al., 1986] and expressed by the presence of north-south trending grabens of Pliocene-Quaternary age in southern Tibet. We note that many of these grabens may have formed as pull-apart structures along northeast trending strike-slip faults, also consistent with model results [Armijo et al., 1986]. Within the model strain field a well-defined zone of rapid, approximately east-west extension occurs slightly north of the the plateau is only moderately weak and channel flow beneath the plateau is absent (a = 1.0 km). However, when the lower crust beneath the model plateau is sufficiently weak that chan- nel flow occurs within the weak crustal channel (a = 0.25 km), a pronounced zone of margin-perpendicular extension occurs at the edge of the high plateau in a location analogous to that of the South Tibetan Detachment. Several interpretations of the margin-perpendicular extension within southern Tibet are possible. First, it may be that channel flow has been occurring within a weak crustal layer beneath the plateau for the past -20 m.y. but that extension of upper crustal rocks occurs only episodically due to the effects of a brittle rheology within the upper crust. Second, it may be that channel flow beneath the plateau has only been active at certain times in the history of the plateau (e.g., between -16 and 12 Ma), perhaps correlating with thermal events that control large-scale anatexis of the lower crust in the same area. In either case, the presence of margin-perpendicular extension along the south Tibetan margin suggests that the lower to midcrust beneath Tibet has, at least at times, been sufficiently weak to allow channel flow beneath the plateau. The apparent lack of predicted extension along the northern and northeastern margin of the plateau may result from the initiation of the tectonic regime only in the last 10 m.y. lacking time to develop the coupling/decoupling relations that are well developed along the southern margin of the plateau. 6. Discussion The three-dimensional model results were generated by assuming a rheologically simplistic, Newtonian-viscous crust with no heterogeneities or anisotropies in any horizontal plane. The

21 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 6813 only free parameters in the model (velocities at base crust, initial crustal thickness, mantle suture geometry, and three parameters that govern the viscosity structure of the crust as a function of depth) are sufficiently well constrained by geological observations (first three parameters) and by requiring that a simple two-dimensional convergence model produce a plateau of the correct elevation and with topographic slopes across the plateau and its margins that are in reasonable agreement with what is observed within Tibet and the Himalaya (last three parameters). All results of the three-dimensional model, including three-dimensional plateau geometry, lateral surface motions, crustal rotations, etc., follow directly from these constraints. The main qualitative difference between model results and observations from Tibet occurs along the eastern and southeastern plateau margin. Here, model results suggest very slow shortening at strain rates below x 10-5 s -, while ob- servations indicate that there has been little to no late Ceno- zoic shortening of the upper crust along this portion of the plateau margin. Model results would be consistent with observations if one assumed that stress differences within a brittle upper crust must be ---5 MPa or more for deformation to occur within the upper crust. If the model results developed here are qualitatively valid for describing the present state of the plateau and its development from the early stages of convergence, several important results follow. First, the plateau is likely to have gone through a two-stage development. During the first "linear mountain belt" stage, convergence would have produced a long, narrow, high orogen whose height may have been as high, or even higher than, the present-day elevation of Tibet. Subsequently, the plateau has grown to the north and east by incorporation of crustal material along the margins of the plateau, without a significant increase in height. The limiting factors on the height of the early plateau would include the strength of the crust involved in the early deformation, the crustal thickness at which the lower to midcrust melts or becomes thermally weak, and the effects of surface erosion, especially glaciation. Because metamorphic events beneath the Himalaya at Ma involved considerably higher temperatures than the older (pre-30 Ma) metamorphism, it is not unlikely that the deep crust beneath southern Tibet was colder and stronger during the early convergence than it is at present. This is also consistent with theoretical studies of metamorphism in orogenic belts, which suggesthat near-maximum temperatures in collisional orogenic belts are commonly achieved several tens of millions of years after the onset of collision and crustal thickening [Huerta et al., 1999]. Thus we suggesthat it is possible for the early plateau to have been significantly higher than at present. Second, significant lateral extrusion of material from the high plateau (which did not involve low-lying foreland areas) and rotation of crustal material around the Himalayan syntaxes probably did not begin until a moderately broad plateau had been established, perhaps after 20 m.y. of convergence. Crustal rotations should have become progressively more rapid and involved larger regions of the plateau with time, presumably being at or near a maximum today. Third, model results suggesthat it is not possible to tell much about mantle motions beneath