Crustal channel flows:

1. Numerical models with applications to the tectonics of the

Himalayan-Tibetan orogen

Christopher BeaumontDepartment of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

Rebecca A. JamiesonDepartment of Earth Sciences, Dalhousie University, Halifax, Nova Scotia, Canada

Mai H. Nguyen1 and Sergei Medvedev2

Department of Oceanography, Dalhousie University, Halifax, Nova Scotia, Canada

Received 23 September 2003; revised 9 March 2004; accepted 28 April 2004; published 25 June 2004.

[1] Plane strain, thermal-mechanical numerical models are used to examine thedevelopment of midcrustal channel flows in large hot orogens. In the models, radioactiveself-heating reduces the viscosity of tectonically thickened crust and increases itssusceptibility to large-scale horizontal flow. Channels can be exhumed and exposed bydenudation focused on the high-relief transition between plateau and foreland. Weinterpret the Himalaya to have evolved in this manner. Channel flows are poorlydeveloped if the channel has a ductile rheology based on wet quartz flow laws, and welldeveloped if there is an additional reduction in viscosity to 1019 Pa s. This reductionoccurs from 700�C to 750�C in the models and is attributed to a small percentage of in situpartial melt (‘‘melt weakening’’). Model HT1 provides an internally consistent explanationfor the tectonic evolution of many features of the Himalayan-Tibetan orogenic system.Erosional exhumation exposes the migmatitic channel, equivalent to the GreaterHimalayan Sequence (GHS), between coeval normal and thrust sense ductile shear zones,corresponding to the South Tibetan Detachment and the Main Central Thrust systems.Outward flow of unstable upper crust rotates these shears to low dip angles. In the modelboth the GHS and the Lesser Himalayan Sequence are derived from Indian crust, with thelatter from much farther south. Similar models exhibit a range of tectonic styles, includingthe formation of domes resembling north Himalayan gneiss domes. Model results arerelatively insensitive to channel heterogeneities and to variations in the behavior of themantle lithosphere beneath the model plateau. INDEX TERMS: 8102 Tectonophysics:

Continental contractional orogenic belts; 8110 Tectonophysics: Continental tectonics—general (0905); 8130

Tectonophysics: Heat generation and transport; 8159 Tectonophysics: Rheology—crust and lithosphere; 9320

Information Related to Geographic Region: Asia; KEYWORDS: thermal-mechanical models, Himalayan-

Tibetan orogen, crustal channel flow, tectonics, flow modes, surface processes

Citation: Beaumont, C., R. A. Jamieson, M. H. Nguyen, and S. Medvedev (2004), Crustal channel flows: 1. Numerical models with

applications to the tectonics of the Himalayan-Tibetan orogen, J. Geophys. Res., 109, B06406, doi:10.1029/2003JB002809.

1. Introduction

[2] An improved understanding of the evolution of largehot orogens, like the modern Himalayan-Tibetan andAndean orogens and their ancient equivalents, is an essen-tial component of research into continental tectonics. Major

questions concern the behavior of the lithospheric mantleand styles of crustal deformation and flow. The primaryfocus of this paper is the style of crustal deformation inlarge hot orogens with particular emphasis on the develop-ment of midcrustal channel flows.[3] The potential importance of gravitationally/pressure-

driven flows in hot, weak orogenic crust has already beendemonstrated [Bird, 1991; Westaway, 1995; Royden, 1996;Royden et al., 1997; Shen et al., 2001; Clark and Royden,2000]. The advance on previous studies offered here and inour earlier work [Beaumont et al., 2001a, 2001b; Medvedevand Beaumont, 2001] is to consider these flows in thecontext of a coupled thermal-mechanical model in which

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 109, B06406, doi:10.1029/2003JB002809, 2004

1Also at Department of Earth Sciences, Dalhousie University, Halifax,Nova Scotia, Canada.

2Now at Fachrichtung Geologie, Freie Universitat Berlin, Berlin,Germany.

Copyright 2004 by the American Geophysical Union.0148-0227/04/2003JB002809$09.00

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the development of channel flow is linked to and controlledby the thermal evolution of the crust.[4] The first part of the paper examines how channel

flows, driven by the differential horizontal pressure betweenthe internal, thick orogenic crust and external, thin crust,may be initiated as radioactive heating progressivelyreduces the effective viscosity of the thickened crust andincreases its susceptibility to large-scale horizontal flow.This process is illustrated using finite element, vertical crosssection, and thermal-mechanical model experiments.Results from generic reference (type 1) models are usedto explore the effects of rheological melt weakening andsurface denudation on the development of channel flows.Next, we focus on the interactions among surface denuda-tion, crustal exhumation, and channel flows. This couplingis illustrated in the type 1 models by investigating the modelresponse to surface denudation that is focused on the steep,high-relief transition zone between the interior plateau andexterior foreland. The interactions are shown to give rise toseveral possible styles of tectonic behavior, including duc-tile extrusion and the formation of domes.[5] The second part of the paper applies these concepts to

the Himalayan-Tibetan orogen using models with modifiedboundary conditions (type 2).Comparisons aremade betweentype 2 model experiments and the inferred evolution of arepresentative north-south section of the Himalayan-Tibetanorogen. It is shown that models in which a low-viscosity,partially molten, midcrustal channel is denudationallyexhumed to the surface provide an internally consistentexplanation for the tectonic exposure of the GreaterHimalayan Sequence (GHS) and its relationship to itsbounding shear zones, the South Tibetan Detachment(STD) system and the Main Central Thrust (MCT) system.In the companion paper, Jamieson et al. [2004] show thatthe results of a representative channel flow model areconsistent with metamorphic and geochronological datafrom the GHS and the Lesser Himalayan Sequence (LHS),and discuss the present results in the context of othermodels for the metamorphic evolution of the Himalaya,some of which also include some form of channel flow[e.g., Grujic et al., 1996; Vannay and Grasemann, 2001].

2. Thermal-Mechanical Model

[6] The basic design of the finite element thermal-mechanical model is the same as that described by Jamiesonet al. [2002]. The two-dimensional (2-D) vertical planestrain model has two regions: the crust (Figures 1a and1b), in which the velocity and deformation are calculateddynamically, and the mantle, where the velocity is pre-scribed kinematically (Figure 1b). The associated modeltemperature field is calculated for the whole model domain.Thermal-mechanical coupling occurs through the thermalactivation of viscous power law creep (Figure 1). Modelparameters and values are given in Table 1. We firstdescribe the mantle kinematics for the type 1 models(section 3) and later introduce variations considered moreappropriate for the Himalayan-Tibetan orogen (type 2models; section 4). In type 1 models (Figure 1), thepromantle lithosphere converges at a uniform velocity, VP,and detaches and subducts beneath the stationary, VR = 0,retromantle at S [Willett et al., 1993] (Figure 1b). The

corresponding velocity boundary condition applied to thebase of the model crust in the mechanical model thereforechanges from VP to zero across the detachment point S(Figure 1a). The subducted mantle lithosphere descends intothe mantle with constant velocity as a slab with constantdip, q (Figure 1b).[7] The 2-D plane strain mechanical model used to

calculate the velocity field and deformation [Fullsack,1995] uses an Arbitrary Lagrangian Eulerian (ALE) meth-odology in which creeping flows with free upper surfacesand large deformation are calculated on an Eulerian finiteelement grid that evolves to conform to the material domain.A Lagrangian grid, which is advected with the modelvelocity field, is used to update the mechanical and thermalmaterial property distributions on the Eulerian grid as theirposition changes. Flow is driven by the basal velocityboundary conditions described above (Figure 1a).[8] The corresponding thermal evolution includes diffu-

sion, advection and radioactive production of heat and iscalculated on the same Eulerian finite element mesh bysolving the heat balance equation:

rCp@T=@t þ v � rT ¼ Kr2T þ A;

where r is density, Cp is specific heat, T is temperature, t istime, v is velocity, K is thermal conductivity, and A isradioactive heat production per unit volume. The advectionvelocities are those prescribed kinematically in the mantleand calculated dynamically in the crust. The flexuralisostatic compensation resulting from changes in crustalthickness is calculated from the elastic flexure of a beamembedded in the model at the base of the crust.[9] The surface denudation model is designed as a

simple approximation of a fluvially controlled regime.The denudation rate is proportional to product of the localslope, and a spatial climate function, g(x), and is modu-lated with a time function, f (t) (Figure 1). To a firstapproximation g(x) is a measure of the spatial variationof aridity (0 = dry, 1 = wet) across the model, and f (t)combines the effects of long-term climate variations, thebedrock incision rate constant, and a parameter that scalesthe model surface slopes, which are determined on a 10 kmspatial resolution, to include higher riverbed slopes atsmaller scales. A more detailed denudation model is notjustified because the model is cross-sectional, and there-fore cannot represent planform drainage patterns, and thescaling effect in f (t) for local slopes at less than 10 kmspatial resolution is not known accurately. Explicitly, therate of denudation at a given surface node on the Eulerianfinite element grid is

_e t; xð Þ ¼ slope� f tð Þg xð Þ;

where slope is the average of the surface slopes of the twoelements adjacent to the node. These slopes change asthe model evolves. The climate function f (t) (Table 1) isscaled to give reasonable denudation rates of the order 0.1–2.0 cm yr�1 for the parts of the model orogen that areconsidered to be subject to strong orographically chargedfluvial denudation. This scaling changes with time toproduce phases of relatively higher and lower denudationrate. When better data are available the value of f (t) can be

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calibrated for a particular orogen or part of an orogen. Thespatial function, g(x) has a value 1.0 where orographicallycharged denudation is considered to be most efficient, thatis, on the windward flank of the model orogen. The value ofg(x) is reduced to values as low as 0.0 on the model plateau

and on the downwind flank of the model orogen (Table 1).The model result figures have insets showing _e (t, x), that is,the current distribution of the rate of denudation in cm yr�1

across the model. The values of f (t) and g(x) for each of themodels are given in Table 1.

Figure 1. Initial conditions, model 1. Other type 1 models are similar but have different melt weakeningand denudation parameter values (Table 1), and model 5 includes a weak, 10 km thick, upper crust. Type2 models are similar to model 5 but have advancing subduction boundary conditions (see section 4 andJamieson et al. [2004, Figure 1]). Only the central region of the model is shown here; full model width is2000 km. (a) Passive marker grid and mechanical layers (light grey, mid and upper crustal layer, details inFigure 1c). Vertical markers numbered to facilitate comparison with deformed grids (e.g., Figure 3); 0,model suture above subduction point, S. (b) Initial thermal structure, radioactive layers, A1 and A2 (seeFigure 1c), initial isotherms (horizontal lines) calculated for conductive steady state with Ts = 0�C andqm = 20 mW m�2, and instantaneous velocity vectors (short dark lines). Velocities VP = 2 cm yr�1 andVS = VR = 0 specified kinematically in mantle lithosphere and determined dynamically in crust. Surfacedenudation rate given by the product of local surface slope, f (t) and g(x); functions defined in Table 1.(c) Relationship between initial mechanical and thermal layers and summary of parameters (see alsoTable 1). (d) Effect of reduction in viscosity from flow law value at 700�C to 1019 Pa s at 750�C (meltweakening). Effective viscosity used in model shown by solid line, that predicted by flow law(s) shownschematically by dashed line. For further details, see text and Table 1.

