slowing of india’s convergence with eurasia since 20 ma ... · since 20 ma and that the...

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Slowing of India’s convergence with Eurasia since 20 Ma and its implications for Tibetan mantle dynamics Peter Molnar 1 and Joann M. Stock 2 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 deforma- tion 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 contempora- neous 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 [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 paleoalti- tudes 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 recon- structions of India’s convergence with Eurasia, however, have shown no indication of a significant change in con- vergence 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 TECTONICS, VOL. 28, TC3001, doi:10.1029/2008TC002271, 2009 Click Here for Full Articl e 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 TC3001 1 of 11

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Page 1: Slowing of India’s convergence with Eurasia since 20 Ma ... · since 20 Ma and that the deceleration seems to have ended near 10 Ma. 2. Plate Reconstructions 2.1. Data, Methods,

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 theIndia and Eurasia plates, using recently revisedhistories of movement between India and Somaliaand between North America and Eurasia and of theopening of the East African Rift, show that India’sconvergence rate with Eurasia slowed by more than40% between 20 and 10 Ma. Much evidence suggeststhat beginning in that interval, the Tibetan Plateaugrew outward rapidly and that radially orientedcompressive strain in the area surrounding Tibetincreased. An abrupt increase in the mean elevationof the plateau provides a simple explanation for all ofthese changes. Elementary calculations show thatremoval of mantle lithosphere from beneath Tibet, orfrom just part of it, would lead to both a modestincrease in the mean elevation of the plateau of �1 kmand a substantial change in the balance of forces perunit 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; Greenet al., 2008; Rowley, 1996, 1998; Zhu et al., 2005], much ofeastern Asia seems to have undergone accelerated deforma-tion 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 ofTibet (Figure 1), poses the question of what process mightbe responsible for such widespread, roughly contempora-neous changes.[3] One explanation for the apparently rapid outward

growth of Tibet since �15 Ma and deformation of itssurroundings is that the plateau rose 1–2 km near 15 Ma;a high plateau will resist further crustal thickening, andcrustal shortening will migrate to the flanks of the plateau

[e.g., Molnar and Lyon-Caen, 1988]. In a summary ofevents occurring both on the plateau and surrounding it,Harrison et al. [1992] proposed that since the collisionbetween India and Eurasia, Tibet began to rise rapidly near20 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 at20 Ma, for Harrison et al. relied on rapid exhumation at thattime [Copeland et al., 1987; Richter et al., 1991], whichdoes not require elevation change, and in a state of isostasywould imply that the surface went down, not up. Thesearguments, however, do not contradict an abrupt rise ofTibet’s elevation at a later time, such as near 8 Ma [e.g.,Molnar et al., 1993]. In either case, two sets of observationshave cast doubt on the inference that Tibet rose as much as1–2 km since 20 Ma, or near �8 Ma.[4] First, essentially all attempts to estimate paleoalti-

tudes of Tibet, most of which apply to times before 11 Maand a couple to the period before 20 Ma, have yieldedestimates 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; Spiceret al., 2003]. As all estimates are uncertain by �1000 m, onecould argue that they permit a post-10 Ma change of thatmuch. Perhaps more importantly, all of these estimates applyto samples taken in the southern half of the plateau; thus,inferences of paleoaltitudes cannot eliminate the possibilitythat 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 achange in India’s rate of convergence with Eurasia during,or shortly after, the hypothesized rise of the plateau. Forvirtually all plausible density structures of crust and uppermantle, with an increased mean elevation a high plateaushould apply a larger force per unit length to the adjacentlower terrain [e.g., England and Houseman, 1989; Molnarand Lyon-Caen, 1988; Molnar and Tapponnier, 1978].Thus, an increased elevation of the plateau should haveresisted India’s penetration into Eurasia and slowed the rateof convergence between them, as seems to have happenedwith the rise of the Altiplano in the central Andes and theslowing of Nazca–South America convergence [Garzioneet al., 2006; Iaffaldano et al., 2006]. Essentially all recon-structions of India’s convergence with Eurasia, however,have shown no indication of a significant change in con-vergence rate since 20 Ma [e.g., Dewey et al., 1989; Molnarand Tapponnier, 1975; Molnar et al., 1993; Patriat andAchache, 1984]. Using improved reconstructions we showthat convergence between India and Eurasia did indeed slow

TECTONICS, VOL. 28, TC3001, doi:10.1029/2008TC002271, 2009ClickHere

for

FullArticle

1Department of Geological Sciences, and Cooperative Institute forResearch in Environmental Sciences, University of Colorado at Boulder,Boulder, Colorado, USA.

