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TECTONICS, VOL. 28, TC3001, doi:10.1029/2008TC002271, 2009
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Slowing of India’s convergence with Eurasia since 20 Ma and its
implications for Tibetan mantle dynamics
Peter Molnar1 and Joann M. Stock2
Received 6 February 2008; revised 8 December 2008; accepted 10 March 2009; published 16 May 2009.
[1] Reconstructions of the relative positions of the
India and Eurasia plates, using recently revised
histories of movement between India and Somalia
and between North America and Eurasia and of the
opening of the East African Rift, show that India’s
convergence rate with Eurasia slowed by more than
40% between 20 and 10 Ma. Much evidence suggests
that beginning in that interval, the Tibetan Plateau
grew outward rapidly and that radially oriented
compressive strain in the area surrounding Tibet
increased. An abrupt increase in the mean elevation
of the plateau provides a simple explanation for all of
these changes. Elementary calculations show that
removal of mantle lithosphere from beneath Tibet, or
from just part of it, would lead to both a modest
increase in the mean elevation of the plateau of 1 km
and a substantial change in the balance of forces per
unit length applied to the India and Eurasia plates.
Citation: Molnar, P., and J. M. Stock (2009), Slowing of India’s
convergence with Eurasia since 20 Ma and its implications for
Tibetan mantle dynamics, Tectonics, 28, TC3001, doi:10.1029/
2008TC002271.
1. Introduction
[2] Although India collided with southern Eurasia at
45– 55 Ma [e.g., Garzanti and Van Haver, 1988; Green
et al., 2008; Rowley, 1996, 1998; Zhu et al., 2005], much of
eastern Asia seems to have undergone accelerated deformation beginning since 15 Ma, and in many cases since only
8 Ma. Evidence for rapid deformation since 15 Ma,
which can be found from virtually all of the margins of
Tibet (Figure 1), poses the question of what process might
be responsible for such widespread, roughly contemporaneous changes.
[3] One explanation for the apparently rapid outward
growth of Tibet since 15 Ma and deformation of its
surroundings is that the plateau rose 1 – 2 km near 15 Ma;
a high plateau will resist further crustal thickening, and
crustal shortening will migrate to the flanks of the plateau
1
Department of Geological Sciences, and Cooperative Institute for
Research in Environmental Sciences, University of Colorado at Boulder,
Boulder, Colorado, USA.
2
Division of Geological and Planetary Sciences, California Institute of
Technology, Pasadena, California, USA.
Copyright 2009 by the American Geophysical Union.
0278-7407/09/2008TC002271$12.00
[e.g., Molnar and Lyon-Caen, 1988]. In a summary of
events occurring both on the plateau and surrounding it,
Harrison et al. [1992] proposed that since the collision
between India and Eurasia, Tibet began to rise rapidly near
20 Ma and reached its current elevation at 8 Ma. Some
[e.g., England and Molnar, 1990, 1993; Molnar et al.,
1993] questioned the evidence for a rise of the plateau at
20 Ma, for Harrison et al. relied on rapid exhumation at that
time [Copeland et al., 1987; Richter et al., 1991], which
does not require elevation change, and in a state of isostasy
would imply that the surface went down, not up. These
arguments, however, do not contradict an abrupt rise of
Tibet’s elevation at a later time, such as near 8 Ma [e.g.,
Molnar et al., 1993]. In either case, two sets of observations
have cast doubt on the inference that Tibet rose as much as
1 – 2 km since 20 Ma, or near 8 Ma.
[4] First, essentially all attempts to estimate paleoaltitudes of Tibet, most of which apply to times before 11 Ma
and a couple to the period before 20 Ma, have yielded
estimates indistinguishable from present-day altitudes
[Currie et al., 2005; DeCelles et al., 2007; Garzione et al.,
2000; Rowley and Currie, 2006; Rowley et al., 2001; Spicer
et al., 2003]. As all estimates are uncertain by 1000 m, one
could argue that they permit a post-10 Ma change of that
much. Perhaps more importantly, all of these estimates apply
to samples taken in the southern half of the plateau; thus,
inferences of paleoaltitudes cannot eliminate the possibility
that the northern half of the plateau rose 1– 2 km (or more)
since 20 Ma.
[5] The second observation inconsistent with a 1 – 2 km
rise since 20 Ma has been the absence of evidence for a
change in India’s rate of convergence with Eurasia during,
or shortly after, the hypothesized rise of the plateau. For
virtually all plausible density structures of crust and upper
mantle, with an increased mean elevation a high plateau
should apply a larger force per unit length to the adjacent
lower terrain [e.g., England and Houseman, 1989; Molnar
and Lyon-Caen, 1988; Molnar and Tapponnier, 1978].
