Kristell Le Dortz

Bertrand Meyer

Michel Sébrier

Regis Braucher

H Nazari

L Benedetti

M Fattahi

B Bourlès

M Foroutan

Lionel Siame

D Bourlès

A Rashidi

M D Bateman

Dating inset terraces and offset fans along the

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Introduction

The Dehshir fault is a 380 km-long, strike-slip fault cutting through the Central Iran plateau, north of the Zagros. It is located between 29. 5°N-54.6°E and 33°N-53.1°E and is part of a series of N-striking dextral faults slicing Central and Eastern Iran (e.g. [START_REF] Berberian | Active faulting and tectonics of Iran, in Zagros, Hindu Kush, Himalaya: geodynamic evolution[END_REF].

The total offset of the fault, denoted by the geological offsets of the Nain Baft suture and the Urumieh Doktar magmatic arc, amounts to 65 ± 15 km (Inset Figure 1; [START_REF] Walker | Active tectonics and late Cenozoic strain distribution in central and eastern Iran[END_REF][START_REF] Meyer | Evidence of quaternary activity along the Deshir Fault[END_REF]. The southern portion of the Dehshir fault that runs across a series of Quaternary alluvial fans shows clear evidence of recent right-lateral motion (Figure 1).

Geomorphologic studies have been performed to estimate the slip-rate of the fault. Combining cumulative offsets of gullies and terrace risers with their inferred Holocene age, [START_REF] Meyer | Evidence of quaternary activity along the Deshir Fault[END_REF] and [START_REF] Meyer | Strike-slip kinematics in Central and Eastern Iran : estimating fault slip-rates averaged over the Holocene[END_REF] suggested the fault slips at 2 mm.yr -1 . This initial estimate has been further investigated by dating of optically stimulated luminescence (OSL) samples collected within colluviums thought to predate the incision of an abandoned fan. [START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF] derived a minimum slip-rate of 0.8-2.5 mm.yr -1 by combining the offset of two gullies incised within the fan with the weighted mean OSL age of the colluviums.

However, neither the offset-gullies nor the surface of the abandoned fan have been dated directly. [START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF] collected primarily the OSL samples for paleoseismic purpose, within the fault zone where fanglomerate layers have been disrupted and/or warped.

In order to date the surface of the fan and provide further constraints on the slip-rate, we have sampled the surface to estimate its cosmic ray exposure (CRE) age and the sediments below the surface for OSL dating of their emplacement. While these two dating techniques are commonly used separately, a few recent studies have combined luminescence dating with cosmogenic data. In some cases the two methods yielded comparable ages though the CRE ages are always slightly older than the OSL ones (e.g. [START_REF] Owen | Timing and style of late Quaternary glaciation in northeastern Tibet[END_REF][START_REF] Owen | Late Quaternary landscape evolution in the Kunlun Mountains and Qaidam Basin, Northern Tibet: a framework for examining the links between glaciation, lake level changes and alluvial fan formation[END_REF]De Long and Arnold, 2007). Other studies yielded to significant differences, CRE ages being as much as twice older than the OSL ones [START_REF] Hetzel | Late Pleistocene/Holocene slip rate of the Zhangye thrust (Qilian Shan, China) and implications for the active growth of the northeastern Tibetan Plateau[END_REF][START_REF] Nissen | The late Quaternary slip-rate of the Har-Us-Nuur fault (Mongolian Altai) from cosmogenic 10 Be and luminescence dating[END_REF][START_REF] Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF]. Some authors favoured the CRE ages whether they used surface samples only [START_REF] Hetzel | Late Pleistocene/Holocene slip rate of the Zhangye thrust (Qilian Shan, China) and implications for the active growth of the northeastern Tibetan Plateau[END_REF] or near-surface samples only [START_REF] Nissen | The late Quaternary slip-rate of the Har-Us-Nuur fault (Mongolian Altai) from cosmogenic 10 Be and luminescence dating[END_REF]. Others (Le [START_REF] Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF] that used both surface and near-surface samples concluded to a variable inheritance for the CRE ages and favoured the OSL ages for dating the abandonment of alluvial surfaces.

We performed the sampling at two sites on the southern portion of the fault where [START_REF] Meyer | Evidence of quaternary activity along the Deshir Fault[END_REF] documented right-lateral offsets of imbricate fan surfaces and riser cuts (Figure 1). To constrain the age of the abandoned fan surfaces and the age of the subsequent Revisedmanuscript 3/12/10 4 incision, we collected 100 samples (73 surface samples and 27 near-surface samples along three profiles) to determine their CRE age by measuring the accumulation of 10 Be and 36 Cl cosmogenic nuclides. Using two isotopes with markedly different half-lives offered the opportunity to better constrain the erosion rate and evaluate the trade-off between erosion and CRE age of the studied surfaces. We also collected six additional samples within quartz-rich sandy layers located below alluvial surfaces to measure by OSL the time elapsed since the last sunlight exposure of the sediment.

First, we describe the detailed morphology of the two sites with emphasis on inset terrace levels imbricate within successive alluvial fan systems. Then, we present the results of the CRE and OSL dating and discuss how far they help constraining the abandonment age of the terrace treads and the age of the riser cuts that bound the treads. Finally, we discuss the slip-rate of the Dehshir fault and the morphoclimatic chronology of the area.

Offset Quaternary fans along the southern portion of the Dehshir fault

Site Dehshir South: Marvast River

The Marvast River is the largest and the most active of the intermittent rivers draining the study area, a dryland part of endorheic Central Iran Plateau. The river course is about 70 km long from its source within the High Zagros to the South of the Marvast city. The incision of the Marvast River is limited because it vanishes into the Marvast salt flat, whose base level stands at the elevation of 1520m. The drainage basin of the Marvast River is about 1100 km 2 , and the upstream catchment drains several distinctive rock units including cover (Zagros platform lithologies) and basement (Sanandaj Sirjan metamorphics). The river and its former tributaries have emplaced the vast Quaternary piedmont made of coalescent fans that cover most of the surface on the satellite imagery of figure 1. The recent incision of the piedmont has resulted in a narrow channel supplying water to the city of Marvast, the formation of inset terraces, and the fan head entrenchment. The Dehshir fault cuts across the Marvast River, the active fans and the abandoned fan systems (Figure 2). To the west of Marvast city, several inset terraces are distinguished (T0, T1a, T1b, T2, T3) and their relative age can be assessed by their relative elevation (Figure 3). The material of each terrace, well layered, is of fluvialtorrential origin and contains polygenic cobbles (Figure 3). The lower terrace T0 corresponds to the present-day overflowing flood channel of the Marvast River. Many braided channels up to 0.5-0.8 m deep incise T0. Very loose conglomerates alternate with silty-sandy layers. The pebbles and the cobbles, either in the riverbed or on the surface of T0 are well rounded and have not experienced cryoclasty. T1 is a terrace located 1 to 3 m above T0. T1 is made of two distinctive levels, T1b slightly older and 1 m above T1a. Both T1a and T1b levels have been probably emplaced during the same climatic period. They contain pebbles and well-rounded cobbles with diameters up to 30 cm. The material is poorly cemented and some sandy layers are found intercalated within the slightly indurate conglomeratic layers. Cobbles on the T1 surface display bar and swell morphology, most of them are well rounded very few have been fragmented suggesting a very limited cryoclasty. T2 is an older terrace standing about 4-5 m above T1 upstream of the Dehshir fault and 2-4 m above the present streambed downstream.

Several indurate sandy layers alternate with coarse conglomerates. T2 surface is flat and many fragmented cobbles are found on it, suggesting that the terrace underwent low temperatures and contrasted seasons during long period of times associated with strong wind deflation, as under glacial climates. The upper part of the terrace is fairly cemented by a discontinuous calcrete up to 1 m thick at some places. T3 is the top surface of the highest alluvial fan system. It stands more than 5 m above T2. Where exposed upstream, by the Marvast incision, T3 contains many cryoclasted cobbles and a few large cobbles. The conglomerate levels are strongly indurate and the upper part of T3 is cemented by a continuous, 0.4-0.8 m thick, reddish calcrete. Numerous gelifracted cobbles can be found on its surface. Many gullies incise T3; they are deeper and wider than the shallow immature rills incising T2. The overall terrace has a characteristic striped-morphology on the satellite imagery with flat strips separated by narrow intervening intermittent gullies (Figure 2).

There are also a few remnants of older fanglomerates cropping out close to the fault (Figure 2). These older conglomerates are assigned to the Pliocene according to the geological mapping by GSI (1981). The layers are mostly tilted to the west and squeezed within the fault zone, but the orientation of the cobbles indicates an eastward paleocurrent direction [START_REF] Meyer | Evidence of quaternary activity along the Deshir Fault[END_REF]. The successive fans have been all emplaced by the Marvast River and progressively deformed through time. The most recent riser cut of the Marvast river stands between T1 tread and the river course (T1b/T0) West of the fault and between T2 tread and the river course (T2/T0) East of the fault. This T2/T0 riser, deflected in a right-lateral sense by an amount of 25 ± 5 m, is not a passive marker and might have been rejuvenated by lateral erosion (Figure 2a). Several larger offsets occur further to the South. About 2 km south of the Marvast River, a large dry river, deeply incised within the oldest fan T3, is right-laterally offset by 380 ± 20 m (Figure 2b). This offset is higher than the 180-200m offset streams described by [START_REF] Meyer | Evidence of quaternary activity along the Deshir Fault[END_REF] a little further to the South. The latter offsets correspond to streams that are narrower and less incised than for the former. Consequently, the value of 380 and provides a minimum bound of the fault motion since the abandonment of T3 tread.

Site Dehshir North

The site Dehshir North is located about 25 km north of the Marvast River (Figure 1).

The site lies close to a 30 km long, north-south trending, intermittent stream in which presentday drainage is mostly restricted to the northern part of the piedmont. The stream is disconnected from the Marvast River but it grades almost back to the Marvast River outlet from the Sanandaj Sirjan Mountains and drains a significant area of the Quaternary piedmont.

At site Dehshir North, the piedmont mainly consists of the distal part of the abandoned fan T3

(Figure 4). Similarly to the site Dehshir South, several lower levels (T2, T1b, T1a) with limited extension are nested within the alluvial fan T3. The material of each terrace is also of fluvial-torrential origin but the gravel sizes are smaller than at site Dehshir South. Fine content is higher and the coarser levels are void of boulders.

The higher level T3, although much resembling that along the Marvast River on the SPOT Imagery, has been a little less incised and dissected by the rivers than at Dehshir South.

At Dehshir North, T3 stands about 4 m only above the active riverbed (Figure 4b) and its surface displays many cryoclasted cobbles. T3 is incised upstream by many short gullies regularly spaced every 20-30 m. Such gullies probably formed as a result of regressive erosion after the abandonment of the terrace T3 and the cutting of the risers. T2 has a very limited extension with respect to T3. It is a lateral fan sloping down gently northward that was aggraded by small local tributaries that are incised within T3 terrace and rework its alluvial material. T2 surface stands 2-4 m below T3 and is much less incised than the old terrace; only a few short gullies irregularly spaced are distinguished on the Quickbird Imagery (Figure 4a).

