the indo-asian continental collision: a 3-d viscous...

Tectonophysics xxx (2013) xxx–xxx

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Tectonophysics

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The Indo-Asian continental collision: A 3-D viscous model

Youqing Yang ⁎, Mian LiuDept. of Geological Sciences, University of Missouri, Columbia, MO 65211, USA

⁎ Corresponding author at: E2509 Lafferre Hall, Colum573 882 9414; fax: +1 573 882 4784.

E-mail address: [email protected] (Y. Yang).

0040-1951/$ – see front matter © 2013 Published by Elhttp://dx.doi.org/10.1016/j.tecto.2013.06.032

Please cite this article as: Yang, Y., Liu, M., Th10.1016/j.tecto.2013.06.032

a b s t r a c t
a r t i c l e i n f o
Article history:Received 13 September 2012Received in revised form 14 June 2013Accepted 30 June 2013Available online xxxx

Keywords:Tectonic extrusionCrustal thickeningContinental collisionHimalayan–Tibetan PlateauGeodynamical modeling

The large-scale physical process of the Indo-Asian continental collision and the formation of the Himalayan–Tibetan Plateau have been simulated in various viscous thin-sheet models, but the thin-sheet simplificationalso kept some important issues from being fully explored. Among these issues are the role of strike-slipfault zones in facilitating large-scale lateral translation of lithospheric blocks (the escaping tectonics) duringthe collision, and the speculated lateral flow of the ductile middle–lower crust under the Tibetan Plateau.Here we present a fully three-dimensional finite element model to simulate the Indo-Asian continentalcollision. The model includes major boundary faults to simulate the escaping tectonics, and vertically variablerheological structures to model lower crustal flow. The collisional process is constrained by the history of theIndo-Eurasian plate convergence and the present crustal thickness and topography of the Tibetan Plateau.Our results indicate that the restrictive boundaries of the Tibetan Plateau, including the rigid Tarim andSouth China blocks, largely control the spatiotemporal patterns of crustal deformation in the collision zone.As the Indian indenter moves toward the Tarim block, higher strain rates and topography developed in thewestern part of the collision zone than in the eastern part, causing the northward migration of the deforma-tion front to gradually change to eastward migration in the past 10–20 Myr, broadly consistent with theinitiation of widespread E–W extension in the Plateau. These restrictive boundary blocks also force the crustalandmantlematerials in the collision zone to flow coherently, hence providing an alternative explanation for theapparently vertically coherent deformation in Tibet. Assuming that the crust weakens as it thickens, our modelpredicts the lateral expansion of the Tibetan Plateau, an important feature of the Tibetan tectonics that ismissing in previous models with constant rheology.

© 2013 Published by Elsevier B.V.

1. Introduction

The Himalayan–Tibetan Plateau, created mainly by the Indian–Eurasian continental collision in the past ~65–50 Myr (Molnar andTapponnier, 1975, 1977; Yin and Harrison, 2000), is the best-studiedexample of collisional tectonics (Patriat and Achache, 1984). The colli-sional process and the resulting large-scale continental deformationhave been simulated in viscous thin-sheet models (England andHouseman, 1986, 1988; Houseman and England, 1993, 1996). Thethin-sheet approximation reduces the three-dimensional (3-D) litho-spheric deformation to 2-D, hence greatly simplifies computation.These models have illustrated some of the basic physics of continentalcollision, including the northward migration of crustal thickening anduplift, and the balance between gravitational potential energy resistingcrustal thickening and the viscous stress from convergent plate bound-aries that drives crustal shortening and thickening (Houseman andEngland, 1996). However, the 2-D simplification also keeps someimportant issues from being fully explored.

bia, MO 65211, USA. Tel.: +1

sevier B.V.

e Indo-Asian continental coll

One such issue is the lateral motion of lithospheric blocks alongmajor strike-slip fault zones, the so called escaping tectonics (Peltzerand Tapponnier, 1988; Tapponnier et al., 1982). Geological evidenceindicates that, in and around the Tibetan Plateau, strain has beenlocalized along major fault zones and large amounts of fault slip, upto hundreds of kilometers or more, have been accumulated alongsome of these faults during the Indo-Asian collision (Peltzer et al.,1989; Replumaz and Tapponnier, 2003). This suggests that lateralextrusion of lithospheric blocks may have played a major role in ac-commodating the Indo-Asian collision. Such escaping tectonics cannotbe simulated in the viscous thin-sheet models, which do not includeinternal fault zones in the finite strain calculations.

Another issue is the role of lower crustal flow during the continentalcollision and mountain building (Royden et al., 1997). Extrapolation ofrock mechanics data suggests for a weak middle–lower crust for mostcontinental lithosphere (Brace and Kohlstedt, 1980), and a weakmiddle–lower crust in eastern Tibetan Plateau has been inferred fromsome seismological studies (Royden et al., 2008). Large-scale lateralflow of the weak ductile middle–lower crust under Tibetan Plateaumay explain the flatness of the plateau (Zhao andMorgan, 1987), topo-graphic gradients across the margins of the plateau (Clark and Royden,2000; Clark et al., 2005), and many other geological features of Tibetantectonics (Beaumont et al., 2001). The lower crustal flow and other

ision: A 3-D viscous model, Tectonophysics (2013), http://dx.doi.org/

http://dx.doi.org/10.1016/j.tecto.2013.06.032

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2 Y. Yang, M. Liu / Tectonophysics xxx (2013) xxx–xxx

depth-dependent deformational processes cannot be simulated in vis-cous thin-sheet models and require models with three-dimensionalrheological structures.

Lechmann et al. (2011) did a detailed comparison of continental col-lision in a viscous thin-sheet model with that in a three-dimensionalviscous model, using a simple geometry of a Cartesian box. They haveshown some importance difference in results from these two models,especially near the indenter and around its corners.We have developeda three-dimensional finite element model with specific model geome-try, boundary conditions, and rheological structures to calculate finitestrain evolution during the India–Eurasian collision. In a previousreport, we used this model to explore the time-dependent partitioningof the shortened crustal material between thickening and lateralextrusion (Yang and Liu, 2009). In this paper we use this model tosystematically explore how boundary fault zones and 3-D variationsof rheological structure of the Eurasian crust affect the crustal deforma-tion and mountain building in the Tibetan Plateau and surroundingregions.

2. Tectonic background

The Indo-Asian collision initiated ~70–45 Myr ago and has continuedto today at an average rate of 40–50 mm/yr. (Avouac, 2007; Molnar andStock, 2009; Patriat andAchache, 1984; Yin andHarrison, 2000). The his-tory of the Indo-Asian collision and the development of the Himalayan–Tibetan Plateau can be found in many review papers (Molnar andTapponnier, 1975; Replumaz and Tapponnier, 2003; Royden et al.,2008; Tapponnier et al., 2001; Yin and Harrison, 2000) (Fig. 1). Theseand other papers show significant advance of our knowledge of thecollisional tectonics from intensive studies of the Himalayan–TibetanPlateau in the past few decades, yet some major questions remain.

Fig. 1. Topographic map of the Himalayan–Tibetan Plateau and the surrounding regions. Grmoving toward Asia in last 55 Myr (from “This Dynamic Earth” by the US Geological Survey).to the web version of this article.)

Please cite this article as: Yang, Y., Liu, M., The Indo-Asian continental coll10.1016/j.tecto.2013.06.032

Here we highlight some of them that further insights may be obtainedfrom 3-D finite strain calculations.

One question is how the Tibetan Plateau developed over space andtime as a consequence of the Indo-Asian collision. The viscousthin-sheet models predict crustal thickening and uplift that propagatenorthward as the Indian plate indent into the Eurasian continent(England and Houseman, 1986, 1988). Now it is clear that the uplifthistory of the Tibetan Plateau is more complicated. Crustal shorteningand uplift in northern and northeastern part of the Tibetan Plateaumay have started as early as Eocene and Oligocene (see (Clark et al.,2010; Molnar et al., 2010; Yin, 2010) and references therein); upliftof the eastern Tibetan Plateau is believed to have occurred morerecently (Clark et al., 2005), yet new evidence shows earlier(30–25 Ma) and multiple phases of uplift in eastern Tibet (Wang etal., 2012). It is also clear that the overall strain pattern over theTibetan Plateau had a major shift around 10–20 Ma, as the dominantlyN–S contraction was replaced by widespread E–W extension. Someworkers attributed the E–W extension to gravitational collapse(England and Houseman, 1989; Liu and Yang, 2003), others linkedthe extension to the development of V-shaped conjugate strike-slipfaults in central Tibet (Yin and Taylor, 2011). The cause of the changefrom N–S contraction to E–W extension, however, is not clear.

