JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. B5, 10.1029/2001JB000636, 2002
Oblique convergence between India and Eurasia
Muhammad A. Soofi and Scott D. King
Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, Indiana, USA
Received 23 May 2001; revised 31 December 2001; accepted 4 January 2002; published 30 May 2002.
[1] Oblique convergence is the general rule along convergent boundaries. Such convergence
produces asymmetric deformation (topography) along the collision boundary. To quantify this
asymmetry, we develop a method that allows us to calculate the asymmetry in topography with
respect to a reference line drawn perpendicular to the collision boundary. The asymmetry in
topography is presented as a number, or series of numbers, called here the asymmetry index. A
positive asymmetry index indicates that there is more area with topography greater or equal to
certain value to the east (right) of the reference line than to the west (left). The asymmetry index is
negative for the opposite topography distribution. We use oblique convergent boundary conditions
with a thin viscous sheet model to investigate the observed topography along the India-Eurasia
collision boundary. The goal of our study is to reproduce the observed asymmetry in the topography
(i.e., the high topography in the Tibetan Plateau is shifted to the east). We consider a laterally
varying velocity (both magnitude and angle, which we call the angle of obliquity) along this
boundary and use a homogeneous lithosphere for Eurasia. With boundary conditions alone we are
unable to account for the degree of asymmetry present in the observed topography. The asymmetry
in the calculated topography is enhanced by considering a rheologically stronger anomalous zone
representing the Tarim basin. The use of a constant velocity (both magnitude and angle) boundary
condition, as in earlier studies, produces topographic asymmetry in the opposite direction to the
observed topography. This indicates that in the study of obliquely converging boundaries it is
important to consider the variation of velocity (magnitude and angle) in the collisional
boundary.
INDEX TERMS: 8110 Tectonophysics: Continental tectonics—general (0905); 8159
Evolution of the Earth: Rheology—crust and lithosphere; 8120 Tectonophysics: Dynamics of
lithosphere and mantle—general; 8102 Tectonophysics: Continental contractional orogenic belts;
KEYWORDS: Convergent boundary, India-Asia collision, viscous flow, oblique convergence
1. Introduction
[2] Reviews of global plate motion [e.g., DeMets et al., 1994]
reveal that the relative motion between two plates at a convergent
boundary almost always contains an oblique component of motion.
Oblique convergence gives rise to both compressional and shear
(transcurrent) components of strain [Lu and Malavieille, 1994; Haq
and Davis, 1997]. Consequently, a variety of structures can be
produced along a collisional boundary depending on the ratio of
compressional to shearing motion. Because oblique convergence is
the rule, rather than the exception, oblique boundary conditions
should be investigated along with rheology and heterogeneities in
the lithosphere when studying convergent boundaries [Lu and
Malavieille, 1994; Sobouti and Arkani-Hamed, 1996; Hu et al.,
1997; Haq and Davis, 1997].
[3] The mechanics of oblique convergence have been studied
using analytical techniques [e.g., Beck, 1986, 1991; McCaffrey,
1992; Platt, 1993; Ellis et al., 1995], numerical models [e.g., Braun,
1993; Hu et al., 1997] and mechanical models [e.g., Pinet and
Cobbold, 1992; Lu and Malavieille, 1994]. Fitch [1972] suggested
that in the case of high-oblique-angle convergence, complete
decoupling occurs, decomposing the velocity vector into strikeparallel and strike-normal components. The strike-parallel component causes lateral displacement of a sliver of the overriding plate.
This type of decoupling was later termed ‘‘Sunda-style tectonics’’
by Beck [1983]; however, McCaffrey [1992] has shown that
complete decoupling is an end-member case and is not common
in nature. Generally, the oblique convergence partitions into strikeCopyright 2002 by the American Geophysical Union.
0148-0227/02/2001JB000636$09.00
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slip and dip-slip components where the dip-slip vector makes an
angle less than the obliquity of the velocity vector, measured from
the trench-normal component, thus producing partial decoupling
[McCaffrey, 1992].
