K Le Dortz
email: ledortz@geologie.ens.fr

B Meyer

M Sébrier

R Braucher

D Bourlès

L Benedetti

H Nazari

M Foroutan

Interpreting scattered in-situ produced cosmogenic nuclide depth-profile data

Modelling the evolution of the concentration of in-situ produced cosmogenic nuclides as a function of depth (depth-profile) has been developed to allow determining both the exposure duration and the denudation rate affecting geomorphic features. However, material sampled through surficial deposits may exhibit an inherited component resulting from exposure to cosmic rays before deposition. In case of homogeneous inheritance, this inherited component may be estimated through sampling at increasing depths and subsequently subtracted. In case of variable inheritance, the measured concentrations are scattered and the random distribution of the depth-profile concentrations prevents modelling confidently a depth-profile and precludes constraining an exposure duration. Often observed in desert and endorheic regions, this greatly restricts the possibilities to determine an accurate abandonment age of alluvial surfaces in such environments. Provided the denudation is demonstrated negligible, a method for determining a more accurate range of minimum inheritance, hence a more accurate maximum abandonment age for a given alluvial surface, is proposed. This method, based on the rejuvenation of depth-profile samples, relies on the simple hypothesis that at least one of the depth-profile samples would be emplaced with no or negligible inherited component and on the obvious principle that none of analyzed sample has been emplaced with a negative

Introduction

Cosmic ray exposure (CRE) dating has been widely used to estimate the age of alluvial surfaces in many regions worldwide. For a long while and still for some recent studies, surface samples only were collected to determine CRE ages (e.g., [START_REF] Ritz | Slip rates along active faults estimated with cosmic-ray-exposure dates: Application to the Bogd fault, Gobi-Altaï, Mongolia[END_REF][START_REF] Regard | 10 Be dating of alluvial deposits from Southeastern Iran (the Hormoz Strait area)[END_REF], Van der Woerd et al., 2006). Measurement of their cosmogenic nuclide concentration (most often 10 Be) yields a CRE age for each collected pebble (Figure 1a, upper panel). If enough pebbles have been collected on a given surface, a suitable statistical treatment may exhibit a Gaussian distribution centred on the weighted mean age eventually assigned to the studied surface (Figure 1b, upper panel). Sometimes, the measured concentrations are scattered and their distribution is multimodal (Figure 1c, upper panel). The occurrence of outliers resulting either from pre-or post-depositional processes is thus extensively discussed. While some authors point to denudation and artificial rejuvenation of the surface and favour the oldest ages (e.g., [START_REF] Brown | Comment on "Slip-Rate Measurements on the Karakorum Fault May Imply Secular Variations in Fault Motion[END_REF], others point to inheritance and artificial ageing of the surface and therefore favour the youngest ages (e.g., [START_REF] Mériaux | The Aksay segment of the northern Altyn Tagh fault: Tectonic geomorphology, landscape evolution, and Holocene slip rate[END_REF][START_REF] Vassallo | Transpressional tectonics and stream terraces of the Gobi-Altay, Mongolia[END_REF]. Pre-depositional exposure indeed implies the accumulation of an inherited component that shifts the final Gaussian distribution towards greater concentrations while post-depositional denudation brings to the surface less concentrated subsurface pebbles that widens and shifts the Gaussian distribution towards smaller concentrations. Neither the inherited component, nor the denudation rate can be estimated using surface samples only. In an attempt to clear up this point, depth-profile sampling has often been undertaken (Figure 1a, lower panel). Providing that the material constituting the deposit of interest has been emplaced over a short period of time, some ka, with respect to the subsequent duration of exposure and that it has been homogeneously pre-exposed, the depthprofile samples, whether individual or amalgamated pebbles, exhibit an exponential decrease M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 3 of their concentration as a function depth controlled by the attenuation length of the producing particles (e.g., [START_REF] Anderson | Explicit treatment of inheritance in dating depositional surfaces using in-situ 10Be and 26Al[END_REF][START_REF] Repka | Cosmogenic dating of fluvial terraces, Fremont River, Utah[END_REF]. An exponential tending asymptotically to zero indicates no inherited component, while an exponential tending asymptotically to a characteristic concentration indicates a homogeneously distributed inherited component whose concentration is given by the asymptotically reached value (Figure 1b, lower panel). A chi-square inversion minimising the difference between the measured and modelled concentrations is often used to constrain from these depth-profiles the exposure duration of the studied surfaces, their denudation rate, and the concentration of their inherited components, if homogeneous (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]. Where the number of surface samples is limited or the distribution of their concentrations multimodal, depth-profiles also help narrowing the range of possible surface ages (e.g., [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] Champagnac | Slip rate at the northeastern front of the Qilian Shan, China[END_REF]. However, scattered surface pebble concentrations are sometimes observed together with random depth distributions of 10 Be concentrations (e.g., [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF]. In such cases (Figure 1c), the distribution of surface pebbles is multimodal and the concentrations of the depth-profile samples do not decrease exponentially with depth, suggesting a variable inheritance and making any conventional modelling useless.

We have investigated such situations encountered in the desert region of central Iran while analysing offset fan surfaces along the Dehshir (Le [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF] and Anar (Le [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF] faults. Although sands appear to be less sensitive to inheritance than gravels (e.g., [START_REF] Matmon | Dating offset fans along the Mojave section of the San Andreas fault using cosmogenic 26Al and 10Be[END_REF][START_REF] Schmidt | A note of caution on the use of boulders for exposure dating of depositional surfaces[END_REF], the overall low sand content in the investigated alluvial material precluded the possibility to perform depth profile analysis on sandy material. Consequently, it was appropriate to collect samples of comparable granulometries (pebbles and cobbles) on the surface and all along depth-profile. To account for the scattering of cosmogenic nuclide concentrations and to determine the possible ranges of both the abandonment ages of the analyzed fan surfaces and the inheritance carried by their gravels, a CRE procedure has been developed. This procedure is based on depth-profile analyses, whose results are subsequently compared to the overlying surface samples. Such a procedure reveals appropriate because the studied sites met two necessary conditions: (1) the negligible denudation rate of the fan surface implies that depth-profile concentrations only depend on two unknowns (pre-exposure and in-situ exposure), and (2) the common source of alluvial material for both the surface and depth-profile samples implies that depth-profile samples can be compared with surface ones. The scatter of the measured cosmogenic nuclide concentrations resulting thus only from a variable inheritance, the concentrations calculated M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 4 using the proposed depth-profile rejuvenation procedure allow estimating a maximum abandonment age for a given fan surface and provide a range of minimum inheritance. The complete description of the sites, the sampling strategy, the details of the performed analyses, and the modelled ages can be retrieved in two previous papers (Le [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF][START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF]. Some of these pebble data are used here to illustrate and discuss the limitations of a method, the profile rejuvenation procedure, which accounts for the variability of inheritance where denudation is negligible.

1 1 1 1

Profile rejuvenation methodology.

Scattering of cosmogenic nuclide surface concentrations at a given site may result from both denudation processes and/or variable inheritance. At the Dehshir and Anar sites, qualitative observations of a desert pavement covering the very pristine surface of the fans made of varnished clasts suggested low erosion rate. This is quantitatively confirmed measuring the concentrations of two distinctive cosmogenic nuclides having different halflives, 10 Be (1.387 Ma; [START_REF] Chmeleff | Determination of the 10 Be half-life by multicollector ICP-MS and liquid scintillation counting[END_REF][START_REF] Korschinek | A new value for the 10 Be half-life by Heavy-Ion Elastic Recoil detection and liquid scintillation counting[END_REF]) and 36 Cl (0.301 Ma; e.g., Gosse & Philipps, 2001) in samples along depth-profiles from the same oldest surface.

The 36 Cl ages calculated assuming no denudation and no inheritance are systematically younger than the 10 Be ages calculated under the same assumptions, indicating that the carbonates samples had nearly reached the steady-state equilibrium -cosmogenic nuclide production balanced by losses due to radioactive decay and denudation, if any -at which the 36 Cl concentration only depends on the denudation rate. Modelling then the evolution of the 36 Cl concentrations along the depth-profiles quantitatively confirmed a denudation rate lower than 10 -3 mm.yr -1 , hence negligible, over the investigated time span [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF].

Even if denudation rate is negligible, the original distribution of the pebbles at the surface of a terrace may be modified since their abandonment on the tread due to their closeness to the risers between two terrace levels, local overfloodings (e.g., [START_REF] Van Der Woerd | Holocene left slip-rate determined by cosmogenic surface dating on the Xidatan segment of the Kunlun fault (Qinghai, China)[END_REF] or surface runoff, and diffusion [START_REF] Owen | Beryllium-10 terrestrial cosmogenic nuclide surface exposure dating of Quaternary landforms in Death Valley[END_REF]. Sampling far from the risers may help mitigating such effects. However, one cannot rule out that a few of the pebbles collected at the surface might have been brought by animals or shepherds either from higher or lower, hence older or younger, levels. Such modifications are excluded for material deeper in a terrace. Unless biopedoturbation, ploughing or cryoturbation has modified the original relative depth position of some pebbles within the terrace material (Frankle et al., 2011), the samples collected at depth do represent the original relative depth distribution of the terrace

