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Tectonophysics 382 (2004) 1–29

Syn-convergent exhumation and lateral extrusion in continental

collision zones—insights from three-dimensional numerical models

M. Seyferth*, A. Henk

Geologisches Institut, Universitat Freiburg, Albertstraße 23 b, D-79104 Freiburg, Germany

Received 13 February 2003; accepted 5 December 2003

Abstract

Three-dimensional thermomechanical finite element models are used to simulate the evolution of collisional orogens of finite

axial extent. Special focus is on the spatial and temporal variations of stress and strain in the resulting orogen leading to lateral

extrusion and syn-convergent exhumation. Besides the collision zone, the model incorporates an area, which is not constrained

by a convergent boundary condition and, thus, allows orogenic material to flow out laterally. Altogether, 17 different model

scenarios were tested. Starting from a model with ‘standard’ material parameters and boundary conditions, several variations

concerning crustal temperature, rheology, convergence rates, crust–mantle coupling as well as the geodynamic setting of the

evolving orogen are examined. Modelling results indicate that orogen-parallel extension is intimately related to continental

collision and occurs even during the early stages of convergence. Unless a rigid block adjoins and prevents lateral extrusion, it

typically reaches 20–40% of the amount of convergence. The models show substantial spatial and temporal variations of stress

and strain in the collision zone and its surrounding. In particular, the near-surface stress field in the orogen’s interior completely

reorganises during convergence. At later convergence stages, the uppermost crust is subject to normal faulting, while

contemporaneously at deeper crustal levels compressive stress fields prevail. The spatial relation of these different stress regimes

in the orogenic crust strongly favours syn-convergent exhumation by tectonic denudation. Finally, a semiquantitative

comparison between the modelling results and three modern collision zones in the Alpine–Himalayan belt addresses the

distribution of different tectonic styles, the respective amounts of lateral extrusion as well as seismological observations.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Collision tectonics; Lateral extrusion; Tectonic escape; Exhumation; Numerical models

1. Introduction

Continental collision zones are sites of intense

crustal deformation resulting in such diverse processes

0040-1951/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.tecto.2003.12.004

* Corresponding author. Present address: Research Center

Ocean Margins, University of Bremen, P.O. Box 330440, D-

28334 Bremen, Germany. Tel.: +49-421-2188779; fax: +49-421-

2188664.

E-mail address: mseyferth@uni-bremen.de (M. Seyferth).

as crustal stacking and vertical thickening, orogen-

parallel extension and exhumation of lower crustal

rocks by tectonic denudation and erosion. Observa-

tions from recent orogens (e.g., Himalayas, England,

1992) document the co-existence of highly variable

stress fields, i.e., normal faulting in the orogen’s

interior contemporaneously with compression in the

fold-and-thrust belts. Here, we present some numeri-

cal models of continental collision zones based on a

first-order description of the thermal and mechanical

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–292

processes in the crust to improve the physical un-

derstanding of these observations. In particular, we

focus on the spatial and temporal variations of stress

and strain in order to get quantitative insights into

processes like lateral extrusion and syn-convergent

exhumation.

Two-dimensional (2D) models of continental col-

lision zones have provided valuable insights into the

evolution and internal structure of an orogen as well

as the potential impact of surface processes on

orogenic evolution (Willett et al., 1993). They have

been applied to various recent and fossil orogens

including the European Alps (Beaumont et al.,

1996), the southern Alps of New Zealand (Beaumont

and Quinlan, 1994) and the Himalayas (Willett and

Beaumont, 1994). However, their applicability is

limited by the plane strain assumption inherited in

the 2D approach as orogen-parallel movements can-

not be described. In reality, however, lateral extrusion

can easily reach several hundred kilometres. For the

India–Asia collision zone, for example, an upper

bound of 1500 km of movement perpendicular to

the convergence direction has been estimated (Tap-

ponnier et al., 1986). On the other hand, thin sheet

models of convergence zones (England and McKen-

zie, 1982) are limited as they cannot take the rheo-

logical stratification of the lithosphere into account.

Thus, a comprehensive quantitative description of

continental collision zones ultimately requires a 3D

approach. Such 3D models of orogenic processes

have rather severe requirements concerning comput-

ing time and only a few studies have been published

so far, e.g., on oblique collision (Braun, 1993; Braun

and Beaumont, 1995).

2. Modelling approach

2.1. Modelling concept

The 3D numerical models presented in this study

build on work of Willett et al. (1993) and Beaumont et

al. (1994) who use 2D finite element models to

simulate the evolution of compressional orogens.

Their models assume that collision of continental

crust is driven by subduction of the underlying lith-

osphere. This concept is transferred to the numerical

model by applying displacement boundary conditions

to the base of one crustal block, while the base of the

other is fixed horizontally (Fig. 1a). The discontinuity

in the boundary condition is termed the S point

(Willett et al., 1993) and represents the locus of

asymmetric detachment and underthrusting of the

mantle lithosphere. As a result, a bivergent orogen

rooting at the S point develops during convergence.

Model orogens are asymmetric in their general topo-

graphic appearance as well as their internal structure

and strain distribution. Typically, a broad zone of

diffuse deformation constitutes the pro-side verging

toward the underthrust plate, while a more localised

zone of stronger deformation verging towards the

stationary plate forms on the retro-side (terminology

after Willett et al., 1993). This basic model set-up has

been varied extensively to study the effects of tem-

perature, convergence velocity, rheological stratifica-

tion, locus of the displacement discontinuity and

erosional denudation on orogenic evolution (Beau-

mont et al., 1994; Beaumont and Quinlan, 1994; Ellis

et al., 1998; Jamieson et al., 1998). The results of the

numerical simulations have been compared to ana-

logue models (Malavieille, 1984), reflection seismic

data (Beaumont and Quinlan, 1994) as well as field

data from various recent and fossil orogens (Beau-

mont et al., 1994; Ellis et al., 1998; Seyferth and

Henk, 2000).

However, 2D models are affected by severe limi-

tations. The plane strain assumption inherited in the

2D approach, i.e., the orogen is assumed to be infinite

in length, implies that orogen-parallel material trans-

port and deformation is negligible. In reality, orogen-

parallel deformation and lateral extrusion, respective-

ly, are common features of continental collision zones.

For example, estimates for movement perpendicular to

the convergence direction are about 170 km for the

Eastern Alps (Frisch et al., 1998; Ratschbacher et al.,

1991a) and up to 1500 km for the Himalayas (Molnar

and Tapponier, 1975; Tapponnier et al., 1986). In order

to take orogen-parallel processes into consideration,

we present a 3D model describing an orogen with

finite axial extent, which is laterally connected to areas

not affected by continental collision. This set-up may

reflect the lateral transition of a continental collision

zone towards a zone of oceanic subduction and/or an

offset of the orogen axis by major transform faults or

plate boundaries. Scenarios, which are not met by

these conditions, are not addressed by the models.

Fig. 1. Modelling concepts. To simplify matters, isostasy is not considered in any plot in this figure. (a) 2D modelling concept after Beaumont

and Quinlan (1994). Convergence is driven by subduction of the underlying lithosphere. The point S marks a discontinuity in the basal

displacement boundary condition. (b) 3D modelling concept showing one half of a compressional orogen and the surrounding crust. Boundary

conditions are based on the mantle subduction approach in the models forepart and generally simulate free margins in its rear part. (c) Sections

(obtained by bisection of the model set-up normal to the x-axis) showing in-plane boundary conditions and the expected style of deformation.

(d) Multilinear erosion function applied to the model surface and underlying data by Summerfield and Hulton (1994). (e) Terms used in this

paper to denote ‘‘geographical’’ locations in the model and respective natural examples.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 3

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–294

The model is assumed to be symmetric with

respect to a vertical plane in the orogen’s interior

and only one half of it is actually modelled (Fig. 1b;

for terminology, see also Fig. 1e). Boundary condi-

tions at this plane of symmetry are identical to that of

2D models (e.g., Willett et al., 1993). The modelled

colliding crustal blocks represent a geometrical extru-

sion of the 2D approach perpendicular to the conver-

gence direction. Consequently, the S point is

transformed into a S line extending towards the centre

of the model. To the left of the S line (pro-side)

displacement boundary conditions are applied to the

base of the frontal part of the model mimicking mantle

subduction as the driving mechanism for conver-

gence. To the right of the S line (retro-side), basal

nodes and the respective model margin are fixed with

respect to horizontal movements.

The rear part of the model represents the area

outside the immediate collision zone and no displace-

ment boundary conditions are applied to its base. The

choice of a free model base in this part of the model

(Fig. 1c) deserves some consideration: at first glance,

it may seem more appropriate to hold the model base

fixed in order to account for an underlying, unmoved

lithospheric mantle and a lower crust strongly coupled

to it. However, if one of these assumptions fails to be

met, either by the existence of a decoupling horizon or

by horizontal movements of the lithospheric mantle,

these boundary conditions would be no longer valid.

