Morphological dating of cumulative reverse fault scarps: examples from the Gurvan Bogd fault system, Mongolia

SUMMARY We relate reverse fault scarp morphology formed by several earthquake dislocations to the average deformation rate, using a morphological dating model based on a diffusion analogue of erosion. Our scarp degradation model includes diffusive erosion during the interseismic period, the gravitational collapse of the coseismic fault scarp just after formation, and the variation of the surface rupture location. Interactions between thrusting and geomorphic processes acting on scarp morphology are analysed along the Gurvan Bogd Range in Mongolia. Four main processes acting on scarp morphology were distinguished: I) gravitational collapse of the frontal scarp, resetting the diffusive scarp if fault offsets are big and faulting is localized; 2) progressive erosion of the fault scarp during the interseismic period; 3) folding associated with the frontal thrust and backthrusts; 4) competing alluvial deposition on mountain piedmont slopes and abrasion of the fault scarp by wash processes. The growth of cumulative reverse fault scarps is suppressed when they are located in the outwash of major drainage basins. They can grow higher in distance from major catchment discharges. The modelling suggests that the morphology of the scarp and its apparent degradation stage, depend on the parameters controlling the amount of frontal collapse; the magnitude of coseismic offsets, the dip of the fault near the surface and the step distance between faults. Folding associated with thrusting creates a convexity on the upper part of the scarp and increases its height. The comparison of different scarp profiles suggests that folding leads to an overestimate of the morphological age. We estimate a diffusion coefficient at 3.3 ± 1.7 m 2 ka - l . Morphological ages calculated with our model confirm that slip rate along reverse faults of the Gurvan Bogd range has not been constant over the last 100 ka. the fault dip assumption. We compute a profile using non-vertical stepping faults and we consider it elevation data. We the true

. The Gurvan Bogd Range in the eastern Gobi Altai of Mongolia, showing our study locations.
The 1957 December 4 Gobi Altay earthquake (magnitude 8.3) led to a 260 km left-lateral surface rupture and 100 km of surface rupture by reverse faulting along the Gurvan Bogd range (Kurushin et al. 1997). This earthquake was the focus of seismotectonic studies (e.g. Florensov & Solonenko 1963;Baljinnyam et al. 1993;Bayarsayhan et al. 1996;Schwartz et al. 1996;Kurushin et al. 1997;Bayasgalan 1999;Bayasgalan et al. 1999a). Recent works (Bayasgalan et al. 1999a,b) investigated the relationships between the strike-slip faults and thrust faults in this region. Both are involved in rotations of crustal blocks about vertical axes, accommodating SSW-NNE shortening due to the India-Eurasia collision. In this context, the thrust faults are directly involved in the recent uplift of the Gurvan Bogd mountains (Bayasgalan et al. 1999a,b;Owen et al. 1999). Other studies were concerned with the climate-related alluvial fans cut by the faults along the Gurvan Bogd range (Ritz et al. 1995;Owen et al. 1997;Carretier et al. 1998), and with the geomorphic evolution of forebergs (Bayasgalan et al. 1999a). Bayasgalan et al. (1999a) observed a wide range of reverse fault scarp morphologies depending on their stages in development and their alluvial environments. The evolution of thrust scarps into topographic ridges seems to be related to fault geometry and the development of backthrusts and folding (Bayasgalan et al. 1999a). In addition Owen et al. (1998Owen et al. ( , 1999 used arguments based on soil development and the dating of Quaternary sediments to propose that the formation of alluvial fans at the foot of the Gurvan Bogd range is mainly controlled by climatic variations. They identified the following succession: 1) sedimentation under humid conditions dominated by perennial streams; 2) an increase in aridity causing a coating of coarse fanglomerates over the precedent fans by ephemeral streams and the development ofpermafrost (22-l 5 ka); 3) the degradation of the permafrost and fan incision during early Holocene (13-10 ka).
According to Owen et al. (1999), deformation of fans by thrusting is contemporary with this last stage. Ritz et al. (1999) dated several alluvial surfaces along the Gurvan Bulag fault using cosmucleides (Fig. 1). Their datings suggest that two major periods of alluviation occurred at 118.6 f 17.8 ka and at 12.7 f 1.95 ka. The offsets of these alluvial surfaces lead to uplift rates at 0.18 f 0.05 mm ye'-' overthelast118.6f17.8ka,and1.37f0.25mmyr~'overthelast 12.7 f 1.95 ka. According to Ritz et al. (1999), the Gurvan Bulag reverse fault evolved from a quiescent fault to a fault generating strong dislocations (-4 m), separated by an interval of a few thousands of years (3.3 f 1 ka). This interval is consistent with results ofpalaeoseismological investigations (Bayasgalan et al. 1997). This 02002FCAS, GJI,148, example of variation of fault activity in time motivated us to study the vertical slip rates in this particular area. Therefore, the fault scarps observed at the front of the Gurvan Bogd Range are particularly suitable for estimating deformation rate from morphology because they are well preserved. Indeed, the aridity, the lack of vegetation, the absence of human activity and the size of coseismic fault displacements (between 1 to 5 m of vertical offset along the Gurvan Bulag thrust fault during a single earthquake in 1957, Fig. 1) allow an unspoilt development of geomorphic markers that is not common elsewhere.
Only few studies have tackled the problem of morphological dating of cumulative reverse faults (Hanks et al. 1984(Hanks et al. , 1997Arrowsmith et al. 1996). Because the interactions between faulting history and erosion can be complex in such tectonic context, it is necessary to identify from field observations the different processes controlling the reverse faults scarps morphology. In this paper, we first analyse the geomorphic relationships between alluvial sedimentation, erosion and faulting for some of the thrust fault scarps along the Gurvan Bogd range. This qualitative analysis is based on descriptions of aerial photographs, precise GPS levelling of scarp profiles and field observations. Then, we apply a simple scarp degradation model to several scarp profiles to estimate the morphological age of the deformation. This approach allows us to identify the dominant geomorphic processes and to test the limitation of our model in each case. Finally, we compare our results with previous results concerning the seismic activity along the Gurvan Bogd range.

GEOMORPHIC ANALYSIS OF THE STUDIED THRUSTS ALONG THE GURVANBOGDRANGE
In this section, the geomorphological evolution ofreverse fault scarp is considered by analysing the interactions between fan formation and thrusting for two reverse faults of the Gurvan Bogd range.

The Gurvan Bulag fault (Figs 1 and 3)
The Gurvan Bulag reverse fault scarp is 23 km long, with an E-W strike, and is roughly 5 km south of the foothills of Ih Bogd massif (Figs 1, 2a,c). The 1957 December 4 earthquake ruptured the entire length of the Gurvan Bulag scarp, producing 3-5 m high vertical offsets (Kurushin et al. 1997). Along the Gurvan Bulag fault ( Fig. l), deformed zones by reverse faulting can vary even over a few kilometres as illustrated by Fig. 3. This figure shows spot images of alluvial fans cut by the Gurvan Bulag reverse fault. In regions A and C of Fig. 3 the fault scarp has reached a height of 1.00 m, associated with the development of a ridge. In region B in the front of a main drainage basin outlet, the fault scarp is less developed. The   . Stereo Spot images of the Gurvan Bulag thrust scam (see Fig. 1 for location). This figure illustrates the differences in scarp morphology along the thrust scarp. White lines underline the active streams flowing from the two main drainage basins. Dotted frames demarcates three regions where cumulative scarps look clearly different. In frames A and C, away from the main drainage outlets, the thrust scarps correspond to well developed ridges -100 m high associated with folding and backthrusting (Bayasgalan et al. 1999a). In frame B, in front of a main drainage outlet, the deformed alluvial fans look more linear, without well developed ridge. topographic ridges developed in regions A and.C, are associated with pure reverse movement on the thrust and en echelon fractures and backthrusts which accommodate a strike-slip component (Bayasgalan et al. 1999a).
