Late Quaternary and present-day rates of slip along the Altyn Tagh Fault, northern margin of the Tibetan Plateau



[1] Both Global Positioning System (GPS) measurements and studies of Late Quaternary faulting are consistent with a slip rate of ∼10 mm/yr along the central segment of the Altyn Tagh Fault and a systematic decrease in that rate toward the eastern end of the fault. Dates of terraces above and below laterally offset terrace risers yield bounds on Quaternary slip rates that range from those that agree with GPS measurements to values as much as three times faster. We argue that offset terrace risers that are protected by topography upstream of them are more closely dated by the age of the upper terrace than by that of the lower terrace. In some cases, valleys upstream of the fault have been incised into bedrock, and few if any terrace risers can be seen within the valleys. Such streams debouch onto alluviated floodplains or fans that become incised, presumably during climate changes, to create terrace risers. The terrace risers are then displaced so that they lie downslope from bedrock ridges on the upstream side of the fault, and thus the risers become protected from further incision. In such cases, dates of upper terraces should more closely approximate the ages of the risers than those of lower terraces. Such dates yield slip rates of ∼10 mm/yr in the central segment of the fault and decreasing rates eastward. Although we cannot with certainty rule out the higher slip rates along the Altyn Tagh Fault, our analysis does show that viable interpretations consistent with GPS measurements are more likely, at least along some segments of the fault. Not only do these rates support the view that the Tibetan Plateau deforms internally by slip on a distributed network of faults in the shallow brittle crust, and hence behaves as a continuum at depth, but the gradual decrease toward the east also shows that the Altyn Tagh Fault does not separate two effectively rigid lithospheric plates. Correspondingly, the relatively low slip rate and the eastward decrease in slip rate suggest that the Altyn Tagh Fault does not transfer a significant portion of the convergence between India and Asia into northeastward extrusion of the Tibetan Plateau. Thus, large-scale extrusion of crustal material in India's path into Eurasia seems to be limited largely to the confines of the Tibetan Plateau.

1. Introduction

[2] Because eastern Asia now serves as the prototype for large-scale intracontinental deformation, how the Asian continent deforms in response to the collision between the India and Eurasia plates influences how we understand the dynamics of continental deformation in general. Two influential end-member views of continental deformation have been debated during the last three decades: (1) deformation occurs primarily by regionally distributed (in the shallow brittle crust), essentially continuous deformation (at depth) [e.g., England and Houseman, 1986; England and McKenzie, 1982; Molnar and Tapponnier, 1975]; or (2) the rules of plate tectonics can be applied to intracontinental deformation with major faults separating a small number of relatively rigid blocks [e.g., Avouac and Tapponnier, 1993; Dewey et al., 1973; McKenzie, 1977; Meade, 2007; Peltzer and Saucier, 1996; Tapponnier et al., 1986, 2001; Thatcher, 2007]. In the former view applied to eastern Asia, strike-slip faults separate deforming blocks, and rates of slip are not large (≤∼10 mm/yr), so that they are comparable with rates of deformation across regions undergoing more distributed strain, such as within the Tibetan plateau. In the latter view, slip rates on major faults not only can be large (∼20–30 mm/yr), but also should be constant along the faults [e.g., van der Woerd et al., 2002], so that deformation of regions between major faults accommodates only a small fraction of the displacement of India with respect to Eurasia. The Altyn Tagh Fault, arguably the most important strike-slip fault in eastern Asia, plays a key role in testing these views; in the latter view, it serves as a transform fault that spans the lithosphere and separates lithospheric plates. Tapponnier et al. [2001] and others have used fast rates, in the range of 20–30 mm/yr, to argue for rigid-block extrusion, but others [e.g., England and Molnar, 2005] suggest that slow rates, about ∼10 mm/yr or slower, are consistent with continuous deformation. (We defer to Appendix A a discussion of the compromise view that an optimal description of the kinematics exploits rigid blocks with dimensions of hundreds of kilometers.)

[3] Global Positioning System (GPS) measurements have been made along the central and eastern parts of the Altyn Tagh Fault during the last decade, and different studies report similar slip rates for the fault. Bendick et al. [2000] first reported a left-lateral slip rate of 9 ± 5 mm/yr near 90°E, which Wallace et al. [2004] later confirmed using a longer time series. Shen et al. [2001] found a similar rate of 9 ± 2 mm/yr. Zhang et al. [2004] reported lower rates east of 93°E: 5.6 ± 1.6 mm/yr at 90°E and 5.0 ± 2.0 mm/yr at 95°E, consistent with those reported earlier by Chen et al. [2000]. From the same data, Meade [2007] inferred a slip rate of 5–6 mm/yr on the central segment of the Altyn Tagh Fault. Relying on one point to define the western end of a block that encompasses the Qaidam Basin, Thatcher [2007] inferred a rate of 8–9 mm/yr.

[4] A recent study of a post-middle Miocene offset supports the rate based on GPS measurements, and estimates of the total offset can be interpreted to support such a rate. In particular, Yue et al. [2004] inferred 165 km of slip since 16.4 Ma, yielding an average rate of 10 mm/yr. Beginning with the work of Ritts and Biffi [2000], most estimates of the total offset on the fault range between 350 and 400 km [e.g., Cowgill et al., 2003; Gehrels et al., 2003a, 2003b; Ritts et al., 2004; Yin et al., 2002; Yue et al., 2001, 2004, 2005]. Most also agree that the fault became active shortly after the collision between India and Eurasia at 45–50 Ma, if not before it. Yin et al. [2002] suggested an average rate since 49 Ma of 9 ± 2 mm/yr, and Yue et al. [2001] suggested a rate of 12–16 mm/yr since late Oligocene time. More recently, however, Ritts et al. [2004] and Yue et al. [2005] pointed out that the combination of their 16.4-Ma offset and 350–400 km since only ∼23 Ma would require rapid slip between 23 and 16.4 Ma. In any case, the GPS rate is consistent with the rate that they infer since middle Miocene time.

[5] Although one geological study carried out in the 1980s reported a Holocene slip rate of only ∼3 mm/yr [Xinjiang Seismological Bureau, 1992], geologic investigations of Quaternary offsets along the Altyn Tagh Fault, both those for which the age of offset features was assumed to be ∼10 ka [e.g., Molnar et al., 1987; Peltzer et al., 1989] and those that relied on cosmogenic, radiocarbon, or thermoluminescence (TL) dating of offset Quaternary landforms, have reported a range of 20–30 mm/yr averaged over several thousand years [Mériaux et al., 2004, 2005; Peltzer et al., 1989; van der Woerd et al., 2002; Xu et al., 2005]. These values suggest that slip on the Altyn Tagh Fault accommodates nearly as much of the Indo-Asian collision as does the Himalaya.

[6] In this paper, first we use GPS data from the Crustal Movement Observation Network of China (CMONOC) to determine decadal slip rates at different localities along the Altyn Tagh Fault. Then, we reinterpret geological slip rates based on the data presented in the published literature, augmented in some cases with satellite imagery available from Google maps http://www.google.com/maps), to examine whether or not the decadal geodetic rates are consistent with inferred long-term geological rates.

2. Slip Rates Along the Altyn Tagh Fault Constrained by GPS Measurements

[7] We rely on GPS measurements from CMONOC, which were collected from 1998 to 2004 and include those from 25 continuously recording stations in China, 56 annually observed stations with an occupation of at least 7 days (∼168 hours of data collection) in each survey, and 961 regional stations observed three times in 1999, 2001, and 2003 with an occupation of at least 3 days (∼72 hours of data collection) in each survey. Additional measurements were made after the 2001 Kunlun earthquake in northeastern part of the Tibetan Plateau south of the Altyn Tagh Faults in 2002, 2003, and 2004. Shen et al. [2000, 2001, 2005] and Zhang et al. [2004] described the procedures used to process these data. To show the resulting magnitude and variations in slip along the Altyn Tagh Fault, we rotated GPS velocities to a reference frame in which the essentially rigid Tarim Basin is held fixed (Figure 1), and we show velocities of control points surrounding the Altyn Tagh Fault in the northern Tibetan Plateau, Tarim basin, Gobi Alashan desert, and the Qilianshan.

Figure 1.

(a) Map of active faults (black lines) and GPS velocities (blue and red arrows) superimposed on the topography of the northern Tibetan Plateau and Tarim basin. Blue arrows show GPS velocities for relative motion with respect to the Tarim block, and red arrows are for control points in the basin. Rectangles show locations of velocity profiles discussed in the text and shown in Figure 2. Profiles E-E′ and F-F′ are shown in Figure 23. (b) Map shows locations of GPS stations with names mentioned in the text. Active faults are taken from “Map of active faults in China” by Deng et al. [2003].

[8] Left-lateral slip on the Altyn Tagh Fault cannot be described by a single slip rate, because, as Figure 1 clearly shows, the GPS velocities for control points south of the fault decrease eastward. To show how the slip rate varies with position along the fault, we constructed four profiles across the fault (Figure 1), and we project N75°E components of each control point onto them (Figure 2).

Figure 2.

Left-lateral slip rates of the Altyn Tagh Fault along the four profiles across the fault. Locations of each profile are shown in Figure 1. Thick black lines in each panel approximate the location of the Altyn Tagh Fault. All of the GPS velocities (N75°E components) are relative to a fixed Tarim block. Red dots are GPS velocities in Tarim basin, and blue dots are those located in the northern Tibetan plateau. Curves show theoretical velocities (arctangent) across the fault assuming elastic deformation due an infinitely long dislocation extending to infinite depth below a fixed locking depth [e.g., Savage and Burford, 1970]. Green lines represent locking depth of 15 km, pink lines represent −30 km, and black line represents −10 km. Note that scales differ in the four panels.

