Int Journ Earth Sciences (1999) 88 : 190–200
Q Springer-Verlag 1999
ORIGINAL PAPER
J.-P. Burg 7 Yu. Podladchikov
Lithospheric scale folding: numerical modelling and application
to the Himalayan syntaxes
Received: 26 November 1998 / Accepted: 27 November 1998
Abstract We describe the eastern and western Himalayan syntaxes, which are large-scale antiforms situated
at geodynamically similar locations and the metamorphic evolution of which is coeval in the India–Asia
collisional history. To understand the mechanical plausibility of the structural interpretation, we present twodimensional finite-element modelling of lithospheric
folding. The models reveal the coeval development of
adjacent synformal basins, analogous to the Peshawar
and Kashmir basins on both sides of the western
syntaxis. Similarities between geological data and
calculated models indicate that lithospheric buckling is
a basic response to large-scale continental shortening
and an efficient mountain building process.
Key words Himalaya 7 Syntaxes 7 Folding 7
Modelling 7 Intermontane basins 7 Pakistan
Introduction
The purpose of this study was to advocate crustal and
lithospheric scale folding as a plausible (and perhaps
the dominant) mechanism of continental shortening,
and to examine the first-order consequences of this
process in terms of P–T–t and structural history.
Folding and buckling instabilities are responses to layer
parallel shortening that have been thoroughly investigated (Turcotte and Schubert 1982). Classical theories
are restricted to initial development of the instability
and to linear viscous (Ramberg 1964), elastic and viscoelastic rheologies (Biot 1961). Recent theoretical development extends to the waning stages of folding and to
non-linear visco-plastic rheologies (Johnson and
J.-P. Burg (Y) 7 Yu. Podladchikov
Geologisches Institut, ETH-Zentrum, Sonneggstrasse 5,
CH-8092 Zurich Switzerland
e-mail: jpb6erdw.ethz.ch;
Tel.: c41-1-6326027;
Fax: c41-1-6321030
Fletcher 1994). These theories are commonly applied in
structural geology to outcrop- and kilometre-scale
folds, in which cases gravity can be ignored. However,
gravity plays a fundamental role at a crustal and lithospheric scale, which means that new methods are
needed to model folding of the oceanic (McAdoo and
Sandwell 1985; Martinod and Davy 1992) and continental (Cobbold et al. 1993; Burov and Diament 1995)
lithosphere.
Non-linearity of lithospheric rheology has an important influence on deformational behaviour and subsequent structures (e.g. see Johnson and Fletcher 1994).
Because the exact analytical treatment of non-linear
rheology is complex, there have been several attempts
to find a compromise between this complexity and relevance to reality. Frequently employed “thin-sheet”
approximations have arisen from the search for “effective” elastic (Burov and Diament 1995) or viscous solutions (Sonder et al. 1987; Houseman and England
1993). In such approximations, the complex rheological
profile of the continental lithosphere is replaced by a
set of “effective” elastic or viscous layers that have an
“apparent” response similar to that of the lithosphere
under simple loading histories. Existing thin-sheet
approximations are only applicable at early stages of
folding and cannot be used to study effects such as fold
locking and loss of symmetry during buckling. Simplified thin-sheet models have been employed previously
particularly for the India–Asia collision belt (Vilotte
and Daignières 1982; England and McKenzie 1983;
England and Houseman 1986; Houseman and England
1986, 1993) assumed constant velocity profiles with
depth, which kinematically excludes folding as a
response to compression. Another approach is based
on pre-description of mechanical motions (Henry et al.
1997). However, such kinematic models require
detailed knowledge of the velocity field, which is
commonly lacking for remote and poorly studied areas.
Two-dimensional FEM modelling using a wide range of
non-linear rheologies is conceptually simpler than
modelling based on either kinematic assumptions or
191
dynamic concepts of “effective” substitutes for depthdependent rheological profiles (i.e. thin-plate models
having a dynamic response similar to that of the lithosphere for certain types of loading). Although the twodimensional FEM method is technically more difficult
to implement than kinematic modelling, the numerical
code can be verified independently of the geological
application. Thus, 2D FEM may be the most reliable
tool for simulating geodynamical histories of areas on
which kinematic information is lacking.