Tibet from observations of deformation, velocity, strain rate, etc., made at the surface. This is because the crust beneath the plateau is sufficiently weak that there should be very little stress coupling between the upper crust and the upper mantle. Most of the deformation within the interior of Tibet is instead controlled by stresses transmitted laterally from the margins of the plateau. Hence the motion and deformation of the plateau margins are coupled to motion of the underlying mantle, but motion and deformation of the interior of the plateau are not. Fourth, slow east-west stretching within the central plateau, rapid but highly localized east-west extension north of the Himalayan syntaxes, and, for very weak lower crust, rapid and highly localized north-south extension along the southern plateau margin occur as natural consequences of the convergence between India and Eurasia and the building of a broad plateau. It is not necessary to postulate large changes in the state of the lithosphere underlying Tibet (such as removal of subcrustal lithosphere) or changes in the India-Eurasia convergence rate to induce stretching. Fifth, lateral extrusion of deep crustal material from the central plateau regions toward the margins may have contributed significantly to the thickening of the crust near the plateau margins, so that thickening of the lower to middle crust near the margins may be anomalously large compared to thickening within the upper crust. Sixth, our results indicate that while crustal inhomogeneities appear to be important in controlling subregional features of deformation and the abrupt transitions observed between different strain domains, the overall deformation structure and topography of the plateau can be understood to first order without incorporation of lateral changes in rheology or intro- duction of discrete faults. These main points give a basis for comparison to other model studies of lithospheric deformation in and around Tibet, as well as a potential "tests" of these various models. The best known models for the deformation of the Tibetan region are those of England and Houseman [1986, 1988, 1989] and Houseman and England [1993], which are similar to our model in that they assume a laterally homogenous lithosphere prior to deformation. The rheology is then modified through progressive deformation (and consequent heating). The fundamental assumption of their models is that the lithosphere behaves to first order as a thin viscous sheet, so that deformation does not vary with depth for any given vertical column through the lithosphere and shear strain can occur only along vertical planes. The primary differences between our model results and those of England and Houseman include the following: 1. In our model, deformation of the upper crust, lower crust, and mantle are not correlated one to one, so that the mantle and crustal sutures can be offset from one another and upper crustal extension can occur in areas of lower crustal shortening, etc. In the case of an extremely weak lower crust, lateral extrusion of material from beneath the plateau occurs in our model by channel flow in the deep crust, causing rapid north-south extension of the upper crust along the northern and southern edges of the plateau, and significanthickening of the lower crust in the southeastern plateau with little upper crustal thickening. Because of the thin viscous sheet assumption of England and Houseman's models, all of these behaviors are explicitly precluded in their results. Observations from the Tibetan Plateau cannot yet define lower crustal or mantle deformation well enough to resolve the general correspondence between crustal and mantle deformation, but the presence of north-south extension (perhaps intermittent?) along the southern margin of the Tibetan Plateau is well documented and occurs in the location predicted by our model. Similarly

22 6814 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU well documented is the lack of late Cenozoic shortening structures in the southeastern part of the Tibetan Plateau (south of 30øN). Because both of these phenomena in our model result from lateral extrusion of deep crust from beneath the plateau and are precluded in the models of England and Houseman, these observations provide a preliminary test that favorably distinguishes our model from theirs. 2. In our model, plateau development occurs in two distinct stages, going first through a linear mountain belt stage and then proceeding to a "plateau" stage, in which east-west stretching of the upper crust develops as a natural consequence of plateau formation. This developmental sequence differs from the results of England and Houseman, where the region of crustal thickening is always distributed, even at the beginning of the crustal thickening process, and where east-west stretching of the plateau does not develop unless the topographic elevation is enhanced by convective removal of the underlying mantle lithosphere, leading to the onset of eastwest extension at that time. At present, geological observations from the Tibetan Plateau do not distinguish unambiguously between these different scenarios, although it is clear that deformation prior to Ma was restricted to the southern part of the plateau and east-west extensional features are, at least locally, as old as middle Miocene (---15 Ma [Coleman and Hodges, 1995]). Future geological work in Tibet should provide much better constraints on this developmental history. (We stress that our results do not preclude removal of the mantle lithosphere; they simply do not require it in order to produce east-west stretching of the plateau.) 