Another question is how the Tibetan Plateau has grown laterally.Molnar and Lyon-Caen (1988) have showed that, theoretically, thegravitational potential energy in a rising mountain belt tends to capthe elevation of the mountain belt and force it to grow laterallyinstead. Although the uplift history of the Tibetan Plateau seemscomplicated, the young and active deformation is concentrated nearthe margins of the Plateau (Clark et al., 2004; Yin, 2010), attestingits lateral growth. However, the Plateau is surrounded by the rigidTarim, Ordos, and the South China (Sichuan) blocks that experiencedlittle internal deformation through the Cenozoic (Fig. 1). How these

ay lines are faults. The inset shows that the approximate trajectory of the Indian plate(For interpretation of the references to color in this figure legend, the reader is referred




Fig. 2. Finite element mesh and boundary conditions of the 3-D viscous flow model.The Tarim and South China blocks are treated as fixed rigid blocks; the rollers on thewestern side allow material to move only in the direction of Indian indentation. Thedash pots indicate viscous resistance boundary through which material may flow outof the collision zone. The dashed line labeled “0 Ma” shows the current position offront of the Indian indenter; the solid line labeled “50 Ma” shows the initial position.The Indian indenter moves at rates based on its convergence history with the Eurasianplate (Fig. 1). In most cases the model base is the base of the crust and changes as thecrust thickens. In selected cases the model extends to 120 km depth to include a layerof mantle lithosphere.

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rigid blocks influence or limit the lateral growth of the TibetanPlateau remains uncertain.

Finally, what happened to the mantle lithosphere during theIndo-Asian collision? Most constraints of continental deformation inthe Tibetan Plateau derived from rocks near the surface, little isknown about the mantle responses to the collision. A comparison ofcrustal strain patterns with seismic anisotropy suggests that, inmany parts of the Tibetan Plateau, the crustal deformation is verticallycoherent with that in themantle lithosphere (Holt, 2000; Silver, 1996;Wang et al., 2008). Some interpreted this coherence as indicatingstrong mechanical coupling between the crust and mantle (Wang etal., 2008), but this would be inconsistent with the notion of lower-crustal channel flow under Tibet, which tends to cause crust–mantledecoupling (Clark and Royden, 2000; Royden et al., 2008). In thispaper we will explore these questions in a fully 3-D finite elementmodel.

3. The 3-D viscous model

Continents deforming slowly over geological timescales may beapproximated as that of viscous flows (England and McKenzie,1982). In viscous thin-sheet models, the deforming continent isapproximated as a viscous thin sheet, with the vertically integratedstresses balanced by lateral stresses. In doing so the three-dimensional (3-D) lithospheric deformation is reduced to 2-D, greatlysimplifying computation (England and McKenzie, 1982). Thecomputing power has been drastically increased in recent years,with new hardware and numerical algorithms, making 3-D modelsof lithospheric deformation viable even for desktop computers. Wehave developed a 3-D viscous flow model for large-scale continentaldeformation (Yang and Liu, 2009; Yang et al., 2003). In this paperwe expand this model to include both internal faults and 3-D viscos-ity variations to explore their impact on the Indo-Asian continentalcollision.

3.1. Governing equations

Similar to viscous thin-sheet models, we assume that long-termlithospheric deformation can be approximated with a nonlinearpower law rheology (Kirby and Kronenberg, 1987):

τij ¼ B _E 1=n−1ð Þ _ε ij ð1Þ

where τij is the deviatoric stress and _ε ij the strain rate tensor, respective-ly, _E is the second invariant of the strain rate tensor, B is a rheologicalconstant, and n is a power-index for nonlinear stress–strain raterelationship. The continental deformation is silumated by solving theequilibrium equation using the finite element method (Yang and Liu,2009; Yang et al., 2003):

∂σ ij

∂xjþ f i ¼ 0 ð2Þ

where σij is the stress tensor and fi is the body force vector. The Einsteinsummation convention over repeated subscript index is followed in allequations.

3.2. Boundary and initial conditions

The boundary and initial conditions of the finite element model isshown in Fig. 2. The collision is driven by the northwardmotion of therigid Indian indenter, whose migration path is based on reconstruc-tion from marine magnetic anomalies (Molnar and Stock, 2009;Patriat and Achache, 1984). The rigid Tarim and the South Chinablocks are treated as fixed. This is an acceptable first order approxi-mation. Although these blocks may have moved relative to stable


Eurasian during the Indo-Asian collision, there is no significantCenozoic deformation within these blocks. Plate reconstruction andother evidence indicate that the position of the South China blockhas been quite stable in the Cenozoic (Replumaz and Tapponnier,2003; Zhang, 1998). This is consistent with limited E–W extensionin southern Tibet (Tapponnier et al., 2001) and along the Weihe rift(Yueqiao et al., 2003). More importantly, it is the relative motion be-tween the Indian plate and these bounding blocks that contributes tocrustal deformations in Tibet. The western side of the model domainis allowed to move only in the direction of the Indian indenter (rollerconditions in Fig. 2), reflecting the geological history of the PamirPlateau (Yin, 2010).

Along the southeastern side of the Tibetan Plateau that bordersthe Indochina block and the northeastern corner that connects theGobi–Mongolia Plateau, crustal material may have flown out of theTibetan Plateau (Clark and Royden, 2000; Le Pichon et al., 1992).We use viscous dashpots on these boundaries (Fig. 2) to simulateviscous resistance to the viscous efflux from the Tibetan Plateau. Ineach model the viscous resistance in the dashpot is adjusted to retainthe right amount of crustal material for having today's crustal volumein the Tibetan Plateau at the end of the runs.

The top of the model domain is a free surface. The bottom boundaryconditions vary in different numerical experiments (Fig. 2). In mostcases we consider only the crust; in these cases the isostatic restoringforces due to a change in surface elevation and the depth of the Mohois calculated by applying the Winkler spring mattress (Desai, 1979;Williams and Richardson, 1991). In selected cases we also include alayer of mantle in the model. In these cases a balance of verticallyintegrated forces, similar to the viscous thin-sheet models, is imposed.

Because the inertia item and damping force are negligible, thedifferential equation describing the deformation of a power-lawviscous fluid becomes a boundary-value problem, so the initial condi-tion is not required mathematically. In our model, however, the initialgeometry of the model domain needs to be specified. In most modelswe started with a flat 35-km think crust (other initial thickness is alsotested), and consider only the shortening and thickening of the crust.





This is because the crustal material is largely preserved during thecollision, whereas the fate of the mantle lithosphere is uncertain(Rowley and Currie, 2006; Tapponnier et al., 2001). Although mantlebuoyancy may have contributed to the high elevation in some part ofthe Tibetan Plateau, to a large extent the high plateau is supported bythe Airy-type crustal root (Fischer, 2002).

3.3. Fault elements

Major boundary fault zones, including the Altyn Tagh fault, theLongmenshan fault, belt, the Sagaing fault, and the Main Boundaryfault, are explicitly included in the model as weak zones. The MainBoundary thrust was used in the model as a marker for the boundarybetween the rigid Indian indenter and the deformable continent, andwas treated as a fault zone (with reduced viscosity) only in the Mio-cene when it became active. Part of the Red River fault is also includedas a boundary fault between the Indochina and the South Chinablocks. These major faults are simulated as 20 km wide week zones.The effective viscosity of these fault zones varies from 1 × 1018 to1 × 1023 Pa s. When the high-end viscosity is used, the faults areeffectively “welded” to the adjacent blocks. With these boundaryfaults, we attempt to illustrate the basic effects of the “escapingõtectonics” and the associated strain rate distribution. The interiorfaults are not simulated with fault elements. Their role is probablylimited within the plateau (Kirby et al., 2007).

We use special fault element originally designed by Goodman et al.(1968) to represent the fault zones. These fault elements are degradedcontinuum elements with a planar geometry but have a physical thick-ness and property. The nodal points in a fault element can share thesame coordinates but may have a different displacement. This represen-tation of fault zones is numerically stable, and converges in all cases forreasonable fault parameters. Because our focus is on long-term continen-tal deformation, the fault zones are assumed to creep at a steady state.

3.4. Mesh updating for finite strain calculations

To simulate large-strain deformation over long geological timescales,we integrate the incremental small strain over time. The incrementaldisplacement is obtained by multiplying velocity with time-steps. Thefinite element mesh needs to be adjusted to minimize serious numericerrors caused by mesh distortion. After each remeshing, the velocity, ac-cumulated displacement, and new vertical coordinate at each new nodalpoint are interpolated through shape function of the finite elementmethod. Because remeshing is time-consuming, we tried to minimizeremeshing as long as the mesh leads to stable results. The positions ofthe major structural boundaries, including the Indian indenter and theBoundary fault, are traced from previous positions. For a given frame ofboundary and major faults, a corresponding mesh is generated whenremeshing is needed. The time-step in our simulation is 1 Myr for thefirst 30 Myr, 0.5 Myr for the following 10 Myr and 0.25 Myr for thelast 10 Myr. These time-steps are chosen to maximize computationalefficiency while they minimize numerical errors from a distorted mesh.