[4] Numerous studies have investigated the effect of the collision
of India with Eurasia [e.g., Molnar and Tapponnier, 1975; Tapponnier and Molnar, 1976; England and McKenzie, 1982; England and
Houseman, 1986; Peltzer and Tapponnier, 1988; Jolivet et al.,
1990; Neil and Houseman, 1997]. These studies have shown that
the amount of topographic uplift along the India-Eurasia plate
boundary and the stress distribution in the adjacent Eurasian plate,
as recorded by earthquake focal mechanisms, can be explained by
the collision; however, the asymmetric pattern of the topography
(i.e., a wide, parallel to convergence, zone of uplift along the eastern
boundary and a narrow zone of uplift along the western boundary)
remains the subject of debate [e.g., England and Houseman, 1985;
Peltzer and Tapponnier, 1988; Houseman and England, 1996].
[5] A stress pattern consistent with crustal thickening was
observed in the plane stress numerical experiment of Vilotte
et al. [1982]. In addition, they found that the pattern of stress
correlated well with the distribution of normal and thrust faults in
the region. In a separate plane stress numerical experiment, where
gravitational effects and boundary forces were considered, England
and McKenzie [1982] showed that most of the topography in Asia
north of India can be accounted for by the collision of India with
Eurasia. In a further modification of the thin viscous sheet formulation, Houseman and England [1986] introduced a ‘‘moving
indenter’’ boundary condition, showing that to obtain the present
topography of the Tibetan Plateau requires 2000 km of crustal
shortening. This is close to the estimated crustal shortening obtained
from paleomagnetic data [Patzelt et al., 1996]. Le Pichon et al.
3-1
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SOOFI AND KING: OBLIQUE CONVERGENCE
60ûE
80ûE
100ûE
120ûE
50N
50N
EURASIA
2000
40N
TAR
2000
IM B
ASIN
40N
2000
0
400
4000
0
2000
A
0
INDIA
B
30N
00
4000 20
400
30N
20N
20N
60E
80E
100E
120E
Figure 1. Observed topography along the India-Eurasia collision boundary and neighboring regions from ETOPO5.
Topography is in meters. The asymmetry in the topography of the Himalayas is apparent by tracing the 4000-m
contour. This contour line is much closer to the AB plate boundary to the west than it is to the east.
[1992] attempted a reconstruction of the India-Eurasia collision over
the last 45 Myr and concluded that the total volume of crustal
shortening is more than the crustal volume needed to explain the
uplifted Himalaya and Tibetan Plateau. They suggested that a
combination of lateral extrusion and eclogitization of the continental crust is necessary to reconcile the crustal shortening with the
observed deformation and topography. A reconciliation between the
lateral extrusion and crustal thickening models can be reached by
considering that the lithosphere deforms first by thickening and
then, as the buoyancy force increases, lateral extrusion by strike-slip
deformation becomes important [England and Houseman, 1986].
Neil and Houseman [1997] showed that a relatively small change in
the strength of the lithosphere, specifically a stronger Tarim basin,
produces an asymmetric topography distribution that is more consistent with the observed Tibetan Plateau.
[6] While the amount and general distribution of crustal thickening can be reconciled with the predicted crustal shortening from the
collision, the shape of the Himalaya and Tibetan Plateau (Figure 1)
is not well predicted by the thin viscous sheet models. Attempts to
produce this asymmetry include consideration of the Tarim basin as
a stronger region [England and Houseman, 1985; Houseman and
England, 1996; Neil and Houseman, 1997] and the use of a
lithostatic boundary condition on the eastern boundary of Eurasia,
to allow the extrusion of Eurasia to the east, and oblique convergence between India and Eurasia [Houseman and England, 1993,
1996]. The results, based on constant velocity (magnitude and
angle) across the convergent boundary, produce topographic asymmetry opposite in sense of the observed topography (Figure 1).
[7] Houseman and England [1996] investigated the collision
boundary between India and Eurasia showing that for normal
convergence, use of a lithostatic eastern boundary for Eurasia
produces the correct sense of asymmetry in the calculated topographic (crustal thickness) distribution. Adding a stronger Tarim
basin further enhances the topographic asymmetry; however, by
adding an oblique but constant convergence boundary condition
(Figure 2c), the topographic asymmetry decreases. The model that
best matches the observed topographic (crustal thickness) distribution includes a lithostatic eastern Eurasia boundary, a strong
Tarim basin, and constant oblique convergence.
[8] Our study differs from previous work in that we use an
oblique and variable velocity boundary condition along the length
of the indenter. This boundary condition not only has a velocity
that is oblique to the boundary, but the obliquity angle and
magnitude of the velocity boundary condition vary along the
length of the boundary (Figure 2d). The variable velocity and
angle of obliquity used in this study are obtained from the Le
Pichon et al. [1992] review of motion of India since collision with
Eurasia.
