the role of crustal strength variations in shaping...

The role of crustal strength variations in shaping orogenic

plateaus, with application to Tibet

Kristen L. Cook1 and Leigh H. Royden1

Received 19 October 2007; revised 27 February 2008; accepted 24 March 2008; published 13 August 2008.

[1] The Tibetan Plateau is the type example of a large orogenic plateau formed as aresult of continent-continent collision. The morphology of the plateau and its marginssuggests that preexisting variations in crustal strength have influenced the growth of theplateau. We have developed a three-dimensional numerical model of deformation in aviscous crust in order to investigate the effects of lateral heterogeneities on plateau growth.The model includes a two layer crust and allows for lateral variation of viscosity in both theupper and lower layers. Model results indicate that crustal strength variations have adramatic effect on the morphology and dynamics of a developing plateau. A region ofstrong crust is characterized by a very steep plateau margin that propagates extremelyslowly, does not accommodate significant shortening strain, and is subparallel to localupper and lower crustal velocities. Aweak crustal region develops a gently sloping margin;uplift propagates rapidly across the weak zone, and crustal material within the plateauis diverted toward the low-strength region. With a relatively simple distribution ofstrength variations, corresponding to strong Tarim and Sichuan Basin crust and a weaksoutheastern corner, our model produces a plateau with many similarities to the TibetanPlateau, including the overall morphology, rotation around the eastern syntaxis, andE–W extension. Analysis of model results suggests that E–W extension of the centralplateau may be related to the rapid eastward flow of crustal material into a weak zone in theSE corner without significant change in plateau elevation.

Citation: Cook, K. L., and L. H. Royden (2008), The role of crustal strength variations in shaping orogenic plateaus, with application

to Tibet, J. Geophys. Res., 113, B08407, doi:10.1029/2007JB005457.

1. Introduction

[2] Unlike oceanic plates, which tend to concentratestrain along discrete boundaries, deformation in continentalcrust may be distributed over areas hundreds or eventhousands of kilometers wide [i.e., Molnar and Tapponnier,1975]. A continental deformation zone may encompassregions of crust with different compositions, histories,thermal structures, and pre-existing anisotropies. As ourunderstanding of the basic processes of continental defor-mation improves and our theories become more refined, werequire a better understanding of the role of crustal hetero-geneity. The effects of rheologic variations in the middleand lower crust on surface topography and deformation areparticularly difficult to evaluate in active orogens becausethe relevant processes occur at depth and must be inferredfrom surface observations, geophysical properties, andcomparison to analogous regions of exhumed lower crust.[3] A prime example of active continental deformation is

the vast region of Central Asia affected by the convergenceof India and Eurasia. The most impressive product ofpostcollisional convergence is the Tibetan Plateau, which

is often used to motivate and evaluate theories of continent-continent collision. Because Tibet is in an active collisionzone, we can combine measurements of current surfacedeformation from GPS data with displacement across activestructures and observation of older structures to makeinferences about the topographic and tectonic evolution ofthe plateau and surrounding regions. Such observations,summarized in the next section, indicate that strengthheterogeneities, distributed laterally and with depth in thecrust and lithosphere, play an important role in defining themode and localization of crustal deformation in and aroundTibet. This study uses numerical modeling to investigate theeffects of lateral heterogeneities in the upper and lower cruston the patterns of uplift and surface deformation in colli-sional orogens, with application to the Tibetan Plateau.

2. Motivation: The Tibetan Plateau

2.1. Modern Morphology and Dynamics of theTibetan Plateau

[4] The uplift of the Tibetan Plateau likely initiated withthe collision of India and Eurasia at approximately 50 Ma[Dewey et al., 1988; Zhu et al., 2005; Guillot et al., 2003;Rowley, 1996], although some parts of the region may havebeen moderately elevated as an Andean-type margin prior tocollision [Murphy et al., 1997]. The modern plateau ischaracterized by a high elevation and extremely low-relief

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B08407, doi:10.1029/2007JB005457, 2008

1Department of Earth, Atmospheric and Planetary Science,Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.

Copyright 2008 by the American Geophysical Union.0148-0227/08/2007JB005457$09.00

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landscape that slopes gently from west to east [Fielding etal., 1994]. Convergence and deformation continue today,but the mechanisms and timing of uplift and deformationremain controversial and a wide variety of end-membertheories have been proposed to describe the development ofthe plateau, including extrusion of rigid blocks [Molnar andTapponnier, 1975], underplating [Powell, 1986] or injectionof Indian crust [Zhao and Morgan, 1987], distributed crustalthickening [England and Houseman, 1986], lithosphericdelamination [Molnar et al., 1993], and lower crustal flow[Royden, 1996].[5] We focus our discussion on the period of evolution

between �12 Ma and the present, when the patterns andtiming of deformation are better known than for older timeperiods, and the uplift of the peripheral regions of theplateau can be reasonably well constrained. Within thecentral plateau, deformation since Pliocene or perhaps lateMiocene time has been characterized by roughly E–Wtrending strike-slip faults and N–S trending extensional

grabens (Figure 1) [Dewey et al., 1988]. It appears thatmuch of the uplift of the central plateau may be EarlyCenozoic [Rowley and Currie, 2006], while Late Cenozoicuplift and crustal thickening have been focused preferen-tially around the northern and eastern margins of the plateau[Dewey et al., 1988]. The relationships between LateCenozoic deformation, plateau morphology, and older geo-logic structures vary widely in different regions of theplateau, as described below.[6] The Tibetan Plateau is bounded on the north and

south by steep, well-defined margins. On the southernplateau margin, the Himalayas absorb almost half of thetotal active convergence between India and Eurasia along alarge north-dipping thrust system [Zhang et al., 2004]. Thesteep topography in the region is a reflection of the activeshortening and deformation along the margin and therelatively strong character of the underlying crust. Theconvergence direction between points in southern Tibetand in the Indian craton is essentially perpendicular to the

Figure 1. Topography and major structures of the Tibetan Plateau and surrounding regions. Strike-slipfaults are drawn in black, normal faults are dark blue, and thrust faults are red. Light blue lines aremajor rivers.

B08407 COOK AND ROYDEN: CRUSTAL STRENGTH AND PLATEAU DEFORMATION

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mountain front. Although the rate of denudation is very highalong the Himalayan margin of the plateau, exhumationseems to be in balance with crustal shortening, and theelevation of this region may not have changed greatly sincethe middle Miocene [e.g., Hodges, 2000].[7] In contrast to the active shortening along the southern

margin, the steep northern margin of the Tibetan plateauparallels the left-lateral Altyn Tagh Fault. The dominantmode of surface deformation along this margin is left-lateral strike slip with only a small component of conver-gence [Yue et al., 2001; Tapponnier et al., 2001; Zhang etal., 2004]. Thrust faults associated with the Altyn TaghFault are oriented oblique to the plateau margin [i.e.,Tapponnier et al., 2001] and GPS data indicate littleconvergence perpendicular to the margin [Zhang et al.,2004]. Only at the eastern and western ends of the AltynTagh Fault, in the Qilian Shan and West Kunlun Shan, isthere significant margin-perpendicular shortening [i.e.,Chen et al., 1999; Cowgill et al., 2003]. The steepnorthern plateau margin appears to coincide spatially withthe transition between the more rigid crust of the Tarimblock [Reigber et al., 2001] and the more rapidly deform-ing crustal terranes to the south.[8] To the west, the plateau narrows considerably before