We used aerial photographs to identify four uplifted alluvial surfaces (sl to ~4, Fig. 4). We based our analysis on the density of drainage networks and relative heights of terraces to give relative ages to the different surfaces (e.g. ~Bull & Pearthree 1988;Siame et al. 1997). The oldest surface (sl) is incised by dendritic drainage networks. Where natural incision reveals a cross-section, it appears that this surface corresponds to alluvial deposits in which granite boulders typically 0.1-I .O m in diameter can be found. These deposits are deformed along the scarp, leading to a deeply incised ridge, 500 m to 1 km wide and parallel to the thrust. In the central part of the Gurvan Bulag foreberg (Fig. 4) a large part of surface sl has disappeared, removed by the two main outwash channels.
The second surface (~2) is also incised by de&tic drainage networks. It cuts into the surface sl starting at the apex of the fans and forms terraces along the fault scarp. This s2 surface is mainly visible within the central part of the region, in front of major outwash systems (Fig. 4). This suggests a period of degradation after the deposition of sl, followed by the deposition of ~2. The vertical offset of this s2 surface along the scarp is 17-20 m high. The age of this surface has been estimated from cosmogenic dating at 118.6 f 17.8 ka (Ritz et al. 1999). Some relics of the s2 surface (s2b) are sometimes difficult to differentiate from a younger surface s3 (Fig. 4).
The s3 surface corresponds to debris flows. Its morphology is characterized by bars and swales, and rill-wash features. It covers a large part of the older fan surfaces north of the foreberg, which provided a barrier to the sedimentation (Bayasgalan et al. 1999a).
The thin coating of this deposit, made of coarse boulders typically 0.1-1.0 m in size, hampers its cartography. Consequently, some portions of surface s3 that we reported on Fig. 4 may correspond to eroded older deposits (in particular s2b). Ritz et al. (1999) dated surface s3 at 12.7 f 1.95 ka. This age is consistent with an estimated age of permafrost relics located around Artz Bogd (Fig. l), which Owen et al. (1998)  The s4 surface corresponds to terraces inset in surface ~3. Its vertical offset along the fault is -6.5 m. The fact that it is located along the scarp suggests a tectonic origin. Ritz et al. (1999) dated this surface at 4.1 f 0.7 ka.
We levelled topographic profiles across these different uplifted surfaces using differential GPS (Fig. 5). The repeatability in altitude is the order of centimetres. This is an acceptable precision to compare the profiles, considering that the scarp offsets exceed several metres.
The gravity-controlled failure associated with the 1957 December 4 event affected the fault scarp differently from place to place. On the profile P5 (Fig. 5), most of the scarp slope has been reset by gravitydriven processes since the 1957 event. Consequently, if we measure the 1957 offset from the vertical height of the gravity-controlled face on the profile P5, we overestimate it (Fig. 5). On other profiles (e.g. P6 and P2,Fig. 5) the 1957 offset is localized at the base of the cumulative fault scarp, that allows the rest of the scarp to be preserved from collapse. The preserved smooth morphology on scarp profiles Pl, P2, P3 and P6 (Fig. 5) corresponds to the previous surface ruptures eroded by slope erosion. This suggests that faulting steps forward in each event.
Scarp profiles P2 and P6 (Fig. 5) show constant slopes, whereas profile Pl levelled between regions A and B (Figs 3, 4 and 5) shows a convexity behind the frontal scarp. This convexity forms a ridge and drainage barrier at the western and eastern ends of the Gurvan Bulag foreberg. Where does this convexity come from and what controls its amplitude? Bayasgalan et al. (1999a) pointed out the occurrence of both thrusts and backthrusts along the Gurvan Bulag fault scarp. Although our profiles are not exactly at the same places as Bayasgalan et al.% observations, we interpret the convexity shown on profile Pl, as morphological consequences of folding and backthrusting. This convexity is located between x -550 m and x -800 m on profile Pl (Fig. 5). The fault scarp is located near x -480 m. Between the fault scarp (x -480 m) and the beginning of the convexity, the slope corresponds to the undeformed alluvial slope (Fig. 5). Consequently, it seems that the folding in this case is associated more with backthrusting than with the main thrust. Profiles P3 and P4 have been levelled across less uplifted zones (Figs 4 and 5). No clear folding appears on topography at this place.  Fig. 5. We identified several alluvial surfaces from their relative elevation, and field observations. Surface sl is the older and the more uplifted surface. Surface s2 corresponds to an alluvial fan incased in sl. We interpret s2b as relics of surface s2 partially covered or washed by posterior alluvial deposits. Surface s3 corresponds to a thin alluvial deposits incased of covering at some places s2. Surface s4 is the youngest surface, and it is located near the fault. Thick black lines indicate the location of topographic profiles shown on . Elevation and slope profiles levelled across the Gurvan Bulag thrust (see Fig. 4 for localization). Note that on profile P5 the vertical height of the gravity-controlled face greatly exceeds the value of the 1957 offset known at this place. Note also that on profile P1 the surface s3 stops at the onset of the convexity that we interpret as a surficial effect of folding and backthrusting. On the contrary, profiles P2 and P6 show constant regional slope upwards from the top of the scarp.
This suggests that folding grows in amplitude with the number of of the convex ridge are drainage and sedimentation. On one hand, events and when backthrusting has taken place. However, we do the convex ridge developed in the oldest surface s 1 disappears in the not have any trench evidence that no folding occurred at this place central part of Gurvan Bulag, in the front of the two main drainage in relation with the main thrust. In some other places along the basins, which have presumably eroded it away during periods of Gurvan Bogd range, trenches show a simple reverse fault cutting high fluvial transport (see frame B of Fig. 3). On the other hand, through undeformed sediments (for example, see Fig. 2d). Other where the ridge acts as a barrier, sedimentation which accumulates examples show that a part of the fault scarp is controlled by bending behind it also tends to level the convexity. By successive alluvial (for example, see Fig. 2f). Consequently, folding is not a general filling, the convexity tends to disappear by burial. On the profile PI feature in this area. When it develops, it can cause the scarp to ( Fig. 5), the alluvial fan s3 stops against the convexity developed in appear older, because it gives an apparent eroded shape upwards s2. This effect explains why profiles P2 and P6 look roughly linear (Fig. 2f). This should strongly limit the morphological dating of (Fig. 5). The area in front of the main drainage basins is also one such scarps. We will evaluate this effect from the analysis of scarp of abundant alluvial supply. Despite the linear fan shape observed profiles in a next Section. The other main controls on the amplitude on profiles P2 and P6 levelled on the surface s2, this surface is  probably not all of one age between the fan apex and the fault scarp (s2) has an intermediate character between dendritic incision and (Fig. 4).