2Division of Geological and Planetary Sciences, California Institute ofTechnology, Pasadena, California, USA.

Copyright 2009 by the American Geophysical Union.0278-7407/09/2008TC002271$12.00

TC3001 1 of 11

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since 20 Ma and that the deceleration seems to have endednear �10 Ma.

2. Plate Reconstructions

2.1. Data, Methods, Uncertainties, and Sources of Error

[6] Several recent studies change our knowledge ofIndia’s convergence with Eurasia. Using a vast Russiandata set from the Indian Ocean, Merkouriev and DeMets[2006] presented a detailed history of relative movementbetween India and Somalia for the past 20 Ma. In particular,they showed a 30% decrease in rate between 20 and 11 Maand a change in direction between 11 and 9 Ma. For theperiod before 20 Ma, we rely on the reconstructions of Indiato Somalia given by Molnar et al. [1988].[7] The opening across the East African Rift system can

now be resolved with magnetic anomalies and fracturezones in the oceans that surround Africa. For the past few

million years, we rely on the angular velocity determined byHorner-Johnson et al. [2007], who revised earlier rotationparameters of Horner-Johnson et al. [2005]. The angularvelocity of Horner-Johnson et al. [2007], appropriate forthe past 3 Ma, agrees within uncertainties with that deter-mined from a decade of GPS measurements [Stamps et al.,2008]. With increasing data, however, it has become clearthat 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 alongthe Southwest Indian Ridge and in the Gulf of Aden andRed Sea [e.g., Horner-Johnson et al., 2007; Patriat et al.,2008]. The inclusion of small plates on the east side of therift improves the fits to both GPS and magnetic anomalydata, but their presence limits the length of the SouthwestIndian Ridge that can be used to constrain movementbetween Nubia and Somalia. Assuming that this ridge wasthe boundary of the Antarctic plate with either Nubia orSomalia, Royer et al. [2006] reconstructed the positions of

Figure 1

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Anomaly 5 to obtain rotation parameters for the relativemovements among those three plates. Their axis of rotationfor Somalia-Nubia lies just south of Africa, not far from theaxes found by Horner-Johnson et al. [2007] and Stamps etal. [2008]. Thus, at first glance, their rotation parametersseem sensible, but subsequent analysis shows that only ashort segment of the eastern half of the ridge formed bymovement between the Somalia and Antarctic plates. More-over, their angle of rotation called for more than 100 km ofopening 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 etal. [2002].[8] To reconstruct the central Atlantic, we used the

parameters given by McQuarrie et al. [2003] for Nubia toNorth America, which are based on work of Klitgord andSchouten [1986]. For North America to Eurasia, we reliedon the recent study by Merkouriev and DeMets [2008],which presented a detailed history of relative movementbetween North America and Eurasia for the past 20 Ma. Forearlier times, again we used the parameters given byMcQuarrie et al. [2003].[9] By combining the reconstructions of these four pairs

of the five plates, India, Somalia Nubia, North America, andEurasia, we calculated India’s position relative to Eurasia atdifferent times in the past (Figure 2). Readers should beaware of two steps that must be taken to combine thereconstructions, but that add uncertainty, if not error, tothe reconstructions.[10] First, Merkouriev and DeMets [2006, 2008] pre-