merging into the Karakoram and Pamir ranges southwest ofthe Karakoram Fault. During Late Cenozoic time, deforma-tion spread northwest of the Tarim Basin into the Tien Shanrange, which began to rise around 10–11 Ma [Bullen et al.,2003]. The Tien Shan currently absorbs as much as 13 mm/a convergence, nearly one third of the convergence ratebetween India and Eurasia [Abdrakhmatov et al., 1996]. TheTien Shan region experienced several episodes of deforma-tion during Paleozoic collision events [Bullen et al., 2001;Windley et al., 1990], and the current localization ofconvergent deformation in the range appears to be relatedto the pre-Cenozoic structure of the region.[9] The eastern plateau margin encompasses a gently

sloping, long-wavelength margin in the southeast, an ex-tremely steep boundary between the plateau and the SichuanBasin, and another gently sloping region north of theSichuan Basin. Low temperature thermochronology studies[Clark et al., 2005b; Ouimet et al., 2005] and the presenceof an intact low-relief relict landscape draping the gentlydipping southeastern margin indicate that the southeasternmargin has experienced little to no surface shortening orexhumation [Clark et al., 2005b]. Pliocene-Quaternarydeformation in eastern Tibet is dominated by left-lateralstrike-slip faults that cut across both the topographic gradi-ent of the margin and the trend of older structures. Short-ening structures of both Mesozoic and Cenozoic age trendoblique or perpendicular to the plateau margin [Burchfiel etal., 1995; Wang et al., 1998].[10] The steep margin adjacent to the Sichuan basin

appears to have uplifted in the past 5–12 Ma with onlyminor upper crustal shortening [Kirby et al., 2002; Burchfielet al., 1995]. In contrast to the high elevation regions of thecentral and eastern plateau, and to the gently dipping marginof the southeastern plateau, the location of this margincorresponds to older structures related to the furthest extentof deformation during the Indosinian orogeny [Burchfiel etal., 1995; Chen and Wilson, 1996], indicating an olderstructural control on the location of the steep topographic

edge of the plateau. GPS data show that there is currently norelative motion across this topographic front [Chen et al.,2000].[11] As the above observations illustrate, deformation

styles vary widely around the margins of the plateau. Insome areas, uplift and crustal thickening are well-correlatedwith surface structures. In other regions topography seemsto have no relationship to recent surface deformation, butabrupt changes in morphology correspond to older struc-tures or terrane boundaries. This contrast may be related tothe relative importance of upper crustal and lower crustaldeformation processes, and suggests that lateral heteroge-neities in the upper crust play a key role in some areas butnot others. The role of lower crustal heterogeneities is moredifficult to determine, but since the strength of the lowercrust partly determines how stress is transmitted in the crust,variations in lower crustal strength have an importantinfluence on both surface deformation and the growth oftopography.

2.2. Lower Crustal Flow in Tibet

[12] Lower crustal flow has been proposed to occurthroughout the Tibetan plateau [Bird, 1991; Royden, 1996;Beaumont et al., 2001; Vanderhaeghe and Teyssier, 2001].High temperatures and/or the presence of even smallamounts of fluids or partial melt can greatly reduce thestrength of continental crust [Rosenberg and Handy, 2005;Kohlstedt et al., 1995], allowing ductile flow in the middleto lower crust in response to pressure gradients resultingfrom topography. This enables a lateral flux of materialthroughout the plateau with minimal deformation of theupper crustal layer. An important consequence of a weaklower crust is that it results in local decoupling betweenthe mantle and the upper crust, and significantly reduces thetransmission of stresses through the weak layer. Thus therecognition of lower crustal flow in an orogenic setting maybe extremely important in the interpretation of large-scaledeformation based on surface observations.[13] A number of geophysical observations point to the

presence of fluids or partial melt in the middle or lowercrust of southern Tibet [Brown et al., 1996; Nelson et al.,1996; Ross et al., 2004; Wei et al., 2001]. Other studiesindicate significant crustal anisotropy and thinning of thelower crust through lateral flow in central and northernTibet [Haines et al., 2003; Ozacar and Zandt, 2004;Shapiro et al., 2004]. The crust beneath the southeasternmargin has slow P wave velocities [Li et al., 2006] and highheat flow values [Wang, 2001]. Recent teleseismic receiverfunction analysis indicates the presence of a midcrustal lowvelocity zone extending from the thick crust of westernSichuan Province south through the thinner crust of Yunnan(L. Xu et al., Structure of the crust beneath the SoutheasternTibetan Plateau from teleseismic receiver functions, sub-mitted to Physics of the Earth and Planetary Interiors,2007, hereinafter referred to as Xu et al., submitted manu-script, 2007).[14] In contrast, the Sichuan Basin has been interpreted as

region of strong lithosphere [Clark et al., 2005a], consistentwith fast seismic velocities down to 200 km depth [Li et al.,2006] and low heat flow measurements [Wang, 2001]. TheSichuan Basin sits atop cratonic crust of the Yangtzeplatform and has remained largely undeformed throughout


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both the Mesozoic Indosinian orogeny and the currentTibetan deformation [Burchfiel et al., 1995]. The TarimBasin also behaves as a rigid undeforming block [Zhang etal., 2004], and has long been regarded as a region of stronglithosphere [Vilotte et al., 1984; England and Houseman,1985; Dewey et al., 1988].

3. Modeling

3.1. Previous Modeling Studies

[15] Because the behavior of the lower crust cannot bedirectly observed, evidence for or against lower crustal flowin an active orogen must be obtained indirectly fromobservable geophysical parameters, by drawing from stud-ies of exhumed lower crust [i.e., Vanderhaeghe et al.,1999a, 1999b; Bouhallier et al., 1995], and through obser-vations of its effects on surface deformation and morphol-ogy. Theoretical modeling proves useful in predicting whatthese effects may be, and thus in generating hypotheses thatcan be tested by geological and geophysical observations.Early studies [Vilotte et al., 1984; England and Houseman,1985] suggested that the presence of a rigid block approx-imating the Tarim Basin will have a significant effect on thedevelopment of a collisional orogen in a vertically homo-geneous crust.[16] Several analytical and numerical models address

lower crustal flow in the context of plateau development[Royden, 1996; Shen et al., 2001; Vanderhaeghe et al., 2003;Jamieson et al., 2002, 2007; Medvedev and Beaumont,2006; Beaumont et al., 2006]; however, these modelsdo not allow for two-dimensional lateral variations incrustal viscosity. Clark and Royden [2000] focused on theeastern margin and used a one dimensional model ofchannel flow to explore the relationship between crustalstrength and margin steepness. Clark et al. [2005a]related channel flow against a rigid cylinder to thedynamic topography observed between the LongmenShan and the Sichuan Basin.[17] These results suggest that there are important links

betweenmorphology, deformation style and crustal rheology,and highlight the need for a treatment of the role of bothvertical and lateral crustal heterogeneities in plateau devel-opment. The modeling results, along with the correlation,described above, of older structures with steep boundariesimply that rheologic variations have almost certainly playedan important role in locally shaping the eastern andnorthern plateau margins, but the extent to which blockssuch as the Sichuan and Tarim Basins may have affecteddeformation throughout the rest of the plateau is unclear.