This article gives a brief description of the western
and eastern Himalayan syntaxes interpreted as antiformal structures. The syntaxes are thousands of kilometres apart but are situated at geodynamically similar
locations and their metamorphic evolution is coeval in
the India–Asia collisional history (Burg et al. 1997). We
then present the main concepts of the numerical
methods we use to model large-scale folding. Because
of the number of parameters controlling folding style,
we do not attempt a systematic study. We restrict this
work to a particular example of continental shortening,
i.e. the West and East Himalayan “syntaxes”. The
particular model set-up chosen to simulate the Indian
continental lithosphere prior to shortening is then
described. Some relevant results of numerical
modelling are reported. Similarities between the
geology of the West and East Himalayan syntaxes and
calculated models are emphasised. We conclude that
lithospheric buckling is a basic and mountain-building
response to shortening.
Himalayan “syntaxes”
The Himalaya is an active mountain belt that terminates at both ends in nearly transverse syntaxes (Wadia
1931), i.e. areas where orogenic structures turn sharply
Fig. 2 Comparison of the
Pressure–time evolution of
basement rocks in the Pliocene–Pleistocene Himalayan
syntaxes. Hatched boxes are
Nanga Parbat data from
Zeitler et al. (1989, 1993) and
the curve through points with
error bars are Namche Barwa
data from Burg et al. (1997,
1998)
Fig. 1 Location of the Namche Barwa (eastern) and Nanga
ParbatcHazara-Kashmir (western) Himalayan syntaxes in the
India–Asia collisional system
about a vertical axis (Fig. 1). Both syntaxes are named
after the main peaks that tower above them, the
Namche Barwa (7756 m) in the core of the eastern
syntaxis and the Nanga Parbat (8126 m) in the western
bend of the Himalayas, in Pakistan (Wadia 1931;
Gansser 1991). Both syntaxes record remarkably
similar thermo-mechanical evolution of basement rocks
overprinted by Himalayan metamorphism and Pliocene–Pleistocene high-grade metamorphism and
anatexis (Fig. 2). The syntaxes are crustal antiforms
that fold the Paleocene Tethyan suture zone around
halfwindows of Indian crust (Wadia 1957; Gansser
1966; Treloar et al. 1991; Burg et al. 1997) Both
syntaxes straddle the same Neogene time span and
have undergone rapid denudation during fold amplifi-
192
cation (Fig. 2), which links their continuing growth to
the uplift that produced Tibet in the last few million
years (Molnar et al. 1993).
A rise of the Moho level is recorded under the
Nanga Parbat (Farah et al. 1984). No information on
the depth of the Moho is available beneath the Namche
Barwa. In Pakistan, the Hazara-Kashmir syntaxis is the
southern continuation of the Nanga Parbat Syntaxis. In
the Arunachal (eastern) Himalaya, the Siang antiform
(Singh 1993) appears as the southwestern continuation
of the Namche Barwa syntaxis. Geological interpretation indicates crustal-scale folding as the mechanism
that produced these orogenic structures. Kinematic
studies indicate that both the western and eastern antiforms result from compression nearly orthogonal to
their axial trace (in the Nanga Parbat, Butler and Prior
1988; in the Namche Barwa, Burg et al. 1998; in the
Hazara-Kashmir antiforms, Bossart et al. 1988).
Across-syntaxis compression is also indicated by
present-day focal mechanisms in Pakistan (Verma et al.
1980) and in the eastern Himalayas (Holt et al. 1991).
The aim of the numerical modelling presented below
was to test the plausibility of these interpretations.