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Table 1. Parameters Used in Modelsa

Parameter Meaning Value(s)

Mechanical Parametersrcrust crustal density 2700 kg m�3

rmantle mantle density 3300/3200 kg m�3

D flexural rigidity (isostasy model) 1022 N mcrustal thickness 35 kmlower crustal thickness 10 km

q subduction dip angle 20�feff effective internal angle of friction 15�c cohesion 10 MPap solid pressure PaJ 02 second invariant of the deviatoric stress tensor Pa2

heffv = B*(_I 02)

(1�n)/2nexp[Q/nRTK] general equation for effective viscosity_I 02 second invariant of strain rate tensor s�2

R gas constant 8.314 J (mol �K) �1

TK absolute temperature �KB*, n, Q as belowWQ wet Black Hills quartzite flow law n = 4.0

[after Gleason and Tullis, 1995] B* = 2.92 � 106 Pa s1/4

Q = 223 kJ mol�1

WQ � 5 (etc.) modified wet Black Hills quartzite flow law B* = B* (WQ) � 5 (etc.)DMD dry Maryland diabase flow law n = 4.7

[after Mackwell et al., 1998] B* = 1.91 � 105 Pa s1/4.7

Q = 485 kJ mol�1

DMD/10 modified dry Maryland diabase flow law B* = B* (DMD)/10‘‘Melt weakening’’ linear reduction in effective viscosity h700 = flow law value

over T range 700–750�C for WQ only h750 = 1019 Pa slength of Eulerian model domain 2000 km

Basal Velocity Boundary ConditionsType 1 modelsVP proside (convergence) velocity 2 cm yr�1

VR retroside velocity 0 cm yr�1

VS S point velocity (subduction advance) 0 cm yr�1

Type 2 modelsVP proside (convergence) velocity 5 cm yr�1

VR retroside velocity 0 cm yr�1

VS S point velocity (subduction advance) 2.5 cm yr�1

Thermal ParametersK thermal conductivity 2.00 W m �K�1

k thermal diffusivity(k = K/rCp, where rCp = 2 � 106)

1.0 � 10�6 m2 s�1

Ts surface temperature 0�CTa temperature at lithosphere/asthenosphere boundary 1350�Cqm basal mantle heat flux 20 mW m�2

qs initial surface heat flux 71.25 mW m�2

A1 (0–20 km) upper crustal heat production 2.0 mW m�3

A2 (20–35 km) lower crustal heat production 0.75 mW m�3

Surface DenudationSlope � f (t) � g(x) denudation rate (m yr�1)Slope local surface slope (see text)f (t) time function, specifies how denudation

rate (m yr�1) varies with timewhen g(x) and slope = 1

g(x) spatial function, specifies how denudation ratevaries with position x

g(x) = 0 = arid

g(x) = 1 = wet

Specific Model ParametersType 1 models (no subduction of lower crust)Model 1feff (0–35 km) 15�WQ � 5 (0–25 km)DMD (25–35 km)‘‘Melt weakening’’f(t) 0.0 t 37.5 Myr

Varies linearly 0.0 ! 0.107 m yr�1 37.5 < t < 45 Myr0.107 m yr�1 45 t 75 Myr

g(x) 1.0 0 < x 450 kmVaries linearly 1.0 ! 0.0 450 < x < 500 km

0.0 x � 500 km

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[10] The finite element model uses a viscous-plasticrheology. The plastic (frictional or brittle) deformation ismodeled with a pressure-dependent Drucker-Prager yieldcriterion. Yielding occurs when

J 02� �1=2¼ cþ p sinfeff

(see Table 1 for symbols) where the value of feff is definedto include the effects of pore fluid pressures through therelation p sin feff = (p – pf) sin f s where f = 30� for dryfrictional sliding conditions (approximately Byerlee’s lawconditions) when the pore fluid pressure, pf = 0.[11] The incompressible plastic flow becomes equivalent

to a viscous flow if an effective viscosity, heffp is defined for

the plastic material [Fullsack, 1995; Willett, 1999] such that

hpeff ¼ J 02� �1=2

=2 _I02

� �1=2:

Setting the viscosity to heffp in regions that are on frictional-

plastic yield satisfies the yield condition and allows thevelocity field to be determined from the finite elementsolution for viscous creeping flows. The overall nonlinearsolution is determined iteratively using h = neff

p (for regionsof plastic flow) and h = heff

v , as defined below (for regions ofviscous flow).

[12] When the stress is below frictional-plastic yield flowis viscous. The power law creep effective viscosity, heff isgiven by

hveff ¼ B* _I2� � 1�nð Þ=2n

exp Q=nRTK½ �;

and the values of B*, n, and Q are based on laboratoryexperiments (Table 1) with ‘‘A’’ values converted to B*assuming cylindrical creep tests. The rheology of the uppercrust (0–25 km in the initial configuration) is based on the‘‘wet Black Hills quartzite’’ flow law [Gleason and Tullis,1995]. In the model experiments (Table 1) the value of B* isscaled by constants with values ranging from 5 to 0.1 torepresent crust that is somewhat higher or lower viscositythan the standard Gleason and Tullis [1995] flow law. Thisscaling is permissible given the range of power law creepproperties for quartz-rich upper crustal rocks and allows us toinvestigate the model sensitivity to a range of upper crustalproperties. The rheology of the lower crust (25–35 kminitially) is based on the ‘‘dry Maryland diabase’’ flow law[Mackwell et al., 1998] (DMD, Table 1). In some experi-ments this value of B* is also scaled. The rheologicalstructure can be considered to represent a two-layer crustcomprising quartzo-feldspathic rocks underlain by an inter-mediate dry granulitic lower crust. Later, we introduce a third

Table 1. (continued)

Parameter Meaning Value(s)

Model 2, as model 1 but no erosionf(t) 0 t > 0g(x) 0 t > 0Model 3, as model 1 but no melt weakeningModel 4, as model 1 but minimummelt weakened viscosity

2 � 1018 Pa s

Model 5, as model 1 except feff (0–35 km) 5�Type 2 modelsModel HT1 (subduction of lower crust)feff (0–10 km) 5�feff (10–25 km) 15�WQ (0–10 km)WQ � 5 (10–25 km)

DMD (25–35 km)f(t) 0.0 t 24 Myr

Varies linearly 0.0 ! 0.133 m yr�1 24 < t < 27 Myr0.133 m yr�1 27 t 39 Myr

Varies linearly 0.133 ! 0.04 m yr�1 39 < t < 48 Myr0.04 m yr�1 48 t 54 Myr

g(x) 1.0 0 < x 500 kmVaries linearly 1.0 ! 0.0 500 < x < 550 km

0.0 x � 550 kmModel HT-HET (no subduction of lower crust)

as model HT1 but lower crust comprisesalternating 200 km regions of

DMD (25–35 km)DMD/10 (25–35 km)f(t) same as model HT1g(x) same as model HT1

Model HT-PS (no subduction of lower crust), as modelHT1 but basal velocity boundary conditions

V (0–400 km) 5 cm yr�1

V (400–1400 km) linear decrease 5 ! 0 cm yr�1

V (1400–2000 km) 0 cm yr�1

f(t) same as model HT1g(x) same as model HT1

aSee also Figure 1.bFor example, gives denudation rate of 1.07 cm yr�1 when slope = 1:10 and g(x) = 1.0.

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layer of weaker surface sediments (section 3) and alsoconsider the effect of weaker lower crust (section 7).[13] The most important additional model property is an

extra increment of viscous weakening in the upper crustalmaterial such that the effective viscosity decreases linearlywith temperature from the dynamically determined powerlaw creep value at 700�C to 1019 Pa s at 750�C and highertemperatures. This weakening is an approximation to thereduction in the bulk viscosity which will be caused by asmall amount of in situ partial melt. The ‘‘weakening’’amounts to approximately a factor of 10 decrease in effectiveviscosity. This is probably a conservative estimate for whatwe term melt weakening. In the models lower crust does not‘‘melt weaken’’ because it is considered to have undergoneearlier granulite facies metamorphism and will therefore bedepleted and not prone to melting. It is also true that thetemperatures achieved in the models would be insufficient tocause melting if an intermediate or mafic composition isassumed. In all instances the model deforms according to themechanism that produces the lowest level of the secondinvariant of the deviatoric stress for the prevailing conditions.[14] Both the mechanical and thermal calculations are

carried out for each time step (Figure 1). The upper 20 kmof the crust has a uniform radioactive heat production, A1 =2.0 mW m�3 which is higher than the corresponding heatproduction, A2 = 0.75 mW m�3 in the lower crust [Jamiesonet al., 2002]. For each model run, the initial steady statetemperature field is calculated at the lithospheric scale witha basal heat flux, qm = 20 mW m�2, a surface temperature of0�C, and no heat flux through horizontal side boundaries.The lithosphere-asthenosphere boundary is defined to be atthe 1350�C isotherm. For these conditions and thermalconductivity, K = 2.00 W (m �K) �1 the initial surface heatflux qs = 71.25 mW m�2, and the Moho temperature is704�C (Figure 1).[15] The effect of a precursor phase of oceanic subduc-

tion, which is included in some of our models [e.g.,Vanderhaeghe et al., 1999], is not included here becauseit has little effect on the evolving crustal temperatures andpeak metamorphic conditions in these models which con-sider long periods of orogenesis after oceanic subductionterminates [Jamieson et al., 2002]. All models are, however,run for an initial setup phase without surface denudation.This is designed to achieve a model state with an embryonicplateau and midcrustal channel flow as a precursor todenudation. The results are similar when moderate denuda-tion occurs during the set up phase but the times to developthe plateau and channel flow are somewhat longer.

3. Type 1 Models: Experiments WithVP = 2 cm yr�1

3.1. Reference Model 1: Two-Layer, Melt-WeakenedCrust With Minimum Viscosity 1019 Pa s

[16] We first describe results from a reference model,model 1 (Figures 2 and 3 and Table 1) and then developsubsequent models by systematically varying a few impor-tant parameters (Table 1). Model layers and correspondingrheological and thermal parameters are described above andshown in Figure 1 and Table 1. Type 1 models have VP =2 cm yr�1, VR = 0, and the S point remains stationary, VS = 0.The initial setup phase (no denudation) ends at 37.5 Myr.