sented 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] deter-mined parameters for times different from those used byMerkouriev and DeMets [2006, 2008]. We present recon-structions for the magnetic reversals used byMerkouriev andDeMets [2006] (chrons 6no to 1o) with the time scale ofLourens et al. [2004], and for earlier times with the timescale of Cande and Kent [1995] (Figures 2–8 and Table 1).Use of such detailed time steps requires the interpolation ofrotations for two plate pairs (Somalia-Nubia and Nubia–North America) to obtain parameters for them for the sametimes. To do this we assumed that no change in rate occurredin the intervals between 3.6 and 11 Ma for Somalia-Nubia,and between each of 0 and 11 Ma and 11 and 20 Ma forNubia–North America. For these interpolated rotations, weused the uncertainty appropriate for that rotation closest intime to the interpolated time. Obviously, if there were achange in rate, our linear interpolation would add an error tothe rotation, but because these rotations are all small, thaterror should be no greater than the error that we assigned torotations for 11 or 20 Ma.[11] Second, what we have done for Somalia-Nubia

almost surely is wrong, for the very different locations ofrotation axes given by Horner-Johnson et al. [2007] andLemaux et al. [2002] imply an unlikely history of movementacross the East African Rift. That history calls for a phaseof largely strike-slip movement, of only modest amount(<20 km), between 11 and 3.6 Ma, followed by nearlypure divergence across the rift. We anticipate that continuedrevisions of the history of spreading along the SouthwestIndian 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 evidenceof rejuvenation or initiation of tectonic activity since �15 Ma. Within the plateau, this includes evidence for the onset ofnormal faulting [e.g., Blisniuk et al., 2001; Harrison et al., 1995; Pan and Kidd, 1992]. Surrounding the plateau, theevidence includes folding of the lithosphere south of India [Cochran, 1990; Gordon et al., 1990; Krishna et al., 2001], theemergence of the Kyrgyz Range on the north flank of the Tien Shan north of Tibet [Bullen et al., 2001, 2003], as well as anabrupt increase in sedimentation rate in intermontane basins in the Tien Shan [Abdrakhmatov et al., 2001], an interpretationof 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 [Petitand Deverchere, 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 theLiupan 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 of1500 m. Changes in deposition rates, clast sizes, and provenance of sediment in basins on the northeastern margin of Tibetsuggest accelerated subsidence in the basins and emergence of adjacent high terrain [e.g., Fang et al., 2003, 2005; Lease etal., 2007]. Elevation transects of cooling ages in the Shillong Plateau south of the eastern end of the Himalaya suggest anemergence of the plateau between 14 and 8 Ma [Clark and Bilham, 2008], or 15–9 Ma [Biswas et al., 2007], and anothersuch profile within the Nepal Himalaya indicates an abrupt change in cooling rate at 10 Ma [Wobus et al., 2008], not muchdifferent from the suggestion by Harrison et al. [1997] for rejuvenation of the Main Central Thrust in that region. Changesin sedimentary facies and deposition rates within the adjacent Siwalik Series suggest that exhumation of the LesserHimalaya 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 Mafrom the base of the Main Central Thrust Zone along the Sutlej Valley [Caddick et al., 2007; Vannay et al., 2004], and alsoin the Nepal Himalaya [e.g., Catlos et al., 2001; Kohn et al., 2001, 2004], are consistent with accelerated exhumation rate atthat time. In addition, though not shown, much paleoclimatic evidence has been associated with growth of the TibetanPlateau 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 Mawith revisions to the geomagnetic polarity time scale.

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will require revision of the earlier phase of movement in EastAfrica. As we show below, however, errors in the history ofmovement between Somalia and Nubia contribute errors tothe calculated history of movement between India andEurasia 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 occurredbefore 30 Ma in much of Ethiopia and surrounding regions[e.g., Chorowicz, 2005; Coulie et al., 2003; Kieffer et al.,2004; Smith, 1994], but rifting seems to have begun near10–11 Ma [Baker et al., 1972; Chernet et al., 1998;WoldeGabriel et al., 1990; Wolfenden et al. 2004]. Al-though there is some evidence for minor faulting in Ethiopiabefore 11 Ma [e.g., Bonini et al., 2005], most of the relative

movement between Nubia and Somalia seems to haveoccurred later. Moreover, the effect of an error in theinitiation of opening across the East African Rift Systemmanifests itself largely as an error in the direction that Indiaconverges with Eurasia, not in the rate.