3. Our model produces results broadly consistent with observations using a linear rheology for the crust, while Houseman and England required a power law rheology with n between 3 and 10 in order to localize the deformation sufficiently to form a plateau. However, this distinction is misleading because our model specifies a priori that deformation within the mantle lithosphere is localized along a narrow suture zone. We believe that our model would have produced nearly the same results for a crust with a power law rheology, provided that the rheology was appropriately calibrated to produce the correct marginal slopes, plateau height, etc., but we have not tested this hypothesis. Nevertheless, the linearity of crustal rheology is not necessarily a distinguishing feature between the two models. A variety of other models that examine the deformation of lithosphere in the region of Tibet have also been published, although none are as well established as those of England and Houseman. These include the analyses of Holt [2000] and Bird [1991], who examine the behavior that might result once the topography of the plateau has been created. However, neither of these studies addresses the issue of how to build the topography initially; hence it is difficult to compare our model results to theirs in a detailed fashion. Our results are consistent with those of Holt [2000] in that they show that the existing topographic relief in Tibet appears to be responsible for much of the current deformation as determined from GPS and seismic observations, and with those of Bird [1991], who predicts that lateral extrusion of deep crust might play an important role in the deformation of Tibet. Finally, there are models that address the effects of lateral variations in lithospheric strength and the effects of discrete faults on the development of the plateau [e.g., l/ilotte et al., 1984]. We agree that lateral variations in foreland rheology are important for understanding the development of the plateau but at a level of detail that is beyond what we have attempted in this study. For example, lateral variations in rheology are probably most important in areas adjacent to the Tarim and Sichuan basins, which appear to be areas of anomalously strong lithosphere relative to adjacent parts of the Eurasian foreland [Grand and Helmberger, 1985; Clark and Royden, 2000]. In these areas the plateau margins are very steep compared to adjacent the margins in adjacent regions, and the margins have not advanced as far toward the foreland as have adjacent parts of the plateau margin (Figure 2 and Plate 1). This creates an irregular plateau margin with "indentations" adjacento areas of strong foreland lithosphere, especially as compared to the smoother plateau margins predicted by models that assume a laterally homogeneous foreland (for example, our model results and those of England and Houseman [1986, 1988]). Quantitative results from model studies that do incorporate the effects of varying foreland rheology strongly suggest that anomalously steepened plateau margins and margin indentation are a direct result of shortening adjacent to stronger foreland blocks, either with [Clark and Royden, 2000] or without [l/ilotte et al., 1984] lateral extrusion of deep crustal material toward the plateau margin. It is always possible to improve the agreement between model results and observations by adding additional levels of complexity and additional parameters to the model assumptions. This is also true for our model, where the agreement between results and observations could be greatly improved by introducing stronger and weaker areas within the foreland and/or by introducing individual faults that correspond to the locations of the major observed faults within Tibet and surrounding regions (such as the Altyn Tagh and Xianshuihe fault systems). Nevertheless, our results indicate that on a regional scale the large-scale structure, strain distribution, evolution, and topographic expression of the Tibetan Plateau can be understood at a surprising level of detail simply as a result of prolonged postcollisional convergence between India and Eurasia acting on a rheologically simple crust. Acknowledgments. This research was supported by grants from the National Science Foundation (EAR and EAR ), National Aeronautics and Space Administration (NAGW-2155), and the Chinese Academy of Science (Key Project for Basic Research on Tibetan Plateau grants KZ951-A1-204 and KZ95T-06). We also thank Nail Toksoz for support of Shen Feng during the completion of this project. Barry Parsons, Greg Houseman, and Peter Bird provided helpful reviews that greatly improved the paper. References Achache, J., V. Courtillot, and Y. X. Zhou, Paleogeographic and tectonic evolution of southern Tibet since middle Cretaceous time: New paleomagnetic data and synthesis, J. Geophys. Res., 89, 10,311-10,339, Armijo, R., P. Tapponnier, J. L. Mercier, and T. L. Han, Quaternary extension in southern Tibet: Field observation and tectonic implications, J. Geophys. Res., 91, 13,803-13,872, Avouac, J.P., and P. Tapponnier, Kinematic model of active deformation in central Asia, Geophys. Res. Lett., 20, , Barazangi, M., and J. Ni, Velocities and propagation characteristics of Pn and Sn beneath the Himalayan arc and Tibetan Plateau: Possible evidence for underthrusting of Indian continental lithosphere beneath Tibet, Geology, 10, , Bilham, R., K. Larson, J. Freymueller, and Projedt Idyhlhim, GPS measurements of present-day convergence across the Nepal Himalaya, Nature, 386, 61-64, Bird, P., Lateral extrusion of lower crust from under high topography in the isostatic limit, J. Geophys. Res., 96, 10,275-10,286, 1991.