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Clearly, there is no evidence for significant biopedoturbation, ploughing, or cryoturbation in the desert environment prevailing in central Iran. If it were, amalgamating 10-30 individual pebbles for each depth-profile sample would ensure diluting the contributions of a few anomalous pebbles. Considering all the above-mentioned remarks, the scatter of cosmogenic nuclide concentrations (Figure 2a) measured both at the surface and along depth-profiles at several sites in central Iran should only result from two unknown contributions: the in-situ cosmogenic nuclide production and the pre-exposure of the analyzed samples. To limit these contributions, we propose to determine the minimum range of inheritance of a terrace, and consequently its maximum abandonment age, analyzing first the depth-profile samples. Providing that the terrace aggraded during a short time interval coeval with a single climatic crisis, as confirmed by OSL ages within some of the alluvial terraces (Le [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF] and was not subsequently affected by significant denudation, the measured depth-profile concentrations should only result from in-situ production and preexposure. Then the proposed method relies on the impossibility for any depth-profile samples to have been emplaced in the terrace material with a negative cosmogenic nuclide concentration. Thus, considering the sampling depth and assuming that the measured concentration would only results from in-situ production (i.e., the sample would have been emplaced with a null cosmogenic nuclide concentration), one can calculate the time needed to bring back to zero each depth-profile concentration. The maximum abandonment age corresponds to the time needed for the depth-profile sample, which could be brought back from its measured concentration to a null concentration without bringing the other depthprofile samples to a negative concentration (Figure 2b, step 1). Therefore, this method is based on the simple hypothesis that, if denudation is negligible, at least one of the depthprofile samples could be emplaced with no inherited component. Subtracting for each profile sample the concentration accumulated at its sampling depth during the thus estimated maximum abandonment age to the measured concentration yields excess concentrations that correspond, when corrected for radioactive decay since the maximum abandonment age, to the minimum inherited components

The accuracy of the maximum abandonment age deduced from the profile rejuvenation method may then be evaluated through its comparison with the abandonment ages deduced from the concentrations measured in the individual pebbles or cobbles collected on the terrace tread. However, a prerequisite to such comparison is to ensure that the material sampled at a given site along a depth-profile and on the fan surface originates from the same source. For two (Anar and Dehshir North) out of three of the analyzed sites, the geologically

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6 homogeneous catchment areas are small enough to reasonably postulate a short transport duration of the alluvial material. In addition, approximately 4-m-high natural or excavated outcrops within the alluvial sediments do not evidence significant change of gravel source during the fan aggradation. Thus, it is qualitatively unlikely that the source of the alluvial material changed during the emplacement of the near-surface and surface samples. To validate these field observations, an a posteriori statistical comparison of the concentrations measured at the surface with those measured along depth-profiles was performed at each analyzed site (see Appendix and following sections). The maximum abandonment age determined using the profile rejunevation method allows calculating a maximum surface concentration at each given sampling site according to its spatial coordinates. Adding that maximum concentration to that found in excess in each profile sample, when using the same rejuvenation procedure (see above), yields to surface equivalent calculated concentrations that thus represent the concentrations that would have been measured if the samples collected along the depth-profile had been exposed solely at the surface. Finally, these calculated values are compared to the concentrations measured in the surface samples. Because nearly all the calculated concentrations fall in the range of those measured at the surface this implies that samples from depth-profiles and surfaces originate at each site from the same source.

Therefore, we consider that the amalgam depth-profile concentrations represent the average concentration that would yield multiple sampling of pebbles at a given depth and the scatter of concentrations between successive amalgams corresponds mainly to the variability of inheritance among a homogeneous source. This scatter of concentrations along depth-profiles corresponds then only to variable pre-exposure duration in the upper catchments, and the accuracy of the maximum abandonment age of the fan surface determined using the profile rejuvenation method may thus be compared to the surface concentrations (Figure 2c, step 2). Thus, if most concentrations of the surface pebbles become negative while subtracting the insitu concentration that would have been accumulated at the surface during the duration that corresponds to the maximum cosmogenic nuclide abandonment age determined from the profile rejuvenation, then that maximum abandonment age is not physically acceptable (Figure 2c, right). On the contrary, if most of these surface concentrations remain positive by performing the same operation, the maximum cosmogenic nuclide abandonment age (t Max ) provides a maximum possible age for the fan surface (Figure 2c, left).

Finally, a minimum cosmogenic nuclide abandonment age (t min ) can be estimated from the lowest surface concentration (Figure 2d, step 3) that, in addition, allows estimating the maximum range of inheritance values for such a t min . This minimum cosmogenic nuclide

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7 abandonment age may be compared with OSL ages, if available, to discuss whether it still could be affected by some inherited component. The following examples highlight the variability of the inheritance and illustrate the methodology to account for this variability and derive accurate limits on the inheritance and hence on the possible range of abandonment ages of a given alluvial terrace unaffected by denudation.

Estimating the ranges of inheritance and abandonment age on an alluvial terrace

To illustrate the principles of the proposed methodology, samples from an intermediate terrace emplaced by the Marvast river at the Iranian Dehshir South site (T2 terrace; Le [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF] are used (Figure 3a, left). Seven surface samples have been analysed and their calculated 10 Be age distribution is multimodal. Discarding the possible outlier DS08S114 (49.9 ± 3.3 ka), their weighted mean 10 Be age is of 175 ± 62 ka (Table 1, Figure 3a, right). In order to try to better constrain the abandonment age of this alluvial deposit, seven samples were taken at increasing depths along a 4-m profile. Each sample is an amalgam of 10-30 pebbles aiming at measuring the mean concentration at each level. The random evolution of the measured 10 Be concentrations as a function of depth does not permit to plainly model the obtained depth-profile and hence to define a limiting isochron as theoretically proposed by [START_REF] Ryerson | Applications of morphochronology to the active tectonics of Tibet[END_REF]. This random distribution excludes uniform pre-exposure of the material, prior to its emplacement as the T2 alluvial terrace, and suggests thus variable inheritance. Recent work dealt with the occurrence of variable inheritance in alluvial terraces (e.g., [START_REF] Schmidt | A note of caution on the use of boulders for exposure dating of depositional surfaces[END_REF]. In the latter, a variable inheritance is evidenced only in boulders collected on the surface while concentration of sand samples decrease exponentially along a depth-profile, suggesting a homogeneous inheritance. [START_REF] Schmidt | A note of caution on the use of boulders for exposure dating of depositional surfaces[END_REF] suggest that the differences in the inherited component are related to the different provenances and pre-exposure histories of the different material. In our case, the variability of inheritance is observed for pebbles and cobbles of different nature (quartz for 10 Be and carbonates for 36 Cl) for which internally coherent results have been obtained on a same terrace (Le [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF]. The method described in section 1 was thus used to account for the variability and derive accurate bounds on the minimum inheritance.

The performed analysis indicates that terrace T2 was abandoned at most 107 ka ago, that is the time required to bring sample P127 concentration back from its current value to zero without bringing back any other depth-profile sample to a negative concentration (Figure 3b). The concentration in excess remaining after subtracting to the measured concentration the concentration accumulated by in-situ production during 107 ka at the sampling depth

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8 corresponds for all samples but P127 to the decay of the original inherited component (Table A.1). Concentration in excess are ranging from 2.15x10 5 at/g(SiO 2 ) (sample P126) to 7.86x10 5 at/g(SiO 2 ) (sample P130). After correcting for the radioactive decay during the last 107 ka, the inherited concentrations corresponding to the maximum abandonment age of the T2 terrace (Table A.1) are ranging from 2.27x10 5 to 8.29x10 5 at/g(SiO 2 ). As mentioned previously, one has to demonstrate that the depth-profile samples and the surface samples originated from the same source area. As discussed above, summing the surface concentration accumulated during 107 ka exposure duration to each concentration in excess determined for the depth samples (see Appendix and Table A.1) yields to depth-profile derived surface concentrations within the range of those measured in the surface samples (Figure A.1).

Moreover, the other possible abandonment ages based either on the lowest surface concentration (minimum cosmogenic nuclide abandonment age of 50 ka) or even on the OSL ages ( 30ka) yield similar conclusions. Thus, all these statistical considerations demonstrate a posteriori that the gravels of the depth-profile and the ones of the fan surface sample originate from the same variably pre-exposed source and can thus be compared. Regarding the surface samples, the profile rejuvenation method using the concentration accumulated at the surface by in-situ production during 107 ka brings only one of the surface samples to a negative concentration (Figure,3b). This remains acceptable as this sample is, in addition, the statistical outlier DS08S114. It is nonetheless important to notice that this age of 107 ka is the uppermost bound for the abandonment age and thus for the in situ exposure duration.

Consequently, exposure ages ranging from 0 to 107 ka are theoretically possible for the T2 surface. On the one hand, exposure ages ranging between 53 ka (oldest possible age of the youngest sample, DS08S114, Table 1) 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. All exposure ages younger than 47 ka (youngest possible age of the youngest sample, DS08S114, Table 1) would imply that the youngest sample collected at the surface has a significant inherited component. At this location, two OSL ages yielded 26.9±1.3 ka at 0.8 m depth and 29.4±5.1 ka at 3.4 m depth, suggesting that the terrace material aggraded on a short period of time and that the youngest CRE sample may still contain some inheritance.

Because surface sampling does not allow accounting for inheritance, while profile rejuvenation permits retrieving the range of variable inheritance, the age range of 175±62 ka obtained considering the sole surface samples is incompatible with the maximum cosmogenic

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nuclide abandonment age deduced from the depth profile samples analysis. As a consequence, the lowest surface concentration (DS08S114, Table 1) measured in the statistical outlier, provides a realistic minimum cosmogenic nuclide abandonment age of 50 ± 3 ka. This T2 minimum abandonment age yields to maximum inheritance ranging between 3.29x10 5 and 8.59x10 5 at/g (Figure 3c and Table A.1). Selecting a youngest abandonment age derived from the OSL ages would increase very slightly the inheritance without changing the overall figure (see Table A.1). Therefore, the cosmogenic nuclide abandonment ages range for T2 abandonment should be narrowed to 47-107 ka and the alluvial material appears to have emplaced with inherited concentrations ranging from 2.27x10 5 to 8.7x10 5 at/g.

Case study

Example of an old terrace

In the same region (Figure 4a, left), the 10 Be concentrations measured along a depthprofile from a higher, hence older, terrace (T3; see Le [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF] were analysed. The in-situ produced 10 Be concentrations increasing with the exposure duration and the 10 Be inherited concentrations radioactively decreasing, it can be anticipated that the proportion of in-situ produced 10 Be with respect to the inherited one increases with the abandonment age.