Figure 2. (a) Boundary conditions and mesh size used in this
study. These remain unchanged for all the models. (b) Boundary
condition for the case of normal convergence. (c) Boundary
condition for convergence with laterally constant velocity (including both magnitude and angle). (d) Boundary condition for
convergence with laterally varying velocity (including both
magnitude and angle).
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SOOFI AND KING: OBLIQUE CONVERGENCE
Table 1. Parameters in the Calculation of Elevation
Parameter
Value
hw
hb
L
rw
rb
rc
rm
2.5 km
5.0 km
100 km
1.03 Mg/m3
2.8 Mg/m3
2.8 Mg/m3
3.33 Mg/m3
Table 3. Normalized Linear Velocity Components Along Line AB
in Figure 1
Latitude, Longitude,
deg
deg
35
33
30
28
28
28
[9] Our objective is to understand how much of the asymmetry
in the topography along the India-Eurasia collision boundary is due
to the oblique convergence. Our numerical investigation indicates
that variable velocity (both magnitude and angle) produces the
correct sense of asymmetry in the calculated topography. This is
then enhanced by inclusion of the Tarim basin as a stronger zone.
2. Model
[10] The assumptions in the thin viscous sheet (TVS) model
have been discussed by England and McKenzie [1982], Houseman
and England [1986], and Houseman and England [1996]. In the
TVS approximation the lithosphere is treated as a continuous
medium (i.e., role of faulting in lithospheric deformation is
neglected) overlying an inviscid fluid (i.e., the asthenosphere is
much weaker than the lithosphere). This implies that the top and
bottom surfaces of the lithosphere are traction free. Further, the
TVS approximation assumes that the lithosphere is isotropic and
incompressible and that gradients of crustal thickness are small, so
that horizontal gradients of vertical stresses can be neglected. We
further assume that the lithosphere deforms by power law creep
with no rheological layering and the crust always maintains Airy
isostatic equilibrium.
[11] We use the finite element program Basil [Houseman and
England, 1986] which is capable of performing both plane stress
(i.e., the thin viscous sheet formulation discussed above) and plane
strain analyses. The program calculates velocity and stress distributions, crustal thicknesses, strain rates, and rotation.
[12] In the TVS model, lithospheric deformation is a function of
two parameters, the Argand number, a ratio of the buoyancy force
to the plate boundary force, given by
Ar ¼
gLrc 1 rrc
m
1=n ;
B ULo
ð1Þ
and n, the exponent in the stress-strain relationship, comes from
1
tij ¼ BE_ ðn1Þ e_ ij ;
ð2Þ
where g is gravity, L is the thickness of the lithosphere, rc is the
crustal density, rm is the mantle density, Uo is the imposed collision
velocity, B is the vertical average of compositional and thermal
influences on the lithospheric rheology, t
ij and e_ ij are the vertically
averaged components of the deviatoric stress and strain rate tensor,
Table 2. Rotation Poles for Postcollision India-Eurasia Relative
Motion
Rotation Pole
3-3
Age,
Ma
North
East
Angular Velocity
w, deg/Myr
0–7
7 – 20.5
20.5 – 49
24.4
16.7
14.4
17.7
38.9
35.0
0.528
0.74
0.69
a
73
77
80
86
92
96
Normal
Tangential Obliquity From PerComponent Component pendicular to Line AB,
deg + cwa
0.62
0.69
0.75
0.85
0.92
0.97
0.42
0.38
0.33
0.29
0.27
0.25
34.1
28.9
23.9
19.0
16.4
14.7
Positive angles clockwise.
respectively, and E_ is the second invariant of the strain rate tensor.
The strength of the lithosphere varies inversely with the Argand
number. As the Argand number increases, the lithosphere is less
able to support topographic loads and topography relaxes more
quickly. An increase in n allows a more rapid decrease in the
effective viscosity with increasing strain rate.
[13] The effect of n and Ar on the style of lithospheric
deformation has been investigated by England and McKenzie
[1982] and Houseman and England [1986]. As Ar increases, the
length scale of deformation increases, and the crustal thickness
decreases because of the decreased ability of the lithosphere to
support topography; however, Ar has little influence on the length
scale of deformation in a transcurrent environment [Sonder et al.,
1986]. From equation (1), as n increases Ar increases if all other
parameters are fixed. From collision studies [e.g., Houseman and
England, 1986; Sobouti and Arkani-Hamed, 1996] it has been
shown that 3 n 5 and 1 Ar 3 are reasonable values for
studying lithospheric deformation.