Table 1 Model parameters for all runs
Box characteristics
Length of model
Depth of model (base of lithosphere)
Granitic layer thickness (upper crust)
Diabase layer thickness (lower crust)
Olivine layer thickness (upper mantle)
Convergence rate
Bulk modulus
Shear modulus
Conductivity
Specific heat
2500 km
120 km
25 km
10 km
85 km
2!10 –10 ms –1
1!10 10 Pa
1!10 10 Pa
2.6 Wm –1 7C –1
1050 m 2s –2 7C –1
Granite properties
Density (Tp0 7C)
Power-law exponent
A coefficient
Activation energy
2700 kg m –3
3.3
3.16!10 –26 Pa –n s –1
1.9!10 5 J mol –1
Diabase properties
Density (Tp0 7C)
Power-law exponent
A coefficient
Activation energy
2900 kg m –3
3
3.2!10 –20 Pa –n s –1
2.76!10 5 J mol –1
Olivine properties
Density (Tp0 7C)
Power-law exponent
A coefficient
Activation energy
3300 kg m –3
3
7.10 –14 Pa –n s –1
5.1!10 5 J mol –1
Numerical modelling
Method
We use a two-dimensional finite-element code that
couples plane strain mechanical and thermal calculations. Finite elements are seven-node quadratic triangles (Poliakov and Podladchikov 1992; Podladchikov et
al. 1993). Robustness of the model has been verified for
salt diapirism (Poliakov et al. 1996). Rheology ranges
from elasticity to Mohr-Coulomb plasticity (Mandl
1988) or thermally activated power-law creep (Carter
and Tsenn 1987) depending on a yield-strength criterion (Poliakov et al. 1996). Effects of gravity, as well as
thermal and compositional buoyancy and viscosity
dependencies, are included. The resolution of finiteelement grids was 901!101.
Model set-up and boundary conditions
The model (Fig. 3; Table 1) is a stratified box with
three compositional layers: (a) upper granitic crust
(25 km); (b) lower mafic crust (10 km of diabase); and
(c) sub-crustal olivine lithosphere (85–120 km). Deformation is produced by the application of lateral horizontal velocities. The mechanical boundary conditions
consist of a bottom boundary, fixed in the vertical
direction and free to slip in the horizontal direction;
lateral boundaries converging at constant velocity and
free to slip in the vertical direction; and a free-surface
upper boundary. At each time step the vertical position
of the entire model box is adjusted (i.e. shifted downwards by constant displacement) to keep the far-field
Fig. 3 Lithosphere model used for numerical experiments
surface elevation at zero level. The technique is justified because the lithosphere is not deforming at
distance from the Himalayas and, therefore, does not
produce any topographic elevation. Our approach
allows adopting a kinematic (vertically fixed) basal
boundary condition as opposed to more complex,
though strictly valid, isostatic condition of vanishing
193
Table 2 Temperatures used at the base of model lithospheres
Model name
T1 7C
T2 7C
T73 7C
Erosion
WARM
COLD
HOT
INTERMEDIATE
WARME
1200
900
1300
1000
1200
1350
1150
1350
1150
1350
1230
930
1310
1030
1230
No
No
No
No
kp10 –7 m 2 s –1
differential stresses at some compensation level. Our
experience has shown that using the isostatic lower
boundary conditions requires smaller time steps but
produces similar results. The starting configuration has
a relaxed stress state with gravitational load and a nonlinear, steady-state temperature distribution. Thermal
boundary conditions are 0 7C at the surface and fixed
basal temperatures, which are: (a) T(x)pT1 beneath
the left “half” of the model; (b) a thermal perturbation
with a maximum temperature T2 exponentially
decaying from the centre; and (c) T(x)pT3 beneath the
right “half” of the model (Fig. 3; Table 2). The thermal
perturbation T2 is employed to localise deformation at
the centre of the model. There is no lateral heat flux
through the sides. Erosion is modelled according to a
linear diffusion equation (Podladchikov et al. 1993).
Compared with other 2D numerical models, we do
not prescribe any deformation mode (e.g. homogeneous pure shear or heterogeneous simple shear at a
forcing point, etc.). For example, fault location is not
pre-ordained by introducing special “slippery” nodes or
employing singular points of abrupt velocity changes as
boundary conditions. Instead, deformation is localised
by the long wavelength variation of the basal temperature. Inherent shorter wavelength, i.e. more localised
structures, develop with growing bulk strain and are
controlled by the instantaneous rheological configuration of the lithosphere. Boundary loading is due to the
constant-velocity convergence of lateral sides, i.e. the
external (far field) deformation mode is restricted to
rigid plate motions. The development of an asymmetry
in the model reflects an inherent physical process triggered by small differences in basal temperature of the
shortened lithospheric plate.