2.2. Results: History of Convergence Between India andEurasia

[13] The rate of convergence between India and Eurasiahas slowed continually since collision near 45–50 Ma, butwith large drops in rates near the time of collision, espe-cially in western India, and since 20 Ma (Figures 2 and 3).Obviously, the sparse sampling of the history with magneticanomalies older than 20 Ma limits our resolution of preciseages of rate changes and of subtle changes at any time.Nevertheless, drops in convergence rates of 30–38% (118to 83 mm a�1 in northeastern India and 109 to 59 mm a�1 innorthwestern India) at �40–45 Ma and of �45% (59–34and 83–44 mm a�1) between 10 and 20 Ma (Figure 3)account for most of the change since collision. Whether thislatter decrease occurred gradually or in steps cannot beresolved, because the uncertainties in reconstructed posi-tions are too large, and we discuss each possibility.[14] Reconstructed positions of the northwest and north-

east corners of India since 20 Ma can be interpreted asshowing a decrease in the rate of convergence betweenIndia and Eurasia of �25% near �11 Ma (Figures 2–8).Not only did the direction that India moved toward Eurasiachange (Figures 4 and 5), but also the rate for the northwestcorner of India dropped from 44 to 34 mm a�1, and that forthe northeast corner of India decreased from 57 to 44 mma�1 (Figure 6). Somewhat surprising is the suggestion ofconstant rates between �20 and 11 Ma and since 11 Ma. We

Figure 2. Map showing reconstructed positions of twopoints on the India plate with respect to the Eurasia plate atdifferent times in the past. Present positions of points onIndia (white squares) are reconstructed to the black dots,with the corresponding 95% uncertainty ellipses. Numbersnext to points identify chrons with the following agesappropriate for the parts of the chrons that were used: chron6no, 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 outlineof Indian continental lithosphere is also reconstructed to itspositions at �47 Ma, close to the time of collision, and at68 Ma, before collision.

Figure 3. Distances of points in the northwestern andnorthwestern corners of India (Figure 2) at different times inthe past, showing average convergence rates duringdifferent intervals and a continual slowing of thatconvergence. A plot for the last 20 Ma is shown in Figure 6.

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assumed constant rates for the central Atlantic in thoseperiods, but divergence of India from Somalia slowedcontinually during that interval [Merkouriev and DeMets,2006]. Moreover, the rate of opening in the North Atlanticchanged 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 remainfixed with respect to all three plates as finite rotations accrue[McKenzie and Morgan, 1969]. Thus, from the perspectiveof at least one plate, but not necessarily the other two, ratesmust change with time. Accordingly, a changing ratebetween India and Somalia, but not between India andEurasia, is quite plausible.

[15] Rates of relative movement between all pairs ofplates changed since 20 Ma, and thus all contributed tothe �25% decrease in rate near 11 Ma. To isolate the effectof each plate pair on the rate change, we carried outmodified calculations holding the rate of that plate pairconstant, and we calculated the difference it would make tothe result. For India-Somalia, Nubia–North America, andNorth America–Eurasia, we carried out separate calcula-tions for the Anomaly 6no (19.722 Ma) reconstruction usingthe same axis as for Anomaly 5n.2o (11.040 Ma), and withthe angle scaled to give a constant angular speed since19.722 Ma consistent with that since 11.040 Ma. To isolatethe effect of the opening of the East African Rift, we

Figure 4. Large-scale map showing reconstructed positions of the northwestern point (in Figure 2) onthe India plate with respect to the Eurasia plate at different times since 20 Ma. Present positions of pointson 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 thatwere 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.

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Figure 5. Large-scale map showing reconstructed positions of the northeastern point (in Figure 2) onthe 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 andnorthwest corners of India from their reconstructed posi-tions relative to Eurasia at selected times in the past.Uncertainties are shown as 1s. Note the marked changenear 11 Ma and the �2 Ma uncertainty in the precise time ofchange.

Figure 7. Plot of reduced distance (distance – 44 km/Ma� age) versus age for a point in the northwestern corner ofIndia at different times since 50 Ma. Note the abrupt slowingsince �20 Ma and the essentially constant rate since�11 Ma.

