Download Constraining the extent of crust–mantle coupling in central Asia

Earth and Planetary Science Letters 238 (2005) 248 – 268
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Constraining the extent of crust–mantle coupling in central Asia
using GPS, geologic, and shear wave splitting data
Lucy M. Flesch a,*, William E. Holt b, Paul G. Silver a, Melissa Stephenson a,c,
Chun-Yong Wang d, Winston W. Chan e
a
Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241 Broad Branch Road, N.W.,
Washington DC 20015, United States
b
Department of Geosciences, State University of New York at Stony Brook, Stony Brook, NY 11794-2100, United States
c
Department of Earth and Atmospheric Sciences, Snee Hall, Cornell University, Ithaca, New York 14853, United States
d
Institute of Geophysics, China Earthquakes Administration, Beijing 100081, PR China
e
Multimax Corporation, 1441 McCormick Drive, Largo, MD, 20774, United States
Received 16 August 2004; received in revised form 26 May 2005; accepted 6 June 2005
Available online 19 August 2005
Editor: R.D. van der Hilst
Abstract
We have obtained constraints on mechanical crust–mantle coupling for Tibet and Yunnan/Indo China, by comparing the
observed surface deformation field inferred from GPS and Quaternary fault slip rate data, with the mantle deformation field
inferred from several SKS shear wave splitting data sets. We first determined whether the anisotropy is dominantly asthenospheric or lithospheric by testing simple models of both types against the observed values of the fast polarization direction, /,
which is assumed to be parallel to the horizontal projection of the direction of maximum shear. For asthenospheric flow, we
solved for a best-fitting uniform sub-asthenospheric velocity model for Eurasia. The fit, however, was not satisfactory (RMS
misfit D/ = 208). Solving for separate uniform flow fields in each region improves the fit (D/ = 158 for Tibet, D/ = 118 for
Yunnan), although the resulting flow fields are inconsistent with several geophysical and geological constraints and thus
considered unlikely. We then considered lithospheric models. For Tibet, vertically coherent deformation (i.e., maximum shear
direction from surface deformation is parallel to /) yields an improved match (D/ = 118) for left-lateral shear. Both the
goodness of fit and the dominance of left-lateral surface faulting in Tibet, argue for a lithospheric source of anisotropy. The
misfit for Yunnan is large for either right- (D/ = 538) or left-lateral (D/ = 498) shear, which argues for complete crust–mantle
decoupling in Yunnan. We show that the fast polarization directions throughout both the Tibet and Yunnan region can be fit by a
single lithospheric dynamic model in which there is strong coupling between crust and mantle beneath Tibet, but a complete
decoupling between crust and mantle beneath Yunnan crust. This dynamic model predicts left-lateral maximum shear directions
within the mantle that align with fast polarization directions in both regions (D/ = 98). These maximum shear directions within
* Corresponding author.
E-mail addresses: [email protected] (L.M. Flesch), [email protected] (W.E. Holt), [email protected] (P.G. Silver),
[email protected] (M. Stephenson), [email protected] (C.-Y. Wang), [email protected] (W.W. Chan).
0012-821X/$ - see front matter D 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.epsl.2005.06.023
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
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the mantle align with the left-lateral maximum shear directions in the crustal deformation field in Tibet, but are not in Yunnan.
Our results have the following implications. First, the coherence between crust and mantle deformation in Tibet implies strong
crust–mantle mechanical coupling, since this is the only way that crustal buoyancy forces, required to account for the surface
deformation field, can be transmitted into the mantle. This behavior is consistent with a uniform-strength lithosphere or strong
crust, but not with a substantially weaker crust. For example, it is inconsistent with the popular bjelly-sandwichQ rheology, and
thus precludes behavior such as large-scale lower crustal flow in Tibet. The crust–mantle coherence is also incompatible with
mantle delamination. Second, crust–mantle decoupling within the Yunnan lithosphere argues that mantle deformation there is
controlled only by boundary conditions; crustal buoyancy forces are not transmitted into the mantle beneath Yunnan. Moreover,
the dynamic model for the mantle shows that the Yunnan crust is moving south with respect to the mantle at rates as high as ~30
mm/yr. Third, there is a fundamental rheological lithospheric transition between Tibet and Yunnan that may provide a key to
understanding this significant orogen.
D 2005 Elsevier B.V. All rights reserved.
Keywords: lithospheric coupling; Tibet and Yunnan; shear-wave splitting
1. Introduction
A fundamental rheological property of continents
that controls their style of deformation is the depth
dependence of lithospheric strength. Yet, this property
is poorly constrained, a point that is best illustrated by
the broad range of strength profiles, lithospheric behaviors, and boundary conditions adopted in modeling
continental deformation [1–15]. Laboratory measurements of both crustal and mantle minerals within both
the brittle and ductile regime have led to an almost
universally accepted bjelly-sandwichQ strength profile
for continental lithosphere (see Molnar and LyonCaen [16]). This model consists of an upper crust,
controlled by Byerlee friction, a weak ductile middle
crust, and possibly lower crust, predicted by the behavior of quartz rheology at high temperatures, and a
strong upper mantle, predicted by laboratory experiments with olivine [17–20]. Despite the popularity of
the bjelly-sandwichQ strength profile, the inferred
behavior of continental lithosphere appears to be
widely variable and can be thought of as having two
end-members. In the first case the crust and upper
mantle lithosphere are kinematically coupled and
deform as a coherent unit [1–3]. Under these assumptions large regions have been modeled by solving the
vertically averaged force balance equations using a
vertically averaged rheology [21,22]. In these models
the vertical coherence is attributed to the fact that
upper mantle dry olivine rheology dominates the
strength profile for continental lithosphere [23].
Hence the seismogenic crust responds passively to
the motions occurring within the upper-most mantle
[24]. A strength minimum in the middle and lower
crust leads to the other end-member deformation
mode, which involves a complete decoupling between
the seismogenic crust and upper mantle and in many
cases it involves lower crustal flow [10,25,26].
