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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: [email protected] (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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