Compared with analogue modelling, the position of
the brittle–ductile transition for each compositional
layer is not prescribed by the choice of different materials (Davy and Cobbold 1991; Willet et al. 1993; Beaumont et al. 1996) and may evolve through time. An
internally consistent result of stress modelling is that
three-layer models presented here would be equivalent
to a six-layer analogue model. For proper comparison
the analogue model should involve adjustment of the
thicknesses of both the brittle and ductile material
layers, because after each strain increment the stressstrength field must be evaluated, brittle material
beyond its yield condition replaced by ductile material,
and vice versa. This is an incremental exercise where
numerical modelling reveals its advantages.
The geometrical parameters and physical constants
we have adopted are based on geophysical information
available for the structure and properties of the Indian
plate (Henry et al. 1997). Rheological laws for dry
granite, diabase and olivine result from laboratory
measurements extrapolated to tectonic time scales, as
assumed in standard modelling studies (e.g. Carter and
Tsenn 1987; Ranalli 1995). Our parameter values
(Table 1) are typical of those adopted for lithospheric
scale modelling. A critical uncertainty is the Indian
geotherm, which was therefore systematically varied in
our experiments. Numerical runs with different upper
crustal thicknesses are not presented here because, in
the context of our modelling, it is an “effective” parameter quantifying complicated rheologies of the heterogeneous crust; however, this parameter is crudely
constrained geophysically and has a relatively minor
influence on results presented herein.
Results
Because of the number of parameters controlling
deformation styles, we do not attempt any systematic
study. We restrict ourselves to a particular example of
continental shortening such as inferred in the West and
East Himalayan “syntaxes”. For all runs T2 1 T3 1 T1,
i.e. the model left part represents the cold portion of
the “Indian Plate” newly involved into collision and the
right part represents the portion of the plate heated by
Fig. 4 Central part of model WARM lithosphere. Note that
buckling is noticeable only after 295 km ( 1 10%) of homogeneous
shortening and quickly amplifies within the next 10–15% shortening. Asymmetry at 411 km shortening faces towards the hot
(i.e. orogenically affected) side of the lithosphere (back-thrusting
effect)
194
its previous orogenic history. Respective values of T1,
T2 and T3 designate the five numerical models
presented herein (Table 2).
A warm lithosphere (WARM; Table 1) is our
preferred model in terms of comparability with amplitude and wavelength of both Himalayan syntaxes.
Figure 4 focuses on deformation of its central part to
emphasise the following points:
1. Buckling is observable only after significant (here
295 km, 1 10%) homogeneous, distributed shortening of the lithospheric plate.
2. The decay in the amplitude of the main hinge, which
began at slightly more than 400 km (ca. 25%) shortening (Fig. 5; WARM), indicates that the main fold
has become locked (does not amplify anymore) and
deformation is being transferred to adjacent hinges;
therefore, the amplitude of the buckle fold pattern is
achieved in the bulk strain range of 10–25%.
3. Crustal and sub-crustal levels are coupled during
symmetrical lithospheric buckling until loss of
symmetry at the locking stage (i.e. 411 km shortening; Fig. 4). At this point decoupling of the gran-
itic and diabase layers is expressed by marked
shearing along their boundary.
4. Asymmetrical folding is facing towards the hot (i.e.
orogenically affected) parts of the lithosphere.
5. The topographic evolution shows the coeval subsidence of small amplitude synforms on both sides of
the growing antiforms (Figs. 5, 6).
The COLD (Fig. 7) and HOT (Fig. 8) models represent two experimental end members (coldest and
hottest lithospheres, respectively). They show remarkable similarities in terms of deformational response to
applied shortening: (a) In both cases, as for run
WARM, ultimately unstable homogeneous thickening
(up to 10–15%) leads to buckling; (b) Symmetrical
buckling terminates at approximately 20% shortening
with occurrence of crustal decoupling and subsequent
asymmetry.