The particular type of scenario we are referring to is

characterised by ‘‘free’’ lateral margins, which are

known to occur in the zone of influence of oceanic

subduction zones (e.g., Anatolia—Aegean Sea

(Dewey et al., 1986), Eastern Alps—Carpathian ‘‘sub-

duction zone rollback’’ (Linzer, 1996)). In this con-

text, mantle behaviour in the respective areas may be

dominated by forces arising from orogeny and oceanic

subduction, making it difficult to predict its particular

influence on the crust. Consequently, we decided to

assume a free crustal base as the more general set-up,

neither implying an unmoved lithospheric mantle nor

one moving in a particular way. Instead, this approach

allows the entire lithosphere to participate in lateral

displacements.

In order to avoid excessive strain localisation bet-

ween areas of different basal boundary conditions,

cessation of the convergent boundary condition is

distributed over a narrow transition zone and a ‘smooth

function’ (Braun and Beaumont, 1995) is used to

decelerate material approaching the S line. In order

to assess the coupling between crust and mantle as well

as the effect of the geodynamic setting on the resulting

model orogen various numerical simulations with

different boundary conditions applied to the base and

vertical sides of the model (fixed, no-tilt, plate bound-

ary forces) were run.

2.2. Terminology

In order to describe the modelling results with

reference to their spatial position the following termi-

nology is used (Fig. 1e). Within the collision zone

proper, the prefixes ‘pro-‘ and ‘retro-‘ are used to

indicate the position of an area with respect to the

subduction polarity. Accordingly, the external fault-

and-thrust belts flanking the internal zone of the

orogen are named pro- and retro-zone, respectively,

while the adjacent foreland areas are termed pro- and

retro-side foreland. The corresponding areas along

strike of the orogen are referred to as orogen centre,

lateral orogenic margin and lateral foreland, respec-

tively. Generally, the term ‘‘lateral extrusion’’ (Ratsch-

bacher et al., 1991b) is used to describe both

displacements arising from horizontal forces (‘‘tecton-

ic escape’’, Burke and Sengor, 1986), and those

induced by gravitational instabilities (Dewey, 1988).

Unlike ‘‘lateral extrusion’’ which refers to the process

itself and the consequent orogen-parallel displacement

of rocks, ‘‘lateral extension’’ is used to address the

related extensional strain.

2.3. Numerical model

Numerical simulations utilise the finite element

(FE) method to calculate crustal temperatures and

deformation. The model is subdivided into an upper

and a lower crustal material domain, each characterised

by specific thermal and mechanical properties. The

size of the modelled crustal block is 700� 700� 32

km and comprises 3750 (25� 25� 6) brick-shaped

eight-node elements. This is the minimum possible

vertical resolution to account for the effects of the

lithological and rheological stratification; a finer

vertical resolution would result in an unfavourable

aspect ratio of the individual elements or in a

significant and computing time consuming increase

Fig. 2. A simple 2D set-up simulating the response of a layered

model crust to cumulative tilting of the left model margin; this set-

up has been used to study the effect of the relatively coarse vertical

resolution of the 3D models. (a) Twenty-four layers of elements;

grey scales indicate the brittle and ductile domain of the upper crust

and the lower crust, respectively. (b) Six layers of elements, as they

have been used in the 3D models presented in this paper; though

simple shear is less localized, particularly at the model base, bulk

deformation is similar to that observed in the higher-resolution

model. (c) Temperature profiles in both models show a nearly

perfect fit.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 5

in the total number of elements. However, extensive

two-dimensional pilot studies using different element

sizes have shown, that the grid size selected does

not have a substantial impact on the modelling

results. Although the thickness of the subhorizontal

shear zones increases with element height as the

strain pattern represents bulk deformation in the

respective domains, the total error in horizontal

displacements is less that 10% in any tested sce-

nario. Fig. 2 shows an example of a stratified simple

shear test set-up that has been run with 6 and 24

element layers. A comprehensive summary of the

material parameters used in this study is given in

Table 1.

Thermal modelling is based on three-dimensional

heat transport by conduction and advection. Temper-

ature-dependent thermal conductivities and lithology-

dependent radiogenic heat production rates are used to

calculate the crustal temperature field and its varia-

tions through time. A constant and laterally uniform

basal heat flow and a constant surface temperature of

0 jC form the boundary conditions for the thermal

model. Some of the models consider also lateral

variations in basal heat flow and, hence, crustal

temperature to account for spatial variations inherited

from the preceding oceanic subduction stage (Jamie-

son et al., 1998).

For the mechanical calculations deformation in the

brittle domain is described by an elastic-perfectly

plastic material law with a pressure-dependent yield

strength approximating Byerlee’s relationship (Bye-

rlee, 1978) for hydrostatic fluid pressure conditions.

Deformation in the ductile domain is described by

temperature-dependent viscous flow laws deduced

from experimental power-law creep parameters under

the assumption of a constant bulk strain rate of

1�10� 14 s� 1. Isostatic forces act on the density

interfaces of the model, i.e., the model base, the

boundary between upper and lower crust and the

model surface (Winkler spring foundation method,

Braun, 1988; Williams and Richardson, 1991). Con-

tinental collision and plate convergence, respectively,

are described by a displacement boundary condition

of 20 mm year� 1 applied to the model base left of the

S line. For the vertical sides of the model, different

boundary conditions like fixed (no horizontal dis-

placements allowed) or no-tilt walls (i.e., walls con-

strained to be vertical) as well as compressive or

tensile plate boundary forces are examined in various

parameter studies.

Since crustal rheology is strongly temperature-

dependent and advective heat transport plays an

important role for the temperature distribution, ther-

mal and mechanical calculations are coupled via

temperatures and displacements. The 3D thermome-

chanical model utilises the commercial FE software

package ANSYSR (ANSYS, Houston, USA) (see

Henk, 1998 for an overview of ANSYSR applications

Table 1

Input parameters of the thermomechanically coupled FE models

Mechanical material propertiesa

Upper crust Lower crust

Density q(at 0 jC)

kg m� 3 2.8� 103 3.0� 103

Young’s

modulus E

Pa 0.5� 1011 0.8� 1011

Poisson’s ratio m – 0.25 0.25

Cohesion c Pa 0.0 0.0

Friction angle l – 0.75 0.75

Strain rate

coefficient a0

Pa� n s� 1 1.63� 10� 26 2.06� 10� 23

Activation

energy Q/R

K 16,238 28,747

Stress exponent

n

– 3.1 3.2h

Thermal material propertiesb

Upper crust Lower crust

Density q at

0 jCkg m� 3 2.8� 103 3.0� 103

Thermal

conductivity K

W m� 1 K� 1 K(T) =A+B/

(350 + T)

with A= 0.64,

B= 807

K(T) =A +B/

(350 + T)

with A= 1.18,

B = 474

Specific heat C J kg� 1 K� 1 1300 1300

Heat production

rate H

W m� 3 2.3� 10� 6 0.52� 10� 6

Model geometry (cf. Fig. 1b)

Model width m 700� 103

Model length m 700� 103

Upper crustal

thickness

m 16� 103

Lower crustal

thickness

m 16� 103

Discretisation and boundary conditions

Number of

elements

– 3750 (25� 25� 6)

Time step FE

calculation

years 5� 104

Time step

remeshing

years 1�106

Convergence

rate vc

mm year� 1 20

Surface erosion

rate ve

mm year� 1 topography-

dependent

(cf. Fig. 1d)

Basal heat flow

qbas

W m� 2 0.018

Surface

temperature

Tsurf

jC 0

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–296

to geodynamic problems). For model generation and

post-processing of the modelling results, our own

software products are used. In particular, a set of

remeshing, mapping and tracking algorithms interact-

ing with ANSYSR has been developed to account for

the large and localised deformation typically encoun-

tered in continental collision zones (Fig. 3; see Sey-

ferth and Henk, 2000 for a description of the 2D

version). As continued convergence results in severe

distortion of the model grid, especially of the basal

elements, an updated-Lagrangian FE grid can no

longer be regarded as a reliable basis for further

mechanical calculations. The remeshing operation

replaces this deformed FE grid by a new one with

vertically aligned nodes and vertical side-walls, re-

spectively, and interpolates the previously achieved

modelling results onto the new FE grid nodes. While

the outer geometry of any material domain (upper

crust, lower crust) is maintained, it is internally

regridded with the same number of elements as

before. The nearly brick-shaped elements can then

be used for the next convergence step until deforma-

tion requires a new remeshing step again.

