Exhumation and relief development in the Pelvoux and Dora-Maira massifs (western Alps) assessed by spectral analysis and inversion of thermochronological age transects



[1] We have used dedicated sampling and analysis of apatite fission track (AFT) and apatite (U-Th)/He (AHe) thermochronological data sets in an attempt to quantify relief evolution and exhumation rates in the Pelvoux and Dora-Maira massifs (western European Alps). A dual approach comparing spectral analysis and thermal-kinematic model inversion was applied. We sampled age-elevation relationships at a range of topographic wavelengths along two north-south transects crossing these massifs. For the 40-km-long Pelvoux transect we report 35 new AFT ages that range between 3.0 ± 0.4 Ma and 12.6 ± 1.0 Ma, and 8 new AHe ages between 3.5 ± 1.5 and 4.7 ± 0.7 Ma. The Dora-Maira transect spans a distance of 60 km and includes 28 (23 new and 5 previously published) significantly older AFT ages, which vary between 13.1 ± 0.2 and 27.3 ± 0.3 Ma. Inferred exhumation rates of 0.7 km m.y.−1 since ∼8 Ma in the Pelvoux and only 0.1 km m.y.−1since ∼20 Ma in Dora-Maira are consistent between methods as well as with previous estimates, although they are associated with large uncertainties due to imperfect sampling and analytical errors. Neither massif displays clear evidence for relief change during the intervals constrained by the data. Data from the Dora-Maria massif suggest moderate recent relief increase, whereas the results from the Pelvoux are inconclusive but could imply relief decrease. Our study highlights the difficulties of applying thermochronology techniques to constrain relief changes. We show that an unreasonable number of samples is needed to perform reliable spectral analysis of age-elevation transects and discuss the overall limitations of both techniques to address relief evolution. We suggest that a more efficient approach would be to apply thermal-kinematic model inversion to relatively small study areas using spatially distributed sampling and multiple thermochronometer analyses per sample.

1. Introduction

[2] The relief of mountain belts results from complex interactions between tectonic and surface processes. Thermochronometric studies have generally focused on quantifying exhumation histories and usually implicitly assumed topographic steady state [e.g., Gallagher et al., 1998; Ehlers, 2005; Reiners and Brandon, 2006]. However, mountain belts are expected to experience frequent phases of transient evolution controlled by both variations in tectonic and climatic forcing on different spatial scales [e.g., Tomkin and Braun, 2002; Willett et al., 2006; Whipple, 2009]. The spatial distribution of relief and its amplitude are indicative of the levels of geomorphic activity in a landscape since they control fluvial and glacial process dynamics [e.g., Brocklehurst and Whipple, 2002; Montgomery, 2002; Whipple, 2004]. Quantifying the topographic evolution of mountain belts is key to evaluate the tectonic and climatic controls that drive it, as well as to understand the controls on sediment flux to basins. However, the limited types of data sensitive to relief evolution render the latter challenging to constrain and require development of new tools and strategies [Olen et al., 2012].

[3] The European Alps (Figure 1) provide a promising study area to explore relief development, since the patterns of modern-day rock uplift [Jouanne et al., 1995; Kahle et al., 1997; Schlatter, 2007], erosion rates on millennial timescales [Wittmann et al., 2007; Delunel et al., 2010; Norton et al., 2011] and long-term denudation rates [Vernon et al., 2008and references therein] are relatively well understood, and since high-frequency oscillations between glacial and interglacial conditions are known to have strongly influenced the morphology [Champagnac et al., 2007; van der Beek and Bourbon, 2008; Valla et al., 2011b, 2012]. Several studies have linked patterns of exhumation and modern relief to Late Miocene to Pliocene climate changes and the onset of Quaternary glaciations in Europe [Cederbom et al., 2004; Willett et al., 2006; Champagnac et al., 2007; Glotzbach et al., 2011]. The Neogene to present-day relief development has been investigated through inversion of local thermochronological data sets but has proven inconclusive in several cases [Valla et al., 2010a; van der Beek et al., 2010]. In this paper, we investigate new and dedicated sampling strategies and analysis using low-temperature thermochronometers to address relief evolution of mountain belts.

Figure 1.

(a) Simplified tectonic map of the western Alps (modified from Schmid et al. [2004] with location of the study areas and external (Aar; MB: Mont Blanc; B: Belledonne; Pe: Pelvoux; Ar: Argentera) and internal (DM: Dora Maira; GP: Gran Paradiso) crystalline massifs. Large boxes indicate extent of the digital elevation models used in Pecube for the inversions and shown in Figure 3. The black lines indicate the location of the composite cross-section shown in Figure 1b. (b) orogen-scale structural cross-section between the Pelvoux and Dora-Maira massifs, showing tectonic relations with surroundings Alpine units [afterTricart et al., 2004].