[9] Profile A-A′ crosses the eastern end of the Altyn Tagh Fault, where there are three control points south of the fault and six north of it in the eastern Tarim Basin (Figure 2a). The N75°E components for the stations in Tarim Basin cluster within 0 ± 1.5 mm/yr range, consistent with negligible deformation of the basin. The three control points south of the fault show a southward increase in the component of velocity parallel to the Altyn Tagh Fault. The southernmost point (GA13), ∼100 km south of the fault and with a velocity of 3.9 ± 1.8 mm/yr, sets upper bound for the profile, which we take to define the left-lateral slip rate across the eastern end of the fault to be 3.9 ± 2.3 mm/yr (Figure 2a).

[10] Profile B-B′ spans the fault between 93°E and 95°E (Figure 1). Velocities of stations north of the fault in the Tarim block cluster with a mean of −0.7 ± 1.5 mm/yr (Figure 2b). The N75°E components of velocity of the stations south of the fault also increase southward except the southernmost (G169). If we took station G170 as the upper bound in this profile, the resultant left-lateral slip rate along this profile would be 8.8 ± 2.3 mm/yr (Figure 2b).

[11] Profile C-C′ is located at the same region as that of Bendick et al. [2000] and Wallace et al. [2004]. Velocity components in the Tarim block give an average of −0.5 ± 2.0 mm/yr (Figure 2c). Those for control points south of the Altyn Tagh Fault increase to 11.4 ± 2.6 mm/yr to the southernmost station Y196 (Figure 2c). Using these data, we obtain a left-lateral slip rate along this profile of 11.9 ± 3.3 mm/yr, which is insignificantly larger than 9 ± 5 mm/yr by Bendick et al. and 9 ± 4 mm/yr by Wallace et al. [2004]. Moreover, the poor fit to points G171 and JB32 lend support to a rate lower than 11 mm/yr (Figure 2c).

[12] West of 90°E, there are no GPS control points south of and close to the Altyn Tagh Fault (Figure 1). The nearest, J043 east of Shiquanhe [Shen et al., 2001; Wang et al., 2001], and J036 in the southern Tibetan Plateau, lie 450 and 560 km, respectively, from the fault. The velocity difference between these two and those in the Tarim Basin north of the fault does not represent the slip rate on the Altyn Tagh Fault, because the Altyn Tagh Fault is not the only fault between them [e.g., Avouac and Tapponnier, 1993; Molnar and Tapponnier, 1978; Taylor et al., 2003], but this velocity difference sets the upper limit for the slip rate to be less than ∼20 mm/yr.

[13] GPS data presented above corroborate slip rates reported in previous geodetic studies [Bendick et al., 2000; Chen et al., 2000; Shen et al., 2001; Wang et al., 2001; Zhang et al., 2004; Wallace et al., 2004]. Our data also reveal a gradual rather than stepwise eastward decrease of left-lateral slip rates along the Altyn Tagh Fault, from <∼12 mm/yr to about 4 mm/yr, rather than from ∼26 to 17 mm/yr [Mériaux et al., 2005], along the eastern 1400 km of the fault.

[14] Elastic deformation, associated with locking of the brittle, upper parts of the faults [e.g., Meade and Hager, 2005], may bias these slip rate estimations, but simple dislocation models show that ∼70% and 80% of elastic deformation takes place within 30 km of a strike-slip fault locked at 15 and 10 km depth, respectively (Figure 2) [e.g., Savage and Burford, 1970]. Since all of the cross-sections span distances of at least 100 km, if not more, on both sides of the fault, the impact of elastic deformation to the calculated slip rates should be negligible. Simple dislocation models for various locking depths show different behavior of the northern Tibetan Plateau south of the Altyn Tagh Fault from that of Tarim basin north of it. Shallow locking depths such as 10 or 15 km commonly fit stations in Tarim basin well suggesting it is indeed behaves as a rigid block. Both shallow locking and deep locking depths (for example, 30 km) do not fit the stations in the Tibetan Plateau very well, which in turn suggest that the elastic dislocation model may not apply to it because the plateau may not be modeled as elastic body because other faults may be present.

3. Relationships Between Strath Terraces and the Evolution of Offset Terrace Risers

[15] Offset terrace risers have commonly been used to determine long-term slip rates along a strike-slip faults [e.g., Sieh and Jahns, 1984; Weldon and Sieh, 1985]. Uncertainties arise, however, from interpretations of the date when the riser began to accumulate displacement. According to modern geomorphic understanding [e.g., Bull, 1991; Hancock and Anderson, 2002; Sklar and Dietrich, 2004], during climate cycles when discharge is high enough that rivers can transport more sediment than is supplied to a reach, the river can incise rapidly. Conversely, when sediment loads are too large, rivers will deposit sediment, but during high discharge events, rivers can widen their floodplains by lateral erosion. Climate affects both the discharge of water and the sediment supply from upstream and, as a result, variations in climate lead to alternating periods of incision and of widening, perhaps with minor deposition. Different views of how climate writes a signature on stream terraces and terrace risers depend on how one views these different parts of the cycle. Moreover, it is not yet obvious that periods of incision, widening, or deposition should occur at the same time everywhere, both because local climates need not vary synchronously with the global average, and because sediment loads from different environments upstream of a reach should respond differently to changes in climate.

[16] In one end-member view, erosion of the terrace riser occurs continuously during fluvial occupation of the floodplain that eventually is abandoned to form the terrace tread adjacent to and below the riser [e.g., van der Woerd et al., 2002]. Thus, displacement of the riser does not accumulate until the adjacent lower terrace forms by incision and abandonment of the floodplain below the riser. By using this logic, Mériaux et al. [2004, 2005] reported slip rates on the Altyn Tagh Fault to be 26.9 ± 6.9 mm/yr near 86°E and 17.8 ± 3.6 mm/yr near 94°E. This condition applies where rivers erode but do not deposit sediment. It is favored where slip on the fault displaces terraces into the path of the active stream [e.g., Kirby et al., 2007]. This view may not apply, however, where topography along a fault can protect the terrace riser from attack by a stream. Where topography along the fault protects the terrace downstream of the fault, as slip occurs the river must turn sharply around the topography for it to erode the riser. Correspondingly, for a stream to constantly erode a terrace riser so that it cannot accumulate an offset, the river must widen its floodplain both upstream and downstream from the fault, and floodplains and terraces upstream of the fault should become increasingly wider with time. In most cases along the Altyn Tagh Fault, however, upstream terraces are much narrower than downstream terraces.

[17] Note also that the assumption that terrace risers form when rivers incise the floodplains that lay adjacent to them cannot be applied to stream channels that have been offset, but for which no distinct lower terrace has formed yet. Applying this logic to the banks of such offset stream channels and banks, and hence treating those offset stream banks as terrace risers, would require dividing the offset of the stream and its banks by a zero age, which would yield an infinite slip rate.

[18] In the alternative view, lateral erosion of a floodplain occurs preferentially on one side of the stream, the side that is offset into the path of the stream (Figure 3). The downstream floodplain can widen as slip occurs, because part of it becomes protected by topography at the fault upstream of it, but the upstream floodplain can remain narrow. Figure 3a shows simple topography of a river system immediately after incision a floodplain, so that abandonment of part of that floodplain leaves a terrace, T2. Subsequent left-lateral offset on the fault moves one side of the downstream terrace into the path of the active stream and hence subjects it to erosion; in the case in Figure 3b, the downstream terrace to the left of the stream is eroded, as indicated in Figure 3c, and as van der Woerd et al. [2002] also supposed. Consequent lateral erosion and deposition may take place after abandonment of the higher terrace such as T2, for example (Figure 3c). This process may also result in minor sedimentary aggradation on the surface of newly formed riverbed (Figures 3c and 3d). When incision occurs again, the active floodplain again will be abandoned to form T1 (Figures 3e and 3f). By contrast, to the right of the stream in Figure 3, left-lateral displacement causes the upstream terrace to shield the terrace riser downstream of the fault from lateral erosion by the river, so that offset of the terrace riser accumulates beginning when T2 forms. The date of abandonment of the upper terrace, T2 in Figure 3, not only places an upper bound on the age of the riser, T2/T1, but also approximates well the age itself.

Figure 3.

Left-lateral strike-slip offset and evolution of strath terraces of a river flowing toward the reader. In Figure 3a, the river has just incised into its floodplain, and the remaining part of that floodplain has been abandoned to form the terrace T2. In Figure 3b, subsequent left-lateral slip on the fault has offset both risers. This slip displaces the downstream terrace on the left side so that it lies in the path of the river, which in turn subjects the downstream riser to erosion. The downstream terrace on the right side and its riser, however, may become protected by topography on the upstream side of the fault. In Figure 3c, lateral erosion on the left side has destroyed evidence of offset of the riser, and some subsequent aggradation, shown by the light gray body, has occurred on the active streambed and floodplain. Because in this example displacement enables the upstream terrace on the right side of the fault to shield the terrace riser downstream of it from lateral erosion by the river, offset can accumulate on the right side of the river immediately after the stream incises to form terrace T2. In Figure 3d, a cross-section across the right side of downstream terrace shows sedimentary accumulation, Td1, on the floodplain that will become terrace T1 when it is incised; thus, in this case, the lower strath terrace becomes buried. In Figure 3e, further incision forms the new terrace T1. Slip continues to accumulate on the right side of downstream channel, but as shown here, the T2/T1 riser to the left of the stream has been eroded by the river as it was displaced by the fault, and the T1/T0 riser on the left side has continued to erode, as van der Woerd et al. [2002] assumed. In Figure 3f, a cross-section through the strath terraces shows is new sediment aggradation, Td0, after the incision that formed terrace T1.