The longer is the in-situ exposure duration, the higher is the dilution of inheritance. Ten quartz samples were collected on the T3 tread (Table 1 andFigure 4a, right). The distribution of these surface CRE ages, considering sample DN06S2 (235.5 ± 35.4) as an outlier, is unimodal and leads to a weighted mean CRE age of 462 ± 55 ka. Amalgamated samples have also been collected along a depth-profile. Their 10 Be concentrations exhibit an overall exponential decrease with depth but the deepest sample displays nonetheless a much higher concentration than the two samples above it. Such a 10 Be depth-profile can theoretically be modelled (pink curve, Figure 4b). The best fit, assuming no denudation, is obtained for an abandonment age of 464 ka and a homogeneous inheritance of 3.8 x 10 5 at/g (SiO 2 ), which would correspond to a pre-exposure duration of ~32 ka, if acquired at the surface in conditions similar to that at the Dehshir North site (Le [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF]. One may find satisfactory the coherence between the abandonment ages deduced from the surface samples and the modelling of the depth-profile samples. However, the fact that the inherited concentration derived from the modelling of the depth-profile is half the concentrations measured for the deepest samples is intriguing, and opens the possibility for the occurrence of For T3, the depth-profile sample, whose concentration can be restored to zero by subtracting a simple in-situ exposure duration at the sampling depth without bringing back any other depth-profile sample to a negative concentration, is P12 (Figure 4b andTable A.1).

The minimum excess concentration (2.43x10 5 at/g (SiO 2 )) is obtained for sample P17, collected at 2.7 m depth, and the maximum excess concentration (9.04x10 5 at/g (SiO 2 )) is obtained for sample P14. Accounting for the radioactive decay, this brackets the minimum inherited component between 2.99x10 5 and 11.1x10 5 at/g. The maximum cosmogenic nuclide abandonment age of 412 ka deduced from the profile rejuvenation method agrees with the range of abandonment ages deduced from surface samples only (462 ± 55 ka). This consistency is significant when considering that summing the surface concentration accumulated during 412 ka exposure duration to each concentration in excess determined for the depth samples yields to depth profile derived surface concentrations within the range of those measured in the surface samples (see Appendix, A.1). This allows narrowing the abandonment age interval to 407-412 ka. It is worth noticing that this rejuvenation would yield only one of the surface samples to a negative concentration, the statistical outlier DN06S2 (Figure 4b). All the other such rejuvenated surface samples display positive excess concentrations. While abandonment ages for the terrace T3 older than 412 ka are not possible because they would imply a negative concentration for at least one depth-profile amalgam (P12), younger exposure ages remain possible. Theoretically, all exposure ages ranging between 0 and 412 ka are possible. On the one hand, exposure ages ranging between 271 ka (oldest possible age of the youngest T3 surface sample DN06S2, Table 1) and 412 ka would make that statistical outlier younger than the age of the terrace. On the other hand, exposure ages ranging between zero and 200 ka (youngest possible age of the youngest T3 sample DN06S2, Table 1) would be compatible with the occurrence of the statistical outlier as well as the other surface samples collected on T3. All ages younger than 200 ka would imply that the youngest surface sample also contains some inheritance.

One may therefore consider the youngest surface sample -i.e., the statistical outlier DN06S2 (235.55±35.38 ka) -as the last pebble emplaced on the T3 tread before its abandonment and subsequent incision. Considering the possibility for a variable inheritance as for T2, the age of sample DN06S2 might be closer to the abandonment age of surface T3.

If the concentration corresponding to 235 ka of in-situ production at their sampling depth is

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11 subtracted to each surface and depth-profile sample, the age distribution of such rejuvenated surface samples remains unimodal (Figure 4c,top). However the concentrations of the "rejuvenated" depth-profile samples remain too scattered to allow for a simple profile modelling, revealing that inheritance is not homogeneous (Figure 4c, bottom). The minimum abandonment age of 235 ka, which is calculated for T3, permits to estimate the range of the variable maximum inheritance. Accounting for the radioactive decay, the range of the maximum inheritance between 3.62x10 5 and 16.12x10 5 at/g appears rather large (Table A.1). This case study illustrates that an unknown and variable inheritance can always be modelled as a homogeneous inheritance once the portion of the concentration that has been acquired at the sampling depth since the deposit emplacement becomes significantly larger than that inherited from surface pre-exposure. 3 5

Example of a young terrace

A similar approach has been applied to the surface and depth-profile samples of a young terrace level (the T1 terrace offset by the Anar fault along the western piedmont of the Kuh-e-Bafq about 150 km east of the Dehshir sites, Figure 5a, left; see Le [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF]. For a young terrace, the proportion of inherited concentration, if there is any, may be large with respect to the in-situ produced concentration acquired at the sampling depth since the deposit emplacement. Ten quartz samples and seven amalgamated samples were collected on the surface and along a depth-profile through a well-defined abandoned fan surface, respectively (figure 5). The CRE ages of the surface samples are scattered and display a multimodal distribution with a weighted mean CRE age of 32 ± 25 ka (Figure 5a,right). This terrace appears significantly younger than the ones studied in the Dehshir area. The error-bars on the mean value are too large to allow tightly constraining an abandonment age. The distribution of depth-profile concentrations is random, dismissing a homogeneous pre-exposure prior to the emplacement of the fan material (Figure 5b). Besides, the deepest depth-profile samples display 10 Be concentrations larger than that of many of the surface samples. This exemplifies the occurrence of a variable inheritance and led Le [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF] to approximate the abandonment age of the terrace by that of the youngest pebble.

Applying the rejuvenation method described above to the depth-profile samples yields a maximum cosmogenic nuclide abandonment age of 46 ka, which implies minimum excess concentrations ranging from 0.7x10 5 to 4.16x10 5 at/g (SiO 2 ) (Figure 5b andTable A.1).

Summing the surface concentration accumulated during 46 ka exposure duration to each concentration in excess determined for the depth samples indeed yields to depth-profile A .1 and Figure A.3). In addition, applying this maximum cosmogenic nuclide abandonment on surface samples implies that all but one of the rejuvenated surface samples would display negative concentrations, highlighting that the maximum cosmogenic nuclide abandonment age of 46 ka deduced from the rejuvenation of the depth-profile data is largely overestimating the actual abandonment age of the terrace.

Minimum inheritance must then be higher than those estimated using the profile rejunevation method, which prevents determining a maximum cosmogenic nuclide age. The abandonment age of the alluvial surface is thus better approximated by the CRE age of the youngest surface sample (17.5 ± 1.1 ka; sample AS06S75 in Table 1). Subtracting a concentration corresponding to a simple exposure duration of 17.5 ka at their sampling depth, one verifies that none of the depth-profile sample has been emplaced with a negative concentration (Figure 5c). This minimum CRE age of 17.5 ka permits to calculate a range of maximum inheritance bracketed between 1.48x10 5 and 4.30x10 5 at/g (SiO 2 ). This confirms that the 10 Be concentration of the deepest sample (P97) results nearly entirely from inheritance whatever the range of theoretical exposure age (0-46 ka). It is nonetheless possible that the youngest surface sample concentration also incorporates some inheritance. This is the case for this studied Anar site as demonstrated by OSL burial ages associated to samples collected below the tread (5.8±3.6 ka at 0.8 m depth and 14.4±3.9 ka at 4.1 m depth) that are younger than the CRE ages of pebbles collected on the tread (Le [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF]. Interestingly summing the surface concentration accumulated during either 17.5 ka (youngest CRE age) or 10 ka (average OSL age of the final fan aggradation) exposure duration to each corresponding concentration in excess determined for the depth samples yields to depth profile derived surface concentrations that are compatible with those measured in the T1 surface samples (see Appendix, Table A .1 and Figure A.3). This again demonstrates that the depth-profile and surface samples originate from the same source. Therefore, this case study illustrates the limitation of the profile rejuvenation method for very young alluvial surfaces (0-20 ka) for which, the portion of variable inheritance is significant with respect to the proportion of the concentration acquired at the sampling depth since the deposit emplacement. In such conditions, it appears more pertinent to rely on the youngest surface sample to approximate the age of the surface. The profile rejuvenation method allows handling the complications raised by variable inheritance when using in-situ produced cosmogenic nuclide concentrations in regions where denudation is demonstrated negligible, a necessary condition which limits the unknowns to the in-situ exposure duration and to the inherited component resulting from pre-exposure. This approach is illustrated by analyses of samples collected from alluvial terraces in the arid environment of the central Iran plateau where denudation has been demonstrated negligible [START_REF] Dortz | Dating inset terraces and offset fans along the Dehshir fault combining cosmogenic and OSL methods[END_REF]. Where depth-profiles cannot be modelled to determine a homogeneous inheritance, this profile rejuvenation procedure may allow to derive from the depth-profile samples a maximum cosmogenic nuclide abandonment age for the surface of an alluvial terrace and to estimate a range of minimum inherited concentrations. The consistency between the surface and depth profile concentrations has to be checked for each site to ensure that both surface and depth profile samples originate from the same source (see Appendix).

When the profile rejuvenation method yields negative concentrations for most of the surface samples, this indicates that the profile derived maximum abandonment age significantly overestimates the actual surface abandonment age. As a consequence, the youngest of the surface samples appears as the best approximation for the abandonment age of the alluvial terrace rather than the weighted mean CRE age of many samples. This youngest age provides the minimum abandonment age based on CRE data and permits to calculate a range of maximum inheritance. Interestingly, this was empirically formulated for Holocene terraces at some places in Mongolia [START_REF] Vassallo | Transpressional tectonics and stream terraces of the Gobi-Altay, Mongolia[END_REF] and at some sites 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]. The different sites we analyzed in the desert environment of central Iran show that the procedure of rejuvenation profile allows handling the variable inheritance of alluvial material whatever the age of the analyzed terrace. In central Iran, where variable inheritance is observed, the inherited concentrations range between 1.48 x10 5 and 16.1x10 5 at/g. However, the range of inheritance for a given site is much smaller, the inheritance concentrations varying approximately in a ratio 1-3. In addition, the maximum inheritance values appear to increase with terrace abandonment ages. Nevertheless, we do not have enough sites to ascertain such conclusion and this observation may only reflect difference in catchments and/or in pre-exposure processes. If the observed inheritances would have accumulated at the surface, they would be equivalent to CRE duration ranging from 15 ka to 130 ka.