If desired, the outer shape of the model can also be

modified during remeshing, so that the effects of

erosion and/or sedimentation can be taken into con-

sideration. The models presented in this study account

for erosion only and use rates derived from a topog-

raphy-dependent multilinear function based on field

data from (Summerfield and Hulton, 1994). Between

two remeshing events, the unloading effect of erosion

is approximated by counterpoises acting on the model

surface. However, the flexural strength of the eroded

material remains present, until it is physically re-

moved during the remeshing procedure. The choice

of the remeshing time step requires some consider-

ation: since the remeshing procedure disturbs the

elastic stress field in the model, remeshing should

Notes to Table 1:

Parameters for the mechanical and thermal calculations are listed

separately. The model geometry is the same for both the mechanical

and the thermal model.a (Mechanical material properties): creep parameters for the

upper and lower crust taken from Paterson and Luan (1990) and

Shelton and Tullis (1981), respectively.b (Thermal material properties): for temperature-dependent

thermal conductivities, see Zoth and Hanel (1988). Heat production

rate data by Cermak (1995).

Fig. 3. Schematic drawing showing the remeshing and mapping– tracking algorithms for a single element and a FE grid. For reasons of

visualisation, a 2D example is shown. The thick solid lines represent the global coordinate system and absolute reference frame, respectively, in

all plots. White circles: FE grid nodes. Black circles: marker points of the tracking grid. The local element coordinate system is indicated by

double solid lines. (a) Mapping determines the initial relative coordinates of a marker point within the element coordinate system of FE grid 1.

(b) Deformation of FE-grid 1, advection of marker point. (c) Tracking determines absolute coordinates of the advected marker point. (d)

Remeshing replaces the deformed FE grid 1 by FE grid 2 with vertical sides. (e) Mapping determines relative coordinates of a marker point

within the element coordinate system of the new FE grid 2.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 7

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–298

not be performed too often. On the other hand, the

error in the flexural strength calls for a small remesh-

ing time step. Pilot studies have shown that the pre-

remeshing stress field is typically re-installed within

about 50 ka and the effect on flexural strength is less

than 1% even after 5 Ma. As a compromise a

remeshing time step of 1 Ma has been used (20 km

convergence under standard conditions).

In order to keep track of the displacement and

strain as well as the thermal evolution with time

experienced by the initial grid nodes and distinct

marker points, respectively, mapping and tracking

algorithms are used (Fig. 3). They lead to true particle

paths in space and time, which are directly compara-

ble to petrologic and geochronologic data (P–T– t

paths). Firstly, the mapping operation determines the

relative position of the relevant points with respect to

the actual FE grid. After a new deformation increment

has occurred, the changed absolute position of the

marker points is recalculated during the tracking

operation on the basis of their relative position and

the incremental displacement of the corresponding

Table 2

Input parameters of standard model S-1 and parameter variations in mode

Model Tmoho vconv Lower crust rheology

(initial)a0 Q/R

K mm year� 1 Pa� n s� 1 K

S-1 (default) 600 20 2.06� 10� 23 28,74

R-2 700

R-3 500

R-4 500 8.83� 10� 22 53,52

R-5 8.83� 10� 22 53,52

R-6 100

R-7 4

B-8

B-9

B-10

B-11

B-12

B-13

I-14 600/413

I-15 600/413

C-16

C-17

If no value is defined, default values of S-1 apply. Due to the nature of the

the following categories: R = rheology, temperature, convergence rate, B = b

conditions. The standard model uses a wet plagioclase rheology (Shelton an

4 and R-5 are based on mafic granulite creep parameters of Wilks and C

element nodes. Assuming that the displacement ve-

locity in the centre of the element is the mean of the

ones calculated for its eight corners, each element can

be subdivided into 24 tetrahedral subvolumes, which

are used as tracking cells. Normals of tetrahedron

sides form an element coordinate system, which is

used to define the relative position of a marker point

in the respective tracking cell. Thereby, the relative

position of a marker point with respect to the FE grid

can be described by five parameters, comprising three

coordinates and the index numbers of the respective

tetrahedral tracking cell and the element containing it.

3. Modelling results

Altogether 17 continental collision scenarios with

different model parameters and boundary conditions

were run (Table 2). The resulting data sets for each 3D

model comprise the spatial distribution and temporal

evolution of stress, strain, displacement and tempera-

ture. In order to give an overview of the large amount

ls R-2 up to C-17

Rigid Plate Crust–mantle

nmodel boundary coupling

–margins forces

7 3.2 none none isotropic

4 4.2

4 4.2

retro-side

pro-/retro-side

rear side

all around

compressive

extensive

anisotropic

retro-side anisotropic

respective parameter variations, the models have been grouped into

oundary conditions, I = indenter models, C = different basal coupling

d Tullis, 1981) to describe creep in the lower crust, while models R-

arter (1990).

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 9

of output data, we will first present the results of a

model with standard input parameters and boundary

conditions in detail. Subsequently, the impact of

changing one or two of the parameters on the results

will be discussed. All models are run for 10 Ma and

200 km of convergence.

3.1. Standard model

Model S-1 is based on the material parameters and

model geometry summarised in Table 1 and Fig. 1.

Convergence is simulated by applying a displacement

boundary condition of 20 mm year� 1 parallel to the x-

axis to the basal nodes to the left of the S line. Basal

nodes to the right and the opposite model wall are

fixed with respect to movements in horizontal direc-

tions. The remaining vertical sides of the model are

no-tilt margins and are not further constrained in their

movement, representing model margins sustained by

lithostatic pressure. This choice of boundary condi-

tions most plausibly and generally describes ‘‘free’’

lateral margins characterised by the availability of

subductable oceanic crust in the lateral neighbourhood

of the orogen. In particular cases, according to the

respective subduction mechanism, this general formu-

lation may be modified by plate boundary forces,

whose effect will be studied by the later model

variations B12 and B13. The fundamentally different

approach of fixed lateral boundaries, in analogue

modelling often referred to as ‘‘rigid backstops’’, will

be tested by another group of parameter variations

(B9-B11).

3.1.1. Strain distribution

Fig. 4a shows the model geometry after 100 km of

convergence contoured for displacements in each of

the three spatial directions, i.e., convergence-parallel

(x) and orogen-parallel ( y) as well as vertical (z).

Convergence has formed an orogen with a maximum

surface topography of about 3000 m. Orogen-parallel

movements and lateral extension, respectively, reach

their maximum value of 37 km in the centre of the

lateral foreland.

Fig. 4b illustrates the temporal evolution of the

deformation components parallel to the convergence

vector, i.e., parallel to the x-axis, and in vertical

direction (z-axis) of the model coordinate system.

The three chosen stages (50, 100 and 200 km plate

convergence) correspond to a total convergence dura-

tion of 2.5, 5 and 10 Ma, respectively. The colour-

coding at 200 km convergence indicates a vertical

succession of different strain regimes. While lower

and middle crustal levels are thickened the upper crust

in the orogenic realm is thinned. This suggests that

besides erosion, tectonic denudation also contributes

significantly to the exhumation of rocks from deeper

crustal levels (see below).

A detailed view into the internal structure of the

orogen is provided by Fig. 10a which shows the strain

distribution in several vertical sections through the

model. It highlights the general bivergent structure of

the model orogen—a familiar feature already known

from the 2D simulations (e.g., Willett et al., 1993).

Deformation on the retro-side of the orogen is more

localised in narrow shear zones while on the pro-side

it is more diffusively distributed over a wide area.

Towards the lateral foreland of the model orogen,

crustal thickening gradually diminishes, although the

model is still shortened significantly parallel to the

convergence direction. This is because convergence is

largely compensated by orogen-parallel extension and

lateral extrusion, instead of crustal thickening. Oro-

gen-parallel extension is greatest in the lowermost

crust near the tip of the S line where boundary

conditions (fixed and ‘smooth function’) restrict the

basal nodes while the remaining crust is moving

outward. The rear part of the model is influenced by

both the convergent kinematics of the frontal part and

by orogen-parallel material influx from the orogen

towards the centre of its lateral foreland. Both factors

result in a rotational movement of the outer flanks of

the lateral foreland, anti-clockwise on the pro-side

flank and clockwise on the retro-side flank. Simulta-

neously, the central part of the lateral foreland is

shortened in orogen-parallel direction, as well as

extended along the x-axis and slightly thinned in the

centre of the rearmost part of the model.