bar-and-swales. The presence of this surface within the apex of sl suggests that it formed during an aggradation period and is thus a 2.2 E-W thrut sarp to te s h of B a B d fan surface (Fig. 6). Surface s2 is also affected by the thrust. The 2.2 E-W thrust scarp to the south of Baga Bogd (Figs 1 trsand 6) tthsoh ofB og most recent surface (s3) has a bar-and-swales character and corresponds also to an alluvial surface. This surface has not been uplifted We identified four geomorphic surfaces at this place (sl, slb, s2, (Fig. 6). Consequently, the thrusting activity on this scarp occurred s3) (Fig. 6). These surfaces were not cut by thrusting in the 1957 before the deposition of s3 and stopped between the depositions of earthquake (Florensov & Solonenko 1963). The oldest one (sl) is s2 and s3. However, we do not have dating information for these incised by dendritic drainage networks and is the highest recogniz-surfaces. So, although surface s3 at this location has the same geoable surface uplifted by the reverse fault. Natural incision reveals morphic features as surface s3 at the Gurvan Bulag fault (dated at that this surface corresponds to alluvial deposits in which granite 12.7 ± 1.95 ka), we can not prove that these surfaces are the same boulders typically 0.1-1.0 m in diameter can be found. The second age. surface (sib), uplifted ~15 m by the thrust, is embedded in sl. We The scarp profile P7 presented in Fig. 6 was obtained on surinterpret slb as a wash surface, probably corresponding to a hu-face sl, uplifted between 18 m and 19 m at this place. This promid pulse during the early history of the uplift. The third surface file was levelled in a portion of the scarp preserved from runoff  Fig. 1 for location). We identified 4 alluvial surfaces from their relative elevation and field observations. The oldest and more uplifted surface sl corresponds to a debris flow surface. Surface sib is embedded in sl and we interpret is as a wash surface. Surface s2 correspond also to a debris flow surface embedded in sl and sib. Surface s3 corresponds to the youngest deposit and is unaffected by the thrust, showing that this fault has not broken the surface from the deposition of ~3. The black line indicates the location of the scarp profile P7. This profile was levelled in a portion of scarp not altered by runoff driven processes. Elevation profile shows a convexity at the top of the scarp which is interpreted as morphological effect of folding. The maximum'cumulative offset including the folding component is 19 m. The cumulative offset associated with faulting only is 518 m. processes. Profile P7 has a roughly symmetric shape that we do not from the upstream fan sources. We will focus our study on portions observe on profiles levelled along the Gurvan Bulag thrust scarp located between incisions, where surfaces have been preserved from (see also the field photograph, Fig. 2e). This morphology can be runoff processes by their offset. In these portions, the fault scarps are explained by a fixed fault cutting the surface at the inflection point eroded only by slope processes which are the only processes taken of the elevation profile. A convexity appears on the elevation pro-into account in our modelling approach. We took profiles far enough file between x -290 m and x -400 m (Fig. 6). This convexity is from drainages to ensure that main gradient is oriented normal to interpreted as a morphological consequence of folding. No obvi-the fault, so that 1-D modelling can adequately reproduce the main ous surficial trace of a backthrust can be observed in association direction of sediment flux. We attempt to interpret the discrepancies with this convexity, but it may have disappeared by erosion from between our model and the data according to the influence of other the cessation of the seismic activity. Because of the folding compo-geomorphic processes that we can identify. nent of the offset, the slope profile shows two populations, separated at x ~ 290 m (Fig. 6). Unlike our interpretation along the Gurvan MODELLING APPROACH Bulag fault scarp, these two populations do not correspond to variable locations of the fault responsible for the surface rupture. The Four approaches are possible to model the evolution of scarp mormaximum cumulative offset including the folding component of phology on active faults: 1) the scarp morphology is assumed to be the uplift is estimated at 19 m (Fig. 6). The cumulative offset cor-controlled by elastic displacements of the surface related to disloresponding to the approximation of the hangingwall surface by a cation at depth (e.g. King et al. 1988;; Taboada planar surface is 18 m (Fig. 6). This offset is an estimate of the et al. 1993); 2) the scarp is assumed to be controlled by surface uplift component due to faulting only. rupture and slope erosion processes (e.g. Culling 1960;Nash 1981;Avouac 1993;Arrowsmith et al. 1998); 3) the scarp evolution is controlled by both effects 1 and 2 (e.g. Arrowsmith et al. 1996); 4) 2.3 General implications for the morphological evolution 2.3 General implications for the morphological evolution the scarp morphology is assumed to be controlled by slip between of forebergs stratified deposits of different rheology (Nino et al. 1998). We chose The observed variability of topographic expression associated with the second approach which involves imposing the surface rupture reverse faulting seems to be related to cessation of alluvial depo-and modelling the erosion of scarps using a linear diffusive anasition and evolution of the fault system itself. The repetition of logue. We did this for several reasons: 1) our goal is to date scarps earthquakes increases the surface deformation, so that the thrust using the erosion of their morphology; 2) elastic dislocation models scarp eventually forms a topographic ridge, which can act as a bar-are very sensitive to the fault geometry and depth ; rier to sedimentation (Fig. 7a). However, for a scarp to achieve this Arrowsmith et al. 1996), which are not well constrained in our area. morphology it must be located either far from outwash channels Therefore, the width of our topographic profiles is short (several of major drainage basins, or to the side of them. When the thrust 100 m) compared to the length of the faults (10-20 km), so the efscarp is close to and in front of a major drainage basin outlet it is feet of the elastic dislocation modelling is diminished (Arrowsmith modified by processes including scarp abrasion and deposition, de-et al. 1996); 3) scarp morphology depends on interactions between pending on the fluvial transport capacity and the sediment supply in successive alluvial deposits and the seismic cycle. In most of the the drainage basin (Carretier et al. 1998). These alluvial processes cases we discuss, uplifted and preserved surfaces do not correspond can cause destruction of the scarp or filling of the depression be-to single surfaces that can be modelled by an elastic dislocation tween the remnant scarp convexity and the range front ( Fig. 7b), model. and may be influenced by climatic variations. The resulting uplifted Morphological dating is the process of comparing modelled and alluvial surfaces can be flat (see profile P2, Fig. 5). Consequently, observed profiles to determine the age of the landform. We use when the thrust scarp is far from main drainage basin, the wave-a linear diffusion analogue to describe scarp erosion preserved length of the deformation associated with thrusting is revealed by from runoff processes (portions of fault scarps located between the distance between the scarp front and the toe of the alluvial de-incisions). In this case, the transport law is that the local flux of posits ( Fig. 7a). However, when the scarp is in front of a main basin sediments is proportional to the local topographic slope (Culling outlet, the distance between the thrust front and the alluvial deposits 1960). We assume that material of faulted alluvial fan has been alis controlled instead by successive erosion and deposition horizons ways available for transport. This is consistent with non-cohesive ( Fig. 7a). In principle, the wavelength over which incised channels alluvial sediments observed on the field. Thus, assumption of transand terraces form is also influenced by the down-dip fault length, port limited conditions and application of the continuity equation as shown in numerical models of elastic displacement fields and for sediment flux will result in a diffusion-like equation relating the diffusive geomorphic processes (Arrowsmith et al. 1996). In prac-local erosion rate and the local topographic curvature (7h = K a0, tice, the real wavelength of the deformation appears to be controlled where h iselevation at point x, and t the time). The proportionality by the location of backthrusts, which may correspond to a flatten-coefficient K [in unit ofm 2 ka -' ] is called the diffusion coefficient. ing of the thrust dip at depth (Fig. 7). The variation in apparent By fitting synthetic topographic profiles computed with these aswavelength along the Gurvan Bulag foreberg ridge is more likely sumptions to observed scarp profiles we can estimate the product to be controlled by the scarp location relative to the main drainage Kt where t is the age of the scarp. We will call this product the basins than by lateral variations in fault dip. The scarp of Dalan "morphological age" of a scarp. Turuu, north ofIh Bogd, illustrates this conclusion (Figs 1 and 2b).
