The topographic analysis carried out in this study relies on a 1 m resolution airborne lidar digital terrain model (DTM) acquired in 2014 as part of the RGE ALTI^® database from IGN (Institut National de l'information Géographique et Forestière) and covering our study area, as well as most of the Valensole and Puimichel plateaus. The core of our analysis consists of the extraction of high-resolution hillslope and channels topographic metrics along a transect located at the northwestern edge of the plateau in order to identify short-wavelength variations in the distribution of surface processes (Fig. ), as opposed to the long-wavelength deformation investigated by previous studies .

The topographic analysis methods described in the previous section allow us to identify relative spatial patterns for the intensity of surface processes such as surface denudation, which can be used to infer rock uplift distribution. We used in situ-produced cosmogenic nuclide concentration measurements to constrain the absolute denudation rate values. Active fluvial sediments are present along the stream network of the studied catchments (Fig. a), and they could be sampled to derive basin averaged denudation rates . However, most of the surveyed channels displayed complex dynamics with localized occurrences of aggradation, splitting of the main channel and local colluvial inputs, such that the required hypothesis of a homogeneous contribution of the whole upstream area was most likely invalid. For that reason, we rather sampled material directly at the hilltops, which allows for a clear identification of the origin of the sampled material and a straightforward comparison with the topographic metrics extracted from the high-resolution DTM. As noted earlier, weathering principally affects the sandy matrix of the conglomerate, liberating the clasts which remain interlocked until they reach the surface, such that vertical mixing within the regolith is minimal at the hilltop.

Samples for 10Be and 26Al concentration measurements were collected at 10 hilltop sites, by amalgamating 30 to 40 individual sandstone clasts derived from the bedrock conglomerate (Fig. a). Samples were crushed and sieved to extract the 250–1000 µm fraction, which was submitted to sequential magnetic separation. The remaining fraction was leached with 37 % HCl to remove carbonate fragments. The samples were then repetitively leached with H2SiF6 and submitted to vigorous mechanical shaking until pure quartz was obtained. Decontamination from atmospheric 10Be was achieved by a series of three successive leaching processes in concentrated HF, each removing 10 % of the remaining sample mass . After addition of an in-house 9Be carrier, the samples were digested in concentrated HF. Be and Al were isolated for measurements using ion-exchange chromatography. 10Be/9Be and 26Al/27Al measurements were performed at the French AMS National Facility, located at CEREGE in Aix-en-Provence. All results and technical characteristics of the measurements and calculations are provided in Tables  and .

Under the assumption that the spatial distribution in erosion rates results from tectonic forcing, observations of absolute or relative variations in the intensity of surface processes are commonly used to derive information on rock uplift patterns and the geometry of associated structures . While the key hypothesis of a tectonic origin for the variability in erosion proxies will need to be discussed in detail, we present here a modeling approach which can be used to interpret surface erosion patterns, which are considered proxies for rock uplift, in terms of the associated structures at depth.

We use a simple elastic dislocation model to predict surface deformation distributions and compare them with our observed E∗ evolution along the investigated profile (Fig. ). This type of modeling approach is usually associated with the study of upper crustal deformation during the seismic cycle, but it has also been successfully applied to interpret surface deformation patterns associated with blind thrusts over longer timescales . As noted by , who used elastic dislocation modeling to study folding in the Los Angeles Basin, it allows us to keep track, at first order, of the displacement of material associated with the activation of the fault, independently of the mechanical parameters. We consider a single planar dislocation embedded in an elastic medium. We define its geometry with four parameters: the horizontal position and depth of its upper limit (varying from 0 to 20 km along the profile and from 0 to 10 below the surface, respectively), dip angle (varying from 0 to 90∘) and length (varying from 0 to 4 km). This set of four parameters allows us to predict a surface deformation profile which is compared to the observed E∗ pattern. We do not fit the absolute value of E∗, which has no significance with respect to the elastic dislocation model, but rather we fit the wavelength of the predicted deformation and simply scale its amplitude to that of the observed E∗ profile.