3.1.2. Stress field variations with time

Modelling results illustrate how the magnitude and

orientation of the stress field inside and outside the

evolving orogen varies during convergence. Fig. 4c

illustrates the near-surface stress fields after of 2.5, 5

and 10 Ma and 50, 100 and 200 km of convergence,

respectively. These plots are based on the orientation

of the three principal stress components (cf. Fig. 10a)

Fig. 4. Selected results of standard model S-1. (a) Total displacement after 100 km plate convergence in convergence-parallel (x), orogen-

parallel ( y) and vertical (z) direction. (b) Strain components ex (horizontal shortening, left) and ez (vertical thickening, right) after 50, 100 and

200 km of convergence. (c) Orientation of the near-surface stress fields after 50, 100 and 200 km convergence. Colours indicate the predominant

style of faulting, i.e., yellow: reverse and thrust faulting; green: strike-slip-faulting; blue: normal faulting. For comparison, the initial outer shape

of the model is also given.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2910

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 11

for selected elements. Since in the near-surface stress

field one of the principal axes is oriented subverti-

cally, the style of faulting can be easily deduced from

the vector orientation. The domains of predominantly

normal, reverse/thrust and strike-slip faulting are in-

dicated by different colours in Fig. 4c. For easier

interpretation, modelling results are also shown like

focal plane solutions of earthquake data (lower hemi-

sphere plots). The largest principal stress axis (r1 =P)

intersects the centre of the white quadrants and the

least principal stress axis (r3 = T) the grey ones. In

reality, reactivation of pre-existing faults could modify

the modelled stress field distribution; however, this

effect is not taken into account in the continuum FE

model.

After 50 km of convergence (Fig. 4c, top) com-

pressive stress fields with j1 oriented parallel to the

convergence direction govern a large part of the

model extending from the orogen centre to both its

pro- and retro-side forelands and the central part of the

lateral foreland. Structural elements in these zones are

expected to be reverse and thrust faults striking

perpendicular to the convergence direction. In most

of the remaining part of the lateral foreland r1 and r3

are both oriented horizontally suggesting predomi-

nantly strike-slip faulting in these areas.

After 100 km of plate convergence (Fig. 4c,

centre), the areas dominated by reverse faulting are

already dramatically reduced. Thrusting still occurs in

the foreland and external wedges on the pro- and

retro-side of the orogen. But the domain of strike-slip

faulting has widened and effects the flanks of the

orogens as well as large parts of the lateral foreland.

Within the centre of the orogen, a zone of normal

faulting oriented perpendicular to the convergence

direction has developed.

A relatively uniform stress field has been estab-

lished after 200 km of plate convergence (Fig. 4c,

bottom). A large area ranging from the rear parts of

the orogen to the flanks of the lateral foreland dis-

plays stress conditions indicative for strike-slip fault

activity. In particular, the transition between the

orogen and its lateral foreland is governed by these

conditions, which would support orogen-parallel ex-

tension by the expulsion of wedge-shaped blocks.

The exact orientation of the principal stresses varies

in space: r1 mostly follows the orogens axis at the

rear central parts of the lateral foreland; a more

outward rotated orientation is observed both towards

the forepart of the model and towards its pro- and

retro-side.

3.1.3. Stress field variations at different crustal levels

As already indicated by the occurrence of different

strain regimes in the thickened crust (Fig. 4b), stresses

vary not only in time and map view, but also vertically

within the orogenic realm for the same time step. Fig.

5 displays the contemporaneous orientation of the

stress fields at four different crustal levels after 200

km of plate convergence. The magnitudes of the

principal stresses as well as their orientations are

much more variable in the lower levels than near the

surface. Already at depths of about 12.5 km (Fig. 5b),

stress vectors are rotated significantly with respect to

their orientation near surface. The main compression

axis r1 is verging towards the retro-side in the pro-

zone and towards the pro-side in the retro-zone of the

orogen. Towards the retro-side the orientation of stress

vectors implies a prominent strike-slip component.

Crustal thinning by normal faulting, which would be

indicated by subvertical r1 axes, is not observed at

this crustal level. Thus, tectonic denudation by normal

faulting is restricted to the uppermost crust, while

vertically beneath at the same time different stress

regimes prevail. The stress pattern in the upper part of

the lower crust (depths around 20 km, see Fig. 5c) is

similar to the one described above, but stress vectors

already tend to rotate towards the stress pattern found

for the crustal base. Near the Moho, i.e., at depths

ranging from 27.5 to 50 km (Fig. 5d), the orientation

of stress vectors is rather uniform. Since the r2-axis is

oriented subhorizontally, r1 dips over large areas of

this level at approx. 45j and verges towards the fixed

model quadrant at the retro-side. It also has to be kept

in mind that at this depth level, deformation of the

crust is actually governed by ductile rock behaviour,

thus implying different modes of stress accommoda-

tion than brittle faulting.

3.1.4. Lateral extrusion versus crustal thickening

The stress and strain patterns and their temporal

variations described above control the surface topog-

raphy as well as crustal thickening and lateral extru-

sion. The distribution of lateral displacement along

strike of the orogen and the surface topography are

shown in Fig. 6. An overview of the amounts of

Fig. 5. Standard model S-1: Orientation of the stress fields at four different crustal levels after 200 km of plate convergence.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2912

lateral extrusion and surface uplift is given in Fig. 7a

and b, respectively.

The column plots of Fig. 7b imply that maximum

surface lateral extrusion does not increase linearly

with convergence, but tends to quicken in later stages

due to thermal weakening in the orogen’s interior.

However, as far as the standard model S-1 is

concerned (see also Fig. 8b), this acceleration is rather

slow, documented by a maximum lateral displacement

of approx. 27 km after 100 km convergence and

additional 38 km achieved during the second conver-

gence increment.

As the initial model surface is defined to be

uniformly at sea level, surface uplift and topographic

Fig. 6. Orogen-parallel sections 50 km to the right of the S-line (cf. Fig. 4a), i.e., in the centre of the evolving orogen, after 100 km of

convergence for the various models. Plots on the left are contoured for displacement ( y-direction). Hatched areas indicate model margins, which

are fixed with respect to orogen-parallel displacements. Model C-16 is also shown with contour values five times higher than in the other plots.

Plots on the right side depict the contemporaneous surface topography along the orogen’s axis. Vertical exaggeration is 20-fold and grey-scale

contours indicate the amount of maximum uplift of rocks.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 13

Fig. 7. (a) Maximum amounts of surface elevation and uplift after 100 (front row) and 200 km of convergence (rear row), respectively. The

maximum possible amount of exhumation is the difference between uplift and surface elevation. (b) Maximum lateral extrusion after 100

(hatched lower part of columns) and 200 km (entire columns) of convergence, respectively. All models display an increase in lateral

displacement during the second convergence increment.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2914

Fig. 8. Standard model S-1: (a) Maximum surface elevation, uplift

and exhumation of the model orogen as a function of plate

convergence and time, respectively. (b) Maximum lateral extrusion

in relation to the amount of convergence. The slight decrease in

maximum uplift rate correlates with the slight increase in lateral

extrusion.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 15

elevation are equivalent. Fig. 7a illustrates the relation

between uplift, surface uplift and exhumation for all

modelled scenarios (for definitions, see England and

Molnar, 1990 and the inlet in Fig. 7a). The maximum

amount of exhumation provides an upper limit for

actual maximum exhumation, which will be achieved

when maximum uplift and maximum topography

occur at the same point. In the standard model S-1

(see also Fig. 8a), the temporal evolution of maximum

elevation is characterised by a short and rapid rise,

reaching its apex at about 100 km of convergence.

Subsequently, the rate of surface uplift in the internal

zone of the orogen is reduced and partly inverted, as

already indicated by the modified surface stress fields

(cf. Fig. 4c) and the total strain evolution (cf. Fig. 4b).

While surface erosion is effectively working due to

the large elevation, surface rocks are also transported

towards the lateral foreland by increased tectonic

denudation. However, crustal thickening is simulta-

neously active in the deeper levels and the more

external parts of the orogen.

3.2. Parameter variations

The 3D models are influenced by a large number of

parameters, e.g., material properties, initial geometry

and physical state of the model, boundary conditions,

which can be modified to evaluate their impact on the

modelling results. We have run 16 variations of our

standard model S-1 to study the effects of different

thermal and mechanical boundary conditions as well

as rheological parameters. While the standard model

S-1 described above is based on the input parameters

and boundary conditions listed in Fig. 2, models R-2

up to C-17 are characterised by variations in one or

two of the input parameters (see Table 2 and Fig. 9 for

summary). In the first set of experiments, thermal

boundary conditions (R-2, R-3), rheological parame-

ters (R-4, R-5) and the convergence velocity (R-6, R-

7) have been modified. A second group of models is

characterised by additional constraints applied to the

model walls, either by assuming fixed margins (B-8 to

B-11) or plate boundary forces (B-12, B-13). For

comparison with published analogue models, some

modelling runs simulate collision of one or two highly

viscous blocks (indenters, I-14, I-15). Finally, the

basal boundary conditions have been changed in

models C-16 and C-17 to study different modes of

crust–mantle coupling.

At the present stage, we have deliberately concen-

trated on orthogonal convergence and the most im-

portant input parameters in order to fully understand

the basic model behaviour. The general modelling

approach, however, is open for further parameter

variations, thus, oblique convergence as well as lateral

and vertical variations in model geometry and rheol-

ogy could be studied.