4. Model results

Our model simulates crustal (and mantle in some cases when themantle lithosphere is included) deformation resulting from thenorthward indentation of the Indian plate; the details of the deforma-tion depend on model parameters and initial and boundary condi-tions. We present first a case with typical rheology parameters andboundary conditions (Fig. 3). Using this case as a reference model,we then vary the major model parameters to explore their effectson the model results.

For this reference model, we assume a power-law viscous rheolo-gy with a power index (n in Eq. (1)) of 3, as used in most thin-sheetmodels (England and Houseman, 1988). Within the orogenic zone,


the effective viscosity is taken to be 6 × 1022 Pa s for the uppercrust (the top 10 km), 4 × 1022 Pa s for the middle crust (10–20 kmdepth), and 1 × 1021 Pa s for the lower crust (Liu and Yang, 2003).For the rigid Indian indenter, the Tarim block, and the South Chinablock, a viscosity of 4 × 1023 Pa s is used for the entire crust. This vis-cosity makes these blocks stiff enough to prevent detectable internaldeformation. Because of the power-law rheology, these viscosityvalues are specified at the strain rate of 10−15 s−1. The only variablelateral boundary conditions in the model are those viscous resistanceboundaries along the boundaries with the Indochina and Gobi ter-ranes (dash pots in Fig. 2). For this case the resistance coefficient is5 × 103 Pa s/m on the Indochina boundary, and 2.8 × 105 Pa s/m onthe Gobi boundary.

Fig. 3 shows snapshots of the simulated Indo-Asian collision andthe rise of the Himalayan–Tibetan Plateau. At the beginning, thefront of the Indian indenter was about 5°N at the eastern and 15°Nat the western corners (Fig. 3a). In front of the indenter, the crust isdeformed with two peaks of uplift, similar to that predicted byviscous thin-sheet models (England and Houseman, 1986, 1988).However, these peaks vanished as the crust increased its thicknessby about 10 km. With continued convergence, a leading front ofcrustal thickening with a NW–SE strike formed (Fig. 3b). The elevatedplateau expanded with time, and its shape is increasingly affected bythe resistance of the Tarim block and the South China block. As theIndian indenter approaches the Tarim block, the orogen experienceda higher strain rate in its western part because of narrower deforma-tion zone, leading to a more rapid uplift there (Fig. 3c–f). Associatedwith this change of orogenic geometry and elevation, the crustalflow also changed from northward to predominantly eastward.After about 40 Myr, two branches of deformation front developed ineastern Tibet, one front propagated toward Mongolia–Gobi andanother toward the Indochina. After 50 Myr, the model produced aplateau comparable to the present topography of the Himalayan–Tibetan Plateau (Fig. 3f).

This predicted change from northward to eastward propagation ofthe orogenic front results mainly from the relative position of theTarim block to the Indian indenter, and the path of the indenter'snorthward motion, and is not sensitive to other model parameters.The main variable of the boundary conditions in the model is the vis-cous resistance along the Indochina and the Gobi boundaries — lowresistance allows too much crustal material flowing out of theorogenic zone, resulting in an overall low elevation of the predictedTibetan Plateau, whereas high resistance has the opposite effects.Comparing the increase of crustal volume within the Tibetan Plateauwith that flowing out of the collision zone, Yang and Liu (2009)showed that, in all cases, the early stage of collision was mainlyaccommodated by crustal thickening, while extrusion (as indicatedby crustal efflux from the collision zone) has increased with time,becoming the dominant way of accommodating the collision in thepast 10–15 Myr.

4.1. Effects of rheology

As with all numerical models, the model results may vary withmodel parameters and initial-boundary conditions. In the followingsections we systematically explore the effects of major model param-eters on the model results. For a viscous model, viscosity and itsspatial variations are clearly important. For the Indo-Asian collisionto produce the Himalayan–Tibetan Plateau, the orogenic zone needsto be weaker (softer) than the surrounding terrains. This meanslarge rheological contrasts between the collision zone and the sur-rounding stable blocks in our model. When the power index is higher(n ≥ 3), crustal thickening tends to concentrate within the weakerorogenic zone. For lower power index such as n = 1 (Newtonianflow), high effective viscosity (N4 × 1023 Pa s) is needed for Indianshield, the Tarim block, and the South China block to behave as




Fig. 3. Snapshots of the predicted surface velocity (arrows) and elevation (background color contours) of the Indo-Asian collision zone. Time in each panel is that after the beginningof the Indo-Asian collision. The color scale applies for all panels. The black solid line in (f) shows the position of a profile illustrated in Figs. 4, 5 and 8. Note that the predicted upliftpropagated from south to north in the early stages and from west to east in the later stages. Model parameters are provided in Appendix A. (For interpretation of the references tocolor in this figure legend, the reader is referred to the web version of this article.)

Fig. 4. Effects of the effective viscosity (in Pa s) of the lower crust on the predictedelevations of the Tibetan Plateau. Location of the profile is shown in Fig. 3f. TheEtopo5 is elevation from the ETOPO5 data (http://www.ngdc.noaa.gov/mgg/global/etopo5.HTML).


rigid blocks. These results are similar to those of previous thin-sheetmodels (England and Houseman, 1985; Neil and Houseman, 1997).

In the viscous thin-sheet model, deformation is controlled by theArgand number (England and McKenzie, 1982), which is essentiallythe ratio of the buoyancy force from the thickened and elevatedcrust that resists further crustal thickening, and the viscous stressfrom the imposed velocity boundaries (indenting Indian plate). Thelatter is limited by the vertically integrated strength of the litho-sphere. In our 3-D model the rheological property varies withdepth, so the Argand number no longer applies. Instead, it is theviscosity of the lower crust (the least viscous layer) that controls thecrustal thickening. Fig. 4 shows the predicted final elevation of theplateau with a different effective viscosity in the lower crust. Whilethese viscosity variations only lead to small changes in the verticallyintegrated lithospheric strength (1.075–1.015 × 1012 N/m for a strainrate of 1 × 10−15 s−1), the resulting elevation is significantly different.In general, less viscous lower crust causes a flatter and lower plateau, asmore crustal material would flow out of the collision zone.

On the other hand, keeping the viscosity of the lower crustal con-stant, a large change of vertically integrated strength (by changingthe viscosity of the upper crust) leads to a little change in the final el-evation. As shown in Fig. 5, doubling the vertically integrated strengthfrom the reference model only increases the elevation by 0.4 km.Reducing the vertically integrated strength by 50% lowers the plateauby less than 10%.

Lateral rheological variations within the Tibetan Plateau can pro-duce differential uplift. Fig. 6 shows how a semi-rigid Qaidam blockwithin the model affects the rise of the Tibetan Plateau. In this case,the upper and middle crust beneath the Qaidam is assumed to be one


third more viscous than those in the surrounding crust. We found thatthe most important factor in controlling the topographic contrast be-tween the Qaidam and the surrounding regions is the effective viscosityin the lower crust under the Qaidam. Increasing the viscosity of thelower crust under the Qaidam from 1 × 1022 Pa s to 6 × 1022 Pa sincreases the elevation contrast between the Qaidam basin and the sur-rounding plateau from 0.3 to 1.2 km. The Qaidam basin is presentlymore than 2 km below the surrounding region. Considering that partof the basin is filled by incoming sediments, the Qaidam crust is likelymuch stronger than the surrounding plateau.


http://www.ngdc.noaa.gov/mgg/global/etopo5.HTML

http://www.ngdc.noaa.gov/mgg/global/etopo5.HTML



Fig. 5. Comparison of the elevation of the Tibetan Plateau (Etopo5) with the predictedelevation assuming various effective viscosities of the upper and middle crusts. Thepercentage is viscosity changes relative to the viscosity of the reference model (seetext).


4.2. Effects of faults

An important issue for the Tibetan collisional tectonics is the later-al extrusion of Asian lithospheric blocks along major strike-slip faultsbounding the plateau (Houseman and England, 1993; Tapponnier etal., 1982). Here we explore the effects of having fault zones includedin the model. As described above, the model treats the fault zones asrheological weak zones. The strength of the fault zone is defined bythe stress required to resist a given slipping rate along a fault plane.

Fig. 6. (a) The final elevations of the Tibetan Plateau predicted from amodel with relativelystrong crust in the Qaidam basin. (b) The predicted evolution of the plateau along theprofile indicated in (a).


Thus, the fault strength is treated as a rheological parameter, linkingto the strain rate through the rheological Eq. (1).