[17] The evolution of model 1 during the initial 30 Myr(Figure 2) shows the deformation of a Lagrangian markergrid and the crustal layers, distribution of radioactive heatsources, and velocity and temperature fields. Thecorresponding evolution of the model topography is shownfor the entire model in Figure 4. Vertical lines in the markergrid are numbered with ‘‘0’’, representing the model ‘‘su-ture’’, initially located above the S point. In regions wherethe crust has not thickened, the velocity is uniform withdepth but viscous decoupling occurs between the upper andlower crust as the crust thickens. The lower crust remainscoupled to the kinematically prescribed mantle lithosphereexcept in the vicinity of S. Variations in the crustal veloc-ities across the S point reflect the degree of couplingbetween the upper crust, lower crust, and upper mantlelithosphere (Figures 2a and 2b). By 22.5 Myr (Figure 2c) amidcrustal velocity minimum develops proward of the Spoint, and by 30 Myr (Figure 2d), there is evidence ofincipient counterflow in melt-weakened upper crust.[18] The deformation shown by the marker grid (Figure 2)

illustrates growth of an asymmetric antiform of thickenedlower crust above S (Figure 2b) that is progressively trans-ported retroward together with the upper crust by an amountmeasured by the offset of the suture (marker 0) from S (e.g.,Figure 2d). This lower crustal wedge forms when the lowerprocrust is not subducted with the underlying promantlelithosphere. The presence of similar regions of thickenedlower crust in natural orogens should therefore be a goodindicator that the primary detachment level in continentallithosphere is at least as deep as the Moho. Conversely, theirabsence suggests that lower crust may be subducted. Later,we use this result to justify subduction of the lower procrustin type 2 models.[19] The thermal structure of the model (Figure 2) is

closely linked to the evolving distribution of thickenedradioactive crust. Temperatures initially rise in the thicken-ing crust and are lowered in the vicinity of the subductingmantle lithosphere. However, by 22.5 Myr radioactiveheating dominates and much of the middle and lower crustin the orogenic core is above 700�C (Figure 2c). At thistime the velocity minimum in the procrust occurs wheretemperatures are below 700�C and therefore corresponds tolow-viscosity flow according to the wet quartzite flow lawrather than to the melt-weakening effect.[20] The setup phase of model 1 ends with the onset of

denudation at 37.5 Myr. The subsequent evolution of themodel demonstrates the interaction between the channelflow and denudation focused at the sloping proflank of theplateau. The climate function precludes denudation on thecorresponding retroflank (Figure 1 and Table 1).[21] Between 45 and 60 Myr (Figure 3) channel flow

initiates in the thickened upper crust where temperatures arebetween 700� and 750�C, corresponding to the region wheremelt weakening reduces the viscosity to a minimum of 1019

Pa s. The lower crust, which is not influenced by meltweakening, does not participate in the channel flow. By45 Myr, a 15 km thick channel is well developed but theflow tip is still a long way from the denudation front(Figure 3a). A plateau develops above the channel and theretrowedge (Figure 4) because both of these regions arenow sufficiently hot (>800�C, Figure 3a) and weak that thecrust cannot maintain lateral topographic gradients. By

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Figure 2. Crustal-scale deformation and thermal evolution of model 1 for 30 Myr of the setup phaseduring which there is no surface denudation (V = H). Top panel in each set shows deformed marker gridand mechanical layers (grey, mid and upper crustal layer); bottom panel shows isotherms (contoured at100�C intervals), velocity vectors, and thermal layers (grey, A1 layer). Heavy line with dots representsposition of model suture (below vertical marker 0). Figures 2a–2d show stages in the evolution for time,t, and convergence Dx.

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Figure 3. Crustal-scale deformation and thermal evolution of model 1 between 45 and 60 Myr (V = H).Top and bottom panels in each set correspond to those described in Figure 1. Also shown in top panelsis the distribution and rate of slope-dependent erosion across the model surface; scale maximum is1 cm yr�1. Figures 3a–3c show stages in the evolution for time, t and convergence Dx. Figure 3d showsthe retroside of the model at 60 Myr.

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52.5 Myr, the channel has expanded outward beneath theplateau and its tip is nearing the denudation front. We refer tothe expansion as ‘‘tunneling’’ by the channel because itinvolves the incorporation of crustal material into the chan-nel. This process is discussed in more detail in section 9. Itcan, however, be seen from Figure 3b that the crustaltemperature has to be between 700 and 750�C for the channelflow to develop either in an instantaneous sense, or to createfinite tunneling. That is, thermal weakening of the thickenedcrust is required as a precursor to channel tunneling. Theupper procrust above the channel is also translated towardthe denudation front (Figure 3b, note the contrast withFigure 3a). Crust therefore converges laterally on the denu-dation front from both directions (Figure 3b). The stronglower crust is, however, unaffected by the denudation andcontinues to underthrust the channel without deformation atlocations proward of S. At this stage the maximum denuda-tion rate is approximately 6 mm yr�1 (Figure 3b). Isothermsare bowed upward at the denudation front and condensed intoa thin high-gradient boundary layer owing to thermal advec-tion bymaterial moving upward beneath the denudation frontto replace eroded material (Figure 3b). In the midcrust,isotherms are advected laterally and inverted by the channelflow, resulting in a near-isobaric temperature increase from600� to 900�C between the edge of the plateau and the S pointat the level of the channel (Figure 3b).[22] By 60 Myr, there is strong coupling between the

channel flow and the denudation front (Figure 3c). Thefocused denudation exhumes channel material to the surfacein a narrow, nearly symmetric zone. Converging procrust isdeformed, rotated, and exposed at the surface in the footwallbeneath the channel material. Correspondingly, a crosssection of plateau edge upper crust is exposed in the hangingwall above the channel (Figure 3c). The extruded channel isbounded by upper normal sense and lower thrust sense shearzones. Isotherms are advected upward and outward by theflow as the channel is exhumed, forming a thermal boundarylayer in which 700�C crust lies at a depth of only 15 kmwhen denudation rates peak at approximately 1 cm yr�1.[23] At 60 Myr, the retroside of the model (Figure 3d)

is still in the process of transition to a plateau [e.g.,

Vanderhaeghe et al., 2003]. The suture has been transportedprogressively retroward and its surface expression is nowlocated more than 300 km from S. Consequently, approx-imately half the retrocrust comprises material advected fromthe proside of the orogen (i.e., material above the trace ofthe suture, Figure 3d). There is no channel flow in thethickened lower crust but a weak channel has developed inthe hot midcrust. In the absence of denudation, the channeltunnels outward at a rate determined by the timescale thatradioactive self-heating and thermal relaxation of the thick-ening crust take to weaken the crust. By 75 Myr (partlyshown in Figure 5) a retroplateau has developed and theplateau edge, plateau flank, and channel tip achieve a steadystate geometry with respect to each other as the orogengrows outward. Tectonic shortening of the upper crust andinflation by channel material both contribute to the crustalthickening across the foreland to plateau transition.[24] The total velocity field of the model can be decom-

posed into components driven by the velocity boundaryconditions and by gravity (Figure 5). This is done by takingthe converged nonlinear solution and then re-solving for theboundary and gravitational forcing separately without chang-ing the converged model properties. The flow caused by theboundary conditions is consistently retroward, although it isgreatly reduced in the hottest part of the channel flow zone. Incontrast, gravitational flow is in the prodirection, i.e., a coun-terflow, on the proside of the system, and is a maximum inthe channel. The velocity decomposition therefore demon-strates that gravity drives the channel flow through thepressure gradient caused by the lateral variation in the weightof the channel overburden [cf. Turcotte and Schubert, 1982,p. 234].

3.2. Effects of Variations in Parameter Values

[25] Models 2, 3, 4, and 5 (Figures 6 and 7) illustrate theeffects of no erosion, no melt weakening, a lower value of theminimum melt-weakened viscosity, and the role of a weakerupper crustal rheology on the tectonic style of the referencemodel (model 1).All othermodel parameters remain the same.[26] Model 2 illustrates tunneling by the channel flow

in the absence of erosion. Channel counterflow initiates at

Figure 4. Evolution of the topography for model 1 shown with respect to the S point, x = 0 (Figure 1).The height scale is shown for two representative isostatic balances which depend on F = Dr/rm, whereDr = rm – rc and rm and rc are the mantle and crust densities, respectively. The scale of the height is mostsensitive to Dr and the results are therefore shown for Dr = 500 and 600 kg m�3, corresponding to F =0.156 and 0.182, respectively.

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30 Myr (Figure 2), and the channel tip tunnels outwardthrough the procrust as a plateau develops above. The rateof tunneling and the channel velocity are both less than inmodel 1, and the propagation of the channel is again limitedby the need to heat and weaken the tectonically thickenedcrust. Crustal thickness reaches a maximum of approxi-mately 75 km by 45 Myr; by 75 Myr the large-scalegeometry is similar to model 1, although there is no surfaceevidence of the underlying channel flow. Lateral expansionof the channel into the converging procrust leads to surfaceshortening across the plateau flank, but little added defor-mation within the plateau. Models with denudation ratesintermediate between those in models 1 and 2 (not shown)partly exhume and expose the channel material.[27] In model 3, there is no melt weakening, and therefore

the viscosity of the upper and midcrust is controlled by thewet quartzite flow law (Table 1 and Figure 1 WQ � 5). Thechannel does not develop until �52 Myr because temper-atures must exceed 850�C before the viscosity is sufficientlyreduced. By comparison with model 1, channel counterflow

is sluggish and the channel tip tunnels slowly. At approx-imately 67 Myr, the velocity field changes and the entireplateau procrust above the channel translates outward withthe channel. The two types of channel flow, flow betweenstationary boundaries and flow with moving boundaries, arerespectively known as Poiseuille and Couette flows [e.g.,Turcotte and Schubert, 1982, p. 234], as discussed furtherbelow (section 9). We refer to the outward translation of theupper crust as an unstable flow because it is caused by agravitational instability of the crust above the viscouschannel. The velocity of the translation is partly controlledby the viscous coupling between these two regions. Thismechanism would lead to what has been termed ‘‘gravita-tional collapse’’. The outward flow of unstable upper crustextends and thins the plateau crust in the region above thelower crustal antiform and slightly increases the rate ofshortening at the denudation front. There is less couplingbetween surface denudation and the channel flow (comparemodel 1 at 52.5 Myr, Figure 3); at 75 Myr the channel tipstill underlies the plateau although a broad, symmetrical

Figure 5. Top panels, crustal-scale deformation and thermal evolution of model 1 at t = 75 Myr,convergence Dx = 1500 km shown as in Figures 1 and 2 (V = H). Bottom panels, total and decomposedvelocity distributions (vectors, short dark lines). See text for explanation.