As T3, the surface of T2 displays cryoclastic material. The emplacement of the lateral fan T2 is partly controlled by the local development of the Dehshir fault. The terrace T1 lies 1 m at most below the terrace T2 and stands 1 m above the riverbed T0. Most of the gullies that incise T3 and T2 merge downstream with T1 and their incision is probably synchronous with the emplacement of T1. The surface of T1 displays only very few cryoclasted cobbles.

Similarly to the site Dehshir South, two levels (T1a and T1b) can be distinguished, with T1b being older and standing 0.5-1 m above T1a. Both the terrace T1 and the lateral fan T2 are nested in the highest terrace T3 and have a very limited extent.

Some small gullies that incise T3 and T2 cross the fault zone at a right angle. Two of these gullies are clearly offset in a right-lateral sense by 20-30 m (figure 4), an amount similar Revisedmanuscript 3/12/10 7 to the deflection of the Marvast River at the site Dehshir South. These gullies postdate the emplacement of T3 and T2 and might have formed as a result of regressive erosion since the last significant incision of the network. Their incision is probably coeval with the emplacement of the terrace T1 with which they merge downstream, and the gullies, according to weighted mean OSL dating in a trench within the fault zone, are supposed to be younger than 21.1 ± 11.2 ka [START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF]. There is also an offset of the right bank of the main river flood channel (Figure 5). Upstream, the most recent riser cut (T3/T0) stands between T3 tread and the riverbed. Downstream, T1 is protected from erosion because of the right-lateral motion of the fault and the most recent riser stands between T1 tread and the riverbed (T1a/T0). The riser that postdates the terrace T1a is offset by 12 ± 2 m (Figure 5).

Chronology of the regional fans

The dating of the alluvial surfaces and inset terraces at both sites is required to establish the chronology of the fans and constrain the age of the offset-risers. Two complementary dating methods, cosmic ray exposure (CRE) and optically stimulated luminescence (OSL), have been performed to estimate the age of abandonment of alluvial surfaces. OSL relies on natural background radioactivity of the material with a small contribution of cosmogenic radiation and measures the time elapsed since the last sunlight exposure of a sediment layer.

CRE provides the time of exposure of superficial material to cosmic rays.

Sampling strategy and analytical procedures for cosmogenic and OSL dating

All the terraces (T0, T1, T2 and T3) were sampled at each site for cosmogenic dating.

For some surfaces (T3 at sites Dehshir North and Dehshir South, T2 at site Dehshir South)

and taking advantage of the occurrence of polygenic cobbles, both the 10 Be and 36 Cl cosmogenic nuclides dating techniques have been applied. We measured the concentrations of in-situ produced 10 Be and 36 Cl accumulated respectively in quartz-rich and carbonates samples exposed to cosmic rays. Surface samples were collected to estimate the CRE ages (Table 1).

Most of the surface samples, 67 over the 73 collected, consists of individual cobbles, 4 correspond to two fragments of the same gelifracted cobble, and 2 only are amalgams of many (about 25) pieces of small pebbles. Near-surface samples were also collected along three profiles to estimate the inheritance, i.e., the concentrations of cosmogenic nuclides accumulated in the cobbles prior to their deposition. Each near-surface sample is an amalgam of pebbles or fragments of cobbles collected at the same depth. Provided that the sediment emplaced in a short period of time and that the pre-exposure is homogeneous, the exponential Revisedmanuscript 3/12/10 8 decrease of concentrations with depth provides an estimate of the homogeneous inheritance (e.g. [START_REF] Anderson | Explicit treatment of inheritance in dating depositional surfaces using in situ 10 Be and 26 Al[END_REF][START_REF] Repka | Cosmogenic dating of fluvial terraces, Fremont River, Utah[END_REF]. The inherited concentration is determined from the asymptotic value that the profile tends to at depth and a chi-square inversion is often used to minimise the differences between measured and modelled concentrations (e.g., [START_REF] Siame | Local erosion rates versus active tectonics : cosmic ray exposure modelling in Provence (south-east France)[END_REF][START_REF] Braucher | Determination of both exposure time and denudation rate from an in situ-produced 10 Be depth profile : A mathematical proof of uniqueness. Model sensitivity and applications to natural cases[END_REF]. Collecting pebbles from the active streambed also helps to estimate the inherited component (e.g. [START_REF] Brown | Estimation of slip rates in the southern Tien Shan using cosmic ray exposure dates of abandoned alluvial fans[END_REF]. However, this method relies on the questionable assumption that the pre-depositional history of the pebbles collected in the present-day streambed is comparable to that of the pebbles collected on abandoned fan surfaces during aggradation stages.

Three main types of secondary particles are involved in the in situ production of 10 Be:

fast nucleons (essentially neutrons), stopping (or negative) muons and fast muons. Each of them has its own effective attenuation length. We used in this paper the same parameters as [START_REF] Braucher | In situ produced 10 Be measurements at great depths: implications for production rates by fast muons[END_REF] for the muonic attenuation lengths that are 1500 g.cm -² for stopping muons and 5300 g.cm -2 for fast muons. For fast neutron, an attenuation length of 160 g.cm -² [START_REF] Gosse | Terrestrial in situ cosmogenic nuclides: theory and application[END_REF] is used rather than the attenuation length of 177 g.cm -² [START_REF] Farber | Attenuation length for fast nucleon production of 10 Be derived from near-surface production profiles[END_REF] modelled at mid-lattitude in California but without accounting for the muonic contribution. Samples were prepared at the CEREGE laboratory in Aix-en-Provence for 10 Be concentration measurements following chemical procedures adapted from [START_REF] Brown | Examination of surface exposure ages of Antarctic moraines using in situ produced 10 Be and 26 Al[END_REF] and [START_REF] Merchel | An update on radiochemical separation techniques for the determination of long-lived radionuclides via accelerator mass spectrometry[END_REF]. After addition in each sample of ~100 µl of an in-house 3.10 -3 g/g 9 Be carrier solution prepared from deep-mined phenakite [START_REF] Merchel | Towards more precise 10 Be and 36[END_REF], all 10 Be concentrations were normalized to 10 Be/ 9 Be SRM 4325 NIST standard with an assigned value of (2.79 ± 0.03).10 -11 . This standardization is equivalent to 07KNSTD within rounding error. All 10 Be data reported in this study (Table 1) have been measured at ASTER (CEREGE, Aix-en-Provence). Analytical uncertainties (reported as 1σ) include uncertainties associated with AMS counting statistics, AMS external error (0.5%), chemical blank measurement. Long term measurements of chemically processed blank yield ratios on the order of (3.0 ± 1.5).10 -15 [START_REF] Arnold | The French accelerator mass spectrometry facility ASTER: Improved performance and developments[END_REF]. Cosmocalc add-in for excel [START_REF] Vermeesch | CosmoCalc: An Excel add-in for cosmogenic nuclide calculations[END_REF] has been used to calculate sample scaling and standard atmospheric pressures. [START_REF] Stone | Air pressure and cosmogenic isotope production[END_REF] polynomial has been used to determine surficial production rate assuming a SLHL production rate of 4.49 at.g -1 .yr -1 for 10 Be. 35 Cl, and direct capture of slow negative muons by K and Ca) and radiogenic production by disintegration of U and Th. To determine the proportion of radiogenic 36 Cl requires measuring the concentrations of U and Th in the target mineral [START_REF] Zreda | Cosmogenic chlorine-36 production rates in terrestrial rocks[END_REF][START_REF] Stone | Cosmogenic chlorine-36 from calcium spallation[END_REF][START_REF] Stone | Cosmogenic chlorine-36 production in calcite by muons[END_REF][START_REF] Gosse | Terrestrial in situ cosmogenic nuclides: theory and application[END_REF]Schimmelpfennig et al., 2009). Major elemental compositions of rock samples were determined by ICP-OES technique by the CNRS service for rocks and minerals analysis at CRPG Nancy. For the 36 Cl measurements, the chemical extraction of chlorine by precipitation of silver chloride has been adapted from the protocol of [START_REF] Stone | Cosmogenic chlorine-36 from calcium spallation[END_REF]. The samples were spiked with a known quantity of stable chlorine carrier (e.g. [START_REF] Desilets | Determination of cosmogenic 36 Cl in rocks by isotope dilution: innovations, validation and error propagation[END_REF] to simultaneously determine 36 Cl and chlorine concentrations by isotope dilution accelerator mass spectrometry (AMS). The chemical treatment of the samples was carried out at the CEREGE laboratory in Aix-en-Provence and the measurements were performed at the Lawrence Livermore National Laboratory, using KNSTD1600 standard. The excel spreadsheet provided by Schimmelpfennig et al., (2009) was used to calculate all 36 Cl production rates and to model 36 Cl data. Accordingly, a surface spallation rate of 48.8 ± 3.4 at.g -1 (Ca).yr -1 [START_REF] Stone | Cosmogenic chlorine-36 from calcium spallation[END_REF] Therefore, the De distribution of the single aliquot De measurements is considered to be almost a true reflection of the actual De distribution within a sample. For some samples the depositional setting, field sedimentary logs and the scatter of the replicate aliquot De data indicated that prior to burial, full resetting (bleaching) of the OSL signal had not taken place and/or that the sediments had undergone some post-depositional disturbance [START_REF] Bateman | Detecting Post-depositional sediment disturbance in sandy deposits using optical luminescence[END_REF]. As a result of this, Finite Mixture Model (FMM; [START_REF] Roberts | Distinguishing dose populations in sediment mixtures: a test of single-grain optical dating procedures using mixtures of laboratory-dosed quartz[END_REF] was used where samples showed skewed, scattered, or multimodal distributions. We used the dominant FMM component for samples displaying multimodal De distributions and the lowest FMM component of De for samples whose De distributions were skewed (assuming partially bleached without significant bioturbation) samples [START_REF] Boulter | Developing a protocol for selecting and dating sandy sites in East Central Texas: Preliminary results[END_REF][START_REF] Bateman | Detecting Post-depositional sediment disturbance in sandy deposits using optical luminescence[END_REF]. Where samples had a low over-dispersion and unimodal, normally distributed De's then the Central Age Model (CAM; [START_REF] Galbraith | Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia, part 1, Experimental design and statistical models[END_REF] De was used for age calculation purposes. The relevant information for OSL ages are presented in Table 3 in years from present with 1 sigma errors.

Cosmic ray exposure ages

Figure 6 displays the results for the site Dehshir North, and figure 7 for the site Dehshir

South. The concentrations are given in Table 1 with the corresponding CRE ages modelled assuming erosion and inheritance are negligible.

Surface T3

For T3, both the 10 Be and 36 Cl zero-erosion, zero-inheritance ages of surface samples are overall consistent and suggest that the terrace tread is old.

At Dehshir North (Figure 6), the CRE ages range between 235 and 519 ka for the 10 Be measurements, and between 268 and 383 ka for the 36 Cl measurements. For the 10 Be concentrations, all but one surface sample provide CRE ages greater than 400 ka. The younger 10 Be exposure age (DN06S2, 235.5 ± 35.4 ka) might be considered as an outlier and excluded from the statistics. Then, the weighted mean of the zero-erosion zero-inheritance 10 Be model age of T3 is 462 ± 55 ka while the 36 Cl one is 325 ± 74 ka (Figure 6b).