23 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU 6815 Brace, W. F., and D. L. Kohlstedt, Limits on lithospheric stress imposed by laboratory experiments, J. Geophys. Res., 85, , Burchfiel, B.C., and L. H. Royden, Tectonics of Asia 50 years after the death of Emile Argand, Eclogae Geol. Helv., 84, , Burchfiel, B.C., Z. Chen, K. V. Hodges, Y. Liu, L. H. Royden, C. Deng, and J. Xu, The South Tibetan detachment system, Himalayan orogen: Extension contemporaneous with and parallel to shortening in a collisional mountain belt, Spec. Pap. Geol. Soc. Am., 269, 48 pp., Burchfiel, B.C., Z. Chen, Y. Liu, and L. H. Royden, Tectonics of the Longmen Shan and adjacent regions, Int. Geol. Rev., 37, , Burg, J.P., and Y. U. Podladchikov, Lithospheric scale folding: Numerical modeling and application to the Himalayan syntaxes, Int. J. Earth Sci., 88, , Burg, J.P., P. Nievergelt, F. Oberli, D. Seward, P. Davy, J. C. Maurin, Z. Diao, and M. Meier, The Namche Barwa syntaxis: Evidence for the inversion of earthquake-released strains, Tectonics, 12, 1-20, Holt, W. E., J. F. Ni, T. C. Wallace, and A. J. Haines, The active tectonics of the eastern Himalayan syntaxis and surrounding regions, J. Geophys. Res., 96, 14,595-14,632, Houseman, G., and P. England, Finite strain calculations of continental deformation, 1, Methods and general results for convergent zones, J. Geophys. Res., 91, , Houseman, G., and P. England, Crustal thickening versus lateral expulsion in the Indian-Asian continental collision, J. Geophys. Res., 98, 12,233-12,249, Houseman, G., and P. England, A lithospheric-thickening model for the Indo-Asian collision, in The Tectonic Evolution of Asia, edited by A. Yin and M. T. Harrison, pp. 1-17, Cambridge Univ. Press, New York, Hubbard, M. S., D. A. Spencer, and D. P. West, Tectonic exhumation of the Nanga-Parbat Massif, northern Pakistan, Earth Planet. Sci. Lett., 133, , exhumation related o compressional crustal folding, J. Asian Earth Huerta, A.D., L. H. Royden, and K. V. Hodges, The effects of Sci., 16, , Che, Z. C., The formation and evolution of the Qaidam basin in relation to the uplift of the Qinghai-Tibet Plateau, Oil Gas Geol. Jiangling Hubei Prov., 7, 87-94, Chen, Z., B.C. Burchfiel, Y. Liu, R. W. King, L. H. Royden, W. Tang, E. Wang, J. Zhao, and X. Zhang, GPS measurements from eastern Tibet and their implications for India/Eurasia intracontinental deformation, J. Geophys. Res., 105, 16,215-16,227, Clark, M. K., and L. H. Royden, Topographic ooze: Building the eastern margin of Tibet by lower crustal flow, Geology, 28, , Coleman, M., and K. V. Hodges, Evidence for Tibetan Plateau uplift before 14 Myr ago from new minimum age for east-west extension, Nature, 374, 49-52, Coward, M.P. I., W. S. F. Kidd, Y. Pan, R. M. Shackleton, and H. Zhang, The structure of the 1985 Tibet geotraverse, Lhasa to Golmud, Philos. Trans. R. Soc. London, Set. A, 327, , Dewey, J., R. M. Shackleton, C. Chang, and Y. Sun, The tectonic evolution of the Tibetan Plateau, Philos. Trans. R. Soc. London, Set. A, 327, , Dong, D. N., The horizontal velocity field in southern California from a combination of terrestrial and space-geodetic