3.2. Model Development

[18] We follow the general approach of Royden [1996],Royden et al. [1997], and Shen et al. [2001] and modelcontinuous crustal deformation using a simple rheology andrelatively few parameters. The crustal flow model devel-oped here treats the crust as an idealized incompressibleNewtonian viscous fluid with two layers representing theupper and lower crust. Viscosity is allowed to vary laterallyin both the upper and lower crust, but within each layerviscosity is invariant with depth (Figure 2). The incorpora-tion of lateral viscosity variations enables the model toevaluate the effects of particularly strong or weak areas on

the evolution of topography. External forcing is provided bya horizontal velocity imposed on the base of the crust, andcrustal thickness evolves in response to a competitionbetween gravity and the assigned basal velocity.[19] We do not model the thermal state of the crust or

relate viscosity to temperature in the crust. The relation-ship between temperature and the bulk strength of thecrust is not straightforward, and explicit modelingrequires many assumptions about the composition andtemperature of the lower crust, and the presence of fluidsand partial melt. Using a 2D coupled thermal-mechanicalmodel, Vanderhaeghe et al. [2003] have shown that thelarge-scale topographic characteristics of an orogen arenot sensitive to whether viscosity is depth-dependent ortemperature-dependent, as long as the viscosity contrastbetween the upper and lower crust is sufficient to alloweffective decoupling between the upper crust and mantle.Thus our simple method of assigning viscosities shouldbe sufficient to capture the large-scale behavior of thesystem.[20] The use of a Newtonian viscous rheology allows the

system to be fully described by the Stokes and continuityequations. With the appropriate assumptions and boundaryconditions, the Stokes and continuity equations can besolved analytically to obtain expressions for the change incrustal thickness with time and the velocities of the surfaceof the crust, as shown in Appendix A.[21] We assume that the crust is always in pointwise

isostatic equilibrium, so that topography is fully compen-sated and scales linearly with crustal thickness, and that thelateral extent of the features of interest is much greater thanthe crustal thickness. We impose the following boundaryconditions: (1) Horizontal shear stresses are zero at thesurface. (2) The gradient in vertical stress at the surface isproportional to the topographic gradient. (3) Shear andnormal velocities, shear stress, and normal stress are con-tinuous across the interface between the upper and lowercrust. (4) Horizontal velocities at the base of the crustare imposed on the model and correspond to plate like‘‘mantle’’ velocities.[22] In Appendix A, we derive equations for the surface

velocities us, vs, and the rate of change in crustal thickness@h/@t. These are solved to compute crustal thickness andsurface velocity as a function of time, which can later beused to determine the velocity field at any depth in the crust.We solve the equations simultaneously using an implicitfinite difference technique on a two-dimensional fixed grid.The models presented here use a grid spacing of 20 km andtimestep of 0.01 Ma Models run with smaller grid spacing(10 km) and timesteps (0.0025 Ma) produced indistinguish-able results.3.2.1. Model Parameters[23] This model incorporates a relatively small number of

independent parameters. These include the viscosity of theupper and lower layers as a function of position, the initialdistribution of crustal thicknesses, the thickness of the upperlayer, and the velocity imposed at the base of the crust.Several additional parameters are introduced by a series ofrules, described below, that we use to control the viscosityevolution of the lower crust. The small number of freeparameters accorded by the adoption of a simplified rheol-


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ogy enables better understanding of the role that eachparameter plays in the model.3.2.2. Viscosity Criteria[24] Since we do not calculate viscosity based on the

temperature distribution in the crust, we need to establishcriteria that allow the viscosity to change with time in thelower crust. The viscosity of the upper crust remainsconstant with time. The method described below is onlyone possible way of assigning viscosities in the generalformulation of this model. Any number of other rulesgoverning viscosity could be applied, but we found thefollowing to be the simplest and most effective method.[25] In the models presented here, the viscosity is initially

uniform with depth over the entire crust and differentiationof a weak lower crust does not appear until some crustalthickening has taken place. Because a weak lower crust isunable to support steep slopes and inhibits further uplift andcrustal thickening, the lower layer must have some initial

strength or a region of high topography cannot develop. Weuse a critical thickness parameter (hcrit+) that controls theonset of weakening in the lower crust and may vary in spaceand time. When the total crustal thickness at any pointreaches this critical thickness value, viscosity in the lowerlayer at that point is reduced gradually until it reaches theprescribed minimum viscosity. The decrease in viscosity islinear with time and does not depend on further increase incrustal thickness. A gradual weakening of the lower crustpromotes stability by ensuring that the lower crust beneathsteep topographic gradients retains some strength.[26] This method of weakening the lower crust simulates

a time lag between crustal thickening and heating due toenhanced concentration of radiogenic isotopes and thepossible introduction of fluids or partial melt. The timescaleof lower crustal weakening has an important effect on thetiming of plateau formation and the rate of plateau propa-gation, as a longer time lag will delay the transition to a

Figure 2. (a) Plan view of model setup for crust with a strong foreland region, illustrating imposedbasal (mantle) velocity and crustal viscosity distribution. A region 2000 km wide is assigned a northwardbasal velocity of 5 cm/a, basal velocity elsewhere is zero. The northern boundary of the indenting regionremains fixed. This viscosity distribution corresponds to the model results discussed in section 4.2.1 andshown in Figure 4. (b) Schematic cross section of a model plateau resulting from the initial setup shownin Figure 2a after 40 Ma of evolution, illustrating both lateral and vertical variations in crustal viscosity. Alow-viscosity lower crust has formed in regions of thick crust, except in the area designated as ‘‘strongcrust’’. Note the vertical exaggeration.


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plateau and will slow the propagation of the plateaumargins. Studies of the thermal evolution of collisionalorogens and plateaus suggest that appropriate timescalesfor heating and thermal weakening of the lower crusttypically range from 10 to 20 Ma [Vanderhaeghe et al.,2003; Medvedev and Beaumont, 2006; Huerta et al., 1998].Factors such as the initial temperature of the lower crust, therate of heat production, the amount of water in the crust, andpresence of partial melt will have a significant effect on theevolution of lower crustal strength in response to thickeningand heating. The timescale that we use for lower crustalweakening begins only after the crust has reached hcrit+,and therefore reflects only the latest stages in the evolutionof the lower crust. Although the rate of crustal thickening inthe modeled plateaus varies with position relative to thesuture, the total timescale for crustal thickening and lowercrustal weakening generally falls within the 10–20 Marange (except for the regions that are weak prior to upliftdescribed in section 4.2.2).[27] A reverse technique for stabilizing the lower crust is

also used. If crustal thickness decreases below hcrit+ by morethan a kilometer, viscosity in the lower crust is graduallyincreased until either the crust thickens again, or the lowerlayer viscosity has returned to its initial value. The valueswe use for the critical thickness parameter are selected toyield crustal thicknesses and plateau elevations similar toTibet.[28] Values used for viscosity and thickness of the lower