Thus, an increased elevation of the plateau should have
resisted India’s penetration into Eurasia and slowed the rate
of convergence between them, as seems to have happened
with the rise of the Altiplano in the central Andes and the
slowing of Nazca – South America convergence [Garzione
et al., 2006; Iaffaldano et al., 2006]. Essentially all reconstructions of India’s convergence with Eurasia, however,
have shown no indication of a significant change in convergence rate since 20 Ma [e.g., Dewey et al., 1989; Molnar
and Tapponnier, 1975; Molnar et al., 1993; Patriat and
Achache, 1984]. Using improved reconstructions we show
that convergence between India and Eurasia did indeed slow
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since 20 Ma and that the deceleration seems to have ended
near 10 Ma.
2. Plate Reconstructions
2.1. Data, Methods, Uncertainties, and Sources of Error
[6] Several recent studies change our knowledge of
India’s convergence with Eurasia. Using a vast Russian
data set from the Indian Ocean, Merkouriev and DeMets
[2006] presented a detailed history of relative movement
between India and Somalia for the past 20 Ma. In particular,
they showed a 30% decrease in rate between 20 and 11 Ma
and a change in direction between 11 and 9 Ma. For the
period before 20 Ma, we rely on the reconstructions of India
to Somalia given by Molnar et al. [1988].
[7] The opening across the East African Rift system can
now be resolved with magnetic anomalies and fracture
zones in the oceans that surround Africa. For the past few
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million years, we rely on the angular velocity determined by
Horner-Johnson et al. [2007], who revised earlier rotation
parameters of Horner-Johnson et al. [2005]. The angular
velocity of Horner-Johnson et al. [2007], appropriate for
the past 3 Ma, agrees within uncertainties with that determined from a decade of GPS measurements [Stamps et al.,
2008]. With increasing data, however, it has become clear
that separating Africa into two plates, Nubia and Somalia,
can account neither for all GPS data in East Africa [e.g.,
Stamps et al., 2008], nor for magnetic anomalies both along
the Southwest Indian Ridge and in the Gulf of Aden and
Red Sea [e.g., Horner-Johnson et al., 2007; Patriat et al.,
2008]. The inclusion of small plates on the east side of the
rift improves the fits to both GPS and magnetic anomaly
data, but their presence limits the length of the Southwest
Indian Ridge that can be used to constrain movement
between Nubia and Somalia. Assuming that this ridge was
the boundary of the Antarctic plate with either Nubia or
Somalia, Royer et al. [2006] reconstructed the positions of
Figure 1
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Anomaly 5 to obtain rotation parameters for the relative
movements among those three plates. Their axis of rotation
for Somalia-Nubia lies just south of Africa, not far from the
axes found by Horner-Johnson et al. [2007] and Stamps et
al. [2008]. Thus, at first glance, their rotation parameters
seem sensible, but subsequent analysis shows that only a
short segment of the eastern half of the ridge formed by
movement between the Somalia and Antarctic plates. Moreover, their angle of rotation called for more than 100 km of
opening across the rift in Ethiopia, which seems excessive.
Accordingly, we followed the suggestion of Patriat et al.
[2008] and resorted to the rotation parameters of Lemaux et
al. [2002].
[8] To reconstruct the central Atlantic, we used the
parameters given by McQuarrie et al. [2003] for Nubia to
North America, which are based on work of Klitgord and
Schouten [1986]. For North America to Eurasia, we relied
on the recent study by Merkouriev and DeMets [2008],
which presented a detailed history of relative movement
between North America and Eurasia for the past 20 Ma. For
earlier times, again we used the parameters given by
McQuarrie et al. [2003].
[9] By combining the reconstructions of these four pairs
of the five plates, India, Somalia Nubia, North America, and
Eurasia, we calculated India’s position relative to Eurasia at
different times in the past (Figure 2). Readers should be
aware of two steps that must be taken to combine the
reconstructions, but that add uncertainty, if not error, to
the reconstructions.