At site Dehshir South (Figure 7), the scattering of the concentrations is greater. The weighted means of the zero-erosion zero-inheritance 10 Be and 36 Cl ages are 481 ± 119 and 344 ± 83 ka, respectively (Figure 7b). The results are nonetheless similar at both sites and confirm the qualitative inference of the synchronism of levels T3 drawn from the resemblance of their surface at distant sites on the Quickbird imagery. They indicate T3 is a rather old surface (several hundreds ka) and that 36 Cl surface ages are a little younger than 10 Be ages. The slight difference between the 10 Be and 36 Cl weighted mean ages may either result from a statistical bias due to the limited number of samples or be meaningful. The 36 Cl half-life (301 ka, e.g. Gosse & Philipps, 2001) being lower than that of 10 Be (1.387 ± 0.12 Ma, Chmeleff et al., 2009;Korshinek et al., 2009) and T3 an old terrace, the difference may suggest the carbonates have reached the steady-state equilibrium for which the production of 36 Cl is balanced by the loss due to radioactive decay and the loss due to erosion, if there is any.

Because there is a trade-off between denudation rate and exposure age, it is important to estimate the erosion. Assuming an infinite age for the emplacement of T3 allows estimating a maximum erosion rate for each of the surface samples, both for 36 Cl and 10 Be isotopes (Table 1). For the carbonates, none of the surface samples provides a 36 Cl maximum denudation rate greater than 2.1 m.Ma -1 , and the averaged value is 1.5 m.Ma -1 . Discarding the outlier DN06S2, the quartz surface samples indicate a 10 Be maximum denudation rate smaller than 1.6 m.Ma -1 with an averaged value of 1.4 m.Ma -1 . This is further strengthened by modelling the depthdistribution of the 36 Cl concentrations in the amalgamated carbonate samples collected along a 3 m depth profile excavated in T3 at the site Dehshir North (Figure 8). The profile shows an overall exponential decrease of concentrations with depth allowing for modelling the erosion rate. The 36 Cl concentration depth profile is modelled with assigning a surface age of 3 Ma; old enough to ascertain the equilibrium between production and disintegration has been reached. Letting the erosion rate and the inheritance free to vary, the profile is modelled for three density values (between 2 and 2.4 g.cm -3 ) within the range of that measured for the samples of the profile (Figure 8). For all the densities tested, the model converges towards zero inheritance solutions and low erosion rates. The solutions with zero inheritance are not surprising because the assigned surface age of 3 Ma makes a homogeneous inheritance of several tens of ka undetectable. By contrast, the solutions with low maximum erosion rates are meaningful. The greatest erosion rate of 1.90 m.Ma -1 is obtained for a density value of 2 g.cm -3 . Smaller erosion rates of 1.48 and 1.18 m.Ma -1 corresponding to densities of 2.2 and 2.4 g.cm -3 are closer to the erosion rate calculated for each of the carbonate surface samples (Table 1).

Whatever the method applied (surface sample, near-surface samples and depth-profile modelling) and whatever the isotope considered, the estimates of the maximum erosion rate are very low. They are close to that found in hyperarid regions (<1 m.Ma -1 , [START_REF] Matmon | Desert pavement-coated surfaces in extreme deserts present the longest-lived landforms on Earth[END_REF] and in good agreement with the pristine morphology of the flat-topped surface of T3.

The 10 Be depth profile can be theoretically modelled with erosion rates ranging between 0 and 1.4 m.Ma -1 , maximum erosion rate averaged from the 10 Be surface samples. Accounting for the trade-off between erosion rate and exposure age (the higher the erosion rate, the older the exposure age), the 10 Be depth profile has been modelled under the assumption of no erosion to minimize the exposure age. We hence tested a range of inheritance values to solve for the zero erosion exposure age (Figure 9). The best fit is obtained for a surface age of 464 ka and a homogeneous inheritance of 3.8 10 5 at.g -1 (SiO 2 ). This inheritance, if acquired at the surface and prior to the emplacement of the terrace, would correspond to a period of pre exposure of about 32 ka, small with respect to the exposure age. Accounting for the trade-off between inheritance and age, several other solutions remain acceptable (Figure 9b). Assuming a homogeneous inherited concentration of 7.6 10 5 at.g -1 (SiO 2 ), twice that obtained for the best fit and close to the concentration measured for the deepest sample of the profile, provides an age of 327 ka. Hypothesizing zero inheritance yields an older age of 686 ka that does not match with the concentrations of surface samples, demonstrating the usefulness of combining both surface and near-surface sampling.

In summary, T3 is a rather old and well-preserved alluvial surface, in which cobbles have incorporated a poorly constrained inheritance of several tens of ka. This amount of inheritance, though limited with respect to the CRE age of T3, contributes to the 469 ± 88 ka weighted mean age of all the quartz cobbles collected on the terrace tread at sites Dehshir North and Dehshir South (Figure 10).

Surface T2

At Dehshir North, only one amalgam quartz-rich surface sample has been dated on T2 fan surface. The zero-erosion zero-inheritance CRE age is 406.5 ± 26.5 ka (Table 1, Figure 6a). This age is a little younger than of the weighted mean age of T3 and agrees with the assumption that T2 aggradation at this site results from reworking of T3 material. Indeed, T2

CRE age is older than several ages that have been used to estimate the weighted mean age of T3 and much older than that of the T3 outlier. At Dehshir South, twelve samples collected on Revisedmanuscript 3/12/10 13 T2 have been analysed (Figure 2a and Figure 7). The 10 Be and 36 Cl concentrations, hence the corresponding CRE ages calculated assuming zero-erosion and zero-inheritance are scattered (Table 1, Figure 7a). The CRE ages of the surface samples range between 49.9 ± 3.3 and 225.8 ± 14.7 ka for the 10 Be and between 104.4 ± 10.5 and 190.3 ± 20.8 ka for the 36 Cl. The youngest 10 Be CRE age on T2 (DS08S114, 49.9 ± 3.3 ka) might be considered as an outlier and excluded from the statistics. Discarding the outlier and keeping in mind the limited number of samples, the ages remain scattered without significant differences between 10 Be and 36 Cl ages. The distribution is multimodal with a weighted mean CRE age of 175 ± 62 ka (Figure 11a). This average is consistent with the intermediate elevation of T2 terrace and its surface characteristics as well as the fact that none of the CRE ages obtained for T2 is older than the youngest age calculated for T3.

Amalgamated samples have also been collected along two depth profiles at site Dehshir South. The 10 Be concentrations are listed in Table 1. The profile PS1 was collected by the riser between T2 and the Marvast riverbed, 300 meters East of the fault zone (Figures 2 and11). The profile PS2 has been collected 1.5 kilometres NE of PS1, close to the fault scarp in a pit dug within the T2 surface and nearby remnants of T3 (Figures 2 and12). For both profiles, the uneven distribution of the 10 Be concentrations dismisses a uniform pre-exposure prior to the emplacement of T2 material and precludes any appropriate modelling of a homogeneous inheritance. As for the study of alluvial surfaces in the Anar neighbouring area (Le [START_REF] Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF], the profile data, together with the scattering of the concentrations of the surface cobbles, suggest the occurrence of a variable inheritance.

Surface T1 and T0

At site Dehshir North, the four surface samples collected on T1a provide CRE ages ranging between 82 and 424 ka (Figures 4 and6a). The sample with the oldest age might be considered an outlier and the CRE age of the terrace would be better determined by the three youngest samples and bracketed between 82 and 134 ka. The T1a outlier has an age close to that of the amalgam on T2 fan surface and close to that of the surface samples collected on T3. This suggests that the T1a outlier is a T2 or T3 cobble reworked by the small gullies incising the surface of T2 and T3 treads and which incision is coeval with the emplacement of T1.

At site Dehshir South, the four surface samples have been collected on T1b. They provide 10 Be exposure ages ranging between 30 and 318 ka (Figures 2 and7a). The oldest sample, even older than the samples collected on T2 tread, is as an outlier. Either it is a the oldest sample collected in the river, the scattering of the concentrations increases and suggests the pre exposure history of a cobble before the abandonment of an alluvial surface is highly variable.

To summarize (Figure 13a), the observed average inheritance in the present stream beds of some 70 ka, as well as the distribution of CRE ages for the inset levels T1 and T2, suggest that T1 and T2 treads are likely to be younger than their CRE weighted mean age.

Thus, the ages of abandonment of the terrace treads may be better approximated by the CRE age of the youngest sample found on each surface. Such a conclusion has already been drawn

for alluvial fan surfaces in the neighbouring region of Anar (Le [START_REF] Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF].

Optically stimulated luminescence ages

OSL dating was performed to better constrain the chronology of alluvial terraces at the two studied sites. Five OSL samples initially sought to determine the ages of faulted deposits for paleoseismology purposes were sampled at site Dehshir North [START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF]. Then, six new OSL samples were collected at site Dehshir South. As no suitable material was found within old terrace T3, OSL ages help only constraining the aggradation timing of terraces T2 3). These similar OSL ages suggest that the material of the terrace T2 emplaced rapidly and that its tread is at most 28.2 ka. The OSL samples of the riser T2/T0 provide ages much younger than the weighted mean 10 Be and 36 Cl CRE age of T2, 175 ± 62 ka (Figure 11a), but closer to 49.9 ± 3.3 ka, the youngest CRE age on T2 tread (DS08S114 in Table 1). Two additional OSL samples (AB/2006-I and II in Table 3) were collected within a colluvium pediment topping T2 in the pit of profile PS2 (Figure 2a and12b). These samples yielded OSL ages of 39.7 ± 2.6 and 20.0 ± 1.3 which confirm this desert pediment was formed both by the end of the emplacement of terrace T2 and after its abandonment. To summarize, the OSL ages obtained These ages are in agreement with the relative elevation of the terraces, the samples from the riser T2/T0 being older than the sample from the riser T1b/T0, itself older than the sample from the riser T1a/T0. Similarly to the terrace T2, the OSL age of T1b is younger than the 10 Be CRE ages of the samples collected on the T1b tread. This OSL age is almost one order of magnitude younger than the three oldest 10 Be samples and 30% younger than the youngest 10 Be sample (DS08S114). There is no direct comparison available between OSL and CRE ages for T1a because this surface has not been sampled for cosmogenic dating.

At the two studied sites along the Dehshir fault, the OSL ages on terraces T2 and T1 are systematically younger than the CRE ones on the same terrace. For a given terrace, the CRE statistical outlier, which is the youngest CRE age and has been consequently removed from the calculation of the weighted mean CRE age, remains slightly older than, but closer to the OSL ages. Two extreme options may be contemplated: either OSL ages have been rejuvenated or CRE concentrations include a high percentage of inheritance. Most of the physical processes that are known to affect the OSL method, such as partial bleaching, incorporate an antecedent signal leading to overestimation of the age of sediment burial. This has been accounted for the studied samples by the statistical processing of the De distributions. Conversely, OSL signal is sensitive to the temperature and a loss of luminescence might occur at temperatures above 50°-60°C. Such temperatures may occur on the Iran plateau during summertime so that OSL ages could be theoretically rejuvenated.

