Gilles Peltzer
email: peltzer@epss.ucla.edu

Nathan D Brown

Anne-Sophie Mériaux

Jerome Van Der Woerd

Edward J Rhodes

Robert C Finkel

Frederick J Ryerson

James Hollingsworth

Anne-Sophie B Meriaux

Stable Rate of Slip Along the Karakax Section of the Altyn Tagh Fault from Observation of Interglacial and Postglacial Offset Morphology and Surface Dating

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The westernmost section of the Altyn Tagh Fault runs along the upper Karakax Valley in the Western Kunlun range (Figure 1). The high elevation of the valley results in abundant quaternary deposits associated with the advances and retreats of neighboring glaciers, especially on the north side of the valley where massive alluvial fans form the piedmont of the Kunlun mountains down to the Karakax River. The sinistral, strikeslip nature of the fault has long been recognized from its morphology on Landsat images [START_REF] Molnar | Cenozoic tectonics of asia: Effects of a continental collision[END_REF][START_REF] Tapponnier | Active faulting and tectonics in China [Article][END_REF]Armijo et al., 1989, e.g.,) and lateral displacements of glacial and post-glacial features have also been mapped from space using the early generation SPOT images [START_REF] Peltzer | Magnitude of late quaternary left-lateral displacement along the north edge of Tibet[END_REF]. Despite the abundance of geomorphic markers displaced by recent movement on this fault section, the estimation of the long-term slip rate on the fault is still debated due to the difficulty to assign a definite age to displaced geomorphic features. Early estimations of the slip rate based on surface dating using cosmogenic methods indicate values of 12-23 mm/yr [START_REF] Ryerson | Active slip-rates on the Altyn Tagh fault -Karakax valley segment: Constraints from surface exposure dating[END_REF]) and 14-18 mm/yr [START_REF] Li | The Kangxiwa section of the Altun Fault zone since the Quaternary, left slip rate and the recurrence period of large earthquakes[END_REF], while [START_REF] Gong | Optical dating of an offset river terrace sequence across the karakax fault and its implication for the late quaternary left-lateral slip rate[END_REF] proposed a slower slip-rate of 6-7 mm/yr using OSL dating of a set of terraces and independent estimates of lateral offsets of associated risers. Large error bars on age determinations and ambiguous associations of surface ages with displaced risers may explain the discrepancy between these studies. Meanwhile, a sub-centimeter slip-rate of 6-7 mm/yr have been estimated for the late Holocene period using 14C dating and the characterization of up to four repeated slip-events of 6-7 m each, every ∼900 years, recorded in lateral offsets of small incising gullies [START_REF] Li | Co-seismic and cumulative offsets of the recent earthquakes along the Karakax left-lateral strike-slip fault in western Tibet[END_REF].

Assigning an age to a terrace riser is difficult. Dating the surfaces of adjacent terraces can only provide upper and lower bounds for the age of the riser, resulting in large intervals of possible values of the fault slip rate, especially when the age difference between adjacent terraces is large [START_REF] Lasserre | Postglacial left slip-rate and past occurrence of M≥8 earthquakes on the western Haiyuan fault, Gansu, China[END_REF][START_REF] Van Der Woerd | Uniform postglacial slip-rate along the central 600km of the Kunlun fault (Tibet), from 26 Al, 10 Be, and 14 C dating of riser offsets, and climatic origin of the regional morphology[END_REF][START_REF] Mériaux | The Aksay segment of the northern Altyn Tagh fault: Tectonic geomorphology, landscape evolution, and holocene slip rate[END_REF][START_REF] Ryerson | Applications of morphochronology to the active tectonics of Tibet[END_REF][START_REF] Cowgill | Impact of riser reconstruction on estimation of secular variation in rates of strike-slip faulting: Revisiting the Cherchen river site along the Altyn Tagh fault, NW China[END_REF][START_REF] Mériaux | The Pingding segment of the Altyn Tagh Fault (91 • E): Holocene slip-rate determination from cosmogenic radionuclide dating of offset fluvial terraces[END_REF].

In this paper we use high resolution digital topography from two different sources to characterize the shape of alluvial fans and incised valleys and better constrain the lateral offsets they record along the fault. By first looking at the shape of the overall fans instead of incision features we avoid the ambiguity of assigning the age of the surface of a terrace to a displaced valley or riser. In a second part of the paper we focus on a narrow valley, west of the village of Shanxili where a shutter ridge partially closes the val- ley. There, the fault scarp is progressively exposed by the movement on the fault, resulting in a progression of its degradation along the fault strike. In the third part of the paper we combine the observed displacements with perviously published and newly obtained ages of terraces using cosmogenic radionuclide (CRN) samples from the upper terrace and optically simulated luminescence (OSL) samples from the inset terrace near Shanxili to estimate the long term slip-rate on the fault over the Holocene and the last glacial period. We finally discuss variable slip rate and variable erosion rate as possible causes of the non-linear relationship between the progressive degradation of the scarp and the cumulative displacement along the fault.