[14] To obtain the topography from our results, we assume
isostatic equilibrium between a column of continental lithosphere
and a reference column at the mid-ocean ridge. The elevation (e)
(i.e., topography) of the continental crust is then given by [England
and Houseman, 1986]
e¼S
rm
r
r
r
r
1 c þ L 1 m hw 1 w hb 1 b ;
ra
rm
ra
ra
ra
ð3Þ
where hw is depth of ocean at the mid-ocean ridge, hb is thickness
of the oceanic crust, L is thickness of the lithosphere, S is thickness
of the continental crust, rm is density of the mantle, rb is density of
the oceanic crust, ra is density of the asthenosphere, rc is density of
the continental crust, and rw is the density of water. We assume
35 km as the precollision thickness of the Eurasian crust. The top
surface of the crust is assumed to be at sea level, and the elevation
corresponding to a given crustal thickness is then calculated from
equation (3) using the values in Table 1.
[15] For the relative motion of India with Eurasia we use three
different rotation poles from three different time periods (Table 2).
For each rotation pole the linear velocity is calculated at six
different locations. The velocities obtained for each time period
are then averaged over time, normalized and resolved into normal
and tangential components with respect to the straight line drawn
between the points 35 latitude, 73 longitude and 28 latitude, 96
longitude (i.e., points A and B, respectively, on Figure 1). These
components are listed in Table 3. A least squares fit is then made to
the normalized velocity components to determine the variation in
the normal and tangential components of the linear velocities. The
correlation coefficients for these fits are 0.99 and 0.96, respectively. This velocity profile is then use as the boundary condition in
the finite element model.
[16] The finite element models are run for the total convergence
of 2000 km corresponding to 40 Myr of convergence at a rate of
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SOOFI AND KING: OBLIQUE CONVERGENCE
Constant Velocity
Normal
Variable Velocity
3
3
3
1
1
1
(a)
(b)
(c)
Figure 3. Calculated topography, in kilometers, for (a) normal
convergence (b) constant oblique convergence, and (c) variable
oblique convergence. The mesh and boundary conditions used are
as given in Figure 2. The stress-strain exponent (n) is 3, and the
Argand number (Ar) is 1. See text for the definition of n and Ar.
50 km/Myr. The horizontal dimension of the model, D, is 5000 km
(Figure 2d), and 16 40 elements are used. The boundary
conditions for (1) variable velocity (including both magnitude
and velocity), (2) constant velocity (including both magnitude
and velocity) and (3) normal (nonoblique) convergence are shown
in Figure 2. The indentation velocity is tapered on both the sides by
a cos2 function. In the initial experiments the velocity boundary
conditions do not vary as a function of time. Experiments with
time-varying velocity boundary conditions produce topographic
distributions that are qualitatively similar to those shown below.
3. Results
[17] The contours of topography for a model with normal
convergence and Ar = 3 and n = 1 are shown in Figure 3a. As
Constant Velocity
Variable Velocity
x
x
y
y
RL
RL
(a)
Figure 5. Calculated asymmetry indices for the case of constant
but oblique velocity corresponding to the boundary condition
shown in Figure 3b. The asymmetry indices are shown
corresponding to (a) 4-km and (b) 2-km topographic contours.
(b)
Figure 4. Profile coverage and location of the reference line used
to determine the asymmetry index. All calculation use n = 3 and
Ar = 1. (a) Constant velocity (both magnitude and angle) and (b)
variable velocity (both magnitude and angle). Profiles are drawn to
cover the 2-km topographic contour.
expected, the deformation and resulting topography are symmetric
about a line through the center of indentation. As the goal of this
work is to explore the effect of oblique convergence on the
asymmetry of topography along the India-Eurasia collision boundary, the normal convergence will not be discussed further. The
resulting topography from calculations with a constant velocity
(Figure 3b) and a variable velocity (Figure 3c) with the same
parameters is shown for comparison.