Nevertheless, to account for gamma rays shielding, OSL samples were taken at least at 0.7 m below the ground surface (Table 3), a depth large enough to prevent strong variations of temperature. In addition, if temperature had affected the OSL signal, such effect would decrease with increasing sampling depth. However, no trade-off is observed between the OSL ages and the sampling depth (Table 3). On the contrary, OSL ages, whatever the depth, appear similar for the same terrace and in agreement with the relative elevation of the terraces. As a consequence, the variable inheritance of CRE concentrations should chiefly explain the discrepancy with OSL ages.

Discussion on the abandonment age of the alluvial surfaces

The overall chronology of the fan surfaces crossed by the Dehshir fault has been established but the abandonment age of each surface is not easily assigned for several reasons (Figure 13). First, the scattering of CRE concentrations on a given surface, the occurrence of more concentrated samples on younger surfaces than on older ones, the occurrence of significant concentrations in active river beds, indicate there is a variable inheritance uneasy to account for. Second, where CRE and OSL data are available for the same terrace, the OSL ages of the late sediments of the terrace are always much younger than the CRE ages of the cobbles abandoned on its tread. Such disparities between OSL and CRE ages appear to result from the high variability of the CRE inheritance that needs further consideration.

3.4.1 Variable CRE inheritance and maximum abandonment ages of alluvial treads.

A rough estimate of the variable inheritance is provided by the CRE weighted mean of 72 ± 20 ka obtained from 8 of the 9 samples collected in the riverbeds once the oldest outlier discarded. Moreover, amalgam sample DS08P130 from profile PS1 (Figure 11c) has a measured concentration (Table 1) of 8.86 10 5 at.g -1 (SiO 2 ), even though it is located at 2.1 m below the T2 surface whose surface samples yielded a weighted mean CRE age of 175 ± 62 ka. Assuming 175 ka represents the actual age of T2 tread and subtracting the concentration acquired in situ, at 2.1 m depth, by sample DS08P130 during these 175 ka of exposure would yield to a remaining, hence inherited, concentration of 7.25 10 5 at.g -1 (SiO 2 ).

Most of the sample concentration would therefore result from inheritance. Such inherited concentration would have been acquired in about 60 ka, if accumulated at the surface. Then, the 70 ka ages of riverbed samples appear to give a good estimate of the amount of inheritance carried by T2 material. Consequently, T2 mean age should be reduced to 105 ± 62 ka. These 70 ka inheritance estimates are larger than the 32 ka of inheritance ageequivalent obtained for T3 by conventional modelling of the 10 Be profile (Figure 9). We have therefore investigated another method to use the inheritance. Assuming each terrace formed during a short-lived aggradation coeval with a single climatic crisis, the near-surface concentrations have been used to fix the maximum abandonment age of the terrace (Figure 14). The principle is simple and rests on the impossibility for any sample to be incorporated into the sediment of the terrace with a negative concentration. Accounting for the depth of each near-surface sample and assuming its measured concentration results only from in-situ Revisedmanuscript 3/12/10 18 exposure; i.e. assuming no inheritance for the sample, it is possible to calculate for any sample of a profile the time required to bring it back from its measured concentration to a null concentration. The maximum abandonment age of the terrace is then obtained from the nearsurface sample of a given profile for which the concentration is restored to zero without bringing back any other sample of the profile to a negative concentration. For the profile PS1 across T2 (Figure 14a), this is obtained for the sample DS08P127 with 107 ka of in-situ exposure. This indicates that T2 was abandoned at most 107 ka ago and that for this maximum time of exposure the concentration remaining in the other samples of the profile correspond to a minimum inheritance. Therefore, this method figures out the variability of the inheritance that amounts, for such an exposure time, to 7.86 10 5 at.g -1 (SiO 2 ) for the nearsurface amalgam collected at 2.1 m depth; such concentration would correspond to a minimum exposure of 66 ka if acquired at the surface prior to the emplacement of the terrace (Figure 14a). It is worth noticing that this rejuvenation would bring back only one of the surface samples to a negative concentration. This remains acceptable, as this sample is the statistical outlier DS08S114. All the other such 107 ka-rejuvenated surface samples would keep positive concentrations. While older depth-profile determined CRE ages of T2 are not possible because they would bring, at least one of the near-surface amalgams, the amalgam 127 (Figure 14a), back to a negative concentration, younger exposure ages remain possible.

Theoretically, all exposure ages ranging between 0 and 107 ka are possible. On the one hand, exposure ages ranging between 53 ka (oldest possible age of the youngest sample, DS08S114, on T2) and 107 ka would make that statistical outlier younger than the age of the terrace. On the other hand, exposure ages ranging between zero and 53 ka would be compatible with the occurrence of the statistical outlier as well as the other surface samples collected on T2.

The same method applied to the depth profile PN across T3 (Figure 14b) demonstrates the terrace was abandoned at most 412 ka ago, confirms the occurrence of a significant inheritance which minimum amounts to 68 ka for the deepest amalgam collected at more than 3m depth, and exemplifies its variability. It is nonetheless important to notice that this is an uppermost bound of exposure duration. This leaves open all the possibilities ranging between the time of abandonment of T2 and 412 ka, hence at least the possibilities between 107 and 412ka.

Abandonment age of terrace treads.

The age of abandonment of the uppermost level T3 is to be discussed with the only data available, the CRE ages (Figures 13 and15). One may rest on the statistical analysis of can be calculated with zero erosion and different choices of inheritance. Whatever the selected value of homogeneous inheritance, none permits to account correctly for the uneven distribution with depth of the measured near-surface concentrations. Nevertheless, two limiting curves appear to bracket these measured concentrations, they correspond to 3.5 10 5 and 9 10 5 at.g -1 (SiO 2 ) of homogeneous inheritances (figure 11c). These values of inherited concentrations would correspond to pre-exposure, if acquired at the surface prior to the emplacement of the terrace, of 30 ka and 75 ka, respectively. Although these values of Revisedmanuscript 3/12/10 20 inherited concentrations result from forward modelling based on the assumption that the inheritance is homogeneous, they indicate the inheritances carried by the amalgam samples of T2 sediments may be nearly as high as 10 6 at.g -1 (SiO 2 ). It is worth noticing that all but one measured surface samples have 10 Be concentrations that are higher than 10 6 at.g -1 (SiO 2 ).

Interestingly, subtracting to the near-surface samples the concentrations corresponding to 30 ka of in-situ exposure makes the residual concentrations, which correspond to inheritance, noteworthy. This inherited concentration amounts to 8.57 10 5 at.g -1 (SiO 2 ) for sample DS08P130 at 2.1 m depth and corresponds to pre-exposure time at the surface of 71 ka. Thus considering 70 ka of inheritance for T2 gravels is a reasonable estimate that can be proposed to average the variable inheritance.

Finally, the OSL ages of the risers T1b/T0 and T1a/T0 indicates their respective tread are at most 23.4 ka and 10.6 ka, respectively. Given the uncertainties associated to the OSL ages of the risers and considering that partial bleaching has been accounted, the youngest possible ages of T2, T1b, and T1a treads are respectively 25.6 ka, 20.4 ka, and 9.4 ka.

Slip-rate estimate and conclusions

The former chronology and offset-risers provide estimates on the minimum and maximum slip-rate of the Dehshir fault. At site Dehshir South, the river course displaced by 380 ± 20 m is incised within the terrace T3. Combining the offset of 380 ± 20 m with the maximum exposure age of 412 ka yields a minimum slip-rate of 0.92 ± 0.05 mm.yr -1 .

Assuming that the regional level T3 is coeval at both sites and that the oldest possible age of the youngest sample collected on T3 (i.e., 271 ka) may approximate its abandonment, the sliprate would be at least 1.40 ± 0.08 mm.yr -1 . The 25m-deflection of the Marvast River might also be used to estimate the slip-rate on a shorter period of time, but this deflection probably overestimates the true tectonic offset because T1 tread is no longer observed downstream. The offset of the gullies incising both T3 and T2 treads at site Dehshir North is a true tectonic offset. This 20-30m offset provides reliable estimates of the upper and lower bounds of the slip-rate. The offset cannot be older than the OSL age collected below the tread of T2 (OSL1 26.9 ± 1.3 ka) and accounts for a minimum slip-rate greater than 0.71 mm.yr -1 (20 m in the last 28.2 ka). The offset cannot be younger than the infilling of T1b and allows determining the upper and lower bounds of the maximum slip-rate. The infilling of T1b being younger than 21.9 ± 1.5 ka, the lower and upper bounds of the maximum slip-rate are respectively 0.85 mm.yr -1 (20 m in the last 23.4 ka) and 1.47 mm.yr -1 (30 m in the last 20.4 ka). The 12 ± 2m-Revisedmanuscript 3/12/10 21 offset of the riser T1a/T0 at Dehshir North is also an estimate of the actual tectonic offset postdating the emplacement of T1a, which is at most 10.6 ka according to sample OSL IV (Table 3, Figure 13). The 12 ± 2m-offset yields a lower bound of the minimum slip-rate of 1.13 ± 0.2 mm.yr -1 . The early estimate of [START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF] can therefore be refined and the actual slip rate ranges between 0.93 mm.yr -1 , largest of the conservative estimates of the minimum slip rate, and 1.47 mm.yr -1 , safe estimate of the maximum slip rate. Therefore, the slip-rate of the Dehshir fault is well determined at 1.2 ± 0.3 mm.yr -1 (Figure 15).

This study demonstrates the usefulness of combining CRE and OSL data to unravel the abandonment ages of alluvial fans and inset terraces in the desert environment of Central

Iran. On the one hand, the use of 10 Be and 36 Cl cosmogenic isotopes with different half-lives allows constraining a very low denudation-rate of 0.001 mm.yr -1 for the terrace treads and alluvial fan surfaces of Central Iran. On the other hand, the combination of surface and nearsurface sampling exemplifies the occurrence and the variability of inheritance in the cosmogenic isotope concentrations and emphasizes the difficulty in assessing abandonment ages of young alluvial surfaces with CRE measurements in such arid environment (e.g., Le [START_REF] Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF]. The scattering of the CRE surface and near-surface concentrations indicates that the cobbles have not been uniformly exposed to cosmic rays prior to their emplacement. This variable inheritance may originate from a differential exhumation and weathering of the bedrock catchments, or more likely for Dehshir sites, from reworking of cobbles originating from different levels of upper, hence older, fans. The abandonment age of an alluvial surface is thus better estimated by the CRE age of the youngest surface sample than by the weighted mean CRE age of many samples, as already formulated in Mongolia (Vassalo et al., 2007) and along the southern rim of the Tarim basin [START_REF] Mériaux | The Aksay segment of the northern Altyn Tagh fault: Tectonic geomorphology, landscape evolution, and Holocene slip rate[END_REF].