crust are similar to those of earlier modeling studies [Clarkand Royden, 2000; Shen et al., 2001] that match modeledtopography to Tibet with a viscosity of 1021 Pa s in theupper crust and 1018 Pa s in a 15 km thick lower crust.These values are consistent with estimates of lower crustalviscosity from a number of actively deforming regions.Kaufman and Royden [1994] estimate that the maximumlower crust viscosity in Basin and Range Province is 1019 Pas for a 10 km thick channel. Independent estimates of lowercrustal viscosity of Rhenish Massif in western Germanygive effective viscosity around 1018 Pa s for a 15–20 kmthick lower crust [Westaway, 2001; Klein et al., 1997].Vergnolle et al. [2003] suggest a viscosity between 1016

and 1019 in western Mongolia for a 15 km thick lower crust.When describing the strength of a layer of crust, viscosityscales with the cube of layer thickness, so estimates of lowercrustal viscosity are highly dependent on the assumedthickness of the lower crust.[29] The appropriate viscosity for upper and lower crust

in ‘‘strong’’ areas is not well constrained, although model-ing by Clark and Royden [2000] suggests that the effectiveviscosity of the Sichuan crustal block must be several ordersof magnitude greater than the viscosity of the southeasternmargin. Estimates of vertically averaged viscosity fromTarim crustal block and southern China are �1023 Pa s[Flesch et al., 2001]. We find that as long as the viscosityused in the strong region is at least an order of magnitudegreater than in the surrounding area and a weak layer isprevented from developing, the general results are notsensitive to the exact value used.[30] The current thickness of the Tibetan crust is well

constrained [Zhao et al., 2001; Molnar, 1988], but theprecollision thickness is less certain; for simplicity, we

Figure 3. Evolution of topography and surface velocities(arrows) of a plateau formed in laterally homogenous crust.(a) 4 Ma after the initiation of convergence the crustalthickness has not yet reached the critical thicknessparameter hcrit+, so the lower crust remains strong and alinear mountain range has formed. (b) By 16 Ma, the lowercrust beneath the center of the orogen has weakened, andthe orogen has stopped growing taller and has transitionedinto a plateau. (c) Between 16 and 40 Ma the plateaucontinues to grow outwards in all directions. The surfacevelocities at 40 Ma indicate significant shortening across thesouthern margin, rotation around the syntaxes, and acomponent of east–west extension in the central plateau.


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assign the crust an initial uniform thickness of 35 km. Theconvergence velocity of India with respect to Eurasia is wellknown from plate motion studies [Michel et al., 2000;DeMets et al., 1994] to be �50 mm/a over the last

�40 Ma. This value was used for the velocity of a2000 km wide ‘‘subducting plate.’’

4. Results

4.1. Homogenous Crust

[31] We first discuss the results when no lateral strengthvariations are present (Figure 3): this will provide a basis forcomparison to cases with a laterally heterogeneous crust.Convergence within a uniformly viscous crust with no weaklower layer results in a linear mountain range with anapproximately triangular cross section (Figure 3a). As therange grows, width and elevation increase while retaining asimilar morphology. Because we assume that a weak layerdoes not develop in the lower crust until a threshold crustalthickness is obtained, this morphology describes the earlyevolution of a convergent system within laterally homoge-neous crust. During this stage, moderate shear stresses arerequired to generate strain in the crust at tectonicallysignificant rates; the flanks of the orogen are able to developrelatively steep topographic gradients. Orogen developmentduring this stage is similar to the evolution of 2D viscouswedges described by Medvedev [2002] and Vanderhaegheet al. [2003].[32] This general morphology is maintained until the

orogen obtains the critical crustal thickness (hcrit+) and theviscosity of the lower crust begins to decrease. Becausethe viscosity of the lower layer decreases gradually, thecrust continues to thicken beyond hcrit+ as the lower crustalviscosity drops. Eventually, the lower crustal viscositybecomes low enough that the maximum elevation of theorogen no longer increases. At this time, the orogen stopsgrowing higher and starts spreading laterally, as a plateaubegins to develop (Figure 3b). In these initial stages ofplateau development, the maximum elevation of the orogendecreases, first rapidly and then more slowly, as the plateaucrustal thickness again approaches the critical thickness(hcrit+). After these initial stages, the elevation of theplateau remains constant, the plateau continues to spreadlaterally and the area underlain by weak, flowing lowercrust expands (Figure 3c).[33] The resulting plateau is quite flat above the weak

layer; steep topographic gradients are only present at themargins, where the lower crust is still strong enough tosupport large shear stresses at relatively low strain rates.Shortening becomes localized along the plateau margins

Figure 4. (a)–(c) Evolution of topography and surfacevelocities (arrows) of a plateau with a region of strong crustin the foreland (see Figure 2). Contours are 500, 2000,3500, and 5000 m elevation. (a) By 12 Ma the northernflank of the growing plateau has reached the region ofstrong crust and a very steep margin has begun to develop.(b) Between 12 and 24 Ma the plateau propagates to theeast, west, and south, while the northern margin remainsstationary. (c) By 40 Ma the plateau has begin to wraparound the eastern and western boundaries of the strongregion. (d) Topography and lower crustal velocities after40 Ma of evolution. Note the change in velocity scale. Theslight asymmetry in the topography and velocities is due tostaggering of the velocity and viscosity grids.


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where the lower crust is still highly viscous. Within theinterior of the plateau, the low viscosity layer in the lowercrust precludes the transmission of significant shear stressesthrough the lower crust. The lack of coupling between uppercrust and mantle results in velocity profiles where themotion of the upper crust can be very different from thatof the underlying mantle. Channel flow (parabolic withdepth) develops in the lower layer beneath the plateau.Rapid flow in the weak lower crust can occur in response toeven small topographic gradients and the velocity of thelower crustal layer can be different from the upper crustalvelocity and the mantle velocity in magnitude and direction.These results are similar to those of earlier modeling studies[i.e., Shen et al., 2001; Royden et al., 1997; Vanderhaegheet al., 2003], despite the differences between their modelsand the one used here.[34] A plateau modeled with a laterally homogeneous

crust has a number of similarities to the Tibetan plateau. Thedimensions, elevation, and general shape of the modeledplateau are broadly similar to those of Tibet. In addition, themodeled surface velocities, particularly in the southern andeastern regions, are reminiscent of upper crustal motions inTibet. However, the homogenous model cannot account for

some of the distinctive characteristics of the plateau, such asthe steepness and accurate shape of portions of the easternand northern margins and the gentle gradients across thesoutheastern and northeastern margins. These are regionswhere lateral heterogeneities in crustal rheology have likelyplayed an important role in shaping the topography and thegeometry of the plateau margin. In order to better under-stand the effects of such heterogeneities, we look at howseveral types of lateral crustal heterogeneities affect plateaudevelopment.