To illustrate the effect of the boundary faults, we first run a case inwhich the fault zones are as strong as the surrounding blocks (i.e., effec-tively no faults). With the stiff blocks bounding the Plateau, the collisiondrives crustal material to flow out of the collision zone through thenortheastern and southeastern corners of the Tibetan Plateau whereefflux is permitted (Fig. 7a). The resulting velocity field is similar tothat of a pipe flow, with the largest velocity in the center of the Plateau.The highest strain rates occur along the bordering blocks where therheological contrast is maximal. The localized strain rates along therheological boundaries suggest that these are the places where newfaults may initiate if they are not already there. Across the northernboundary of the Plateau, the eastward flowing of the Tibetan crustspeeds up over time (Fig. 7b).

Bounding the northern Tibetan Plateau and the Tarim block is theAltyn Tagh fault zone, which may have existed before the Cenozoiccontinental collision (Liu et al., 2007; Yang et al., 2001). In a secondcase (Fig. 8) we included the Altyn Tagh fault and other major bound-ary faults as a weak zone through the entire experiment. Theseboundary faults localize strain, allowing the plateau interior tomove more coherently than the previous case (Fig. 8a). The velocitygradient across the boundaries depends on the strength of faults(Fig. 8b). When the Altyn Tagh fault is weak (effective viscositylower than 1020 Pa s), the velocity across the fault zones changes al-most as a step function, meaning that crust across the fault zonewould move as different blocks (Fig. 8b).

The model-predicted slip rates along the boundary faults dependcritically on the location and geometry of these faults, although faultstrength clearly matters (Fig. 9a). Along the Altyn Tagh fault, thelargest slip rate always occurs on the central segment, betweenE85° and E92°, assuming no along-strike variations of fault strength.This spatial pattern of slip rates along the Altyn Tagh fault is consis-tent with geologically determined slip rates (Ding et al., 2004;Gehrels et al., 2003; Ritts and Biffi, 2000). Our model also predicts aslight dexterous slipping on the Altyn Tagh fault west of E77°, consis-tent with the displacement along faults in the border of northeasternPamir and the Tarim basin (Fu et al., 2010).

The slip rate on the Altyn Tagh fault is predicted to increase withtime (Fig. 9b), driven by the increased strain rates (because ofnarrowing of the orogenic zone) and the increased topographic gradi-ent. This result is similar to previous viscous thin-shell models withfaults (Kong et al., 1997). Whether or not such an increase of theslip rates on the plateau boundary faults actually occurred remainsto be tested. The slip rates on the Altyn Tagh fault derived fromvarious sources varies considerably, as summarized by Ryerson et al.(2006), and initiation and slip variations on other faults within orbounding the Tibetan Plateau may also affect the slip rates on aparticular fault (Luo and Liu, 2012).

4.3. Effects of boundary conditions on crustal flow

While having fault zones included as weak zones in the model al-lows some aspects of the escaping tectonics (Tapponnier et al., 1982)to be simulated, such as strain localization near fault zones and rela-tively coherent motion of crustal blocks between faults, our modeldoes not fully simulate translation of lithospheric blocks alongstrike-slip faults as suggested by the escaping tectonics. This ispartly due to the fact that we do not have good constraints on therelative motions between the Tibetan Plateau and the surroundingterrains during the history of the Indo-Asian collision. To simplify,we assumed the rigid Tarim and the South China blocks to be fixedin the model, because it is the relative motion between these blocksand the Indian indenter that matters for the deformation in the Tibet-an Plateau. Hence in our model, some of the crustal material squeezedinto the orogenic zone by the Indian indenter is trapped within the




Fig. 7. (a) Surface velocity (arrows) and effective strain rate (color background) of the collision zone in a case that does not simulate the boundary faults. Note the high strain ratesin the western part of the plateau and along the boundaries. (b) The surface velocity along a profile across the Tibetan Plateau and the Tarim boundary (location indicated in (a)).Note the increase of velocity with time across the rheological boundary. Model parameters are provided in Appendix A. (For interpretation of the references to color in this figurelegend, the reader is referred to the web version of this article.)


plateau, contributing to crustal thickening and rise of the plateau, andsome of the crustal material flows out of the orogenic zone, throughthe northeastern and southeastern corners of the plateau into theGobi platform and the Indochina (Clark and Royden, 2000). Suchcrustal outflow is simulated by the viscous resistance boundaries inour model (Fig. 2).

These viscous resistance boundaries act like a vault to controlcrustal efflux. An acceptable range of values for the resistance coeffi-cient (5.0 × 103–2.8 × 105 Pa s/m) are found to retain the rightamount of crustal material needed to build the Tibetan Plateau,for the reasonable range of crustal viscosity in the Tibetan Plateau.Although both the conditions of the viscous resistance boundariesand the viscosity affect the outflow of the crustal material, hencethe average elevations of the predicted plateau, their impactsare different. Fig. 10a shows that, when the viscous resistancecoefficient is too low, too much crustal material will flow out of theorogenic zone, leading to a low stand plateau. This is the case whenonly lithostatic pressure is applied to these viscous resistanceboundaries. Increasing the viscosity (to 1.2 × 1023 Pa s) for the entirecrust in the orogenic zone would lead to more crustal thickening anduplift (Fig. 10b), but the high viscosity leads to highly unevenelevation within the plateau. Hence the impact of viscosity on crustal

Fig. 8. (a) The predicted surface velocity and effective strain rate when the boundary faulvarious effective viscosities of the boundary faults after 50 Myr of collision. The weaker bou


thickening is distinguishable from that of the viscous resistanceboundary conditions.

4.4. Lateral growth of the plateau

One important aspect of the Tibetan tectonics not captured in themodel results presented so far is the lateral growth of the Plateau.This is because of the fixed boundaries and constant rheologyassumed in the models, which lead to the continued narrowing ofthe orogenic zone. In reality, however, lithospheric rheology in thecollision zone is likely to change during the deformation; the thick-ened crust would be weakened by increased radioactive heating(Bird, 1991; Huerta et al., 1996) or simply by its thickening (Liu andFurlong, 1993), or by the upwelling asthenosphere (England, 1993).Crust weakening, together with the increase of gravitational potentialenergy within the uplifted plateau, may explain the observed lateralexpansion of the Tibetan Plateau through the Cenozoic (Molnar andLyon-Caen, 1988).

Temperature-dependent rheology has been incorporated inthermomechanic models (Jamieson et al., 2004; Medvedev andBeaumont, 2006). The challenge for this approach is the lack ofconstraints on the thermal parameters and the initial and boundary

ts are simulated in the model. (b) The velocity across the Tibet–Tarim boundary withndary faults allow the Tibetan crust to move more coherently as blocks.




Fig. 9. (a) Predicted accumulative displacement along the Altyn Tagh Fault (ATF) withvarious viscosities for the boundary fault zones. b) Predicted time evolution of the slipalong the ATF for the reference model (the effective viscosity of the boundary faultzones is 1 × 1020 Pa s).


conditions for heat transfer. A simple and intuitive approach is toassume a thickness-dependent rheology (Bird, 1991; Royden, 1996;Shen et al., 2001). Using this approach, we explore here the

Fig. 10. (a) The effects of the viscous resistance boundary conditions (pistons in Fig. 2)on the predicted elevation of the Tibetan Plateau. Numbers are the viscous coefficientvalues of these boundaries, in Ns/m. Free BC refers to the case when the lithostaticpressure is applied to these boundaries. Lower resistance allows more crustal materialto flow out of the collision zone, resulting in a lower plateau. (b) The different rolesof high crustal viscosity (12 × 1022 Pa s for the entire crust compared to 0.1–6 × 1022 Pa s in the reference model) and the low viscous resistance (using lithostaticpressure) along the northeastern and southeastern corners of the Plateau. The strongercrust leads to higher elevation away from these corners, but the low viscous resistancealong the boundaries leads to lower elevations near these corners.


first-order role of the evolving crustal rheology on the lateral expan-sion of the Tibetan Plateau. Here we assume that the effective viscos-ity of the lower crust beneath the Tibetan Plateau would drop from1.0 × 1022 Pa s to 5.0 × 1020 Pa s when the crust exceeds somepreset critic value (40–50 km). The results (Fig. 11) are similar to thereference model with constant viscosity (Fig. 3), the main difference isa clearer deformation front with the thickness-dependent rheology. Inthis case the uplift starts from the eastern syntaxes of the Himalayas,forming a NW-trending front of uplift in southern and western Tibetin the early stages. The deformation front gradually broadens andmigrates north- and northeastward, showing lateral expansion. If thecrust is weakened stepwise for individual terrains, the model wouldpredict a stepwise uplift of the Plateau (Tapponnier et al., 2001).

Fig. 12 shows the effects of using a different critical crustal thick-ness. The lower value means lower overall crustal viscosity, whichleads to a lower and flatter plateau, with more uniform crustal short-ening and plateau growing (Fig. 12a). With a thicker critical crustalthickness, the uplift pattern is more uneven, with uplift initiallyconcentrated near the indenter (Fig. 12b–c). Regardless of the details,it is clear that weakening associated with crustal thickening couldlead to lateral expansion of the Tibetan Plateau.