We use a standard Monte Carlo Markov Chain (MCMC) approach to move through this parameter space and estimate the posterior distributions . The consecutive displacements during the sampling procedure were driven by the Metropolis–Hastings algorithm, with an acceptance rate of 20 %. We ran 16 independent chains, each 106 in length with a 104 length burn-in phase. The multivariate potential scale reduction factor is 1.004, suggesting that convergence was achieved .

Most hillslope profiles display a clear convexity and progressive downward increase in slope, with almost linear portions at the bottom of the hillslope and gradients close to 0.6 mm-1 (Fig. a). Calculation of average hillslope gradient shows that most hillslopes have average gradients below 0.6 mm-1 (Fig. b). Following , we determined the value of Sc for which 99 % of hillslopes have a relief inferior to the maximum value (LHSc) and obtained Sc=0.52 mm-1. In the following we use Sc=0.6 mm-1 for the critical gradient value (Fig. c). This Sc value is lower than what was found in other settings , but it is close to the natural angle of repose in many granular materials (∼ 30∘). We note that two particularities of our study area are the nature of the regolith, which is mostly constituted of highly mobile conglomerate-derived clasts moving downslope by both creep and dry ravel, and the isolated vegetation providing little cohesion (Fig. b), as opposed to the finer-grained soils supporting denser root networks observed in many other similar studies. Most topographic metrics extracted at the hillslope scale display important variations along the studied profile, both in terms of basin averaged or binned values. Nondimensional erosion rate E∗ increases 2-fold from south to north (Fig. a). This variation is not evenly distributed along the profile but occurs over less than 4 km of horizontal distance. The hilltop curvature CHT pattern closely mimics that of E∗, increasing from 0.01 to 0.02 m-1 (Fig. b). For both metrics, basin averaged values are highly consistent from one catchment to the other and delineate a clear trend along the section, with the exception of one outlying small catchment at ∼ 4 km distance. The evolution of hillslope relief is less pronounced but also shows an increase from ∼ 40 to ∼ 60 m (Fig. c). On the contrary, no clear systematic changes in hillslope length can be observed along the profile, with values ranging from 140 to 160 m (Fig. c).

For all studied basins, the river profiles display a regular concave-up shape, and in most situations χ-transformed main trunk profiles, as well as the main tributaries, collapse along a linear trend, suggesting the absence of a major transient perturbation propagating through the river network (Fig. ). Small tributaries usually show higher dispersion due to changes in processes in small colluvial valleys. Usual topographic indexes, such as m/n ratio and normalized steepness index (ksn), were extracted from the fluvial network. The m/n ratio ranges from 0.2 to 0.4, with an average of 0.24 ± 0.06, and a reference value of 0.25 was used in the following analysis. While this m/n value is lower than the often reported 0.4 to 0.5 ratio, it is within the range of observations from for high erodibility lithologies, such as the setting we consider here. These fluvial metrics display a larger amount of scatter from one basin to another when compared with the patterns extracted from the hillslope morphology analysis (Fig. d). However, it can be noted that the four northernmost basins display higher ksn values than the rest of the section, and that basin averaged E∗ and ksn are significantly positively correlated (Fig. ).

Measured concentrations in our hilltop samples range from 43 to 117×103 atomsg-1 and 281 to 867×103 atomsg-1 for 10Be and 26Al, respectively (Tables  and ). The corresponding 26Al/10Be ratios vary from 6.5 ± 0.8 to 8.2 ± 1.2. While some of these ratios are slightly higher than the theoretical value, confidence ellipses are always overlapping the steady-state denudation curve (Fig. ). These concentrations correspond to denudation rates ranging from 42 to 115 mmkyr-1 and from 38 to 114 mmkyr-1 for 10Be and 26Al, respectively (Tables  and ). The denudation rates calculated from both nuclide concentrations are consistent but display a small deviation from the 1:1 line, with 26Al denudation rates slightly lower than their 10Be equivalents. The observed 26Al/10Be values argue against a significant contribution of an inherited CRN inventory from the history of the clasts prior to their deposition inside the Valensole conglomerate, in particular if they derived from the Valensole II formation. In the following we only consider 10Be data for our analysis of the relationship between high-resolution topography and denudation rates, due to their lower uncertainty.