Recently, Maggi et al. [27] have proposed that the
upper mantle beneath continents is aseismic and is
weak relative the seismogenic crust. This model is at
odds with the bjelly-sandwichQ model and suggests
that the strength of the continental lithosphere resides
within the seismogenic portion of the crust [28]. On
the other hand, Chen and Yang [29] have observed
mantle earthquakes beneath Tibet, providing support
for a seismogenic, and potentially strong, upper mantle lithosphere there.
The rheologies discussed above control how the
lithosphere responds to the applied driving forces.
Whereas the forces induced by a collisional boundary
force are expected to be applied throughout the depth
extent of the lithosphere, and therefore produce vertically coherent deformation for either rheology, the
response to body forces associated with density variations is a function of whether or not there is mechanical coupling between the crust and upper mantle. For
example, if topography is primarily compensated via
the Airy mechanism, then body forces associated with
lateral variations in topography are contained within
the crustal layer, and will either be transmitted
through the entire lithosphere (mechanically coupled)
or only through the crust (decoupled). If there is
coupling between crust and upper mantle and the
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crust is at least as strong as the upper mantle, then the
mantle deformation field will respond passively to the
dynamics that control crustal motions. On the other
hand, if the upper mantle is strong relative to the
seismogenic crust, and there is lithospheric coupling,
then body and boundary forces applied to the mantle
portion of the lithosphere will have a dominant control
and signature on the surface deformation field.
The key to discriminating between the different
rheological profiles is the quantitative measurement
of both the surface kinematics and mantle kinematics,
and quantitative modeling of crust and mantle dynamics in response large-scale body forces and collision
boundary conditions. The kinematics of crust and mantle can be inferred from analysis of two data sets: the
observed surface deformation field inferred from geodesy, seismicity, and Quaternary fault slip rates (e.g.,
[30–32]), and observed mantle deformation inferred
from mantle anisotropy (e.g., [33–38]).
In this study we investigate the relationship
between mantle deformation inferred from shear
wave splitting measurements in Tibet, and within
the Yunnan Province/Indo China region (referred to
herein as Yunnan), which lies to the southeast of
Tibet, and the continuous surface deformation field
determined from GPS data and Quaternary fault slip
rate data. We utilize a three-step process. First, we
quantify the surface deformation field, using all available data to date. Second, we dynamically model the
crustal and mantle deformation fields considering the
two primary sources of stress: collisional boundary
forces and the topographically induced body forces.
Third, we compare these modeled deformation fields
to the mantle field inferred from SKS shear wavesplitting measurements, and use any similarities or
differences to ascertain the extent to which the crust
and mantle are affected by the same forces.
As we will show, we observe a distinct change in
the rheology between Tibet and Yunnan. In the case of
Tibet, the coherence of the crustal and mantle deformation fields shows that both sources of stress, topographically induced stresses and collisional boundary
conditions, are transmitted throughout the depth range
of the lithosphere. In particular the transmission of
topographically induced body forces argues for a
mechanically coupled lithosphere. In contrast, in Yunnan, while both the crust and mantle appear to respond
to the collisional boundary conditions, the stresses
associated with body forces are limited to the crust,
thus arguing for an effective decoupling between the
crust and mantle in Yunnan. The strong contrast in
vertical rheological profiles between these two regions
argues for a fundamental rheological boundary at the
edge of the Tibetan Plateau.
2. Quantification and modeling of the surface
deformation field in Asia
Deformation in central Asia is unique in that it
encompasses the largest zone of diffuse continental
deformation on the surface of the Earth [16,39,40]. It
exhibits the Earth’s highest topography, with the Tibetan Plateau possessing an average elevation of 5 km,
and an average crustal thickness of 65–70 km. In
addition, this region exhibits a variety of deformational styles. There is a fanning of compression
around the Tibetan Plateau, with orientations of principal axes of compression parallel to the topographic
gradient [3], and roughly N–S compression in the
Tien Shan. There is also E–W extension occurring
in southern Tibet [41–44] with principal axes of
extension that rotate around to N–S extension east
of the eastern syntaxis and back again to E–W extension in Yunnan, China [45]. The extension in Yunnan
is accommodated by a series of NE–SW striking leftlateral strike slip faults, NW–SE striking right-lateral
faults, as well as N–S striking grabens [45]. These
faults are bounded by the Sagaing fault to the west
that is a N–S trending right-lateral strike slip fault
[46]. In addition, there has been past subduction of
the Burma plate beneath the Yunnan/Indo China
region [47]. With the advent of space-based geodetic
measurements, the understanding of how strain is
accommodated across this broad zone of deformation
has increased dramatically [30–32]. This new constraint on the surface deformation field in Asia,
together with information on mantle anisotropy, provides an excellent opportunity to investigate the vertical dependence of lithospheric deformation and its
relation to rheology. The surface deformation field
likely represents deformation down to a depth of at
least 15 km and is thus a good proxy for deformation
of the upper crust.
To determine a continuous surface strain rate and
velocity field, we follow the method of Haines and
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
Holt [48], which uses estimates of strain rates from
Quaternary fault slip rate data (both rate and style) and
GPS measurements, to invert for a continuous velocity
and strain rate field [31]. The kinematic model is
treated using a rotation vector function x(x̂),
expressed as bi-cubic interpolation [49] on a curvilinear grid (Fig. 1) [50] that describes the horizontal
components of a continuous velocity field u(x̂)
uðx̂
x Þ ¼ rxðx̂
x Þ x̂
x
ð1Þ
where r is the radius of the Earth, and x̂ is the
position of the unit radial vector on the Earth’s surface. We assign the spatial derivatives of the rotation
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vector function x(x̂) to zero on what we define as
the Indian and Eurasian plates to provide the constraint of rigidity for those plates. Even though we
are modeling the horizontal components of the strain
rate and velocity field, this modeling allows for
thickening and thinning of the lithosphere (i.e.,
ė xx + ė yy = ė zz) (see Holt et al. [31] for details).