[19] It seems likely that in some situations the age of the lower terrace closely approximates the age of a riser below it, such as with the deep incision of terraces along the western Kunlun fault studied by Li et al. [2005]. In others, the onset of the sedimentary aggradation on lower terrace tread could also approximate the age of a riser above it (Figures 3d and 3f). One to a few meters of stream gravel overlie nearly all strath terraces, for only rare large floods can remove such sediment to expose bedrock. Surely on some terraces, such gravel accumulated in the last major flood that occurred only a short time before the river incised both the previous gravel cover and the underlying bedrock strath to abandon it to form a terrace. In others, however, the gravel may have accumulated slowly over the entire duration that the terrace served as an active floodplain. Thus, in some situations, the onset of gravel deposition could also date the age of the terrace riser above that gravel.

[20] As noted above, whether the age of the upper or of the lower terrace more closely approximates the age of the riser will depend upon how the stream flowing over the floodplain that becomes the lower terrace alters the riser, and therefore at least in part on whether the offset riser moves into the path of the active stream or becomes shielded from it. As Mériaux et al. [2004, 2005] stated, the age of the riser should be neither greater than the age of the upper terrace nor smaller than the age of the lower terrace. In an ideal situation, the ages of both would be sufficiently similar that they would place nearly equal upper and lower bounds on the slip rate, as Kirby et al. [2007], Li et al. [2005], and van der Woerd et al. [2002] found for different parts of the Kunlun fault. In many regions, however, the ages of the two terraces are so different that the bounds that they place on the slip rate are too large to be useful.

[21] In an effort to resolve the question of which terrace should be used to define the age of an adjacent terrace riser, Cowgill [2007] suggested six criteria. Most depend on detailed knowledge of the topography and field relationships and hence cannot be applied to regions for which we rely only on published data or remotely sensed images. One of his criteria, however, can be applied to such regions. Cowgill considered an implication of assuming that the offset of a terrace riser dates from the abandonment of the terrace tread beneath the riser. He noted that the amount of offset of the youngest riser should equal or exceed the sum of the offset of the present-day channel plus the width of the present-day floodplain. He applied this logic to one of the sites considered by Mériaux et al. [2004], Cherchen He, which we discuss below, to argue that the age of the lower terrace could not define the terrace riser above it, and hence that the slip rate given by Mériaux et al. is too high.

[22] A corollary to this criterion should apply where rivers, gullies, or valleys emanate from steep terrain and then cross the fault at a break in slope. Upstream channels commonly are trapped in narrow gorges through bedrock, which commonly is more resistant to erosion than the poorly indurated alluvial material downstream of the fault (Figure 4a). In many such situations, river terraces are found only on the downstream side of the fault. The fault trace not only presents itself as a geomorphically linear feature, but it also separates more resistant bedrock upstream of the fault from less resistant alluvial material downstream of it. In a reference frame fixed to the upstream side of the fault, the horizontal position of the valley is trapped in a narrow slot, while material on the downstream flank of the fault progressively moves into the path of the stream and then past it. If the stream incises only during intermittent intervals, as will be the case if abrupt climate changes affect incision rates, then river terraces should be preserved on only one side of the river, the side that is protected by bedrock upstream of it along the fault (Figure 4). Terraces that form on the other side would be continually destroyed as slip on the fault brought them into the path of the river. Moreover, the confinement of the channel upstream of the fault should restrict its downstream path to a narrow zone, at least where the stream crosses the fault.

Figure 4.

Conceptual models of river emanating into a gentle dipping floodplain. (a) Upstream channel is shown trapped in a narrow gorge of bedrock and then debouches onto floodplain below the fault. As the river abruptly incises into floodplain, abandonment forms a terrace named T2. (b) Displacement moves one side of the riser below T2 away from the upstream thalweg where it is protected by the topography of the upstream shoulder. Slip also moves the other side of the terrace T2 into the thalweg and subjects it to erosion. (c) Later, the river incises the downstream floodplain to abandon terrace tread T1. Displacement of T2/T1 should begin to occur immediately after incision of the floodplain led to its abandonment and the formation of terrace T2; hence the age of T2 would be defined when the T2/T1 riser formed, and similarly, that of T1 would define the age of the T1/T0 riser. (d) During subsequent slip on the fault, one side of riser moves away from and the other moves toward the thalweg of the river downstream of the fault. If the river continued to erode the riser (between T2 and floodplain) that moves away from the thalweg, the separation of the riser to the shoulder of upstream valley would be larger than the displacement on the fault, but this would require that the river undergo an abrupt change in course at the fault. (e) River incision occurs to abandon previous thalweg and floodplain to form a new terrace T1 and new thalweg. The separation between upstream riser shoulder and terrace riser T2/T1 would be larger than fault displacement in this case. These latter conditions in Figures 4d and 4e require that the river fortuitously bend at the fault, a condition that clearly cannot continue for long geologic durations.

[23] To understand the relationship of ages of terraces to separations between terrace risers on the downstream side of the fault to the narrow gorges upstream of them, let us consider two possible sequences of events in such a setting (Figure 4).

[24] Suppose that as a river debouches below the fault, the stream has maintained a wide floodplain, and then it incises into that floodplain to leave a higher surface, which we call T2 for now (Figure 4a). As slip takes place, the downstream thalweg is displaced toward the right side of the river gorge (in the coordinates of Figure 4). One of the risers below T2 would be protected by the topography of upstream shoulder. Slip also moves the other side of the terrace T2 into the course of upstream thalweg to subject to erosion (Figure 4b). Subsequent river incision abandons the downstream floodplain to form terrace tread T1 and terrace riser T2/T1 (Figure 4c). Displacement of T2/T1 should begin to occur immediately after incision of the floodplain led to its abandonment and the formation of terrace T2; hence the age of T2 would define when the T2/T1 riser formed.

[25] Suppose instead that as slip occurs, and as one edge of the new channel downstream of the fault is displaced away from the thalweg of the upstream channel, the river continued to erode edge of the terrace. The apparent offset of the valley wall would increase (Figure 4d). As the other edge of the valley downstream of the fault moved into the path of the river, it would erode, and the floodplain downstream of the fault would widen. Then when the river incises this floodplain to leave another terrace T1 (Figure 4e), the terrace riser T2/T1 will have become separated from the thalweg of the valley upstream of the fault by a larger amount than slip on the fault can account for; its apparent offset would overestimate the slip on the fault. For this to occur, such widening would require that the river turn an abrupt corner where it debouches from the higher terrain on the upstream side of the fault (Figure 4d). Such an effect might occur in some cases, but clearly the rivers could not continue to bend sharply at the fault and continue to refresh the terrace riser as it moves far from the upstream channel.

[26] If the river does not erode the edge that has been protected by the bedrock upstream shoulder, the downstream terrace risers and the upstream shoulder define the displacement since the abandon time of terrace tread above the riser (Figures 4b and 4c). Similar to the arguments that we made on Figure 3, the age of abandon of terrace tread above the riser more approximates the onset of the terrace riser. In the discussion below, we adopt the view that where streams debouch from narrow channels in bedrock onto wide floodplains or fans, the age of the upper terrace more closely approximates the age of the riser below it than does the age of the lower terrace.

4. Examples of Late Quaternary Offsets

[27] Mériaux et al. [2004] obtained a slip rate of 26.9 ± 6.9 mm/yr based on studies at two sites on the central section of the Altyn Tagh Fault (Figure 5). They also studied three sites on the eastern section of the fault (Figure 5) and reported a rate of 17.8 ± 3.6 mm/yr slip rate [Mériaux et al., 2005]. In addition, Xu et al. [2005] reported, in less detail, offsets and ages from eight other sites along the fault. Using the logic discussed in the previous section, we reexamine their evidence for published slip rates along the Altyn Tagh Fault.

Figure 5.

Map of the Altyn Tagh Fault showing approximate places of GPS profiles and the locations of sites studied by Mériaux et al. [2004, 2005] (black solid bars with number adjacent to them) and Xu et al. [2005] (circles with letters next to them). Faults are from Xu et al. [2005]. Numbers from 1 to 5 denote Cherchen He, Sulamu Tagh, Old Aksay, Huermo Bulak, and Bang Guo Ba sites, respectively. Letters A to H indicate Dalaku'an, Qinbulak, Huermo Bulak, Xishui'er, Luchaowan, Shibaochen, Niuyagou, and Hongliugou sites, respectively. Polygons show approximate areas covered by GPS profiles A-A′, B-B′, C-C′, and D-D′ shown in Figure 1.

[28] “Dalaku'an site” (37°09.433′N, 85°08.009′E, site A in Figure 5). This site is located in the western part of the Altyn Tagh Fault, where two fault strands overlap to form a small step-over (Figure 6). The Dalaku'an River debouches from a bedrock range onto an alluvial floodplain north of the fault. A hill has formed about 800 m north of the fault on the eastern side of Dalaku'an River, and a flat valley between the hill and the fault has been slightly incised by surface runoff and small streams. The left-lateral displacement of rivers and terraces is unlikely to have been affected by vertical displacement along the fault or other geomorphological features.

Figure 6.