Interestingly, parameters extracted from the analysis of river long-profiles such as steepness indexes, which are commonly used to decipher tectonic patterns in erosional landscapes , do not display as clear a pattern as hillslope metrics (Fig. d). Normalized steepness index values (ksn) are on average higher in the northern part of the transect with respect to the southern part and positively correlated with E∗ (Fig. ), but the data are scattered and we do not observe a clear progressive increase comparable to what is displayed by E∗ or CHT. In each of the studied basins, the main trunk and its tributaries display regular concave-up profiles, which collapse along a single trend in χ plots (Fig. ). This observation suggests that, at the scale of each catchment, the river network is globally equilibrated with respect to a common rock uplift rate , and argues against the impact of local perturbation along the river profile as an origin for the observed scatter. An underlying assumption of our river profile analysis is that the streams behave as purely detachment-limited systems. While our field survey did not allow us to identify thick alluvial cover along the stream network, local and intermittent shifts toward transport-limited behavior could explain the apparent subdued response of ksn across the inferred rock uplift gradient. We note, however, that in such a situation, stream concavity (m/n) should display some sensitivity to changes in rock uplift , which is not observed here (Fig. d).

A key difference between the two approaches is the very high spatial density of the metrics extracted for the hillslope dataset, which is several orders of magnitude denser than the evaluation of steepness index and concavity at 18 basins. This comparison illustrates the resolving power of high-resolution hillslope morphology analysis, which allows us to document short-wavelength patterns of erosion and uplift that are undersampled by scarcely distributed fluvial metrics. We note that observed a clear response of both hillslope and channel metrics across the tectonic gradient they studied in the vicinity of the San Andreas Fault. Two important differences compared to our study are the existence of transient channel adjustment along the Bolinas Ridge and the dimension of the section, which is ∼ 30 km long in their case compared to the ∼ 10 km of our profile. Combined with a longer wavelength of the underlying tectonic signal, this latter difference might be a reason for the better sampling through fluvial metrics by , and the clearer relationship they observe with hillslope properties.

One prominent feature of the hillslope evolution across the rock-uplift gradient is the lack of significant changes in hillslope length, contrasting with the other extracted metrics (Fig. ). Hillslope length, LH, remains nearly constant across the transect between 140 and 160 m, whereas hilltop curvature, CHT, which can be considered a proxy for erosion and rock uplift under a steady-state assumption, undergoes a nearly 2-fold increase. There is no significant inverse correlation between LH and CHT as observed by . The characteristic horizontal length scale of landscapes, which can be evaluated through different types of measurements such as drainage density, spacing of first-order valleys or hillslope length, has been shown to be highly sensitive to external tectonic and climatic forcings, as well as internal parameters controlling erosion processes e.g.,. For example, studied in detail the relationship between denudation rate and drainage density with analytical and numerical models as well as high-resolution topographic and cosmogenic nuclide data. They show a sensitivity of drainage density to erosion rates, which is very pronounced in the 50–100 mmkyr-1 range corresponding to our CRN data (Fig. ) and conflicts with the observation of a nearly constant LH along our transect. However, this relationship is highly dependent on the parameters used for the fluvial and hillslope erosion laws, as shown by the formulation of the landscape Péclet number proposed by as the ratio between characteristic fluvial and hillslope timescales: 14Pe=Kl2(m+1)-nDζ1-n, where K is the erodibility parameter for fluvial incision; D the hillslope diffusion coefficient; m and n are the area and slope exponents of the fluvial incision law, respectively; and l and ζ are horizontal and vertical length scales for the landscape. In the special case where the slope exponent n of the stream power formulation for river incision is equal to 1, this Péclet number becomes independent from relief ζ, and hence uplift rate. Considering Pe=1 allows us to retrieve lc as a characteristic length scale for hillslope or channel transition, which again, in the n=1 case, does not depend on erosion or uplift rates. Therefore, the stability of LH across a two-fold erosion rate gradient, observed in our dataset, would hint toward a value of n close to unity. While the ratio m/n can usually be constrained from the measured concavity of river profiles, the absolute values of the slope and area exponents of the stream power description for fluvial incision are debated, with many pieces of evidence pointing to n>1 . However, it is noteworthy that values closer to unity have often been reported for high-erodibility sediments or small catchments affected by colluvial processes , which are both notable characteristics of the area we investigate. In any case, our study clearly illustrates the potential of high-resolution hillslope morphological properties to resolve short-wavelength variations in rock uplift that are difficult to capture from the conventional methods based on fluvial profile analysis.