3.2.1. Effects of rheology, temperature and conver-

gence rate (R-models)

If basal heat flow is increased to 0.023 mW m� 2

an initial Moho temperature of about 700 jC (Model

R-2) results. Due to the strong temperature-depen-

dence of the crustal rheology and thermal weakening a

zone of intense deformation develops close to the base

of the crust. It effectively results in mechanical

Fig. 9. Schematic diagram giving an overview of the parameter variations performed in this study. The standard model S-1 is situated in the

centre of each of the diagrams. Parameter variations leading to different modelling scenarios are indicated by the following prefixes:

R = rheology, temperature, convergence rate, B = boundary conditions at the margins of the model, I = indenter models and C= different basal

coupling conditions. For models only differing from S-1 in their rheologic set-up initial strength profiles are given; differential stresses in the

brittle domain(s) refer to failure along thrust faults, for the ductile domain(s) a strain-rate of 1�10� 14 has been assumed. The strength profile

associated to the I-models refers to the higher-viscous blocks (grey-shaded model base in the respective plots) only.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2916

decoupling between most of the crust and the driving

mantle. As already observed in 2D plane strain

models (e.g., Seyferth and Henk, 2000), crustal thick-

ening is diffusely distributed over a wide area and

orogenic topography (cf. Fig. 7a) does not exceed

2000 m. Even after 100 km convergence, large parts

of the upper crust in the internal zone of the model

orogen are controlled by an extensional stress regime.

At deeper crustal levels, however, compression and

crustal thickening still continues. Lateral extrusion is

more prominent than in model S-1 and increases

significantly during further convergence (Fig. 7b).

If basal heat flow is reduced to 0.0135 mW m� 2

initial Moho temperatures are about 500 jC (model

R-3). In contrast to the standard model and the

previous parameter variation crustal strength is in-

creased and strong crust–mantle coupling occurs. This

results in a more localised orogen with a maximum

topography exceeding 3000 m (Fig. 7a). However,

surface erosion and lateral extrusion towards the free

lateral margin prevent further significant thickening as

convergence continues. Lateral extrusion amounts are

slightly reduced with respect to the standard model,

especially the increase with time is lower (Fig. 7b).

Strong crust–mantle coupling can also be achieved

by lower crustal creep parameters yielding a more

viscous rheology. Models R-4 and R-5 assume a

stiffer rheology for the lower crust (mafic Pikwitonei

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 17

granulite data from Wilks and Carter, 1990) and initial

Moho temperatures of 500 and 600 jC, respectively.In these cases the surface topography of the evolving

orogens increases slowly, but substantial amounts of

uplift and exhumation are reached as lateral extrusion

is limited (Fig. 7a and b). The strong crust–mantle

coupling also projects into the uppermost crustal layer

and the zone of maximum lateral extrusion is offset

towards the retro-side. Similarly, the lateral foreland

flanks are strongly rotated and its centre is thinned

significantly.

The evolution and geometry of an orogen are also

influenced by the velocity of plate convergence. Due

to the different time available for syn-convergent

thermal equilibration in the thickened crust, rapid

convergence (100 mm year� 1 in model R-6) results

in narrowly localised orogens, whereas low conver-

gence rates (4 mm year� 1 in model R-7) lead to

widened zones of deformation. Since surface erosion

is also a time-dependent process, the amounts of

surface uplift and exhumation are strongly affected

by variations in the convergence rate (Fig. 7a). Lateral

extrusion amounts are modified in a less dramatic

manner, reflecting a partial compensation of poor

thermal weakening through high gravitative potential

(model R-6) and vice versa (model R-7), respectively.

3.2.2. Effect of boundary conditions applied to the

side-walls (B-models)

The boundary conditions applied to the vertical

sides on the rear part of the model describe the general

geodynamic setting of the continental collision zone.

Alternatively, these boundaries can approximate the

effect of lithostatic pressure (using no-tilt walls), plate

boundary forces (using no-tilt walls and additional

forces) or adjoining rigid blocks (using zero displace-

ment constraints); the respective type of boundary

condition is schematically illustrated in the small

insets in Fig. 10.

In case of model B-8, the entire retro-side of the

model is defined as a fixed wall (Fig. 10c). A similar

set-up has been used in analogue models describing

the Indian–Asian collision, assuming the Siberian

Platform to behave as a rigid buttress (Peltzer, 1983;

Tapponnier et al., 1982). As a result of these boundary

conditions, an asymmetric strain pattern (in map view)

develops. Asymmetry is due to an intensified anti-

clockwise rotation of the pro-side flank of the lateral

foreland, whereas the retro-side remains unchanged.

Maximum lateral extrusion is shifted towards the

retro-side flank, while some areas of the pro-side

flank are actually shortened in the orogen-parallel

direction (Fig. 10c). In the pro-side transition zone

the topography rises up to 1000 m.

Asymmetry can also be observed in the near-

surface stress fields (Fig. 10c, upper plot). While the

retro-side is dominated by a rather uniform stress

distribution giving rise to strike-slip faulting, parts

of the pro-side flank are superficially thinned by

normal faults. In terms of strain, orogen-parallel

extension reaches its peak in a zone parallel to the

rigid retro-side margin (Fig. 10, lower plot).

The stress and strain pattern changes completely, if

both the retro- and the pro-side model margin are

assumed to be rigid walls (model B-9). In this case,

the entire pro-side margin is moving at plate conver-

gence velocity, while a basally coupled part in the

front abuts on a basally uncoupled rear part. As

before, the entire retro-side wall is fixed with respect

to orogen-orthogonal (x) movements. In plan view,

crustal thickening in the rear part of the model is

indistinctly localised in a V-shaped set of two zones

verging against the rear model margin. However,

topographic elevation in this area is limited to a

maximum of 500 m, since shortening is compensated

by lateral extrusion in a more effective way. Orogen-

parallel extension is very large as material can only be

squeezed out in one horizontal direction and accumu-

lates to about 50 and 140 km after 100 and 200 km of

convergence, respectively.

Models B-10 and B-11 have been designed to test

the efficiency of rigid walls to obstruct lateral move-

ments. A fixed rear margin, located 400 km from the

orogen’s lateral margin (model B-10), reduces orogen-

parallel extension by a factor of about 2 with respect

to the standard model S-1. After 100 and 200 km of

convergence, only 17 and 37 km of lateral extrusion,

respectively, are reached. Any lateral extrusion has to

be accommodated by orogen-parallel shortening and

material movements towards the pro- and retro-side

flank. In the orogen-parallel topography profile (Fig.

6), a steep lateral margin reflects the change in

foreland kinematics, even if the maximum topography

remains unaffected.

In model B-11, all margins are assumed to behave

rigidly, implying a scenario which does not allow any

Fig. 10. Results of selected parameter variations. Upper plots show the surface stress field distribution after 200 km plate convergence; for

comparison, the initial outer shape of the model is also given. Lower plots depict the lateral (orogen-parallel) finite strain component ey after 100km plate convergence. (a) Standard model S-1. (b) Model R-5 with more viscous lower crust. (c) Model B-8 with a fixed retro-side model

margin. (d) Model C-16, boundary conditions at the entire base of the model allow for orogen-parallel movements, i.e., only orogen-orthogonal

displacement constraints are applied to the frontal part of the model. For a detailed listing of the respective model set-ups, see Table 2.

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2918

Fig. 10 (continued).

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 19

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2920

material to escape laterally. In an overall compressive

regime, the lateral foreland is significantly thickened

and raised up to 1500m above sea level. Though

maximum lateral extrusion is reduced by a factor of

about 4 and maximum extension reaches only 5%,

some orogen-parallel material transport still occurs.

Any further decrease in extrusion amounts requires a

fixed rear wall closer to the orogen’s lateral margin,

which will finally result in a 2.5D model without any

lateral motions when the wall reaches the orogens

margin.

Modelling results obtained by applying moderate

plate boundary forces to the model margins surround-

ing the lateral foreland are characterised by only

minor deviations from the standard models deforma-

tion and kinematics. However, the stress field in the

lateral foreland may be changed significantly. 10 MPa

compressive (model B-12) and tensile forces (model

B-13) are able to shift planes of equal extensional

offset by an amount of approx. 50 km towards the

orogen’s centre and towards the lateral foreland,

respectively.

For all B-series models, the variations in maxi-

mum topography and uplift are rather small (Fig.

7a). However, there is an influence on the topo-

graphic profile along the orogens axis, which is

illustrated in Fig. 6. Compressive stresses or rigid

margins (models B-10, B-11 and B-12) constraining

the lateral foreland lead to a steep lateral orogenic

margin. Conversely, a weak lateral foreland (models

S-1, B-8, B-9 and B-13) results in a more gentle

slope.

3.2.3. Effect of highly viscous blocks (I-models)

Rigid pro- and retro-side blocks, referred to as

indenters and foreland buttresses, respectively, have

been employed in analogue model set-ups to force

lateral extrusion of orogenic crust (e.g., Ratsch-

bacher et al., 1991b; Tapponnier et al., 1982).