Geologic setting and morphology of the upper Karakax Valley

The Kunlun Shan extends from the Pamirs in the West to the Qaidam Basin in northeastern Tibet in the East. The western part of the range separates the western corner of the Tibetan plateau from the Tarim Basin to the north (Figure 1). With its highest summits exceeding 6000 meters along its southern edge, the elevation of the range gradually decreases to the north with an average slope of 1.9 • over a distance of 120 km, tween 70 mm/yr in the valleys to 350 mm/yr in the glaciated areas [START_REF] Nakawo | Climatic information from Chongce ice cap, the West Kunlun, China[END_REF][START_REF] Liu | Kunlun mountains[END_REF]. [START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF] The valley has a narrow floor of ∼3.0 km in width carved by the floods of the Karakax River and covered with massive alluvial deposits mostly preserved along its northern side (Figure 2). The overall shape of the valley in the transverse direction is asymmetric with peaks up to 2300 m above the river level and steep slopes on the north side and more gentle slopes up to the mean elevation of the Plateau, 1500 m above the river level on the south side (Figure 3). The lower profile in Figure 3 represents the minimum incision profile achieved by tributaries of the Karakax River, north and south of the valley. Both the north and south side profiles have a typical shape with a lower section curved upward up to a knick-point, beyond which the profile slope is reduced. On the north side of the valley, the knick-point is located 1 km upstream from the Altyn Tagh Fault where it might have originated. Knick-points are often observed in profiles of rivers crossing faults with a vertical component of movement such as along this section of the Altyn Tagh Fault [START_REF] Bull | Tectonic geomorphology of mountains: A new approach to paleoseismology[END_REF]. On the south side profile however, the knick-point occurs 7 km south processes affecting the surface of abandoned alluvial terraces include aeolian deposition, salt weathering, desert varnish coating, the formation of desert pavement, and alluvial dissection [START_REF] Bull | Geomorphic response to climate change[END_REF]. Except for channel incision, these processes tend to reduce the roughness of the surfaces with age. [START_REF] Farr | Geomorphic processes and remote sensing signatures of alluvial fans in the Kunlun Mountains, China[END_REF] the first age determination of the surface using cosmogenic radionuclides [START_REF] Ryerson | Active slip-rates on the Altyn Tagh fault -Karakax valley segment: Constraints from surface exposure dating[END_REF]. Below we report new results based on CRN and OSL samples that place additional constraints on the ages of alluvial surfaces in the valley.

Digital topography data analysis

We use two digital elevation models (DEM) to characterize the shape of alluvial structures in the Karakax Valley. First we use the TanDEM-X DEM [START_REF] Hajnsek | TanDEM-X Ground Segment Announcement of Opportunity: TanDEM-X Science Phase[END_REF] covering the entire section of the valley discussed in this paper, and second, a DEM generated from Pleiades tri-stereo images (Centre National d'Etudes Spatiales, 2016) over Site 1 for a detailed analysis of scarp degradation using a diffusion model. The TanDEM-X data obtained from the German Aerospace Center (DLR) correspond to the High Resolution Terrain Elevation, level-3 (HRTE-3) model specifications of 12 m posting and 2 m relative height accuracy for flat terrain [START_REF] Hajnsek | TanDEM-X Ground Segment Announcement of Opportunity: TanDEM-X Science Phase[END_REF]. These specifications allowed us to define the shape of alluvial structures and estimate their lateral displacement with unprecedented precision. The Pleiades images were processed using the AMES Stereo Pipeline (ASP) software [START_REF] Beyer | The Ames Stereo Pipeline: NASA's open source software for deriving and processing terrain data[END_REF] into a 1 m posting DEM. The actual spatial resolution of the map is not quite 1 meter because of the size of the correlation window used by the ASP software but is sufficient to constrain scarp slopes of up to 40 • over the height of the scarps we surveyed (Table 1). Given the angle of repose of colluvium of 35 • , these specifications are adequate to perform degradation analysis of terrace risers and fault scarps in the Karakax Valley.

Offset of the Eemian terrace

The upper terrace along the north side of the Karakax River is characterized by a series of alluvial fans at the mouth of each tributary valley, with radii of ∼2 km and average radial slopes of 4.2-4.9 • (Figure 2). At sites 3, 4, 5, and 6 the conical shape of the fans is conspicuous in the shaded topography and all fans appear to be incised by broad channels in various ways with the formation of cut terraces and the deposition of smaller units at lower levels (Figures 2 and4). The surface trace of the Altyn Tagh Fault is clearly visible in the upper half of the fans as a straight feature parallel to the axis of the Karakax Valley. The complex assemblage of fan structures and inset terraces has been cut and offset by repeated displacement along the Altyn Tagh Fault.

We selected three alluvial fans where the upper terrace is well preserved and can be used to estimate the horizontal and vertical displacements on the fault since their emplacement (Figure 4). At Site 3 the conical surface of the fan is entirely preserved except where a ∼300 m-wide channel has incised its surface down ∼10 m on the eastern side of the fan. At sites 4 and 5, a large part of each fan's upper surface has been removed by incision and subsequent channel widening and deposition on their western sides. Only the preserved part of the upper surface of the fans can be used for estimating the offsets at those sites. For each of these 3 fans we reconstruct the lateral and vertical shifts on the fault using a four-step procedure (Figure 4): (1) The elevation of points within 100 m from the fault are projected in a profile as a function of distance along the fault.

(2) The surface slope perpendicular to the fault is removed by using a slanted projection direction, parallel to the fan surface slope.

(3) The vertical throw on the fault is restored by aligning the elevation of the apexes of the conical shape of the profiles on both sides of the fault. ( 4) Finally the horizontal shift is restored by aligning the parts of the profiles corresponding to the upper surface. The restored offset of the upper surface at these sites is ∼300± 20 m with a south side down vertical throw of ∼12-15 m. The confidence interval of ±20 m of lateral shift estimates is based on the dispersion of the profile points in the horizontal direction parallel to fault strike along fans lateral slopes. Assuming that the emplacement of the bulk of the fans occurs on a relatively short period of time, these values can be associated with the exposure age of the upper terrace determined using the cosmogenic radionuclide method without ambiguity (Mériaux et al., 2012, e.g.). The vertical movement along the fault is generally south side down but can vary depending on the local direction of the fault trace, which in places forms compressional and releasing bends. At Site 6 for example, a 700 m-long pull apart structure has developed in the upper terrace as the result of the sinistral slip on fault segments forming a left step (Figure 2). The development of the pull-apart modified the shape of the upper surface at this site, making it difficult to restore its shape using the method used at sites 3-5.

Note that features incising the upper surface of the fans appear laterally offset by a lesser amount, consistent with a younger age of formation. For example at Site 3, the clear-cut incised channel on the eastern slope of the fan appears to be left-laterally offset by ∼80±10 m (Figure 4). Similarly, the main risers incising the upper surface at Site 4 and 5 appear to be offset by 200-240 m and therefore must have been formed some time after the deposition of the terrace they bound (Figure 4). race (T2), which is well preserved on the right-hand side of the river, south of the fault.