We use Quaternary fault slip rates [30–31], and
geodetic data [32,51–63], to determine a continuous
self-consistent strain rate and velocity field model
(Fig. 2). The Kostrov [64] moment rate tensor summation is used to determine strain rate estimates from
Quaternary fault slip rate estimates. The calculated
kinematic strain rate and velocity fields are similar to
Fig. 1. The SKS shear wave splitting measurements used in this study; data in Tibet are from McNamara et al. [37]; Hirn et al. [34]; Guilbert et
al. [33]; Sandoval et al. [38] (blue bars) and Huang et al. [36] (green bars). Data in Yunnan (yellow bars) are from this study, yellow stars
indicate the location of 9 seismometers installed, and blue stars the two permanent stations. Also shown is the curvilinear grid used in the
modeling (red region), which is defined by the geologic structures. Light blue lines represent Quaternary faults [30] used in the kinematic
modeling. Black outlines delineate lithospheric blocks used in the mantle deformation forward models (TB=Tarim Block, G=Gobi Block,
O=Ordos Block, S.C.=South China Block, S=Sunda Block). The solid black line over the Indian plate denotes the boundary of what we model
as the rigid Indian plate and the solid black line over the western and northern sections of the grid denotes the rigid Eurasian reference frame.
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Fig. 2. The continuous velocity field (black vectors) determined from the joint inversion of GPS data (white vectors) [32,51–59,61–63] and
Quaternary fault slip rate data [30,31] plotted relative to a Eurasian reference frame fixed. The ten spatially averaged SKS splitting
measurements are plotted as blue bars. There is no GPS information surrounding the most northern point on the Huang et al. [36] line.
that determined by Holt et al. [31], and yield a
reduced chi squared of ~1.2 indicating a good fit
to the GPS data.
3. Quantification and modeling of the dynamics of
lithosphere in Asia
Flesch et al. [12] have shown that this surface
deformation field in central Asia can be successfully
modeled by a relatively simple dynamic model that
consists of roughly equal contributions from two
driving forces: those associated with a collisional
boundary condition resulting from relative plate
motions, and those associated with gravitational
potential energy (GPE) produced by the high topography of the Tibetan plateau. An important result
from this dynamic modeling is that stress field
boundary conditions and GPE variations produce
distinctly different stress fields. The stress boundary
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condition is consistent with a spatially uniform
mostly N–S directed compressive stress associated
with India’s convergence with Asia. However, deviatoric stresses associated with GPE variations are
responsible for the spatial variation in principal
axes of deviatoric stress and strain around the Tibe-
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tan Plateau — compression parallel to topographic
gradients in lowlands, roughly E–W extension
throughout much of Tibetan plateau, N–S extension
in southeastern Tibetan plateau, E–W extension in
Yunnan province, and a strike slip style of deformation at intermediate elevations throughout the region.
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Hotspot Reference Frame
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Fig. 3. A) The SKS splitting measurements (black bars), the continuous velocity field (Fig. 2) plotted in a hotspot reference frame (white bars),
and the velocity field plotted at the SKS splitting measurements (white bars with black outline). There is no correlation between the splitting
measurements and the velocity field in the hotspot reference frame. D/ a = 588. B) The same as (A) only with the Eurasian velocity plotted in the
no-net-rotation reference frame. D/ a = 208. C) The best-fit rotation (65.8, 104.1, 0.388/my) for the sub-asthenosphere (white vectors) and the
surface velocity (black vectors) determined from GPS measurements and Quaternary fault slip rates, plotted relative to a fixed Eurasian
reference frame. The difference in these two vectors (grey bars) should be parallel to the observed SKS splitting measurements (black bars) if a
simple asthenospheric flow hypothesis is the origin of the anisotropy. D/ a = 188.
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NNR Reference Frame
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Fig. 3 (continued).
Therefore GPE variations are responsible for the
curvature of active left-lateral faults around the Tibetan Plateau (e.g., Kun Lun Fault, Xianshuihe Fault)
and for the dramatic curvature of surface velocity
observed around the eastern Himalayan syntaxis into
Yunnan (Fig. 2). If, to first order, the topography
beneath Tibet is supported by crustal thickness variations (e.g., [65]) then the bulk of the horizontal
density variations (GPE variations) responsible for
the spatial variation of the surface deformation field
described above are embedded within the crust, not
the mantle [16].
4. Shear wave splitting measurements in Asia:
analysis and interpretation
Since anisotropy is related to the finite strain tensor
[66], with the a-axes of polycrystalline olivine aggregates tending to align parallel to the direction of
maximum shear for strain greater than 75% and the
maximum extension direction of finite strain for strain
less than 75% [67], mantle anisotropy provides a
means of constraining the orientation of the mantle
deformation field. An extensively utilized manifestation of mantle anisotropy is shear wave splitting as
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Athenosphere
surface
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30 mm/yr
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Fig. 3 (continued).
measured from near-vertically propagating shear
waves such as the phase SKS. In this geometry, the
fast polarization direction, /, is parallel to the direction of maximum shear ([68] and references therein).
The question we seek to ask from the splitting observations is the extent to which the surface deformation,
and by implication the forces that produce this deformation, extend into the mantle.
Silver [68] argued for vertically coherent deformation beneath Tibet based on the observation that the
SKS shear wave splitting measurements correlated
with the orientation of surface faults (i.e., vertical
shear planes). Davis et al. [69] used thin viscous
sheet methodology to model deformation within central Asia, and found that for Tibet, the direction of
maximum extension was within 308 of the fast polarization direction predicted from the SKS splitting
measurements. They used this to argue for vertically
coherent lithospheric deformation. Assuming that
dynamic recrystalization plays a role in the development of the mantle anisotropy (in which case the aaxis of olivine would follow the direction of maximum shear [67]), Holt [70] found that the direction of
maximum left-lateral shear in the horizontal velocity
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field of Tibet, determined from Quaternary fault slip
rate data and somewhat limited GPS data, was
remarkably close to the fast polarization directions
from the shear wave splitting results, producing an
RMS variation of 108–158 (1r). This correlation suggested that planes of finite left-lateral shear in the
mantle beneath Tibet are oriented parallel to the active
planes of finite shear (faults) within the crust. Holt
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[70] concluded that this correlated deformation
between crust and upper mantle was the result of
these two levels of the lithosphere being subject to
the same collisional boundary conditions.