4.2. Heterogeneous Crust

4.2.1. Strong Foreland Regions[35] The most striking contrasts between the morphology

of the Tibetan Plateau and the model results describedabove occur along the margins adjacent to the Tarim andSichuan basins. Clark and Royden [2000] have proposedthat this is due to the presence of anomalously strong crustbeneath these basins. In this section we investigate the effectthat regions of stronger crust embedded in the forelandlithosphere have on plateau development.[36] Regions of stronger crust are modeled by assigning

higher viscosities to both the upper and lower crust; webegin with a high viscosity zone embedded in the forelandnorth of the developing plateau. As the plateau growsnorthward and encounters this zone of strength, there is adramatic effect on the morphology of the plateau margin(Figure 4). In essence, the strong region acts as an obstruc-tion to plateau propagation, controlling the position andslope of the adjacent margin. The plateau margin does notpropagate across the high-viscosity region, which remainslargely undeformed and experiences crustal thickening onlyright at the boundary of the region. The strong region is notdesignated as a completely rigid block and is able todeform, but the high viscosities assigned to the upper andlower crust of the strong region result in very slow strainrates, and deformation is unable to penetrate beyond theboundary of the obstruction. Instead, the flow of crust isdiverted around the strong zone, causing an indentation, orconcavity, in the plateau margin. The plateau margin adja-cent to the ‘‘obstruction’’ is significantly steeper than allother plateau margins except the southern margin. Thus theregion of anomalously strong crust shows up clearly in themorphology of the resulting plateau.[37] A region of anomalously strong crust located in the

path of convergence also results in somewhat higherelevation in the center of the plateau. This occurs becausecrustal material is constricted between the obstructioncaused by the strong crustal block and the incoming‘‘plate’’ on the opposite side of the plateau. As deformation

Figure 5. Topography and surface velocities (arrows) after40 Ma of evolution of a plateau with a region of strong crusteast of the suture zone. Contours are 500, 2000, 3500, and5000 m elevation.

Table 1.

Maximum Thicknessof Upper Crust, h1

Critical Thickness forViscosity Transition, hcrit+

Viscosity ofUpper Crust, m1

Minimum Viscosityof Lower Crust, m2

Timescale of ViscosityTransition in Lower

Crust, tchange

Normal crust 50 km 60 km 1021 Pa s 1017 Pa s 4 MaWeak crust 36–50 km 36–60 km 1021 Pa s 5 � 1017 Pa s 2 MaStrong crust 50 km 60 km 1023 Pa s 7.5 � 1022 Pa s 4 Ma

Parameters for Tibet SetupWeak crust 36–50 km 36–60 km 1021 Pa s 1019 Pa s 2 MaStrong crust 50 km 60 km 1023 Pa s 7.5 � 1022 Pa s 4 MaIndian crust 50 km 60 km 1.25 � 1021 Pa s 1017 Pa s 4 Ma


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proceeds, the crust of the high plateau begins to propagatearound the ends of the strong region, and eventually‘‘wraps’’ around the obstruction, leaving the strong regionas a topographic low surrounded by the high topography ofthe plateau (Figure 4c).[38] Obstruction of plateau growth by a strong crustal

region can also have a significant effect on crustal veloci-ties. Figure 4 shows that a strong crustal region in front ofthe convergence zone may affect the motion of the uppercrust over much of the central plateau. Compared to thehomogeneous case discussed above, the northward compo-nent of upper crustal velocity is greatly reduced, and uppercrust is instead deflected to the east and west. Over 80% oftotal N–S convergence is accommodated on the southernmargin; the remainder is distributed across the centralplateau, and no north–south extension occurs within theupper crust of the central plateau. There is very littleconvergence across the boundary adjacent to the strongcrustal block, and flow is largely directed parallel to themargin. The lower crust moves rapidly around the obstruc-tion, although in some places it has a component of motiontoward the plateau margin. As the plateau wraps around theobstruction, velocities remain parallel to the boundaries ofthe strong region, particularly in the lower crust (Figure 4d).[39] A high-viscosity region embedded in the foreland to

the east of the convergence zone has a similar effect on themorphology of the adjacent plateau margin (Figure 5). Asteep margin, concave in planform, develops adjacent to theheterogeneity, which remains as an undeformed low-lyingregion. Again, most of the motion in the upper crust isoriented parallel to the boundary of the obstacle and there isno convergence across the margin. Although the localeffects of a high viscosity zone are not dependent on itsposition relative to the convergence zone, a high viscosityzone to the side of the convergence zone has a less far-reaching effect on the motion of the upper crust than anobstacle located in the path of convergence. Surface veloc-ities in the central plateau are not significantly affected bythe presence of an obstruction in this location. The patternof rotation in the southeastern plateau is also only slightlyaffected by the strong crustal block.4.2.2. Weak Foreland Regions[40] In the context of our model, there are several

different methods of specifying how zones of weak conti-nental crust may be embedded into a foreland region. Forexample, the crust could begin with lower viscosity in both

Figure 6. (a)–(c) Evolution of topography and surfacevelocities (arrows) of a plateau with a region of weak crustin the foreland. Contours are 500, 2000, 3500, and 5000 melevation. The blue box indicates the boundary of the weakzone. At 16 Ma (a) the plateau margin has barely reachedthe weak zone, between 16 and 23 Ma (b) the weak zoneexperiences rapid crustal thickening and northward propa-gation of the plateau. By 40 Ma (c) the plateau margin hasreached the northern end of the weak zone, rapid northwardpropagation has ceased, and a steeper northern margin hasbeen reestablished. (d) Topography and lower crustalvelocities after 40 Ma of evolution. The lower crust stillflows rapidly into the weak zone causing the crust tocontinue thickening.


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the upper and lower crust; the upper crust could have‘‘normal’’ viscosity while the lower crust begins with lowerviscosity; the lower crust could weaken more rapidly oncehcrit+ is reached; or the upper crustal thickness and thecritical thickness for weakening the lower crust could belower, allowing a weak lower layer to develop in thinnercrust. Here we use a combination of these criteria, anddefine a ‘‘weak’’ area as one in which the lower crust beginswith slightly lower viscosity, the upper crust is thinner, thehcrit+ is smaller than in the rest of the crust, and thetimescale for weakening is shorter (see Table 1). Thus ourdefinition of a ‘‘weak’’ region is crust that is initiallyslightly weaker, and in which the development of a weaklower crust is accelerated.[41] The presence of a weak crustal zone located to the

north of the convergent zone has a profound effect on themorphology and crustal velocities of the developing oro-gen. Because crust is assumed to be attached to a strongmantle lithosphere, deformation cannot move into the weakregion until the topographic front reaches it. At this point,as the plateau margin grows northward to encompass thezone of weakness, a broad, gently sloping margin is rapidlydeveloped across the weaker area (Figures 6a and 6b).

Despite the gentle topographic slope that that is developedabove the weak crustal zone, the margin does not developby synchronous tilting of the entire margin in a ramp-likegeometry. Instead, crust in areas closer to the central plateaubegins to thicken first, and surface uplift propagates north-ward (Figure 7). Once the plateau margin reaches the farside of the weak zone, northward propagation slows(Figure 6c). The weaker region then begins to slowly inflateas lower crustal material continues to flow in from thecentral plateau. The increased flow of crust to the northresults in a plateau that is lower in elevation, slightlynarrower from east to west, and that does not propagateas far to the south as in the homogenous case.[42] Crustal velocities exhibit a dramatic response to the

presence of the weak zone; a weak region results in crustbeing diverted toward the heterogeneity and rapid flowtoward and across the developing margin (Figures 6 and 8).The effect of a weaker region is most remarkable in thevelocities in the lower crust (Figures 6d and 8). Even arelatively narrow weak region will draw in lower crust froma significant portion of the plateau. Almost all of the lowercrust in the central plateau flows toward the weak zone,flow toward the southern margin is greatly reduced, and

Figure 7. Plot of elevation versus time for locations as shown. (a) Progression of uplift from south tonorth. Point b, located closest to the suture, experiences early, relatively rapid uplift, while points c, d, ande, located in the region of weak crust, experience rapid uplift that progresses from south to north. Rapidflow of crust into the weak region causes the decrease in elevation of points b and c in conjunction withthe uplift of points farther north. (b) Rapid uplift of points b and c relative to slower uplift at points a andf, located to the south and west of the mantle suture. (c) Locations of points a through f.