The lateral offset of the river channel is between 118±5 m (east side wall offset between arrows c and e in Figure 5a) and 165±5 m (west side wall offset between arrows a and b in Figure 5a). However, the actual value of the channel offset may lie between these extreme values because the channel walls on both sides, north of the fault seem to have been eroded by water flow in a channel coming from the west at point a and in the main river channel at point d, thus increasing the apparent maximum offset between piercing points a and b and decreasing the apparent minimum offset between piercing points c and e (Figure 5a). Finally, the terrace riser below the inset terrace (T2) appears to have a minimum offset of 23±2 m across the fault, between piercing points c and d (Figure 5a).

Progressive exposure and degradation of fault scarp along shutter ridge

A remarkable feature of the evolution of this site over time is the gradual exposure of the fault scarp as the shutter ridge is being displaced into the channel by fault movement. This particular setting requires that the degradation of the exposed fault scarp due to surface erosion must increase toward the west between piercing points e and d (Figure 5) because the western part of this section has been exposed to erosion a longer time than its eastern part. To test this hypothesis we estimate the scarp degradation along the exposed fault scarp as a function of distance along the fault. Scarp erosion in arid environment has long been studied using a diffusive mass transport models [START_REF] Wallace | Profiles and ages of young fault scarps, north-central Nevada [Article[END_REF][START_REF] Nash | Morphologic dating of degraded normal fault scarps[END_REF][START_REF] Andrews | Scarp degraded by linear diffusion: Inverse solution for age[END_REF][START_REF] Avouac | Analysis of scarp profiles: Evaluation of errors in morphologic dating[END_REF]Hilley et al., 2010, e.g.,). Following a similar approach, we assume here that the fault scarps and terrace risers start to collapse soon after their formation to achieve a slope at the angle of repose of coarse colluvium. This phase takes a relatively short time compared to the diffusion period of several thousands of years that follows [START_REF] Wallace | Profiles and ages of young fault scarps, north-central Nevada [Article[END_REF]. The evolution of the scarps during the diffusion period is modeled using a convolution with a Gaussian curve of width √ 2kt, where t is the time since the formation of the scarp and k is the mass diffusivity constant of the terrace material under the prevailing climatic conditions. The value of kt represents the degradation coefficient of the scarp and its age t can be estimated if the diffusivity constant k is calibrated. Under arid conditions in the western United States and Central Asia, values ranging from 1 to 5 m 2 /kyr have been estimated for the mass diffusivity constant [START_REF] Avouac | Analysis of scarp profiles: Evaluation of errors in morphologic dating[END_REF].

Using the 1 m-posting DEM generated using the Pleiades tri-stereo images, we extract elevations profiles of fault scarps and terrace risers and estimate their degradation coefficients as follows. We first adjust a gaussian curve plus a constant term by non-linear least squares regression of the slope profile derived from the elevation profile (Figure 6a).

This step defines the center of symmetry of the scarp, the slope of the terraces on both sides of the scarp, and the vertical separation between them. Using these defined parameters, we construct a synthetic scarp profile representing the shape of the scarp after its collapse into a colluvial wedge with an angle of repose of 35 • (Figure 6b). Two straight segments are parallel to the slope of the adjacent terraces and the middle segment is parallel to the slope of the colluvial wedge. We then iteratively convolve the synthetic scarp curve with a series of gaussian functions, varying their width within a range of possible values, and compute the quadratic misfit between the convolved curve and the observed profile (Figure 6d). Finally we select the optimal degradation coefficient kt that minimizes the misfit (Figure 6b,c). It is often observed that the lower part of scarp profiles is modified by the erosion of a lateral channel or by the deposition of sediments at their base, leading to the loss of symmetry of the profile. We therefore compute the misfit between the modeled and the observed profiles using only the upper half of the profile. The erosion coefficient is then constrained by the curvature of the upper part of the scarp and is not influenced by the modified base of the scarp profile. We adopt this approach at Site 1 because the profiles of both risers below terraces T2 and T3 and the exposed fault scarp show evidence of erosion or channel incision at their base (Figures S1 andS2).

We extracted a series of twelve elevation profiles separated by 5 m across the exposed fault scarp at Site 1 (S1-S12 in Figure 5). The method described above is applied to each scarp profile to estimate its degradation coefficient (Table 1 andFigures S1 andS2). Figure 10 shows the variations of the optimal values of kt as a function of the horizontal distance along the fault. The degradation increases westward along the scarp, which is consistent with a westward movement of the northern side with respect to the southern side. Between 10 m and 65 m along the fault scarp, its degradation coefficient varies from 22 to 74 m 2 , giving an average degradation rate of 0.94 m 2 /m (Figure 10). This value means that if the mass diffusivity constant was 1 m 2 /ka for the colluvium in the Karakax Valley during the last 100 ka, the average slip-rate of the fault would be 1.06 mm/yr. Estimating the actual fault slip-rate requires a calibration of the mass diffusivity constant.

It is interesting to note that the rate of degradation per meter along the fault is not constant. Figure 10 shows two periods of low degradation rate along the 10-20 m and 35-65 m segments, separated by a period of higher degradation rate along the 20-35 m segment. This non-linear relationship could be the result of a variable slip-rate on the fault during the gradual emplacement of the shutter ridge or due to variations of the mass diffusivity with time through this period. We will discuss the implications of these two non-exclusive options together with constraints on the mean diffusivity constant using surface age estimates in a later section.

Degradation of terrace risers at Site 1

Site 1 main alluvial surfaces are the upper terrace (T3) and the inset terrace (T2).

A lower terrace (T1) exists in places along the stream flowing from the south into the Karakax River but it is discontinuous and narrow. Both terraces have been incised by the stream, forming steep risers on the eastern side of the valley (Figure 5). We extracted six elevation profiles across the terrace risers from the Pleiades DEM and assessed the degree of degradation using the same method as for the fault scarp (Table 1). The lower riser below the T2 terrace is close to the present location of the stream and may have been reshaped during storms when the stream flow increased. This may explain the anomalously low degradation coefficients for profile 3 compared to profiles 1 and 2 (Table 1).