However, the youngest sample on a surface may also incorporate inheritance and still overestimate the abandonment age. The amount of CRE inheritance potentially remaining in the youngest sample of a given surface may be obtained by comparing with the OSL age of the late sediments aggraded before the abandonment of the surface. For alluvial surfaces that are young with respect to the considerable amount of inheritance, up to 70 ka in the desert environment of Central Iran, the upper bound on the abandonment age of an alluvial surface appears best estimated by the OSL dating of the late sediment aggraded. For such young surfaces, the CRE measurements are complementary of OSL dating and can be used to unravel the complex history of weathering and transport in the catchment of desert alluvial [START_REF] Chmeleff | Determination of the 10 Be half-life by multicollector ICP-MS and liquid scintillation counting[END_REF]Korshincek et al., 2010) and 301 ka (Gosse & Philipps, 2001). For surface samples, a density of 2.2 g.cm -3 and 2 g.cm -3 have been used for quartz and carbonates samples respectively. An attenuation length of 160 g.cm -2 (Gosse & Philipps, 2001) has been used. [START_REF] Stone | Air pressure and cosmogenic isotope production[END_REF] polynomial has been used to determine surficial production rate assuming a SLHL production rate of 4.49 at.g -1 .yr -1 for 10 Be with 6% of uncertainty. The 36 Cl production rate of 48.8 ± 3.4 at.g -1 .yr -1 is from [START_REF] Stone | Cosmogenic chlorine-36 from calcium spallation[END_REF]. 10 Be ages have been calculated using Cosmocalc (Vermeesh 2007). 36 Cl ages have been calculated using Excel spreadsheet of Schimmelpfening et al. (2009). N.M means no or incoherent measure. Maximum erosion rates have been calculated

for the surface cobbles collected on T3 tread, with an infinite time of exposure hence at the steady state equilibrium. About 20-30 pebbles with centimetre size have been generally

collected for the amalgamated samples of the profiles. For the T2/T0 riser profile, the amalgams are made of a dozen of larger cobbles. The weighted mean ages published in [START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF] have been refined following the statistical analysis used by Fattahi et al (2010) to account for partial bleaching. Ages have been calculated for Quartz grains with size ranging between 90 and 150 microns.

  they also permit comparison with CRE ages. The ages of all the OSL samples, including those previously published by[START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF], have been recalculated in section 3.1 using CAM or FMM techniques to account for the scatter of the De distributions.OSL samples were collected at site Dehshir North, in a trench excavated within T3 and T2 (Figure4in[START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF]. Within this trench, the distal alluvial and colluvial deposits corresponding to the T2 and subsequent levels provide refined OSL ages of 60.0 ± 5.7 ka, 45.5 ± 4.6 ka, and 20.1 ± 1.6 in accord with the stratigraphic succession (Table3, sample HI/2008-IX in unit E1, sample HI/2008-VII in unit D3b, sample HI/2008-VIII in unit D4,[START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF]. In addition, recent colluviums incised by small streams flowing through the Dehshir fault zone and which base level matches with the tread of T1 yielded two OSL ages of 26.0 ± 1.0 ka for the lower colluviums and 20.2 ± 0.8 for the upper ones (Table3, sample HI/2008-I in unit B1 and sample HI/2008-VI in unit B2,Fattahi et al., 2010). These two latter OSL ages, which postdate the incision of T2, are coeval with the emplacement of T1. They imply that the T1b tread, all the more the T1a tread, is at most 21 ka (oldest possible age of the most superficial sample). Notwithstanding that the OSL samples have not been directly collected under the terrace treads sampled for CRE dating, the data available at site Dehshir North indicate large discrepancies between the CRE and OSL ages. The cannibalism of the old T3 terrace by subsequent alluvial deposits may explain such discrepancies by locally recycling T3 cobbles during the aggradation of the lower terraces T2 and T1. This possibility is further examined at site Dehshir South for which OSL samples have been taken right below the terrace treads T2 and T1 where sampled for CRE dating.For T2 at Dehshir South, two OSL samples, OSL I and OSL II, have been collected from the riser between T2 and the active riverbed, very close to the profile PS1 (Figure2aand 11b). OSL I has been collected 15 m to the West of PS1 and at a depth of 0.8 (OSL I) and OSL II, 10 m to the East of PS1 and at a depth of 3.4 m. The samples OSL I and II yielded ages of 26.9 ± 1.3 ka and 29.4 ± 5.1 ka, respectively (Table

  its aggradation occurred during the time-interval 25.6-65.7 ka. This suggest that the samples collected on T2 tread, providing exposure ages older than 66 ka, contain an inherited CRE component, For T1, two OSL samples, OSL III and IV, were collected at Dehshir South in fine sands respectively below the surface of T1b and T1a (Figure3b). The error bars on sample OSL III, taken by the riser T1b/T0, provide minimum and maximum OSL ages of 20.4 ka and 23.4 ka for the T1b tread. The sample OSL IV, taken by the riser T1a/T0, provides minimum and maximum OSL ages of 9.4 ka and 10.6 ka for the T1a tread.

  Figures captions

Figure 2 :

 2 Figure 2: Site Dehshir South. a) Quickbird imagery. The fault trace cuts across the Marvast River, intermittent channels and successive abandoned fans and terraces (T3 in orange, T2 in yellow, T1 a and b in green). The numbered dots show the position of the surface samples collected for 10 Be and 36 Cl CRE dating (red and blue dots, respectively). The black squares show the position of the near-surface samples collected along depth profiles PS1 and PS2 (Figure 11, 12 and 13). The black dots locate the OSL samples taken below the ground surface. AB locates the topographic profile of figure 3. b) Close up on the 380 ± 20m dextral offset of a river course, incised within the oldest (T3) fan surface.

Figure 3 :

 3 Figure 3: a) Topographic profile across the abandoned fan system (see location on figure 2) highlights the relative elevation of the terraces and their degree of incision by the Marvast river. The profile is work out from a differential GPS survey. b) Field photograph of the inset terraces. Location of OSL III and IV are indicated on the close up pictures of the risers T1b/T0 and T1a/T0 respectively.

Figure 4 :

 4 Figure 4: Site Dehshir North. a) Quickbird imagery. Different coloured shading denotes the successive abandoned fans (same code as for Figure 2). Numbered dots show the position of the surface samples collected for 10 Be and 36 Cl CRE dating (red and blue dots, respectively). The black square shows the position of the near-surface samples collected along the depth profiles PN (Figure 7 and 8). The black dots locate the OSL samples taken below the ground surface. Rectangle denotes the close up on the offset riser on figure 5. Dotted circles indicate location of 20-30 m right-lateral offset-gullies. Black (AB and CD) and white (RI) lines locate topographic sections on each side of the fault and on the riverbed respectively. b) Topographic profiles, achieved from differential GPS survey and projected along fault strike, highlight the amount of stream incision upstream and down stream of the fault. The offsetgullies are indicated.

Figure 6 :

 6 Figure 6: Summary of observations at site Dehshir North. a) 10 Be and 36 Cl CRE ages of surface samples modelled without erosion and without inheritance are indicated by red and blue dots above each surface. The shaded columns extend from the minimum age to the maximum age given by the error bars of the samples. The OSL samples collected beneath each surface are indicated in stratigraphic order (see text for discussion). The plot of CRE ages is given for each surface sample, in relative position from north to south. Dots and errors bars are in red and blue for 10 Be and 36 Cl, respectively. b) Distribution of in-situ produced 10 Be (left panel) and 36 Cl (right panel) CRE ages modelled without erosion and without inheritance for the surface samples collected on T3 tread. The thin curves represent the CRE age probability as Gaussian distribution for each individual sample and the thick curves correspond to the summed Gaussian density probability function. The weighted mean CRE age is obtained with errors equal to two standard deviations (2σ). Outlier sample DN06S2 (235.5 ± 35.4 ka) has not been included in the 10 Be statistics.

Figure 7 :

 7 Figure 7: Summary of observations at site Dehshir South. a) 10 Be and 36 Cl CRE ages of surface samples modelled without erosion and without inheritance are indicated by red and blue dots above each surface. The shaded columns extend from the minimum age to the maximum age given by the error bars of the samples. The OSL samples collected beneath each surface are indicated in stratigraphic order (see text for discussion). The plot of CRE ages is given for each surface sample, in relative position from north to south. Dots and errors bars are in red and blue for 10 Be and 36 Cl, respectively. b) Distribution of in situ produced 10 Be (left) and 36 Cl (right) CRE ages modelled without erosion and without inheritance for the surface samples collected on T3 Tread. The thin curves represent the CRE age probability as Gaussian distribution for each individual sample and the thick curves correspond to the

Figure 8 :

 8 Figure8: Plot of the near-surface, measured36 Cl concentrations (black dots) as a function of depth at profile PN (location on figure4). Surface samples (blue dots) are shown but not included in the modelling. The erosion rate is modelled for a 3 Ma-old surface to ensure that the steady state equilibrium between production and disintegration has been reached. For the three different densities tested (obtained from the near-surface samples), the best-fit erosion rate -inheritance is indicated.

Figure 9

 9 Figure 9. a) Plot of the near-surface, measured 10 Be concentrations (black dots) as a function of depth at profile PN (location on figure 4). Surface samples are indicated as red dots. The modelled curves fit distributions of concentrations, without erosion, and for three assigned inheritances. The modelling includes both the near-surface samples and the weighted mean age of the surface samples (DN06S2 excluded). b) Log (χ 2 ) values for a range of inheritance and CRE ages modelled without erosion are plotted below. T he modelling converges towards a best-fit age of 460 ka and inheritance 3.8 10 5 at.g -1 (SiO 2 ) (star).

Figure 10 :

 10 Figure 10: Weighted mean 10 Be CRE age of T3 tread including the surface sample exposure ages of North and South sites and excluding outlier sample DN06S2. The thin curves represent the CRE age probability as Gaussian distribution for each individual sample and the thick curves correspond to the summed Gaussian density probability function. The weighted mean age is obtained with errors equal to two standard deviations (2σ).

Figure 11 :

 11 Figure 11: a) Weighted mean CRE age for the 10 Be and 36 Cl surface samples collected on T2 tread at Dehshir South site. The ages have been calculated assuming no erosion and no inheritance and the sample DS08S114 (49.9 ± 3.3 ka) has not been included in the statistics. The thin curves represent the CRE age probability as Gaussian distribution for each individual sample and the thick curves correspond to the summed Gaussian density probability function. The weighted mean age is obtained with errors equal to two standard deviations (2σ). b) Field photograph showing the 4m high T2/T0 riser sampled for profile PS1 (see Figure 2 for location). c) Profile of 10 Be concentrations through the terrace T2 at site PS1. Red and blue dots are surface and near-surface samples, respectively. The two OSL samples collected by

Figure 12 :

 12 Figure 12: Plot of the measured 10 Be concentrations as a function of depth (left panel) and simplified stratigraphy (right panel) through profile PS2. Depth profile PS2 has been excavated within T2 tread, North of the Marvast River (see location on figure 2). Relative positions of OSL samples AB/2006/I and II and CRE near-surface amalgams are shown (blacks arrows).

Figure 13 :

 13 Figure 13: Synthesis of observations and plot of sample ages in relative position from north to south for site Dehshir North (left panels) and site Dehshir South (right panels). Dots and errors bars are in red, blue and black for 10 Be, 36 Cl and OSL dating, respectively. a) The thick lines and shaded regions are the weighted mean with 2σ confidence interval for the CRE surface age. Samples DN06S2 and DN08S114 have been omitted for the T3 and T2 statistics, respectively. The thin lines are the oldest possible CRE age of the youngest CRE sample collected on the terrace treads. b) Upper part, relative positions and OSL ages of the samples collected below the terrace treads of T2, T1b and T1a. Samples HI (Nazari et al., 2009; Fattahi et al., 2010) and AB have been collected within trenches excavated for paleoseismic purposes and samples OSL I-IV by the terrace risers. Lower part, CRE and OSL ages available for terraces T2 and T1. The thick black line is the oldest possible age of the most surficial OSL sample collected below each terrace tread.