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Figure 6. Crustal-scale deformation and thermal evolution of models 2–4 at 75 Myr (Figures 6a–6c)shown as in Figures 1 and 2. Models are variations on model 1 (Table 1). (c) Also total and decomposedvelocity distributions at 75 Myr (vectors, short dark lines). See text for explanation.

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exhumation zone (compare model 1, 60 Myr, Figure 3) isevident on the plateau flank.[28] In model 4 the effect of melt weakening is enhanced

by decreasing theminimum effective viscosity from 1019 Pa sat 750�C to 2 � 1018 Pa s. Crustal velocities, deformation,and thermal fields evolve in a similar manner to those ofmodel 1 (Figures 3, 5, and 6), and the velocity field,decomposed into boundary and gravitationally forced com-ponents, is also similar to that in model 1 (Figures 5 and 6). Ininfinitely long channel flows [e.g., Turcotte and Schubert,1982], the gravitationally induced velocity is predicted toscale with the inverse of the viscosity. A comparison ofmodels 1 and 3 shows a much smaller difference thanpredicted because the high-viscosity crust at the end of thechannel impedes the flow, an effect not considered in simpleunrestricted channel models. This result highlights thepotential importance of thermal-mechanical coupling inlimiting crustal channel flows, a point addressed in section 9.[29] Model 5 tests model sensitivity to the presence of a

weak upper crust, approximating an unmetamorphosed

sedimentary sequence above crystalline middle crust. Theweak upper crustal layer affects the model because it maybecome unstable under the basal drag from the channelcounterflow, particularly when it is progressively thinned byerosion at the denudation front. In model 5 the internalangle of friction (feff) of the upper 10 km of crust is reducedto 5�, which can be interpreted to represent moderateoverpressuring by pore fluids. Otherwise the model is thesame as model 1, and initially evolves in a similar way.However, focused erosion at the denudation front, whichthins and weakens the upper crust further, leads to atransition from stable to unstable upper crust between 60and 67.5 Myr (Figure 7). In this case the gravitationalinstability of the channel and overlying crust is sufficientthat the outward translating upper crust overrides theexhumation front (Figure 7; compare model 3, Figure 6b),creating an asymmetric, thrust sense extrusion zone. Thistype of behavior is discussed in more detail below (type 2model HT1). The outward translation of the upper crust alsocauses the plateau crust adjacent to the lower crustal anti-

Figure 7. Crustal-scale deformation and thermal evolution of model 5 at 75 Myr shown as in Figures 1and 2 except weak upper crustal layer (Table 1) which is white. Bottom panels show the total anddecomposed velocity distributions (vectors, short dark lines) for comparison with model 1 (Figure 5).

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form to extend and thin, allowing upwelling of the low-viscosity channel material (Figure 7) in a broad dome-likeregion beneath the plateau.

4. Type 2 Models: Himalayan-Tibetan StyleExperiments

[30] In the second part of the paper we compare modelresults with a representative north-south cross section ofthe Himalayan-Tibetan orogen (Figure 8; sources cited incaption). The purpose of the comparison is to show that arepresentative type 2 model (HT1), in which a low-viscosity, midcrustal channel is exhumed to the surfaceby erosion, provides an internally consistent explanationfor the large-scale geometry and tectonic features of theHimalaya and southern Tibet (Figure 8b). In particular, weconsider the rapid erosion of the southern flank of theHimalaya, the surface position of the Indus-Tsangposuture, the origin of the GHS, including the mechanismfor its uplift and exposure and its relationship to itsbounding shear zones (STD and MCT), the tectonicprocesses that juxtaposed the GHS and LHS across theMCT zone, and the origin of the north-south extension inthe southern Tibetan Plateau and associated north Hima-layan gneiss domes. We also demonstrate model response,and corresponding tectonic styles, to variations in denu-dation rates, crustal strength, and assumed mantle kine-matics. Some of these tectonic styles may currently existin parts of the Himalayan-Tibetan system, or may haveexisted at earlier stages of its development. In the com-panion paper, Jamieson et al. [2004] test predictions frommodel HT1 against a variety of metamorphic and geo-chronologic data from the GHS and LHS in the centralpart of the orogen.

4.1. Type 2 Models: Primary Assumptions

[31] The simplifying assumptions used in the HT modelexperiments are as follows. The boundary conditions do notchange with time, and there is no movement of crust normalto the cross section. In the Himalayan-Tibetan system thecumulative out-of-plane flow of material has been estimatedto be approximately 15–30% of the total convergence[Dewey et al., 1988; Le Pichon et al., 1992; Westaway,1995; also see Johnson, 2002] and GPS data suggest thatthis flow is currently significant [Wang et al., 2001]. Itsimportance for modeling the Himalayan-Tibetan orogen canbe assessed from Royden et al. [1997] and Shen et al. [2001].[32] Resorption of lithosphere by the mantle under large

hot orogens, and beneath the Himalayan-Tibetan orogen inparticular, is poorly understood and may involve subductionand/or underthrusting [e.g., Owens and Zandt, 1997],downwelling [Tilmann et al., 2003], delamination [Bird,1978], and/or slab break-off and/or slab retreat [e.g., Willettand Beaumont, 1994; van der Voo et al., 1999;Maheo et al.,2002], or convective removal [e.g., Houseman et al., 1981;Molnar et al., 1993]. Here, we initially assume that sub-duction and/or underthrusting dominates and also considermigration of the S point as described below. Royden et al.[1997] and Shen et al. [2001] showed that these boundaryconditions are compatible with the planform evolution ofthe orogen. Results presented here complement theirs byproviding a more complete analysis of the plane strain

thermomechanical evolution. Although the subductionboundary condition may not be correct, in section 8 wedemonstrate that for the region of interest (proward of themodel suture) the model results are relatively insensitive tothis particular choice. We also assume that the lowerprocrust remains attached to, and is subducted with, itsunderlying mantle lithosphere. Subduction of lower procrustis preferred because in Tibet there is no known large lowercrustal antiform, as seen in the previous models (e.g.,Figure 3), and therefore an alternative sink for lower crustis required.[33] For simplicity, we first investigate models with

laterally uniform initial mechanical and thermal properties.In section 7 we consider the effects of crustal heterogeneity.

4.2. Type 2 Models: Advancing SubductionBoundary Condition

[34] In type 2 models the boundary conditions arechosen to be compatible with the average 5 cm yr�1

postcollisional convergence rate (VP) in the Himalayan-Tibetan orogen (Figure 9) [Dewey et al., 1988; Searle,1996; Hodges, 2000; Hauck et al., 1998]. In both natureand the models, the S point location (Figure 1) maymigrate, leading to subduction zone advance (Figure 9)or retreat [Royden, 1993; Willett and Beaumont, 1994;Waschbusch and Beaumont, 1996]. Evidence for advanc-ing subduction in the Himalayan-Tibetan orogen comesfrom the manner in which precollisional suture zones northof the Tsangpo suture wrap around India [Dewey et al.,1988]. This geometry is compatible with crustal deforma-tion driven by northward advancing subduction [Royden etal., 1997] and relict slabs imaged by tomography [van derVoo et al., 1999; DeCelles et al., 2002]. We show belowthat models with advancing subduction are compatiblewith the current surface position of the Tsangpo suture,whereas stationary S point models (Figure 9a) are not. Inthe proterminology/retroterminology/S point terminology,advance of the S point (VS same direction as VP; Figure 9b)implies that convergence of the prolithosphere is partitionedbetween subduction zone advance, at rate VS, and subduc-tion, at rate VP-VS. Figure 9 also shows the advancingsubduction boundary condition applied at the base of thecrust (Figure 9b), and combined with subduction of the lowerprocrust (Figure 9c). In the Himalayan-Tibetan modelsdescribed below, VP = 5 cm yr�1, VS = 2.5 cm yr�1, andVR = 0, chosen from a sensitivity analysis and also compat-ible with the position of the inferred Tethyan relict slab[DeCelles et al., 2002].[35] From the perspective of the tractions exerted at the

base of the crust, any transformation that preserves the twoindependent velocities, VP-VS and VR-VS (Figure 9), pro-duces equivalent boundary conditions. For example, a fixedS point reference frame model equivalent to that shown inFigure 9b is obtained by subtracting 2.5 cm yr�1 from allvelocities. In this reference frame, subduction at the S pointcan be interpreted to be symmetric, involving both mantlelithospheres. Similarly, subtracting 5 cm yr�1 from allvelocities changes the reference frame to one in which Indiais fixed and the S point retreats as Indian mantle lithospheresubducts. The mechanics of crustal deformation in all ofthese models is the same, which implies that in equivalentnatural orogens information on the crustal deformation

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alone is insufficient to allow VP, VS, and VR to bedetermined independently. Additional constraints, such asslab dip, the thermal effect of the mantle on the crust, orindependent estimates of velocities with respect to anexternal reference frame, are required to remove this uncer-tainty. For the Himalayan-Tibetan system, we prefer tointerpret the results in the fixed Asia reference frame(Figures 9b and 9c). However, to minimize the width of

subsequent figures, the results (e.g., Figure 10) are shownwith a fixed S point.

5. Model HT1

[36] Model HT1 is a representative channel flow modelthat produces results in broad agreement with generalizedobservations from the Himalayan-Tibetan orogen. Except

Figure 8

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for the advancing S point and subduction of lower procrust,the initial configuration of HT1 is the same as model 5above (Figure 1), with three laterally uniform crustal layers[Jamieson et al., 2004, Figure 1]; its properties are also

similar to model 3 of Beaumont et al. [2001b] except thatmodel 3 had a weaker upper crust B*(WQ/2) versusB*(WQ) in HT1. Model HT1 represents the end-memberin which denudation is focused on the proflank of the model

Figure 8. Representative north-south cross sections of the Himalayan-Tibetan orogen. (a) Lithosphere-scale sectionmodified from Owens and Zandt [1997] using information compiled by DeCelles et al. [2002] and from Johnson [2002],Tillmann et al. [2003], andHaines et al. [2003]. (b) Crust and uppermost mantle scale section showing Himalaya and southernTibet, modified from Nelson et al. [1996] using information from Hauck et al. [1998] and DeCelles et al. [2002]. Numbersdenote problems and processes considered fundamental to a comprehensive model of the orogen [Hodges, 2000], including(1) rapid erosion of the southern flank of the Himalaya; (2) shortening on the Main Central Thrust (MCT) system and thrustfaults to the south; (3) extension on the South Tibetan Detachment (STD) system; (4) high-grade metamorphism and anatexisin the Greater Himalayan Sequence (GHS); (5) melting in the middle crust beneath Tibet; (6) juxtaposition of contrastingprotoliths across the MCT zone; (7) ‘‘inverted’’ metamorphism within the MCT zone and subjacent Lesser Himalayansequence; (8) the position of the Indus-Tsangpo suture; and (9) north-south extension in the southern Tibetan Plateau.