data, Ph.D. thesis, 157 pp., Mass. Inst. of Technol., Cambridge, England, P., and G. Houseman, Finite strain calculations of continental deformation, 2, Comparison with the India-Asia collision zone, J. Geophys. Res., 91, , England, P., and G. Houseman, The mechanics of the Tibetan Plateau, Philos. Trans. R. Soc. London, Set. A, 326, , England, P., and G. Houseman, Extension during continental convergence, with application to the Tibetan Plateau, J. Geophys. Res., 94, 17,561-17,579, England, P., and D. P. McKenzie, A thin viscous sheet model for continental deformation, Geophys. J. R. Astron. Soc., 70, , England, P., and P. Molnar, Active deformation of Asia; from kinematics to dynamics, Science, 278, , Freymueller, J., R. Bilham, R. Burgmann, K. M. Larson, J. Paul, S. Jade, and V. Gaur, Global Positioning System measurements of Indian plate motion and convergence across the Lesser Himalaya, Geophys. Res. Lett., 23, , Goetze, C., and B. Evans, Stress and temperature in the bending lithosphere as constrained by experimental rock mechanics, Geophys. J. R. Astron. Soc., 59, , Grand, S. P., and D. V. Helmberger, Upper-mantle shear structure beneath Asia from multi-bounce S-waves, Phys. Earth Planet Inter., 41, , Guzman-Speziale, M., and J. F. Ni, Seismicity and active tectonics of the western Sunda Arc, in The Tectonic Evolution of Asia, edited by A. Yin, and T. M. Harrison, pp , Cambridge Univ. Press, New York, Hauck, M., L., K. D. Nelson, L. D. Brown, W. Zhao, and A. R. Ross, Crustal structure of the Himalayan orogen at -90 ø east longitude from project INDEPTH deep reflection profiles, Tectonics, 17, , Holt, W. E., Correlated crust and mantle strain fields in Tibet, Geology, 28, 67-70, Holt, W. E., and A. J. Haines, Velocity fields in deforming Asia from accretion, erosion, and radiogenic heat production on the metamorphic evolution of collisional orogens, J. Metamorph. Geol., 17, , Hurtado, J. M., Jr., K. V. Hodges, and K. X. Whipple, Neotectonics of the Thakkohola graben and implications for Recent activity on the South Tibetan Fault System in central Nepalese Himalaya, Geol. Soc. Am. Bull., in press, King, R. W., F. Shen, B.C. Burchfiel, Z. Chen, Y. Li, Y. Liu, L. H. Royden, E. Wang, X. Zhang, and J. Zhao, Geodetic measurement of crustal motion in southwest China, Geology, 25, , Larson, K. M, R. Burgmann, R. Bilham, and J. T. Freymueller, Kinematics of the India-Eurasia collision zone from GPS measurements, J. Geophys. Res., 104, , Li, T., The process and mechanism of the rise of the Qinghai-Tibet Plateau, Tectonophysics, 260, 45-53, Lyon-Caen, H., and P. Molnar, Gravity-anomalies, flexure of the Indian plate, and the structure, support and evolution of the Himalaya and Ganga Basin, Tectonics, 4, , Metivier, R., Y. Gaujdemer, P. Tapponnier, and B. Meyer, Northeastward growth of the Tibet Plateau deduced from balanced reconstruction of two depositional areas: The Qaidam and Hexi Corridor basins, China, Tectonics, 17, , Molnar, P., and W. P. Chen, Evidence for large Cainozoic crustal shortening of Asia, Nature, 273, , Molnar, P., and Q. Deng, Faulting associated with large earthquakes and the average rate of deformation in