4.5. Vertically coherent deformation

One interesting observation of the Tibetan tectonics is the appar-ent coherence deformation between the crust, inferred from GPSmeasurements and geological fabrics, and the upper mantle, inferredfrom seismic anisotropy (Holt, 2000; Lev et al., 2006; Silver, 1996;Wang et al., 2008). Assuming that mantle flow under Tibet is drivenby gravitational spreading of the thickened and uplifted Tibetancrust, Wang et al. (2008) interpreted this vertically coherent defor-mation (VCD) in Tibet as evidence for strong mechanical couplingbetween the Tibetan crust and mantle. This interpretation is contra-dictory to the notion of widespread lateral flow of ductile lowercrust under the Tibetan Plateau (Clark and Royden, 2000; Royden etal., 1997, 2008).

The motion and deformation of various layers of the Tibetanlithosphere can be investigated in our 3-D model. Fig. 13 comparesthe predicted upper and lower crustal motion of two cases. Whereasthe upper crust has an effective viscosity of 6.0 × 1022 Pas in bothcases, the lower crust in Fig. 13a is much stronger (viscosity is1.0 × 1021 Pa s) than that in Fig. 13b (1.0 × 1020 Pa s), whichwould be the case for a stronger crust–mantle mechanical coupling.However, the predicted velocity vectors for the upper and lowercrusts are similar in both cases (Fig. 13). The main differences arefound near the eastern syntaxes of the Himalayas, where the lowercrustal flow make a greater clockwise rotation and flows faster thanthe upper crust. This is clearer in Fig. 13b when the lower crust hasa much lower viscosity.

Amore direct comparisonwith the observedVCD is shown in Fig. 14.In this case the mantle lithosphere, extending to 120 km depth, isincluded in the model. The model parameters for this case are inAppendix A. The boundary conditions are the same as the referencemodel (Fig. 3), the only difference is at the bottom where the mantlematerial is allowed to flow across the bottom. Fig. 14a compares thesurface velocity with that in the upper mantle; they are similar withinthe Tibetan Plateau even though a weak lower crust is assumed in themodel. The calculated principle axis of the extension strain is mostlyparallel to the S-wave splitting data (Fig. 14b).

These results suggest an alternative explanation for the TibetanVCD — that the apparent VCD can be the consequence of the restric-tive boundary conditions surrounding the Tibetan Plateau. Both theTarim and the South China blocks are nearly rigid, with high seismicvelocities extending to more than 250 km depth (Huang and Zhao,2006; Liu et al., 2004). They act as deep walls, forcing the crustaland mantle materials in the collision zone to flow eastward and to




Fig. 11. Predicted surface velocity (arrows) and elevation (color contours) of the collision zone assuming that crust weakens as it thickens to more than 45 km. Thethickness-dependent crustal rheology leads to northeastward expansion of the Tibetan Plateau (compared with the case of constant rheology in Fig. 3).


exit from the less restrictive boundaries along the northeastern andsoutheastern corners. In this case the entire orogenic zone deformsas a channel flow bounded by the lateral “walls”, and the resultingdeformation is vertically coherent within the Plateau except wherethe flow takes sharp turns. Hence the Tibetan VCD does not need toexclude lateral crustal flows under Tibet. Similar conclusions havebeen reached by Lechmann et al. (2011).

5. Discussion

With this 3-D viscous flow model, we simulated the continentaldeformation and building of the Tibetan Plateau as the Indian plateconverges with the Eurasian continent. The general spatiotemporalpatterns of crustal thickening and uplift predicted by our 3-D modelhave some similarities with those predicted by the viscousthin-sheet models, including the northward migration of the defor-mation front in the early stages of the collision. However, our resultshave significant differences from those of the viscous thin-sheetmodels because of the different boundary conditions used in thesemodels, and the 3-D rheological variations and boundary faultsincluded in our model. Not all these boundary conditions andrheological parameters are well constrained, hence their impact onthe model results needs further discussion.

The lateral boundary conditions in our model include rigid Tarimand South China blocks treated as fixed boundaries relative to theindenting Indian plate. Treating these blocks as rigid is reasonable,because there is little internal deformation within these blocks duringthe Cenozoic (Replumaz and Tapponnier, 2003; Sun and Zhang, 1995;Yang and Liu, 2002). Treating them as fixed boundary blocks, howev-er, is clearly an approximation, as these blocks havemoved during the


Cenozoic, and their motion could influence the predicted strain ratepatterns. On the other hand, the predicted deformation within thecollision zone depends mainly on the relative positions betweenthese bounding blocks and the Indian indenter. As long as the motionof the Indian indenter is much greater than that of the boundingblocks, which is likely true, treating these bounding blocks as fixedin the model should be an acceptable approximation. The majoruncertainty of the lateral boundary conditions in our model arisefrom the viscous resistance boundaries along the northeastern andsoutheastern corners of the Plateau, where crustal material is allowedto flow out of the collision zone. The only constraints we have forthese boundaries is the present crustal volume and elevation of theTibetan Plateau — the viscous resistance along these boundariesneed to retain the right amount of crustal material to build theobserved Tibetan Plateau. There is some trade-off between theviscous resistance along these boundaries and the effective viscosityof the Tibetan crust, but their impact on the predicted topography isdistinguishable (Fig. 10). Whereas these parameters are not wellconstrained, an acceptable range of values are tried by requiringthat the collision, as constrained by the history of Indo-Asian conver-gence, should produce a plateau with the crustal volume and overallelevation comparable to today's Tibetan Plateau.

With these lateral boundary conditions, the vertical variation ofcrustal rheology, especially the viscosity of the weakest lower crust,controls both the overall crustal thickening and elevation of the Tibet-an Plateau. The effective viscosity in the lower crust is constrained tobe 1 × 1020–5 × 1021 Pa s under the plateau, which is slightly lowerthan the averaged crustal viscosity in Tibet (England and Houseman,1986; Liu and Yang, 2003) but much higher than that deduced from2-D lower crust channel flow models (Clark and Royden, 2000). The




Fig. 12. Profiles (position is shown in Fig. 11b) of the predicted growth and lateralexpansion of the collision zone with thickness-dependent crustal weakening asshown in Fig. 11. (a)–(c) shows three cases with the critical crustal thickness set at40, 45, and 50 km, respectively. In each figure, the curves are the elevation at 10, 20,30, 40, and 50 Myr after the initial collision, with the location of the plateau movingnorthward (higher latitude) with time.

Fig. 13. Upper and lower crust velocity fields (arrows) predicted from (a) a model withstronger lower crust (viscosity = 1021 Pa s) and (b) a model with a weaker lowercrust (viscosity = 1020 Pa s). The color filled contours show the crustal thicknessafter 50 Myr of collision. Note that in both models the velocities at the surface andthe bottom of the crust have similar magnitude and direction. (For interpretation ofthe references to color in this figure legend, the reader is referred to the web versionof this article.)


reason is that channel flows depend on both the viscosity and thethickness and geometry of the flow channel. In our model the thick-ness of the flowing middle–lower crust is much thicker than in theprevious 2-D models, and in 3-D the flow is also easier than in the2-D channels, so significant lower crustal flow can be predictedwithout requiring extremely low viscosities.

We have systematically explored the parameter space. Whereasmany details vary with model parameters, some general patternsare predicted in all cases. One of the patterns is the temporal changeof relative partitioning of shortened crustal material between crustalthickening within the plateau and lateral extrusion (including flowof middle–lower crustal material out of the collision zone). All ourmodels show that crustal thickening is the dominant mechanismto accommodate the collision in the early stages. In the past10–20 Myr, however, lateral extrusion has gradually overtaken


crustal thickening as the primary way to accommodate collision.Details of this process and its implications for Tibetan tectonics arediscussed by Yang and Liu (2009).

Another stable prediction is the spatiotemporal evolution of therise and growth of the Tibetan Plateau. All our models show north-ward propagation of the plateau in the early stage, as predicted inthe viscous thin-shell models. However, in our models the deforma-tion front propagates from northward gradually to eastwardbetween 30 and 10 Ma, and to the northeastern and southeasterncorners of the Plateau in the past 10 Myr. These changes resultedmainly from the shape and relative locations of the Tarim and theSouth China blocks with respect to the Indian Indenter, and are notsensitive to particular rheological parameters we use. The changingto an eastward flow of crustal material within the Tibetan Plateau inthe past 10–20 Ma may be linked to the development of V-shapedconjugate strike-slip faults in the south-central Tibet and theinitiation of the E–W extension in the Tibetan Plateau (Taylor et al.,2003).