Our understanding of landscape dynamics relies on the formulation of geomorphic transport laws (GTLs), such as Eq. (), as the foundation of landscape evolution models . In most situations such models can be expressed as a differential equation involving spatial and temporal derivatives of the topographic surface elevation. More precisely, these equations will often relate the spatial structure of the landscape involving topographic slope or curvature with its rate of evolution as, for example, hillslope denudation rate or fluvial incision. Evaluating the relevance of such models requires obtaining actual measurements for these spatial and temporal descriptions of the landscape. Spatial properties of landscapes are usually derived from the analysis of DEMs at various resolutions, from which topographic gradient and curvature can be computed. On the other hand, geochronology techniques, such as cosmogenic nuclide concentration measurements in bedrock or sediment samples, allow for constraining the rate of lowering of the topographic surface though time and provide the framework to evaluate the temporal component of the landscape evolution problem.

For example, the comparison of catchment-wide denudation rates (CWDRs) calculated from measured 10Be concentrations in river sediments with topographic gradient extracted from digital elevation models has provided critical tests of GTLs for hillslope sediment flux . While not often explicitly formulated in terms of the evaluation of a GTL, this kind of connection between some spatial property of landscapes (slope, relief, steepness index, etc.) and their rates of evolution is now standard in CWDR studies. However, it is to be noted that the interpretation of CRN concentrations in river sediments in terms of spatially averaged denudation rates suffers from important limitations resulting from the heterogeneity and stochasticity of erosion processes in space and time e.g.,. Furthermore, the overwhelming majority of these studies rely on the evaluation of topographic metrics derived from medium-resolution DEMs (pixel size > 10 m) for which the computation of the spatial derivatives controlling erosion rates and sediment fluxes is inaccurate at the scale of hillslopes. Only a handful of studies have actually attempted to reconcile CRN-based denudation data with topographic metrics extracted from high-resolution DTMs into a GTL-based physical framework e.g.,.