Fig. 5 Vertical motion of antiformal hinges and the intercalated
synformal basin during shortening of models WARM (Fig. 4),
COLD (Fig. 7), HOT (Fig. 8) and INTERMEDIATE. No erosion
is admitted. Boundary conditions are given in Table 1
195
Comparison of end-member experiments emphasises three differences:
1. Buckle wavelength (200 km in Fig. 7 vs ca.100 km in
Fig. 8) and amplitude (ca. 25 vs ca. 5 km; Fig. 5) are
larger on the cold lithosphere.
2. Lateral propagation of buckling is more strongly
manifest in cold than in hot lithosphere (compare
Figs. 7 and 8).
3. Intercalated basins on cold lithospheres subside less
than on hot lithospheres (Fig. 5). In particular, subsidence is short lived, and starts to reverse, on the cold
lithosphere (Fig. 5; COLD). The subsidence accelerates with time for a hot lithosphere, for the duration
of these experiments. The INTERMEDIATE model
illustrates the situation between cold and hot models
(Figs. 5, 6). These four models, all with no erosion,
reproduce the fast and exponentially growing differential topography suggested from the geological
record in both Himalayan syntaxes (see above);
however, the final topography of the cold-type
models is clearly too high. We attribute this shortcoming to unrealistic “no-erosion” simplification of
the models. Indeed, variations of the effectively
unconstrained coefficient of erosion have the
obvious effect of reducing topographic elevation.
To enlarge upon our comparison between models
and geological information we have solved the “too
high topography problem” by setting a geologically
reasonable erosion coefficient. Figure 9 displays the
topography and exhumation histories of the main hinge
zone or our preferred model WARM with erosion
(WARME; Table 1). Topography due to buckling is
5–10 km. The amount of exhumation is limited by fold
locking and is typically ca. 20 km. At the fold-locking
stage (ca. ~400 km shortening) both uplift and denudation rates start to decrease. Subsidence in the basins
adjacent to the main hinge zone is under-compensated
because the sedimentation rate (ca. 5 mm/year) is
slower than basement subsidence (Fig. 10). At the foldlocking stage the sedimentation rate keeps accelerating,
whereas the subsidence rate slows down.
Relevance of modelling results to the Himalayan
syntaxes: associated synformal basins
The simultaneous subsidence of synformal basins on
either side of a lithospheric antiform in the numeric
models is an important result. We argue that this
pattern is documented in Pakistan where the HazaraKashmir syntaxis is the southern continuation of the
Nanga Parbat syntaxis. The synclinal Peshawar Basin to
the west is readily recognisable on geological maps as
the structural analogue to the synclinal Kashmir Basin
to the east of the Hazara-Kashmir syntaxis (Fig. 11).
The lithological and stratigraphical correlation between
these two synformal depressions were noted by Yeats
and Lawrence (1984).
The Kashmir Basin includes Paleozoic and Mesozoic
sequence overlying a metamorphosed sequence (Wadia
1931). The Paleozoic includes the Permo-Carboniferous sequence of Panjal volcanic and volcanoclastic
rocks and is overlain by a Lower Mesozoic sedimentary
sequence. The Mesozoic is, in turn, overlain by a
1 1300 m thick cover from late Cenozoic and Quaternary fluvio-lacustrine sedimentation that continues in a
few lakes presently (Burbank and Johnson 1982).
Volcanic ashes in the lower levels of the late Cenozoic
cover show that sedimentation began approximately
4 m.y. ago. A deeply weathered palaeosol below the
late Cenozoic unconformity attests to a long period of
surface exposure during which the shallow marine
Eocene limestones, known elsewhere in the Himalayan
realm, were eroded (Burbank et al. 1986). Centripetal
drainage dominated the period 1.7–0.4 Ma, whereas
sediment accumulation rates from 32 to 16 cm kyr –1
were maintained (Burbank and Johnson 1982; Burbank
et al. 1986).