(a) Geomorphological map and satellite image draped onto a (b) digital elevation map of the Dalaku'an site (37°09.433′N, 85°08.009′E, site A in Figure 5). (a) The geomorphological map shows the locations of terraces and displacements of terrace risers of the Dalaku'an River valley [from Xu et al., 2005]. (b) View down onto the Dalaku'an River valley where it crosses the Altyn Tagh Fault. White arrows mark fault traces noted by Xu et al. [2005], and the fan symbol shows the approximate view of the image in Figure 7.

[29] Xu et al. [2005] described faulting where the Dalaku'an River crosses the Altyn Tagh Fault near a right step in the fault (Figure 6). They reported a left-lateral offset of 79 ± 10 m of the T2/T3 terrace riser on the west bank of the Dalaku'an River. Using thermoluminescence (TL) dating, they obtained an age of 4.9 ± 0.4 ka for material from terrace T2 and 7.9 ± 0.6 ka from terrace T3. Using age of T2 terrace, they report slip rate of 16.1 ± 1.1 mm/yr. From the high-resolution satellite image of Figure 7, we can identify a clear offset of terrace riser T3/T2. Applying logic argued in Figure 4, for the 79 ± 10 m offset, the subsequent slip rate would be 10.0 ± 2.1 mm/yr. This offset and these ages would put upper and lower bounds of 16.1 ± 1.1 mm/yr and 10.0 ± 2.1 mm/yr for the slip rate.

Figure 7.

View south-southeast upstream along the Dalaku'an River valley where it crosses the Altyn Tagh Fault, using a satellite image draped onto a digital elevation map. White arrows mark fault traces noted by Xu et al. [2005], and successively older terraces are labeled T1, T2, and T3.

[30] “Qinbulak site” (37°39.556′N, 86°26.11′E, site B in Figure 5). Xu et al. [2005] reported offsets along a southward flowing tributary of the Cherchen He (“He” means river in Chinese): a left-lateral separation of the T2/T1 riser from the present upstream channel of 115 ± 10 m and a larger separation of 355 ± 10 m for the T3/T2 riser, though in the latter case their map does not assign a unique upstream counterpart for this riser (Figure 8). Construction of a road or canal near the fault trace, and crossing it in places, has made correlations more difficult than otherwise, but the T2/T1 riser is clear on satellite imagery (Figure 8b). For T1, Xu et al. reported 10Be and 26Al cosmogenic exposure dates that average 5.2 ± 1.2 ka; excluding outliers, all dates are less than 7.1 ka. For T2, ignoring one sample with an unusually large age near 40 ka, eight others yielded 10Be and 26Al cosmogenic exposure dates that average of 15.3 ± 4.2 ka with the oldest among them near 20 ka [Xu et al., 2005]. Using these ages (5.2 and 15.3 ka) to define ages of the two offset risers, they reported a slip rate of 19 ± 4 mm/yr.

Figure 8.

(a) Geomorphological map and satellite image draped onto a (b) digital elevation map of the Qinbulak site (37°39.556′N, 86°26.11′E). (a) The geomorphological map shows displacements of terraces of the Qinbulak site [from Xu et al., 2005]. (b) White arrows on the satellite image mark the trace of the Altyn Tagh Fault, terraces are labeled T1, T2, and T3 according the definitions of Xu et al. [2005], and letters “H” denote hills on the north side of the fault. Note that the 115-m offset reported by Xu et al. [2005] might be an underestimate, and that from what is shown on the image the riser between T3 and T2 cannot be uniquely assigned the same stream as that for the T2/T1 riser.

[31] The offset stream passes through hilly topography on the north side of the fault before crossing it and debouching onto an alluvial fan surface south of the fault (Figure 8). Xu et al. [2005] reported no upstream remnants of terraces T1 and T2. Thus, while the stream was incising into the fan to abandon the higher surface T2, the western edge of T2 would have moved behind the middle of three sets of hills shown in Figure 8b. The offset of 115 m is much greater than the width of the valley upstream of the fault (a few tens of meters at most), and applying Cowgill's [2007] criterion discussed above prohibits the age of the T1 from being used to date the T2/T1 riser. In a much more likely scenario, when the stream incised into its floodplain to abandon T2, T2/T1 lay immediately downstream of the valley north of the fault. Thus, if the age of abandonment, 15.3 ± 4.2 ka, defines the age of the T1/T2 riser, then the slip rate would be 7.5 ± 2.9 mm/yr.

[32] We note that the use of this age for T2 ignores two sources of uncertainty that partially cancel one another. First, cosmogenic nuclides may have accumulated in the cobbles before they were deposited, which would make the dates greater than that for when the cobbles were deposited. Second, burial of the cobbles for some unspecified time might make the measured dates too young. Moreover, from the satellite imagery (Figure 8b), we suspect that the offset of T2 from the upstream channel is greater than 115 m. We ignore these possible sources of error and merely note that if one accepts the 15.3-ka date, the slip rate is likely to be less than 16 mm/yr and closer to 10 mm/yr.

[33] “Cherchen He site” (37.60°N, 86°0.36′E, site 1 in Figure 5). Mériaux et al. [2004] measured a 166 ± 10-m left-lateral displacement of the T2/T1 terrace riser. They used an age of 6.4 ± 0.1 ka for T1 to give a slip rate of 25.9 ± 1.6 mm/yr, but Cowgill [2007] pointed out that the present-day floodplain reaches a maximum width of 75 ± 10 m. Thus, the age of T1 does not date the T2/T1 riser. Cosmic ray exposure dating (10Be-26Al) suggests abandonment of the higher terrace T2 at 16.6 ± 3.9 ka [Mériaux et al., 2004]. That age for the onset of displacement of terrace riser T2/T1, yields a slip rate of 10.0 ± 2.4 mm/yr (Figure 9), or if ones uses Cowgill's revised offset of 156 ± 10 m for T2/T1, the slip rate is 9.4 ± 2.3 mm/yr. Cowgill used his other criteria to justify his rate of 9.4 ± 2.3 mm/yr. We point out some aspects of geomorphology and of the dating that he did not discuss that also support a rate of ∼10 mm/yr, not 25–30 mm/yr.

Figure 9.

Map and possible slip rates at Cherchen He site. (a) Map of the site from Mériaux et al. [2004; Figure 2b] shows where they measured 166 ± 10 m of left-lateral displacement of the T1/T2 terrace riser. They reported abandonment of the higher terrace T2 at 16.6 ka and the lower terrace T1 at 7.3 ± 2.2 ka. (b) Estimates of slip rate calculations. Using the abandonment age of the lower terrace, the way Mériaux et al. [2004] used it to calculate slip rate, the slip rate would be 25.9 ± 1.8 mm/yr (shown by red color). Using an abandonment age of the higher terrace (16.6 ka) to date the onset of offset of terrace riser T1/T2, the logic argued in this paper, the resultant slip rate is 10.0 ± 2.4 mm/yr (shown by blue color). Using the estimated age of sediment at the base of T1, 14.6 ka, to date the emplacement of terrace T1 and dating the onset of T1/T2, the slip rate is 11.4 ± 2.3 mm/yr (shown by orange color). Cowgill [2007] used his revised offset of 156 ± 10 m and his other criteria to justify his rate of 9.4 ± 2.3 mm/yr at this site (shown by black color).

[34] Mériaux et al. [2004] reported radiocarbon ages in sediment deposited on the lower terrace, T1. At the depth 1.9 m below the surface of T1, they obtained a corrected 14C age of 6.8 ± 1.0 ka and another of 7.8 ± 0.4 ka at a depth of 2.1 m. Suppose that these dates define the deposition rate to be 0.2 m/ka. An additional 1.35 m of aggradational deposits lie below the depth of 2.1 m [Mériaux et al., 2004]. For a constant deposition rate, an extrapolation to the base of the sediment yields an age of the oldest sediment deposited on terrace T1 of 14.6 ka. Using this age to date incision to form the T1 strath and arbitrarily taking 2 ka as its uncertainty, the slip rate of T1/T2 riser would be 11.4 ± 2.3 mm/yr, or 10.7 ± 2.3 mm/yr using Cowgill's [2007] estimate of the offset. We recognize that this rate is not precisely determined, but its agreement with that based on the age for the abandonment of T2 is noteworthy.

[35] Mériaux et al. [2004] also argued that the stream shown as PC in Figure 9 was offset 418 m from the stream labeled DP, and assuming a date of 16.6 ka for that offset, they inferred a rate of 25.2 ± 5.9 mm/yr. We contend, however, that the size of this stream is shown to be similar to that of the stream 300–500 m to its east, for which there is a much smaller watershed than that drained by DP. The source of PC seems to be RG, which has been offset from PC by 150–200 m. Thus, we do not agree with Mériaux et al. that PC has been offset from DP, or that the rate in this region is as large as 25–30 mm/yr.

[36] “Sulamu Tagh site” (37.7°N, 87.4°E, site 2 in Figure 5). Mériaux et al. [2004] reported offsets and ages for them from this site, ∼60 km east of the Cherchen He site. Because the observations are shown only with sketches, we cannot confidently evaluate the correlations of features on opposite sides of the fault, and therefore we cannot interpret data from this region either as support for their reported rate of 32.6 ± 2.8 mm/yr or to offer a different rate. An examination of satellite imagery of the topography and of the relationships of landforms south of the fault to the glaciers north of it, however, raises doubts about the interpretation given by Mériaux et al. [2004].