[18] To compare the results of the constant velocity boundary
condition (i.e., Figure 3b) with the variable velocity boundary
condition (i.e., Figure 3c), we define a parameter which we call the
asymmetry index (AI). The asymmetry index is defined as the
volume of a profile on one side of the reference line (RL) that
equals or exceeds a minimum topography minus the volume of the
profile on the other side of the reference line (RL) that equals or
exceeds the same minimum topography. In both the calculations
and the data we use 2-km elevation as the minimum topography. In
Figure 4 we choose our coordinate systems such that x is parallel to
RL and y is perpendicular to RL with y = 0 at RL. Thus a positive
asymmetry index indicates a greater volume above 2-km elevation
on the positive y side of RL than on the negative y side of RL. The
asymmetry index is negative for the opposite distribution of topography about RL. The orientation of RL is obtained geometrically
by calculating a line perpendicular to the endpoints of the boundary
condition, and the location of RL along the boundary is chosen so
SOOFI AND KING: OBLIQUE CONVERGENCE
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3-5
as the cutoff for the asymmetry index, this case is nearly symmetric
for all distances from the indenter. With the 4-km cutoff the
asymmetry index profiles quantify what is apparent visually in
the crustal thickness contour plot (Figure 3b), the region of high
elevation is skewed to the left (west) of the center of the indenter.
In addition, the profile shows that the skewed topography extends
700 km perpendicular from the indenter.
[20] For the case of variable velocity (Figure 3c) the calculated
asymmetry index profiles are shown in Figure 6. In this model the
higher elevations are skewed to the right (east) of the reference line
in contrast to the previous model. The extent of the anomalous
topography is 700 km from the indenter, identical to the previous
model. When considering the elevation within the 2-km contour,
there is a transition between right (east) skewed and left (west)
skewed topography at 400 km; however, the degree of asymmetry is smaller.
[21] The relatively small difference in the boundary conditions,
between a variable oblique indenter and a uniform oblique indenter
where the angle of obliquity is the average value of the variable
case, has a pronounced effect on the distribution of topography
within the 4-km elevation contour. The asymmetry profile of the
uniform oblique boundary condition is opposite to the distribution
observed with the variable oblique boundary condition.
[22] To decide whether either of the models discussed above
better explain the asymmetry observed in the topography along the
Figure 6. Calculated asymmetry indices for the case of variable
oblique velocity corresponding to the boundary condition shown in
Figure 3c. The asymmetry indices are shown corresponding to (a)
4-km and (b) 2-km topographic contours.
that there is an equal volume of anomalous topography on either
side of the line. The asymmetry index can be written mathematically as
Z
Z
yp
AIð yÞ ¼
RL
topoðx; yÞ dx RL
topoðx; yÞ dx;
ð4Þ
yn
where RL is the reference line (in this case, y = 0), yn is the
coordinate where the profile crosses the 2-km contour in the
negative y direction, and yp is the coordinate where the profile
crosses the 2-km contour in the positive y direction. To obtain the
asymmetry index, uniformly spaced, parallel profiles with a
horizontal spacing of 0.02D, or 100 km in the x direction, are
drawn across the region enclosed by the 2-km contour line
(Figure 4). The integral in equation (4) is divided by a
characteristic volume, which is one half the length of the indenter
times the space between the profiles (100 km) times 4 km
elevation. With this scaling, the asymmetry index ranges between
±1. For the case where the topography on the positive y side of
RL was 4 and 0 km on the negative y side of RL, the asymmetry
index would be 1.
[19] The asymmetry index obtained for the constant velocity
boundary condition (Figure 3b) is shown in Figure 5. The first
observation that can be made is that when using the 2-km contour
Figure 7. Calculated asymmetry indices for the topography along
the India-Eurasia collision boundary using the ETOPO5 data set.
(a) Asymmetry indices for the topography 4 km. (b) Asymmetry
indices for the topography 2 km.
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SOOFI AND KING: OBLIQUE CONVERGENCE
the magnitude of the asymmetry index for the 2-km contour.
Comparing the asymmetry index profiles for the observed IndiaAsia topography (Figure 7) and the strong Tarim basin model
(Figure 8), the 2-km profiles have the same transition from leftskewed (west) to right-skewed (east) and back to left-skewed (west)
asymmetry. This is most clear in the 2-km profile of the model. The
4-km profile from the model is not as clear; however, 4-km
elevation is close to the maximum elevation attained anywhere in
the model. In the 2-km profile of the model the transition between
left-skewed (west) and right-skewed (east) topography occurs
closer to the indenter than in the observed topography.