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flow toward the eastern and western margins is only seenrelatively close to these margins. The E–W component ofvelocity in the central and northern plateau is directedinward due to the diversion of the lower crust toward theweak zone (Figures 6d and 8). Deformation in the uppercrust is less sensitive to the presence of the weak zone;although there is a greater component of northward velocity,

the upper crust is not diverted into the weak zone from theeast and west.[43] The rapid flow of material into the weak region

results in a large amount of north–south surface extensionin the central plateau. Although the southern margin doesaccommodate �60% of the mantle convergence velocity,surface velocities on the plateau exceed convergence veloc-

Figure 8. (a) Magnitude and direction of the upper crustal velocity (white arrows) and the maximumlower crustal velocity (black arrows) for 40 Ma plateaus shown in Figures 3, 4, and 5. Letters indicate thelocations of profiles in Figures 8b and 8c. (b) North–south velocity-depth profiles, with north positive.(c) East–west velocity-depth profiles, with east positive. Note the rapid northward flow of both upper andlower crust in the weak foreland model, and the margin parallel of both upper and lower crust flow in thestrong foreland model.


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ities near the transition into the weak zone. Extension in thecentral plateau is balanced by a commensurate amount ofshortening distributed across the weak margin, as thetopographic gradient across the margin results in a largegravity-driven flux of material into the weak zone.[44] The presence of a weak crustal zone located in a

region to the east of the convergent zone has a similar effecton the morphology and crustal velocities of the plateaumargin (Figure 9). A broad, gently sloping margin is rapidlydeveloped across the weaker area. Surface velocities areaffected into the central part of the plateau, so that the dividebetween eastward- and westward-flowing upper crust islocated in the western part of the plateau. Thus more crustflows eastward than westward and the elevation of theplateau is lower than in the homogeneous case (Figure 9).

4.3. Application to Tibet

[45] We have evaluated the effects of several differenttypes of crustal heterogeneities on the development of anorogenic plateau and have shown that variations in crustalstrength may have significant effects on the morphologyand dynamics of a plateau. In order to investigate thecombined effect of such heterogeneities in the context ofthe Tibetan Plateau, we set up a model that incorporateshigh-viscosity heterogeneities approximating the Sichuanand Tarim crustal blocks and a weak region east and southof the convergence zone (Figure 10), as suggested by theplateau topography and the model results shown above. Inaddition, because Indian crust is thought to be relativelyrigid, we assign a slightly higher viscosity to the upper crustof the indenting block, resulting in a slightly slowersouthward propagation of the plateau.[46] This model, after 40 Ma of evolution, produces a

plateau that is similar to the Tibetan Plateau in a number ofways, particularly near the eastern and northern margins. Thecombination of a strong Sichuan Basin and a weak south-eastern region result in a modeled eastern margin that

Figure 10. Initial setup and evolution of a plateau with aTibet-like distribution of strong and weak regions asindicated in top. Regions of strong crust are analogous tothe Sichuan and Tarim Basins, and a region of weaker crustis placed to the east and south of the eastern indenter corner.Contours are 500, 2000, 3500, and 5000 m elevation.Arrows show surface velocity. See text for discussion.

Figure 9. Topography and surface velocities (arrows) after40 Ma of evolution of a plateau with a region of weak crusteast of the suture zone. Contours are 500, 2000, 3500, and5000 m elevation. The black box indicates the boundary ofthe weak zone.


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Figure 11


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matches the morphology of Eastern Tibet quite well. Theslope and wavelength of the southeastern margin are repro-duced (Figure 10), as are the steep margin adjacent to theSichuan Basin, the intermediate slope northeastern margin,and the concave shape of the margin around the SichuanBasin. The model also predicts the east–west asymmetry ofthe plateau, as the plateau’s width increases and elevationdecreases from west to east, despite a uniform convergencevelocity.[47] Modeled surface velocities are comparable to surface

velocities obtained with geodetic studies of Tibet [Chen etal., 2000; Zhang et al., 2004], as well as to crustal motionsinferred from geologic mapping in eastern Tibet (Figure 11)[Wang et al., 1998]. In particular, the model predictssignificant amounts of shortening across the southern mar-gin/Himalayan front, a lack of shortening between thenorthern plateau and the Tarim Basin, and east–westextension in the central plateau. In eastern Tibet, the modelalso predicts the rotation of material around the easternHimalayan syntaxis, a zone of left lateral shear approxi-mately corresponding to the location of the Xianshuihefault, a lack of convergence in the Longmen Shan, distrib-uted right-lateral shear northwest of the Sichuan Basin,margin-parallel motion north of the Sichuan Basin, andshortening across the northeastern margin in the QilianShan (Figure 11).

5. Discussion

[48] The results in this paper suggest that crustal hetero-geneities have profoundly influenced the development ofthe Tibetan Plateau, and that many of the distinctive featuresof the plateau may be related to the distribution of thesestrength heterogeneities. In particular, the overall shape andasymmetry of the plateau can be largely explained bypreexisting variations in crustal rheology and temperature(with the possible exception of southeastern Tibet, whichmay have resulted from a young thermal anomaly ofunknown origin, see below). The plateau morphology isconsistent with anomalously strong crust beneath the TarimBasin, which appears to have acted as an obstruction to thenorthward growth of the plateau. This has limited thenorth–south extent of the western plateau, resulting in aplateau that is narrower in the west than in the east. Theeastern extent of the plateau may also have been affected bythe presence of weaker crust on the southeastern margin.Our results suggest that transfer of crustal material from thewestern plateau to the volumetrically greater eastern plateauis the result of diversion of crust around the strong Tarimblock and the rapid influx of crustal material toward aregion of weak crust along the southeastern margin. Thusthe asymmetry of the plateau may be largely attributed tothe position of the Tarim Basin relative to the convergencezone, although the latitudinal variation in convergencevelocity [i.e., Soofi and King, 2002], and the possible

influence of a stress-free eastern boundary condition [i.e.,Tapponnier et al., 1982] may also play a role.[49] The strong (and recognizable) effects of crustal

strength heterogeneities on the development of orogenicplateaus highlights the need to understand the origin andnature of such heterogeneities. Continental lithosphere istypically an amalgamation of crustal domains with differentages, composition, and geologic and thermal history; thusspatial variations in crustal properties should be expected.However, the juxtaposition of crustal units does not alwaysproduce the large effects seen in eastern and northern Tibet.For example, in the central Tibetan Plateau, the Bangong-Nujiang and Jinsha sutures, boundaries between differentcrustal blocks, are not reflected in the morphology of thecurrent plateau.

5.1. Strong Regions

[50] The apparently anomalous strength of the crust andlithosphere beneath the Sichuan and Tarim Basins is con-sistent with the current thermal state and the deformationhistory of these regions. Both regions lack previous epi-sodes of penetrative deformation that affected and may havefurther weakened other regions of Tibetan crust, and bothbasins have formed in old cratonic lithosphere. Althoughour model focuses on the influence of heterogeneities in thecrust, such strength variations are not necessarily confinedto the crust, and may involve the mantle lithosphere as well.The Sichuan Basin, in particular, appears as a distinctivefast anomaly in P wave velocity models at lithosphericdepths [Li et al., 2006], suggesting that the lithosphere iscolder than the surrounding regions.