Dating scarps becomes more uncertain when repeated faulting is This thrust scarp forms a topographic ridge 200-300 m high, with involved, as Avouac & Peltzer (1993) show for cumulative normal a constant width along the fault. No major drainage basin crosses fault scarps. In this case the unknown parameters controlling erosion the thrust. and tectonics are multiplied by the number of events. This is even In the second part of this study, we will model scarp profiles to es-more difficult in the case of cumulative reverse faults because of timate their morphological ages. These scarps are incised by locally-the variability of the surface faulting itself. Numerous descriptions formed drainages and also thorough-going or antecedent drainages of trenches across reverse active faults show that the position of the . Conceptual sketches that illustrate alluvial sedimentation contexts and foreberg morphologies. (a) When the foreberg is away from a major drainage basin outlet, the geomorphic limit between alluvial surfaces is mainly controlled by the development of a folded and backthrust ridge that forms a barrier to sedimentation. In this last case, the distance between the fault trace and the lower limit of recent fans shows the true wavelength associated with the folding and backthrusting. (b) However, when the foreberg is located in front of a major drainage basin outlet, the fluvial transport (abrasion or sedimentation) tends to level the regional scarp slopes. Limits between alluvial geomorphic surfaces in map view are mainly due to the interplay between stream incision and the development of terraces rather than the surface displacement due to folding and backthrusting.
rupture at each event is usually variable, unlike most cases of normal suggest that the rupture steps forward in each event (Figs 2 and 5). faulting (see for example McCalpin, 1996,pp. 107-211;Meghraoui Hanks et al. (1984) proposed a simple analytical model for datet al. 1988;Swan 1988;Philip et al. 1992;Yeats et al. 1997, ing cumulative scarps, involving diffusion of continuous uplift on p. 352). Along the Gurvan Bulag ranges, the position of the 1957 a fixed and vertical fault. His model cannot be applicable in such event trace at the base of cumulative scarps and trench observations cases.

(a) NATURAL CASE
during interseismic period (1) instantaneous collapse of the hanging wedge due to reverse movement, (2) development of a gravity-controlled face at the angle of repose of the material over several years. At the end of this stage, material is equally distributed between hangingwall and footwall. 3) Diffusive transport. (b) Model. The surface rupture is modelled by a translation of the profile in the hangingwall according to specified dip of fault and vertical offset and from the middle of the hangingwedge. The gravitational collapse is modelled by reducing all slopes greater than the specified slope of repose. These two steps preserve the mass-balance between hangingwall and footwall. Linear diffusion is then applied during a specified morphologic duration (KAt).

1end of interseismic period
We thus introduced some extra complications in our model al-model used by Avouac & Peltzer (1993) for cumulative normal fault lowing the position of each rupture, which can be variable in each scarps. Gravity-controlled failure of scarps has been well described event, and the fault dip at the surface to be specified (Fig. 8).
and is common when faulting occurs in non-cohesive material We also allow the surface slope to collapse after a surface rup- (Wallace 1977;Machette 1987) leading over several years to ture when the slope exceeds the slope angle of repose of the a gravity-controlled face that forms after the collapse of the non-cohesive material. In that sense, our model is similar to the hangingwall-wedge by a normal fault whose position can be  (Fig. 8a). The gravitational col-4 THEORETICAL RESULTS lapse is not a diffusive process. It is driven by internal friction of unconsolidated material (Roering et al. 1999). Thus, when the scarp Fig. 9 illustrates schematically two extreme cases observed in our slope reaches a threshold slope (or "slope of repose"), it collapses numerical experiments. They differ by the relative magnitude of quickly. We observed that this process is a strong controlling factor parameters. The inherited diffusive scarp morphology may or may of scarp evolution. For example, Fig. 2A and profile P5 (Fig. 5) not be preserved when a new seismic event occurs. This depends show a cumulative reverse fault scarp for which the frontal portion on gravity-driven processes that tend to maintain scarp slopes at collapsed during the 1957 event. This process affected a large part the angle of repose of detritic material, resetting the diffusive scarp of the scarp, which consequently lost its diffusive morphology. The morphology. In terms of morphological dating, such resetting is resulting gravity-controlled face will then erode by diffusion until equivalent to resetting the clock. Indeed, large offsets and repeated the next surface rupture. The future diffusive morphology will only surface rupture at the same place (Fig. 9, case A) enhance the deprovide information about the age of the 1957 event. Consequently, velopment of a gravity-controlled face. In this case, the gravityit is clear that this process is a strong limitation for dating of the initi-controlled height exceeds the true value of the vertical component ation of uplift. Along the Gurvan Bulag range, the vertical height of associated with a single surface rupture. As mentioned previously, the gravity-controlled face acquired several months after the 1957 such behaviour has been observed along the Gurvan Bulag range dislocation is variable, even between places separated by only a few (see Fig. 2a and profile P5 on Fig. 5). This effect can have important hundred of metres (compare for example profiles P5 and P2, Fig. 5).
implications in palaeoseismology, as well as for scarp morphology These observations show that slope collapse can refresh reverse fault and dating. When estimating the vertical component of a surface scarp morphology to varying degrees, and consequently it must be rupture from the total vertical height of the gravity-controlled face, taken into account in our morphologic dating model. Some authors this effect will lead to an overestimate of the last vertical offset. This used forward modelling in which gravitational collapse is computed suggests that 1957 offsets along the Gurvan Bulag range could have at the same time as diffusion (e.g. Arrowsmith et al. 1998). This is been overestimated by Kurushin et al. (1997) when using height very useful to estimate slip rates when processes are demonstra-of the gravity-controlled face (e.g. Kurushin et al. 1997 site 17, tively continuous. In the case of repeated faulting with large offsets, p. 99), and some cumulative scarps considered previously as one the possible variation of the surface rupture location and the vari-event scarp could be in fact two-events scarps (see for example proable degree of frontal collapse impose to respect the succession of file P4 in Fig. 5). By contrast, distinct forward-stepping faults with geomorphic processes.