The northward propagation of the front of crustal thickening andplateau building during the Indo-Asian collision, as predicted by theviscous thin-sheet models, is clearly oversimplified. The spatiotempo-ral patterns of crustal shortening and uplift in the Tibetan Plateau arebecoming increasingly complicated from many recent studies (Yin,2010). Some parts of the plateau, such as the part of the southernTibet, may have stood as high as today when the Indo-Asian collision




Fig. 14. (a) The predicted velocity field (arrows) at the surface and in the top mantlelayer. (b) Comparison of the SKS data (black bars) and the principal axis of extensionalstrain (red bars). (For interpretation of the references to color in this figure legend, thereader is referred to the web version of this article.)The SKS splitting data are from Wang et al. (2008).


started (Murphy et al., 1997). Evidence for Eocene–Oligocene crustalshortening and uplift has been found in northern Tibet (Clark et al.,2010) and even as far north as the Tienshan mountains (Sobel et al.,2006; Yang and Liu, 2002). Nonetheless, there appears to bea NW–SE front of crustal shortening that gradually migrated north-eastward (Fig. 10 in Yin, 2010), broadly consistent with our modelpredictions (Figs. 3 and 11).

The main purpose of this 3-D viscous model, however, is to explorehow the 3-D boundary conditions, rheological variations, and boundaryfaults may influence crustal deformation during the Indo-Asian colli-sion. When comparing the model predicted spatiotemporal evolutionof the plateau building to the uplift history of the Tibetan Plateau, weneed to remember that the predicted gradual propagation of the defor-mation front is a basic consequence of the viscous assumption, which isa reasonable approximation of the long-term large scale continentaldeformation (England and McKenzie, 1982), but cannot capture allaspects of the collisional tectonics. While the ductile parts of the crustand mantle lithosphere are best suited for viscous representation, theupper crust may be better represented by elasto-plastic rheology (Luoand Liu, 2009). In plasticine analog models (Tapponnier et al., 1982),the impact of the collision can be immediately felt in the far-field ofthe collision zone, and the deformation would be largely controlled bythe lateral boundary conditions and the internal faults. Future numeri-cal models, if they consider more realistic viscoplastic rheology and its3-D variations including internal faults, may allow a more detailedcomparison of predicted uplift history with the observed regionalvariations in the Tibetan Plateau.


6. Conclusions

We have developed a 3-D viscous model to explore some impor-tant aspects of the Indo-Asian collision that cannot be readily studiedin the viscous thin-sheet models. Major conclusions we may drawfrom our modeling include the following.

1) During the Indo-Asian collision, the relatively strong blocks to thewest, north, and east of the collision zone play an important role inshaping the Himalayan–Tibetan Plateau. The positions of theseblocks relative to the Indian indenter control the strain rates. Inthe early stages when the Indian plate was far away from theTarim block to the north, the predicted crustal thickening anduplift migrated northward, similar to the prediction of viscousthin-sheet models. As the Indian plate approaches the Tarimblock, the rigid Tarim block started to restrict this northwardpropagation of deformation. Because the Tarim is closer to theIndian indenter in its western side than the eastern side, morecrustal shortening in terms of strain and uplift occurred in thewestern part of the collision zone. Consequently, the migrationof the deformation front changed from northward to northeast-ward, with the South China block playing an increasingly impor-tant role in blocking the lateral expansion of the Tibetan Plateau.In the past 10 Myr, most of the collision is accommodated bycrustal material flowing out of the collision zone through thenortheast and southeast corners of the Tibetan Plateau.

2) The rheological structure of the Tibetan crust, and its contrast withthe surrounding terrains, control both the overall amount of crust-al thickening (hence elevation) of the plateau and its internal var-iations. The key rheological parameter is the effective viscosity ofthe weakest layer, the lower crust. The effective viscosity of thelower crust under Tibet needs to be greater than 1 × 1021 Pa sfor sufficient crustal material to be trapped within the TibetanPlateau to account for the present crustal volume and elevation.

3) During the Indo-Asian collision, strain is localized along the rheo-logical boundaries between the Himalayan–Tibetan Plateau andthe surrounding blocks. When these rheological boundaries arealso weak fault zones, they facilitate lateral extrusion of theTibetan crust. In this case, strain is largely concentrated alongthe boundary fault zones, and within the plateau deformation isrelatively small and laterally coherent.

4) As the crust in the collision thickens, it may be also mechanicallyweakened by a number of processes. Considering this thickness-dependent weakening of the crust, our model is able to predictthe lateral expansion of the Tibetan Plateau, an important featureof the Tibetan tectonics that is missing in models with constantrheological structures. In particular, this model predicts a clear de-formation front that initiated near the syntaxes of the Himalayas,migrated northeastward in the first 30 Myr of the Indo-Asiancollision, and turned predominantly eastward in the past 20 Myr.

5) The apparently coherent deformation between the Tibetan crust andthe upper mantle can be explained by the restrictive lateral bound-ary conditions, namely the rigid blocks surrounding the TibetanPlateau. With such boundary conditions, the collision drives agenerally coherent flow of the crust and mantle lithosphere. In thiscase, the vertically coherent deformation observed in Tibet does notnecessarily exclude large-scale lateral flow in a weak lower crust.

Acknowledgments

This workwas supported by NSF grants EAR0207200 and 0710354.Liu's work in Tibet is also supported by the Chinese Academy ofScience. We thank F. Gomez and E. Sandvol for helpful discussions.We benefited from the constructive criticisms by reviewers An Yin,Norm Sleep, an anonymous reviewer, and guest editor SimonKlemperer.





Appendix A

Provided here are the model parameters for the numerical experiments presented in the figures and discussed in the text.

Table 1Rheological parameters for finite element models described in the text.

Upper crust(top 10 km)

Middle crust(10–20 km)

Lower crust(N20 km depth)

Referred to

Reference model 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s Figs. 3, 4, 13Weak lower crust 1 6 × 1022 Pa s 4 × 1022 Pa s 0.1 × 1021 Pa s Figs. 4, 13Weak lower crust 2 6 × 1022 Pa s 4 × 1022 Pa s 0.5 × 1021 Pa s Fig. 4Strong lower crust 1 6 × 1022 Pa s 4 × 1022 Pa s 3 × 1021 Pa s Fig. 4Strong lower crust 2 6 × 1022 Pa s 4 × 1022 Pa s 5 × 1021 Pa s Fig. 4Weak upper 3 × 1022 Pa s 2 × 1022 Pa s 5 × 1021 Pa s Fig. 5Strong upper 12 × 1022 Pa s 8 × 1022 Pa s 5 × 1021 Pa s Fig. 5

All faults are 1 × 1020 Pa s in effective viscosity.

Table 2Heterogeneous rheology used for models with a strong Qaidam block.

Upper crust (top 10 km) Middle crust (10–20 km) Lower crust (N20 km depth) Topographic contrast

Reference model 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 0.0 kmStrong lower 1 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1022 Pa s 0.3 kmStrong lower 2 6 × 1022 Pa s 4 × 1022 Pa s 6 × 1022 Pa s 1.2 km (Fig. 6)Strong upper 15 × 1022 Pa s 9 × 1022 Pa s 1 × 1021 Pa s 0.3 km

All faults are 1 × 1020 Pa s in effective viscosity.

Table 3Rheology parameters for models with fault zones.




Fault viscosity Referred to

No fault model 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 1 × 1026 Pa s Fig. 7Reference model 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 1 × 1021 Pa s Figs. 7, 8Strong fault 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 3 × 1020 Pa s Fig. 8Reference model 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 1 × 1020 Pa s Figs. 7, 8Weak fault 1 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 0.3 × 1020 Pa s Fig. 8Weak fault 2 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 1 × 1019 Pa s Fig. 7

Table 4Boundary resistant coefficient (referred to Fig. 10).




Boundary resistant coefficient

Strong BC 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 2.8 × 105 Ns/m3 at the Indochina side and Gobi sideReference model 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 5 × 103 Pa s/m at the Indochina side, 2.8 × 105 Pa s/m on the Gobi sideWeak BC 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 5 × 103 Ns/m3 at the Indochina side and Gobi sideLithostatic BC with normal crust 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa s 0 (Lithostatic pressure) at the Indochina side and Gobi sideLithostatic BC with strong crust 12 × 1022 Pa s 12 × 1022 Pa s 12 × 1022 Pa s 0 (Lithostatic pressure) at the Indochina side and Gobi side

All faults are set to be 1 × 1020 Pa s in effective viscosity.

Table 5Parameters for thickness-dependent crustal rheology (referred to Figs. 11 and 12).

Upper crust (top 10 km) Middle crust (10–20 km) Lower crust (N20 km depth)

Reference model 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1021 Pa sOrogen zone with crust thinner than critical thickness 6 × 1022 Pa s 4 × 1022 Pa s 1 × 1022 Pa sOrogen zone with crust thicker than critical thickness 6 × 1022 Pa s 4 × 1022 Pa s 0.5 × 1021 Pa s

All faults are 1 × 1020 Pa in effective viscosity. Boundary resistant coefficient 5 × 103 Pa s/m at the Indochina side, 2.8 × 105 Pa s/m on the Gobi side.