The occurrence of such high, inherited concentrations for the sites analyzed in central Iran may result from the endorheic drainage of the Iranian plateau that prevents significant fluvial incision (Le [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF]. Thus, low denudation rates and weak incision favour M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 14 the feeding of alluvial fans or terraces by reworking older alluvial material. As a consequence, this older alluvial material has been previously exposed to cosmic rays and carries a variable amount of inheritance according to the depth where it was eroded and/or the number of times it was reworked. This alluvial "cannibalism" may also characterize many arid endorheic regions such as Altiplano, central Asia (Tarim, Mongolia, Tibet…), where the amount of denudation is thought negligible. Therefore, this method could be usefully applied to analyze the cosmogenic nuclide concentrations in such regions to determine bounds of maximum insitu CRE duration and ranges of inheritance.

Even more interesting than the important amount of inheritance is the high variability of that inheritance expressed by the random distribution of the concentrations of the amalgams along a given profile. Indeed, smaller variations between two successive samples amalgamating 10-30 pebbles at a given depth are expected, anticipating they average the cosmogenic nuclide concentrations at that depth. The variability among amalgams may thus represent sudden and uneven episodes of aggradation of material exhumed from different places of the upper catchments. This would explain a rapid aggradation of the fanglomerates together with the lack for exponential decrease of the concentrations with depth. These observations may result from the fact the cosmogenic nuclide concentrations, which built up in landscape, are not completely reset by erosional climatic crisis. As a consequence, OSL ages may help constraining the history of alluvial aggradation (e.g., [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF]2011;[START_REF] Fruchter | Revealing sediment sources, mixing, and transport during erosional crater evolution in the hyperarid Negev Desert, Israel[END_REF][START_REF] Guralnik | Constraining the evolution of river terraces with integrated OSL and cosmogenic nuclide data[END_REF]. Finally, this study demonstrates the usefulness of combining both surface and depth-profile sampling either to approach confidently the abandonment age of alluvial fans or to document their aggradation history. The comparison between surface concentrations and depth-profile concentrations cannot be performed directly because cosmogenic nuclide production rate is extremely sensitive to depth. Theoretically, concentrations only resulting from accumulation at any depth below the surface (i.e., in-situ production with no denudation and no inheritance) may be converted to concentrations the samples would have accumulated at the surface during the same exposure duration using the inverse function of neutron attenuation. However, concerning the analyzed Iranian sites, where scattering of both depth-profile and surface concentrations is observed within alluvial material, this depth to surface conversion cannot be achieved a priori because the measured concentrations are the result of two unknown components: the in-situ exposure duration and the variable inheritance. Consequently, it is only possible to perform an a posteriori comparison, which relies on the estimated abandonment ages of an analyzed alluvial surface. For each abandonment age, the corresponding in-situ contribution may be calculated for any depth-profile sample.

Subtracting this calculated in-situ contribution from the measured concentration yields the current excess concentration of a given depth-profile sample. Then, adding this current excess concentration to the in-situ concentration accumulated at the surface, during an exposure duration corresponding to the abandonment age, yields to the concentration that the depthprofile samples would have if emplaced and remaining at the surface. Performing such concentration conversion for all the samples of a depth-profile allows comparing depthprofile samples to surface samples. Table A.1 provides all the measured cosmogenic nuclide concentrations and all the results of the calculation that have been performed to convert depth-profile concentrations to surface ones. For each analyzed site, these concentration conversions have been made at least for two exposure durations: (1) the maximum abandonment age (t Max ), which has been determined by the profile rejuvenation method (see section 2 and 3), and (2) the minimum abandonment age (t min ), calculated from the lowest surface concentration. When OSL ages were available, they have also been used to perform a depth to surface conversion. In addition, a last column provides the inherited concentration at the time of alluvial aggradation (i.e., the inheritance resulting form pre-exposure). It corresponds to the current excess concentration corrected for radioactive decay.

Three figures illustrate the distribution of the measured surface concentrations and of the differently converted depth-profile concentrations to surface ones. These figures are

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

19 presented in the same order as the sites analyzed in the text. Concerning the site of T2 terrace (see section 2), three abandonment ages are considered: 107 ka (t Max ), 50ka (t min ), and 30 ka (t OSL ). All the converted depth-profile concentrations, calculated using these abandonment ages are compared to the surface concentrations (Figure A.1 and Table A.1). This comparison indicates that the depth-profile and surface samples originate from the same source. Thus, they can be compared and analyzed jointly. Nevertheless, it appears that the converted depthprofile concentrations systematically exhibit a narrower range of values than the surface concentrations. This should be the consequence of the sampling amalgamation that tends to average the actual sample variability. The converted depth-profile concentrations decrease with the abandonment ages. Nevertheless, while the in-situ contribution decreases with the abandonment age, inheritance remains comparable within the range 3 to 8.5x10 5 at/g. For the T3 site (section 3.1), only two abandonment ages may be considered. All the converted depth-profile concentrations, calculated using both cosmogenic nuclide abandonment ages are compared to the measured surface concentrations (Figure A.2 and Table A.1). However, the two abandonment cosmogenic nuclide ages yield significant differences as the two possible ranges of converted concentrations do not nearly overlap. The depth-profile concentrations converted using 412 ka (t Max ) are within the range of the measured surface concentrations that defines the Gaussian distribution (see figure 4a, right) while those converted using 235 ka (t min ) lie between the Gaussian distribution of the measured surface concentrations and the measured lowest surface concentration. Depending on whether the lowest surface concentration is interpreted as the best t min approximation or as an outlier, this solution may be considered as valid or not. Whatever the choice, as mentioned in section 3.1, the solution based on 412 ka provides a significantly higher value for the maximum inheritance than the mean determined by profile modelling (see Figure 4b andTable A.1). Concerning the T1 terrace site (see section 3.2), three abandonment ages are considered: 46 ka (t Max ), 17.5 ka (t min ), and 10 ka (t OSL ). All but the one based on 46 ka of the converted depth-profile concentrations are within the range of the surface concentrations (Figure A.3 and Table A.1).

However, it is noteworthy to stress that the results obtained considering t Max are inconsistent with the T1 surface data. Then, this maximum cosmogenic nuclide abandonment age is most likely unrealistic. Considering the two younger abandonment ages of 17.5 ka and 10 ka, the obtained converted concentrations are compared with the measured surface concentrations (Figure A.3). As for the T2 site, they appear to determine a narrower range of values than the surface concentrations. At this site, the range of inheritance, from ∼1.5 to 4.5x10 5 at/g, also remains approximately stable even if the abandonment age decreases. The shift corresponds to the inherited 10 Be concentration that the modelling of a depth-profile may evidence. The homogeneous inheritance is the concentration value toward which the modelled profile asymptotically tends. c) With a variable inheritance, CRE surface ages are often scattered and their distribution is multimodal. There is no exponential decrease of the concentrations with depth making helpless any profile modelling (dashed curve). Table 1: The 10 Be concentrations and CRE modelled ages for surface and depth-profile samples along the Dehshir and Anar fault. Propagated analytical uncertainties (reported as 1) include uncertainties associated with AMS counting statistics, chemical blank measurements and AMS internal error (0.5%). Zero erosion zero inheritance model ages are calculated for surface samples taking into account their associated analytical uncertainties, their sampling geographic coordinates and no shielding, in agreement with site topography. The used 10 Be half-life is 1.387 Ma [START_REF] Chmeleff | Determination of the 10 Be half-life by multicollector ICP-MS and liquid scintillation counting[END_REF][START_REF] Korschinek | A new value for the 10 Be half-life by Heavy-Ion Elastic Recoil detection and liquid scintillation counting[END_REF]. For surface samples, a density of 2.2 g.cm -3 has been used for quartz. An attenuation length of 160 g.cm -2 (Gosse & Philipps, 2001) has been used for fast neutrons. [START_REF] Stone | Air pressure and cosmogenic isotope production[END_REF] polynomial has been used to determine surface production rate at the sampling geographic coordinates assuming a SLHL production rate of 4.49 at.g -1 .yr -1 for 10 Be with 6% of uncertainty. 10 Be ages have been calculated using Cosmocalc (Vermeesh 2007). About 10-30 pebbles with centimetre size have been generally collected for the amalgamated samples of the profiles. Anar samples ages Table A.1: The table presents the measured and calculated parameters used to compare depthprofile and surface concentrations for different abandonment ages (t Max obtained from the profile rejuvenation method, t min , obtained from the youngest surface pebble and t OSL when OSL ages are available) of each analyzed alluvial terrace, T2, T3, and T1. The excess concentrations correspond to the concentrations remaining in depth-profile samples after using the rejuvenation method. For each depth-profile sample, adding up this excess concentration to the concentration corresponding to the in-situ surface duration (t Max ; t min or t OSL ) permit to calculate the profile 10 Be concentration converted to the surface for each abandonment age. This concentration would correspond for each depth-profile sample to their concentration if they had emplaced and remained at the surface ; it can be compared to the concentrations measured in the surface samples. Correcting the excess concentration for radioactive decay allows calculating the 10 Be inheritance in each depth-profile sample, which corresponds to the inheritance value at the time of the alluvial aggradation.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

  As for T2, the methodology described to estimate the minimum inheritance considering only the depth-profile samples has thus been applied to T3.

Figure

  Figure A.2 and TableA.1). This allows narrowing the abandonment age interval to 407-412

  that are not fully compatible with those measured in the surface samples (see Appendix, Table

  This study benefited from initial funding by PNTS and 3F INSU programs. Université Pierre et Marie Curie (UPMC) and Geological survey of Iran (GSI) provided the complementary funding and the 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. L.Leanni, F. Chauvet, M. Arnold and G. Aumaître are acknowledged for their help during chemistry and measurements. We acknowledge Ari Matmon and one anonymous reviewer for constructive remarks that helped to greatly improve our manuscript.