However, since rigid behaviour is not an a priori

property of any structural unit, rigid blocks of

analogue models have been replaced by highly

viscous material in some of the numerical experi-

ments. These blocks are situated on the retro-side (I-

14) or on both the pro- and retro-side foreland (I-

15). They are characterised by a reduced basal heat

flow of 0.009 mW m� 2 yielding an initial Moho

temperature of only 413 jC.

The forced strain localization induced by the high-

ly viscous blocks results in more effective thickening

and a consequent increase in maximum topography

and exhumation potential (Fig. 7a). However, Fig. 7b

implies that lateral displacements are influenced only

to a minor degree. Only model I-15 displays a clear

temporal increase of lateral extrusion rates, where the

remaining space between the stiffer blocks is signif-

icantly smaller. A large portion of lateral extrusion is

actually taken up by the indenting blocks in spite of

their low temperature and high strength. Thus, it

appears that stiffer blocks with a rheological stratifi-

cation do not change the resulting strain pattern as

much as proposed by analogue models using rigid

indenters.

3.2.4. Effect of crust–mantle coupling (C-models)

The boundary conditions applied to the base of

the numerical model reflect the mode of crust–

mantle coupling. Under standard conditions, the

colliding blocks are constrained with respect to the

x- and y-axis (isotropic coupling). If the basal nodes

are set free with respect to movements in orogen-

parallel ( y) direction (model C-16, anisotropic cou-

pling), lateral extension and extrusion is no longer

dependent on the formation of a decoupling level in

the lower crust, but acts over the whole crustal

profile. Thereby, the locus of maximum crustal

thickening (situated in the deeper crustal root) repre-

sents also a zone of maximum lateral extension (see

Fig. 10d, lower plots). The resulting efficiency of

lateral extrusion in this area relates to the formation

of a decoupled extrusion channel below the more

static middle and upper crust. However, the amounts

of lateral extrusion also profit by this set-up and yield

up to 60-70% of the contemporaneous amount of

crustal shortening.

Increased amounts of lateral extrusion have to be

balanced by a loss in crustal thickening and there-

fore also affect topography and exhumation poten-

tial. As illustrated by Fig. 7a, topographic elevation

for C-16 does not exceed 2000 m above sea level.

Maximum exhumation is kept low both by the small

erosion potential and by the fact that lateral extru-

sion is more efficient in the lower than in the upper

crust. Consequently, the related surface stress pattern

completely lacks areas with dominant subvertical r3-axes (see Fig. 10d, upper plot). Thus, superficial

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 21

crustal stacking occurs only in the beginning stages

of continental collision. Later, most areas are dom-

inated by strike-slip tectonics, and thinning by

normal faults plays an important role in a broad

wedge-shaped domain extending to the outer half of

the orogen.

Model C-17 represents a combination of a free

model base and a fixed retro-side margin. Though the

rigid wall forces the models horizontal kinematics to

reorganise, changes are most salient with respect to

the distribution of lateral displacements in the foreland

but barely affect the ratio of crustal thickening and

lateral extrusion.

4. Discussion of modelling results

The modelling results provide various insights into

the strain distribution, the related tectonic displace-

ments and stress fields of growing orogens; different

styles of brittle deformation can be inferred from the

surface stresses. Strain, displacement and stress quan-

tities underlie a complex temporal evolution. In order

to summarise these individual results and interrela-

tions between them, the observed structures and

Fig. 11. Schematic overview of prominent structures and processes observe

superficial crustal thinning, possible occurrence of normal faults; (3) an

amounts of lateral extrusion; (6) zone of extension in convergence-parallel

thickening; (9) successive mechanical decoupling along the vertical c

convergence vector.

processes are shortly discussed in the following

(numbers refer to the synoptic diagram shown in

Fig. 11).

(1) The collision zone in the forepart of the models

is characterized by crustal thickening and the con-

sequent surface uplift. Exhumation of rocks is driv-

en by surface erosion and tectonic denudation.

Taking into account the resolution limitations, the

observed pattern is consistent with that of previous

2D models (e.g., Beaumont and Quinlan, 1994;

Beaumont et al., 1994; Ellis et al., 1998; Jamieson

et al., 1998).

(2) The 3D model set-up allows to study the process-

es mentioned above along the orogen axis and to

consider the lateral (orogen-parallel) deformation

component. At later stages of convergence, as shown

in Fig. 11, the centre of the orogen is characterised by

maximum exhumation due to erosion and the activity

of normal faults, which accommodate lateral exten-

sion. This area is encircled by a zone of inferred

strike-slip movements, while the pro- and retro-wedge

advance towards the respective forelands. The tem-

poral shift of these zones makes the finite strain

pattern more and more diffuse.

d in the numerical models: (1) maximum uplift of rocks; (2) zone of

d (4) areas of maximum orogen-parallel extension; (5) maximum

direction; (7) rotation of foreland flanks; (8) zone of diffuse crustal

rustal profile; (10) additional decoupling by partitioning of the

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2922

(3) Further to the rear part of the model, at the

lateral margin area of the orogen, localised (‘chan-

nelled’) lateral extrusion occurs, usually character-

ized by the maximum lateral extension (ey) amounts.

Dependent on the respective model, this extrusion

channel can extend 50–150 km towards the orogen

centre. Typically, extrusion amounts reach 20-40% of

the respective total convergence. Since the crust is

tightly coupled to the mantle under standard con-

ditions, the lowermost parts of the crust experience

significant orogen-parallel simple shear. However,

maximum lateral extension (ey) is situated in the

upper crust.

(4)–(7) Since lateral extension is partly compensated

by orogen-parallel shortening in the rear parts of the

lateral foreland, the zone of maximum extension

usually forks into two branches extending towards

the foreland flanks. The zone of maximum lateral

displacement, which is still characterised by lateral

extension in its forepart, but experiences shortening in

its rear part, is encircled by these branches. Rotation

of the foreland flanks and crustal thinning in the

rearmost part of the model are typically related

features.

(8) Slightly shortened, thickened and elevated areas

in the neighbourhood of the orogen’s lateral margin

(transitional area) are due to continued overall plate

convergence although these parts are not directly

driven by basal mantle drag. In the more external

parts of the lateral foreland, which cover about 50%

of the model surface, topography is not significantly

affected by the collision. Surface stress patterns are

highly variable with time and low differential

stresses imply occasional strike-slip or normal fault

activity.

Similar to the spatial distribution of strain, dis-

placements and stress, its temporal evolution strong-

ly depends on the particular model parameters.

However, some general trends can be formulated:

During initial convergence, surface elevation rises

rapidly. Later convergence is primarily accommo-

dated by lateral extrusion, erosion and widening of

the orogenic belt rather than by an increase in

crustal thickness and elevation. However, lateral

extrusion is directly related to continental collision

and its onset is contemporaneous with that of

convergence. The rate of lateral extrusion increases

with time as thermally induced weakening, especial-

ly of the lower crust, leads to basal decoupling at a

major simple shear horizon and permits the upper

crust to move rather independently in the orogen-

parallel direction.

Crustal temperatures and/or the creep parameters

defining lower crustal rheology (cf. R-models) con-

trol the degree of both vertical and horizontal

transmission of the forces applied by the basal

boundary condition. Vertical transmission (intra-

crustal coupling) affects the localisation of deforma-

tion: narrow, high and deeply eroded orogens are

achieved by low temperatures and/ or highly viscous

rheologies. It also controls the degree of horizontal

partitioning of the convergence vector into a con-

vergent and an orogen-parallel ‘escaping’ compo-

nent. Generally, the escaping component becomes

more important with increasing distance from the

model base. With respect to lateral extrusion, weak

vertical coupling results in high amounts of extruded

material without localisation in a distinct extrusion

channel. Conversely, a distinctly channelled extru-

sion maximum at lower absolute amounts of extrud-

ed mass occurs if vertical coupling is strong.

Besides this vertical transmission of the displace-

ment boundary condition, a highly viscous lower

crust is also capable to transmit the asymmetry of

the collision zone horizontally to the lateral foreland,

resulting in a retro-directed offset of the extrusion

channel.

The mode of crust–mantle coupling (cf. C-mod-

els) is the most efficient parameter to control the

amount of lateral extrusion. In all numerical experi-

ments, which are based on isotropic coupling,

lateral extrusion does not exceed 30% of the overall

amount of convergence. In contrast, if lateral move-

ments of the model base are allowed by defining an

anisotropic coupling mode, lateral extrusion is much

more efficient and the corresponding displacements

reach up to 70% (see Fig. 10d). In the lower crust,

an extrusion channel forms, thus limiting crustal

thickness and supporting lateral extrusion in the

upper crust. Surface stress fields of later collision

stages show that the structural expression of plate

convergence can almost lack reverse faulting and

thrusting in the neighbourhood of an orogen’s

lateral margin (see Fig. 10d, upper plot). However,

low surface elevation also obstructs efficient exhu-

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 23

mation by surface erosion as well as by tectonic

unroofing.