In all Tables 1–3, the boundary resistant coefficient is 5 × 103 Pa s/m at the Indochina side, 2.8 × 105 Pa s/m on the Gobi side.

Please cite this article as: Yang, Y., Liu, M., The Indo-Asian continental collision: A 3-D viscous model, Tectonophysics (2013), http://dx.doi.org/10.1016/j.tecto.2013.06.032



Table 6Parameters for models exploring vertical coherent motion model (referred to Fig. 14).

Layer Initial depth range Orogen zone Transition zone Rigid blocks

Upper crust 0 to 10 km 6 × 1022 Pa s 1.8 × 1023 Pa s 4 × 1023 Pa sMiddle crust 10–20 km 4 × 1022 Pa s 1.2 × 1023 Pa s 4 × 1023 Pa sLower crust 20–35 km depth 1 × 1021 Pa s 1.2 × 1023 Pa s 4 × 1023 Pa sTop lithospheric mantle 35–40 km 1 × 1022 Pa s 1.2 × 1023 Pa s s 4 × 1023 Pa sLithospheric mantle 40 to 120 km 2 × 1022 Pa s 1.2 × 1023 Pa s 4 × 1023 Pa s sViscous resistance at Indochina 5 × 103 Pa s/m (crust section) 2.8 × 105 Pa s/m (mantle section)Viscous resistance at Gobi 2.8 × 105 Pa s/m (crust section) 5 × 103 Pa s/m (mantle section)


References

Avouac, J.P., 2007. Dynamic processes in extensional and compressional settings —mountain building: from earthquakes to geological deformation. In: Watts, A.(Ed.), Treatise on Geophysics. Elsevier, pp. 377–439.

Beaumont, C., Jamieson, R.A., Nguyen, M.H., Lee, B., 2001. Himalayan tectonicsexplained by extrusion of a low-viscosity crustal channel coupled to focusedsurface denudation. Nature (London) 414, 738–742.

Bird, P., 1991. Lateral extension of lower crust from under high topography in theisostatic limit. Journal of Geophysical Research 96, 10275–10286.

Brace, W.F., Kohlstedt, D.L., 1980. Limits on lithospheric stress imposed by laboratoryexperiments. Journal of Geophysical Research 85, 6248–6252.

Clark, M.K., Royden, L.H., 2000. Topographic ooze: building the eastern margin of Tibetby lower crustal flow. Geology (Boulder) 28, 703–706.

Clark, M.K., Schoenbohm, L.M., Royden, L.H., Whipple, K.X., Burchfiel, B.C., Zhang, X.,Tang, W., Wang, E., Chen, L., 2004. Surface uplift, tectonics, and erosion of easternTibet from large-scale drainage patterns. Tectonics 23.

Clark, M.K., House, M.A., Royden, L.H., Whipple, K.X., Burchfiel, B.C., Zhang, X., Tang, W.,2005. Late Cenozoic uplift of southeastern Tibet. Geology 33, 525–528.

Clark, M.K., Farley, K.A., Zheng, D., Wang, Z., Duvall, A.R., 2010. Early Cenozoic faultingof the northern Tibetan Plateau margin from apatite (U–Th)/He ages. Earth andPlanetary Science Letters 296, 78–88.

Desai, C.S., 1979. Elementary Finite Element Method. Prentice-Hall, Englewood Cliffs,NJ.

Ding, G.Y., Chen, J., Tian, Q.J., Shen, X.H., Xing, C.Q., Wei, K.B., 2004. Active faults andmagnitudes of left-lateral displacement along the northern margin of the TibetanPlateau. Tectonophysics 380, 243–260.

England, P., 1993. Convective removal of thermal boundary layer of thickenedcontinental lithosphere: a brief summary of causes and consequences with specialreference to the Cenozoic tectonics of the Tibetan Plateau and surrounding regions.Tectonophysics 223, 67–73.

England, P.C., Houseman, G., 1985. Role of lithospheric strength heterogeneities in thetectonics of Tibet and neighbouring regions. Nature (London) 315, 297–301.

England, P.C., Houseman, G.A., 1986. Finite strain calculations of continental deforma-tion 2. Comparison with the India–Asia collision. Journal of Geophysical Research91, 3664–3676.

England, P., Houseman, G., 1988. The mechanics of the Tibetan Plateau. PhilosophicalTransactions of the Royal Society A 327, 379–413.

England, P.C., Houseman, G.A., 1989. Extension during continental convergence withspecial reference to the Tibetan Plateau. Journal of Geophysical Research 94,17,561–17,579.

England, P.C., McKenzie, D.P., 1982. A thin viscous sheet model for continentaldeformation. Geophysical Journal of the Royal Astronomical Society 70, 295–321.

Fischer, K., 2002. Waning buoyancy in the crustal roots of old mountains. Nature 417,933–936.

Fu, B., Ninomiya, Y., Guo, J., 2010. Slip partitioning in the northeast Pamir–Tian Shanconvergence zone. Tectonophysics 483, 344–364.

Gehrels, G.E., Yin, A., Wang, X.F., 2003. Magmatic history of the northeastern TibetanPlateau. Journal of Geophysical Research 108.

Goodman, R.E., Taylor, R.L., Brekke, T.L., 1968. A Model for the Mechanics of JointedRock. American Society of Civil Engineers, New York, NY, United States637–659.

Holt, W.E., 2000. Correlated crust and mantle strain fields in Tibet. Geology (Boulder)28, 67–70.

Houseman, G., England, P., 1993. Crustal thickening versus lateral expulsion inthe Indian–Asian continental collision. Journal of Geophysical Research 98,12233–12249.

Houseman, G., England, P., 1996. A lithospheric-thickening model for the Indo-Asiancollision. In: Yin, A., Harrision, T.M. (Eds.), The Tectonic Evolution of Asia.Cambridge University, pp. 3–17.

Huang, J., Zhao, D., 2006. High-resolution mantle tomography of China and surround-ing regions. Journal of Geophysical Research 111, B09305. http://dx.doi.org/10.1029/2005JB004066.

Huerta, A.D., Royden, L.H., Hodges, K.V., 1996. The interdependence of deformationaland thermal processes in mountain belts. Science 273, 637–639.

Jamieson, R.A., Beaumont, C., Medvedev, S., Nguyen, M.H., 2004. Crustal channel flows:2. Numerical models with implications for metamorphism in the Himalayan–Tibetan orogen. Journal of Geophysical Research 109, B06407 (06401–06424).

Kirby, S.H., Kronenberg, A.K., 1987. Rheology of the lithosphere: selected topics.Reviews of Geophysics 25, 1,219–1,244.

Kirby, E., Harkins, N., Wang, E.Q., Shi, X.H., Fan, C., Burbank, D., 2007. Slip rate gradientsalong the eastern Kunlun fault. Tectonics 26.


Kong, X., Yin, A., Harrison, T.M., 1997. Evaluating the role of preexisting weakness andtopographic distributions in the Indo-Asian collision by use of a thin-shell numer-ical model. Geology 25, 527–530.

Le Pichon, X., Fournier, M., Jolivet, L., 1992. Kinematics, topography, shortening, andextrusion in the India–Eurasia collision. Tectonics 11, 1085–1098.

Lechmann, S.M., May, D.A., Kaus, B.J.P., Schmalholz, S.M., 2011. Comparing thin-sheetmodels with 3-D multilayer models for continental collision. Geophysical JournalInternational 187, 10–33.

Lev, E., Long, M.D., van der Hilst, R.D., 2006. Seismic anisotropy in Eastern Tibet fromshear wave splitting reveals changes in lithospheric deformation. Earth and Plane-tary Science Letters 251, 293–304.

Liu, M., Furlong, K.P., 1993. Crustal shortening and Eocene extension in the southeast-ern Canadian Cordillera: some thermal and mechanical considerations. Tectonics12, 776–786.

Liu, M., Yang, Y., 2003. Extensional collapse of the Tibetan Plateau: results of three-dimensional finite element modeling. Journal of Geophysical Research 108, 2361.http://dx.doi.org/10.1029/2002JB002248.

Liu, M., Cui, X., Liu, F., 2004. Cenozoic rifting and volcanism in eastern China: a mantledynamic link to the Indo-Asian collision? Tectonophysics 393, 29–42.

Liu, Y.J., Neubauer, F., Genser, J., Ge, X.H., Takasu, A., Yuan, S.H., Chang, L.H., Li, W.M.,2007. Geochronology of the initiation and displacement of the Altyn Strike-SlipFault, western China. Journal of Asian Earth Sciences 29, 243–252.

Luo, G., Liu, M., 2009. How does trench coupling lead to mountain building in theSubandes? A viscoelastoplastic finite element model. Journal of GeophysicalResearch F: Earth Surface 114.