small offsets preserve the diffusive scarp morphology (Fig. 9, case In summary, we model topographic scarp profiles as follows B). Between these two extremes cases, we obtained a lot of differ- (Fig. 8a): ent morphologies which can not be summed up in a general graph. These morphologies differ by their relative record of past events. (i) we chose the position of the surface rupture and of the dip of Thus, preservation of diffusive morphology depends on local facthe fault; tors which must be evaluated in the field and by modelling. (ii) we specify the offset on the fault; Consequently, it is clear that dating the beginning of the ramp (iii) we simulate the initial collapse of the hangingwall by form-formation is not always possible. In the worst cases, we can only ing a vertical step in the middle of the offset (Fig. 8b). This choice date the penultimate event (in this case, the event before 1957). allows to preserve the mass-balance between eroded material from For example, our theoretical simulations of ruptures localized on the hangingwall and the deposited sediment in the footwall at the a 45°dipping fault suggest that incremental offsets greater than end of the next modelling step, whatever the position of the nor-3 m will imply a total resetting of the diffusive scarp at each event, mal fault is, until its dip is greater than the critical slope (Fig. 8b).
whatever values the other parameters have. This is in contrast to This modelling preserves the shortening associated with the reverse the case of repeated normal faulting. Although development of a component.
gravity-controlled face can occur in both cases, in normal faulting (iv) We allow the slope to collapse under gravity in order to bring the increase of the scarp length (distance between two symmetrical the scarp slope to the angle of repose of the material (~30°). To points in the hangingwall and in the footwall) preserves diffusive achieve this we apply diffusion with very high diffusion coefficient scarp morphology. to slopes exceeding the slope of repose (Andrews & Hanks 1985). Although gravitational collapse is not a diffusive process, this numerical method enables to respect mass balance of transport. It also 5 BE ST fiTTING MORPHO L OGICAL enables us to reduce slope instantaneously by using a sufficiently AGE DETERMINATION high diffusion coefficient. The transport-limited condition implies In order to determine the best fitting values of morphological age In order to determine the best fitting values of morphological age that this process affects all slopes greater than the angle of repose, . r " for the different processes, we performed a parameter search by and thus that the free face formed just after the earthquake is very quickly degraded. .This is consistent with our field bforward modelling in which KAt (product of diffusion coefficient quickly degraded. This is consistent with our field observations. (  interval of the inferred age, we related the range of acceptable fit-GPS method which is accurate to less that 5 cm. Consequently, this tings to the RMS values lower than RMSmin + 5 cm. By doing this, value is adapted to define confidence intervals of morphological we retained the same criterion proposed by Avouac (1993)  . This criterion has been used to determine an objective es-intersections between the RMS curve and the horizontal line defined timation of the precision with which morphological ages are esti-by RMS = RMSmin + 5 cm. We define the morphological age by mated, taking into account topographic levelling with precision of KAt^in+A'mA and its uncertainty by K Atmax minus the morphological about 5 cm. In that sense, if several models can match the same data age. When converting morphological ages into diffusion coefficient, with RMS lower than RMSmin + 5 cm, they will not be differen-we propagate the uncertainty associated with each parameter as foltiated. The levelling of our profiles has been made by differential lows: considering that 8 Kt and St are the uncertainties associated with values of Kt and t respectively, then K is given by ' S K, scarp would be lower than the slope of repose of the material, espewhere SK is /( t I)2 + (Is)2 (Bevington & Robinson 1992). We ap-cially in the case of one event scarps. Nevertheless, all our profiles ply the same method to convert morphological ages into numerical display a slope at the front of the scarp (~0.7) which corresponds ages or slip rates.
to classical values for slope of repose of detritical sediments (e.g. Morphological age is not the only parameter which controls the Wallace 1977; Machette 1987; Avouac & Peltzer 1993) (Fig. 5). accuracy of fittings between observed and modelled profiles. The Although this hypothesis can not be rejected by direct evidence, determination of the best fitting morphological age and uncertainty morphological arguments seem to favour the stepping of successive requires estimation of several parameters such as number of events, faults. the incremental offsets, the dip of the faults, their location, the angle To determine the location of the successive faults responsible of repose of material, and the regional (initial) slope of the profile.
for the surface rupture requires one to look at slope profiles. A Some of these parameters can be evaluated from field data, namely surface rupture associated with a seismic event causes an abrupt the regional slope corresponding to the portion of profile far from perturbation of the slope profile. When a surface rupture is followed the scarp, and the angle of repose which is given by the portion by an interseismic period this perturbation acquires a "Gaussian" of the scarp associated with the 1957 event. Other parameters are shape, that is predicted by a diffusion model ( Fig. 9 case A, slope more difficult to determine. For example, the dip of the faults and profile) (Avouac 1993;Nivi&re et al. 1998). Assuming that their their location remained uncertain in most of the cases. A trench formation is only related to surface rupture, the identification of across a fault scarp, which is necessary to determine the fault ge-these "Gaussians" or inflections of a slope profile depends on the ometry, has not always been possible, especially when scarps are distance between the successive surface ruptures (compare Fig. 9 several metres high. Consequently, the solution given for each mod-case A and case B). Consequently, we can estimate the location of elled profile should not be unique. Therefore, estimated morpholog-the successive faults from the slope profile independently of the ical ages and their uncertainty should depend on the assumptions morphological age, in such a way that the locations of observed and made about fault geometry, values of incremental offsets and num-modelled slope inflections fit. ber of events. Keeping this in mind, we fix these parameters using The dip of faults is one of the parameters controlling the gravmorphological arguments, and compare our results with previous itational collapse of the scarp, and thus the preservation of the estimations of slip rates and time recurrence intervals based on cos-diffusive scarp morphology (Fig. 9). This parameter cannot be evalmogenic dating of uplifted surfaces in our study site (Ritz et al. uated in this study. However the estimation of the best fitting mor-1999).
phological age does not depend on this parameter when the mor-We assume that the interseismic duration At and the diffusion phology associated to past events is preserved (see Appendix A, coefficient K are constant, so that RMS is computed with constant Figs Ala,b). et al. (1998) as well as others showed (e.g.

KAt. As Arrowsmith
The successive steps of our fitting method are the following: Niviere & Marquis 2000), the uncertainty of morphological age increases with the age of the scarp. Consequently, the single value (i) The incremental offset and the number of events are estimated of K At relative to a past event can not be resolved with a good from the elevation profile, and the slope of repose and the regional accuracy (see Appendix A, Fig. Alc). On the contrary, constant slope are estimated from the slope profile. The slope of repose is KAt between events allows us to estimate a best fitting value with a estimated from the mean slope of the gravity-controlled face rather good accuracy (see Appendix A, Fig. Alc). The best fitting value of than local maximum. KAt that we compute has consequently the sense of a mean value, (ii) The successive fault locations are estimated from the slope which giyes mean dating and uplift rate.
profile. The fault dip is taken arbitrary lower than vertical (500) to We assume that the incremental offsets are equal to the local reduce the uncertainty of the best fitting morphological age (see value associated with the 1957 event (Kurushin et al. 1997), and Appendix A). in this sense the successive events are "characteristic" as suggested (iii) Forward modelling assuming non-vertical faults is carried by Ritz et al. (1999) and Kurushin et al. (1997). Consequently, to out to evaluate if the scarp could have been reset during the uplift. estimate the number of events, we divided the cumulative offset by This step aims at determining whether the initiation of the uplift or this incremental offset.