Indenter models (cf. I-models) simulate highly

viscous blocks by assuming a very low basal heat

flow in the pro- and retro-side foreland. Such model

conditions result in a modified strain distribution

between the pro- and retro-wedge. Further, due to

the forced localisation of crustal thickening, the

corresponding maximum surface elevation is strongly

increased. Finally, the shape of the extrusion channel

is modified by the stiff blocks squeezing orogenic

crust outward. However, the maximum amounts of

lateral displacement do not rise significantly until the

outer shape of the squeezed lower viscous domain

reaches an elongate aspect ratio. Even at this stage, a

large portion of lateral extrusion is actually taking

place within the viscous blocks. Therefore, semi-rigid

behaviour of the indenter blocks is not supported by

the modelling results, even if extremely low crustal

temperatures are employed. From this point of view,

rigid indenters, which have been used to deform

analogue material in order to simulate lateral extru-

sion, are useful as a first-order modelling approach

only. Semi-rigid behaviour can be diagnosed in the

field after deformation has finished, but it will only

occur where weak units are capable to accommodate

shortening instead. Even the eastern southern Alps,

which are commonly referred as an ‘rigid’ indenter,

have been shortened internally by about 100 km

(Roeder, 1989) and have been extruded eastward as

well (Frisch et al., 1998). Thus, it appears that

explicitly rigid indenters are not a realistic approach,

and that stiffer blocks with a rheological stratification

do not change the resulting strain pattern as much as

proposed by the analogue models.

Variations in the behaviour of the model walls

surrounding the lateral foreland (cf. B-models) have

a comparatively low influence on the evolution of the

collisional orogen itself. However, the kinematic pat-

tern governing the foreland deformation show signif-

icant variation. Whereas rigid pro- and retro-side

walls tend to channel the lateral extrusion of orogenic

crust and therefore support high amounts of maximum

lateral displacement, these amounts can be distinctly

reduced by assuming a rigid wall at the rear model

margin. In contrast, plate boundary forces acting at the

lateral foreland margins do not influence the total

displacement significantly.

Altogether, the modelling results illustrate pro-

nounced strain and stress field variations in space

and time. At the root zone of the orogen, crustal

thickening prevails throughout the model run, while

at higher crustal levels it is primarily restricted to the

pro- and retro-zone of the orogen. The uppermost part

of the internal zone experiences thickening only in the

early stages of convergence. Even after 100 km plate

convergence, surface stress fields in this area indicate

strike-slip tectonics, and during further convergence,

r1 successively rotates towards a subvertical orienta-

tion marking the onset of normal fault activity. Con-

sequently, crustal areas under extension rest on crustal

rocks under compression, thus favouring syn-conver-

gent exhumation in the internal zone of the orogen.

Assuming uniform topography-dependent erosion

rates all over the model surface, maximum uplift and

exhumation occur at the retro-verging part of the

internal zone. Maximum exhumation for the standard

model set-up amounts to about 2 km for the first (100

km, 5 Ma) and additional 6 km for the second (200 km,

10 Ma) convergence increment. This increase is

caused by higher erosion rates due to higher surface

elevation and by increased tectonic unroofing related

to lateral extrusion of the uppermost crustal layers.

Strike-slip faults should result in wedge-shaped blocks

being extruded towards the lateral foreland, i. e. the

rear part of the model; normal faults strike perpendic-

ular with respect to the orogens axis, thus also accom-

modating orogen-parallel extension.

5. Comparison to field examples

Although the numerical simulations are not scaled

to real orogens with respect to model geometry,

material parameters, convergence velocity etc. they

reproduce many characteristics of actual continental

collision zones. Thus, we present a qualitative to

semiquantitative comparison between the modelling

results and three examples of active collision zones

from the Alpine–Himalayan belt.

5.1. Tectonic escape of the Anatolian microplate

A comparatively small-scale example of continen-

tal collision and lateral extrusion is known from

Turkey, where Neogene continental collision of the

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2924

Arabian and the Eurasian plate has resulted in thrust-

ing along the Bitlis Zone and in west-directed extru-

sion of a small crustal fragment referred to as the

Anatolian microplate (see Fig. 12b for the general

plate tectonic setting). Collision commenced in Serra-

vallian (middle Miocene, approx. 12 Ma bp) times

(Dewey et al., 1986) and is still active today. A large

portion of the westward lateral displacement of the

Anatolian microplate towards the Aegean Sea is

accommodated by two major strike-slip faults, i.e.,

the dextral North Anatolian Transform Fault (NATF)

and the sinistral East Anatolian Transform Fault

(EATF). Estimates of the total offset at the NATF

vary significantly, but 100 km appears to be a reason-

able first-order approximation (Barka, 1992; Platzman

et al., 1998). Total offset along the EATF is less,

resulting in anti-clockwise rotation of the Anatolian

microplate (Le Pichon et al., 1995; Reilinger et al.,

1997). Based on average slip rates estimated for the

last 9 Ma (NAFT: 8.9 mm year� 1 and EATF: 1.7 mm

year� 1 (Sengor, 1979)) Dewey et al. (1986) conclude

that only a minor proportion of the total convergence

rate (15.3 mm year� 1) is actually accommodated by

Fig. 12. (a) FE model B-8 at 200 km plate convergence. Background colou

thrust faults; grey: strike-slip faults. The orientation of possible strike-sli

principles stress axes. Only one set is shown for the pro- and the retro-side

zone between Arabia (Syria) and Eurasia leading to westward escape of A

given with respect to Eurasia: averaged values for the last 9 Ma (Dewey e

present-day slip rates (Kiratzi, 1993; Oral et al., 1995; Reilinger et al., 19

tectonic escape. However, present-day slip rates de-

rived from GPS data (NAFT: 16 up to 27 mm year� 1

(Oral et al., 1995) and EATF: 15 mm year� 1 (Rei-

linger et al., 1997)) indicate a significant increase of

the lateral extrusion rate, which may be correlated

with Pliocene decoupling of Anatolia and Eurasia

along the NATF (Platzman et al., 1994; Reilinger et

al., 1997).

The dimensions of this field example are roughly

comparable to the geometry of the numerical simu-

lations. A comparison of the field data with the results

of model B-8 shows striking similarities. The mod-

elled asymmetric pattern of lateral displacement, the

anti-clockwise rotation and the pattern of slip lines

(Fig. 12a) strongly resemble the geodynamic setting

of the Anatolian microplate (Fig. 12b). Thrust-domi-

nated areas in the model are in good correlation with

the actual positions of the Bitlis and the Anti-Lebanon

Zone and the maximum eastward extent of normal

faults approximately coincides in model and nature. In

this scenario, the fixed retro-side wall of the model

would represent the almost rigid behaviour of the

European Plate. Based on the data and interpretation

rs indicate style of faulting. White: normal faults; black: reverse and

p faults is shown by slip-lines inferred from the orientation of the

portion of the model. (b) Plate tectonic sketch map of the collision

natolia (modified after Dewey et al., 1986). Displacement rates are

t al., 1986; Sengor, 1979 and references therein) and—in brackets—

97).

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 25

given by Dewey et al. (1986), Anatolia’s total lateral

displacement is of the same order of magnitude as the

amounts modelled with an isotropic basal coupling.

Recent acceleration of extrusion rates may be due to

deep vertical decoupling at the major strike-slip faults,

circumscribing a whole-plate extrusion channel.

5.2. India–Asia collision zone and tectonic escape of

South East Asia

Convergence between the Indian and the Eurasian

plate not only has formed the world’s largest conti-

nental collision zone and orogen, but also the most

prominent zone of tectonic escape. Le Pichon et al.

(1992) estimate that one third to one half of the

material input due to a total plate convergence of

about 2000 km (Molnar and Tapponier, 1975) is

compensated by tectonic escape. Estimates of the total

amount of orogen-parallel displacement have been as

large as 1500 km (Molnar and Tapponier, 1975;

Tapponnier et al., 1986, 1982). Even though more

recent studies imply that displacements have possibly

Fig. 13. Geophysical and geological data from eastern Asia in comparison

mirrored, at 200 km plate convergence (original data and full legend, see F

1987 (after England, 1992). As in the numerical model, white quadrants i

formation reproduced by plane-strain plasticine models (from Peltzer, 198

been overestimated and amounts of some hundred

kilometres are more plausible (England and Molnar,

1997), it is clear that lateral extrusion plays a signif-

icant role in Asian tectonics. Large-scale sinistral

strike-slip-faults delimit the area of lateral extrusion

to the North: the NW-SE trending Red River Fault

(50–17 Ma bp) and the more W–E oriented Altyn-

Tagh Fault (17 Ma bp to present). Today, the offset of

the Altyn-Tagh Fault is 13 mm a� 1 (Westaway, 1995),

thus taking up most of the total eastward displacement

of 17 mm a� 1 estimated for central Tibet (Westaway,

1995). In central Tibet, tectonic escape is also accom-

modated along N–S trending normal faults (England,

1992).