central and eastern Asia, J. Geophys. Res., 89, , Murphy, M. A., A. Yin, T. M. Harrison, S. B. Durr, Z. Chen, F. J. Ryerson, W. S. F. Kidd, X. Wang, and X. Zhou, Did the Indo-Asian collision alone create the Tibetan Plateau?, Geology, 25, , Nelson, K. D., et al., Partially molten middle crust beneath southern Tibet: Synthesis of Project INDEPTH-II results, Science, 274, , Pan, G. T., P.S. Wang, Y. R. Xu, S. P. Jiao, and T. X. Xiang, Cenozoic Tectonic Evolution of the Qinghai-Xizang Plateau, 152 pp., Geol. Publ. House, Beijing, Roecker, S. W., R. M. Sabitova, L. P. Vinnik, Y. A. Bjurmakov, M. I. Golvanov, R. Mamatkanova, and L. Munirova, Three-dimensional elastic wave velocity structure of the western and central Tien Shan, J. Geophys. Res., 98, 15,779-15,795, Rowley, D. B., Age of initiation of collision between India and Asia: A review of stratigraphic data, Earth Planet. Sci. Lett., 145, 1-13, Royden, L., Coupling and decoupling of crust and mantle in convergent orogens: Implications for strain partitioning in the crust, J. Geophys. Res., 101, 17,679-17,705, Royden, L. H., B.C. Burchfiel, R. W. King, Z. Chen, F. Shen, and Y. Liu, Surface deformation and lower crustal flow in eastern Tibet, Science, 276, , Schneider, D. A., M. A. Edwards, W. S. F. Kidd, M. Asia Khan, L. Seeber, and P. K. Zeitler, Tectonics of Nanga Parbat, western Himalaya: Synkinematic plutonism within the doubly vergent shear zones of a crustal-scale pop-up structure, Geology, 27, , Tapponnier, P., B. Meyer, J.P. Avouac, G. Peltzer, Y. Gaudemer, S. Guo, H. G. Xiang, K. Yin, Z. Chen, and H. Dai, Active thrusting and folding in the Qilian Shan, and decoupling between upper crust and

24 6816 SHEN ET AL.: CRUSTAL DEFORMATION OF THE TIBETAN PLATEAU mantle in northeastern Tibet, Earth Planet. Sci. Lett., 97, , Vilotte, J.P., M. Daignieres, R. Madariaga, and O. C. Zienkiewicz, The role of a heterogeneous inclusion during continental collision, Phys. Earth Planet. Inter., 36, , Wang, E., and B.C. Burchfiel, Interpretation of Cenozoic tectonics in the right-lateral accommodation zone between the Ailao Shan shear zone and the eastern Himalayan syntaxis, Int. Geol. Rev., 39, , Wang, E., B.C. Burchfiel, L. H. Royden, L. Chen, J. Chen, and W. Li, Late Cenozoic Xianshuihe-Xiaojiang and Red River fault systems of southwestern Sichuan and central Yunnan, China, Spec. Pap. Geol. Soc. Am., 327, 108 pp., Willet, S. D., C. Beaumont, and P. Fullsack, Mechanical model for the tectonics of doubly vergent compression orogens, Geology, 21, , Zeitler, P. K., C. P. Chamberlain, and H. A. Smith, Synchronous anatexis, metamorphism, and rapid denudation at Nanga Parbat, Pakistan Himalaya, Geology, 21, , Zhang, K. J., Y. J. Zhang, and B. D. Xia, Did the Indo-Asian collision alone create the Tibetan plateau?: comment, Geology, 10, , Zhao, W. L., and W. J. Morgan, Uplift of Tibet Plateau, Tectonics, 4, , B.C. Burchfiel and L. H. Royden, Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Green Building, Cambridge, MA (lhroyden@mit.edu) F. Shen, Department of Geology, Peking University, Beijing , China. (Received January 19, 2000; revised October 10, 2000; accepted October 18, 2000.)