To calibrate the mass diffusivity constant we use the largest degradation coefficient to associate with the time of deposition of the terrace. We therefore take the value of 15.6 m 2 to characterize the degradation of the lower riser at Site 1. The values of degradation coefficients for the higher riser between terraces T2 and T3 range from 59 to 75.0 m 2 . Similar to the lower riser, the higher riser may have experienced episodes of reshaping when the stream was still flowing along its base before being permanently abandoned 5. Distance is westward distance along fault scarp from riser T2-T3.

after the deposition of terrace T2. Thus, we choose the largest value of 75 m 2 to represent the degradation coefficient of the riser between T2 and T3 at Site 1.

Age of Quaternary surfaces in the Karakax Valley

Studies conducting direct age estimates of the Karakax Valley terraces started in the mid 1990s and only partial results have been published so far [START_REF] Ryerson | Active slip-rates on the Altyn Tagh fault -Karakax valley segment: Constraints from surface exposure dating[END_REF][START_REF] Li | The Kangxiwa section of the Altun Fault zone since the Quaternary, left slip rate and the recurrence period of large earthquakes[END_REF][START_REF] Li | Co-seismic and cumulative offsets of the recent earthquakes along the Karakax left-lateral strike-slip fault in western Tibet[END_REF][START_REF] Gong | Optical dating of an offset river terrace sequence across the karakax fault and its implication for the late quaternary left-lateral slip rate[END_REF]). Here we report on new analyses of samples collected at Site 1 and Site 4 along the valley (Figure 2). At Site 1, fine grain fluvial sediments collected in an inset terrace of the tributary valley are analyzed using the OSL method [START_REF] Aitken | Thermoluminescence dating[END_REF][START_REF] Wintle | Luminescence dating: laboratory procedures and protocols[END_REF][START_REF] Aitken | Introduction to Optical Dating[END_REF][START_REF] Duller | Luminescence dating of quaternary sediments: recent advances[END_REF]. At Site 4, quartz-bearing cobbles and pebbles were collected at the surface of terraces and in depth-profiles in the shallow (∼2 m) subsurface [START_REF] Ryerson | Active slip-rates on the Altyn Tagh fault -Karakax valley segment: Constraints from surface exposure dating[END_REF]. Here we present new results obtained with surface samples only.

4.1 Age of terraces at Site 4 using cosmogenic radionuclide dating 10 Be cosmic-ray exposure model ages were determined for 28 surface samples from terraces at Site 4 (Figure 7). All of the 10 Be measurements were made at the Center for

Accelerator Mass Spectrometry at Lawrence Livermore National Laboratory following chemical separation methods described by [START_REF] Kohl | Chemical isolation of quartz for measurement of in situ-produced cosmogenic nuclides[END_REF]. Hand size cobbles and fragments from boulders with dimensions up to 0.5 m in diameter, similar to those in the active channel, were collected from surfaces T2 and T2". The surfaces above these levels, T3 and T4, are essentially smooth and covered with a 5-20 cm-thick layer of silt, which appears to be a mixture of shattered cobbles and loess, partially paved with small quartz pebbles (∼1 cm in diameter). Given the absence of cobbles on the T3 and T4 surfaces, quartz pebbles were collected from a number of ∼1 m diameter, roughly circular patches on the surfaces. The collection of pebbles within each patch constituted a single sample for CRN dating; individual pebbles were too small for dating. Subsurface observations obtained by refreshing terrace risers indicated that cobbles, similar to those on the surface of T2 and T2" are present at depth and are progressively shattered closer to the surface. The pebbles on the surface are interpreted to represent the remnants of these shattered cobbles as the result of salt weathering [START_REF] Farr | Geomorphic processes and remote sensing signatures of alluvial fans in the Kunlun Mountains, China[END_REF].

The 10 Be concentrations were converted to model ages using the CRONUS online calculator version 3 (https://hess.ess.washington.edu/), which accounts for the various exposure constraints and incorporates a number of production rate scaling models [START_REF] Balco | A complete and easily accessible means of calculating surface exposure ages or erosion rates from 10 Be and 26 Al measurements[END_REF]Phillips et al., 2016, cf). Numerous scaling frameworks have been proposed

to correct for latitude, elevation, atmospheric pressure anomalies, dipole and non-dipole geomagnetic field changes, and solar modulation, etc... (Borchers et al., 2016, cf). The current online version of the CRONUS calculator includes the original model by [START_REF] Lal | Cosmic-ray labeling of erosion surfaces -in situ nuclide productionrates and erosion models[END_REF], further developed by [START_REF] Stone | Air pressure and cosmogenic isotope production[END_REF] (referred to as St), a version of the St model incorporating paleomagnetic corrections described in [START_REF] Nishiizumi | Cosmic ray production rates of 10 Be and 26 Al in quartz from glacially polished rocks[END_REF] (referred to as Lm) and a model employing analytical approximations fit to nuclear-physics simulations of the cosmic-ray cascade (referred to as LSDn) [START_REF] Lifton | Scaling in situ cosmogenic nuclide production rates using analytical approximations to atmospheric cosmic-ray fluxes[END_REF].

Chauvenet's criterion, a well established statistical method to define clusters and outliers in a sample set [START_REF] Bevington | Data reduction and error analysis for physical sciences[END_REF], was used to eliminate statistical outliers in the sample populations for T2", T3, and T4 surfaces [START_REF] Mériaux | The Pingding segment of the Altyn Tagh Fault (91 • E): Holocene slip-rate determination from cosmogenic radionuclide dating of offset fluvial terraces[END_REF] (Table 2). In addition to variations associated with the production rate scaling, CRN model ages may be influenced by the effects of sample inheritance, leading to an overestimation of the age, and surface erosion and shielding, resulting in an underestimation of the age. A preliminary analysis of the samples from depth-profiles at Site 4 indicated negligible inheritance [START_REF] Ryerson | Active slip-rates on the Altyn Tagh fault -Karakax valley segment: Constraints from surface exposure dating[END_REF]. This is supported by the steep slopes and short drainages observed on the North side of the valley, suggesting a rapid exhumation and transport of the colluvium material before deposition (Figure 4). Furthermore, in a recent study [START_REF] Guilbaud | Kinematics of active deformation across the western kunlun mountain range (xinjiang, china) and potential seismic hazards within the southern tarim basin[END_REF] estimated that erosion rates on alluvial terraces along the northern piedmont of the Western Kunlun mountains near Pishan were low (<1.5 mm/ka) (Figure 1). Transient shielding by snow, eolian deposition of loess, and vegetation may also influence CNR model ages. The arid climate of the valley limits the amount of snow fall and the vegetation is essentially non existent on these alluvial fans.