Luo, G., Liu, M., 2012. Multi-timescale mechanical coupling between the San JacintoFault and the San Andreas Fault, southern California. Lithosphere. http://dx.doi.org/10.1130/L1180.1131.

Medvedev, S., Beaumont, C., 2006. Growth of continental plateaus by channel injection:models designed to address constraints and thermomechanical consistency.Geological Society — Special Publications 147–164.

Molnar, P., Lyon-Caen, H., 1988. Some simple physical aspects of the support, structure, andevolution of mountain belts. Geological society of America Special Paper 218, 179–207.

Molnar, P., Stock, J.M., 2009. Slowing of India's convergence with Eurasia since 20 Maand its implications for Tibetan mantle dynamics. Tectonics 28, TC3001.

Molnar, P., Tapponnier, P., 1975. Cenozoic tectonics of Asia: effects of a continentalcollision. Science 189, 419–426.

Molnar, P., Tapponnier, P., 1977. Relation of the tectonics of eastern China to the India–Eurasia collision: application of slip-line field theory to large-scale continentaltectonics. Geology 5, 212–216.

Molnar, P., Boos, W.R., Battisti, D.S., 2010. Orographic Controls on Climate andPaleoclimate of Asia: Thermal and Mechanical Roles for the Tibetan Plateau. 77–102.

Murphy, M.A., Yin, A., Harrision, T.M., Durr, S.B., Chen, Z., Ryerson, F.J., Kidd, W.S.F.,Wang, X., Zhou, X., 1997. Did the Indo-Asian collision alone create the TibetanPlateau? Geology 25, 719–722.

Neil, E.A., Houseman, G.A., 1997. Geodynamics of the Tarim Basin and the Tian Shan incentral Asia. Tectonics 16, 571–584.

Patriat, P., Achache, J., 1984. India–Eurasia collision chronology has implications for crust-al shortening and driving mechanism of plates. Nature (London) 311, 615–621.

Peltzer, G., Tapponnier, P., 1988. Formation and evolution of strike-slip faults, rifts, andbasins during the India–Asia collision: an experimental approach. Journal ofGeophysical Research 93, 15085–15117.

Peltzer, G., Tapponnier, P., Armijo, R., 1989. Magnitude of late Quaternary left-lateraldisplacements along the north edge of Tibet. Science 246, 1285–1289.

Replumaz, A., Tapponnier, P., 2003. Reconstruction of the deformed collision zonebetween India and Asia by backward motion of lithospheric blocks. Journal ofGeophysical Research 108, 2285. http://dx.doi.org/10.1029/2001JB000661.

Ritts, B.D., Biffi, U., 2000. Magnitude of post-Middle Jurassic (Bajocian) displacement onthe central Altyn Tagh fault system, northwest China. Geological Society ofAmerica Bulletin 112, 61–74.

Rowley, D.B., Currie, B.S., 2006. Palaeo-altimetry of the late Eocene to Miocene Lunpolabasin, central Tibet. Nature 439, 677–681.

Royden, L., 1996. Coupling and decoupling of crust and mantle in convergent orogens:implications for strain partitioning in the crust. Journal of Geophysical Research101, 17,679–17,705.

Royden, L.H., Burchfiel, B.C., King, R.W., Wang, E., Chen, Z., Shen, F., Liu, Y., 1997. Surfacedeformation and lower crustal flow in Eastern Tibet. Science 276, 788–790.

Royden, L.H., Burchfiel, B.C., van der Hilst, R.D., 2008. The geological evolution of theTibetan Plateau. Science 321, 1054–1058.

Ryerson, F.J., Tapponnier, P., Finkel, R.C., Meriaux, A.S., Van der Woerd, J., Lassiere, C.,Chevalier, M.L., Xu, X., Li, H., King, G.C.P., 2006. Applications of morphochronologyto the active tectonics of Tibet. In: Saiame, L.L., Bourles, D.L., Brown, E.T. (Eds.), In


http://refhub.elsevier.com/S0040-1951(13)00398-3/rf0330
























































http://dx.doi.org/10.1029/2005JB004066
























http://dx.doi.org/10.1029/2002JB002248








http://dx.doi.org/10.1130/L1180.1131


























http://dx.doi.org/10.1029/2001JB000661


















Situ-produced Cosmogenic Nuclides and Quantification of Geological processes.Geological Society of America, Special Paper, 415, p. 146.

Shen, F., Royden, L.H., Burchfiel, B.C., 2001. Large-scale crustal deformation of theTibetan Plateau. Journal of Geophysical Research 106, 6793–6816.

Silver, P.G., 1996. Seismic anisotropy beneath the continents: probing the depths ofgeology. Annual Review of Earth and Planetary Sciences 24, 385–432.

Sobel, E.R., Chen, J., Heermance, R.V., 2006. Late Oligocene–Early Miocene initiation ofshortening in the Southwestern Chinese Tian Shan: implications for Neogeneshortening rate variations. Earth and Planetary Science Letters 247, 70–81.

Sun, Z., Zhang, Y., 1995. Phanerozoic tectonic evolution of Tarim Basin. AAPGBulletin 79, 1258.Tapponnier, P., Peltzer, G., Le Dain, A.Y., Armijo, R., Cobbold, P., 1982. Propagating

extrusion tectonics in Asia; new insights from simple experiments with plasticine.Geology (Boulder) 10, 611–616.

Tapponnier, P., Xu, Z., Roger, F., Meyer, B., Arnaud, N., Wittlinger, G., Yang, J., 2001.Oblique stepwise rise and growth of the Tibet Plateau. Science 294, 1671–1677.

Taylor, M., Yin, A., Ryerson, F.J., Kapp, P., Ding, L., 2003. Conjugate strike-slip faulting alongthe Bangong–Nujiang suture zone accommodates coeval east–west extension andnorth–south shortening in the interior of the Tibetan Plateau. Tectonics 22, 25.

Wang, C.Y., Flesch, L.M., Silver, P.G., Chang, L.J., Chan, W.W., 2008. Evidence for mechanicallycoupled lithosphere in central Asia and resulting implications. Geology 36, 363–366.

Wang, E., Kirby, E., Furlong, K.P., Van Soest, M., Xu, G., Shi, X., Kamp, P.J.J., Hodges, K.V.,2012. Two-phase growth of high topography in eastern Tibet during the Cenozoic.Nature Geoscience 5, 640–645.

Williams, C.A., Richardson, R.M., 1991. A rheological layered three-dimensional modelof the San Andreas Fault in central and southern California. Journal of GeophysicalResearch 96, 16597–16623.


Yang, Y., Liu, M., 2002. Cenozoic deformation of the Tarim basin and implications formountain building in the Tibetan Plateau and the Tian Shan. Tectonics 26. http://dx.doi.org/10.1029/2001TC001300.

Yang, Y., Liu, M., 2009. Crustal thickening and lateral extrusion during the Indo-Asiancollision: a 3D viscous flow model. Tectonophysics 465, 128–135.

Yang, J., Xu, Z., Zhang, J., Chu, C., Zhang, R., Liou, J.G., 2001. Tectonic significance ofPaleozoic high-pressure rocks in the Qilian–Qaidam–Altun mountains, NW China.Geological Society of America Bulletin 194, 151–170.

Yang, Y., Liu, M., Stein, S., 2003. A 3-D geodynamic model of lateral crustal flowduring Andean mountain building. Geophysical Research Letters 30, 2093. http://dx.doi.org/10.1029/2003GL018308.

Yin, A., 2010. Cenozoic tectonic evolution of Asia: a preliminary synthesis. Tectonophysics488, 293–325.

Yin, A., Harrison, M., 2000. Geological evolution of the Himalayan–Tibetan orogen.Annual Review of Earth and Planetary Sciences 28, 211–280.

Yin, A., Taylor, M.H., 2011. Mechanics of V-shaped conjugate strike-slip faults and thecorresponding continuum mode of continental deformation. Bulletin of theGeological Society of America 123, 1798–1821.

Yueqiao, Z., Yinsheng, M., Nong, Y., Wei, S., Shuwen, D., 2003. Cenozoic extensionalstress evolution in North China. Journal of Geodynamics 36, 591–613.

Zhang, Y.-S., 1998. Three-dimensional upper mantle structure beneath East Asia and itstectonic implications. In: Flower, M.F.J., Chung, S.-L., Lo, C.-H., Lee, T.-Y. (Eds.),Mantle Dynamics and Plate Interactions in East Asia. American Geophys. Union,Washington, D.C., pp. 11–23.

Zhao, W.-L., Morgan, W.J., 1987. Injection of Indian crust into Tibetan lower crust; atwo-dimensional finite element model study. Tectonics 6, 489–504.


























http://dx.doi.org/10.1029/2001TC001300






http://dx.doi.org/10.1029/2003GL018308


















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