[37] The Altyn Tagh Fault crosses the south side of the Sulamu Tagh and passes through valleys parallel to the fault east and west of two major glaciers that flow south from the Sulamu Tagh (Figure 10). At present, the eastern glacier ends ∼1 km north of the fault, and the western glacier crosses the fault at the saddle between the two valleys that follow the fault to the east and west. The western glacier itself seems to be ablating most rapidly at the saddle, but to its south a large expanse of hummocky topography, described by Mériaux et al. [2004] as a “till-covered bench,” extends ∼1 km south of the end of the glacier and spreads over an east-west region >2 km in length parallel to the fault trace (Figure 10). There seems little doubt that the ridge on the south side of the fault blocks the glacier. Hence during glacial advances, we suppose that upon reaching the ridge south of the fault zone the glacier would have flowed parallel to fault until reaching an outlet to the south. As a result, moraines and other landforms derived from glacial outwash along southward-sloping valleys south of the fault need not have been aligned with the glacier on the north side of the fault. Dividing distances between them by the age of the moraines could lead to overestimates of slip rates for moraines east of the glaciers and underestimates for any to the west. Mériaux et al. [2004] reported offsets only for landforms east of this glacier.

Figure 10.

Oblique view toward the west-southwest along the Altyn Tagh Fault showing topography near the Sulamu Tagh. An east-west trending ridge blocks the modern glacier that flows south across the Altyn Tagh Fault. Debris, either till or moraine and called a “till-covered bench” by Mériaux et al. [2004], has spread out to the east and west from the present terminus of the glacier. Because of the blockage of the glacier by the ridge, we question whether landforms formed either by larger glaciers or by fluvial systems below the glaciers can be assumed to have lain directly south of the present glacier when they formed. Mériaux et al. [2004] also reported an offset of 3660 m of the eastern edge of a wide valley on the south side of the fault from the valley continuing from the eastern of the two large glaciers emanating from the Sulamu Tagh. Note the deep valley parallel to the fault and east of the glacier. This valley isolates the offset feature from the glacier. Because of this juxtaposition, we doubt that the age of 113 ka applies to a 3660-m offset.

[38] The nature of the topography east of the eastern glacier makes it difficult to interpret offsets along this segment of the fault too. A large broad valley slopes gently west from near the fault, but to the north, either the eastern glacier itself or rivers emanating from it have cut a deep valley that has isolated the broad valley to the south from drainage emanating from the eastern glacier (Figure 10). Mériaux et al. [2004] suggested that the eastern edge of the wide valley has been offset 3660 ± 300 m from the southern end of the eastern glacial valley (Figure 10). We cannot demonstrate either that this correlation is wrong or that the age (112.7 ± 7.3 ka) that they assign for this feature is incorrect, but we find the data and arguments presented to support this information to be unconvincing.

[39] We do not discuss here all of the suggested offsets that Mériaux et al. [2004] used to infer their rate. We cannot assert that none is valid, but we do not find sufficient information to accept them, particularly in light of the present-day relationship of the western glacier to the topography in this region.

[40] “Old Aksay site” (39.41°N, 94.38°E, site 3 in Figure 5). Mériaux et al. [2005] reported a displacement of 225 ± 10 m for terrace riser T3/T2′ along a stream valley that they called R2 (Figure 11) and 145 ± 10 m for terrace riser T2/T1 along Sa1 (Figure 12), plus other similar values for other channels, which they described as less well constrained. They also suggested that terrace risers T1/T0 along streams Sa1 and Sa2 were offset 45 ± 5 and 40 ± 5 m, respectively (Figure 12). We question whether reliable offsets can be estimated for these sites.

Figure 11.

Vertical view of the town of Old Aksay and the offset of 225 ± 10 m along the Altyn Tagh Fault. The short dashed line shows the trace of fault; a line of en echelon hills defines the fault trace west of the town, and a scarp facing south marks the trace east of the valley of R2. Long dashes show the boundary between T2, on which the (now ghost) town of Aksay was built, and T3, with the 225-m offset. White arrows point toward another scarp that we presume reflects active faulting.

Figure 12.

Vertical view of the Altyn Tagh Fault trace just east of the river R2 and showing the courses of Sa1 and Sa2. Mériaux et al. [2005] reported 45 and 40 m of offset of the present-day channels for these streams. We question whether the 40-m offset of Sa2 occurs at the fault; it appears that the stream is deflected north of the fault and that this deflection is not related to slip on the fault. Mériaux et al. [2005] also reported that terrace riser T2/T1 has been offset to 145 ± 10 m. The satellite imagery does not show clearly the terrace risers, but we have no reason to doubt the measured separation of the riser. Because the stream Qa1 flows toward a hill on the north side of the fault, however, we are not convinced that this offset results from 145 m of displacement, or that the 45-m offset of the present-day stream reflects 45 m of strike-slip. The vertical component of slip on the fault has allowed the northern side to block northward flowing drainage.

[41] For the 225-m offset, the fault zone does not seem to reflect pure strike slip along a narrow zone (Figure 11). Mériaux et al. [2005] noted that the town of Old Aksay was built on an elevated surface bounded by a thrust fault to its north and dipping south toward the Altyn Tagh Fault. In addition, the surface expression of Altyn Tagh Fault is marked by a series of en echelon ridges, some of which seem to be cut by short fault segments striking obliquely to the main trace (white arrows in Figure 11). Moreover, the T3/T2′ terrace riser trends northwest, oblique to the fault over most of its length, and only near the fault on the north side is it approximately perpendicular to the fault. Thus, we consider 225 m to be an upper bound of the left-lateral offset, but not necessarily close to the amount.

[42] Other observations cast doubt on the 145-m offset. First, a clear vertical offset along the Altyn Tagh Fault in this segment obstructs northward drainage (Figure 12). The stream Sa1 flows toward a hill that must have deflected it when floodplains were abandoned to form terraces T1, T2, and T2′. Second, the gully Sa1 trends obliquely to the fault trace (Figure 12). Thus we question whether apparent offsets of these terrace risers define reliable strike-slip displacements. Similarly, for the 45- and 40-m offsets of Sa1 and Sa2, we suspect that the vertical component has played a role in the deflections of the streams. From the satellite imagery, it appears that the deflection of Sa2 used to infer a 40-m offset lies north of the scarp, not at it, and therefore does not mark an offset.

[43] “Aksay, Huermo Bulak (39.42°N, 94.47°E, site 4 in Figure 5), and Bang Gou Ba sites” (39.50°N, 94.81°E, site 5 in Figure 5). In addition to doubts that we have about offsets in the Aksay region, we question the utility of dates that Mériaux et al. [2005] reported. For some terraces, thin layers of gravel and soil cover straths cut in bedrock, but in others deposition of thicker layers implies that significant intervals of time elapsed during deposition before the surfaces were abandoned to form terraces. Thus, as Mériaux et al. recognized, interpreting the dates obtained from them in terms of offset landforms is more complex than when only strath terraces formed. At all three of the neighboring Aksay, Huermo Bulak, and Bang Gou Ba sites, Mériaux et al. reported both radiocarbon dates from charcoal below terrace surfaces, and concentrations of both 10Be and 26Al from quartz-rich samples taken from the tops of terraces and from vertical profiles within terraces. Because of both the complexity of the geomorphic history of the various valleys and adjacent terraces and the large scatter in cosmogenic nuclides from many terraces, Mériaux et al. [2005] offered a number of possible rates depending on the age assigned to an offset landform.

[44] A measure of the difficulty in interpreting the ages can be gained from depth profiles of concentrations of 10Be and 26Al from the three regions. Production of cosmogenic nuclides should decay exponentially with depth, z, according to P(z) = P0 exp (−λz), where P0 is the production rate at the surface and λ scales the decreased production with depth and is proportional to density. For the relatively low density of sediment that characterizes terraces, Mériaux et al. [2005] used λ = 1.2 m−1. For times short compared with the half-lives of 10Be or 26Al, the concentrations of these nuclides, C(z), should be given by C(z) = P0t exp (−λz) + C0, where C0 is the initial (or inherited) concentration of the nuclide when the cobble was buried at depth z. As Anderson et al. [1996] showed, if profiles of concentration obey this form, they can be used to determine the average inherited concentration, C0, of a nuclide in the samples. A plot of such concentrations from the three depth profiles made by Mériaux et al., however, shows a huge scatter (Figure 13). In fact, for the two of them, the best fitting exponential profile increases rather than decaying with depth. The wide range of concentrations suggests both that the terraces have not been constructed in a simple way and that inheritance of radionuclides can be large. Thus, assigning ages to the terraces requires more assumptions than can be justified.

Figure 13.

Plot of concentrations of 10Be versus depth for three profiles: (triangles) Aksay, (solid dots) Huermo Bulak, and (open dots) Bang guo ba. The black line shows an exponential decay with depth for λ = 1.2 m−1 assumed by Mériaux et al. [2005]. (We show only profiles for 10Be because those for 26Al are similar but concentrations are six times larger.)