[4] As topography strongly influences the thermal structure of the crust and the position of the closure isotherms of low-temperature thermochronometers [Stüwe et al., 1994; Braun, 2002b; Ehlers, 2005], exhumation rates and relief development can theoretically be quantified simultaneously by analyzing age-elevation relationships at various wavelengths of topography for samples collected along transects characterized by spatially homogenous rock-uplift rates [Braun, 2002a] (Figure 2). This approach has been tested using a published data set from the Sierra Nevada, Western USA [Braun, 2002a] and it was used to predict relief development in the Dabie Shan, China [Braun and Robert, 2005], and the Southern Alps of New Zealand [Herman et al., 2007, 2010b]. Here, we test the method further by employing low-temperature apatite fission track (AFT) and (U-Th)/He (AHe) data sampled specifically for this objective; we also develop a methodology for quantifying the uncertainty in inferred exhumation rates and relief development.

Figure 2.

Predicted perturbation of closure isotherms (using analytical model of Mancktelow and Grasemann [1997]) induced by different wavelengths of topography, effect of relief evolution and predicted age-elevation relationships. (a) Short-wavelength topography (λ= 2 km) with 3-km relief amplitude, exhumation rateE = 0.7 km m.y.−1 and stable geothermal gradient of 25°C km−1: the geometry of closure-temperature isotherms (∼70°C for AHe; ∼120°C for AFT) is not affected by the short-wavelength topography; the age-elevation relationship provides a direct estimate of the exhumation rate (slope of 0.71 km m.y−1for both systems); a1 and a2 indicate the time required by valley-bottom and ridge-top samples to reach the surface, respectively (i.e., their thermochronological ages). (b) Long-wavelength topography (λ= 40) with 3-km relief amplitude (other parameters as in a): the long-wavelength topography strongly affects the shape of the closure isotherms; ages become independent of elevation. (c) Increase in relief by a factor R = 0.6 with initial amplitude of topography h0= 3 km. At long topographic wavelengths, any relationships between age and elevation is indicative of a relative change in relief amplitude. Spectral analysis extracts information on age-elevation relationships over the spectrum of wavelengths that compose the topography. See text for further discussion.

[5] Samples were collected along north-south oriented transects in two basement massifs of the western Alps that present contrasting tectonic histories: the Pelvoux massif, which is part of the external zone of the Alps, and the Dora-Maira massif located in the internal zone (Figure 1). An extensive database of apatite and zircon fission track ages [Vernon et al., 2008] shows a strong asymmetry between rapid and accelerating exhumation rates in the external zone of the orogen and much slower and decelerating exhumation rates in the internal zone, with the exception of the Lepontine Dome in the central Alps, which appears to have maintained high exhumation rates throughout its history [Garzanti and Malusa, 2008; Vernon et al., 2009]. This contrast is consistent with now well-established structural observations indicating that the Miocene to present evolution of the western Alps took place under a bimodal tectonic regime, with the core of the belt undergoing extension while the peripheral massifs experience transpressive to transcurrent deformation [Selverstone, 2005; Sue et al., 2007].

[6] We quantitatively interpret the data collected in both transects using both the spectral method mentioned above and the Pecube3D thermal evolution code coupled to the Neighborhood-Algorithm inversion [Braun et al., 2012]. Both methods provide estimates of denudation rates and relief evolution, as well as information on the robustness and the resolution of these estimates. We discuss the suitability and implementation of both methods for studying relief evolution in mountain belts, as well as the implications of our findings for the exhumation and relief history of the western Alps.

2. Study Areas

2.1. Pelvoux Massif

[7] The Pelvoux massif is one of the “external crystalline massifs” (ECM) of the western Alps (Figure 1). These massifs correspond to the proximal part of the former European passive margin, which was overthrusted during Oligocene times by high-pressure/low-temperature metamorphic thrust sheets (Briançonnais and Piemontais zones) of the Alpine orogenic prism along the Penninic Front [Tricart, 1984]. The Pelvoux massif is made up of blocks of crystalline basement, which was intruded by granites and metamorphosed during the Hercynian orogeny. Interspersed between these basement blocks are remnants of Early Jurassic grabens that record the extension leading to opening of the Tethyan Ocean [Tricart, 1984; Lemoine et al., 1986] and that were subsequently inverted and thrust along W-SW to N-NW directions during the Alpine orogeny [Ford, 1996; Dumont et al., 2008].