We make use of six shear wave splitting data sets
for this study. For Tibet we use previously published
SKS shear wave splitting data from McNamara et al.
[37]; Hirn et al. [34]; Guilbert et al. [33]; Sandoval et
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Surface Deformation Field
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Fig. 4. The continuous surface deformation field associated with the velocity field shown in Fig. 2, plotted as the left-lateral maximum shear
direction of deformation (white bars). Also plotted are the right-lateral (grey bars) and left-lateral (white bars black outline) maximum shear
directions at the SKS splitting measurements (black bars). There is a correlation between the SKS splitting measurements and the left-lateral
maximum shear directions in Tibet (D/ s = 118) and no correlation with the left-lateral maximum shear directions in Yunnan (D/ s = 498). There is
no correlation between the right-lateral maximum shear directions in either region and the SKS splitting measurements in either region
(D/ s = 778, Tibet; D/ s = 538, Yunnan).
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
al. [38]; and Huang et al. [36] (Fig. 1). We spatially
average the 57 splitting measurements (Fig. 1) for
Tibet into 9 regional measurements (Figs. 3–8) so as
to give equal weight in our models to each area in
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Tibet. We only choose regions where there is both
well-constrained surface deformation and splitting
data. There are several GPS measurements (Fig. 2)
along the McNamara et al. [37]; Hirn et al. [34];
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Modeled Mantle Deformation Field
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Fig. 5. The left-lateral maximum shear directions (white bars) of the continuous modeled mantle deformation field resulting from rigid body
rotations of the Indian plate, the Tarim Basin, Ordos Block, the Gobi platform, the south China block, and the Sunda block relative to a stable
Eurasia and assuming uniform viscosity for upper mantle lithosphere. We assume that the leading edge of the Indian plate is located in southern
Tibet. We assume that these blocks are rigid throughout the lithosphere. Therefore with knowledge of the angular velocities of the blocks at the
surface from GPS measurements, the angular velocities of the mantle portion of these blocks are also known. Also plotted are the left-lateral
(white bars black outline) and right-lateral (grey bars) maximum shear directions of the modeled mantle deformation field at the SKS splitting
sites, along with the SKS splitting measurements (black bars). We observe correlation between the modeled deformation field and the left-lateral
maximum shear direction in Yunnan (D/ m = 88), but the fit to the left-lateral maximum shear directions in Tibet (D/ m = 218) is degraded from
the fit to the surface deformation field. Again, there is no correlation for the right-lateral shear plane for either case (D/ m = 488, Tibet;
D/ m = 828, Yunnan).
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Hybrid Mantle Deformation Field
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Fig. 6. The left-lateral maximum shear directions (white bars) of the hybrid mantle deformation field that were determined using the method
described in Fig. 5 with an additional surface boundary condition placed over the shear wave splitting measurements in Tibet to simulate a
coupling between the crust and mantle layers. The left-lateral (white bars black outline) and right-lateral (grey bars) maximum shear directions
are plotted at the splitting sites, along with the shear wave splitting measurements (black bars). There is an excellent fit between the modeled
mantle deformation field and the observed mantle deformation from shear wave splitting in both Tibet (D/ m = 108) and Yunnan (D/ m = 98).
Guilbert et al. [33]; Sandoval et al. [38] lines (blue
bars, Fig. 1) and therefore the surface deformation
there is well known. Along the Huang et al. [36]
line (green bars, Fig. 1) there is no GPS coverage
(Fig. 2), only GPS observations on either side of the
southern part of the splitting observations. This splitting data shows a rapid spatial variation in / from the
NE–SW in the south to NW–SE in the north, a rapid
variation not observed in our surface deformation
model, possibly due to lack of GPS data there to
constrain it. Thus, we give results without the northern
most splitting observations to only compare the mantle anisotropy with known surface deformation.
For the Yunnan China region we utilize new SKS
shear wave splitting measurements, which represent
data from an eight-month deployment from 08/2000
to 04/2001 of 9 STS-2 broadband seismographs as
shown in Fig. 1. The technique of Silver and Chan
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Fig. 7. The modeled surface velocity field (black vectors) determined from the joint inversion of GPS and Quaternary fault slip rate data and the
modeled mantle velocity field (white vectors) that yield the left-lateral maximum shear directions shown in Fig. 6. The mantle velocity field was
derived assuming a uniform viscosity upper mantle lithosphere with applied side boundary conditions of rigid geologic blocks along with an
approximated top boundary condition associated with crustal motions (Fig. 2), applied only to Tibet (see text for details). There is significant
differential horizontal velocity between crust and upper mantle, starting around the eastern Himalayan syntaxis and throughout Yunnan.
[71], as well as the stacking procedure of Wolfe and
Silver [72] was used to analyze the data. 7 of the 9
stations provided usable splitting data. The stacked
results are shown in Table 1, and the specific events
and phases used for each station are given in Tables
T1 and T2, and the quality of the station stacks is
illustrated in Figs. S1 and S2, including the results of
two permanent stations CHTO and KMI. As seen in
Fig. 1, the orientations are surprisingly uniform. All
stations give a consistent E–W oriented fast polarization direction with delay times that range from 0.5 to
1.7 s.