[45] Although we do not find the evidence presented by Mériaux et al. [2005] to allow useful constraints to be placed on slip rates in the Huermo Bulak region, independent evidence presented by Xu et al. [2005] for left-lateral offset of terrace risers at Huermo Bulak does allow us to evaluate the possible slip rate. Xu et al. identified five terraces on the western side of the Huermo Bulak stream: named T3, T2, T1, T0′, and T0 (originally labeled as T4, T1, T0″, T0′, and T0, respectively, in Figure 2c of Xu et al.). The Huermo Bulak stream has incised into a relative flat floodplain (Figure 14) so that small vertical displacements do not obscure the much more significant strike-slip faulting. The highest terrace with its riser T3/T2 has been offset 255 ± 10 m, but there are no constraints on the abandonment age of terrace T3. Terrace risers T2/T1 and T1/T0′ on western side of the stream have been offset for 36 ± 2 and 24 ± 2 m, respectively (Figure 14). Xu et al. obtained two charcoal samples (H-C-3 and H-C-4) from alluvial gravel about 0.7 m below T1 terrace, which yielded calibrated ages of 2140 ± 90 and 2030 ± 65 years BP, respectively. We suggest terrace T1 was abandoned sometime around 2080 ± 100 years. They also found one C14 sample (H-5) about 1 m below the surface of terrace T2 with an ago of 4120 ± 210 years, and another three C14 samples (AKSA1, AKSA2, and AKSB1) at depth 2.9 m below the T2 surface with ages of 4250 ± 100, 4240 ± 110, and 4385 ± 45 years, respectively (Figure 14). We use their youngest age, 4120 ± 210 years, as abandonment age of T2. Using ages of upper terraces to date the offset risers, the displacements of T2/T1, 36 ± 2 m, and T1/T0′, 24 ± 2 m yield rates of 8.5 ± 0.7 and 11.6 ± 1.5 mm/yr, respectively. We suggest the slip rate at this site to be 10 ± 2.5 mm/yr. If the age of T1, 2080 ± 100 years, dated the T2/T1 offset of 36 ± 2 m, the rate would be 18 ± 1 mm/yr, which is much higher than the GPS data suggest.

Figure 14.

(a) Geomorphological map and (b) oblique photograph of the Huermo Bulak site (39.42°N, 94.47°E, site 4 in Figure 5). (a) The geomorphological map shows offsets of terraces west of the Huermo Bulak stream [from Xu et al., 2005]. Xu et al. [2005] mapped 5-level terraces named as T0, T0′, T1, T2, and T3, and they identified offsets on T0′/T1, T1/T2, and T3/T2 to be 24 ± 2, 36 ± 10, and 255 ± 20 m, respectively. Black rectangle marks the approximate region shown by the photograph. (b) Photograph of the site from Mériaux et al. [2005] with identifications of terraces by Xu et al. [2005].

[46] “Xishui'er site” (39°27′N, 94°48′E, site D in Figure 5). Xu et al. [2005] reported that they could identify seven terraces, which they associated with the Xishui'er gully. They measured offsets of 65 ± 10 m for the T3′/T2 terrace riser and 160 ± 20 m for the T4/T3″ terrace riser (Figure 15). From 14C dates, they inferred abandonment ages of 4582 ± 172 years for T1, 9025 ± 45 years for T3′, and 9235 ± 130 years for T3″. Using an age of 6300 ± 150 years that they estimated for T2 from the Huermo Bulak site, Xu et al. inferred a rate of 10.3 ± 1.6 mm/yr from the offset of the T3′/T2 riser, and using 9235 ± 130 years for T3″, they reported a rate of 17.3 ± 2.5 mm/yr for the T4/T3″ riser. These two estimates are based on the same assumption of Mériaux et al. [2004, 2005], stating that the age of the lower terrace dates the onset of displacement of the riser above it. Obviously, using the logic argued above (Figures 3 and 4), for 65-m displacement of T3′/T2, 9025 years yields a lower rate, of 7.2 ± 1.2 mm/yr. We suspect that the lower rate more likely correct, but we cannot employ Cowgill's [2007] criteria to decide this question.

Figure 15.

Geomorphological map shown offsets of terrace risers at the Xishuier site. The Altyn Tagh Fault, marked by a thick red line, offsets three terrace risers: T4/T3″, T3″/T3′, and T3′/T2.

[47] “Lucaowan site” (39°33′N, 95°50′E, site E in Figure 5). Xu et al. [2005] reported five fill terraces along the Dang He, with 140 ± 27 m of left-lateral displacement of the T4/T3 terrace riser (Figure 16a). They reported two nearly identical calibrated 14C dates with an average of 14,693 ± 200 years from below the surface of T3, and an abandonment age of 13.3 ± 1.8 ka for terrace T4 using 10Be cosmic ray exposure dating (Figure 16b). Notice that for both T2 and T0, Xu et al. reported a wide scatter of ages. They ignored two 10Be dates near 30 and 50 ka and three others near 20 ka (Figure 16). Including those latter three dates in the average yields an age of terrace T4 of 16 ± 7 ka and a resulting slip rate of 8.8 ± 4.4 mm/yr. If we simply took the oldest, 20 ± 2.2 ka rather than 16 ± 7 ka, as giving the most reliable age of the surface [e.g., Brown et al., 1998, 2002] and of the age of abandonment of terrace T4, the resulting slip rate would be 7.0 ± 1.6 mm/yr. In fact, because of the scatter in ages, and the possibility of inherited 10Be concentrations, we are hesitant to interpret any of the ages in terms of dates of abandonment of floodplains, but a sensible interpretation of the dates is consistent with a rate less than about 10 mm/yr.

Figure 16.

(a) Geomorphological map and (b) ages of terraces from the Lucaowan site. (a) The geomorphological map shows displacement of terrace riser T4/T3. (b) 10Be-26Al cosmic ray exposure dates as a function of distance from the fault [from Xu et al., 2005]. T0, T1, T3, and T4 are terraces from riverbed upward. Block solid dots show 10Be-26Al samples collected north of the fault, and circles show samples south of the fault. The black box shows the samples that Xu et al. [2005] used to obtain an abandonment age of 13.3 ± 1.8 ka for terrace T4. We think there is no reason to discard the three samples above the black box, and instead we suggest the age of abandonment of T4 might be represented by the samples within the dashed box, whose average is 16 ± 7 ka. If the oldest age obtained from cosmic ray exposure dating represent the most reliable age of the surface [Brown et al., 1998; 2002], however, the three samples above the black box might give the most reliable age of terrace T4 abandonment. As shown in the white box, the age would be 20 ± 2.2 ka.

[48] “Shibaocheng site” (39°57.33′N, 96°24.169′E, site F in Figure 5). Xu et al. [2005] reported six terraces along a small stream that emanates in the Altyn Tagh, flows north through bedrock, and then debouches onto a large alluvial (or perhaps debris-flow) fan north of the Altyn Tagh Fault (Figure 17). They reported left-lateral offsets of four terrace risers at this site: T2/T1 – 12 m, T3/T2 – 70 ± 20 m, T4/T3 – 100 ± 20 m, and T5/T4 – 260 ± 20 m (Figure 17). Because the river debouches from bedrock, and Xu et al. traced only the T1 terrace upstream of the fault into the bedrock, we suspect that terrace risers downstream of the fault should have been protected from modification as they slid westward and out of the path of the river. Thus, following the logic given above, we expect that ages of the upper terraces would define the ages of the risers more closely than lower terraces. Xu et al. took samples of silt and sand in the upper part of the terraces or from the top of gravel layers just below the silt and sand cover of the terrace surfaces for thermoluminescence dating, and they reported ages for terraces T1–T5 of 4.59 ± 0.35, 13.09 ± 1.01, 21.21 ± 1.65, 41.66 ± 3.25, and 45.17 ± 3.52 ka BP, respectively. From these ages, they reported an average slip rate of 5.5 ± 2.0 mm/yr, which is consistent with the GPS measurements.

Figure 17.

Geomorphological map shown offsets of terrace risers for the Eastern Shibaocheng site according to field mapping by Xu et al. [2005].

[49] From the map that Xu et al. [2005] presented (Figure 17), it appears that the T1 terrace south of the fault spreads outward toward the north and is not aligned parallel to valley near the fault. Thus, we suspect that the 12-m offset that they assigned underestimates offset since the riser formed. The T3/T2 riser is aligned parallel of the valley south of the fault and to the T1/T0 and T2/T1 risers north of it. The T4/T3 and especially the T5/T4 risers, however, are oriented oblique to the fault trace, and the current drainage system includes a channel along the fault trace. Thus, we are most confident of the T3/T2 offset, and least so for T1/T0 and T5/T4. Using the offsets and ages given by Xu et al., we consider a number of possible rates (Figure 18). Using only T3/T2, the ages for T3 and T2 place bounds of 3.3 ± 1.0 and 5.3 ± 1.7 mm/yr, respectively. If we used the ages of T5 and T4 to place a bound on the rate for the T5/T4 riser, we would obtain the tight constraints of 5.8 ± 0.6 and 6.2 ± 0.7 mm/yr, respectively. A least squares fit for the three oldest risers using ages of the lower terraces gives 5.9 mm/yr, but if we considered only the T3/T2 and T4/T3 risers, the bounds from the upper and lower terraces would be 2.6 and 4.9 mm/yr, respectively. We suggest that a cautious estimate of the slip rate at this site is 2 to 6 mm/yr, or 4 ± 2 mm/yr, since ∼45 ka, which is not significantly different from that given by Xu et al., but because the river emanated from a narrow valley, we suspect that the upper terraces define the ages of the terraces risers better than the lower terraces. Thus, a rate closer to 3 mm/yr seems more appropriate than 5 mm/yr.

Figure 18.

Estimated offsets of terrace risers at the Eastern Shibaocheng site as a function of ages of upper and lower terraces given by Xu et al. [2005], with a number of possible rates shown. Three plausible rates are shown: 5.9 mm/yr is a least squares fit to the three largest offsets and using dates from the upper terraces; 4.9 and 2.6 mm/yr correspond to least square fits using only the 70- and 100-m offsets and for dates of the lower and upper terraces, respectively.