[10] First, Merkouriev and DeMets [2006, 2008] presented reconstructions for many times, but none of the
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others did so, and in general, Horner-Johnson et al. [2007],
Lemaux et al. [2002], and McQuarrie et al. [2003] determined parameters for times different from those used by
Merkouriev and DeMets [2006, 2008]. We present reconstructions for the magnetic reversals used by Merkouriev and
DeMets [2006] (chrons 6no to 1o) with the time scale of
Lourens et al. [2004], and for earlier times with the time
scale of Cande and Kent [1995] (Figures 2 – 8 and Table 1).
Use of such detailed time steps requires the interpolation of
rotations for two plate pairs (Somalia-Nubia and Nubia –
North America) to obtain parameters for them for the same
times. To do this we assumed that no change in rate occurred
in the intervals between 3.6 and 11 Ma for Somalia-Nubia,
and between each of 0 and 11 Ma and 11 and 20 Ma for
Nubia – North America. For these interpolated rotations, we
used the uncertainty appropriate for that rotation closest in
time to the interpolated time. Obviously, if there were a
change in rate, our linear interpolation would add an error to
the rotation, but because these rotations are all small, that
error should be no greater than the error that we assigned to
rotations for 11 or 20 Ma.
[11] Second, what we have done for Somalia-Nubia
almost surely is wrong, for the very different locations of
rotation axes given by Horner-Johnson et al. [2007] and
Lemaux et al. [2002] imply an unlikely history of movement
across the East African Rift. That history calls for a phase
of largely strike-slip movement, of only modest amount
(<20 km), between 11 and 3.6 Ma, followed by nearly
pure divergence across the rift. We anticipate that continued
revisions of the history of spreading along the Southwest
Indian Ridge (or perhaps of the Red Sea and Gulf of Aden)
Figure 1. Map of Asia showing places within the Tibetan Plateau, on its margins, and far from it, where there is evidence
of rejuvenation or initiation of tectonic activity since 15 Ma. Within the plateau, this includes evidence for the onset of
normal faulting [e.g., Blisniuk et al., 2001; Harrison et al., 1995; Pan and Kidd, 1992]. Surrounding the plateau, the
evidence includes folding of the lithosphere south of India [Cochran, 1990; Gordon et al., 1990; Krishna et al., 2001], the
emergence of the Kyrgyz Range on the north flank of the Tien Shan north of Tibet [Bullen et al., 2001, 2003], as well as an
abrupt increase in sedimentation rate in intermontane basins in the Tien Shan [Abdrakhmatov et al., 2001], an interpretation
of fission track ages and lengths suggesting rapid cooling and emergence of Ih Bogd, the highest peak in the Gobi Altay
[Vassallo et al., 2007], and increased sedimentation in Lake Baikal, suggesting a marked deepening of the basin then [Petit
and Déverchère, 2006]. Cooling ages from elevation transects in parts of southeastern and eastern Tibet [Clark et al., 2005,
2006; Kirby et al., 2002], from the Qilian Shan [Clark et al., 2008], and from sequences of sedimentary rock from the
Liupan Shan [Zheng et al., 2006] suggest accelerated cooling beginning near 10 Ma in these localities. Ritts et al. [2008]
discuss possible marine sedimentation in the southern Tarim Basin near 15 Ma, with that sediment now at an elevation of
1500 m. Changes in deposition rates, clast sizes, and provenance of sediment in basins on the northeastern margin of Tibet
suggest accelerated subsidence in the basins and emergence of adjacent high terrain [e.g., Fang et al., 2003, 2005; Lease et
al., 2007]. Elevation transects of cooling ages in the Shillong Plateau south of the eastern end of the Himalaya suggest an
emergence of the plateau between 14 and 8 Ma [Clark and Bilham, 2008], or 15– 9 Ma [Biswas et al., 2007], and another
such profile within the Nepal Himalaya indicates an abrupt change in cooling rate at 10 Ma [Wobus et al., 2008], not much
different from the suggestion by Harrison et al. [1997] for rejuvenation of the Main Central Thrust in that region. Changes
in sedimentary facies and deposition rates within the adjacent Siwalik Series suggest that exhumation of the Lesser
Himalaya accelerated near 12– 10 Ma [e.g., Brozoviæ and Burbank, 2000; DeCelles et al., 1998; Huyghe et al., 2001;
Najman, 2006; Robinson et al., 2001; Szulc et al., 2006], and perhaps that the Main Boundary fault became active at
11 Ma [Meigs et al., 1995]. Finally, rapid exhumation of rock buried to 25– 30 km (800 MPa to 1 GPa) since 11 – 8 Ma
from the base of the Main Central Thrust Zone along the Sutlej Valley [Caddick et al., 2007; Vannay et al., 2004], and also
in the Nepal Himalaya [e.g., Catlos et al., 2001; Kohn et al., 2001, 2004], are consistent with accelerated exhumation rate at
that time. In addition, though not shown, much paleoclimatic evidence has been associated with growth of the Tibetan
Plateau near 8 Ma [e.g., An et al., 2001; Kroon et al., 1991; Prell et al., 1992; Quade et al., 1989] but closer to 9– 10 Ma
with revisions to the geomagnetic polarity time scale.