The Kunlun Mountains also offer a natural barrier to the flux of eolian sediments emanating from the Tarim Basin, as confirmed by the limited amount of loess in the mixed layer at the top of terraces [START_REF] Farr | Geomorphic processes and remote sensing signatures of alluvial fans in the Kunlun Mountains, China[END_REF]. Based on these arguments, the CRN model ages we present here assume that the effects of inheritance, erosion, and shielding are small and lie within uncertainty defined by analytical error of CRN concentration and scaling models.

Overall, the ages of surface samples correlate with surface morphology and position relative to the active channel with terraces T2 and T2" yielding younger ages than those of T3 and T4 (Figure 7). The model ages vary depending upon the choice of production rate scaling model, however, and the disparity among models becomes greater with nuclide concentration/age. The mean age and standard deviation for the T2" samples (minus statistical outliers) derived from the production rate scaling models St, Lm and LSDn models are the same within error, 11.3 ± 1.8 ka, 11.7 ± 1.5 ka and 11.7 ± 1.3 ka, respectively. However, the highest surface, T4, yields more disparate mean ages of 134.3 ± 9.1 ka, 120.4 ± 7.5 ka, and 112.9 ± 6.5 ka, respectively, for St, Lm and LSDn scaling models (Figure 8). While these disparate ages indicate that there are still unresolved difficulties in modeling cosmogenic nuclide production and the calibration of production rates (Borchers et al., 2016, cf), the range of ages correlates well with the transition from δ 18 O isotopic stages MIS-6 to MIS-5 (Figure 8). Alluvial fan deposition during the presumably dry Stage MIS-6 glaciation is unlikely, thus we argue that the younger The CRN model ages indicate 2 main phases of aggradation of the imbricated alluvial fan at site 4 (Figure 8). The majority of the model ages of surface samples on the lower levels, T2 and T2", are younger than the Last Glacial Maximum (LGM at ∼19ka).

Moreover, the final distribution of CRN model ages for surface samples is younger than 15 ka, which indicates that the lower level of the fan formed during the warm post-glacial period of increased run-off that followed the dry glacial age, as found in several other regions of Tibet and central Asia [START_REF] Mériaux | The Pingding segment of the Altyn Tagh Fault (91 • E): Holocene slip-rate determination from cosmogenic radionuclide dating of offset fluvial terraces[END_REF]Van Der Woerd et al., 1998, i.e.,).

The upper levels T4 and T3 yield CRN model ages ranging from ∼115 ka to ∼100 ka, respectively and coincide with the δ 18 O isotopic stages MIS-5e and -5c (Figure 8) consistent with the alluvial fan complex deposition during the Eemian interglacial, which ended ∼115 ka ago [START_REF] Dahl-Jensen | Emian interglacial reconstructed from a Greenland folded ice core[END_REF]. the various surfaces (color code is the same as in the left-hand panel) with SPECMAP marine isotope stages [START_REF] Imbrie | The orbital theory of pleistocene climate: support from a revised chronology of the marine d18o record[END_REF][START_REF] Winograd | Duration and structure of the past four interglaciations[END_REF] in red, δ 18 O changes of the Guliya ice-cap core [START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF]. The age distributions for T3 and T4 surface correlate well with MIS 5e and MIS 5c, while T2 and T2" distributions are consistent with deposition of these surfaces after the LGM. Due to differences in lithology between the mountains north and south of the valley and the lack of time during our field visit, we did not collect samples for cosmogenic analysis at Site 1. Instead, we collected samples in a fine grain layer of the inset terrace (T2) for OSL analysis (Figure 9). The inset terrace is a 10 m-thick terrace deposited in the 100-200 m-wide valley entrenched in the upper terrace (T3). Its flat surface is dipping ∼4.8 • to the north and abuts the fault scarp against the shutter ridge (Figure 5).

!∀ !∀## !∃ !% ! ∀ #! #∀ ∃! ∃∀ %!
The inset terrace is formed mostly of medium coarse colluvium of debris flow origin. Approximately 6 m from the top of the terrace, a ∼50 cm-thick sequence of alternating fine sand and silt narrow beds has been deposited. This section of the stratigraphic sequence was well exposed due to the erosion of the riser in a meander of the stream flowing at its base (Figure 9). Fist-size silt blocks were collected ∼50 cm into the wall of the riser and kept away from light in sealed aluminum boxes.

A cubic centimeter volume of the fine grains was extracted from the center of each of the two sample blocks, hereafter referred to as J1232 and J1233 samples, and prepared using a standard preparation procedure [START_REF] Porat | Re-examination of common extraction and purification methods of quartz and feldspar for luminescence dating[END_REF] (see Supplementary Information for a full description of the sample preparation and measurement procedure).

The emission of K-feldspar multi-grain aliquots from sample J1232 and single grains from sample J1233 was stimulated using a post-infrared infrared stimulated luminescence (pIRIR) protocol [START_REF] Buylaert | Testing the potential of an elevated temperature IRSL signal from K-feldspar[END_REF]. The emission of quartz aliquots of the J1232 sample was stimulated using blue LEDs. All measurements were performed on a Risø TL/OSL-DA-20 automated luminescence reader. The geologic dose rates of the samples were determined by estimating the concentration of U, Th, and K elements using spectrometry methods and corrected for cosmic ray contributions (Table 3). A description of the geologic dose rate determination can be found in the Supplementary Materials.