Figure 9. Explanation of model boundary conditions. In each panel, procrusts and retrocrusts (India andAsia) are grey and black, respectively. S marks the subduction point (mantle suture) and Su marks thecorresponding surface suture. Basal velocities are shown by arrows and labeled VP, VS, and VR in the Asiafixed reference frame. (a) Boundary conditions for model 1 with VP = 2 cm yr�1 and VS = VR = 0 and nosubduction of the lower crust. (b) Corresponding boundary conditions for the Himalayan-Tibetan orogen,again with no lower crustal subduction. (c) Boundary conditions and progressive evolution of modelHT1, with lower crustal subduction, showing the effect of advancing subduction on the position of S anddistributions of Indian and Asian crusts in the Asia fixed reference frame. For reference, in this model aTethyan oceanic slab that detached at the onset of collision and remained stationary in the mantle wouldnow be located below S (t = 0 Myr panel), a distance Dx = 1350 km south of the current position of S (t =54 Myr panel). Note model results in subsequent figures are shown in a fixed S reference frame.

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Figure 10

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orogen, the region corresponding to the Himalayan front,with no denudation of the interior plateau or of the northernretroflank of the system. However, similar results areobtained for the proside of the model when there are lowdenudation rates on the retroflank. Advancing subductionrequires removal of the retromantle lithosphere, which wemodel by subduction/ablation of the retromantle lithosphere[Tao and O’Connell, 1992; Pope and Willett, 1998] (seemantle kinematics in Figure 1 of Jamieson et al. [2004]), inorder to conserve mantle lithosphere. To allow for uncer-tainties in age, total convergence, and convergence velocity,current Himalayan-Tibetan properties should be comparedwith the model results in the range 48–54 Myr. Here wefocus on the tectonic results; the corresponding thermal andmetamorphic results are described by Jamieson et al.[2004].[37] Model HT1 evolves like model 5, with corre-

sponding phases of channel counterflow beneath stableupper crust, coupling between the channel and the erosionfront, instability of the upper procrust above the channel,and finally outward flow of the upper crust together withthe underlying channel, leading to overthrusting and asym-metry at the erosion front. Both models have similar thermaland tectonic styles in the region corresponding to theHimalaya and southern Tibetan Plateau, although theydevelop at different times because the convergence veloc-ities differ. The similarities demonstrate that this region ofthe model is insensitive to the difference between theboundary conditions for the two types of model experi-ments. The predicted tectonic styles are also similar to thatof the Himalayan front (Figure 8). Models 5 and HT1 do,however, differ in regard to the respective presence andabsence of the large lower crustal antiform at the S point(Figures 7 and 10), because the lower crust is not subductedin model 5.

5.1. Effect of Boundary Conditions onSuture Migration

[38] Models 5 and HT1 also differ in regard to theevolution of the surface position of the suture (marker 0,Figures 7 and 10). When VS = VR = 0 (type 1 models), theorogenic crust is mostly derived from the prolithosphere,and consequently, the surface position of the suture istransported progressively retroward with respect to the Spoint (Figures 2 and 7). This process would create a mid/upper Tibetan crust composed primarily of Indian platecrust, contrary to observation [e.g., Yin and Harrison,2000; DeCelles et al., 2002]. In contrast, when type 2boundary conditions are used as in Figure 9b, the orogenic

crust is derived approximately equally from both sides ofthe system. This result is easily understood in the fixed Spoint reference frame (VS = 0) in which crustal convergenceis symmetric above the S point. Therefore in the absence ofdenudation, the surface position (0) of the suture (Su) in amodel like that shown in Figure 9b, remains above themantle suture (S point) and would be located in the center ofthe orogen, corresponding to the middle of the TibetanPlateau in the Himalayan-Tibetan context. This resultremains approximately the same in a model in which lowerprocrust subducts, corresponding to HT1 but with nodenudation. In summary, the tectonically driven motion ofthe surface suture with respect to the S point is retroward ifjVP – VSj > jVR – VSj and the converse if the inequality isreversed.

5.2. Effect of Denudation on Suture Migration

[39] Denudation also causes the surface position of thesuture to migrate. This is because it removes material andadds a second source of imbalance in the crustal materialfluxes, in addition to the one from the basal boundaryconditions. In model HT1 the surface and mantle suturesremain aligned, as explained above (Figure 10a), untilasymmetric denudation of the proflank of the orogencauses progressive proward translation of the surface suture(Figures 10b–10d). The resulting position of the surfacesuture at 51–54 Myr (Figure 10d, marker 0) correspondswell to the equivalent average position the Indus-Tsangposuture in the Tibetan Plateau (Figure 8). The combination ofthe choice of VS and cumulative denudation in HT1therefore reproduces the observed surface suture position.However, this choice is not unique because there is a trade-off between the two processes. HT1 probably represents theend-member in which VS is a minimum and cumulativedenudation is a maximum. Equivalent results could beachieved with VS > 2.5 cm yr�1 and less cumulativedenudation. For example, Willett and Beaumont [1994]favored the higher VS boundary condition and interpretedthe behavior in terms of subduction zone retreat of the Asianmantle lithosphere. That is, when VS > 2.5 cm yr�1 Asianmantle lithosphere is subducted/ablated more rapidly thanIndian mantle lithosphere. Models with VS > 2.5 cm yr�1

may be shown to be preferable once an accurate estimate ofthe total denudational mass per unit cross-sectional lengthof the orogen can be made. The converse, VS < 2.5 cm yr�1

with more cumulative denudation, is probably not accept-able because this would require unreasonably high averagedenudation rates throughout the development of the orogen.The trade-off between VS and denudation has implications

Figure 10. Crustal-scale deformation and thermal evolution of model HT1 (V = H) [see also Jamieson et al., 2004,Figure 2]. Top panel in each set shows deformed marker grid and mechanical layers (grey, midcrustal layer); bottom panelshows isotherms, velocity vectors, and thermal layers (grey, A1 layer). Heavy line with dots represents position of modelsuture (vertical marker 0). Also shown is the distribution and rate of slope-dependent erosion across the model surface,scale maximum = 1 cm yr�1. (a–d) The 30–54 Myr evolution during which overall convergence, Dx, increases from 1500to 2700 km. Note the migration of the surface suture, marker 0, with respect to the mantle suture, S, and the ‘‘Himalayan’’denudation front. For ease of display the results are shown in the fixed S point reference frame thereby avoiding anexcessively wide figure (compare equivalent to Figure 9c). Transformation into the Asia fixed frame offsets successivelylower panels farther to the right so that the S point would be positioned at Dx = 750, 975, 1200, and 1350 km, respectively,as shown. (Animations are available at http://geodynam.ocean.dal.ca/jgr/test54_1.gif and http://geodynam.ocean.dal.ca/jgr/test54_2.gif.)

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for the thermochronology of exhumed rocks [Jamieson etal., 2004].

5.3. Crustal Geometry and Properties

[40] Model HT1 has properties consistent with the ob-served Himalayan-Tibetan orogen in regard to crustal thick-ness, plateau width, and extent of underthrusting ofpromantle lithosphere (Figures 8 and 10; similar to model3 of Beaumont et al. [2001b]). The long-wavelength topog-raphy (Figure 11) develops first by uplift of the surfaceadjacent to the suture to levels equal to or greater than theeventual plateau height (e.g., model 1, Figure 2). This regionof high elevation then propagates outward in both directionsand forms a plateau as the midcrust becomes hot and weak[Royden, 1996; Beaumont et al., 2001b; Vanderhaeghe etal., 2003]. By implication, in planform the plateau expandsoutward from a high, linear, narrow core, as predicted byShen et al. [2001], and is not created by late stage ‘‘plateauuplift’’ over a broad region. The testable prediction is thatlocations close to the Indus-Tsangpo suture have had per-sistently high elevations, perhaps even higher than today,throughout Cenozoic Himalayan-Tibetan orogenesis [e.g.,Rowley, 2002; Spicer et al., 2003].[41] At this point the provenance of channel material is

worth noting. Channel material is derived from two sources.Initially, melt weakening occurs in midcrustal materiallocated just proward of the S point. This is shown bycomparing the channel position with the location of themodel suture and its trace with depth (vertical marker 0,Figure 10a), which represents the boundary between pro-crust and retrocrust. Material located proward of this line isequivalent to Indian crust. Later, as the suture is advectedproward (Figures 10b–10d), material from retroward of thesuture, equivalent to Asian crust, is advected in the channelacross the S point. However, even at 54 Myr this materialremains close to or retroward of the surface location of thesuture (Figure 10d). The results therefore predict thatexposed channel midcrust located proward of the Indus-Tsangpo suture (Figure 8 and marker 0, Figure 10) will haveIndian crustal characteristics; in contrast, retroward of thesurface suture, exposed midcrustal rocks and plutons de-rived from melting of the crust should exhibit Asianaffinities. The GHS, having been derived from the midcrust

of the leading edge of the prolithosphere, is predicted tohave Indian crustal characteristics, a result that is consistentwith geological observations [e.g., DeCelles et al., 2002;Myrow et al., 2003].

6. Effects of Denudation Rate and Upper CrustalStrength: Tunneling, Extrusion, and Doming

[42] The models illustrated in Figures 12 and 13 all havethe same advancing subduction boundary conditions asHT1, but variations in surface denudation rate and uppercrustal strength lead to a variety of predicted deformationstyles. Both upper crustal rheology and denudation contrib-ute to the stability of the crust above the channel and to thegeometry of the exhumation/thrust front. In the limit of nodenudation and moderately strong upper crust, the channeltunnels outward into the converging crust (Figure 12a).However, significant erosion of the model plateau flankproduces five different tectonic exhumation and domingstyles, resulting from interactions among denudation, uppercrustal deformation, and the channel flow.

6.1. Near-Symmetric Exhumation

[43] Denudation of the plateau flank leads to exhumationof the channel as material is removed from the surface.Active channel flow will continue during exhumation ifthe channel viscosity remains low, which depends on thecooling rate during exhumation. Rapid denudation andexhumation remove surface material at high thermal Pecletnumber and the channel is advected upward with littlecooling. The same advection also thins the surface thermalboundary layer and weakens the upper crust. The positivefeedback between denudation and channel exhumation isreinforced by other processes that weaken the crust. Forexample, high pore fluid pressure reduces the crustalstrength, by reducing the effective internal angle offriction (section 2). Figure 12b illustrates a case wherefeff = 5�, corresponding to significantly higher thanhydrostatic fluid pressure in the upper crust. Conversely,sedimentation that buries the channel will have the oppo-site effect, thickening and strengthening the upper crustand therefore acting against the positive feedback thatleads to channel exhumation.

