Slowing of India's convergence with Eurasia since 20 Ma and its implications for Tibetan mantle dynamics

Authors


Abstract

[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.

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.

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.

[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 [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 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 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 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.

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.

[10] First, Merkouriev and DeMets [2006, 2008] presented reconstructions for many times, but none of the 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 28 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.

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.

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.

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 1σ. 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.

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.

Table 1. Rotation Parameters for Positions of India in a Reference Frame Fixed to Eurasia
ChronAge (Ma)Lat °NLong °EAngle (deg)σXXaσXYaσXZaσYYaσYZaσZZa
  • a

    In units of ×10−4 steradians.

1o0.78127.3122.15−0.3540.06610.01010.02270.1042−0.01510.0426
2y1.77833.5423.13−0.8140.0469−0.02120.02270.0415−0.02000.0350
2An.1y2.58134.2522.67−1.1460.07790.01710.00870.1075−0.02190.0493
2An.3o3.59631.2326.05−1.7050.07490.01340.01320.1057−0.01790.0506
3n.1y4.18731.2721.18−1.8910.10820.05550.00130.1677−0.03090.0615
3n.4o5.23529.7824.34−2.4400.06820.00950.02180.1010−0.02150.0438
3An.1y6.03328.6022.97−2.7000.48630.0075−0.56550.14020.00890.8779
3An.2o6.73325.8025.45−3.0350.07390.01600.01300.1156−0.02600.0560
4n.1y7.52826.7924.53−3.4020.10620.08300.02150.2666−0.01750.0624
4n.2o8.10824.6325.13−3.7110.10310.06440.01300.2007−0.04110.0615
4Ay8.76924.2624.95−3.9450.10210.03430.00990.1628−0.02920.1034
4Ao9.09823.9325.02−4.1500.08520.00510.03510.0737−0.02980.0830
5n.1y9.77923.4225.20−4.3990.10390.02890.03900.1414−0.01940.0862
5n.2o11.04022.4324.34−4.8000.10840.07010.03180.2396−0.01460.0690
5An.2o12.41522.8023.32−5.5340.19280.03300.07670.1367−0.05140.1886
5ADo14.58123.3322.62−6.4241.2751−0.20951.53200.2512−0.38822.0335
5Cn.1y15.97423.8422.06−7.3650.2232−0.02970.18090.1195−0.07650.2585
5Dy17.23524.0922.88−8.1090.40570.0548−0.03340.1426−0.12680.3974
5Ey18.05623.4523.25−8.5860.2274−0.01540.21410.1743−0.08540.3116
6no19.72225.8322.62−9.7980.97640.5291−0.48610.8325−0.22900.7041
1333.3018.3833.31−22.5570.24700.04350.04500.3308−0.23880.3423
1839.2821.7630.41−27.5762.56692.2256−0.33153.7146−1.47701.1300
2043.1623.5728.69−30.6583.38541.88550.34533.6785−1.94192.2214
2147.0923.9024.36−33.4292.91662.1435−0.45413.3274−1.70291.4478
2556.1525.4914.74−41.4830.80100.14020.18820.5905−0.42950.6431
3167.6719.2614.47−54.6954.64430.6678−0.56251.4243−2.45347.4102

[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) 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 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

[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 a−1 in northeastern India and 109 to 59 mm a−1 in northwestern India) at ∼40–45 Ma and of ∼45% (59–34 and 83–44 mm a−1) 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 28). 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 a−1, and that for the northeast corner of India decreased from 57 to 44 mm a−1 (Figure 6). Somewhat surprising is the suggestion of constant rates between ∼20 and 11 Ma and since 11 Ma. We 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 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 India-Eurasia convergence rate near 11 Ma, we found that the separate reconstructions do account for the 13 mm a−1 decrease in rates for northeastern India and the 10 mm a−1 decrease for northwestern India. For the former, India-Somalia accounts for 6 mm a−1 of the decrease, Somalia-Nubia accounts for 2 mm a−1, Nubia–North America accounts for 7 mm a−1, and North America-Eurasia would yield a 1 mm a−1 increase. Similarly, for northwestern India, the 10 mm a−1 decrease includes the following contributions: India-Somalia 3 mm a−1, Somalia-Nubia 1 mm a−1, Nubia-North America 6 mm a−1, 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 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 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 ρc of crust, ρm of mantle lithosphere, and ρa of asthenosphere, the change in mean elevation, Δh, associated with replacement of cold by warmer material, under isostatic balance is expressed by ρch + ρmL = ρch + ρa(L + Δh), where L is the thickness of mantle lithosphere and h is the thickness of the crust (Figure 9). Simplified, this gives

equation image
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 ΔT, hence by a mean density of ρaαΔT, leads to a surface elevation change, Δh, 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.

[21] Here, ρmρa = ρaα ΔT, where ΔT 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 α (≈3 × 10−5 °C−1) is the coefficient of thermal expansion. Thus, (1) becomes

equation image

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, ΔT = 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 Δh = 1 km.

[22] The change in potential energy per unit area, given by the area between the curves in Figure 9, is simply

equation image

Thus, with ρc = 2.8 × 103 kg m−3, ρm = 3.3 × 103 kg m−3, Δh = 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 m−1. 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 elevation, 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 ΔT, L and h, as well as for deviations from lithostatic pressure, can yield a range of values of both Δh and ΔPE 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 Δh 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 potassium-rich 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 high-resolution studies of relative movement between India and Somalia [Merkouriev and DeMets, 2006], between Somalia 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 38).

[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.

Acknowledgments

[27] 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.