only the last events can be dated (see Fig. 9). We assume that the fault responsible for the surface ruptures (iv) The RMS is calculated for different values of KAt and the steps forward at each event. We have no direct evidence of this best fitting morphological age and its associated uncertainty is debehaviour for the studied profiles because it has been impossi-termined graphically. ble to trench across scarps which can reach 20 m height. How-We apply this methodology to the examples previously described. ever, some other trenches across reverse fault scarps around the In each case, the RMS between observed and modelled profiles is Gurvan Bogd range displayed suchpattern, while some other showed computed only on the apparent diffusive portion of the scarp. unique faults or more complex geometry (Bayasgalan et al. 1997;Bayasgalan 1999). We argue for a forward stepping of the faults from the scarp morphology: first, the portion of the scarp associated with the more recent event (1957) is generally located at the front of scarps (Fig. 5); secondly, slope distribution across scarps is usually 6.1 The Gurvan Bulag reverse fault (Figs 1, 3 and 4) not symmetrical, and slope decreases upwards from the position of a the last rupture (Fig. 5). This suggests that the upper part of scarps As mentioned earlier, cosmogenic dating of uplifted alluvial fans is more degraded and thus older than the lower one. Such morphol-allowed Ritz et al. (1999) to propose that seismic activity resumed ogy may also result from the ridding of the hangingwall over the on this fault from at least the deposition of surface s3 dated at land surface by the way of a flat fault, prolongating a shallow ramp 12.7 + 1.95 ka. By the morphological dating of cumulative reverse fault geometry. In this case, the frontal part of the scarp would cor-fault scarps, we want to date the beginning of the uplift of the older respond to the propagating flat fault. Thus, the slope of the frontal surface s2 (deposition at 118.6 + 17.8 ka, Ritz et al. 1999).  Fig. 4 for location). Triangles are data and solid lines are models for the best fitting morphological age, using two events of 3.2 m offset on faults dipping 50°with 10 m distance between the two slip surfaces. The best fitting morphological age and associated uncertainty is determined graphically from the RMS versus constant K At. The RMS is calculated from the elevation data, over the length corresponding to the diffusive morphology (horizontal arrow on the elevation profile). To define the range of acceptable values of KAt, we retain all models for which the RMS lies between RMSmax and RMSmin +5 cm (see text for details).

Profile P3 (Figs 4 and 10)
15 m and 12 m stepping of the successive faults (dipping at 50°) responsible for the surface ruptures, we estimate a mean KAt ranging This profile is levelled across surface s4, uplifted 6.5 m (Fig. 10). from 6.5 m 2 to 19 m 2 from the RMS curve (KAt = 12.75 6.2 m 2 ) This cumulative offset is twice the vertical offset of the 1957 event . ). T r i f c w t l (Fig. 11). This result is fairly consistent with the last morphologi-(3.25 m). The gravity-controlled face associated with the 1957 event cacu frm ri i. .,," . cal interseismic duration KAt calculated from profile P3 (Fig. 10). is located at the front of the scarp, allowing to preserve the diffusive n r ic , , . ,., " . . The mean value of the morphological age at the profile P1 locamorphology associated with the last interseismic period. .morphological ages determined from the RS range from initiation of the uplift responsible of the cumulative offset of sur-KAt = 7 to 20 m 2 (Fig. 10). The mean morphological age of the ad te p im e a 3. evntithu3 .5 2. Rie a .
(I 99 face s2 at 11.7 ± 8.1 ka, and the penultimate event at 3.9 ± 2.7 ka. penultimate event is thus 13.5 ± 6.5 m 2 . Ritz et al. (1999) estimated ' l ,~ " " " , .These estimates are consistent with 10Be dates (Ritz et al. 1999) the age of the uplifted surface s4 at this place to be 4.1 ± 0.7 ka, as well as with preliminary results from palaeoseismological invesbased on cosmogenic measurements. It allows us to calibrate the . . .coefficient of diffusion K in our model at K = 3.3 _i 1.7 m 2 kal tigations giving the penultimate event at ~4 ka (Schwartz et al.  Bayasgalan et al. 1997). The uplifted surface s2 being dated close to other estimates in the same climatic conditions (for example et al. 19) h esu c at 118.6 ± 17.8 ka (Ritz et al. 1999), these results confirm that the in the Dsungar desert located in Central Asia; Avouac & Peltzer .
consequently, that this fault was almost quiescent between -118 ka and -12 ka. Over the last 11.7 ± 8.1 ka, we estimate from the 14 m cumulative offset of s2 an uplift rate on the Gurvan Bulag fault at 6.1.2 Profile PI (Figs 4 and 11) 1.2 + 0.8 mm yr-'. This value is consistent with the previous es-This profile is levelled across surface s2, uplifted between 14 m and timate at 1.37 ± 0.25 mm yr-1 given by Ritz et al. (1999) for the 18 m (Figs 4 and 5). The gravity-controlled face is localized at the same duration. base of the scarp and most of the inherited diffusive morphology is preserved, allowing us to estimate the morphological age of the 6.1.3 Profile P6 (Figs 4 and 12) cumulative uplift (Fig. 9, case B). We identified on profile P1 the folding component of the uplift, which seems to not affect the slopes This profile is levelled across surface s2, uplifted 17 m, in front of near the fault scarp (Fig. 5). Thus, we will estimate the morpholog-a major drainage basin (Figs 4 and 12). Just as we detected 4 events ical age of the scarp from the data located in the region presumably on profile P1 responsible for the uplift the surface s2, we modundeformed by folding (x < 520 m, Figs 5 and 11). The correspond-elled the cumulative offset on profile P6 also using 4 events, with ing cumulative offset (14 m) is four times the local vertical offset vertical incremental offsets of 4.25 m. The 1957 gravity-controlled associated with the 1957 event (~3.5 m) (Fig. 11). The decreasing face is located at the base of the scarp, suggesting a forward stepslope from the bottom to the top of the scarp and the frontal loca-ping of the fault. The slope profile shows a peak corresponding to tion of the gravity-controlled face suggest that the rupture stepped the gravity-controlled face, followed by a roughly gaussian shape. forward (Fig. 11). Using 4 events with 3.5 m offsets, and 15 m, Our numerical experiments suggest that the fault scarp collapsed x (m) Figure 11. Morphological dating from profile P1 (see Fig. 4 for location). Triangles are data and solid lines are models for the best fitting morphological age, using four events of 3.5 m offsets on faults dipping at 50°, with 15 m, 15 m and 12 m distance between successive slip surfaces. The best fitting morphological age and associated uncertainty is determined graphically from the RMS versus constant KAt. The RMS is calculated from the elevation data, over the length corresponding to the diffusive morphology (horizontal arrow on the elevation profile). To define the range of acceptable values ofK At, we retain all models for which the RMS lies between RMSmin and RMSmin +5 cm (see text for details).