Figure 14 :

 14 Figure 14: Depth-profile PS1 and PN of 10 Be concentrations respectively through terrace T2 (a) and T3 (b). Violet and red dots are the measured concentrations of the near-surface amalgams and surface samples, respectively. Blue dots and black dots are the respective concentrations of the near-surface amalgams and surface samples once one near-surface amalgam is restored to a null concentration without bringing back any other near-surface sample to a negative concentration (see text for discussion). The time of in-situ exposure to bring that near-surface sample to its measured concentration is indicated in red, and the residual concentrations remaining in the other near-surface samples by black arrows materializing the sample inheritance for such duration of exposure. The only rejuvenated surface sample displaying a negative concentration is the sample DN06S2 on T3, therefore a

Figure 15 :

 15 Figure 15: Summary of offsets and ages available to assess the slip-rate of the Dehshir fault.Dashed boxes and boxes correspond to weighted mean CRE age with and without removal of the estimated inheritance (see text for discussion). The oldest possible abandonment ages of T3 and T2 (thick vertical black lines) are determined from the near-surface concentrations (Figure14). The exposure age of the youngest sample (black cross) on each terrace is also indicated. Grey boxes correspond to the OSL age domains of the late sediments emplaced below the treads of T2 and T1. Light grey slip-rate domain is the range of minimum slip-rate of[START_REF] Nazari | First evidence for large earthquakes on the Deshir fault, Central Iran Plateau[END_REF]. The dark grey domain narrows the uncertainties and demonstrates the Dehshir fault slips faster than 0.93 mm.yr -1 but slower than 1.47 mm.yr -1 .

  Figure3

  T3 locally reworked by the small gullies incising T3 or a cobble exposed to cosmic rays for a long time in the upstream catchment of the Marvast River. In any case, such an outlier indicates that the inheritance of individual cobbles collected on T1 tread can be very important. Off the three remaining samples collected on T1b, two provide CRE ages that

	Revisedmanuscript	3/12/10
	former cobble of are not distinguishable from the CRE weighted mean age (175 ± 62 ka) of T2, the terrace
	immediately above. Only one sample (DS08S124, 32.1 ± 2.1 ka) provides an age
	significantly younger than the ages on T2. This CRE age on T1b surface is significantly
	younger than the CRE ages on the T1a surface at site Dehshir North, suggesting that at this
	latter location, the surface cobbles of the T1a terrace contain an important amount of inherited
	10 Be.
		14

At site Dehshir South, five samples have been collected in the present day streambed of the Marvast River. Whatever the isotope considered, all provide non-zero CRE ages ranging between 54 and 96 ka, suggesting the occurrence of a significant inheritance. The CRE ages of T0 are younger than the CRE ages of T1b except for the youngest sample of T1b (DS08S124, 32.1 ± 2.1 ka). At site Dehshir North, four samples have been collected in the main river flood plain T0. Discarding the outlier, three samples (two 10 Be ages and one 36 Cl age) provide non-zero CRE ages ranging between 57 and 84 ka, confirming the occurrence of a significant inheritance averaging some 70 ka. When including the outlier corresponding to

  and retains the weighted mean age of 469 ± 88 ka. To account for the inheritance incorporated in the former estimate, it is possible to subtract to that weighted mean age the 32 ka of inheritance age-equivalent obtained from the modelling of the 10 Be profile. It is nonetheless worth noticing that this average inheritance has been modelled under the incorrect assumption that the inheritance is homogeneous. Accounting for the variability of the inheritance, the near-surface profile data are incompatible with an age older than 412 ka (Figure14b) and the large uncertainties of the former estimate (437 ± 88 ka) can be reduced to the interval 349-412 ka (Figure15). Alternatively, retaining the youngest sample and allowing for the occurrence of a greater amount of inheritance would provide a much younger abandonment age of 271 ka (oldest possible CRE age of the youngest sample). As there is ample evidence for a large variability of the inheritance on the younger surfaces, one cannot rule out the later hypothesis and may consider an age of 271 ka for the abandonment of T3.

	Revisedmanuscript	3/12/10
	the surface samples
		19

The age of abandonment of the intermediate level T2 is easier to estimate because both OSL and CRE ages are available. The weighted mean of the zero-erosion CRE age (175 ± 62 ka) is of little use for constraining the age of abandonment because of the variable inheritance. Subtracting a possible inheritance of 70 ka (Figure

14a

), a value similar to the average obtained for the cobbles collected in the active riverbed, takes back the former estimate to 105 ± 62 ka. Although limiting the uncertainties to the range 43 -107 ka, the upper bound on the abandonment age (Figure

14a

) allows for a wide range of possibilities, including the oldest possible CRE age (53 ka) of the youngest surface cobble. Accounting for the occurrence of a variable inheritance, this latter solution is a better estimate of the maximum age of abandonment of the surface although the youngest cobble may also bear an inherited component. This inherited component may correspond to the difference with the oldest possible age of the youngest OSL collected below the tread of T2. The surface of T2 is younger than the oldest possible age of the superficial OSL sample and is at most 28.2 ka at site Dehshir South (Figure

13b

). Assuming this OSL age is close to the actual abandonment age of T2 tread, a forward modelling of near-surface concentrations of PS1 profile

(fig 11c)

Table 1 :

 1 The 10 Be and 36 Cl nuclide concentrations and CRE modelled ages for surface and near-surface samples along the Dehshir fault. Propagated analytical uncertainties include error

	blank, carrier and counting statistics. Zero erosion model ages are calculated for surface
	samples with propagated analytical uncertainties, including error blank, carrier and counting
	statistic; corresponding geographic correction factors and without shielding in agreement with
	site topography. 10 Be and 36 Cl half-life are respectively 1.387 Ma

Table 2 :

 2 Mean chemical composition of the samples collected for 36 Cl dating. Measurements of the major elements were undertaken at the SARM facility (Nancy, France).

	Revisedmanuscript

Table 3 :

 3 Equivalent dose (D e ), annual dose rate (D a ) and calculated OSL ages for each sample.

Be model age (ka) no erosion Be maximum erosion rate (m.Ma -1 ) Cl (ppm) Measured 36 Cl (10 7 at.g -1 rock) Cl model age (ka) no erosion Cl maximum erosion rate (m.Ma -1 )

	DN06S27	DN06S25	DN06S24	DN06S22	DN06S20	DNS06S9	DNS06S8	DNS06S5	DN06S4	DN06S3	DN06S28	DN06S26	DN06S23	DN06S21	DN06S19	DN06A11	DN06S10	DN06S7	DN06S6	DN06S2	DN06S1	T3	DN08A119	T2	DN08S118	DN08S117	DN08S116	DN08S115	T1	DN06S29	DN08S121	DN08S120	DN06S30	T0	North	Dehshir	Samples
	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (15 cm)	2 fragments of the same gelyfracted cobble	cobble (10 cm)	cobble (10 cm)	cobble (20 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	Amalgam (20 pluricentimetric clasts)	cobble (10 cm)	cobble (15 cm)	cobble (10 cm)	2 fragments of the same gelyfracted cobble	cobble (10 cm)		Amalgam (25 pluricentimetric clasts)		cobble (15 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)		cobble (15 cm) in the river bed	cobble (15 cm) in the river bed	cobble (10 cm) in the river bed	cobble (15 cm) in the river bed				Sample description
	2	2	2	2	2	2	2	2	2	2	2.2	2.2	2.2	2.2	2.2	2.2	2.2	2.2	2.2	2.2	2.2		2.2		2.2	2.2	2.2	2.2		2	2.2	2.2	2.2			(g.cm -3 )	Density
	4	3	3	3	5	5	3	4	5	8	9	8	7	4	4	-	5	4	5	3	3		-		6	7	6	6		7	7	8	6			(cm)	Thickness
	30.64099	30.64108	30.64129	30.64189	30.64208	30.640361	30.640389	30.640333	30.640333	30.640417	30.64038	30.64101	30.64177	30.64189	30.64208	30.6405	30.6405	30.64045	30.640361	30.64065	30.64068		30.64337		30.64362	30.64355	30.64351	30.64343		30.64571	30.64111	30.64414	30.6457			(°N)	Latitude
	54.02521	54.02507	54.02508	54.0251	54.02504	54.020972	54.021055	54.021083	54.021083	54.021222	54.02512	54.02506	54.0251	54.02503	54.02502	54.020917	54.020917	54.02092	54.021083	54.01907	54.01913		54.02239		54.02177	54.0218	54.02167	54.02151		54.02366	54.01947	54.02172	54.0236			(°E)	Longitude
	1550	1550	1549	1550	1550	1552	1555	1556	1556	1554	1550	1550	1550	1550	1550	1550	1550	1550	1550	1550	1550		1550		1549	1550	1549	1550		1539	1547	1548	1539			(m)	Elevation
											2.66	2.66	2.66	2.66	2.66	2.66	2.66	2.66	2.66	2.66	2.72		2.66		2.65	2.66	2.65	2.66			2.65	2.65	2.64
											45.92±0.99	46.99±1.02	50.72±2.12	54.60±0.75	46.84±0.65	48.37±0.66	49.21±0.69	48.78±1.19	51.88±0.72	26.55±3.66	N.M		43.97±1.11		14.55±0.39	14.42±0.39	10.30±0.28	43.06±1.17			7.18±0.19	27.16±0.71	9.23±0.22
											426.74±27.23	437.88±27.94	477.09±34.88	518.71±31.93	436.33±26.88	452.25±27.83	461.15±28.42	456.66±29.58	489.51±30.15	235.55±35.38	-		406.54±26.47		125.69±8.26	124.44±8.19	88.19±5.81	397.28±26.16			61.15±4.03	241.55±15.80	79.42±5.14				10 Be
											1.53	1.49	1.35	1.23	1.49	1.43	1.40	1.42	1.31	2.91	-		1.74		6.53	6.60	9.62	1.79			14.30	3.16	8.98
	38	40	18	19	24	13	28	26	18	16																				52
	1.41±0.02	1.53±0.024	1.31±0.014	1.25±0.019	1.36±0.013	1.30±0.018	N.M	N.M	1.18±0.014	1.21±0.011																				0.32±0.005
	354.70±47.24	383,59±53.46	307.95±39.30	297.22±37.59	345.97±45.90	351.98±48.07	-	-	268.43±33.33	291.88±37.60																				56.40±5.16							36 Cl
	1.57	1.40	1.68	1.79	1.48	1.33	-	-	2.10	1.80																				17.16

Stone scaling factor Measured 10 Be (10 5 at.g -1 SiO2) 10 Be model age (ka) no erosion 10 Be maximum erosion rate (m.Ma -1 ) Cl (ppm) Measured 36 Cl (10 7 at.g -1 rock) 36 Cl model age (ka). no erosion 36 Cl maximum erosion rate (m.Ma -1 )