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movement between Nubia and Somalia seems to have
occurred later. Moreover, the effect of an error in the
initiation of opening across the East African Rift System
manifests itself largely as an error in the direction that India
converges with Eurasia, not in the rate.
2.2. Results: History of Convergence Between India and
Eurasia
Figure 2. Map showing reconstructed positions of two
points on the India plate with respect to the Eurasia plate at
different times in the past. Present positions of points on
India (white squares) are reconstructed to the black dots,
with the corresponding 95% uncertainty ellipses. Numbers
next to points identify chrons with the following ages
appropriate for the parts of the chrons that were used: chron
6no, 19.722 Ma; 13, 33.30 Ma; 18, 39.28 Ma; 20, 43.16 Ma;
21, 47.09 Ma; 25, 56.15 Ma; and 31, 67.67 Ma. An outline
of Indian continental lithosphere is also reconstructed to its
positions at 47 Ma, close to the time of collision, and at
68 Ma, before collision.
will require revision of the earlier phase of movement in East
Africa. As we show below, however, errors in the history of
movement between Somalia and Nubia contribute errors to
the calculated history of movement between India and
Eurasia that are merely comparable to, if not smaller than,
those due to uncertainties in the other rotations.
[12] Also, we assumed that motion between Nubia and
Somalia began at 11 Ma. Extensive volcanism occurred
before 30 Ma in much of Ethiopia and surrounding regions
[e.g., Chorowicz, 2005; Coulié et al., 2003; Kieffer et al.,
2004; Smith, 1994], but rifting seems to have begun near
10 – 11 Ma [Baker et al., 1972; Chernet et al., 1998;
WoldeGabriel et al., 1990; Wolfenden et al. 2004]. Although there is some evidence for minor faulting in Ethiopia
before 11 Ma [e.g., Bonini et al., 2005], most of the relative
[13] The rate of convergence between India and Eurasia
has slowed continually since collision near 45– 50 Ma, but
with large drops in rates near the time of collision, especially in western India, and since 20 Ma (Figures 2 and 3).
Obviously, the sparse sampling of the history with magnetic
anomalies older than 20 Ma limits our resolution of precise
ages of rate changes and of subtle changes at any time.
Nevertheless, drops in convergence rates of 30 –38% (118
to 83 mm a1 in northeastern India and 109 to 59 mm a1 in
northwestern India) at 40– 45 Ma and of 45% (59 – 34
and 83– 44 mm a1) between 10 and 20 Ma (Figure 3)
account for most of the change since collision. Whether this
latter decrease occurred gradually or in steps cannot be
resolved, because the uncertainties in reconstructed positions are too large, and we discuss each possibility.
[14] Reconstructed positions of the northwest and northeast corners of India since 20 Ma can be interpreted as
showing a decrease in the rate of convergence between
India and Eurasia of 25% near 11 Ma (Figures 2 – 8).
Not only did the direction that India moved toward Eurasia
change (Figures 4 and 5), but also the rate for the northwest
corner of India dropped from 44 to 34 mm a1, and that for
the northeast corner of India decreased from 57 to 44 mm
a1 (Figure 6). Somewhat surprising is the suggestion of
constant rates between 20 and 11 Ma and since 11 Ma. We
Figure 3. Distances of points in the northwestern and
northwestern corners of India (Figure 2) at different times in
the past, showing average convergence rates during
different intervals and a continual slowing of that
convergence. A plot for the last 20 Ma is shown in Figure 6.
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MOLNAR AND STOCK: INDIA-EURASIA CONVERGENCE RATE CHANGE
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Figure 4. Large-scale map showing reconstructed positions of the northwestern point (in Figure 2) on
the India plate with respect to the Eurasia plate at different times since 20 Ma. Present positions of points
on India (white dots) are reconstructed to the black dots, with the corresponding 95% uncertainty ellipses.
Line styles and shading are varied to help visually distinguish the ellipses; they have no other meaning.