between each event prior to 1957. Coseismic scarp resetting occurs for P3). It is difficult to evaluate the contribution of folding to the at each event because of the high offsets and because the fault steps cumulative offset on P6, because this folding is masked by alluvial at this locality (adjusted to fit the locations of inflexions on the slope sedimentation, that leads to a constant slope in the hangingwall. profile) is smaller than at the location of profile P1 (Fig. 11). This However, the cumulative offset estimated from profile P6 is similar occurs if we consider either faults dipping at 50°or vertical faults, to the maximum cumulative offset given by profile P1 (18 m). The Only the 1957 event allowed to preserve remaining diffusive mor-maximum offset on P1 includes the folding component of the upphology because it is located far from the penultimate rupture. This lift, which appears more clearly than for profile P6. If our estimates suggests that the remaining diffusive morphology has developed of offsets are higher than the real ones, we will overestimate the from the penultimate event, from a stage where the scarp was domi-morphological age (for two scarps with different offsets but with nated by the stable gravity-controlled slope. Consequently, from the identical degradation states, the diffusion model will predict higher profile P6 we can estimate only the value of K At corresponding to K/At for the greater offset). the duration between the penultimate event and the 1957 event. This The overestimate due to folding and offset values is likely to be value is determined from the RMS curve at 21.5 ± 5.5 m 2 (Fig. 12). predominant here. We base this choice on the consistency between We tried to explain the slopes between x 200 m and x -240 m calculations in the two first profiles (P3 and P1), and because we by a large stepping of the fault between the two first events. The know from numerical experiments that offset values have a strong fit of our synthetic slope to profile P6 requires a KAt between the influence on age estimates (Avouac 1993). two first events greater than 150 m 2 . This is inconsistent with KAt calculated from profiles P3 and P1 ([6.5-20] m2). Alternatively, we could interpret the slope profile between x ~ 200 m and x ~ 240 m 6.2 E-W thrust scarp to the south of Baga Bogd as the folding component of scarp morphology that has no meaning (Figs 1 and 6) in terms of morphological dating. Although the elevation profile P6 W s f t p g a o We stated from the previous geomorphic analysis of uplifted alluvial looks roughly linear after x ~ 250 m, folding seems to appear here, alooks rtoughly linear after x -. 250 , folding seems to appear here, fans, that this fault has not broken the surface from the deposition although we have no direct evidence.
although we have no direct evidee of the more recent surface s3 (Fig. 6). A far as we do not have Moreover, the morphological age of the penultimate event on pro-fieP 'suhgete2. -5.5 in) than in the previous estimates numerical dating of the uplifted surfaces, can we bound the age of file P6 is much greater (21.5 ± 5.5 m2) than in the previous estimates with profiles P3 (13.5 ± 6.5 m 2 ) and Pi (12.75 ± 6.2 m2). In order the last event by morphological methods? to explain this, we suggest two possibilities: 1) the morphologic age calculated from profiles P1 and P3 could be underestimated. Folding 6 P P ( 6 6.2.1 Profile P7 (Figs 6 and 13) tends to increase the scarp slopes and thus decrease the morphological age.
2) The estimate from profile P6 could be overestimated. The symmetric shape suggests that rupture has remained localized While the folding can increase the scarp slopes, it can broaden the near the inflection point of the scarp profile. The curved trace of part of scarp profile apparently eroded, making it older morpholog-the fault in plan view suggests that the fault has a relatively low ically. Therefore, offsets that we use to model the cumulative offset dip (Fig. 6). We also have no clear indication of local incremental of P6 may also be too high (4.25 m for P6, compared with 3.5 m offset values, this scarp being unaffected by the 1957 earthquake.  The morphology between x-300 m and x 400 m is controlled 7 DISCUSSION AND CONCLUSIONS by folding (Fig. 6). The cumulative offset associated with faulting is estimated at 18 m (Fig. 6).
The examples that we described illustrate a variability that depends We postulate that incremental offsets are similar in size to those on the balance between four processes (Bayasgalan et al. 1999a): at Gurvan Bulag with a maximum at ~5 m. We carried out ex-1) surface dislocation on faults, 2) folding associated with thrustperiments varying the incremental offset between 3 and 5 m (cor-ing and backthrusting, 3) alluvial erosion and sedimentation, and responding to 6 and 4 events responsible for the cumulative offset 4) slope erosion. These factors have general implications for the of 18 m), the dip of the fixed fault between 45°and 90°. We fixed morphological dating of any transport-limited reverse fault scarps. the value of the slope of repose at 0.7, which corresponds to the slope of the gravity-controlled face commonly observed for similar 7.1 Alluvial environment sediments along the Gurvan Bulag scarp. Such range of parameters implies the total removal of the synthetic scarp after two or Our examples suggest that cumulative reverse fault scarps can three events, because of gravitational collapse associated with the be dated when they are in front of drainage basins. In this case, reverse component and the large offsets (Case A of Fig. 9). Conse-climatically-controlled abrasion or deposition isolates surfaces that quently, we can only date the last event from this scarp. To explain have been uplifted by different numbers of earthquakes. This alluthe observed smooth morphology, this scenario requires a long pe-vial environment controls the vertical growth of forebergs whose riod of quiescence during which the fault is inactive. We date the morphology is dominated by slope erosion. last event at 235 ± 39 m 2 (Fig. 13). This morphological age is determined from the RMS versus KAt computed over the portion of the scarp profile presumably unaffected by folding (x < 290 m, Figs 6 and 13). This tends to reduce the possible overestimate of Folding may decrease the apparent morphological age by increasthe morphological age due to folding, which is expressed morpho-ing the scarp slope. It is difficult to quantify this effect. On the logically at the upper part of the scarp. If we use the diffusion co-other hand, if folding is masked by sedimentation, producing flat efficient calibrated on the Gurvan Bulag Fault (which has the same topography (e.g. profile P2, Fig. 5), we may overestimate the fault orientation and same materials), we date the last event occurring on offsets and therefore the morphological age of the scarp. A second the Southern Baga thrust at 71 + 38 ka. The uncertainty is large, effect which can lead to an overestimate of the morphological age but this age may correspond to the pause in surface rupture activ-is the surface bending associated with folding, which may be misity observed in Gurvan Bulag between approximately 118 ka and taken with diffusive-controlled morphology (e.g. Fig. 2f). The last x (m) KAt (m2) Figure 13. Morphological dating from the profile P7 (see Fig. 6 for localization). The symmetric shape of the elevation profile suggests that faulting has remained located at the inflection point of the scarp. Assuming a fault dipping at 45°, and 4.25 m offsets, the modelling suggests that the scarp collapsed at each event. Consequently, only the last event can be dated. The best fitting morphological age and associated uncertainty is determined graphically from the RMS versus constant KAt. The RMS is calculated from the elevation data, over the length corresponding to the diffusive morphology (horizontal arrow on the elevation profile). The right part of the profile (from x ~ 300 m) is interpreted as folding. The RMS curve refers to the last interseismic duration only. To define the range of acceptable values ofK At, we retain all models for which the RMS lies between RMSmin and RMSmin +5 cm (see text for details).
gradient variation helps identify folding, even if it does not appear distributed fractures because gravitational collapse is less efficient obviously on the scarp profile itself (profile P6, Fig. 12). Folding at removing variations at the surface in this case (Fig. 2f). associated with reverse faulting could be present in all our studied profiles, leading in overestimated values of morphological ages. If so, our estimated morphological ages for large cumulative offsets 7.4 Reverse component, variable position of the main (for which folding can affect significantly the dating) are maximum thrust, fault offsets and gravity-driven collapse values. These values allow to bound the age of the initiation of the uplift, which is the aim of our study on the Gurvan Bulag fault.