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calculated reconstructions with no movement at all betweenSomalia and Nubia. Although the contributions of eachought not add linearly to account for the decrease in India-Eurasia convergence rate near 11 Ma, we found that theseparate 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 Americaaccounts for 7 mm a�1, and North America-Eurasia wouldyield a 1 mm a�1 increase. Similarly, for northwestern India,the 10 mm a�1 decrease includes the following contribu-tions: 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 decreasein rate between India and Somalia, and hence we weresurprised to learn that the change in rate near 10 Ma in thecentral Atlantic contributes more to the decrease in conver-gence rate between India and Eurasia. Note that the axis ofrotation for Somalia-Nubia lies southwest of India’s positionin a frame fixed to Eurasia, and that for North America liesin eastern Siberia, northeast of India. Thus, errors either inpositions of axes or in rotation angles have small effects onIndia’s north-northeastward convergence with Eurasia. Bycontrast, the axes of rotation for India to Somalia and forNubia to North America lie northwest of India (in Europeand in the North Atlantic, respectively), and errors in anglesof rotation map directly and proportionally into rates ofnorth-northeastward movement of India with respect toEurasia. Thus, the large contributions of slowing of spread-ing in both the Indian and central Atlantic Oceans to thedecrease in India’s rate of convergence toward Eurasiamakes sense.[17] Uncertainties in the reconstructed positions of India

at different times prohibit assigning a date to the slowdownwith an uncertainty as small as 1 or 2 Ma, or to the durationof the transition, especially if we allow for uncertainty due

Figure 8. Plot of reduced distance (distance – 57 km/Ma�age) versus age for a point in the northeastern corner ofIndia at different times since 50 Ma. Note the abruptslowing since �20 Ma and the essentially constant ratesince �11 Ma.

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 sXY

a sXZa sYY

a sYZa sZZ

a

1o 0.781 27.31 22.15 �0.354 0.0661 0.0101 0.0227 0.1042 �0.0151 0.04262y 1.778 33.54 23.13 �0.814 0.0469 �0.0212 0.0227 0.0415 �0.0200 0.03502An.1y 2.581 34.25 22.67 �1.146 0.0779 0.0171 0.0087 0.1075 �0.0219 0.04932An.3o 3.596 31.23 26.05 �1.705 0.0749 0.0134 0.0132 0.1057 �0.0179 0.05063n.1y 4.187 31.27 21.18 �1.891 0.1082 0.0555 0.0013 0.1677 �0.0309 0.06153n.4o 5.235 29.78 24.34 �2.440 0.0682 0.0095 0.0218 0.1010 �0.0215 0.04383An.1y 6.033 28.60 22.97 �2.700 0.4863 0.0075 �0.5655 0.1402 0.0089 0.87793An.2o 6.733 25.80 25.45 �3.035 0.0739 0.0160 0.0130 0.1156 �0.0260 0.05604n.1y 7.528 26.79 24.53 �3.402 0.1062 0.0830 0.0215 0.2666 �0.0175 0.06244n.2o 8.108 24.63 25.13 �3.711 0.1031 0.0644 0.0130 0.2007 �0.0411 0.06154Ay 8.769 24.26 24.95 �3.945 0.1021 0.0343 0.0099 0.1628 �0.0292 0.10344Ao 9.098 23.93 25.02 �4.150 0.0852 0.0051 0.0351 0.0737 �0.0298 0.08305n.1y 9.779 23.42 25.20 �4.399 0.1039 0.0289 0.0390 0.1414 �0.0194 0.08625n.2o 11.040 22.43 24.34 �4.800 0.1084 0.0701 0.0318 0.2396 �0.0146 0.06905An.2o 12.415 22.80 23.32 �5.534 0.1928 0.0330 0.0767 0.1367 �0.0514 0.18865ADo 14.581 23.33 22.62 �6.424 1.2751 �0.2095 1.5320 0.2512 �0.3882 2.03355Cn.1y 15.974 23.84 22.06 �7.365 0.2232 �0.0297 0.1809 0.1195 �0.0765 0.25855Dy 17.235 24.09 22.88 �8.109 0.4057 0.0548 �0.0334 0.1426 �0.1268 0.39745Ey 18.056 23.45 23.25 �8.586 0.2274 �0.0154 0.2141 0.1743 �0.0854 0.31166no 19.722 25.83 22.62 �9.798 0.9764 0.5291 �0.4861 0.8325 �0.2290 0.704113 33.30 18.38 33.31 �22.557 0.2470 0.0435 0.0450 0.3308 �0.2388 0.342318 39.28 21.76 30.41 �27.576 2.5669 2.2256 �0.3315 3.7146 �1.4770 1.130020 43.16 23.57 28.69 �30.658 3.3854 1.8855 0.3453 3.6785 �1.9419 2.221421 47.09 23.90 24.36 �33.429 2.9166 2.1435 �0.4541 3.3274 �1.7029 1.447825 56.15 25.49 14.74 �41.483 0.8010 0.1402 0.1882 0.5905 �0.4295 0.643131 67.67 19.26 14.47 �54.695 4.6443 0.6678 �0.5625 1.4243 �2.4534 7.4102