4.1. Lithosphere or asthenosphere?
We first seek to test simple models constrain the
dominant process that is producing the anisotropy. As
in all shear wave splitting studies using teleseismic
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Fig. 8. A) The east–west (horizontal) shear strain rates (ė xz) produced as a result of the differential horizontal velocities between crust and
mantle, shown in Fig. 7. B) The north–south (horizontal) shear strain rate (ė yz) produced as a result of the differential horizontal velocities
between crust and mantle, shown in Fig. 7. Note the large shear strains in Yunnan China where the crust is moving southeast relative to Eurasia
but the underlying mantle is moving NE.
shear waves, the splitting observed at the surface can
be due to either asthenospheric flow [73–75] or deformation of the lithosphere [68,71]. We can distinguish
between these two possibilities by comparing the
success of predictions of / under the assumption of
a lithospheric or asthenospheric source. We first test
the hypothesis that there is negligible lithospheric
anisotropy and that the anisotropy is within the asthenosphere due to simple asthenospheric flow [68]. In
this case the orientation of / will be parallel to the
differential velocity vectors defined by the velocity at
the top and bottom of the asthenosphere. In this test
we furthermore assume that the surface velocity field
is equal to the velocity at the base of the lithosphere
(vertical coherence) and then specify a lithospheric
velocity relative to a deep mantle frame. We consider
two commonly held assumptions about the motions of
the surface plate velocity field relative to deeper mantle: the hotspot frame and the no-net-rotation (NNR)
reference frame. To evaluate the asthenospheric flow
model for these two reference frames, we rotate the
velocity field shown in Fig. 2 into the hotspot reference frame with the pole of rotation given by Gripp
and Gordon [76] ( 44.8, 58.1, 0.098/my) and a NNR
reference frame with the rotation pole from Argus and
Gordon [77] (50.6, 112.4, 0.248/my). The resulting
differential velocity vectors, which should be parallel
to the orientation of /, are plotted in Fig. 3A and B
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
Table 1
The Yunnan, China splitting measurements
Station
/
(8)
r/
(8)
yt
(s)
r yt
(s)
Latitude
(8)
Longitude
(8)
CHTO
DY
JC
KMI
LC
LK
ML
NJ
NL
105
102
000
94
102
93
87
87
000
2
9.5
000
8.1
3
2
3.5
4.5
000
1.65
1.23
000
0.56
1.33
1.25
0.88
0.95
000
0.05
0.3
000
0.10
0.10
0.08
0.08
0.10
000
18.79
25.73
26.54
25.12
23.88
25.83
21.48
25.05
27.29
98.98
101.32
99.90
102.74
100.07
98.85
101.56
100.52
100.84
The fast polarization is represented by /, yt is the delay time, and
r / and r yt are the 1r uncertainties in / and yt respectively. Null
stations are indicated by 000.
for both reference frames. The RMS misfit for the
simple asthenospheric flow models, D/ a, is very large
for the hotspot reference frame (D/ a = 588), which
was also noted by Davis et al. [69]. For the NNR
frame, while D/ a is lower (D/ a = 208), there remain
systematic misfits that are much larger than the errors
in the splitting data, which are about 58–108 (Table 2).
There remains the possibility that the sub-asthenospheric velocity field has some other velocity. Indeed,
there are two studies where simple asthenospheric
flow dominates the anisotropy [74,75], but the
inferred sub-asthenospheric flow field is non-zero in
both of the frames adopted. Moreover, the reference
frame for Eurasia relative to the deep mantle frame is
uncertain. Therefore, following the method of Silver
and Holt [74] we invert for the best-fitting reference
frame that will align the motion of the lithosphere
with the splitting observations in Asia (Fig. 3C; Table
2). The best-fit rotation pole applied to the Eurasian
frame is given by (43.5, 88.0, 0.418/my). The
resulting shear directions between lithosphere and
deeper mantle frame do not provide an especially
good fit to the splitting observations over all of Asia
(D/ a = 188).
It is possible to have two distinct flow models (one
for Tibet and one for Yunnan). Because of the uniformity of the splitting observations in Yunnan, such a
model is consistent with the Yunnan observations
(D/ a = 118) with a pole relative to Eurasia of (39.2,
98.8, 1.08/my) that again produces a uniform westward-directed sub-asthenospheric mantle velocity of
~30 mm/yr. In Tibet, solving for a single pole of
261
rotation also produces an acceptable fit to the splitting
data (D/ a = 158) for a pole of rotation relative to
Eurasia of ( 29.7, 92.8, 0.908/my). The resultant
velocity field produces NNW velocities of ~30 mm/yr
in eastern Tibet (in a Eurasia-fixed reference frame)
that rotate around to WSW velocities, ranging from 1–
15 mm/yr in central and western Tibet. Although the
fit to the shear wave splitting data is acceptable in
Tibet and Yunnan, we reject the hypothesis that two
independent asthenospheric flow fields are responsible for the observed anisotropy in Asia for the following reasons. First, these two predicted flow fields are
divergent at the eastern Himalayan syntaxis, corresponding to ~6 cm/yr of relative divergence within
the sub-asthenospheric mantle flow field. If this were
the case, there should be manifestations of such an
upwelling at the surface. Second, the estimated subasthenospheric flow for either region is not consistent
with the motion of the subducting Indian plate. In a
Eurasia-fixed frame, the velocity of the Indian plate
beneath Tibet is northeast, whereas the estimated flow
direction is northwest. In Yunnan, the best-fitting
velocity is westward, while the subduction direction
is northeast. In addition, these velocities are not consistent with any large-scale deep mantle flow model.
We note that in two regions where simple asthenospheric flow appears to dominate, such flow models
predict non-stationary sub-asthenosphere flow which
successfully account for the observed anisotropy (e.g.,
[74,75]).
The limited success of simple asthenospheric flow
models motivates our consideration of lithospheric
models for the anisotropy. The simplest to such
model is vertically coherent deformation [68], where
Table 2
The RMS misfit for the 5 different models to the shear wave
splitting measurements
RMS misfit to:
Tibet
Yunnan
Both regions
Hotspot model
NNR model
Active mantle (1 rotation)
Active mantle (2 rotations)
Surface right-lateral
Surface left-lateral
Mantle right-lateral
Mantle left-lateral
Hybrid right-lateral
Hybrid left-lateral
56.38
18.48
24.18
15.08
76.68
11.28
48.38
20.58
66.08
9.58
60.98
21.48
13.98
11.38
53.08
49.08
81.78
8.18
79.38
9.08
58.38
19.78
18.18
–
67.38
33.48
65.18
16.38
72.18
9.38
262
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
the crust and mantle portions of the lithosphere
deform coherently with no horizontal shear, as
would be the case for a mechanically coupled lithosphere. In this case, the direction of maximum shear
for a highly strained region like Tibet for the surface
field should be parallel to the orientation of / from
the splitting measurements [67]. To test this hypothesis we compare the surface deformation field associated with the velocity field shown in Fig. 2 with the
shear wave splitting observations. This involves comparing the maximum shear directions from the modeled instantaneous strain rate field, determined using
GPS and Quaternary fault slip data, / s, with SKS fast
polarization directions, inferred to represent finite
maximum shear directions in lithospheric mantle.