Numbers next to points identify chrons with the following ages appropriate for the parts of the chrons that
were used: chron 1o, 0.781 Ma; 2y, 1.778 Ma; 2An.1y, 2.581 Ma; 2An.3o, 3.596 Ma; 3n.1y, 4.187 Ma;
3n.4o, 5.235 Ma; 3An.1y, 6.033 Ma; 3An.2o, 6.733 Ma; 4n.1y, 7.528 Ma; 4n.2o, 8.108 Ma; 4Ay,
8.769 Ma; 4Ao, 9.098 Ma; 5n.1y, 9.779 Ma; 5n.2o, 11.040 Ma; 5An.2o, 12.415 Ma; 5ADo, 14.581 Ma;
5Cn.1y, 15.974 Ma; 5Dy, 17.235 Ma; 5Ey, 18.056 Ma; and 6no, 19.722 Ma.
assumed constant rates for the central Atlantic in those
periods, but divergence of India from Somalia slowed
continually during that interval [Merkouriev and DeMets,
2006]. Moreover, the rate of opening in the North Atlantic
changed slightly since 11 Ma [Merkouriev and DeMets,
2008]. Here it is worth recalling that when three (or more)
plates are considered, the three rotation axes cannot remain
fixed with respect to all three plates as finite rotations accrue
[McKenzie and Morgan, 1969]. Thus, from the perspective
of at least one plate, but not necessarily the other two, rates
must change with time. Accordingly, a changing rate
between India and Somalia, but not between India and
Eurasia, is quite plausible.
[15] Rates of relative movement between all pairs of
plates changed since 20 Ma, and thus all contributed to
the 25% decrease in rate near 11 Ma. To isolate the effect
of each plate pair on the rate change, we carried out
modified calculations holding the rate of that plate pair
constant, and we calculated the difference it would make to
the result. For India-Somalia, Nubia – North America, and
North America – Eurasia, we carried out separate calculations for the Anomaly 6no (19.722 Ma) reconstruction using
the same axis as for Anomaly 5n.2o (11.040 Ma), and with
the angle scaled to give a constant angular speed since
19.722 Ma consistent with that since 11.040 Ma. To isolate
the effect of the opening of the East African Rift, we
5 of 11
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Figure 5. Large-scale map showing reconstructed positions of the northeastern point (in Figure 2) on
the India plate with respect to the Eurasia plate at different times since 20 Ma. Symbols are as in Figure 4.
Figure 6. Plot of distance of points in the northeast and
northwest corners of India from their reconstructed positions relative to Eurasia at selected times in the past.
Uncertainties are shown as 1s. Note the marked change
near 11 Ma and the 2 Ma uncertainty in the precise time of
change.
Figure 7. Plot of reduced distance (distance – 44 km/Ma
age) versus age for a point in the northwestern corner of
India at different times since 50 Ma. Note the abrupt slowing
since 20 Ma and the essentially constant rate since
11 Ma.
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MOLNAR AND STOCK: INDIA-EURASIA CONVERGENCE RATE CHANGE
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Figure 8. Plot of reduced distance (distance – 57 km/Ma age) versus age for a point in the northeastern corner of
India at different times since 50 Ma. Note the abrupt
slowing since 20 Ma and the essentially constant rate
since 11 Ma.
calculated reconstructions with no movement at all between
Somalia and Nubia. Although the contributions of each
ought not add linearly to account for the decrease in IndiaEurasia convergence rate near 11 Ma, we found that the
separate reconstructions do account for the 13 mm a1
decrease in rates for northeastern India and the 10 mm a1
decrease for northwestern India. For the former, India-
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Somalia accounts for 6 mm a1 of the decrease, SomaliaNubia accounts for 2 mm a1, Nubia – North America
accounts for 7 mm a1, and North America-Eurasia would
yield a 1 mm a1 increase. Similarly, for northwestern India,
the 10 mm a1 decrease includes the following contributions: India-Somalia 3 mm a1, Somalia-Nubia 1 mm a1,
Nubia-North America 6 mm a1, and North America –
Eurasia makes a negligible change.