aIn units of �10�4 steradians.

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to interpolation of rates in the central Atlantic Ocean.Moreover, the change in rate centered on �20 Ma is greaterthan that since �20 Ma (Figure 3). Thus, we should alsoconsider the possibility that the rate decreased continuouslybetween 20 and 10 Ma. To do so, we normalize distances bysubtracting from them the average rate between �10 and20 Ma times age and plot those normalized (or reduced)distances versus age (Figures 7 and 8). If one extrapolatesaverage rates for the periods 33 to 20 Ma and 11 Ma to thepresent, the lines intersect at �17 Ma. Clearly, however, therate could have decreased gradually between 20 and 11 Ma,without an abrupt change. Plotted this way (Figures 7 and8), the data suggest two conclusions. First, the convergencerates of both northeastern and northwestern India withEurasia 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 suggestionthat 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 ratewith deformation surrounding Tibet and an outward growthof the plateau raises the question of what process could

effect both the slowing of convergence and the outwardgrowth of Tibet.[19] For plausible densities of crust and upper mantle, an

increase in the mean elevation of a region in isostaticequilibrium requires that work be done against gravity.Accordingly, the potential energy per unit area stored in acolumn of crust and mantle lithosphere will increase [e.g.,England and Houseman, 1989; Molnar and Lyon-Caen,1988]. Moreover, insofar as the horizontal compressivestress differs little from the vertical compressive stress insuch a column, and the vertical compressive stress is givensimply by the lithostatic pressure, then the change inpotential energy per unit area equals the change in thehorizontal force per unit length that the lithospheric columnapplies to its surroundings [Molnar and Lyon-Caen, 1988].[20] Removal of cold mantle lithosphere and replace-

ment by hotter asthenosphere will require that the surfacerise. For simple assumptions of constant densities rc ofcrust, rm of mantle lithosphere, and ra of asthenosphere,the change in mean elevation, Dh, associated with re-placement of cold by warmer material, under isostaticbalance is expressed by rch + rmL = rch + ra(L + Dh),where L is the thickness of mantle lithosphere and h is thethickness of the crust (Figure 9). Simplified, this gives

Dh ¼ L rm � rað Þ=ra ð1Þ

[21] Here, rm � ra = ra a DT, where DT is the averagechange in temperature across the thickness of lithospheredue to removal of its mantle part, and thus half of thechange in temperature at the base of the crust (if the entiremantle lithosphere is removed), and a (�3 � 10�5 �C�1) isthe coefficient of thermal expansion. Thus, (1) becomes

Dh ¼ LaDT ð2Þ

As examples, suppose that the temperature at the Mohowere initially 700�C (or 900�C) and with removal of mostof the mantle lithosphere it became 1300�C. Thus, DT =300�C (or 200�C). For an initial thickness of mantlelithosphere of L = 110 km (or 160 km), as might beexpected following horizontal shortening of Tibetan litho-sphere, 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 Dhgðrchþ rmL=2Þ ð3Þ

Thus, with rc = 2.8 � 103 kg m�3, rm = 3.3 � 103 kg m�3,Dh = 1 km, and h = 65 km, the increase in potential energyper unit area, which also equals the increase in force per unitlength that Tibet should apply to the India plate, would be4.4 (or 3.6) � 1012 N m�1. Such a force per unit length issomewhat greater than that applied by a hot column of massat 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 initiallyrelatively thick crust and mantle lithosphere, removal ofmantle lithosphere leads to a small change in mean eleva-