The dimensions of the Indian–Asian collision zone

are much larger than the FE models, but there are

phenomenological similarities concerning the recent

strain and stress field distributions (Fig. 13). Follow-

ing the plasticine analogue models of Peltzer (1983)

and Tapponnier et al. (1986) the cold, rheologically

strong crust making up the Siberian Platform is

similar to model B-8, which has a rigid retro-side

to numerical and analogue models. (a) FE model B-8, rotated and

ig. 10c). (b) Focal plane solutions of earthquakes between 1900 and

ndicate compression. (c and d) Successive stages of strike-slip fault

3 in Tapponnier et al., 1986).

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2926

margin. Though their particular set-up has been a

matter of some debate (e.g., Houseman and England,

1993), plasticine models are well suited to reproduce

the formation of transform faults and the sequential

clockwise rotation of extruded wedges along these

elements. While discrete tectonic elements cannot be

reproduced by continuum models, the general clock-

wise rotation is well reflected in the results. Addition-

ally, zones of normal and thrust fault activity can be

assigned by the model. A map of historic focal plane

solutions after England (1992) indicates that the area

governed by pure strike-slip tectonics is comparative-

ly small and limited to the Altyn-Tagh Fault, the

Eastern Tibetan Plateau and Indochina.

Focal planes report active thrusting from the Hi-

malayan deformation front as well as the Tien Shan

north of the Tibetan Plateau; similarly, thrust belts in

the model are restricted to the pro- and retro-Zone

already after 200 km convergence. The reproduction

of E–W directed extension documented in Central

Tibet (England, 1992) is limited in the model by its

minor amount of total convergence. The models

predict additional areas of crustal thinning for the

outer centre of the lateral foreland and the margin of

Fig. 14. Schematic sketch map of the Eastern Alps and the adjoining

the rotated quadrant; in the natural counterpart, nor-

mal fault activity can be deduced from focal plane

solutions in some parts of Indochina and the western

part of the Tibetan Plateau.

5.3. Lateral extrusion in the Eastern Alps

While crustal stacking was still active in the more

western parts of the Alps, eastward extrusion of up to

170 km has been documented for the Eastern Alps,

lasting for some 10 Ma between 23 and 13 Ma bp

(Frisch et al., 1998; Ratschbacher et al., 1991a,b). A

free lateral margin was provided by the northward

offset of the collision zone between the eastern margin

of the Alps and their continuation in the western

Carpathians (see Fig. 14). There, lateral extrusion

may have been further supported by back-arc-spread-

ing behind the Carpathian arc resulting in an exten-

sional regime and the formation of the Pannonian

Basin (Royden, 1993). The tectonic boundary be-

tween the European Eastern and Central Alps in the

north and the Adriatic Southern Alps in the south is

represented by the Periadriatic line system. In detail,

the Eastern Alps are directly juxtaposed against the

Pannonian Basin (modified after Ratschbacher et al., 1991b).

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–29 27

so-called Apulian indenter. It is generally accepted

that the Apulian indenter and its northern counterpart,

the Bohemian promontory behaved in a rheologically

strong way forcing the Eastern Alps to spread east-

ward (Frisch et al., 1998; Ratschbacher et al., 1991a).

Two aspects of the Alpine evolution can be

compared to the numerical models in a semiquanti-

tative manner. One concerns the extreme, nearly 1:1

ratio between E- and W-extension of about 170 km

and total N–S shortening of about 150–200 km (up

to 100 km in the Eastern Alps (Frisch et al., 1998)

and 60 km in the adjacent Southern Alps (Roeder,

1989)). The second is related to the obviously ‘‘event-

like’’ occurrence of the extrusion process. Structural

data imply that the extrusion event was predated by

crustal stacking and the formation of a NW- to N-

verging orogenic wedge (Decker et al., 1994; Linzer

et al., 1997; Peresson and Decker, 1997). However,

there is sedimentological evidence from the distribu-

tion of the so-called Augenstein formation, that the

Northern Calcareous Alps, which form a main portion

of the extruded area, did not experience significant

surface uplift before ca. 18 Ma bp (Frisch et al.,

1998). Thus, when lateral extrusion started, no par-

ticularly thick crust had yet developed. If there was

no mountainous topography in the area of the later

Eastern Alps before the onset of lateral movements,

and lateral extrusion was contemporaneous with con-

vergence, it must have been induced by tectonic

escape rather than by gravitational forces. The almost

1:1 ratio of convergence vs. lateral extrusion implies

the existence of a basal decoupling horizon (cf. model

C-16). As the parameter studies have shown, other

proposed causes like the indentation of a more

viscous indenter (cf. models I-14 and I-15) or an

extensional regime in the Pannonian basin (cf. model

B-13) could have modified the resulting structural

pattern but fail to explain the amount of lateral

motions by a factor of 2.

6. Conclusions

3D finite element models have been applied to gain

quantitative insights into the complex relationships

between crustal thickening, syn-convergent exhuma-

tion and lateral extrusion in collisional orogens of

finite axial extent. Modelling results are consistent

with a first-order description of thermal and mechan-

ical processes acting in the continental crust and

reproduce several prominent features observed in

orogenic belts and their forelands.. Orogen-parallel extension is intimately related to

continental collision and occurs contemporaneously

with convergence. Thereby, significant lateral extru-

sion occurs where the collision zone adjoins a weakly

constrained lateral foreland, which is just balanced by

lithospheric pressure.. The numerical experiments suggest that the hori-

zontal forces induced by collision provide a more

effective driving force for lateral extrusion than the

gravitational instability of the thickened crust, because

the onset of lateral motions is generally contempora-

neous with that of collision and increases only slightly

during further convergence due to thermal weakening.. The various studies show that for a wide range of

material parameters and boundary conditions orogen-

parallel movements reach 20–40% of the amount of

convergence. Only if the boundaries of the lateral

foreland are kept fixed in order to simulate the

presence of a rigid block, does tectonic escape de-

crease to only 10% of the respective convergence

value. In contrast, anisotropic decoupling at the

crust–mantle boundary can result in up to 70% of

lateral extrusion.. The models indicate substantial spatial and tempo-

ral variations of stress and strain in the collision zone

and its surrounding. In particular, the near-surface

stress field in the orogen’s internal zone completely

reorganises during convergence. While the initial

collision stage is still governed by compression, stress

patterns of advanced convergence stages allow the

formation of strike-slip and normal faults within the

internal part of the orogen.. Even if the uppermost part of the internal zone is

already under extension, model orogens continue to

grow. Stress patterns illustrate a temporal spreading of

compressive areas towards the external zones repro-

ducing foreland-directed propagation of fold- and

thrust-belts. Of special relevance for syn-collisional

exhumation are the vertical stress field variations in

the internal zone of the orogen. While the upper crust

is thinned, at deeper crustal levels vertically beneath

compressive stress fields prevail at the same time.

This spatial pattern of stress domains strongly favours

syn-collisional exhumation in the internal zone by

M. Seyferth, A. Henk / Tectonophysics 382 (2004) 1–2928

tectonic denudation in upper crustal levels in addition

to erosion.. Modelling results have been compared to observa-

tions from three recent orogens, i.e., the tectonic

escape of Anatolia, the Indian–Asian collision and

the lateral extrusion of the Eastern Alps. Whereas the

amount of lateral displacement of Anatolia roughly

matches the values modelled at standard conditions,

the Eastern Alps extrusion event exceeds them by a

factor of 2. According to the modelling results, its

almost 1:1 ratio of shortening vs. lateral displacement

cannot be explained by indenter tectonics and an

extensional regime in the Pannonian Basin alone,

but additionally suggests a major decoupling horizon

between crust and mantle. Due to the large scale of the

Indian–Eurasian collision, modelling results can be

compared with tectonic escape in Eastern Asia only in

a qualitative fashion. However, there are similarities

between present-day focal plane solutions and the

modelled stress field. In a similar way, Anatolia’s

large-scale fault pattern strikingly fits the models

predictions. Scaled 3D simulations of real orogens

are therefore challenging tasks for future modelling

work.

Acknowledgements

Christopher Beaumont, Lykke Gemmer, Greg

Houseman, Susan Ellis, Roberto Weinberg and Jean-

Pierre Burg are thanked for their helpful comments on

an earlier version of the manuscript. Financial support

by the Deutsche Forschungsgemeinschaft as part of

the programme ‘Orogene Prozesse-ihre Simulation

und Quantifizierung am Beispiel der Varisciden’ is

gratefully acknowledged.

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