Figure 1 :

 1 Figure 1: Usual strategies of surface and depth-profile sampling for determining exposure age of alluvial surfaces. a) Individual quartz pebbles are collected for surface sampling while amalgams of 10-30 centimetre-sized pebbles are used for depth-profile sampling. b) Surface exposure age determination using (top) weighted mean 10 Be CRE age for surface samples and (bottom) modelling an exponential decrease of the concentrations with depth for depth-profile samples. Blue and black samples for theoretical cases, dark pink and light pink domains figure out the in-situ production acquired with and without homogeneous inheritance, respectively. With homogeneous inheritance, the Gaussian distribution of the surface samples is shifted providing an artificial CRE age older than the current age of surface abandonment.

Figure 2 : 8 Figure 3 0 Figure 4 2 Figure 5

 2830425 Figure 2 : Illustration of the rejuvenation method. a) Red dots are the concentrations measured for the depth-profile amalgams and the surface samples. If there is no denudation, then the scatter of concentrations results only from a variable inheritance. b) The first step requires calculating the time needed for one of the depth-profile samples to be brought back to a null concentration without bringing the other samples to a negative concentration. The concentration of that sample is indicated in red while the theoretical in-situ concentration expected at the depth of the other profile samples is indicated by blue dots. The in-situ exposure duration required to bring that depth-profile sample to its measured concentration corresponds to the maximum abandonment age (t Max ) of the terrace and is indicated in red with the pink domain figuring the corresponding in-situ production. The blue arrows indicate the excess concentrations remaining in the other depth-profile samples. c) The second step consists in comparing these rejuvenated profile concentrations with the rejuvenated surface samples (blue dots with error bars). If the profile rejuvenation shifts most of the surface concentrations to positive values (left panel), then the calculated abandonment age provides a maximum possible age for the surface. On the other hand, if most of the rejuvenated surface concentrations are shifted to negative values (right panel), there is inconsistency and the

  those published in Le[START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript 16 Le Dortz | Holocene right-slip rate determined by cosmogenic and OSL dating on the Anar fault, Central Iran[END_REF] because they have been recalculated with updated half-life and attenuation length.

•

  Surface and depth profile cosmogenic sampling • If scattering of concentrations (profile & surface), there is variable inheritance • If erosion is negligible, we use profile rejuvenation method • Minimum inheritance, hence, maximum abandonment age for the surface is obtained

		ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT
	Highlights T2 Surface	T2
	M A N U S C R I P T A C C E P T E D Sample description Density (g.cm -3 ) Thickness (cm) Latitude (°N) Longitude (°E) Elevation (m) Measured 10 Be cobble (10 cm) 2.2 5 30.4476 54.12655 1622 cobble (20 cm) 2.2 6 30.44765 54.12751 1619 cobble (20 cm) 2.2 6 30.447 54.1284 1620 cobble (10 cm) 2.2 6 30.44792 54.13517 1612 cobble (10 cm) 2.2 7 30.44793 54.13371 1615 cobble (10 cm) 2.2 7 30.44708 54.13213 1618 cobble (10 cm) 2.2 6 30.44803 54.13074 1623 1 6 4 5 amalgam 30 cm below ground surface Terrace T2 (Dehshir South) Samples  Samples Depth Surface sampling DS06S32 DS06S34 DS06S36 DS08S111 DS08S112 DS08S113 DS08S114 Profile sampling DS08P126 2.2 -30.44823 54.12648 DS08P127 amalgam 60 cm below ground surface 2.2 -30.44823 54.12648 DS08P128 amalgam 100 cm below ground surface 2.2 -30.44823 54.12648 DS08P129 amalgam 150 cm below ground surface 2.2 -30.44823 54.12648 DS08P130 amalgam 210 cm below ground surface 2.2 -30.44823 54.12648 DS08P131 amalgam 270 cm below ground surface 2.2 -30.44823 54.12648 DS08P132 amalgam 370 cm below ground surface 2.2 -30.44823 54.12648 Terrace T3 (Dehshir North) Surface sampling DN06S2 2 fragments of the same gelyfracted cobble 2.2 3 30.64065 54.01907 1550 DN06S6 cobble (10 cm) 2.2 5 30.64036 54.021083 1550 DN06S7 cobble (15 cm) 2.2 4 30.64045 54.02092 1550 DN06S10 cobble (10 cm) 2.2 5 30.6405 54.020917 1550 DN06A11 Amalgam (20 pluricentimetric clasts) 2.2 -30.6405 54.020917 1550 DN06S19 cobble (10 cm) 2.2 4 30.64208 54.02502 1550 DN06S21 cobble (10 cm) 2.2 4 30.64189 54.02503 1550 DN06S23 cobble (10 cm) 2.2 7 30.64177 54.0251 1550 DN06S26 cobble (10 cm) 2.2 8 30.64101 54.02506 1550 DN06S28 cobble (20 cm) 2.2 9 30.64038 54.02512 1550 Profile sampling 1 5 5 0 DN06P12Q amalgam 25 cm below ground surface 2.2 -30.64114 54.02133 DN06P13Q amalgam 55 cm below ground surface 2.2 -30.64114 54.02133 DN06P14Q amalgam 95 cm below ground surface 2.2 -30.64114 54.02133 DN06P15Q amalgam 165 cm below ground surface 2.2 -30.64114 54.02133 DN06P16Q amalgam 230 cm below ground surface 2.2 -30.64114 54.02133 DN06P17Q amalgam 270 cm below ground surface 2.2 -30.64114 54.02133 DN06P18Q amalgam 305 cm below ground surface 2.2 -30.64114 54.02133 M A N U S C R I P T A C C E P T E D A C C E P T E D (cm) (10 5 at.g -1 SiO 2 ) Terrace T1 (Anar) DS06S32 0 21.01±0.52 Surface sampling AS06S73 Amalgam -pluricentimetric fragment 2.2 -31.19474 55.15243 1574 DS06S34 0 21.95±0.32 AS06S74 Amalgam -pluricentimetric fragment 2.2 -31.19404 55.15357 1562 DS06S36 0 15.08±0.24 AS06S75 3 fragments of the same gelyfracted pebble 2.2 4 31.19263 55.15304 1571 DS08S111 0 18.52±0.49 AS06S76 conglomerate with pebbles of quartz (cm) 2.2 9 31.19405 55.15330 1559 DS08S112 0 22.12±0.60 AS08S89 fragment of a cobble 2.2 5 31.20095 55.15331 1571 AS08S91 several fragments of the same gelyfracted pebble 2.2 -31.19915 55.15242 1571 AS08S92 Amalgam -pluricentimetric fragment 2.2 -31.19874 55.15221 1570 AS08S94 two fragments of the same gelyfracted pebble 2.2 6 31.19391 55.15297 1570 AS08S95 pebble (10 cm) 2.2 6 31.19499 55.15471 1570 AS08S96 pebble (10 cm) 2.2 5 31.19358 55.15577 1570 Profile sampling 1567 AS08P97 amalgam 370 cm below ground surface 2.2 -31.19526 55.15340 AS08P98 amalgam 270 cm below ground surface 2.2 -31.19527 55.15341 AS08P99 amalgam 170 cm below ground surface 2.2 -31.19527 55.15341 AS08P100 amalgam 100 cm below ground surface 2.2 -31.19527 55.15341 AS08P101 amalgam 70 cm below ground surface 2.2 -31.19527 55.15341 AS08P102 amalgam 30 cm below ground surface 2.2 -31.19527 55.15341 AS08P108 amalgam 150 cm below ground surface 2.2 -31.19527 55.15341 M DS08S113 0 26.61±0.68 DS08S114 0 6.16±0.17 T2 Depth profile Abandonm Samples Depth (cm) Abandonment Excess A N U S C R I P T ent age age concentration (10 5	Stone scaling factor 2.78 2.77 2.77 2.76 2.76 2.77 2.78 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 2.66 2.66 2.66 2.66 2.66 2.66 2.66 2.66 2.66 2.66 2.73 2.71 2.73 2.71 2.73 2.73 2.73 2.73 2.73 2.73 2.72 2.72 2.72 2.72 2.72 2.72 2.72	Measured 10 Be (10 5 at.g -1 SiO2) 21.01±0.52 21.95±0.32 15.08±0.24 18.52±0.49 22.12±0.60 26.61±0.68 6.16±0.17 11.23±0.30 6.10±0.17 5.82±0.16 5.91±0.16 8.86±0.24 3.62±0.10 4.31±0.12 26.55±3.66 51.88±0.72 48.78±1.19 49.21±0.69 48.37±0.66 46.84±0.65 54.60±0.75 50.72±2.12 46.99±1.02 45.92±0.99 33.77±0.85 25.80±0.66 22.12±0.45 13.60±0.34 6.89±0.17 4.37±0.07 9.68±0.24 7.86 ± 0.18 3.93 ± 0.12 2.20 ± 0.05 2.55 ± 0.06 3.53 ± 0.086 3.47 ± 0.08 3.96 ± 0.10 5.20 ± 0.12 2.70 ± 0.067 3.83 ± 0.10 4.29 ± 0.12 3.48 ± 0.09 4.21 ± 0.11 2.24 ± 0.06 5.15 ± 0.14 3.8 ± 0.10 1.8 ± 0.05	zero inheritance zero erosion 10 Be model age (ka) 175.57±11.39 184.19±11.38 124.58±7.73 154.99±10.15 186.22±12.26 225.76±14.73 49.87±3.29 235.55±35.38 489.51±30.15 456.66±29.58 461.15±28.42 452.25±27.83 436.33±26.88 518.71±31.93 477.09±34.88 437.88±27.94 426.74±27.23 64.27 ± 4.12 31.86 ± 2.16 17.45 ± 1.12 20.34 ± 1.30 28.90 ± 1.87 28.40 ± 1.84 32.50 ± 2.11 42.74 ± 2.77 22.06 ± 1.43 31.45 ± 2.08

at.g -1 SiO 2 ) 10 Be inheritance (10 5 at.g -1 SiO 2 ) Profile 10 Be concentration converted to surface (10 5 at.g -1 SiO 2 )