Figure 11. Evolution of the topography for model HT1 shown in the fixed S point reference frame inthe same manner as Figure 10. The height is shown for the same representative isostatic balances as thoseshown for model 1 in Figure 4.

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[44] When the upper crust above the channel remainsstable, that is it does not extend or detach and move with thechannel, the surface exhumation zone is nearly symmetricand the exhumed channel dips steeply (Figure 12b). The

boundaries of the exhumed channel record evidence of itsevolution. If channel flow is not active during exhumation,the channel will have relict thrust and normal sense bound-ary layer ductile shears that were produced during the earlierphase of subhorizontal high-temperature channel flow.Channel flow that continues during exhumation will pro-duce additional ductile and brittle shear fabrics superim-posed on the earlier ones. The near-symmetric tectonic style(Figure 12b) is primarily the result of exhumation driven bydenudation. This is less likely within a plateau becausedenudation is usually focused on plateau flanks. In unusualcircumstances, channel exhumation may occur within aplateau where fluvial and/or glacial incision is sufficientto trigger the positive feedback mechanism.

6.2. Asymmetric Thrust Extrusion

[45] The unstable outward flow of weak upper crusttogether with the channel converts the near-symmetricexhumation style to asymmetric thrust extrusion, as ob-served in the Himalaya (Figure 8). The upper and lowerbounding shears dip at low angles (Figure 12c) and thrustsense shearing is enhanced by outward flow of upper crust.During this type of extrusion the upper shear zone may benormal or thrust sense depending on the relative velocitybetween the upper crust and the underlying extrudingmaterial. Most HT models of this type predict an overallcumulative normal sense of offset but this offset on the uppershear zone is less than that across the lower bounding shear.

6.3. Hinterland Doming by Crustal Extension

[46] Outward motion of the plateau upper crust duringasymmetric thrust extrusion may be balanced by localizedupper crustal extension within the plateau at positionsranging from near the exhumation front to above the modelS point (Figure 7). Localized tectonic extension thins thecrust, causing positive feedback between crustal thinningand channel exhumation. In this case surface denudation isunnecessary, and crustal thinning could even be accompa-nied by surface subsidence and sedimentation. When chan-nel flow is efficient, the channel may inflate and balloonupward to form a dome that fills the space created byextension (Figures 12d and 13d). In contrast, when channel

Figure 12. Crustal-scale deformation shown for a regioncorresponding to the Himalaya and southern Tibet for aseries of models that exhibit differing tectonic styles inresponse to variations in denudation rate and upper crustalstrength (shown in white) (V = H). All models have thesame advancing subduction boundary conditions as HT1.They differ from HT1 in regard to maximum denudationrate; labeled H, high (>1.4 cm yr�1); M, moderate (0.4–1.4 cm yr�1); and L, low (<0.4 cm yr�1) on Figures 12a–12g. They also differ from HT1 in regard to upper crustalfrictional properties (labeled as 5� and 15�, the effectiveinternal angle of friction, see section 2), and upper crustalrheology with effective viscosity, based on the wet quartzflow law [Gleason and Tullis, 1995], WQ, scaled up by 1, 5or scaled down by 2 or 3; see section 2. Line above modelsurface indicates denudation front; marker grid is removedwhere strongly deformed; arrows show flow direction; 8indicates the suture; and 9 indicates structures resemblingnorth Himalayan gneiss domes.

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flow is slower than the rate of upper crustal extension thewhole crust together with the channel is uplifted isostaticallywithout inflation, in response to the upper crustal extension.

6.4. Doming Triggered by Underthrusting

[47] Doming may also be triggered during asymmetricthrust extrusion when the leading edge of the converging,relatively strong procrust is injected into the midcrustalchannel. The frontal ramp underthrusts the channel, upliftsit, and squeezes it against the overlying upper crust. Givensufficiently elevated stress, this squeezing will destabilizethe upper crust and trigger extension, forming a dome abovethe frontal ramp (Figure 12e). Subsequently, this dome maybe translated over the ramp and toward the exhumationfront. Domes created in this way lie between the suture andthe denudation front. Recently formed domes of this typeshould be spatially correlated with the frontal ramp of theunderthrust procrust.

6.5. Extruded Domes

[48] Rather than destabilizing the upper crust, domesformed by the underthrusting mechanism described abovemay be rotated, flattened, and inserted into the channel as itflows over the frontal ramp (Figures 12f and 13f ). If thisprocess continues, deformed domes will be extruded andexpelled at the denudation front. The expulsion mechanismmay resemble the ‘‘pip’’ mechanics proposed by Burchfieland Royden [1985], but in this case the pip is initially partof the ductile channel, not strong cold crust, and it deformsas it is extruded.

6.6. Extrusion Zones Advected Into the Plateau

[49] Decreasing denudation rates can lead to renewedchannel tunneling in the midcrust (Figure 13g). In suchinstances, as continued convergence thickens the plateauflank, the abandoned extrusion zone becomes embedded inthe newly thickened crust and is advected into the plateau(Figure 12g).

7. Sensitivity of Model Results to CrustalHeterogeneity

[50] In all the models discussed above the crust consists oflaterally uniform layers. However, in the Himalayan-Tibetanorogen, the Indian and Asian crusts are likely to havedifferent compositions and, moreover, the earlier accretion-ary history [e.g., Yin and Harrison, 2000] may have given theAsian crust considerable internal heterogeneity. Although wehave not undertaken an exhaustive sensitivity analysis topotential crustal heterogeneities, model HT-HET (Figure 14)provides some insight into the effect of variations in lowercrustal properties on the thermal-tectonic style of the models.In particular, we focus on whether or not such variations leadto obstructions that block channel flows.[51] Model HT-HET is similar to model HT1 except for the

properties of the lower crust, which is the strongest region ofthe model and therefore has the greatest potential to disrupt orimpede channel flows. The lower procrust, which is notsubducted (compare type 1 models), comprises alternating200 km wide zones with the standard dry Maryland diabase(DMD) rheology and with the same rheology but with B*/10(DMD/10; section 2, Table 1). The strong and weak regions

Figure 13. Thermal evolution of models corresponding tothose shown in Figure 12 (V = H). Panels show isothermscontoured at 100�C intervals, velocity vectors (short darklines), and thermal layers (grey, A1, and white, A2). Otherproperties are described in Figure 12.

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Figure 14

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in the lower crust therefore have a nominal viscosity contrastof 10, which is modulated during the evolution of the modelby the effect of power law flow and temperature variations.[52] The results (Figure 14) show a complexly deformed

crust which can be understood in terms of two main super-imposed deformation phases. The first phase activates anddeforms the zones of weaker (DMD/10) lower crust. Thisdeformation starts in the transition zone between the fore-land and the plateau (Figures 14a and 14b), where thehorizontal pressure gradient acts in the same way as thatcaused by sediment prograding over salt [Lehner, 2000].The weak lower crust is first squeezed and evacuated, andthen thrust along with its overlying crust over adjacentstrong lower crust, forming allochthonous tongues ornappes (Figures 14a and 14b). The transport direction isproward on the proside, and the converse on the retroside.Shears at the leading edges of the nappes propagate upwardthrough the crust, and the allochthonous nappes and theiroverburden evolve into shear-bounded lozenges of upliftedand transported crust. Evacuated lower crust is replaced bysubsiding midcrust, which preferentially shortens and thick-ens during further contraction (e.g., vertical markers �1 to�2 and �3 to �4, Figure 14a).[53] In the second phase, a channel flow develops in the

heterogeneous crust created during phase one. The over-thrust weak lower crustal nappes become entrained in thechannel flow. The remaining zones of strong lower crust aretransported into the center of the plateau and detached at S.However, instead of creating a progressively growing anti-form of thickened lower crust, as in type 1 models (e.g.,Figure 3), lozenges of thickened strong lower crust areincorporated into the channel flow and are carried towardthe plateau flank by the counterflow (Figure 14). The resultsimply that widespread channel flows can develop evenwhere deformation of heterogeneous lower crust leads tocomplex middle and lower crustal geometry and composi-tion. If natural channels are similarly heterogeneous, theymay be difficult to recognize using geophysical techniquesthat focus on evidence for homogeneous channels (laterallycontinuous reflectors and low-velocity zones) and distrib-uted melts (bright zones). Given that models with homoge-neous crust are unlikely to be representative of naturalcrustal composition, results from models with heteroge-neous lower (e.g., HT-HET, Figure 14) and/or middle crust(not shown) may provide better analogues for lower crustaldeformation in large natural orogens.

8. Sensitivity of Model Results to AssumedMantle Kinematics

[54] All models described above have prescribed kine-matic subduction and thermal conditions in the mantle. We

have investigated the potential role of the suborogenicmantle by testing the sensitivity of the results to theassumed dip of the underthrust mantle lithosphere and toconditions that correspond to pure shear thickening of themantle without subduction.[55] Varying the dip of the underthrust mantle lithosphere

in type 2 models (not shown) causes small variations in thecrustal temperature field but has no significant effect on theoverall tectonic character of the results. This result is notsurprising because at these high convergence rates (VP +VR = 5 cm yr�1), the temperature in the model mantle isdominated by the horizontal advection of the mantle litho-sphere, which screens the crust from the effects of deeperthermal perturbations. These results mean that little signif-icance should be attributed to the assumed dip of subduc-tion. The subduction zone could equally well dip in theopposite direction [cf. Willett and Beaumont, 1994], forexample, if the subducting slab steepens and overturns as itis overridden by the retroward motion of the S point.[56] Similarly, most of the HT1 characteristics are

retained in model HT-PS (Figure 15) in which the pre-scribed mantle kinematics correspond to homogeneousthickening of the mantle lithosphere in a 1000 km wideregion extending for 500 km on either side of the HT1 Spoint position. This pure shear type of boundary conditionrepresents the opposite end-member to subduction, whichassumes no thickening of the mantle lithosphere. Thelower crust is included in the dynamical part of modelHT-PS, as in type 1 models because there is no simplemechanism consistent with pure shear thickening that wouldallow the lower crust to be absorbed by the mantle withoutdeformation.[57] The primary difference between HT1 and HT-PS is

the large region of thickened lower crust that forms in thecenter of the orogen in HT-PS (Figure 10 versus Figure 15).The thick, relatively high-viscosity, lower crust inhibits thedevelopment of channel flow in the center of the model.Consequently, the upper crust and surface suture in thecenter of the model are not transported toward the exhu-mation front during denudation. In other respects, HT-PS(Figure 15) is similar to models with subduction boundaryconditions; the various tectonic styles seen in the earliermodels can be reproduced by small changes in the denuda-tion model.[58] These sensitivity tests demonstrate that the model

characteristics in the region corresponding to southern Tibetand the Himalaya, the focus of this and the companionpaper [Jamieson et al., 2004], are relatively insensitive tothe assumed mantle kinematics below the center of theplateau. This is not surprising because the presence of thelow-viscosity channel decouples the middle and uppercrustal tectonics from the behavior of the lower crust and

Figure 14. Crustal-scale deformation and thermal evolution of model HT-HET (V = H) which is similar to HT1 but inwhich the lower crust comprises a series of 200 km long regions with alternating effective viscosities based on dryMaryland diabase (DMD, white, and DMD/10, dark grey, Table 1). Top panel in each set shows deformed marker grid andmechanical layers (grey, middle crustal layer); bottom panel shows isotherms (contoured at 100�C intervals), velocityvectors (short dark lines), and thermal layers (grey, A1 layer). Heavy line with dots represents the position of the modelsuture (vertical marker 0). Also shown are distribution and rate of slope-dependent erosion across the model surface; scalemaximum is 1 cm yr�1. Figures 14a–14d show the procrusts and retrocrusts at t = 30 and 48 Myr corresponding to totalconvergence, Dx of 1500 and 2400 km. Note heterogeneous deformation and mixing despite apparent laminar flow regime.