Our dataset allows for carrying out such a comparison of CRN denudation rates determined at hillslope sites with high-resolution hillslope topographic properties. In particular, we test the consistency of our dataset with prediction of simple hillslope diffusion formulations such as Eq. () relating hilltop curvature CHT with denudation rate. We observe that no single diffusion coefficient can explain the distribution of our data, but that, at most sites, the values of CHT and erosion rates are compatible with D in the 0.003 to 0.006 m2a-1 range (Fig. ). The very high denudation rate observed for sample P, and resultant high diffusion coefficient, can be a consequence of a recent anthropogenic disturbance, with the presence of small walls made from collected cobbles and possible shallow excavation in the vicinity of the sampling site. This data point is not further considered in the following analysis. The range of observed diffusion coefficients is consistent with values reported by available compilations for similar lithologies and climate (mean annual precipitation of 700 mm) . There is no climatic gradient over the limited extent of our study area, so this cannot be invoked as a possible control for the ∼ 2-fold variations for the estimates of D in our dataset, which in any case do not present a clear spatial pattern or clustering. Similarly, bedrock geology is homogeneous between the different sites, with conglomerates of Miocene and Pliocene ages releasing clasts of an homogeneous 5–10 cm size group. We amalgamated up to 40 clasts at each sampling site and carefully selected well-defined near-horizontal ridges with negligible topographic shielding, such that we do not consider that this spread in D can arise from a systematic sampling bias. We note that the amplitude of variability for our estimates of D at individual hilltops is similar to the uncertainty range for D from studies based on CWDRs e.g.,. We consider the distribution of the observed D values to be mostly controlled by the natural variability of the hillslope processes and persistent internal transience at the ∼ 100 m wavelength. Such variability, observed here at individual hilltop locations, is usually averaged out in studies relying on CWDR rather than local estimations based on bedrock CRN inventories.

We use the estimated distribution for D to convert the CHT pattern along the transect into denudation rates using Eq. (). We repeatedly sample the cumulative distribution for D and use CHT aggregated for hillslope patches. The resulting values for denudation rates are binned at 1 km intervals along the transect (Fig. ). The interquartile ranges of the bins are largely overlapping, but a systematic increase can still be observed, consistent with the underlying variation in CHT. The estimated median denudation values are ∼ 30 and ∼ 50 mmkyr-1 in the southern and northern parts, respectively, which is comparable to denudation rates reported in surrounding landscapes . We note that the denudation rate values measured at the various sites (blue circles in Fig. c) display an overall similar increasing trend but with systematically higher values. This deviation results from a sampling bias toward high-curvature ridges due to better field conditions at such sites. Indeed, measured CHT at these sites are ≥0.02 m-1 (Fig. a), whereas continuously averaged CHT along the transect are on average below 0.02 m-1 (Fig. b). Transport-limited conditions were prevailing at all surveyed sites such that we have no reason to question the validity of Eq. (). For that reason the predominance of high-curvature/high-denudation sites in the dataset should not introduce a systematic deviation in the calibration of the diffusion coefficient D.

Under an assumption of steady-state conditions, we can propose that the observed 21 ± 17 mmkyr-1 differential denudation rate between the southern (distance < 5 km in Fig. c) and northern (distance >10 km) parts of the transect reflects a similar differential rock uplift rate across the transect. Considering a dip angle of 64 ± 11∘ (Fig. e) for the hypothetical fault responsible for the uplift pattern, it converts into a slip rate of 23 ± 20 mmkyr-1, which implies that slip rate is most likely < 50 mmkyr-1 on this blind thrust. This slow slip rate estimation is consistent with observations on slowly slipping faults of western Provence, where deformation usually cannot be resolved from geodetic data, and proposed long-term slip rates are < 100 mmkyr-1. For example, on the Trévaresse ridge fault, which produced the last major earthquake in metropolitan France (1909) with an estimated Mw=6 , trenches have yielded a late Quaternary slip rate in the 50 to 300 mmkyr-1 range , whereas accumulated deformation since the late Miocene indicates a slip rate of 30 ± 20 mmkyr-1 . For the Middle Durance Fault, which is located directly west of our study area, across the Durance river, a slip rate ranging from 10 to 70 mmkyr-1 has been proposed over the last Ma . At last, the uplift rate we calculated is of the same order of magnitude as the one reported for the Lambrussier anticline by , directly north of our study area. In these slow-tectonics landscapes, erosion processes often outpace uplift rates, eroding passive deformation markers. While some aspects of the investigated area, such as the lithology, size and orientation of our basins, present favorable characteristics, our study illustrates the potential of tracking active erosion processes through hillslope morphology analysis to retrieve tectonic information in this type of environment.