The Peshawar Basin comprises a sequence of
Cambrian to Jurassic rocks resting on a Precambrian
basement (Pogue et al. 1992). Like the Karewas of
Kashmir, the Peshawar Basin has a thick Plio-Pleistocene to Holocene fill of alluvial sediments that began
accumulating at least 2.8 m.y. ago (Burbank 1983;
Burbank and Khan Tahirkheli 1985). Sediments accumulated at an average rate of 15 cm kyr –1 (Burbank
and Khan Tahirkheli 1985).
The acceleration and deceleration of sedimentation
rates are reproduced by our model calculation (Fig. 10).
In light of our models, we propose that the symmetrically oriented Peshawar and Kashmir basins are
synformal depressions on both sides of, and directly
related to, the Nanga Parbat–Hazara-Kashmir syntaxis.
Our interpretation explains a first-order feature,
namely their location. The syntaxes are traditionally
interpreted as the surface expression of low-angle
detachment faults that ramp upward farther south
(Burbank and Johnson 1982); however, both basins
began receiving sediments in Pliocene time. Both
basins are coeval with the syntaxis and lacustrine sedimentation, although their overall history is that of
surface uplift (Burbank and Johnson 1982). Burbank
and Khan Tahirkheli (1985) emphasise that this lacustrine sedimentation contrasts with the fluvial sedimentation that is predominant in adjacent areas. Differences in basin history recognised by the latter authors
might be explained by the development of the westward verging syntaxis, a geometrical character that we
have not yet modelled. This geometrical asymmetry
would account for a 1-m.y. younger onset of sedimentation in the Peshawar Basin where accumulation of PlioPleistocene sediments is not as thick as in the Kashmir
Basin.
An interesting model feature is the spontaneous
large-scale asymmetry developing in the course of
shortening once initially symmetrical buckling is
suddenly replaced by a “thrusting” mode. The dip
196
Fig. 6 Perspective view of the evolution of the topography
profiles during shortening in the absence of erosion
direction is controlled by the small difference in bottom
temperatures of the colliding plates. Future investigation will show if this asymmetry is relevant to the
vergence of the natural syntaxes.
Discussion
Modelling of the India–Asia collision belt has been
based on thin-sheet approximations (Vilotte and Daignières 1982; England and McKenzie 1983; England and
Houseman 1986; Houseman and England 1986, 1993)
that allow consideration of the 3D geometry of convergent zones and treat first-order questions such as the
relative amounts of lateral extrusion vs homogeneous
thickening. However, thin-sheet models kinematically
exclude folding as a response to compression. Exclusion of folding mechanisms is unfortunate because the
stresses necessary to engender folding are less than
those for homogeneous thickening. This implies that
homogeneous thickening is dynamically unstable.
Therefore, the amount of intraplate shortening vs other
modes of localised deformations (strike slip, thrusting)
is intrinsically underestimated by “dynamic” thin-sheet
modelling.
Our FEM numerical modelling yields exhumation
rates similar to those recognised in the eastern and
western Himalayan syntaxes, without prescription of
the vertical velocity field. In the model we prescribe
only the bulk shortening, whereas the exhumation and
the anticline formation are dynamic responses to the
shortening. The present thermo-mechanical modelling
ensures force balance in addition to the heat and mass
balance, which are satisfied in thermo-kinematic
models; therefore, our results support the plausibility of
crustal folding as envisioned by the kinematic model of
Burg et al. (1997). In addition, the model simultaneously covers the formation of the adjacent basins,
well developed next to the West Himalayan syntaxis.
Tuning of the coefficient of erosion and selecting a
“preferred” thermal model successfully and simultaneously reproduced the sedimentation rate, the exhu-
197
Fig. 7 Shortening experiment of the COLD lithosphere
Fig. 8 Shortening experiment of the HOT lithosphere
198
Fig. 9 Topography and exhumation histories of the main hinge
zone of our preferred model WARME. Topography due to buckling is up to 5–10 km. Exhumation is limited by fold locking and
the typical amount is ca. 20 km
Fig. 11 Tectonic sketch map and simplified cross section of the
Nanga Parbat–Hazara-Kashmir syntaxes showing the synclinal
Peshawar Basin to the west as a structural analogue of the
synclinal Kashmir basin to the east. Location in the Himalaya
System in inset. Facing black arrows are compression directions
from focal mechanism solutions. Moho projected from Ni et al.