	DS08P126	30	11.23±0.30		2.15±0.06	2.27±0.06	15.74±0.42
	DS08P127	60	6.10±0.17		0	0	13.59±0.37
	DS08P128	100	5.82±0.16		2.18±0.06	2.30±0.06	15.77±0.44
	DS08P129	150	5.91±0.16	107 ka	3.96±0.11	4.17±0.12	17.54±0.48
	DS08P130	210	8.86±0.24		7.86±0.21	8.29±0.22	21.45±0.57
	DS08P131	270	3.62±0.10		3.05±0.08	3.22±0.09	16.64±0.47
	DS08P132	370	4.31±0.12		4.00±0.11	4.22±0.12	17.59±0.48
	DS08P126	30	11.23±0.30		6.92±0.19	7.10±0.19	13.09±0.35
	DS08P127	60	6.10±0.17		3.21±0.09	3.29±0.09	9.37±0.25
	DS08P128	100	5.82±0.16		4.09±0.11	4.19±0.12	10.25±0.30
	DS08P129	150	5.91±0.16	50 ka	8.38±0.13	5.11±0.14	11.15±0.31
	DS08P130	210	8.86±0.24		3.35±0.26	8.59±0.23	14.54±0.39
	DS08P131	270	3.62±0.10		4.16±0.09	3.44±0.09	9.51±0.27
	DS08P132	370	4.31±0.12		4.16±0.12	4.27±0.12	10.32±0.28
	DS08P126	30	11.23±0.30		8.63±0.23	8.76±0.23	12.44±0.33
	DS08P127	60	6.10±0.17		4.36±0.12	4.42±0.12	8.17±0.22
	DS08P128	100	5.82±0.16		4.78±0.13	4.85±0.14	8.59±0.24
	DS08P129	150	5.91±0.16	30 ka	5.35±0.14	5.43±0.15	9.16±0.25
	DS08P130	210	8.86±0.24		8.57±0.23	8.70±0.23	12.38±0.31
	DS08P131	270	3.62±0.10		3.46±0.09	3.51±0.10	7.27±0.21
	DS08P132	370	4.31±0.12		4.21±0.12	4.28±0.12	8.03±0.22
				T3
	T3 Surface
	Samples	Depth
		(cm)

Measured 10 Be (10 5 at.g 1 SiO 2 )

	DN06S2	0	26.55±3.66
	DN06S6	0	51.88±0.72
	DN06S7	0	48.78±1.19
	DN06S10	0	49.21±0.69
	DN06A11	0	48.37±0.66
	DN06S19	0	46.84±0.65
	DN06S21	0	54.60±0.75
	DN06S23	0	50.72±2.12
	DN06S26	0	46.99±1.02
	DN06S28	0	45.92±0.99
	T3 Depth profile
	Samples	Depth
		(cm)

Measured 10 Be (10 5 at.g -1 SiO 2 ) Abandonment age Excess concentration (10 5 at.g -1 SiO 2 ) 10 Be inheritance (10 5 at.g -1 SiO 2 ) Profile 10 Be concentration converted to surface (10 5 at.g -1 SiO 2 )

			ACCEPTED MANUSCRIPT
	DN06P14Q	95	22.12±0.45		9.04±0.18	11.10±0.22	54.56±1.10
	DN06P15Q		13.60±0.34		8.04±0.20	9.88±0.24	53.57±1.33
	DN06P16Q		6.89±0.17		4.12±0.10	5.06±0.13	49.65±1.25
	DN06P17Q		4.37±0.07		2.43±0.04	2.99±0.05	47.96±0.77
	DN06P18Q		9.68±0.24		8.18±0.20	10.06±0.25	53.71±1.33
	DN06P12Q	25	33.77±0.85		13.68±0.34	15.38±0.39	40.28±1.01
	DN06P13Q	55	25.80±0.66		12.73±0.33	14.32±0.36	39.33±1.00
	DN06P14Q	95	22.12±0.45		14.33±0.29	16.12±0.33	40.93±0.83
	DN06P15Q DN06P16Q DN06P17Q DN06P18Q T1 Surface Samples AS06S73 AS06S74 AS06S75 AS06S76 AS08S89 AS08S91 AS08S92 AS08S94 AS08S95 AS08S96 T1 Depth profile Depth (cm) 0 0 0 0 0 0 0 0 0 0 Samples Depth (cm)	13.60±0.34 6.89±0.17 4.37±0.07 9.68±0.24 Measured 10 Be (10 5 at.g -1 SiO 2 ) 7.86 ± 0.18 3.93 ± 0.12 2.20 ± 0.05 2.55 ± 0.06 3.53 ± 0.086 3.47 ± 0.08 3.96 ± 0.10 5.20 ± 0.12 2.70 ± 0.067 3.83 ± 0.10	10.29±0.25 5.24±0.13 3.22±0.05 8.79±0.22 A N U S C R I P T 11.57±0.29 36.89±0.91 5.89±0.15 31.84±0.80 3.62±0.06 29.82±0.48 9.89±0.24 35.39±0.87 T1 M 235 ka
	A C C E P T E D
	DN06P12Q	25	33.77±0.85	412 ka	0	0	45.53±1.15
	DN06P13Q	55	25.80±0.66		3.84±0.09	4.71±0.12	49.36±1.25

Measured 10 Be (10 5 at.g -1 SiO 2 ) Abandonment age Excess concentration (10 5 at.g -1 SiO 2 ) 10 Be inheritance (10 5 at.g -1 SiO 2 ) Profile 10 Be concentration converted to surface (10 5 at.g -1 SiO 2 )

	AS08P97		4.29 ± 0.12		4.16±0.11	4.26±0.12	9.80±0.27
	AS08P98		3.48 ± 0.09		3.24±0.09	3.32±0.09	8.88±0.24
	AS08P99		4.21 ± 0.11		3.55±0.09	3.64±0.10	9.19±0.25
	AS08P100		2.24 ± 0.06	46 ka	0.70±0.02	0.72±0.02	6.34±0.17
	AS08P101	70	5.15 ± 0.14		2.89±0.08	2.96±0.08	8.53±0.23
	AS08P102	30	3.8 ± 0.10		0	0	5.64±0.15
	AS08P108		1.8 ± 0.05		0.97±0.03	0.99±0.03	6.61±0.19
	AS08P97		4.29 ± 0.12		4.24±0.12	4.28±0.12	6.44±0.17
	AS08P98		3.48 ± 0.09		3.39±0.09	3.42±0.09	5.59±0.15
	AS08P99		4.21 ± 0.11		3.95±0.11	3.99±0.11	6.15±0.17
	AS08P100		2.24 ± 0.06	17.5 ka	1.63±0.04	1.65±0.05	3.83±0.11
	AS08P101	70	5.15 ± 0.14		4.26±0.12	4.30±0.12	6.46±0.17
	AS08P102	30	3.8 ± 0.10		2.29±0.06	2.31±0.06	4.49±0.12
	AS08P108		1.8 ± 0.05		1.47±0.04	1.48±0.04	3.67±0.10
	AS08P97		4.29 ± 0.12		4.26±0.12	4.29±0.12	5.49±0.15
	AS08P98		3.48 ± 0.09		3.43±0.09	3.45±0.09	4.66±0.13
	AS08P99		4.21 ± 0.11		5.07±0.11	4.09±0.11	5.30±0.14
	AS08P100		2.24 ± 0.06	10 ka	1.90±0.05	1.91±0.05	3.13±0.08
	AS08P101	70	5.15 ± 0.14		4.65±0.13	4.68±0.12	5.88±0.16
	AS08P102	30	3.8 ± 0.10		2.96±0.08	2.97±0.08	4.18±0.11
	AS08P108		1.8 ± 0.05		1.61±0.05	1.62±0.05	2.28±0.08


Antonio Luna Arriaga

Francis Bony

Thierry Bosch

Digital to Analog Conversion Methodology Applied to Self-Mixing Displacement Signals

Keywords: Adaptive algorithm, signal reconstruction, optical feedback, displacement measurement PACS: 42.60.-v, 06.30.Bp

Digital to analog conversion methodology applied to self-mixing displacement signals

Antonio Luna Arriaga, Francis Bony, Thierry Bosch

INTRODUCTION

Self-mixing (SM) interferometry for metrological purposes has been studied with more interest in the last ten years as an inexpensive and auto-aligned optical sensing technology [START_REF] Donati | A review of self-mixing techniques for sensing applications[END_REF]. The reduced number of components required for its setup and the precision achieved with this technique, place it as a prominent candidate for development of embedded applications. In the field of displacement measurement the SM signal processing is rather complex due to the strong dependance to the target reflectivity [START_REF] Bosch | Optical Feedback Interferometry[END_REF]. Efforts are still carried to consolidate it as a reliable instrumentation scheme.

In a classical displacement reconstruction algorithm [START_REF] Bes | [END_REF], the optimization procedure launched to reach more precision works over a full signal acquisition and requires several cycles to converge. Hence, this algorithm is not suitable for real time implementation, although their main objective was to enlighten the precision and feasibility of their method. Accuracy improvement has been reported by using an electro-optic modulator (EOM) which provides a better resolution to detect the shape of SM signals [4]. However the fact of adding external optics breaks the premise of conceiving a low-cost sensor. A recent algorithm has been proposed in [5] providing a solution to discriminate the error arising from the different reflective index of the materials under measure and their media. In that case, the study was oriented to the robustness achieved and not in the implications of the real time elaboration.

The self-mixing interferometer setup is presented in Fig. 1. It only requires a laser diode (LD) as a source, a collimating lens and a photodiode (PD) to measure the optical output power (OOP) of the laser beam. The processor unit required to interpret the incoming SM signals, provides information about the target's displacement with a precision inferior to half-wavelength. When the LD is focused on a moving target, a small portion of the emitted beam is back-reflected by the target's surface into the laser cavity. This produces a variation of power and frequency in the emission stage. The equation describing the power monitored as seen by PD is

P(t) = P 0 1 + m.F 4πD(t) λ F (t) . (1)
The emitted optical power from the laser without back-reflection is P 0 . The modulation index for the laser diode is m. The target displacement is D(t). The emission wavelength subject to optical feedback is λ F , and F is a cosine function related to the feedback coupling factor (C), used to characterize the shape of the signal when the internal oscillation of the laser is affected. When the target approaches to the source, SM signals exhibit a certain tilt. It is mirrored when the target goes in the opposite sense [START_REF] Bosch | Optical Feedback Interferometry[END_REF]. SM features can be compared to classical Michelson interferometers, however an important difference is that SM phenomenon occurs in the semiconductor active medium and not in the free space.