The maximum shear direction is independent of reference frame so that our comparison applies for all
possible reference frames.
We plot the right- and left-lateral maximum shear
directions [70] embedded in the velocity gradient
tensor field (Fig. 2) and compare these shear directions with the fast polarization directions (Fig. 4). For
the Tibet region, while there is a large misfit observed
between the surface and mantle deformation for the
right-lateral case, D/ s, (D/ s = 778), we observe a
close correspondence between the left-lateral shear
directions and values of / (D/ s = 118) (Fig. 4; Table
2). Note that the left-lateral shear planes in the instantaneous deformation field are parallel to the left-lateral
faults in Tibet, which are features of finite strain. The
correlation of / with the left-lateral shear planes in the
deformation field makes several important points.
First, the anisotropy-inferred mantle deformation
within Tibet is most likely lithospheric. Second, the
lithospheric deformation is vertically coherent with
the surface, since the surface deformation field (leftlateral direction of maximum shear) match so closely
with the fast polarization directions, and hence the
inferred mantle finite shear directions [67,70]. Third,
the left-lateral maximum shear direction is a better
predictor of / than the maximum extension direction
of finite strain. The RMS misfit found by Davis et al.
[69] using the modeled maximum extension direction
(D/ = 198) is almost twice as large as for this study.
Much of the systematic misfit that Davis et al. [69]
observed can in fact be dramatically reduced by
adopting the direction of maximum shear rather than
maximum finite-strain extension direction. Fourth and
most importantly, since the dynamic modeling of the
surface deformation field requires ~50% contribution
from body forces contained within the crustal layer
[12], it follows that the stresses associated with crustal
GPE variations must be transmitted into the mantle to
produce the observed coherent deformation field,
which argues for strong crust–mantle coupling
beneath Tibet.
In contrast to Tibet, the misfit between maximum
shear and splitting directions in Yunnan is large.
Neither the right-lateral (D/ s = 538) nor the left-lateral
(D/ s = 498) maximum shear directions for the surface
deformation field show a close correspondence to the
shear wave splitting measurements in Yunnan (Fig. 4;
Table 2), indicating that the crust and mantle layers
are decoupled. This observation suggests that there is
a fundamental difference between Tibet and Yunnan
province.
5. Dynamic modeling of the mantle lithosphere
beneath Asia
We hypothesize that the difference between these
two regions is that in contrast to the crust–mantle
coupling in Tibet, there is complete decoupling in
Yunnan. Thus the deformation field and associated
anisotropy in the Tibetan mantle is a result of mantle
boundary forces, as well as buoyancy forces that are
transmitted through the crust, while the deformation
field and associated anisotropy in the Yunnan mantle
are a result of mantle boundary forces alone. This
hypothesis is testable because it makes specific predictions for both Tibet and Yunnan. Since the decoupling removes the influence of crustal GPE variations
on the mantle, then a mantle model including only
boundary conditions should correctly account for the
style of mantle deformation in Yunnan. In contrast,
such a model should not work for Tibet, due to the
influence of GPE variations there.
We thus constructed a model for the entire collision
zone in which the mantle is completely decoupled
from the overlying crust (this is justified as long as
there are negligible density variations within the anisotropic mantle lithosphere), so that it only includes
the influence of boundary conditions through the prescribed motions of rigid geologic blocks, in the
absence of body force variations. We first identify 5
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
geologic blocks (Tarim Basin, Gobi platform, Odros
block, south China block, and Sunda Block) that show
relatively low strain rates in the GPS and lack active
large-scale geological deformational structures (see
outlined areas in Fig. 1). We then make the assumption that these 5 geologic blocks and the Indian plate
are rigid throughout the vertical extent of the lithosphere. These rigid blocks surround the Tibetan Plateau and Yunnan (Fig. 1) and their relative motions are
known from GPS (Fig. 2). We assume that the leading
edge of the Indian plate is located in southern Tibet,
where it has been imaged seismically [78]. The shapes
and relative motions of these lithospheric blocks, as
well as the leading edge of the Indian plate, provide
precise velocity boundary conditions that indeed constrain the mantle deformation field beneath Tibet,
which is surrounded by these blocks. Moreover, the
resulting lithospheric deformation field is independent
of any reference frame that can be adopted for the
block motions and is only dependent on their relative
motions. With the velocity boundary conditions
applied to the 5 geologic blocks and the Indian plate
we perform standard continuum-mechanics forward
modeling to predict a mantle deformation field and
resulting maximum shear directions within the upper
mantle beneath Asia. Flesch et al. [12] have shown
that the minimization of the rate of work functional
Z Z
H¼
½ D ma fa dxdy
ð2Þ
s
with respect to the strain rate and velocity fields
provides a deviatoric stress field that solves the
force balance equations [79,80]. In Eq. (2) f a is the
body force distribution, m a is a velocity, and D is the
dissipation potential given by:
nþ1
n
2n
B ėe ab ėe ab þ ėe 2cc
D¼
ð3Þ
nþ1
where n is the power law exponent, ė gg = (ė xx +
e yy) = ė zz is the strain rate, and B is a constant related
1
to˙ the viscosity, ḡ ¼ BE n 1q, ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
that is sensitive to temperature [2,22] where E ¼ ėe ab ėe ab þ ėe 2cc . We follow the
method of Flesch et al. [12] and use Eq. (2) to forward
model the central Asian mantle for a decoupled lithosphere (free-slip top boundary) in the absence of body
forces, assuming a uniform B value distribution and
n = 1. We then apply the velocity boundary conditions
of the 5 geologic blocks and the Indian plate, known
263
from the GPS measurements (see velocity vectors,
Fig. 2) (Fig. 1) and calculate the resultant velocity,
strain rate, and deviatoric stress field within the interior of the grid.