(1991)
Fig. 10 Topography and basement subsidence of basins next to
the main antiformal hinge (as in Fig. 4) in the erosional model
WARME
mation rate and the magnitude of the differential
relief.
Examination of the Himalayan syntaxes supports
the concept of lithospheric buckling as a basic response
to shortening, a complementing mechanism to the
conventionally accepted subduction/accretion mechanisms. Lithospheric buckling may produce elevated
regions with associated synformal basins. We emphasise that dominant geological and physiographical
features of northern Pakistan formed during the past
4 Ma have been controlled by the growth of the Nanga
Parbat syntaxis. This is true also for the less well-known
eastern Himalayan syntaxis.
The next question to address is whether there is a
link between the tectonic location of syntaxis areas and
the dominance of lithosphere-scale folding as a shortening mechanism. The Himalayan syntaxes are areas of
“laterally constrained shortening” between major faults
that prevent widening of the deformation area. We
suspect that lateral constraints are of consequence
because the out-of-plane (lateral) extensional strain
rate strongly decreases the development rate of the
folding instability, which minimises the magnitude of
fold hinge magnification achieved at given amounts of
shortening; therefore, constrained areas are expected to
be preferential for large-scale buckling instead of
vertical thickening as shortening mechanism. Late
convergence stages would favour the buckling mode
because it needs some strain to develop and the presence of topographical loads along with the lack of
accommodation space prohibit lateral escape in
deforming areas.
Conclusion
Our 2D finite element numerical experiments systematically reproduce deformation features independently
199
recognised by analogue modelling (Burg et al. 1994;
Martinod and Davy 1994). This result suggests that
certain behaviours are characteristic:
1. Numerical and analogue models initially undergo
homogeneous shortening and coeval thickening
before they become unstable and buckle. Hot lithospheres undergo more distributed shortening than
cold ones. Regardless of thermal regime, buckling is
a basic response of stratified lithospheres to applied,
far-field compression.
2. Lithospheric folding is mechanically preferable to
homogeneous thickening and can cause/drive mountain building and exhumation of deep-seated rocks.
The coefficient of erosion, the parameter controlling
the erosion rate, has major importance for (a) the
amount of exhumation possible in the core of crustal
antiforms, and (b) the maximum topography
achieved during shortening.
3. Buckle amplification is limited by fold locking-up. A
cold (strong) lithosphere tends to exhibit higheramplitude folding with a longer wavelength of ca.
200 km than a hot lithosphere. Kilometre-scale
amplification is achieved in the strain range of
10–25%.
4. With shortening beyond the locking condition, buckling propagates laterally and adjacent crustal folds
develop. Propagation is less pronounced in hot than
in cold lithospheres.
5. Folding of both crustal and sub-crustal levels indicates coupling of all lithospheric layers during this
deformation mode.
6. In all cases asymmetry grows gradually and becomes
dominant after approximately 25% shortening.
7. Synformal, small-amplitude basins develop on both
sides of the growing anticlines.
The Himalayan syntaxes are preferential sites of
large-scale folding. This deformation has been quantified by 2D FEM modelling that couples plane strain
mechanical and thermal calculations with non-linear
lithospheric rheologies. Both syntaxes have grown
within the past 4 m.y. and were accompanied by the
formation of quickly subsiding synformal basins.
Geological and modelling information indicate that
these structures have reached their locking stage.
Vertical movements should decelerate and buckling of
the Indian lithosphere is expected to propagate laterally.
Acknowledgements These results were obtained thanks to the
support of the Swiss National Science Foundation (projects 2139080.93 and 20-49372.96) and the ETH (project 1-20-888-94).
Comments by J. Connolly improved a previous draft of the manuscript.
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