The morphology of cumulative reverse fault scarps is strongly conuplift, which is the aim of our study on the Gurvan Bulag fault. Moreover, the consistency of our results and previous estimations tolled by gravitatioal collapse if faulting remains localized and if incremental vertical offsets are large (> 1 m). Gravitational colof uplift rates and resumption of the seismic activity on the Gurvan ncreenal ertica sets ae age r ona Bulag fault is encouraging (Ritz et al. 1999). Our study attempted lapse and scarp shortening caused by the reverse component act * fault is* enorgn Rtta.199Oto reset the diffusive shape. If a large part of the scarp is affected also to test the application of morphological dating method to cu-reset the duse o t s aete mulative reverse faults scarps. We use a simple model to discuss the ths reduces the number of unknowns by givi a new iitial state rule of several processes. To improve further works on such scarps, of gradation at each event and by smoothing irregularities. On the other hand, such resetting removes information about the older it will be necessary to add the folding in models for a more general e e events. parametrical analysis.
It is difficult to justify the use of analytical models that do not take this reverse component and its consequent gravity-driven collapse into account, unless this is demonstrably unimportant in that 7.3 Distributed secondary faults particular case. We prefer to used a forward model which, although Trenches excavated in cumulative fault scarps can exhibit a main simplistic, allows us to assess the importance of slope collapse by thrust with associated secondary fractures and colluvial wedges varying local parameters such as the slope angle of repose, the dis-(e.g. Meghraoui et al. 1988;Philip et al. 1992). Other examples tance between successive faults and incremental rupture offset valshow a single fault cutting through alluvial deposits at each event ues. Our approach helps evaluate whether a whole scarp or only (Figs 2d,f). Distributed faults within a scarp can cause several in-the penultimate event can be dated. Our model is, however, limflections of the scarp morphology at each seismic event. At the ited by the value of the cumulative offset. Beyond a certain offsame time, folding may develop with variable amplitude (e.g. Philip set, the morphology of scarp is only controlled by folding and & Megrhaoui 1993). When a cumulative fault scarp develops with incision. large incremental offsets (> 1 m), the resetting effect of gravitational A recent study pointed out that calibrated diffusivity on the shorecollapse smooths surface irregularities and folding is only expressed line of Lake Bonneville that non-linear diffusion matches the data in the morphology in the upper part of the scarp. In this case, the better than linear diffusion (Mattson & Bruhn 1999). At the scale geomorphic evolution of a cumulative scarp is mainly controlled of hillslopes, Roering et al. (1999) showed also that erosion is betby the successive gravitational collapse after each event and dif-ter described by non-linear erosion. Non-linear erosion effects usufusive slope erosion during interseismic periods. The morphology ally imply that the morphological ages estimated by linear diffuof scarps formed by small offsets is more sensitive to bending and sion will be overestimated. We expect that these non-linear effects r A iv Thus, only a mean value of KAt can be estimated from a cumulative Dorjnamjaa, D., 1997. Quaternary alluvial fans in the Gobi of southern s ol a Mongolia: evidence for neotectonics and climate change, J. Quatern. Sci.,12,[239][240][241][242][243][244][245][246][247][248][249][250][251][252] First, we want to evaluate how the morphological age depends on Owen, L.A., Richards, B., Rhodes, E.J., Cunningham, W.D., Windley, B.F., the fault dip assumption. We compute a profile using non-vertical Badamgarav, J. & Dorjnamjaa, D., 1998. Relic permafrost structures in stepping faults and we consider it as elevation data. We compare the Gobi of Mongolia: age and significance, J Quatern. Sci.,13,[539][540][541][542][543][544][545][546][547] then the RMS versus K At when assuming true dip or vertical faults. Fig. Al (a) shows the elevation profiles and the slope profiles of these the scarp. The distance between faults allows us to identify several two synthetic models. The first one ("reference profile") corresponds inflections of the slope profile corresponding to the successive surto a scarp formed by four successive surface ruptures caused by a face ruptures. The second profile ("adjusted profile") fits with the stepping fault dipping 50°and three interseismic periods during previous one, assuming that successive faults are vertical. The fitting which diffusion is applied after gravitational collapse at the front of of this profile is based on the analysis of the slope profile of the refthe scarp. The last event has not been followed by the interseismic erence profile, as we do when we want to model real data. Fig. Al (b) period, so that the gravity-controlled face is preserved at the front of shows the RMS versus constant KAt obtain for both assumptions Both models use four successive stepping faults and 3.5 offsets. The reference profile uses faults dipping at 500, while the adjusted profile uses vertical faults.
To obtain this profile, we adjusted the location of the vertical faults so that inflections of its slope profile corresponds with those of the reference slope profile, as we would do when modelling real data. b) RMS versus constant K At when assuming true dip of faults (50°) or incorrect vertical faults. Reference profile is sampled at constant intervals and taken as data. The horizontal dotted lines correspond to the RMSmin +5 cm limits beneath which we consider that models are acceptable. Both RMS curves have a minimum value at K At = 10 m 2 . However, the uncertainty of the best fitting value of K At is larger when assuming incorrect vertical faults. This shows that fault dip does not affect the determination of the best fitting K At when morphology is preserved from collapse, but it affects the precision of the estimate. c) RMS versus constant K At when assuming true dip of faults (50°). Reference profile is taken as data. The different RMS curves were obtained using either all interseismic durations as free parameters, or only one of them. In the second case, the other interseismic durations are fixed at the best fitting value (K/At = 10 m 2 ). The horizontal line corresponds to the RMSmin +5 cm limit beneath which we consider that models are acceptable. It shows that uncertainty grows when the parameter search procedure is applied to only one interseismic duration. In particular, the value of K At is poorly resolved for the first (older) interseismic duration.
(vertical and non-vertical faults). Computation of RMS is restricted a more general parameter search, including dip and location of the to the portion of the scarp located back to the gravity-controlled faults. face (for which the slope has no meaning in terms of morpholog- Fig. Al(c) deals with the accuracy expected when determining ical age). In order to obtain the RMS curve corresponding to the the value of KAt for old events. We have computed RMS curves faults dipping at 50°(dashed line) we sampled the corresponding from the reference profile, assuming correct dip of faults (50°). We elevation profile ("reference profile") at specified intervals and we have incremented the value of KAt for all events (solid line), or incremented K At. The resulting RMS curve has a zero value at the only one of them (dashed and dotted lines). In the last case, the expected best fitting value K At = 10 m 2 . The second curve (solid other values ofK At are fixed at the best fitting value. The horizontal line) corresponds to RMS values computed from "reference profile" line corresponds to the value of minimum RMS plus 5 cm which assuming vertical faults. This RMS curve has also a minimum value allows to determine confidence intervals on the best fitting values. at the best fitting K At = 10 m 2 . We define confidence intervals on As expected, RMS curves have a zero value at the best fitting value. the best fitting value of KAt by considering all profiles that fit data However, the confidence intervals are larger when varying a single within 5 cm of minimum RMS (see horizontal lines in Fig. Alb).
KAt. The accuracy of the estimate becomes poor if we want to While best fitting K At does not depend on the assumed dip of faults, estimate the value of K At associated with the oldest event (dashed Fig. Al(b) shows that this interval is clearly greater when assuming line, Fig. Alc). This implies that it is not possible to estimate each incorrect dip. As far as reverse faults are usually not vertical, it is rea-interseismic duration with a good accuracy. On the contrary, a mean sonable to assume arbitrary dipping faults to reduce the uncertainty value of K At can be determined, which leads to a mean value of the on best fitting value. The foregoing illustrates the need to improve morphological age of a cumulative scarp by multiplying this value the determination of morphological ages on cumulative scarps by by the number of interseismic periods.