4. Discussion
Figure 8. Calculated asymmetry indices for the model with an
embedded anomalous zone 10 times stronger than the surrounding
material. The surrounding material has the rheology n = 3 and Ar = 1.
(a) Asymmetry indices for the topography 4 km. (b) Asymmetry
indices for the topography 2 km.
India-Eurasia collision boundary, we also calculate the asymmetry
index for the observed topography using the ETOPO5 data set
regridded to 15 min. The distribution of the asymmetry indices for
the 4-km and 2-km contours is shown in Figure 7. In the IndiaAsia topography, there are two obvious feature that are not
reproduced by either model. First, there is a shift in both the
2-km and 4-km profiles from left (west) skewed to right (east
skewed) asymmetry. This occurs at 500 km from the indenter in
both cases. Second, the topography extended to distances >1500
km from the indenter.
[23] Because the asymmetry indices obtained from our variable
oblique boundary condition model (Figure 3c) are still not consistent with the topographic data, we investigate the effect of a stronger
anomalous zone such as the Tarim basin [England and Houseman,
1985] on the development of the asymmetric topography. We use
the same rheology for this case (i.e., n = 3, Ar = 1) as before. The
anomalous zone is considered to be 10 times stronger than the
surrounding material, and the boundary condition is identical to that
used for Figure 3c (i.e., variable velocity). The calculated topographic asymmetry indices for the 4-km and 2-km contours are
shown in Figure 8.
[24] One noticeable difference between the topographic asymmetry obtained from the model with a strong Tarim basin (Figure 8)
and that without an anomalous zone (Figure 6) is the difference in
[25] In our study of the collision of India with Eurasia the
convergence rate and the obliquity angle remain constant for the
whole period of convergence. Our boundary condition represents
the average of the convergence rate and obliquity angle for the
period of convergence from 0 to 45 Ma. This average is obtained
from the kinematic history of India-Eurasia collision summarized
by Le Pichon et al. [1992]. According to Le Pichon et al. [1992],
convergence velocity between India and Eurasia since 49 Ma falls
in the range 40 – 60 km/Myr, and our convergence velocities vary
from 46 to 61 km/Myr, consistent with this range. Also, in this study
the obliquity angle (measured from the perpendicular to the line
between points A and B in Figure 1) varies from 14.7 in the east
(location B, Figure 1) to 32.8 in the west (location A, Figure 1).
This distribution follows the same trend as that reported by Le
Pichon et al. [1992] (i.e., 20 in the east and 30 in the west);
however, according to them the obliquity angle has decreased
considerably due to 20 clockwise rotation of the motion vectors
at 7 Ma.
[26] In our estimation of the linear velocities, geographical
location of the boundary between India and Eurasia remains
unchanged over the last 45 Myr. We have only considered the
change in the location of the pole of rotation, as indicated by Le
Pichon et al. [1992]. In the real world the geographical location of
a plate boundary changes continuously. Thus our approach in
estimating the average linear velocities along the India-Eurasia
collision boundary over the last 49 Myr is a simplification of the
collisional history along this boundary. Still, this approach represents an improvement over the constant oblique velocities or
normal velocities that have been used in previous studies.
[27] In the case of constant velocity (Figure 6) the topography
has negative asymmetry indices, whereas topography along the
India-Eurasia collision boundary has positive asymmetry indices
near the indenter. This has led investigators to consider a lithostatic
eastern boundary condition. For the case of variable velocity,
however, the asymmetry indices near the indenter (Figure 7) are
consistent with the observed topography.
[28] The reason for the pronounced difference in the topographic distribution with boundary conditions can be explained
by looking at the normal and tangential components of the velocity
vector with respect to the boundary. When a constant obliquity and
velocity are applied across the collision boundary, the normal and
tangential components of velocity remain constant across the
boundary. The normal component of velocity remains constant
along the boundary, and it does not contribute to the asymmetric
distribution of deformation along the collision boundary (as in
Figure 4a). Thus the asymmetry is due entirely to the tangential
component of velocity. Along the India-Eurasia collision boundary,
where the average obliquity is 22 counterclockwise from the
normal to the boundary (Table 3), the tangential component of
the velocity remains constant, directed from east to west. This is
the applied boundary condition in Figure 3b. More deforming
material is piled to the west than to the east, producing an
asymmetric distribution of topography that is opposite to the
observed topography near the indenter.