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Figure 15

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mantle [see also Shen et al., 2001]. It follows that the modelresults should also be relatively insensitive to other mantleprocesses, such as break-off of the subducted continentalmantle slab, provided that break-off occurs in the sublitho-spheric mantle and does not involve delamination andremoval of mantle lithosphere from beneath the proside ofthe orogen. We speculate that the main effect of retromantleremoval by convective instability or delamination will be toinduce buoyant uplift in the manner proposed by Molnar etal. [1993] and Platt and England [1993]. The added buoy-ancy will uplift the plateau above the region subject to theconvective removal or delamination and may increase thetendency for domes to form in this region. At more distantlocations, such as the Himalaya and southern TibetanPlateau in the present context, the main effect may be toincrease the pressure gradient in the channel and perhapsenhance channel flow. These effects can be investigated inmodels that include the underlying upper mantle, and weanticipate reporting on these model results in the nearfuture.[59] It can also be seen that the character of the crustal

flow and temperature regime in HT-PS is totally differentfrom that predicted by thin sheet models that assumeuniform thickening with depth throughout the lithosphere[e.g., England and Houseman, 1986]. This difference existsdespite the use of a basal boundary condition that corre-sponds to uniform pure shear thickening of the mantlelithosphere. The low-viscosity mid and upper crust simplydecouples from the boundary condition and is driven bygravity. One consequence is the near-isothermal mid andlower crust which allows crust at 20 km to have approxi-mately the same temperature as the uppermost mantle.These conditions are also very different from the conductivesteady state assumptions often used to estimate lithosphericrheological stratification and corresponding strength pro-files [e.g., Ranalli, 1987, chapter 12] and suggest caution inthis approach for actively deforming large, hot orogens.

9. Discussion: Model Flow Modes and TectonicStyles, With Implications for the Himalayan-Tibetan Orogen

[60] The model results presented above exhibit a range oftectonic styles. These can be considered to represent thesuperposition of one or more short-term flow modes, whichare simplified velocity patterns (e.g., Poiseuille channelflow) that characterize particular flow regimes [Beaumontet al., 2001a, Figure 17]. The flow modes reflect theimmediate response of the system to various controls, forexample the evolving crustal properties and surface denu-dation, and the tectonic style measures their cumulative

effect. Figures 12 and 13 show specific model results thatdemonstrate particular tectonic styles; in Figure 16, a moreconceptual interpretation of the model results is presented interms of the flow modes, shown by vertical velocityprofiles, associated with various stages of model evolution.[61] The tunneling mode (Figure 16a) occurs when the

denudation is too slow to influence the channel. Procrustfrom the foreland is tectonically shortened, thickened, andaccreted to the plateau, which conversely grows progres-sively outward by advancing into the foreland. The channeltunnels outward near the edge of the plateau and thetunneling is achieved by incorporating the crust into thechannel as it heats and thermally softens. This means that inthe tunneling mode the velocity near the channel tip has anoutward component that includes the effect of the incorpo-ration of new crust into the channel. When the lower crust isnot converging, the velocity of flow in the channel below theplateau is parabolic, equivalent to laminar plane-Poiseuilleflow for linear viscous materials [Turcotte and Schubert,1982, p. 234]. When the lower crust is converging the flowdevelops a high-shear lower boundary layer (Figure 16a).The crust overlying the channel is stable, i.e., it does not flowoutward with the channel.[62] Under the plateau, away from the channel tip, the

channel flow is pumped by gravity at a rate proportional tothe pressure difference between the plateau and the forelandand the square of the channel thickness, and inverselyproportional to the viscosity. In the transition zone betweenthe plateau and the foreland, the horizontal flow velocity inthe channel decreases as the channel narrows toward its tip,even though the pressure gradient increases with proximityto the edge of the plateau. The channel is inflated by thedecelerating flow, and this effect contributes locally tocrustal thickening.[63] In our thermal-mechanical models, the channel tip is a

rheological boundary and its rate of advance in the tunnelingmode is controlled by crustal temperature. In particular, therate is determined by the lag time, approximately 20 Myr, forheating of tectonically thickened crust, and correspondingdecrease in viscosity, to the point that the channel can bepropagated by the available pressure gradient [Medvedevand Beaumont, 2001, also personal communication, 2004].This approach contrasts with that of Clark and Royden[2000], who addressed injection into an existing channelflanking the plateau without considering the thermal evolu-tion of the system or the change in channel characteristicsacross the plateau edge. It seems unlikely that a suitablyprepared channel region, with sufficiently low viscosities forinjection, will exist in normal crust or crust that has recentlybeen tectonically thickened. For this reason we suggest thatchannel flows will normally be thermally limited at the

Figure 15. Crustal-scale deformation and thermal evolution of model HT-PS, which is similar to HT1 except the basalboundary condition to a distance of 500 km on either side of the suture corresponds to pure shear thickening of lithosphericmantle (see arrows indicating basal velocities) and there is no subduction of the lower crust (V = H). Top panel in each setshows deformed marker grid and mechanical layers (grey, midcrust); lower panel shows isotherms (contoured at 100�Cintervals), velocity vectors (short dark lines), and thermal layers (grey, A1). Heavy line with dots represents the position ofthe model suture (vertical marker 0). Also shown is distribution of slope-dependent erosion across the model surface; scalemaximum is 1 cm yr�1. Figures 16a–16d show the procrusts and retrocrusts at t = 30 and 48 Myr corresponding to totalconvergence, Dx of 1500 and 2400 km. Note development of midcrustal channel flows that decouple upper and lower crustand associated near-isothermal, disequilibrium thermal conditions in the mid and lower crust.

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boundaries of plateaus [Medvedev and Beaumont, 2001,also manuscript in preparation, 2004].[64] The tunneling mode shown in Figure 16a may be a

reasonable approximation to the Himalayan tectonic styleprior to significant exhumation of the channel. This is alsoinferred to be the current style of parts of the eastern marginof the Tibetan Plateau [Royden et al., 1997; Wang et al.,1998; Chen et al., 2000; Clark and Royden, 2000; Kirby etal., 2000, 2003] except that the lower crust may bestationary or moving slowly eastward as part of the SouthChina block [Holt, 2000; Wang et al., 2001].[65] The model response to efficient denudation of the

plateau flank is to raise the channel progressively toward thesurface in a near-symmetric exhumation mode (Figure 16b).Once the channel is exposed, channel flow per se may or

may not be active. Active extrusion of channel material(e.g., Figure 16b) will only occur if the channel flow breaksthrough to the surface. In the models, this is determined bythe upper crustal properties, frictional strength, and degreeof advective thinning of the surface boundary layer. Con-ceptually, a threshold exhumation rate must be achieved tokeep the channel sufficiently hot so that the material doesnot ‘‘freeze’’ until it is close to the surface. This situationmay have been achieved in the Nanga Parbat–Hormuzmassif [Craw et al., 1994; Zeitler et al., 2001; Koons etal., 2002]. In nature, crustal fluid pressures and strain-dependent rock properties that lead to strain localizationwill also determine whether the channel remains open. Alimitation of the current models, which do not include strainlocalization, is that the threshold exhumation rate for

Figure 16. Diagram showing conceptual interpretation of a range of model crustal flow modes that leadto uplift, exhumation, folding, extrusion, and doming mechanisms. Panels show weak upper crust(white), midcrust (grey), lower crust (white), and currently (pattern) or formerly (stipple) melt-weakenedcrust.

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extrusion is probably too high, requiring denudation ratesof 1 cm yr�1 or more for surface extrusion as shown inFigure 16b. A related Himalayan problem is whether thecurrently exposed GHS more closely resembles an exhumedplugged channel, with little extrusion during exhumation, orwhether there was (and perhaps still is) active extrusion atthe surface [Hodges et al., 2001; Wobus et al., 2003] like avery sluggish salt fountain [Talbot et al., 2000].[66] If efficient denudation exhumes the channel and

allows active extrusion, inefficient denudation causes crustalshortening and thickening to be focused at the plateau flank.This creates antiforms, crustal-scale folds and plug-likestructures, and focused thrust sense shear zones adjacent tothe end of the channel (Figure 16c). Under these circum-stances the channel is not exhumed. Instead, the procrust istectonically thickened and then exhumed in similar way tothe behavior of denuding prowedges and retrowedges insmall, cold orogens [Willett et al., 1993; Willett, 1999].[67] If the crustal overburden above the channel becomes

unstable, the channel flow regime may convert to Couetteflow and the overburden will flow outward with a uniformvelocity with depth above the channel (Figure 16d). TheCouette flow velocity in the channel decreases linearly withdepth when the horizontal pressure gradient is negligible, orhas a superimposed parabolic, Poiseuille, component whenforced by the pressure pumping. This flow mode is facili-tated by efficient flank denudation and exhumation of thechannel, which help to create a ‘‘free’’ outer end to the uppercrust above the channel. The upper crust may then glideunder gravity or be dragged by the underlying channel flow.Outward moving upper crust then overrides the exhumedchannel and converts the geometry of the exhumation zonefrom the near-symmetric mode (Figure 16b) to the asym-metric thrust exhumation/extrusion mode (Figure 16d).Creation of conditions leading to upper crustal instabilityrequires efficient denudation, which implies that the flowmode should normally progress from the steeply dippingchannel (Figure 16b) to the moderate dips typical of theHimalaya (Figure 8b). Intermediate tectonic styles are alsopossible, and in some cases the crustal overburden maymove faster than the channel material.[68] Superimposed flow modes will be recorded by super-