	DS08S114	DS08S113	DS08S112	DS08S111	DS06S40	DS06S36	DS06S34	DS06S32	DS06S31	T2	DS08S125	DS08S124	DS08S123	DS08S122	T1	DN06S63	DS06S62	DS08S110	DS08S109	DS06S64	T0	South	Dehshir
	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (10 cm)	cobble (20 cm)	cobble (20 cm)	cobble (10 cm)	cobble (10 cm)		cobble (15 cm)	cobble (10 cm)	cobble (15 cm)	cobble (10 cm)		cobble (10 cm) in the river bed	cobble (10 cm) in the river bed	cobble (15 cm) in the river bed	cobble (15 cm) in the river bed	cobble (15 cm) in the river bed
	2.2	2.2	2.2	2.2	2.2	2.2	2.2	2.2	2.2		2.2	2.2	2.2	2.2		2	2	2.2	2.2	2.2
	6	7	7	6	5	6	6	5	4		6	6	7	4		5	4	6	5	7
	30.44803	30.44708	30.44793	30.44792	30.44663	30.447	30.44765	30.4476	30.4476		30.44695	30.44716	30.44741	30.44743		30.44881	30.44866	30.44926	30.44742	30.44864
	54.13074	54.13213	54.13371	54.13517	54.12945	54.1284	54.12751	54.12655	54.12655		54.11975	54.12017	54.12083	54.12096		54.12454	54.12527	54.13	54.11986	54.12418
	1623	1618	1615	1612	1620	1620	1619	1622	1622		1627	1627	1626	1626		1615	1615	1613	1626	1620
	2.78	2.77	2.76	2.76	2.77	2.77	2.77	2.78	2.78		2.79	2.79	2.79	2.79				2.76	2.79	2.77
	6.16±0.17	26.61±0.68	22.12±0.60	18.52±0.49	N.M	15.08±0.24	21.95±0.32	21.01±0.52	N.M		16.28±0.44	3.99±0.11	19.96±0.52	34.77±0.93				10.97±0.29	7.63±0.21	7.11±0.15
		225.76±14.73	186.22±12.26	154.99±10.15	-	124.58±7.73	184.19±11.38	175.57±11.39	-		134.22±8.83	32.07±2.12	165.94±10.87	298.60±19.60				90.34±5.94	61.83±4.08	57.78±3.68
		3.41	4.22	5.18	-	5.66	3.77	3.96	-		6.07	28 .42	4.80	2.48				9.37	14.13	12.41
																52	60
																0.40±0.012	0.45±0.007
																65.04±6.54	72.83±6.82
																14.45	12.94

Be model age (ka) no erosion Be maximum erosion rate (m.Ma -1 ) Cl (ppm) Measured 36 Cl (10 7 at.g -1 rock) Cl model age (ka). no erosion Cl maximum erosion rate (m.Ma -1 ) Dehshir North 10 Be Pit in the surface T3 PN a

	DS06P71	DS06P70	DS06P69	DS06P68	DS06P67	DS06P66	DS06P65	PS2 a	surface T2	Pit in the	DS08P132	DS08P131	DS08P130	DS08P129	DS08P128	DS08P127	DS08P126	PS1 b	Riser T2/T0	10 Be	South	Dehshir	DN06P18C	DN06P16C	DN06P15C	DN06P14C	DN06P13C	DN06P12C	surface T3	Pit in the	North 36 Cl a	Dehshir	DN06P18Q	DN06P17Q	DN06P16Q	DN06P15Q	DN06P14Q	DN06P13Q	DN06P12Q
	amalgam 300 cm below ground surface	amalgam 280 cm below ground surface	amalgam 200 cm below ground surface	amalgam 155 cm below ground surface	amalgam 80 cm below ground surface	amalgam 50 cm below ground surface	amalgam 20 cm below ground surface				amalgam 370 cm below ground surface	amalgam 270 cm below ground surface	amalgam 210 cm below ground surface	amalgam 150 cm below ground surface	amalgam 100 cm below ground surface	amalgam 60 cm below ground surface	amalgam 30 cm below ground surface						amalgam 305 cm below ground surface	amalgam 230 cm below ground surface	amalgam 165 cm below ground surface	amalgam 95 cm below ground surface	amalgam 55 cm below ground surface	amalgam 25 cm below ground surface					amalgam 305 cm below ground surface	amalgam 270 cm below ground surface	amalgam 230 cm below ground surface	amalgam 165 cm below ground surface	amalgam 95 cm below ground surface	amalgam 55 cm below ground surface	amalgam 25 cm below ground surface
	2.2	2.2	2.2	2.2	2.2	2.2	2.2				2.2	2.2	2.2	2.2	2.2	2.2	2.2						2.2	2.2	2.2	2.2	2.2	2.2					2.2	2.2	2.2	2.2	2.2	2.2	2.2
	-	-	-	-	-	-	-				-	-	-	-	-	-	-						-	-	-	-	-	-					-	-	-	-	-	-	-
	30.45705	30.45705	30.45705	30.45705	30.45705	30.45705	30.45705				30.44823	30.44823	30.44823	30.44823	30.44823	30.44823	30.44823						30.64114	30.64114	30.64114	30.64114	30.64114	30.64114					30.64114	30.64114	30.64114	30.64114	30.64114	30.64114	30.64114
	54.11839	54.11839	54.11839	54.11839	54.11839	54.11839	54.11839				54.12648	54.12648	54.12648	54.12648	54.12648	54.12648	54.12648						54.02133	54.02133	54.02133	54.02133	54.02133	54.02133					54.02133	54.02133	54.02133	54.02133	54.02133	54.02133	54.02133
								1628										1645											1550										1550
	2.79	2.79	2.79	2.79	2.79	2.79	2.79				2.82	2.82	2.82	2.82	2.82	2.82	2.82																2.66	2.66	2.66	2.66	2.66	2.66	2.66
	2.32±0.10	6.51±1.17	10.33±0.25	12.72±0.33	N.M	30.80±0.60	16.67±0.24				4.31±0.12	3.62±0.10	8.86±0.24	5.91±0.16	5.82±0.16	6.10±0.17	11.23±0.30																9.68±0.24	4.37±0.07	6.89±0.17	13.60±0.34	22.12±0.45	25.80±0.66	33.77±0.85
																							22	26	38	20	32	29
																							0.18±0.004	0.34±0.007	0.63±0.024	1.10±0.011	1.30±0.015	1.78±0.018

Acknowledgments.

This study would have been impossible without financial assistance from INSU-CNRS (PNTS and 3F programs) and CNES-SPOT Image (ISIS program contracts ISIS0403-622 and ISIS0510-812). Université Pierre et Marie Curie (UPMC) and Geological survey of Iran (GSI) provided complementary funding and logistic assistance. KL received a Ministry of Research and Education scholarship granted by the President of UPMC. The 10 Be measurements were performed at the ASTER AMS national facility (CEREGE, Aix en Provence) that is supported by the INSU/CNRS, the French Ministry of Research and Higher Education, IRD and CEA. The 36 Cl measurements were performed at the LLNL-CAMS. We thank L. Leanni, K. Pou, B. Finkel, F. Chauvet, M. Arnold and G. Aumaître for their help during chemistry and measurements at CEREGE and acknowledge B. Oveisi and M. Nazemzadeh for efficient organization and help during fieldwork. We acknowledge thorough reviews by Richard Walker and Anne-Sophie Mériaux. We are very thankful to Anne-Sophie Mériaux for her acute verification of the cosmogenic calculations.


Investigating 19 th century mathematical journals:

Importance and use of other periodicals in Nouvelles Annales de mathématiques from 1842 to 1870

Liliane ALFONSI 1 The topic of this communication is to investigate the importance and the use of others journals, by the different editors of Nouvelles Annales, from its creation in 1842 to 1870.

I wish to make it clear that what I mean by "other journals" is any regular scientific publication with mathematical articles, such as mathematical journals (Crelle, Liouville, etc..) but also academic publications (memoirs compilation or proceedings of an academy).

To understand the use of other journals in Nouvelles Annales, it is important to know that Nouvelles Annales is a journal for youngsters aiming to the Polytechnique and Normale schools.

•This is the first page in 1842, which points out the complete title and aim of journal as well as the editors:

NOUVELLES ANNALES DE It's not a journal for mathematical researchers, it's a journal for students and professors who are concerned by these schools and, more generally, for any people who have an interest for this level of mathematics.

MATHÉMATIQUES

Terquem and Gerono created it in 1842, but, as we see on the first page of the journal, Terquem seems to be the most important editor. Nouvelles Annales is his own journal and, as we will see, he uses it to serve his own goals and his own vision of what the teaching should be in high-level schools.

From 1842 to 1870, the editorial staffs were:

-1842 creation, editors TERQUEM and Gérono 1862: the death of Terquem After this first glance, it appeared to me that I had to focus on: 1842, 43, 44 because these are the first years of the journal 1848 because it is the year of a revolution (against the king), which had an influence on École Polytechnique because École Polytechnique students were essentially republicans and because it was in that year, that studies became free at this school. For all of these years, I noted for all occurrences, the journal, the author, the subject and the nature of occurrence:

-either a full article of another journal -or an extract or a revised version of the article -or an Nouvelles Annales article based on another journal's article (contestation, prolongation…)

-or a summary -or claims of order of priority -or questions asked / answers given -or cited reference points and works used -or miscellaneous. After this work, what were the quantitative and qualitative results?

I. Quantitative results

The first quantitative results are the number of occurrences for every year pointed out. Liliane ALFONSI Laboratoire GHDSO. Université PARIS-SUD 3 I only put on the graph significant years. We see that occurrences rise from 26 to 55 and that there is a regular progression with Terquem. There is a peak in 1855 which has a lot of reasons, among these, the creation of a new part of Nouvelles Annales: The Bulletin de Bibliographie, d'Histoire et de Biographie Mathématiques.

Despite the peak in 1868 with Bourget's beginning as editor, it's not true that other journals had a more important role in Nouvelles Annales, in 1868 than in 1855. We see that point now with another graph, knowing that an article from another journal (f another J) is a Nouvelles Annales (NA) article made of -either a full article -or selected passages -or summary -or analysis -or in reference to an article published in another journal or in academic publications.

Here we have the curve of the percentage of foreign articles in the Nouvelles Annales. We can see that it is in 1852 with Terquem, that there are the most foreign articles in Nouvelles Annales whereas Bourget (1868) who had the most occurrences appearing, had far less foreign articles. There is a trough in 1863 when Prouhet arrives and a peak in 1852 with Terquem's fight against the programs. Another graph shows that with Terquem, occurrences are most of all, articles from other journals, except from 1855, because Terquem changes his mind and acknowledges himself beaten.

The most remarkable thing is the last diagram: With Bourget, in 1868, there is a peak of occurrences but a trough of articles from other journals because of occurrences are footnotes reference points, questions, etc.

II. Qualitative results

For a qualitative study, I took, for every year, the five journals that have the greatest number of quotations. With Terquem it's Crelle Journal, a German Journal very important for researchers that is number one. This is a proof of the use by Terquem of other journals in Nouvelles Annales: he tries, with researcher's journals, to raise the level of teaching mathematics in the higher French schools. With Prouhet in 1863, Italian journals arrive first: the journal of Institute of Bologna and the Annali delle scienze mathematiche. And with Bourget, in 1868, Nouvelles Annales sticks more closely to the Polytechnique and Normale schools' program and there are more old journals and French journals: the Mémoires de l'Académie des sciences de Paris and the Annales de Gergonne, a French journal which is over from 1854.