5.2. Uplift of the Southeastern Margin

[51] Anomalously slow seismic velocities in the region ofapparently weak crust in the southeastern plateau stronglysuggest elevated temperatures in the lithosphere as com-pared to surrounding regions. The origin of such a thermalanomaly is not known; it may be related to mantle processesactive above the slab in the Indo-Burman subduction zoneto the west. However, much of southern China, includingregions offshore, appears to show anomalously slow inP wave velocities at shallow mantle (lithospheric) depths,suggesting a possible, regional-scale anomaly related to asyet unknown processes [Li et al., 2006]. Potentially, thetime at which the crust in this region became weak mayshed light on the process by which this occurred. There aretwo end-member possibilities: first that the crust of thesoutheastern margin was weakened prior to plateau devel-opment, but that initiation of crustal thickening and lowercrustal flow in this region occurred only after the south-eastward edge of the plateau encountered the already-weakened crust. The second possibility is that the upliftand development of the southeastern plateau occurred at thesame time as, and was initiated by, the weakening of thecrust in this region. In the first scenario, the weakening is

Figure 11. Comparison of Tibet-like model to the topography, GPS velocities, and structures of the Tibetan Plateau.(a) Topography, and selected major strike-slip and normal faults for Tibet. (b) Elevation and surface velocities from themodel presented in Figure 8 after 40 Ma of evolution. Thick black lines suggest possible correspondence with structures inTibet. (c) Contours of elevation and GPS velocities [after Chen et al., 2000; Zhang et al., 2004] for Tibet. Contours in allpanels are 500, 2000, 3500, and 5000 m elevation. See text for discussion.


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potentially unrelated to the growth of the plateau, while thesecond scenario is more suggestive of a link between crustalweakening and plateau propagation. In either case, crustalweakening cannot be simply related to crustal thickeningand increased radiogenic heating because the region ofweak lower crust appears to extend across the entiresoutheastern margin to regions of normal thickness crustin southern Yunnan [Xu et al., submitted manuscript, 2007;Clark and Royden, 2000]. Hence even areas of normalcrustal thickness appear to have a weak layer in thelower/middle crust. Medvedev and Beaumont [2006] alsoconclude, based on modeling of channel injection, that thecrust of the southeastern margin was likely initially weak.[52] The deformation history of the southeastern margin

can provide some constraints on the timing of weakening.The crust of the southeastern margin contains largelithosphere-scale strike slip shear zones such as the AilaoShan, which accommodated large lateral motions between�34 and �17 Ma [Leloup et al., 2001]. Gneissescurrently exposed in the Ailao Shan shear zone weremetamorphosed at depths up to �18 km, indicatingsignificant localized topography, erosion and exhumation[Schoenbohm et al., 2005]. This suggests that the crust inthis region was sufficiently strong to support a narrow,localized mountain belt during this time period. Uplift ofthe southeastern margin without significant surface short-ening appears to have been initiated around 8–12 Ma[Clark et al., 2005b; Ouimet et al., 2005], suggesting thatby this time the crust had become weak. Thus the timingof weakening is approximately constrained to between�20 and �10 Ma. The current eastward-directed subduc-tion regime in the Indo-Burman region and the openingof the Andaman Sea appear to have initiated around13 Ma. The similarity in timing suggests that this changein boundary conditions may be related to the large-scaleweakening of the lower crust in southeastern Tibet.

5.3. Structures

[53] The distribution and development of structural fea-tures on the Tibetan Plateau can be understood in light ofthis distribution of crustal strength heterogeneities. Ourmodel treats the crust as a linear viscous material; thereforethere is less strain partitioning in our results than wouldoccur if we had incorporated a nonlinear rheology or strainweakening along faults. Nevertheless, even this linearviscous rheology produces many features of plateau defor-mation, many of which can be related to the location,orientation, and timing of observed structural features, asdescribed below.5.3.1. East–West Extension[54] Models that incorporate a weak crustal area east of

the convergence zone produce westward flow of crust and adramatic increase east–west extension across the centralplateau. Significantly, this is the result of and occurscontemporaneously with uplift of the eastern plateau. Theobservations from the plateau show a similar pattern, withthe onset of rapid uplift of the southeastern plateau (at�10 Ma) being approximately the same age as the onset ofeast–west extension in the central plateau (�8 Ma). Wepropose that east–west extension within the central plateauis due largely to the rapid motion of crustal materialeastward into the region of weak crust in the southeastern

plateau. If our interpretation is correct, the onset of east–west extension should be associated with a small overalldecrease in plateau elevation as material is evacuated frombeneath the high plateau. This is in contrast to the hypoth-esis that extension results from a rapid increase in plateauelevation, perhaps due to convective removal of the lowerlithosphere beneath Tibet. [i.e., Molnar et al., 1993].5.3.2. Strike-Slip Faults[55] Important strike-slip faults exist adjacent to both the

Sichuan and Tarim basins and accommodate movement ofcrustal material parallel or oblique to the margin. The AltynTagh Fault, which occurs near the boundary between theplateau and the Tarim basin, appears to have had a longhistory with varying rates of motion. Its role in the devel-opment of the Tibetan Plateau, especially its early history, isthe subject of much debate [i.e., Meriaux et al., 2004; Shenet al., 2001; Yue et al., 2001]. However, the location of theAltyn Tagh Fault and its role in accommodating eastward,margin parallel motion in the upper crust suggest that thestrong Tarim block has played an important role in thelocalization of this fault along the plateau margin. Althoughthe Altyn Tagh Fault may have accommodated largeamounts of displacement prior to and in the early stages ofthe India-Asia collision, we propose that the primary role ofthe current fault is the diversion of the upper crust eastwardpast the Tarim Basin, with transfer of shortening in the uppercrust to the eastern and western ends of the fault.[56] The Xianshuihe Fault is a younger feature that is

generally thought to accommodate clockwise rotation ofcrustal material around the eastern Himalayan syntaxis. Thetiming of motion along the fault is not well constrained, butextrapolation of current rates indicates that the fault initiatedat �8–10 Ma [Wang et al., 1998], making it approximatelycoeval with the initial uplift of the eastern plateaumargin. Comparison with model results indicates thatthe Xianshuihe Fault accommodates a diversion of crustalmaterial to the south around the strong crustal block of theSichuan Basin. It also accommodates a rapid flow ofcrustal material into the weak crust region of southeasternTibet. Our modeling suggests that the Xianshuihe Faultmay have developed as the result of these two majorstrength heterogeneities. If so, then its development iscausally linked to rapid uplift of the eastern plateau andthe onset of rapid southeastward flow in the lower crust, asboth result from the interaction of the developing plateauwith areas of anomalously strong or weak crust.