imposed phases of finite shear of the boundary layer betweenthe channel and the overburden. For example, in a system thatevolves through the stages illustrated in Figures 16a, 16b, and16d, the boundary layer between the channel and overburden,corresponding to the STD zone in the Himalaya, shouldrecord early normal sense shear, followed by features indi-cating reduced strain rates, quiescence, or even thrust senseshear. In contrast, the base of the channel, corresponding tothe MCT zone, should record protracted thrust sense shear.[69] If the stability of the crustal overburden varies later-

ally, the intervening region will deform, most likely byextension (Figure 16e). Upper crustal extension and thinningwill result in doming of the channel and its overburden(Figure 16e) if the characteristic timescale for channel flowinto the extending region is less than the timescale forextension. Under these circumstances, the channel materialbehaves as a fluid and is pumped into the region of relativelylow pressure caused by crustal extension and thinning(Figure 16e). Similar behavior has been inferred to occur inthe footwalls beneath extensional metamorphic core com-

plexes [e.g.,Wernicke, 1990; Block and Royden, 1990;Kruseet al., 1991], and domes created in this way (Figure 16e)could be interpreted as core complexes.[70] Continued convergence after exhumation of the

channel can trigger additional tectonic effects (Figures 16fand 16g) related to underthrusting by converging middleand lower procrust. A fundamental change in flow mode andcorresponding tectonic regime would result if outwardchannel growth by tunneling is replaced by channel con-traction as it is underthrust and squeezed by the convergingcrust. A mode change of this type in the Himalayan-Tibetsystem would represent an event that punctuates the other-wise progressive evolution of the system through theflow modes illustrated in Figures 16a, 16b, and 16d. Whenthe channel is deflected upward during exhumation (e.g.,Figures 16b and 16d) it may cease to tunnel through themidcrust. If convergence continues, relatively cold, strongpromidcrust inserts itself into the channel, forming a ramp-flat geometry at its leading edge (Figure 16f) that is inheritedfrom the footwall geometry of the channel beneath theexhumation zone (e.g., Figure 16b). Squeezing of thechannel above the ramp can destabilize the upper crustaloverburden, triggering the formation of a dome (Figure 16f ).This may provide a possible explanation for the formation ofthe belt of gneiss domes, including the Kangmar [Lee et al.,2000] and Mabja domes [Lee et al., 2001], associated withthe north Himalayan antiform and interpreted by Hauck etal. [1998] to be above a ramp in the Main Himalayan Thrust(Figure 8b). Domes of this type are initially formed abovethe crustal ramp, but with additional convergence they willbe transported relatively proward, toward the plateau flank.This process can trigger an isolated dome in the plateau(compare Figures 16e and 16f ), or smaller domes with lessstructural relief can be expelled/extruded along the channellike a deforming egg in a snake (Figure 16g), eventuallyemerging at the surface. Structural domes reported from someGHS localities (e.g., Zanskar-Lahul region [Stephenson etal., 2000; Walker et al., 2001; Robyr and Steck, 2001]) mayrepresent features formed beneath the southern TibetanPlateau and then extruded in this manner.[71] An analogous model involving crustal injection and

hydraulic uplift was proposed by Zhao and Morgan [1987].In this case, only crust was injected [Zhao and Morgan,1987, Figure 1] and the resulting hydraulic pumping effectof the crustal plunger was proposed as a mechanism for theuplift of Tibet. In the present models, the inserted crustremains attached to underlying lower crust and mantle andthe process occurs during overall lithospheric convergence.Our current model results suggest that the plateau would betectonically unstable during uplift by hydraulic pumping,leading to extension and doming that would prevent thismechanism causing a general increase in the elevation of theTibetan Plateau. In other respects the Zhao and Morgan[1987] results and our results are quite similar, with ourmodels illustrating how the proposed configuration of theirmodel may have developed.

10. Conclusions

[72] Results have been presented for a range of planestrain thermal-mechanical finite element models of colli-sional orogenesis in large hot orogens. The purpose is to

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investigate the styles of deformation as radioactive self-heating progressively reduces the viscosity of the crustfollowing tectonic thickening, and increases its susceptibil-ity to large-scale horizontal flow. Under certain conditionsthe models develop midcrustal channel flows driven bydifferential pressure, and the channel material tunnels out-ward in the midcrust from beneath the model plateau towardits flanks. The channel may be exhumed and exposed atthe surface by climatically enhanced surface denudationfocused on the steep, high-relief transition region betweenthe plateau and the foreland.[73] Generic type 1 models, used to test the model

sensitivity to the denudation and the choice of effectiveviscosity of the channel, demonstrate that channel flows donot develop, or are sluggish, if the mid and upper crust has aductile rheology based on the wet quartzite flow law ofGleason and Tullis [1995]. However, further reduction ofthe effective viscosity to 1019 Pa s or less leads to well-developed channel flows and we interpret this additionaldecrease to the effect of a small in situ component of partialmelt. This effect is included in the models by empiricalcrustal melt weakening at temperatures between 700� and750�C corresponding to muscovite dehydration melting. Wetherefore conclude that crustal anatexis and the developmentof a migmatitic midcrust will promote channel flows.However, in situ melt is not required if other processesreduce the effective viscosity to the same degree over thesame temperature range.[74] Models in which the effective viscosity was reduced

to 2 � 1018 Pa s do not show the corresponding factor of 5increase in channel flow velocity predicted by the simpletheory for infinitely long channels. This is because thechannel flow regime is limited by the low-temperature,high-viscosity crust in the transition region between theplateau and foreland. The rate at which the channel tiptunnels outward is determined by the same restriction, the

lag time, approximately 20 Myr, for tectonically thickenedcrust to heat sufficiently and for the viscosity to decreasesufficiently so that the midcrust will participate in thechannel flow.[75] Type 2 models were designed for comparison with a

representative north-south cross section of the Himalayan-Tibetan orogen. In model HT1, the channel is erosionallyexhumed to the surface, and this exhumation also leads toinstability of the upper crust and its outward flow togetherwith the channel. This model (Figure 10) is in broadagreement with many Himalayan observations (Figure 17)and it provides an internally consistent explanation for thedynamical behavior of the Himalaya as a system. Partiallymolten Indian crust tunneled outward beneath the TibetanPlateau and was exhumed to the surface by rapid erosion ofthe southern flank of the Himalaya (1) (numbers refer toFigure 17). The channel material was extruded between thecoeval MCT and STD ductile shear systems (2 and 3),thereby accounting for their opposite shear sense, andexposed as the high-grade, migmatitic GHS (4). Equivalentpartially molten crust continues to exist beneath Tibet (5) andfurther diachronous erosion may expose this crust as a futureGHS. The contrast in protoliths across the MCT system(6) results from tectonic juxtaposition of the extruded GHS,which is derived from crust that entered the orogen early inits evolution, and the recently accreted LHS which is derivedfrom crust located up to 1000 km farther to the south. Themodel also accounts for the ‘‘inverted’’ metamorphism of theMCTand LHS zones (7) and is compatible with a range of P-T and geochronological data [Jamieson et al., 2004]. Theposition of the Indus-Tsangpo suture (8) is replicated by themodel, but this result is nonunique because it depends onthe trade-off between the total amount of crust eroded fromthe Himalayan flank of the model and the total northwardadvance in the subduction point in the basal boundarycondition.

Figure 17. Illustration of a representative north-south tectonic cross section of the Himalaya and southernTibet showing the processes that act together to provide an internally consistent explanation for thedynamical behavior of this system. This system behavior is seen in model HT1 (Figure 10), for example,and in variants (Figures 12 and 13). See text for explanation of numbers. MBT, Main Boundary Thrust;FTB, fold-thrust belt (Siwaliks); MCT, Main Central Thrust system; GHS, Greater Himalayan sequence(stippled pattern); STD, South Tibetan Detachment system; LHS, Lesser Himalayan sequence; MHT,MainHimalayan Thrust (modified from Beaumont et al. [2001b]; reprinted by permission from Nature).

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[76] A sensitivity analysis of model behavior indicatesthat a single or unique Himalayan tectonic style isunlikely. Several flow modes (Figure 16) are recognizedand lead to differing tectonic styles (Figures 12 and 13).That relatively small differences in denudation rates andcrustal properties lead to this range of tectonic stylessuggests that the Himalayan system will also exhibit anequivalent range of styles because variations in denuda-tion rates and crustal properties will certainly exist alongthe length of the Himalayan front [see Jamieson et al.,2004, section 10.4]. Flow modes that cause extension ofthe upper crust can lead to the development of domesthat resemble at least some of the north Himalayan gneissdomes (Figure 17, marker 9). In particular, the Kangmardome is interpreted to be a dome triggered by under-thrusting of a ramp in the MHT (10).[77] Preliminary tests indicate that channel flows will

operate in the models even when zones of stronger, notmelt-weakened, lower crust become entrained in the chan-nel and cause it to become heterogeneous. Equivalentheterogeneous natural channels may prove difficult torecognize geophysically.[78] Tests of the model sensitivity to the choice of

kinematic basal boundary conditions indicate that the over-all tectonic regime, and, in particular, the channel flow,remain similar even under boundary conditions that corre-spond to regional uniform thickening of the mantle litho-sphere beneath the center of the model. This is notsurprising because the weak channel decouples the crustfrom motion of the lower crust and mantle on all but thelargest orogen scales. It also follows that deformation andtemperature regimes in models with channel flows will becompletely different from those predicted by ‘‘thin sheet’’models which require velocities to be constant with depththrough the lithosphere. This is because models with chan-nels behave as three weakly coupled layers whereas thinsheet models are constrained to act as a single layer.

[79] Acknowledgments. This work is dedicated to the memory ofDoug Nelson, who challenged us to produce model results compatible withobservations from the Himalayan-Tibetan orogen. The research was fundedby Natural Sciences and Engineering Research Council and LithoprobeSupporting Geoscience grants to C.B. and R.A.J. C.B. has also beensupported by the Inco Fellowship of the Canadian Institute for AdvancedResearch and by the Canada Research Chairs program. The models weredeveloped and run with the assistance of Phillippe Fullsack and Bonny Lee.The work has benefited greatly from discussions with many colleagues,including Doug Nelson, Djordje Grujic, and Yani Najman and members ofthe CIAR-ESEP. We thank the reviewers, Greg Housman and JosephMartinod, and the Associate Editor, Jean Braun, for their constructivecomments.

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�����������������������C. Beaumont andM. H. Nguyen, Department of Oceanography, Dalhousie

University, Halifax, Nova Scotia, CanadaB3H 4J1. (chris.beaumont@dal.ca;mhnguyen@dal.ca)R. A. Jamieson, Department of Earth Sciences, Dalhousie University,

Halifax, Nova Scotia, Canada B3H 3J5. (beckyj@dal.ca)S. Medvedev, Fachrichtung Geologie, Freie Universitat Berlin, Malteser-

strasse 74-100, D-12249 Berlin, Germany. (sergeim@zedat.fu-berlin.de)

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