As expected, the mantle strain rate field from this
dynamic model is considerably different from the
surface deformation field (Fig. 5; Table 2), due to
the absence of crustal GPE variations. In Yunnan the
left-lateral maximum shear directions for this model
provide a very good fit to the splitting directions
(D/ m = 88). This correlation provides further support
for the hypothesis that deformation and observed
anisotropy in the Yunnan mantle is driven exclusively
by boundary conditions imposed from the edges of
adjacent lithospheric blocks and is decoupled from the
overlying crustal velocity field.
For Tibet, the fit provided by the left-lateral maximum shear directions for this mantle model is
degraded, compared to the fit to the surface deformation field, with the RMS misfit nearly doubling
(D/ m = 218 vs. D/ m = 118) (Fig. 5). This is expected
because this model lacks the topographically induced
body forces (i.e., crustal GPE variations) that are
required to explain the surface deformation field, as
noted above [12]. There are three diagnostic stations
in Tibet: the two eastern stations and the most southern station in the middle line (Fig. 5). These stations
delineate a rotation or curvature of the fast polarization directions that is not present in the boundarycondition-only mantle deformation model. This lack
of rotation lends further support to the conclusion that
in the Tibetan mantle is deforming in response to the
near-surface topography-induced forces (GPE variations) that are transmitted through the entire depth of
the lithosphere. For this to occur there must be a
mechanical coupling between the crust and upper
mantle (Fig. 4, Table 2). In addition, the mantle
layer cannot be stronger than the crustal layer. If the
mantle is the strong controlling layer then any crustal
buoyancy forces transmitted into the mantle would not
influence mantle deformation and one would not
expect the observed rotation of /.
In order to model both the strong coupling in Tibet
and weak coupling in Yunnan, we now consider a
bhybridQ mantle model where we again impose rotations of lithospheric geologic blocks as boundary
conditions, but now add a second constraint to
approximate the top coupling boundary condition
264
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
that the crustal velocity field in Tibet (Fig. 2) might
impose on the mantle below. To approximate the
effect of top coupling boundary conditions we again
minimize the functional [Eq. (2)] with applied side
boundary conditions, but with the additional constraint of fitting the surface strain in the vicinity of
the splitting measurements within Tibet, but not
within SE Tibet or Yunnan. This moderate constraint
is different from the applied side velocity boundary
conditions in that the model does not have to fit the
top boundary conditions precisely in minimizing the
functional in Eq. (2). We again use a uniform B value
distribution and power law exponent of 1 and impose
the rotation of each of the 5 geologic blocks and the
Indian plate to solve for the resulting velocity, strain
rate, and stress field within the deforming region (Fig.
6). This hybrid model produces a good fit in both
Tibet (D/ m = 108) and Yunnan (D/ m = 98) regions to
the values of / for the left-lateral case, with an overall
misfit of D/ m = 98 (Table 2). This is consequently our
preferred model.
The velocity field of the dynamic hybrid solution
for the mantle with side boundary conditions, and
approximated top boundary conditions within Tibet
only, is shown in Fig. 7 along with the surface velocity field. As expected, this model has minimal relative crust–mantle velocities beneath Tibet, but large
differential horizontal velocities between crust and
mantle beneath Yunnan. These differential horizontal
velocities are as large as ~30 mm/yr in Yunnan where
the crust is moving to the S–SE with respect to Eurasia, but the underlying mantle is being pushed NE–E
by the effect of the collision. The transition between
the primarily coupled crust–mantle motions in Tibet to
the decoupled crust–mantle motions in Yunnan occurs
in the vicinity of eastern Himalayan syntaxis. The
resulting horizontal shear within Yunnan between
the crustal and mantle layers predicts large N–S
shear strain rates (ė yz) (Fig. 8), with the crust moving
southward with respect to the mantle.
6. Discussion and conclusions
We have modeled both kinematically and dynamically central Asian tectonics through the joint analysis
of surface deformation (Fig. 2) inferred from observations of GPS and Quaternary fault slip data, and
mantle deformation observations inferred from available SKS shear wave splitting observations, including
a new data set for Yunnan (Fig. 1). We first used these
data to determine whether the mantle anisotropy was
due to lithospheric deformation or to flow in the
asthenosphere by comparing observed splitting fast
polarization directions to those predicted by simple
asthenospheric flow. Asthenospheric flow was tested
by predicting values of / under a variety of assumptions about the sub-asthenospheric velocity field. A
sub-asthenospheric velocity field that is stationary in
either the hotspot (Fig. 3A) or NNR (Fig. 3B) reference frame provides an unsatisfactory fit to the data,
as does a best-fit model predicted by a uniform velocity rotation over the entire region (Fig. 3C). While
allowing separate velocities under Tibet and Yunnan
do provide a reasonable fit of data, the resulting flow
field appears to be incompatible with several firstorder geophysical and geological constraints and is
therefore unlikely to provide a physically reasonable
explanation for the splitting data.
We then investigated if the source of the anisotropy
could be lithospheric. We initially compared the maximum shear directions derived from the observed surface deformation field with the splitting fast
polarization directions (Fig. 4), which should be parallel to each other if the lithosphere is deforming
coherently. For Tibet, we found a correspondence
for the left-lateral maximum shear directions, but not
for right-lateral. Both this close correspondence and
the predominance of left-lateral surface faulting in
Tibet, argue strongly for a lithospheric source for
the mantle anisotropy.
Previous modeling [12] has shown that the surface
deformation field in Tibet can be successfully fit by a
model that includes equal contributions of stress associated with the accommodation of relative plate
motions and those associated with GPE variations
within the lithosphere. As noted earlier, GPE variations are effectively concentrated within the crust if
topography is compensated by the Airy mechanism
[16]. Therefore, in order for crustal buoyancy forces
in Tibet to influence mantle deformation, they must be
transmitted through the crust and into the mantle,
arguing for strong mechanical coupling between the
crustal and mantle layers. In addition, the mantle layer
cannot be stronger than the crustal layer. If this were
the case then the transmitted crustal buoyancy forces
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
would have no influence on the mantle deformation
field and / would not exhibit the observed curvature
associated with crustal GPE variations [12].