[16] We were motivated to carry out this study by the
work of Merkouriev and DeMets [2006] showing a decrease
in rate between India and Somalia, and hence we were
surprised to learn that the change in rate near 10 Ma in the
central Atlantic contributes more to the decrease in convergence rate between India and Eurasia. Note that the axis of
rotation for Somalia-Nubia lies southwest of India’s position
in a frame fixed to Eurasia, and that for North America lies
in eastern Siberia, northeast of India. Thus, errors either in
positions of axes or in rotation angles have small effects on
India’s north-northeastward convergence with Eurasia. By
contrast, the axes of rotation for India to Somalia and for
Nubia to North America lie northwest of India (in Europe
and in the North Atlantic, respectively), and errors in angles
of rotation map directly and proportionally into rates of
north-northeastward movement of India with respect to
Eurasia. Thus, the large contributions of slowing of spreading in both the Indian and central Atlantic Oceans to the
decrease in India’s rate of convergence toward Eurasia
makes sense.
[17] Uncertainties in the reconstructed positions of India
at different times prohibit assigning a date to the slowdown
with an uncertainty as small as 1 or 2 Ma, or to the duration
of the transition, especially if we allow for uncertainty due
Table 1. Rotation Parameters for Positions of India in a Reference Frame Fixed to Eurasia
Chron
Age (Ma)
Lat °N
Long °E
Angle (deg)
sXXa
sXYa
sXZa
sYYa
sYZa
sZZa
1o
2y
2An.1y
2An.3o
3n.1y
3n.4o
3An.1y
3An.2o
4n.1y
4n.2o
4Ay
4Ao
5n.1y
5n.2o
5An.2o
5ADo
5Cn.1y
5Dy
5Ey
6no
13
18
20
21
25
31
0.781
1.778
2.581
3.596
4.187
5.235
6.033
6.733
7.528
8.108
8.769
9.098
9.779
11.040
12.415
14.581
15.974
17.235
18.056
19.722
33.30
39.28
43.16
47.09
56.15
67.67
27.31
33.54
34.25
31.23
31.27
29.78
28.60
25.80
26.79
24.63
24.26
23.93
23.42
22.43
22.80
23.33
23.84
24.09
23.45
25.83
18.38
21.76
23.57
23.90
25.49
19.26
22.15
23.13
22.67
26.05
21.18
24.34
22.97
25.45
24.53
25.13
24.95
25.02
25.20
24.34
23.32
22.62
22.06
22.88
23.25
22.62
33.31
30.41
28.69
24.36
14.74
14.47
0.354
0.814
1.146
1.705
1.891
2.440
2.700
3.035
3.402
3.711
3.945
4.150
4.399
4.800
5.534
6.424
7.365
8.109
8.586
9.798
22.557
27.576
30.658
33.429
41.483
54.695
0.0661
0.0469
0.0779
0.0749
0.1082
0.0682
0.4863
0.0739
0.1062
0.1031
0.1021
0.0852
0.1039
0.1084
0.1928
1.2751
0.2232
0.4057
0.2274
0.9764
0.2470
2.5669
3.3854
2.9166
0.8010
4.6443
0.0101
0.0212
0.0171
0.0134
0.0555
0.0095
0.0075
0.0160
0.0830
0.0644
0.0343
0.0051
0.0289
0.0701
0.0330
0.2095
0.0297
0.0548
0.0154
0.5291
0.0435
2.2256
1.8855
2.1435
0.1402
0.6678
0.0227
0.0227
0.0087
0.0132
0.0013
0.0218
0.5655
0.0130
0.0215
0.0130
0.0099
0.0351
0.0390
0.0318
0.0767
1.5320
0.1809
0.0334
0.2141
0.4861
0.0450
0.3315
0.3453
0.4541
0.1882
0.5625
0.1042
0.0415
0.1075
0.1057
0.1677
0.1010
0.1402
0.1156
0.2666
0.2007
0.1628
0.0737
0.1414
0.2396
0.1367
0.2512
0.1195
0.1426
0.1743
0.8325
0.3308
3.7146
3.6785
3.3274
0.5905
1.4243
0.0151
0.0200
0.0219
0.0179
0.0309
0.0215
0.0089
0.0260
0.0175
0.0411
0.0292
0.0298
0.0194
0.0146
0.0514
0.3882
0.0765
0.1268
0.0854
0.2290
0.2388
1.4770
1.9419
1.7029
0.4295
2.4534
0.0426
0.0350
0.0493
0.0506
0.0615
0.0438
0.8779
0.0560
0.0624
0.0615
0.1034
0.0830
0.0862
0.0690
0.1886
2.0335
0.2585
0.3974
0.3116
0.7041
0.3423
1.1300
2.2214
1.4478
0.6431
7.4102
In units of 104 steradians.
a
7 of 11
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MOLNAR AND STOCK: INDIA-EURASIA CONVERGENCE RATE CHANGE
Figure 9. Lithostatic pressure beneath two high regions
with different thicknesses of mantle lithosphere beneath
them. At any depth, lithostatic pressure increases downward
proportionally to the product of density and gravity.