[50] “Niuyagou site” (39°58.190′N, 96°35.960′E, site G in Figure 5). Xu et al. [2005] showed six terraces north of the fault along the Niuyagou gully, which lies west of the Shule He. They show all six terraces west of the gully, but only the oldest, T5 and T6, east of it, and only T2 and an isolated remnant of T6 upstream of the fault, where the Niuyagou gully is incised into bedrock (Figure 19). Xu et al. reported thermoluminescence ages from sand and silt taken 0.35–0.40 m beneath the top surfaces of T3 (28.82 ± 2.25 ka), T2 (10.06 ± 0.76 ka), and T1 (6.97 ± 0.53 ka). They reported offsets of each riser: T6/T5 (210 ± 20 m), T5/T4 (160 ± 20 m), T4/T3 (120 ± 20 m), T3/T2 (40 ± 10 m), and T2/T1 (6.4 m). From the offsets of the T4/T3 and T3/T2 terrace risers and ages of the T3 and T2 risers, Xu et al. estimated a slip rate of 4.2 ± 1.0 mm/yr since 30 ka (Figure 20).

Figure 19.

Geomorphological map shown offsets of terrace risers for the Niuyagou site according to the field map of Xu et al. [2005].

[51] Because Niuyagou gully seems to pass through bedrock before crossing the fan and debouching onto an alluvial fan surface, we consider it more likely that the older terraces define the ages of the risers, because the risers would have been protected when it slipped west relative to the mouth of the gully at the fault. Accordingly, we estimate the slip rate in this segment to be 1.4 ± 0.4 mm/yr (Figure 20).

Figure 20.

Estimated offsets of terrace risers at the Niuyagou site as a function of ages of upper and lower terraces given by Xu et al. [2005]. Two plausible rates are shown: 4.2 ± 1.0 mm/yr, given by Xu et al., fits the offsets of two risers using dates from the lower terraces, and 1.4 ± 0.4 mm/yr corresponds to the ratio of the 40 ± 10 m offset to the age of the upper terrace, T3, of 28.81 ± 2.25 ka.

[52] “Hongliugou site” (40°01.236′E, 96°55.796′E, site H in Figure 5). Xu et al. [2005] reported that three “proluvial fans” have developed at the “outlet of the Hongliugou Gully.” They measured an offset of 19–20 m of the oldest of the abandoned alluvial fans. They also dated the surface of the alluvial fan to be 8.99 ± 0.68 ka using the thermoluminescence method and deduced a slip rate of 2.2 ± 0.3 mm/yr, which agrees with the GPS rate for the adjacent area. Because the onset of offset should be later than the abandonment age of the alluvial fan, we regard this slip rate as a maximum for this site.

[53] Our reexamination of data constraining slip rates on the Altyn Tagh Fault published by Mériaux et al. [2004, 2005] and Xu et al. [2005] demonstrates that slip rates of ∼10 mm/yr or lower are possible, and that rates as high as 20–30 mm/yr are not required. This reinterpretation of published geological data, in fact, suggests that the left-lateral slip rate of the Altyn Tagh Fault in its central segment is in the range of 8–12 mm/yr, and that this rate is uniform west of 93°E, but decreases eastward to only ∼1–2 mm/yr near 97°E.

5. Discussion

5.1. Evidence Supporting Low Slip Rates

[54] GPS measurements place an upper bound on the left-lateral slip rate along the Altyn Tagh Fault to be ∼12 mm/yr, at least where measurements have been made. If we use 8 mm/yr slip rate as the lower bound, a slip rate of 10 ± 2 mm/yr would characterize the central sections of the fault (Figure 21). Most previous geodetic rates lie within this range [Bendick et al., 2000; Chen et al., 2000, Shen et al., 2001; Wallace et al., 2004; Wang et al., 2001]. Apart from GPS studies, another study using space-based technology, satellite radar interferometry (InSAR), shows slip rate along western segment of the Altyn Tagh Fault to be 5 ± 5 mm/yr or less than 10 mm/yr [Wright et al., 2004].

Figure 21.

Inferred slip rates on the Altyn Tagh Fault from various data sources. Pink bars (and arrow) show ranges of slip rates allowed by the GPS analysis. Green bars show geological slip rates based on our reinterpretation of the data presented by Xu et al. [2005]. Black bars show the slip rates reported by Mériaux et al. [2004, 2005], and the blue bar shows our reinterpretation of their data. The cyan band shows the range allowed by these various data and inferences. Geological sites and GPS profiles are also marked.

[55] Long-term geological slip rates given by various authors also point toward a low slip rate. Using ∼475 km of displacement on the Altyn Tagh Fault, Yin et al. [2002] suggested an average rate of 9 ± 2 mm/yr since 49 Ma. Yue et al. [2001] inferred 375 ± 25 km of offset, beginning in late Oligocene-early Miocene time and suggested a long-term rate of 12–16 mm/yr. Yue et al. [2004] further measured a 165-km displacement along the Altyn Tagh Fault since 16.4 Ma, and obtained an average rate no more than 10 mm/yr. Based on these long-term average slip rates, we may at least conclude that the post-middle Miocene slip rate since at least 16 Ma is consistent with present-day GPS and Late Quaternary rates, suggesting the slip has been stable during such a long time interval.

[56] A low slip rate along the fault agrees with the historical seismicity of the region. Only two major historical earthquakes (M = 7.2) have occurred west of 85°E along the fault, both in 1924 [Gu et al., 1989]. Moreover, contemporary instrumental recordings reveal only a minor level of seismicity along the entire fault system. Paleoseismological studies suggest recurrence intervals of major earthquakes in the range of 700 ± 400 and 1100 ± 300 years for offsets of 4 to 7 m, consistent with a rate of ∼10 mm/yr (or less) [Washburn et al., 2001a, 2001b]. Even if paleoseismological studies fail to record all major earthquakes, it is unlikely that the recurrence interval would be less than 1000 years. Thus the resulting slip rate ought not to exceed ∼10 mm/yr.

[57] It appears that the slip rate of the Altyn Tagh Fault is ∼10 ± 2 mm/yr rather than 20–30 mm/yr (Figure 21). This rate covers time periods from decades to millions of years. Thus, slip on the Altyn Tagh Fault accounts for a significant but not dominant fraction of the present convergence between India and Eurasia. This relatively low slip rate, smaller than the rate at which the east-west dimension of Tibet extends [e.g., Zhang et al., 2004], concurs with deformation being distributed over the Tibetan Plateau rather than being so concentrated along its northern margin that Tibet can be treated as a rigid plate.

5.2. Deformation Along the Fault and Its Implications

[58] A number of authors have noted a decrease in the left-lateral slip rate eastward along the Altyn Tagh Fault [e.g., Burchfiel et al., 1989; Mériaux et al., 2005; Meyer et al., 1996, 1998; Tapponnier et al., 1990]. Mériaux et al. [2005] reported a decrease from 26–30 mm/yr at longitudes 86°–87°E to about 17 mm/yr at ∼92°E, and further east to ∼96°E to about 4 mm/yr [Meyer et al., 1996]. Xu et al. [2005] inferred that the slip rate decreases from 17.5 ± 2 mm/yr west of 94°E, to ∼11 mm/yr west of 95–96°E, and then to ∼2 mm/yr at 97°E. Our synthesis of various geological and geodetic rates confirms this eastward decrease: the slip rate can be described well as 10 ± 2 mm/yr west of 95°E decreasing to 1–2 mm/yr near its east end (Figure 21). Beyond the eastern end of the Altyn Tagh Fault, GPS measurements detect at most negligible strain, where there is no present-day relative motion across and beyond the eastern end of the Altyn Tagh Fault between 96°E and 100°E (Figure 1). Similarly, Kirby et al. [2007] showed that slip rates decrease systematically from >10 to <3 mm/yr at the eastern end of the Kunlun fault, and inferred that the slip rate gradients imply that regions surrounding the fault tip must be deforming internally in order to maintain strain compatibility.

[59] If the Altyn Tagh Fault acted as a transform fault bounding two rigid blocks, as some have proposed, the slip would either be transformed to another fault or be absorbed by a structure at its tip [Tapponnier et al., 1990]; in either case, there would be no deformation within the blocks bounding central section of the fault. We test this by measuring velocity gradients in blocks on both sides of the Altyn Tagh Fault to determine whether there is internal straining in the direction parallel to the fault (Figure 22). We constructed two profiles parallel to and on both sides of the Altyn Tagh Fault. Each profile covers a breadth of 200 km.

Figure 22.

Velocity profiles parallel to the Altyn Tagh Fault. Red dots show components of velocity parallel to the fault for GPS control points located on the Tarim block (Profile E-E′, Figure 1). Profile E-E′, located north of the fault, includes control points within 200 km of the Altyn Tagh Fault. Blue diamonds show components of velocity parallel to the fault for control points located in the northern Tibetan Plateau. Profiles F-F′ (Figure 1) includes control points located south of the fault and within 200 km of it. The cyan rectangle circumscribes velocity components parallel to the fault indicating shortening, and the pink rectangle circumscribes velocity components east of the terminus of Altyn Tagh Fault on the same profile.