In order to dimension a system for an embedded usage, a time constraint must be imposed based on the requirements specification. Besides, the algorithm characterization provides knowledge of the needed resources for the target architecture. If we take as example two different applications from recent literature: (a) The monitoring of independent displacement of individual surface portions in an ablation drilling process [6], and (b) a prototype to estimate the motion of a human chest wall [7]. One can realize that there are different reflection coefficients generating a particular SM signal shape and thus, the difficulty of modeling each system for an optimal implementation.

The algorithm proposed in this paper, named (CNA) is inspired from the well known First-Order-Hold (FOH) interpolator model used in some Digital-to-Analog Converters (DAC) [START_REF] Proakis | Digital Signal Processing -Principles, Algorithms and Applications[END_REF]. It aims to provide a consistent displacement reconstruction and an ease of system resources estimation. It is intended to be coupled with other algorithms dealing with the detection of the SM signals, face to changes of C parameter and the correction of degradation artifacts over the signal like the speckle and fringe loss. The focus is on an efficient implementation and a high degree of maintainability in order to be synthesized for different processor architectures.

RECONSTRUCTION PROCESS Overview

Consider Fig. 2 to illustrate the proposed method: The SM signal is digitized and fed into a detector system. It helps to transform the complex SM shape to a train of pulses corresponding to the temporal maxima and minima of each phase transition. From literature [START_REF] Bosch | Optical Feedback Interferometry[END_REF] we know that each SM fringe corresponds to a target displacement of λ /2, so this value is multiplied by the output of the transition pair (TP) block. On the other hand, there is a module counting the number of samples (T) between two transitions needed to command the generation of a normalized triangular window (TRI). Depending on the TP values the zone detector module selects an upsample procedure. Each upsampled pair is filtered with TRI and thus, produces an interpolated segment as in a classical FOH model. The linear model approach for SM analysis was proposed by [START_REF] Plantier | [END_REF]. That lead us to privilege this interpolation scheme instead of the conventional sinc interpolation.

The transitions detected at the input are not equally spaced, so they can be interpreted as belonging to an irregular sampling of the calculated displacement. A pure DAC interpolation is not feasible due to aliasing phenomenon. While sophisticated reconstruction methods from non uniform samples are an active research in signal processing [10], they are mainly based on the use of time-invariant low pass filtering. In the case of SM signals a static temporal input cannot be guaranteed. To privilege the simplicity of calculations and the integration into a hardware-software system, the essence of the DAC integrator mechanism is kept as the heart of this algorithm.

Formulation

The TP vector is composed by the present and previous detected transitions tr(N) and tr(N -1) respectively, where N = 0, 1, 2, ... is the number of accumulated fringes detected. It is increased for positive fringes and decreased for negatives. TP can be represented as [tr(N -1) tr(N)].

The signal x(n) to convolve, is the resulting vector of upsampling TP by the factor T as denoted by expression (2). On every new fringe arrival, TP is updated as well as the T factor.

x(n) = T P(n/T ), n = 1, 2, ..., T 0, otherwise. (2)
The convolution kernel h(k) gets a size 2T as established by Shannon's sampling theorem. Its shape is T RI, corresponding to the impulse response of a delayed FOH interpolator [START_REF] Proakis | Digital Signal Processing -Principles, Algorithms and Applications[END_REF] h(k) = (1/T ) T RI((k -T )/T ).

(

) 3
The convolution of ( 2) and ( 3), results in the interpolated segment (x FOH ) denoted by

x FOH (n) = T ∑ k=0 h(k)x(n -k). ( 4
)
This equation is graphically understood with the example of Fig. 3, where a segment of two upsampled negative transitions is represented.

From literature [START_REF] Bosch | Optical Feedback Interferometry[END_REF] [3], it is known that target displacement can be calculated by

D(t) = N λ 0 2 + ε (5)
where λ 0 is the laser diode wavelength without back-reflection. The excess fringe 'ε' is the point where the displacement changed direction. It helps to provide the precision inferior to λ 0 /2. Since the interpolated segments keep track of the accumulated transitions, the reconstructed displacement for our algorithm is

D(n) = x FOH (n) λ 0 2 . ( 6
)
The heart of the algorithm is the convolution, which is one of the most well understood algorithms in signal processing domain. It can pass from a complexity O(n 2 ) to O(n log n) with no big effort or even be implemented entirely into hardware [11]. In consequence, optimized implementations can be analyzed according to particular needs.

Algorithm Details

Signal Detection

Figure 4 shows the model of SM signals at two different laser feedback conditions, belonging to the same displacement. The weak back-scattered signal presents a sinusoidal shape, while the moderate regime offers a sawtooth like signal. A sawtooth shape is typically treated by implementing a high pass filter and a threshold comparison in order to extract the phase transitions. They are set positive for one direction of the target movement and negative for the opposite direction. SM shape obeys a non-linear behavior and as mentioned earlier, its analysis is adapted according to the given application. In order to validate our algorithm, we work with with a preprocessed vector of transitions. The discussion of the different methods for fringe detection at different C values is out of the scope of this work.

Segments Interpolation

The transitions vector is fed by pairs to TP module, if they share the same sign (positive or negative), then are assigned to a f ringes zone. Conversely, when the target changes its direction there is a TP with a positive value and a negative value or vice-versa. This is assigned as a lobe zone. For the fringes zone, TP vector is simply upsampled by the current T counted samples. When reconstructing the lobe zone, TP vector is compensated by adding a value in the middle of TP vector, allowing the segment to bump providing more resolution to the signal shape. The precision achieved in (5) relies thus on this compensation.

Figure 5 shows in dotted lines the result of a linear interpolation for a TP segment in the two defined zones. The offset observed in lobe section degrades the shape reconstruction but it can be corrected by a smoothing filter to provide a clean signal at the output.

Algorithm Validation

The relevance and precision of the algorithm has been validated for different signal scenarios. In Fig. 6 we show the displacement reconstruction from the transitions of Fig. 4 for weak and moderate feedback. It can be seen that in both cases the periodic sinusoidal movement if retrieved by interpolating every two transitions. Hence, this is the real time constraint to consider when developing a system using this algorithm.

The error between the original displacement and the reconstructed signal is calculated from the sample to sample difference, the maximum error of about 250 nm shows that the algorithm doesn't follow a perfectly smooth sinusoidal displacement. This is due to the inherent segment by segment treatments. However in displacement measurement we are mainly concerned by the amplitude of the reconstructed signal as they provide us the displacement information of the target. Moreover, since the reconstructed displacement is in digital format an smoothing filter can be performed without penalize resources before taking out signal.

Finally we acquired a real signal with a LD from Hitachi (HL7851G) with λ = 785nm. The moving target was a piezoelectric transducer with nanometric resolution [START_REF]P-753 LISA Linear Actuator and Stage[END_REF], configured to produce an harmonic displacement of 2.25µm i.e. 3λ in forward direction and symmetrically backwards. The displacement observed by the PD alongside the transitions from the real signals is shown in Fig. 7. The maximum value is 2.32µm and the minimum is 2.3µm, that means a total error of 120nm per swing.

CONCLUSION

The presented methodology reduces the problem of SM displacement reconstruction to the efficient usage of an adaptive filter, driven by the number of samples separating two transitions. Its simplicity allows a straightforward estimation of the resources needed to synthesize a given application as well as an implementation maintainability. The precision is kept below λ /2, in accordance to the classical reported works. Due to its modularity, it is intended to be coupled to recent research leading to the apparition of robust SM sensors. Notably in terms of robustness against external signal degradations introduced in real scenarios. Its founding basis allows to establish a real time constraint in the development of a system and adapt the algorithm complexity by classical signal processing implementations. The perspective is to integrate this algorithm in different hardware and software architectures in order to provide optimal systems for a wide variety of displacement measurements.

FIGURE 1 .

 1 FIGURE 1. Self-mixing setup.

FIGURE 2 .

 2 FIGURE 2. Block diagram for displacement reconstruction.

FIGURE 3 .

 3 FIGURE 3. Representation of the generation of an interpolated fringe segment by convolution.

FIGURE 4 .

 4 FIGURE 4. Modeled SM signals for a displacement of 5λ with different feedback levels, alongside its detected transitions.

FIGURE 5 .

 5 FIGURE 5. Comparison of a normal interpolation in the fringes zone and a compensated one for the lobes zone.

FIGURE 6 .

 6 FIGURE 6. Displacement reconstruction and comparative error for two different feedback levels.

FIGURE 7 .

 7 FIGURE 7. SM signal monitoring a piezoelectric in movement and its reconstructed displacement from detected transitions.

ACKNOWLEDGMENTS

The first author would like to thank CONACYT for financial support.


Formant Structures of Vowels Produced by Stutterers in Normal and Fast Speech Rates

The aim of this study is to analyse the steady-state portion of the first two formants (F1) and (F2) in the production of [CV] sequences, containing vowels [i, a, u], pronounced in two speech rates (normal and fast), by groups of untreated and treated stutterers, and control subjects. Locus equations have been calculated to observe for potential differences in coarticulatory strategies between the three groups. Data analyses reveal a reduction of vowel space for stutterers at a normal speaking rate. When speech rate increases, no reduction of vowel space is noticeable for the latter group of speakers, contrary to treated stutterers and controls. No significant differences between the three groups have been observed in coarticulatory strategies.