6. General Conclusions

[57] As regions of anomalously strong or weak crust areincorporated into an actively developing plateau system,they cause systematic and recognizable effects on plateaushape, plateau margin steepness, and crustal velocity. Thecontrasting styles of deformation and morphology accom-panying these lateral strength variations enable us to recog-nize crustal strength variations in actual orogens. Themorphology of the northern and eastern margins of Tibetis consistent with the presence of strong crust in the regionsof the Sichuan and Tarim Basins and weak crust beneath thesoutheastern margin.[58] As a developing plateau encounters regions of strong

crust, the adjacent plateau margin becomes steep, and is


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localized along the boundaries of the strong crustal block,and is commonly concave in map view. Despite the steep-ness of these margins, they do not accommodate significantshortening strain, and crustal material within the plateaudoes not generally move toward this plateau edge. Instead,velocities in both the upper and lower crust are directedsubparallel to the plateau margin (Figures 4 and 8).[59] As regions of weak crust become incorporated into a

developing plateau, the plateau margin acquires character-istics that are nearly opposite to those of a strong region.The weak crustal region develops a gently sloping marginthat propagates rapidly across the weak zone and accom-modates large amounts of shortening. Crustal materialwithin the plateau moves toward the low-strength region,with rapid flow toward and across the low-gradient plateaumargin (Figures 4 and 8).[60] We emphasize that the models presented here treat

the entire crust as a continuously deforming material. In areal system, the dynamics of the upper crust will becomplicated by strain partitioning along discrete structuresand by the possibility of more block-like motion or thedevelopment of brittle fold and thrust belts. We emphasizethat the goal of this study is to explore some of the large-scale dynamics that result from the presence of crustalstrength heterogeneities, and not to reproduce a detaileddeformation history of plateau deformation. However,despite the simple rheology used in this model, a modelset up with the appropriate geometry creates a plateau thatmatches a number of key features of the Tibetan Plateau.The similarities between the surface deformation predictedby the model and the GPS velocities in eastern Tibetsuggest that the model is accurately capturing some ofthe fundamental controls of the dynamics of the plateauand can therefore be used with some confidence to moreclosely investigate the role of crustal heterogeneities inshaping the Tibetan Plateau.

Appendix A: Derivation of the Analytical Solution[61] The crustal flow model developed here treats the

crust as a Newtonian viscous fluid composed of two layers.The upper layer has viscosity m1 and thickness h1, while thelower layer has viscosity m2 and thickness (h � h1), whereh is the total thickness of the crust. Both layers have thesame density rc, and m1 is always greater than or equal tom2. Viscosity is dependent only on depth, total crustalthickness, and the initial viscosity distribution imposed.Deformation is described by the Stokes and continuityequations. For a fluid with variable viscosity the balanceof forces in the x-direction can be expressed as

@xP ¼ 2@x m@xuð Þ þ @z m@zuþ m@xwð Þ þ @x m@yuþ m@xv� �

ðA1Þ

with similar formulations for y and z-directions. Flow isdriven by pressure gradients caused by variations in thevertical compressive stress resulting from gradients in thesurface topography. Pressure and viscous stress contributeto the total normal stress in the fluid. Thus the verticalcompressive stress is given by (Turcotte and Schubertp. 236)

szz ¼ P � tzz ¼ P � 2m@zw ðA2Þ

In order to solve to solve the Stokes equations explicitlyfor velocity in the x and y directions, we define a streamfunction Y such that

r �Y1;Y2; 0ð Þ ¼ u; v;wð Þ; u ¼ �@Y2

@z; v ¼ �@Y1

@z;

w ¼ @Y2

@xþ @Y1

@y

ðA3Þ

Differentiating equation (A2) and combining withequation (A3) yields

@2xzP ¼ @2

xz szzð Þ þ 2@2xz m@zwð Þ

¼ @2xz szzð Þ þ 2@xz m@2

zxY2 þ m@2zyY1

� �ðA4Þ

equation (A4) can be combined with equation (A1) toyield equation (A5):

@2xz szzð Þ ¼ � 4@2

xz m@2xzY2

� �þ @2

zz m@2xxY2 þ m@2

xyY1 � m@2zzY2

� �

� 2@2xz m@2

yzY1

� �� @2

yz m@2zyY2 þ m@2

xzY1

� �ðA5Þ

We make the approximation that higher order lateralderivatives of Y are small compared to vertical derivatives,so the terms @xxY, @xyY, and @yyY can be neglected.Equation (A4) can then be restated in terms of u and v,and integrated over the crustal thickness. After applyingthe surface boundary conditions: @x(szz)jz=0 = @xTrcg,where T is the elevation of the surface above sea level,and the surface velocity us = u(0), this yields:

@xTrcg ¼ 4@x m@xusð Þ þ @z m@zuð Þ þ 2@x m@yvs� �

þ @y m@yus þ m@xvs� �

ðA6Þ

Equation (A6) can then be solved explicitly for u(z), thex-component of velocity, by repeated integration of@z(m@zu) over the thickness of the crust.

u zð Þ ¼ us �Zz

0

1

m

Zz

0

�4@x m@xusð Þ þ 2@x m@yvs

� �

þ @y m@yus� �

:þ@y m@xvsð Þ�dzdzþ

Zz

0

1

m

Zz

0

@xTrcgdzdz

ðA7Þ

Evaluating equation (A6) for basal velocity ub = u(h)gives an explicit expression for velocity at the surface:

us ¼ ub �@xTrcg

2

h21m1

þ h2 � h21m2

� þ h� h1

m2

udsh1Dm� �

þ h212m1

udsm1

� �þ h2 � h21

2m2

udsm2

� �ðA8Þ

Performing the analogous derivation for the y-directiongives

vs ¼ vb �@yTrcg

2

h21m1

þ h2 � h21m2

� þ h� h1

m2

vdsh1Dm� �

þ h212m1

vdsm1

� �þ h2 � h21

2m2

vdsm2

� �ðA9Þ


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where

udsm1¼ 4@x m1@xusð Þ þ 2@x m1@yvs

� �þ @y m1@yus

� �þ @y m1@xvsð Þ; and

vdsm1¼ 4@y m1@yvs

� �þ 2@y m1@xusð Þ þ @x m1@xvsð Þ þ @x m1@yus

� �;

with analogous expressions for udsm2, vdsm2, udsm2,udsh1Dm, and vdsh1Dm. We use equations (A7) and (A8),and the equivalent equations for v(z) and versus to obtainthe flux through a column of crust in the x and y directions.The difference in flux across the column gives the amountof material added to or removed from the column andtherefore the rate of change in crustal thickness:

@h

@t¼ � @

@xU þ @

@yV

�

¼ � @

@x

ubhþ

@xTrcg3m2

�h3 þ h31Dmm1

� þ h2 � h21

2m2

udsh1Dm� �

þ h313m1

udsm1

� �þ h3 � h31

3m2

udsm2

� ��

þ� @

@y

ubhþ

@yTrcg3m2

�h3 þ h31Dmm1

� þ h2 � h21

2m2

vdsh1Dm� �

þ h313m1

vdsm1

� �þ h3 � h31

3m2

vdsm2

� ��

ðA10Þ

Equations (A8), (A9), and (A10) are nondimensionalizedand solved simultaneously on a two-dimensional grid toobtain the surface velocities and crustal thickness at eachtimestep.

[62] Acknowledgments. This work was supported by the NationalScience Foundation (NSF) Continental Dynamics Program (grant EAR-0003571) and an NSF graduate student fellowship (to K. L. Cook). We alsothank Chris Beaumont and Olivier Vanderhaeghe for extremely helpful andconstructive reviews.

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��K. L. Cook and L. H. Royden, Department of Earth, Atmospheric and

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