SOOFI AND KING: OBLIQUE CONVERGENCE
[29] In the variable velocity boundary condition case the convergence velocity decreases from east to west, while the obliquity
increases is the same direction. This produces normal component
of convergence that decreases from east to west, resulting in a
greater accumulation of deforming material to the east than to the
west. The asymmetry so obtained is consistent with the observed
topography. The decreasing linear velocity from east to west makes
the tangential component of velocity less effective in producing the
asymmetry.
[30] A comparison of Figures 5 and 6 indicates that use of
variable velocity produces the correct sense of asymmetry in the
topography near the indenter; however, through boundary conditions alone, we are not able to produce the transition in asymmetry
observed in the actual topography. There is a pronounced transition
in the skewness of the topographic asymmetry in the IndiaEurasian collision (Figure 7) that we have been unable to reproduce with changes along the collisional boundary alone. The model
that most closely resembles the observation has a mechanically
strong zone representing the Tarim basin (Figure 8). This is
consistent with the findings of England and Houseman [1985]
and Houseman and England [1996].
[31] We did not find any improvement in the topography by
considering the boundary between Eurasia and Pacific plates as a
lithostatic boundary. In addition, we do not incorporate the effect of
lateral movement along the strike-slip faults present near and
farther north of the India-Eurasia collision boundary. The presence
of right-lateral strike-slip faults north of this collision boundary
could also contribute to the asymmetry in the observed topography
of southern Eurasia. Peltzer and Tapponnier [1988] have used
Landsat images and geological maps to decipher the geological
history of eastern Eurasia. They suggested that right-lateral movement on the order of 1000 km along the Karakorum-Zangbo strikeslip fault moved central Tibet to the east with respect to India. If
true, such movement would give rise to significant asymmetry in
the topographic distribution.
[32] There are several other assumptions in the thin viscous
sheet model that could be important in the India-Asia collision
problem. First, in our formulation the indenter (India) does not
deform. This seems justified by the observation that the anomalous
topography associated with the collision boundary is primarily on
the Eurasian plate. Second, we have not included any effect from
the underthrusting plate. It is possible that shear traction from the
underthrusting Indian plate is responsible for deformation north of
the collision boundary. Especially if the underthrusting part of the
Indian plate is continental crust which should be strongly coupled
to the Eurasian plate because of its relative buoyancy. Finally, the
thin viscous sheet approximation assumes a simple relation
between topography and crustal thickness (equation (3)). If lithospheric thinning has occurred in part of the region [England and
Houseman, 1989; Neil and Houseman, 1997], then the relationship
between topography and crustal thickness is not as simple as we
have assumed.
5. Conclusions
[33] In this study we have investigated the factors responsible
for the topographic asymmetry along the collision boundary
between India and Eurasia. In the process, we have developed a
technique to quantify the asymmetry present in the topographic
data set and in the results of our models. The technique is
applicable to a digital data set once the orientation of the reference
line is defined. The estimated parameter, which we call the
asymmetry index (AI), is positive when more area with topography
equal or greater than a specified topography is to the east (right) of
the reference line and is negative when more area with such
topography is to the west (left) of the reference line. The technique
enables us to quantify the asymmetry in the topography as a
function of distance from the collision boundary.
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3-7
[34] In this study we observe that the laterally varying
obliquity angle and convergence rate between India and Eurasia
are responsible for some of the asymmetry in the topography
along this collision boundary. This boundary condition more
realistically captures the tectonic history along the India-Asia
collision boundary, although it is insufficient to explain the
asymmetric distribution of elevation with respect to the collisional
boundary. The topographic asymmetry is significantly enhanced
when a heterogeneous block (i.e., Tarim basin) is considered
reinforcing the conclusion that the presence of nonhomogeneous
blocks (e.g., Tarim and Qaidam basins) is most likely responsible
for the majority of the asymmetry in the India-Eurasia collision
zone.
[35] Acknowledgments. We wish to thank G. A. Houseman, L. J.
Sonder, and an anonymous reviewer for constructive comments on this and
an earlier version of this manuscript. M. Soofi was supported by a David
Ross Fellowship at Purdue University.
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S. D. King and M. A. Soofi, Department of Earth and Atmospheric
Sciences, 1397 CIVL, Purdue University, West Lafayette, IN 47907-1397,
USA. ([email protected]; [email protected])