The results are summarized in Table 3. The equivalent dose, determined using the central age model [START_REF] Galbraith | Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part i, experimental design and statistical models[END_REF] for K-feldspar from both samples, are in excellent agreement (within 1σ) and exhibit low overdispersion (Figure 9, Table 3). After normalization by the total geological dose rate, the equivalent dose values lead to ages of 9.49±0.89 ka and 8.46±0.46 ka for samples J1232 and J1233, respectively.

The equivalent dose distribution for the quartz aliquots from sample J1232 is skewed towards lower values because of the presence of unstable components within the measured signal (see discussion in Supplementary Information). We used the maximum age model, as implemented by [START_REF] Burow | calcMaxDose(): Apply the maximum age model to a given De distribution[END_REF] to estimate the equivalent dose of 35.4±6.5 Gy yielding an age of 7.91±1.5 ka after normalization by the geologic dose rate. This age is less precise than the age derived from K-feldspar samples but is internally consistent within 1 σ (Table 3). Finally, the narrow confinement imposed by the 200-wide valley and the absence of sedimentological evidence for paleo-surfaces in the 10 m-thick section of the terrace argue for a rapid emplacement of the inset terrace at this site.

In the following, we will use the weighted mean of 8.8±0.6 ka of the two K-feldspar ages above for the age of Terrace T2 at Site 1. This early Holocene age corresponds to the end of the 7-15 ka warm period defined by the δ 18 O variations observed in the ice core from the Guliya Ice Cap [START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF], located in the western Kunlun range, ∼330 km ESE of Site 1 (Figure 1). alluvial fan that are multiples of 6±2 m, suggesting that similar earthquakes of M∼7.5

repeatedly broke this section of the Altyn Tagh Fault. Three such events may have occurred during the 7-17 kyr fast slip period highlighted in Figure 10a, following a 20 kyrperiod of lower activity. Earthquake clustering and apparent changes is surface slip rate have been well documented along the Mojave section of the San Andreas Fault in California [START_REF] Weldon | Wrightwood and the earthquake cycle: What a long recurrence record tells us about how faults work [Article[END_REF]. The 6000 yr-long record of earthquake recurrence at Wrightwood, California showed that the San Andreas fault surface slip rate increased by up to three times the mean slip-rate on the fault during periods of higher seismic activity. There is no such long record of earthquakes along the western section of the Altyn Tagh Fault but such a behavior may explain the apparent slip-rate variations shown in Figure 10a.

Alternatively the variable rate of degradation with distance along the fault could be explained by variations of the diffusion rate through time, forced by changes in climatic conditions during the last glacial and post-glacial periods. This could be the result of an enhancement of the diffusion creep process or the action of other processes such as rain splash or surface runoff. Assuming diffusion is the dominant process at work on the alluvial slopes in the valley, a constant fault slip rate of 2.6 mm/yr would imply that the process was significantly enhanced during the 7.7-11.4 ka period with a mass diffusivity exceeding 10 m 2 /ka. Before and after this period, the value of the mass diffusivity was low, consistent with values reported for arid environments Figure 10b. For comparison, [START_REF] Small | Estimates of the rate of regolith production using 10Be and 26Al from an alpine hillslope[END_REF] report landscape diffusion coefficients as large as 18±2 ka/m 2 for frost-dominated, un-vegetated hillslopes in the Wind River Range, Wyoming.

The origin of the distance axis along the fault was fixed at the intersection point between the fault trace and the T2-T3 riser, a location that is not precisely defined due to the rounded shape of both scarps, thus allowing a possible shift of the time axis in Figure 10b. However, it is remarkable to note that the inferred period of enhanced diffusion on the scarp slope coincides with the warm period identified by the δ 18 O variations observed in the ice core of the near-by Guliya Ice Sheet [START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF].

In addition, various observations of paleo-shorelines and sediments in Tibetan lakes point to an intensification of the monsoon and warmer and more humid climatic conditions in Central Asia in the early part of the Holocene [START_REF] Fang | Lake evolution during the past 30,000 years in China, and its implications for environmental change[END_REF][START_REF] Gasse | A 13,000-year climate record from western Tibet[END_REF]. This climatic episode led to the emplacement of the early Holocene fluvial terrace widely observed in the Karakax Valley, but may have also increased the erosion rate of scarps, terrace risers, and other morphological features in the valley.

Conclusion

Cosmogenic nuclide and OSL dating methods and analysis of high resolution topography data show that the upper alluvial surface of the Karakax valley is of Eemian age (115±7 kyr) and has been displaced by 300±20 meters by the Altyn Tagh Fault since deposition. This leads to an average slip-rate of 2.6±0.3 mm/yr during that time. This rate is consistent with the mean Holocene rate at a Site 1, west of Shanxili, which may be explained by a constant slip rate on this section of the fault over the last 115 ka. However, the degradation analysis of a fault scarp progressively exposed by slip movement reveals a non-linear relationship between degradation coefficient and distance along the fault strike. We propose two non-exclusive explanations for this observation: First, assuming the mass diffusivity of the landforms to be constant during the last glacial and post glacial periods, a variable surface slip-rate on the fault may account for the observations. Such a rate change can be attributed to seismic clustering, as it has been documented for the Mojave section of the San Andreas Fault in California [START_REF] Weldon | Wrightwood and the earthquake cycle: What a long recurrence record tells us about how faults work [Article[END_REF] and suggested to explain the displacement of Holocene landforms along the central Altyn Tagh Fault [START_REF] Gold | Pulsed strain release on the altyn tagh fault, northwest china[END_REF]. Second, if the slip rate on the fault remained constant, the observations require a variable diffusion rate through time, with an increase of the mass diffusivity constant to a value exceeding 10 ka/m 2 in the early Holocene. Such a high diffusion rate may have been caused by the change of the climatic conditions to a hotter and more humid environment at the end of the last glaciation, as revealed by variations in the δ 18 O record from the Guliya Ice Cap in the Western Kunlun range [START_REF] Thompson | Tropical climate instability: The last glacial cycle from a Qinghai-Tibetan ice core[END_REF]. The data do not rule out a case where both the fault slip-rate and erosion rate would vary at the same time, with a trade-off between the two effects.