[60] The N75°E GPS components north of the fault on the Tarim block (profile E-E′ in Figure 1) cluster within the 0 ± 2 mm/yr range along the 1600 km length of the fault (Figure 22). The relatively constant, negligible velocities and the absence of a velocity gradient indicate quasi rigidity of the Tarim block. The profile south of the fault, however, does show internal deformation as a velocity gradient exists from ∼90°E to ∼97°E (Figure 22). The N75°E velocity components decrease from 11.4 ± 2.6 mm/yr ∼90°E to about 1 ± 2 mm/yr east of 97°E along Profile F-F′. Since there are no GPS control points west of 90°E and south of the fault, we cannot determine whether the velocity increases continuously westward or perhaps decreases because of east-west extension in this region. The velocity gradient from 90°E to 97°E requires that 10.4 ± 3.2 mm/yr of convergence in the direction parallel to the strike of the fault be absorbed over a region 600 km wide.

[61] How is the ∼10 mm/yr convergence parallel to the fault accommodated? We consider two possibilities illustrated by cartoons in Figure 23. In the one that we prefer (Figure 23a), internal shortening across the Qilian Shan and parallel belts accommodates shortening and matches the velocity distribution. As noted by Meyer et al. [1996, 1998], coeval crustal shortening and strike-slip faulting occurring in almost the entire Qaidam basin and the Qilian Shan testify to widespread deformation south of the Altyn Tagh Fault. In contrast, tectonic activity in Tarim basin is very weak, consistent with its rigid block nature. The second possibility that we consider is shown in Figure 23b. To explain the eastward decrease of slip rate along the Altyn Tagh Fault, Meyer et al. [1998] invoked the rules of plate tectonics and suggested that the surface kinematics and slip transfer between faults obey rigid block motion. If this were the case, velocities of points south of the fault, relative to the Tarim block, would jump where the profile crossed the fault to form a step, as illustrated in Figure 23b. Obviously, the observations shown in Figure 22 do not fit the velocity profile predicted by rigid block interactions. If rigid block (or plate) movement described deformation in the region including the eastern 300 km of the Altyn Tagh Fault, those blocks must be deep, such that the upper crust strains over a wide zone and obscures rigid block movement tens of kilometers below the surface.

Figure 23.

Cartoons illustrating how a decrease in slip rate along a strike-slip fault might be accommodated by deformation in one block. (a) Internal deformation requires a velocity gradient toward the end of the fault. (b) Rigid blocks require a step in the velocity profile along the fault.

[62] The convergence parallel to the Altyn Tagh Fault manifests itself as internal deformation within the region south of the fault, the northeastern Tibetan Plateau. The convergence rate (10.4 ± 3.2 mm/yr) parallel to the fault matches the slip rate decrease along the fault from 90°E to 98°E. This compatibility implies that virtually the entire slip along the Altyn Tagh Fault has been absorbed by convergence along the eastern segment of the Altyn Tagh Fault between longitudes 90°E and 98°E [Burchfiel et al., 1989; Tapponnier et al., 1990]. The Altyn Tagh Fault, therefore, does not seem to act as a transform fault that transfers a significant portion of the convergence between India and Asia into northeastward “strike-slip extrusion” of Asian crust [e.g., Tapponnier et al., 2001], at least to the extent that strike-slip extrusion implies conservation of surface area. Insofar as “strike-slip extrusion” does occur, it must be limited to the confines of the Tibetan Plateau, so that lateral transfer of material along the Altyn Tagh Fault manifests itself as crustal thickening in the Qilian Shan, and hence as merely a redistribution of crustal thickening.

6. Conclusions

[63] GPS data across four segments of the Altyn Tagh Fault reveal low slip rates of <∼10 mm/yr and corroborate previous geodetic findings. GPS data also show a gradual decrease of left-lateral slip rates along the Altyn Tagh Fault, from ∼10 ± 2 to 0 ± 2 mm/yr along the eastern section of the fault.

[64] From an examination of the relationship of offset river terraces near the Altyn Tagh Fault, we conclude that some offsets do not necessarily reflect horizontal displacements on the fault, and that dating of some is too imprecise to yield reliable slip rates. For those with reliable dates, all bounds on slip rates include rates determined from GPS measurements. Moreover, for many offsets, simple arguments suggest that the age of the upper terrace more closely approximates the age of the riser below it than does the age of the lower terrace. Using this logic, we reinterpreted geological offsets and terrace ages published by Mériaux et al. [2004, 2005] and Xu et al. [2005] to show that the left-lateral slip rate of the Altyn Tagh Fault in its central segment appears to be in the range of 8–12 mm/yr. This rate seems to be uniform west of 93°E, but decreases eastward to only ∼1–2 mm/yr near 97°E. This slip rate, which applies to a time period of several thousand years, and the pattern of eastward decrease agree not only with the GPS measurements but also with longer term average rates spanning millions of years.

[65] Components of GPS velocity parallel to the Altyn Tagh Fault (N75°E) north of the fault on the Tarim block cluster within the 0 ± 2 mm/yr range along the 1600 km length of the fault indicating effective rigidity of the Tarim block without internal deformation. The profile south of the fault, however, shows internal deformation for the N75°E velocity components decrease from 11.4 ± 2.6 mm/yr at ∼90°E to about 1 ± 2 mm/yr east of 97°E. The velocity gradient requires 10.4 mm/yr (±3.2 mm/yr) of convergence in the direction parallel to the fault.

[66] The low slip rate, the pattern of eastward decrease in slip rate, and parallel convergence south of the fault suggest the Altyn Tagh Fault does not transfer a significant portion of the convergence between India and Asia out of India's path into Eurasia, but merely redistributes crustal thickening. If “strike-slip extrusion” occurs, it must be limited to the confines of the Tibetan Plateau.

Appendix A:: The Kinematics of Deformation in Asia in Terms of Relative Movements of Blocks

[67] A number of recent studies have shown that the GPS velocity field from continental regions, including Asia, can be interpreted in terms of relative movements of rigid or elastic blocks that slide past one another by slip on faults. In fact, one might describe the range of views as spanning that, for instance, of Mériaux et al. [2004, 2005], Tapponnier et al. [2001], and van der Woerd et al. [1998, 2000, 2002] who employ a relative small number of blocks to that of England and Molnar [2005] who rely on a description in terms of a continuum, but who cannot reject a description in terms of many blocks with dimensions of ∼300 km or less. Recent studies have filled out the spectrum between these two end-member ranges.

[68] Meade [2007] used the velocity field of Zhang et al. [2004] and solved for the angular velocities of relative motion not only among Eurasia, India, South China, and Tarim, but also among 12 other smaller elastic blocks. Although Meade reported a variance reduction of 96%, his solution requires high slip rates on faults either not obviously present, or not likely to slip rapidly. One such example is 11 mm/yr along a westward extrapolation of the Kunlun Fault, where no fault is apparent on topographic maps or satellite imagery. Another locus of predicted high rates lies in southeastern Tibet where convergence at 15 mm/yr is predicted but not suggested by any structure. We find Meade's description of blocks inadequate to describe well the kinematics of deformation.

[69] Using much the same data, Thatcher [2007] solved for relative velocities of 11 “quasi-rigid blocks” in eastern Tibet, in regions where Meade used 10 blocks (including Tarim and South China). Although some of Thatcher and Meade's block boundaries lie close to one another, others do not. Quoting Thatcher, “The fit of model to data is generally very good.” The solution, however, calls for 11 mm/yr of oblique convergence across the Xianshuihe Fault, a left-lateral strike-slip fault with no hint of convergence, and as much as 10 mm/yr of convergence across a block boundary within Tibet where Quaternary faulting offers no indication of convergence.

[70] Using an updated velocity field that includes the control points of Zhang et al. [2004] and velocities of new points, Shen et al. [2005] used eight blocks, including South China, to describe the kinematics of deformation in eastern Tibet, in a region where Meade [2007] used seven blocks, and Thatcher [2007] used five. Shen et al. allowed each block to deform homogeneously, and they solved for mean translations relation to Eurasia, mean rotations about axes through the middles of the blocks, and three average strain rates for each block. They obtained rates of slip on major faults that match within errors those suggested from studies of Quaternary faulting. By allowing the blocks to deform, Shen et al. explicitly treat Asia in terms of continuous, if laterally varying, deformation.

[71] Finally, Calais et al. [2006] subdivided eastern Asia into nine regions, including Eurasia, India, Tarim, and South China, and they used a combination of GPS observations from several networks to address the relative motion of the regions and internal deformation within them. They considered an area larger than that considered by Meade [2007] and much larger than that considered by Shen et al. [2005] and Thatcher [2007]. They ignored southern Tibet and the Himalaya, and among the other eight regions, they reported that with the data that they used the velocity field of Tibet could be not described by the movements of two rigid blocks.

[72] GPS data cannot rule out a description of the velocity field for Tibet and surroundings in terms of relative movements of many of blocks, with dimensions of <300 km [e.g., England and Molnar, 2005]. By contrast, some of the studies reported above take the opposite view; that is, a description in terms of blocks with these dimensions matches the velocity field well. Whether one finds a description in terms of blocks satisfactory or not depends as much on how one imagines continental deformation to occur as on the degree to which existing GPS data can resolve such a question. In any case, it seems clear that if blocks are needed, the number must be large, many tens, if the deformation of Tibet is to be treated as movement among blocks.


[73] First, we acknowledge that although we differ with Mériaux et al. [2004, 2005] in the interpretation of their work, our paper is completely dependent on the high quality of their field measurements, dating, and presentation. We thank Gan Weijun, Shen Zhengkang, and Min Wang in GPS data processing and presentation and E. Kirby, E. Cowgill, and T. C. Hanks for thorough, constructive reviews. We also thank E. Cowgill for his preprint prior to publication. This research was supported in part by the National Key Basic Research Program (2004CB418400), by the National Science Foundation of China (40234040), and by the National Science Foundation (NSF) under grant EAR-0507330.