Replacement of mantle lithosphere with material that is
hotter on average by DT, hence by a mean density of
raaDT, leads to a surface elevation change, Dh, given by
(1). The area of the shaded region gives, by (3), the increase
in potential energy per unit area, and therefore the increase
in the force per unit area that the high terrain and
surrounding lowlands apply to one another.
to interpolation of rates in the central Atlantic Ocean.
Moreover, the change in rate centered on 20 Ma is greater
than that since 20 Ma (Figure 3). Thus, we should also
consider the possibility that the rate decreased continuously
between 20 and 10 Ma. To do so, we normalize distances by
subtracting from them the average rate between 10 and
20 Ma times age and plot those normalized (or reduced)
distances versus age (Figures 7 and 8). If one extrapolates
average rates for the periods 33 to 20 Ma and 11 Ma to the
present, the lines intersect at 17 Ma. Clearly, however, the
rate could have decreased gradually between 20 and 11 Ma,
without an abrupt change. Plotted this way (Figures 7 and
8), the data suggest two conclusions. First, the convergence
rates of both northeastern and northwestern India with
Eurasia decreased by more than 40% since 20 Ma. Second,
that decrease seems to have stopped by 10 Ma.
3. Discussion
[18] The decrease in rate since 20 Ma and the suggestion
that the plateau may have risen since that time, if not near it,
raises the question of how these events might be correlated.
Moreover, the approximate correlation of this change in rate
with deformation surrounding Tibet and an outward growth
of the plateau raises the question of what process could
TC3001
effect both the slowing of convergence and the outward
growth of Tibet.
[19] For plausible densities of crust and upper mantle, an
increase in the mean elevation of a region in isostatic
equilibrium requires that work be done against gravity.
Accordingly, the potential energy per unit area stored in a
column of crust and mantle lithosphere will increase [e.g.,
England and Houseman, 1989; Molnar and Lyon-Caen,
1988]. Moreover, insofar as the horizontal compressive
stress differs little from the vertical compressive stress in
such a column, and the vertical compressive stress is given
simply by the lithostatic pressure, then the change in
potential energy per unit area equals the change in the
horizontal force per unit length that the lithospheric column
applies to its surroundings [Molnar and Lyon-Caen, 1988].
[20] Removal of cold mantle lithosphere and replacement by hotter asthenosphere will require that the surface
rise. For simple assumptions of constant densities rc of
crust, rm of mantle lithosphere, and ra of asthenosphere,
the change in mean elevation, Dh, associated with replacement of cold by warmer material, under isostatic
balance is expressed by rch + rmL = rch + ra(L + Dh),
where L is the thickness of mantle lithosphere and h is the
thickness of the crust (Figure 9). Simplified, this gives
Dh ¼ Lðrm ra Þ=ra
ð1Þ
[21] Here, rm ra = ra a DT, where DT is the average
change in temperature across the thickness of lithosphere
due to removal of its mantle part, and thus half of the
change in temperature at the base of the crust (if the entire
mantle lithosphere is removed), and a (3 105 °C1) is
the coefficient of thermal expansion. Thus, (1) becomes
Dh ¼ LaDT
ð2Þ
As examples, suppose that the temperature at the Moho
were initially 700°C (or 900°C) and with removal of most
of the mantle lithosphere it became 1300°C. Thus, DT =
300°C (or 200°C). For an initial thickness of mantle
lithosphere of L = 110 km (or 160 km), as might be
expected following horizontal shortening of Tibetan lithosphere, the surface should rise Dh = 1 km.
[22] The change in potential energy per unit area, given
by the area between the curves in Figure 9, is simply
DPE ¼ Dhgðrc h þ rm L=2Þ
ð3Þ
Thus, with rc = 2.8 103 kg m3, rm = 3.3 103 kg m3,
Dh = 1 km, and h = 65 km, the increase in potential energy
per unit area, which also equals the increase in force per unit
length that Tibet should apply to the India plate, would be
4.4 (or 3.6) 1012 N m1. Such a force per unit length is
somewhat greater than that applied by a hot column of mass
at mid-ocean ridges to old, cold oceanic lithosphere [e.g.,
Chapple and Tullis, 1977; Forsyth and Uyeda, 1975; Frank,
1972; McKenzie, 1972]. Thus, largely by virtue of initially
relatively thick crust and mantle lithosphere, removal of
mantle lithosphere leads to a small change in mean eleva-
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MOLNAR AND STOCK: INDIA-EURASIA CONVERGENCE RATE CHANGE
tion, compared to the mean elevation of Tibet itself, but that
small change nevertheless can profoundly alter the balance
of forces affecting convergence between India and Eurasia.