The long-term rate of 2.6±0.3 mm/yr is only 25% of the present-day slip rate of 10.5±1 mm/yr on the western part of the central section of the Altyn Tagh fault [START_REF] Daout | Strain partitioning and present-day fault kinematics in nw tibet from envisat sar interferometry[END_REF]. If the movement of the central section of the fault is transferred to the west into the Karakax section of the fault and the Gozha Co-Longmu Co fault, approximately 75% of the central Altyn Tagh Fault slip rate is required on the latter, exceeding the value of less than 3 mm/yr estimated earlier for this fault (Q. [START_REF] Liu | Palé oclimat et contraintes chronologiques sur les mouvements récents dans l'Ouest du Tibet: failles du Karakorum et de Longmu Co-Gozha Co, lacs en pull-apart de[END_REF][START_REF] Chevalier | First tectonic-geomorphology study along the Longmu-Gozha Co fault system, Western Tibet[END_REF].

Further work will be needed to assess slip-rate stability of western Tibet faults over the Late Quaternary period to reconcile these observations.

  Fig. 2

Figure 1 .

 1 Fig. 3

Figure 2 .

 2 Figure 2. Shaded topography of upper Karakax Valley area from TanDEM-X digital elevation data (Hajnsek et al., 2014). Artificial illumination is from NW with elevation angle of 45 • . Sites discussed in text are labeled by numbers. White boxes indicate detailed areas of sites 1, 3, 4, and 5 shown in Figures 4 and 5.

  report accumulation of 200 mm (H 2 O equivalent) per year over the Guliya Ice Cap in the eastern part of the western Kunlun range (Figure 1).

Figure 3 .

 3 Figure 3. Mean topographic transect across Karakax Valley corresponding approximately to section shown in bottom panel of Figure 2 (see Figure 1 for location). Solid line is mean of 75 transect profiles distributed every 0.4 km over 30 km along valley. Elevation of each transect profile is referred to elevation of Karakax river at intersection point. Shaded area is bounded by profiles of minimum and maximum elevation within profiles set.

3. 2 Figure 4 .

 24 Figure 4. Offset fan surface at sites 3 (left), 4 (center), and 5 (right). For each site, top image shows shaded topography of alluvial fan from TanDEM-X data with illumination from NW.White box represents area used in elevation profiles. Profiles show elevation vs distance along fault strike. Black and grey points correspond to southern and northern sides of fault, respectively. Top is raw profile, second from top is profile with slanted projection parallel to fan surface slope, third from top is profile after restoration of fault vertical throw to align apex of profiles between two sides of fault, and bottom is profile after restoration of left-lateral shift to align older surface (eastern slope) between two sides of fault.

Figure 5 .

 5 Figure 5. Detailed view of Site 1. a: High resolution ortho-rectified Pleiades image. White arrows with labels point to piercing points of offset morphological features discussed in text. b: Shaded DEM obtained from Pleiades images. c: Map of main alluvial terraces at Site 1. Solid lines indicate location of profiles used for degradation analysis (Figure6, Table1). Note sun illumination from SE direction in satellite image (a) and NW direction in shaded DEM (b, c).

Figure 6 .

 6 Figure 6. Example of observed and modeled profiles of scarp across Altyn Tagh Fault (S10 in Figure 5). a: Simple Gauss plus constant function (red curve) fit to observed slope profile (blue symbols). b: Observed elevation data for profile S-10 (blue symbols). Green curve is synthetic profile after formation of colluvial wedge. Red curve is best fit model after erosion by mass diffusion. c: Observed (blue symbols) and best fit model (red curve) slope profiles. d: RMS misfit between observed and modeled elevation profiles for explored range of kt values. Red curve is polynomial fit to data points to define minimum.

Figure 7 .

 7 Figure 7. Composite 3D scene of Site 4 assembled by draping Pleiades image over Pleiadesbased DEM. Terrace surfaces are numbered and shaded as a function of increasing age and elevation from river bed (T2: pale green, T2": green, T3: pale orange and T4: orange). White circles correspond to general locations of amalgamated samples for CRN surface exposure dating.

Figure 8 .

 8 Figure 8. Left: CRN model ages of surface samples collected on T2, T2", T3 and T4 at Site 4 (T2: pale green, T2": green, T3: pale orange and T4: orange). Only model ages determined using the St and LSDn production scaling schemes in CRONUS, with outliers eliminated using Chauvenet's Criteria are shown. As described in the text, the LSDn ages are preferred here. The error bars include both analytical and model uncertainty. The boxes include the LSDn model ages minus the statistically defined outliers. The mean age and standard deviations of the LSDn cluster are also indicated. Right: Comparison of the normalized model age distribution for

5

  Discussion: Glacial and post-glacial slip-rate on the Karakax section of the Altyn Tagh Fault The ages of the alluvial terraces provided by the OSL and CRN dating methods place constraints on the slip-rate on the Altyn Tagh fault over the last glacial and postglacial periods. The 300±20 m lateral offset of the upper surface of the alluvial fans at sites 3, 4, and 5 integrates the fault movement since the deposition of the units at the

Figure 10 .

 10 Figure 9. a. Field picture of Site 1, looking North from edge of upper terrace. Inset shows close-up view of sedimentary series where OSL samples were collected (circle) with pen for scale. b, c. Radial plots showing equivalent dose distributions of samples J232 (b) and J233 (c).

Table 1 .