In contrast, for Yunnan, neither left- nor right-lateral maximum shear directions from surface deformation successfully predict the values of /. We therefore
reject the model of vertically coherent lithospheric
deformation for Yunnan, and then considered the
hypothesis that the crust and mantle portions of the
lithosphere are mechanically decoupled. In this case
the mantle deformation beneath Yunnan crust is dominated by the velocity boundary conditions of the lithospheric blocks that surround Yunnan, while the crustal
topographically induced stresses are not transmitted to
the mantle. In order to test this hypothesis, we constructed a dynamic mantle model that was subject only
to velocity boundary conditions by imposing the relative motions of 5 undeformed geologic blocks as well
as the motion the of Indian plate, with no body force
variations within the mantle portion of the lithosphere.
The resulting mantle model provides a good fit to the
values of / in Yunnan for the left-lateral maximum
shear direction. Given this correspondence, we view
this as a successful model. Furthermore, we conclude
that the Yunnan lithosphere is decoupled, and
observed anisotropy in the Yunnan mantle is the result
of strain associated with the motion of the surrounding
lithospheric blocks. As expected, this decoupled,
boundary-condition-only mantle model degrades the
fit for Tibet, which provides further confirmation that
the crust and mantle cannot be decoupled there; the
observed coherence between crustal shear directions
and / can only occur if crustal buoyancy forces are
transmitted from the crust into the mantle beneath
Tibet via mechanical coupling.
We then constructed a bhybridQ mantle dynamic
model for mantle deformation that accounts for side
velocity boundary conditions of blocks as well as
approximated top velocity boundary conditions associated with the motions of the overlying crust within
regions where coupling between crust and mantle is
hypothesized to be occurring. The top velocity boundary conditions were placed only within Tibet, but not
within SE Tibet or Yunnan. This model provides an
excellent fit to the overall splitting data set, and as a
result, is our preferred model to explain deformation
and vertical strength variations within the central
Asian lithosphere. By comparing the mantle model
265
with the surface deformation field, assumed to be a
proxy for the motion of the upper crust, we are then
able to quantify the horizontal differential velocity
between crust and mantle. As expected this difference
is largest in Yunnan (reaching a maximum of ~30 mm/
yr), where the crust appears to be moving southward
with respect to the mantle.
In the hybrid model there is only imposed crust–
mantle coupling out to the eastern edge of Tibet above
338 N, where there are splitting measurements to
constrain the coupling. Thus a broad transition zone
is permitted from 338 N in Tibet (where we observed
the lithosphere to be coupled) to 268 N in a decoupled
Yunnan. Preliminary shear wave splitting observations
from a recent portable experiment in the eastern
Himalayan syntaxis region [81] provide both additional support for the existence of this predicted transition and also a tighter bound on its location and
spatial extent. We find that the coupled solution, (Fig.
4), successfully explains these additional data, suggesting that the Tibetan lithosphere is still coupled as
far south as 298 N, which implies a narrow north–
south transition zone of no more than ~300 km. In
addition, recent shear wave splitting measurements
south and east of the eastern Himalayan syntaxis
argue for a decoupled lithosphere [82] further narrowing the width of this transition zone. The results for
Tibet from the models described above provide three
important conclusions concerning the vertical rheological profile of the lithosphere of Tibet. First, it
implies a strong coupling between the crust and mantle within the Tibetan plateau. Secondly we infer that
this coupling causes stresses associated with buoyancy forces originating in the upper crust, to be transmitted into the mantle. An upper crust that is
substantially weaker than the mantle is not compatible
with our results. Third, the coupling between crust
and upper mantle is only possible if the lower crust
and upper mantle are of similar strength within Tibet;
thus a bjelly-sandwichQ rheology with a weak middle
or lower crust can be ruled out for Tibet. In addition,
our results are inconsistent with other forms of crust–
mantle decoupling, such as large-scale lower crustal
flow in Tibet [10,11,13] or large-scale delamination of
the Eurasian mantle in northern Tibet [15,83].
The contrast between the behavior of Tibet and
Yunnan is striking. The inferred change from strongly
coupled to decoupled lithosphere suggests that there is
266
L.M. Flesch et al. / Earth and Planetary Science Letters 238 (2005) 248–268
a profound lateral transition in the strength profile of
the lithosphere over the central Asian region. It
implies that there are large horizontal shear strains
(ė xz, ė yz, Fig. 8) in the transition region around the
eastern Himalayan syntaxis [84], as if the Yunnan
crust is sliding off the plateau, while the underlying
mantle continues to be compressed by the collision.
This change in vertical rheology between Tibet and
Yunnan may be due to the different ways each region
was formed, or to the specific way in which this
particular orogen has evolved. As more shear wave
splitting observations are made in this region, we will
gain a much clearer view of the lithosphere’s actual
role in the most dramatic of collisions.
Acknowledgements
We thank S. Cai, P. Burkett and W. Jiao for leading
the installation and data collection of the Yunnan portable seismic network. This manuscript was improved
by the comments of two anonymous reviewers and R.
van der Hilst. The field-work was supported by Multimax, China Earthquake Administration Institute of
Geophysics, and the Carnegie Institution of Washington. This research was supported by NSF grants EAR0215616 to PGS, EAR-0215625 to WEH, EAR9909621 to WEH, and the Carnegie summer intern
program. Part of this research was conducted under
the support from the Continental Dynamics program
of the State Natural Scientific Foundation of China
(Grant No. 40334041) and the International Cooperation Program of the Ministry of Science and Technology of China (Grant No. 2003DF000011).
Appendix A. Supplementary data
Supplementary data associated with this article can
be found, in the online version, at doi:10.1016/j.epsl.
2005.06.023.
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