Allowance for other values of DT, L and h, as well as for
deviations from lithostatic pressure, can yield a range of
values of both Dh and DPE that differ by as much as a
factor of two from those given above. Obviously, ignorance
of all of the requisite quantities and of constraints on
Dh makes it difficult at present to refute the suggestion
that mantle lithosphere was removed from northern Tibet, if
not from beneath the entire plateau, since 20 Ma.
[23] This idea needs to be tested further in two ways:
first, by direct demonstration that the surface did rise, using
paleoaltimetry, and second, by analyses of magmatic rock
and entrained mantle xenoliths to look for changes in
magma sources and pressure-temperature conditions in the
mantle. Turner et al. [1993, 1996] argued that the high
potassium content and high 87Sr/86Sr ratios in basaltic lavas
erupted in northern Tibet since 13 Ma implied that lithosphere had melted. They use these facts to infer that at least
the lower part of the mantle lithosphere had been removed,
so that hotter asthenosphere brought into contact with
mantle lithosphere enabled the latter to melt. From phase
equilibrium experiments on melted lavas from northern
Tibet, Holbig and Grove [2008] also concluded that the
source was metasomatized mantle in the spinel and garnet
stability fields that was heated by close proximity to hotter
asthenosphere. Others, however, interpret these potassiumrich lavas to be derived from melting of subducted sediment
or continental crust [e.g., Arnaud et al., 1992; Guo et al.,
2006]. To the best of our knowledge, mantle xenoliths
suitable for resolving this issue, and for further constraining
the mantle dynamics, have not yet been found.
4. Conclusions
[24] Plate reconstructions that incorporate recent highresolution studies of relative movement between India and
Somalia [Merkouriev and DeMets, 2006], between Somalia
TC3001
and the rest of Africa (Nubia) [Horner-Johnson et al., 2007;
Lemaux et al., 2002], and between North America and
Eurasia [Merkouriev and DeMets, 2008] call for a marked
slowdown in the convergence between India and Eurasia
since 20 Ma (Figures 2, 7, and 8). The decrease was greater
than 40%, but precisely when that decrease occurred cannot
yet be resolved. If rates before 20 Ma and since 11 Ma are
extrapolated, they intersect near 17 Ma. Alternatively, the
rate decreased continuously between 20 and 10 Ma, after
which it seems to have been constant (Figures 3 – 8).
[25] In either case, the change in rate occurred at essentially the same time that deformation within and surrounding Tibet seems to have increased (Figure 1). This needs to
be explained by an additional short-term event, not just
progressive plate convergence. One possibility is that somehow the crust and upper mantle beneath Tibet suddenly
exerted an increased outward force per unit length on
Tibet’s surroundings, including on the Indian lithosphere.
[26] For an initially thick crust, like that beneath Tibet,
and for removal of relatively thick mantle lithosphere, as
one might expect after tens of millions of years of horizontal
shortening, such removal can yield a relatively small change
in mean elevation (1 km), but a large change in the force
per unit length that the plateau applies to its surroundings.
That change can be comparable to the force per unit length
that the column beneath mid-ocean ridges applies to old
lithosphere. Thus, although still deservedly controversial,
the idea that mantle lithosphere was removed from beneath
Tibet since 20 Ma gains some support from the change in
convergence rate between India and Eurasia.
[27] Acknowledgments. One of us was justifiably provoked by
Marin Clark’s question in 2003, ‘‘Wouldn’t you expect a change in plate
motions at 8 Ma’’? C. DeMets both offered useful suggestions for
improving the manuscript and supplied us with preprints in advance of
publication. This research was supported in part by the National Science
Foundation under grants EAR-0440004, EAR 0507330, EAR 0636092, and
OPP-0338317. Figures 2, 4, and 5 were made using Generic Mapping Tools
(GMT) software.
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P.Molnar,
Department
of Geological Sciences,
University of Colorado at Boulder, Boulder, CO
80309-0399, USA. ([email protected])
J. M. Stock, Division of Geological and Planetary
Sciences, California Institute of Technology, Pasadena,
CA 91125, USA.