 1 Scarp degradation analysis using diffusion model at Site 1. Profile numbers refer to labels in Figure

	Profile	Distance	Scarp	kT (m 2 )	RMS	Type
	Number	(m)	height (m)		(m)
			Fault scarp
	S1	65	27.89	74.0 +9.0/-8.5	0.24	Fault scarp
	S2	60	27.97	73.0 +8.5/-8.0	0.17	Fault scarp
	S3	55	27.84	69.0 +8.5/-8.0	0.15	Fault scarp
	S4	50	27.84	69.0 +8.5/-8.0	0.17	Fault scarp
	S5	45	26.51	65.0 +8.5/-8.5	0.18	Fault scarp
	S6	40	24.60	62.0 +9.0/-8.0	0.16	Fault scarp
	S7	35	23.70	62.0 +8.5/-8.5	0.17	Fault scarp
	S8	30	22.22	57.0 +9.5/-8.5	0.20	Fault scarp
	S9	25	20.27	40.0 +7.5/-6.5	0.16	Fault scarp
	S10	20	19.77	29.2 +4.5/-4.2	0.07	Fault scarp
	S11	15	19.80	24.6 +4.5/-4.3	0.10	Fault scarp
	S12	10	19.45	22.2 +4.7/-4.4	0.13	Fault scarp
			Terrace risers
	R1	-	10.21	15.6 +3.6/-3.2	0.09	T1/T2 Riser
	R2	-	9.68	11.5 +5.7/-4.1	0.29	T1/T2 Riser
	R3	-	11.20	6.8 +3.7/-2.6	0.20	T1/T2 Riser
	R4	-	18.96	71.0 +13.0/-11.5 0.36	T2/T3 Riser
	R5	-	22.30	75.0 +11.0/-10.0 0.22	T2/T3 Riser
	R6	-	22.75	59.0 +9.0/-8.5	0.21	T2/T3 Riser

Table 2 .

 2 CRN model ages for different production scaling models

	Scaling Model	St		Lm		LSDn
		Age (yr) Error Age (yr) Error Age (yr) Error
	T2
	KR4-1	7468	638	8060	659	8166
	KR4-9 *	24496	2113	23247	1918	22295
	T2"
	KR4-2	9610	798	10313	817	10411
	KR4-5	10745	1238	11336	1276	11359
	KR4-3	10944	1101	11488	1120	11493
	KR4-6	13735	1143	13811	1097	13595
	KR4-8 *	16463	1465	16267	1389	15830
	KR4-7 *	24921	2115	23621	1915	22610
	KR4-4 *	38189	3196	35699	2849	34087
	Average (ka)	11.3		11.7		11.7
	Std-Dev (ka)	1.8		1.5		1.3
	T3
	KR4-T1E *	85988	7718	79980	6876	75948
	KR4-T1J	105265 10686	96878	9500	92308
	KR4-T1G	105533	9187	97094	8065	92512
	KR4-T1C	107182	9215	98436	8065	93734
	KR4-T1I	109797	9464	100586	8262	95633
	KR4-T1D	111581	9619	102044	8382	96912
	KR4-T1K	112293 10061	102620	8792	97420
	KR4-T1H	114387 10123	104283	8814	98935
	KR4-T1F	115352 10312	105039	8975	99639
	KR4-T1B *	140798 12276	125666 10429	117794
	KR4-T1Kb *	161371 14654	143887 12471	133085
	Average (ka)	110.2		100.9		95.9
	Std-Dev (ka)	3.9		3.2		2.8
	T4
	KR4-STO-E	120741 10878	109337	9418	103288
	KR4-STO-C	126232 11907	113814 10300	107083
	KR4-STO-F	128396 11428	115561	9818	108624
	KR4-STO-I	131748 10765	118313	9148	110999
	KR4-STO-J	136040 11966	121743 10205	114107
	KR4-STO-H	140862 11974	125701 10145	117552
	KR4-STO-B	144336 13054	128638 11109	120067
	KR4-STO-G	146350 12790	130360 10843	121448
	Average (ka)	134.3		120.4		112.9
	Std-Dev (ka)	9.1		7.5		6.5

Table 3 .

 3 Luminescence results for samples collected at Latitude 36.3609 • N, Longitude 77.9848 • E, depth 6 m.

	Lab	Field code Mineral	K	Th	U	Grain size	Total	Equivalent	Age (ka)
	code			(%)	(ppm)	(ppm)	(µm)	dose-rate	dose (Gy)
								(Gy/ka) a
	J1232 J1232 J1233	K2-TL-1 K2-TL-1 K2-TL-2	K-feldspar 2.5 Quartz 2.5 K-feldspar 2.2	14.1 14.1 13.8	4.43 4.43 3.83	125 -175 63 -100 175 -200	5.18± 0.24 4.47± 0.20 4.76± 0.19	49.2 ± 4.0 2 9.49 ± 0.89 35.4 ± 6.5 3 7.91 ± 1.50 40.3 ± 1.5 2 8.46 ± 0.46

Calculated using DRAC v1.2(Durcan et al.,

2015), using the factors of[START_REF] Liritzis | A reevaluation of radiation dose-rate conversion factors[END_REF];[START_REF] Huntley | The K content of the K-feldspars being measured in optical dating or in thermoluminescence dating[END_REF];[START_REF] Brennan | Attenuation of alpha particle track dose for spherical grains[END_REF];[START_REF] Guérin | On the use of the infinite matrix assumption and associated concepts: A critical review[END_REF];[START_REF] Bell | Attenuation factors for the absorbed radiation dose in quartz inclusions for thermoluminescence dating[END_REF].2 Central age model of[START_REF] Galbraith | Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part i, experimental design and statistical models[END_REF] used. Calculated overdispersion of 10 and 17% for J1232 and J1233, respectively. 3 Maximum age model[START_REF] Burow | calcMaxDose(): Apply the maximum age model to a given De distribution[END_REF] used assuming an overdispersion of 15%.

Acknowledgments

The field work was carried out in collaboration with Guo Huadong, Wang Chao and Wang Changling from Institut for Remote Sensing and Applications, Diane Evans and Tom Farr from JPL, Oliver Chadwick from UCSB, and Doug Clark from University of Washington. The initial effort was supported by a NASA SIR-C investigation. The OSL sample analysis was supported by the UCLA EPSS department internal funding of the OSL lab. The cosmogenic dating was supported by the Laboratory Directed Research Project (01-ERI-009) at Lawrence Livermore National Laboratory operating under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under

Geochronology and topography data resulting from the present study are available on the UCLA Dataverse repository at https://dataverse.ucla.edu/dataverse/atf kx landforms crn osl.

The manuscript benefited from the constructive reviews of Austin Elliott and Marie-Luce Chevalier.