1842

Acad

III. The use of others journals by the different editors of Nouvelles Annales

Now I will try to show the use of other journals by the different editors and I begin with Terquem.

1-Terquem (1842-1862)

As we can see in the first example below, articles are clearly noted as being from another journal (here Crelle's journal, 1835), in the beginning of the text, the author (here Jacobi) is named at the same time.

It's an opportunity for Terquem to give his advice on Polytechnique program and to criticize it in a footnote.

Terquem also gives often his advice in long commentaries after an article, as we can see in this second example. After a Salmon's article in Cambridge & Dublin Mathematical Journal 4th International Conference of the European Society for the History of Science Barcelona, 18-20 November 2010

Liliane ALFONSI Laboratoire GHDSO. Université PARIS-SUD 6 (1848), in which Salmon says that English students learn cono-spheric curves, Terquem hardly criticizes the higher schools' programs in France: « Teaching in France, has been made throughout the year on the basis of conics which nevertheless remain cono-spheric cases, because the plane constitutes a particular case of a sphere. The fact that these curves are not mentioned in colleges is a pity; but that they are not even mentioned in the higher schools such as the École Normale and the École Polytechnique, is totally unacceptable.

To the credit of German and English universities, these curves are commonly taught which is perfectly right. » His criticism on the Polytechnique program, about conics, is very strong and he doesn't mince his words.

Terquem uses also articles of foreign journals as an educative tribune and to criticize French teaching. Giving a summary of the Dublin calendar for 1850, he writes: « I read with great interest a report on Oxford University […] It finished with remarkable conclusions that would be of a great interest in France, when the French government will be able to do other things than an arms' factory, sometimes in favour of, sometimes against University and when the principal goal will be education and not hierarchical trivial rewards. These questions show what is the state of teaching and enable us to make comparisons that, for mathematics, as I can see, aren't to our advantage. Overseas, there is a spirit of progress : teaching follows science. In France, there is a stationary spirit, often, retrograde spirit. » He uses caustic humour to criticize teaching choices for the Polytechnique program, always starting from other journals: In 1850, « In M. Crelle's Journal (t. XL, 2) there are three articles on number theory, by M. E.-E. Kummer, a famous professor at Breslau University. M. Crelle has acquired eternal rights to the mathematicians' gratefulness for having published tremendous works on this most noble, generous and sublime part of mathematical science. (See the note at the end)

Note. The number theory is very little known and even disdained in France and for good reasons. This theory doesn't make wheels turn round, watergates open, gas condense and, worse than all that, isn't used in examinations; because of these reasons, calculating persons, in a majority position, ask why there is any need to study a theory which doesn't bring anything. My stubborn intelligence doesn't give me any answers to such questions. Rumour has it, by the same calculating mind that the next program for the École Polytechnique will throw away rational mechanics by Lagrange, Laplace, Poisson, and will put in place industrial mechanics.

As I believe in decency, I don't believe in this news: there is some misunderstanding. » And in 1851, concerning Hess's article in Crelle's Journal: « Determinants (Cramerian functions) today rule over all mathematics. So, I suppose, it's a right thing that they have been taken away from the new program. They have been replaced by the auxiliary plane, logarithm, elementary work which have taken fruitfully their place; lovely triad, without forgetting Saint Gunther's ruler that every mathematician needs to have all the time in his pocket or in his hands. » With the same humour, he also strongly criticizes Le Verrier, the most important responsible of the Polytechnique program, for his choices, in contradiction with his own work, starting from the Connaissance des temps, which is a publication of French Institute: « In the Connaissance des Temps for 1849, there is, in a Le Verrier's report on Uranus planet, lots of linear equation systems with four unknowns; exercises of the day, taken from good authority.

At page 169, he uses determinants. That's what we shouldn't copy. Because we have removed these

4th International Conference of the European Society for the History of Science Barcelona, 18-20 November 2010 Liliane ALFONSI Laboratoire GHDSO. Université PARIS-SUD

formulae from the Education program; but how would this illustrious mathematician have used them if they hadn't been taught to him?

(*) The famous mathematician astronomer used the Sturm theorem judiciously; An academician of the same name has taken away from the education program this theorem as belonging to high-level theory, useless thing; A representative of the same name has declared a high theory to be an indispensable thing. Do these three names designate the same person? O. TERQUEM. » After an article from M. Jacobi, (Crelle's Journal, t. XXX, p. 51-94; 1846) concerning a particular system of first degree equations Terquem wrote (1851):

« Astronomic application: The aim of the present report is not purely analytical. The illustrious author offered to put forward a simple process to solve numerically the equations present in the theory of the secular perturbations of the planets. The numeric data are taken from the remarkable work of Le Verrier on the same subject. The compared results show that the Jacobi process is far more exact than the one Le Verrier used. Due to the dire lack of a journal of Astronomy, M. Liouville would fill the gap, as far as he could, to such a shameful lack for the country by inserting in extenso the report of the illustrious Prussian and other analogous works in his precious journal also destined to applied mathematics. » After this vigorous fight, Terquem in 1855 acknowledges himself beaten. He doesn't think that the Nouvelles Annales hadn't followed sufficiently the Polytechnique program but that it was the official program, which hadn't given sufficient attention to the Nouvelles Annales and their ideas. That what he writes in the editorial of 1855: « The Nouvelles Annales de Mathématiques are entering their fourteenth year and despite the sacrifices we have often imposed ourselves, they haven't yet, we have to admit, been able to give us a just remuneration. Would they have missed the goal pursued, to offer youngsters aiming to the Ecoles Polytechnique and Normale the solutions to problems that can interest them most? We think not. In fact, the Annales have dealt with the beautiful and difficult questions of passed exams, and also the questions of the new exams, when they presented some interest. There was given numerical calculus exercises, logarithms with a scope that are to be found nowhere else. Despite the narrow position given to the Nouvelles Annales by the official programs, we shall as from January 1855 make new efforts in the interest of science. » And he announces the creation of the Bulletin de Bibliographie, d'Histoire et de Biographie mathématiques where he will put from now on, the most parts of articles of others journals:

« Each month there will include an added brochure with at least a pagination of its own under the title: Bulletin de Bibliographie, d'Histoire et de Biographie mathématiques, par M. O. Terquem. The title of the brochure makes the object clear. The history of Science is that of the human mind […] All the dignity of Man is in the thought process. Mathematics are a perpetual thought process. May we be worthy of our new mission! »

2-Prouhet (1863-1867)

It is Prouhet's arrival, which gives a greater respect of programs. He decides the end of the Bulletin, initiated by Terquem as we have seen before, and gives fewer articles of other journals but more quick summaries in biographical articles. In fact, the Nouvelles Annales loose their great originality, due to Terquem, to become only a way to prepare seriously Polytechnique and Normale examinations.

The part "questions asked/answers given" takes more and more place in the journal, and when articles are chosen, they are articles which subject is part of the program examination.

For the articles of other journals, he takes only fragments and he rewrites them. He only puts as a footnote the sources of the articles, such as the author and the name of the journal, 4th International Conference of the European Society for the History of Science Barcelona, 18-20 November 2010 Liliane ALFONSI Laboratoire GHDSO. Université PARIS-SUD 8 whereas Terquem is more explicit on his sources and makes it perfectly clear where his articles are taken from.

We can see the difference between the two editors, looking at the first example of Terquem (article of Jacobi took in Crelle's journal) and at the example of Prouhet below:

It is only in a footnote that we learn in which journal and from what author Prouhet took the article. Prouhet stops definitively to use other journals with the aim to give advice and criticism on the programs.

3-Bourget (1868-1870 the end of our study)

This trend increases with Bourget as editor. He choices to put in the Nouvelles Annales still fewer articles of other journals and more historical articles than mathematical articles. The fact that an article is taken from another journal is much badly indicated as it was by Prouhet.

As an example which we can see below, we will know that « Etude sur des surfaces algébriques », is taken from the Journal des savants and who is the author, only at the end of the article and this is written in very small letters: Bourget uses of other journals most of all in footnotes and used as reference points. He respects official programs and so the articles of Nouvelles Annales are, for the most, of the Polytechnique and Normale schools' level and made especially by authors who writes for the journal. Nouvelles Annales becomes a journal, which lives essentially in autarky. For these years, the most important editor was Terquem who founded Nouvelles Annales in 1842. He wanted to use the journal for the aim of influence program examination of Polytechnique and Normale schools and, more generally, French teaching, in a sense of a higher level.

He took articles in researchers journals (Crelle, Liouville, etc.) that he put in Nouvelles Annales as full articles or long selected passages, by one hand to improve the level of students and teachers who buy his journal, and by another hand to write at the government and at the men responsible of mathematical French teaching what they have to do.

He took also articles on the history of mathematics to give examples to follow and a more general mathematic culture at youngsters. For all articles, the author and the original journal are mentioned at the beginning and very clearly and Terquem used of their authority to serve his purpose and to give lessons at the ministry of French education and at his staff.

It is only in 1855 that he changed his mind, seeing that his journal was not very bought, because of the non-respect of the real program examination. So he took minus mathematical articles in researcher journals and more in books or revues of mathematical history, creating the Bulletin de Bibliographie, d'Histoire et de Biographie mathématiques in appendix of Nouvelles Annales.

His successors, Prouhet and Bourget, were more classical. They did not use many articles from researcher's journals, and the few they used were in footnotes or cited referenced points. Criticism of French teaching and of program examination, which was the principal aim of articles of others journals with Terquem, disappeared completely. And if the Nouvelles Annales became more sold, it loosed (from 1863 to 1870) his high mathematical and culture level, his function of mathematics teaching consciousness, and as Terquem said "his mission:

  -1863: editors Gérono and Prouhet 1867: the death of Prouhet -1868: editors Gérono and Bourget I would now like to explain what my method was. 1 Laboratoire GHDSO. Université Paris-Sud 4th International Conference of the European Society for the History of Science Barcelona, 18-20 November 2010 Liliane ALFONSI Laboratoire GHDSO. Université PARIS-SUD 2 At the beginning, I looked at the volumes from 1842 to 1870, from page to page, noting all occurrences of other journals and trying to determine the most important years for my study.

  1850, 51, 52, 53, 54 because there was a very important program change in November 1850, and Terquem vigorously fought against this change, as we will see, using foreign journals till 1854. 1855 Terquem acknowledges himself beaten, and fought in another way. 1863, 64, 65, it is Prouhet's beginning as editor and a great change for Nouvelles Annales and the use of other journals 1868, 1869, 70, it is the same thing for Bourget.

4th

  International Conference of the European Society for the History of Science Barcelona

Years 1842 1844 1852 1854 1855 1863 1868

	4th International Conference of the European Society for the History of Science
			Barcelona, 18-20 November 2010
	Number of	26	24	34	31	43	32	55
	occurences

« All the dignity of Man is in the thought process. Mathematics are a perpetual thought process. May we be worthy of our new mission! »