Figure 9. Lithostatic pressure beneath two high regionswith different thicknesses of mantle lithosphere beneaththem. At any depth, lithostatic pressure increases downwardproportionally to the product of density and gravity.Replacement of mantle lithosphere with material that ishotter on average by DT, hence by a mean density ofraaDT, leads to a surface elevation change, Dh, given by(1). The area of the shaded region gives, by (3), the increasein potential energy per unit area, and therefore the increasein the force per unit area that the high terrain andsurrounding lowlands apply to one another.

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tion, compared to the mean elevation of Tibet itself, but thatsmall change nevertheless can profoundly alter the balanceof forces affecting convergence between India and Eurasia.Allowance for other values of DT, L and h, as well as fordeviations from lithostatic pressure, can yield a range ofvalues of both Dh and DPE that differ by as much as afactor of two from those given above. Obviously, ignoranceof all of the requisite quantities and of constraints onDh makes it difficult at present to refute the suggestionthat mantle lithosphere was removed from northern Tibet, ifnot 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, usingpaleoaltimetry, and second, by analyses of magmatic rockand entrained mantle xenoliths to look for changes inmagma sources and pressure-temperature conditions in themantle. Turner et al. [1993, 1996] argued that the highpotassium content and high 87Sr/86Sr ratios in basaltic lavaserupted in northern Tibet since 13 Ma implied that litho-sphere had melted. They use these facts to infer that at leastthe lower part of the mantle lithosphere had been removed,so that hotter asthenosphere brought into contact withmantle lithosphere enabled the latter to melt. From phaseequilibrium experiments on melted lavas from northernTibet, Holbig and Grove [2008] also concluded that thesource was metasomatized mantle in the spinel and garnetstability fields that was heated by close proximity to hotterasthenosphere. Others, however, interpret these potassium-rich lavas to be derived from melting of subducted sedimentor continental crust [e.g., Arnaud et al., 1992; Guo et al.,2006]. To the best of our knowledge, mantle xenolithssuitable for resolving this issue, and for further constrainingthe mantle dynamics, have not yet been found.

4. Conclusions

[24] Plate reconstructions that incorporate recent high-resolution studies of relative movement between India andSomalia [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 andEurasia [Merkouriev and DeMets, 2008] call for a markedslowdown in the convergence between India and Eurasiasince 20 Ma (Figures 2, 7, and 8). The decrease was greaterthan 40%, but precisely when that decrease occurred cannotyet be resolved. If rates before 20 Ma and since 11 Ma areextrapolated, they intersect near 17 Ma. Alternatively, therate decreased continuously between 20 and �10 Ma, afterwhich it seems to have been constant (Figures 3–8).[25] In either case, the change in rate occurred at essen-

tially the same time that deformation within and surround-ing Tibet seems to have increased (Figure 1). This needs tobe explained by an additional short-term event, not justprogressive plate convergence. One possibility is that some-how the crust and upper mantle beneath Tibet suddenlyexerted an increased outward force per unit length onTibet’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, asone might expect after tens of millions of years of horizontalshortening, such removal can yield a relatively small changein mean elevation (�1 km), but a large change in the forceper unit length that the plateau applies to its surroundings.That change can be comparable to the force per unit lengththat the column beneath mid-ocean ridges applies to oldlithosphere. Thus, although still deservedly controversial,the idea that mantle lithosphere was removed from beneathTibet since �20 Ma gains some support from the change inconvergence rate between India and Eurasia.

[27] Acknowledgments. One of us was justifiably provoked byMarin Clark’s question in 2003, ‘‘Wouldn’t you expect a change in platemotions at 8 Ma’’? C. DeMets both offered useful suggestions forimproving the manuscript and supplied us with preprints in advance ofpublication. This research was supported in part by the National ScienceFoundation under grants EAR-0440004, EAR 0507330, EAR 0636092, andOPP-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, CO80309-0399, USA. ([email protected])

J. M. Stock, Division of Geological and PlanetarySciences, California Institute of Technology, Pasadena,CA 91125, USA.

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