Introduction

The aim of this research is, firstly, to analyse the formant structure of vowels produced by stutterers and treated stutterers, and to compare their data with those of control subjects. Secondly, we will examine the effects of speech rate increase on the formant structures of vowels, and also on the behaviour of the three groups of speakers. Finally, locus equations will be calculated to observe for potential differences in coarticulatory strategies between the three groups. Concerning control subjects, several studies [START_REF] Lindblom | On vowel reduction[END_REF] have shown that an increase in speech rate could provoke a compression of durations and a reduction of the vowel space, i.e. a certain centralisation of vowels in this space. What would the result be for stutterers or treated stutterers, knowing that the majority of studies [START_REF] Klich | Spectrographic study of vowels in stutterers' fluent speech[END_REF] have shown vowel space reduction in a normal speech rate condition for stutterers? In this perspective, a Blomgren et al. [START_REF] Robb | A note on Vowel Centralization in Stuttering and Nonstuttering Individuals[END_REF] work confirmed reduction of the vowel space in fluent speech of stutterers. However the Prosek et al. [START_REF] Montgomery | Formant frequencies of stuttered and fluent vowels[END_REF] work had not shown such conclusions, as no vocalic centralisation had appeared in fluent or disfluent speech of stutterers. The present investigation is of double interest: a) it attempts to provide additional data concerning a possible reduction of the vowel space of stutterers in normal speech rate; b) it tries to verify whether an "undershoot" phenomenon in fast speech rate would appear or not. Our hypotheses are: a) a more restricted vocalic space should be noticed in stutterers' fluent speech; b) consequently, no further vowel centralisation should be observed when stutterers speak faster; c) the more reduced vocalic space expected in stutterers' production could be explained by the fact that they use different coarticulatory strategies, in terms of gestural economy (see, e.g., [START_REF] Van Lieshout | Searching for the weak link in the speech production chain of people who stutter: A motor skill approach, Speech Motor Control, Normal and Disordered Speech[END_REF][START_REF] Fauvet | Formant structures of vowels produced by stutterers at normal and fast speech rates[END_REF]), compared with control speakers and treated stutterers.

Experimental procedure

Speakers and corpus

Fifteen adult speakers from 25 to 30 years, comprising five control subjects without speech disorders, five stutterers and five treated stutterers, had to pronounce sentences containing [CVp] It should be mentioned that no subject had any particular regional accent. By the term 'treated stutterers', we refer to stutterers who had followed a treatment program against stuttering in the last five years, anterior to this work.

Only fluent repetitions were analysed, i.e. sentences which had been pronounced without any abnormal pause (due to stuttering).

Repetitions were recorded with the help of a Sennheiser e845S© microphone, which was connected to a computer (Sound Card RealTek AC97©) by using the Audacity© freeware (Sampling frequency: 44100 Hz -16 bits).

Findings graphically represented in this article relate to data from three groups: the control group (CG), the non-treated stutterers' group (NTS) and the treated stutterers' group (TS).

Acoustic measures and vocalic space 2.2.1. Acoustic measures

Measurements carried out were: duration of the vowels, from onset of a clear formant structure to its offset, triggered by the subsequent [p], in the [CVp] span; the vowel formant structure (F1 and F2) in order to obtain vowel space area; F2 vowel onset and F2 vowel mid-point values were also extracted in order to calculate locus equations. Other measures were also taken but will not be reported here as they are not relevant to this investigation.

Calculation of vowel space

The area of the triangle in the F1xF2 space was calculated using Heron's formula:

) )( )( ( c p b p a p p    with : ) ( 2 1 c b a p   
and a,b and c corresponding respectively to the length of the three sides of the triangle.

) yb)² - (yc xb)² - (xc (   a ) yc)² - (ya xc)² - (xa (   b ) yb)² - (ya xb)² - (xa (   c
This value (in kHz²) provides information about the space used to obtain distinctions between vowels.

Results

Formant structures

Before analysing formant structures, it is important to mention that vowel durations were shorter in fast speech rate compared with normal speech rate, for all groups.

Figures 1 and2 show average values of the first two formants of vowels [i, a, u] in [pV] context, pronounced by the three groups in normal and fast speech rates, respectively.

Vowel [i]

For vowel [i], the mean value of F1 was 256 Hz, and F2 was 2108 Hz for the control group (CG). The same sound was evaluated with a first resonance at 286 Hz and a second one at 1847 Hz for stutterers (NTS). Therefore, the main difference between the two productions comes from F2, i.e. presumably tongue advancement in the oral cavity. Thus, the tongue may be in a less anterior position for the NTS group.

Productions of treated stutterers (TS) looked like those of control speakers (CG), since the first formant is at 255 Hz and the second one at 2110 Hz for TS. Non-pathological subjects and treated stutterers present similar results relating more or less to aperture of the oral cavity (F1) and the forwardbackward movement of tonguebody (F2).

In summary, values of vowel [i] are comparable for treated stutterers and controls but not for stutterers, because the latter apparently show lesser tongue-body advancement. Increase in speech rate only provokes a minor increase of the F1 value from 256 Hz to 272 Hz, when the control group speaks faster. F2 decreases to attain 1954 Hz in fast speaking rate. The same phenomenon was observed for TS: F1 increases very slightly in fast speech rate (257 Hz) and F2 decreases to 1976 Hz. This fact is not confirmed for stutterers: a stability of F1 (286 Hz vs. 282 Hz) and F2 values (1847 Hz vs. 1855 Hz) is noticed in normal and fast speech rates. Consequently, no significant difference appears between the productions of vowel [i] in normal and fast speaking rates for stutterers.

Vowel [a]

For non-pathological speakers, CG, pronouncing [a], F1 is at 545 Hz and F2 at 1276 Hz. These values differ from those of non treated stutterers, NTS, since the F1 mean value was 489 Hz and 1203 Hz for F2 in normal speech rate. F1 and F2 values were respectively 626 Hz and 1288 Hz for the group of treated stutterers, TS.

Therefore, tongue elevation seems to be higher for NTS, and lower for TS. When speech rate increases, it is mainly the value of the first formant which is modified, since it decreases from 545 Hz to 467 Hz in the control group. The second resonance remains stable (1276 Hz in normal speech rate vs. 1258 Hz). Some modifications were observed for the same vowel in treated stutterers' speech. Thus, the value of F1 diminishes (626 Hz vs. 565 Hz) when the speaker is given instructions to speak as fast as possible. F2 values are stable across normal and fast speech rates (respectively 1288 Hz and 1334 Hz). No significant differences were noted when stutterers' speech rate increased, F1 remaining relatively stable between 489 Hz in normal speech and 482 Hz in fast speech. So also is F2, whose values are stable in normal and fast speech at 1203 Hz and 1200 Hz, respectively.

Vowel [u]

The first formant average value of vowel [u], produced by the control group, was 268 Hz. No difference was revealed for stutterers, with measures at 274 Hz, contrary to treated subjects, with F1 at 280 Hz.

F2 was measured at 817 Hz for CG, at 882 Hz for TS and at 978 Hz for NTS. Accelerating speech rate provokes a slight modification of [u] for the control group: F2 increases from 817 Hz to 931 Hz. However, this difference is not significant (because of a relatively high standard deviation) and must be carefully considered. F1 is located at 290 Hz when speech rate increases. Similar remarks can be made for TS, since F2 was 1037 Hz in the same condition. Finally, it is interesting to note that F1 and F2 values are comparable for stutterers in the two speech rates: F1 attains 274 Hz in normal speech rate and 272 Hz in fast speech rate; F2 corresponds to 978 Hz, when subjects speak without tempo instructions, and to 948 Hz when they are asked to speak quickly.

Comparison of vowel space areas

It is important to notice that calculation of vowel space area has no functional significance in itself; it serves as an index of the general pattern of change in the vowel space. Analysis of the area of the vocalic triangle in sequences [pV] reveals higher values for control speakers and treated stutterers, compared with results obtained for stutterers. For CG, the area is 0.18 kHz², for TS, it is 0.22 kHz² and for NTS, it is 0.09 kHz². As regards CG and NTS, this area decreases in fast speech rate: measures for CG and TS correspond respectively to 0.09 kHz² and to 0.14 kHz² when speaking rate increases. Comparison of the vocalic triangle area for stutterers does not show any difference between the two speech rates: 0.09 kHz² in normal speaking rate, and 0.09 kHz² in fast speech rate.

Consequently, the area of the vowel space is systematically smaller for stutterers than for the other speakers in normal speech rate. In fast speech, vowel space areas are comparable for all groups.

Similar patterns have been obtained for [tVp] and [kVp] sequences.

Locus equations

We thought that differences observed in formant structures between stutterers and the control group could be explained by the use of different coarticulatory strategies. Such a hypothesis gave us the idea to calculate locus equations. However, we did not observe significant differences between the three groups, as can be seen, for an example, on Figure 3. To sum up, locus equations do not explain formant structure differences observed between stutterers and controls.

Conclusions

In conclusion, although vowel durations were compressed in fast speech for all subjects, this reduction was, however, not directly correlated with centralisation in stutterers, as the vowel space of the latter was already significantly reduced (hypothesis a and b). Contrary to hypothesis c, locus equations did not reflect expected differences in coarticulatory behaviour. Results for stutterers could be interpreted in terms of lack of articulatory flexibility [START_REF] Van Lieshout | Searching for the weak link in the speech production chain of people who stutter: A motor skill approach, Speech Motor Control, Normal and Disordered Speech[END_REF]. This means that stutterers would not adapt their gestures to demands related to articulatory speeding up, in fast speech conditions. However, such an assumption needs to be verified experimentally.

[Figure 1 :

 1 Figure 1: Vocalic triangle CG, NS and NTS for [pVp] sequences pronounced in normal speech rate.

[Figure 2 :

 2 Figure 2: Vocalic triangle NS, CG and NTS for [pVp] sequences pronounced in fast speech rate.

Figure 3 :

 3 Figure 3: Locus equations for [pu] sequences pronounced by control speakers and stutterers.

Table 1 .

 1 Comparison of vocalic triangle areas.

		Area (kHz²)	CG	NTS	TS
	[pVp]	Normal speech rate Fast speech rate	0.18 0.09	0.09 0.09	0.22 0.14
	[tVp]	Normal speech rate Fast speech rate	0.17 0.1	0.09 0.08	0.17 0.11
	[kVp]	Normal speech rate	0.17	0.12	0.18
		Fast speech rate	0.11	0.13	0.11

Acknowledgments: This research work was supported by an ANR grant (ANR-07-CORP-018-01, DOCVACIM), 2007 -2011 and a MISHA Programme ACM, 2005 -2008.