[8] Paleomagnetic, mica 40Ar-39Ar and zircon fission track data indicate that cooling of the massif started at ∼24 Ma from temperatures of 300–350°C [Crouzet et al., 2001; Simon-Labric et al., 2009; van der Beek et al., 2010]. Previous AFT studies in the massif revealed scattered ages ranging between 3 and 14 Ma [Sabil, 1995; Seward et al., 1999] but the sampling schemes in these studies did not allow constraint of age-elevation relationships. New fission track and (U-Th)/He ages on both apatite and zircon were recently acquired along an altitudinal profile at La Meije peak [van der Beek et al., 2010]. Inverse numerical modeling of these data, using a similar approach of coupling Pecubeand the Neighborhood Algorithm to that applied here, led these authors to propose a 3-stage cooling scenario, including moderate exhumation rates (0.4 ± 0.3 km m.y.−1) between 30 and 6.0 ± 3.3 Ma, a short pulse of rapid exhumation (2.6 ± 1.1 km m.y.−1) between 6.0 ± 3.3 and 5.5 ± 3.3 Ma and a return to moderate exhumation rates (0.6 ± 0.3 km m.y.−1) from 5.5 ± 3.3 Ma to the present (the quoted uncertainties are the 1σ standard deviation of the posterior distribution of the parameter values). The data did not permit unambiguous resolution of relief development, but the authors considered on the balance of evidence that relief may have been lower than today before 6.0 ± 3.3 Ma, and the apparent pulse of rapid denudation may have been associated with higher relief than at present.

[9] The exhumation history derived for the Pelvoux massif is consistent with recent thermochronological data from several other external crystalline massifs, which also indicate a phase of rapid exhumation between ∼6 and 9 Ma in the Mont Blanc [Leloup et al., 2005; Glotzbach et al., 2008], Aar [Vernon et al., 2009] and Argentera [Bigot-Cormier et al., 2006] massifs, followed by slower rates. A significant (∼100%) increase in relief since ∼1.0 Ma, has been inferred in the Mont Blanc [Glotzbach et al., 2011] and Aar [Valla et al., 2011b, 2012] massifs.

[10] Similar to other external crystalline massifs of the Alps, the Pelvoux massif has high present-day relief, with the highest peaks at around 4000 m elevation and deeply incised valleys bottoming out below 1000 m (Figure 3a). The massif was extensively glaciated during Quaternary glaciations [van der Beek and Bourbon, 2008; Delunel, 2010]; the glacial imprint is particularly well expressed in the geomorphology by numerous hanging valleys, valley steps and overdeepenings [Montjuvent, 1974; van der Beek and Bourbon, 2008; Valla et al., 2010b]. In contrast, Miocene-Pliocene fluvial deposits around the massif indicate that the planform drainage pattern is pre-glacial in origin [Montjuvent, 1978].

Figure 3.

Digital Elevation models of the (a) Pelvoux and (b) Dora-Maira massifs, based on Shuttle Radar Topography Mission (SRTM) 90-m resolution digital topography data. Sample locations are indicated by black and white circles. Orange and purple patterns indicate the extent of the Pelvoux and Dora-Maira basement outcrops, respectively; major valleys and peaks are indicated.

[11] Seismicity within the massif is low and mainly concentrated in the adjacent Belledonne massif, north of the Pelvoux, where seismotectonic analyses reveal transpressive deformation along the NE-SW trending Belledonne Fault [Thouvenot et al., 2003; Delacou et al., 2004]. No significant deformation is currently accommodated through the massif, as shown by continuous GPS measurements [Sue et al., 2007and references therein]. However, present-day rock uplift with respect to the foreland may reach 1 mm y−1 in the Belledonne massif, as suggested by leveling studies [Jouanne et al., 1995].

2.2. Dora-Maira Massif

[12] The Dora-Maira massif is one of three internal crystalline massifs of the western Alps (Figure 1). It represents a window of European pre-Alpine basement exposed in the internal zone of the western Alps, structurally beneath the high pressure-low temperature Piemontais zone [Vialon, 1966]. The massif represents an ultra-high pressure metamorphic province with coesite-bearing units in its southern part [Chopin, 1984; Henry, 1990]. The peak of UHP metamorphism took place at ∼35 Ma [Tilton et al., 1991; Di Vincenzo et al., 2006; Ford et al., 2006] at pressures of 3.5–4.2 GPa and depths of 100–120 km [Gabalda et al., 2009]. ZFT data indicate cooling below 240 ± 20°C at ∼29 Ma [Gebauer et al., 1997], suggesting extremely high exhumation rates of 20–30 mm y−1between ∼35–29 Ma, consistent with rates inferred from metamorphic pressure-temperature-time paths [Rubatto and Hermann, 2001]. Both in situ [Cadoppi et al., 2002; Tricart et al., 2007] and detrital [Carrapa et al., 2003] thermochronological data indicate slow rates (<0.2 km m.y.−1) of erosional exhumation across this region during Oligocene-Miocene times (∼29–10 Ma).

[13] The drainage pattern of the Dora-Maira massif is characterized by large valleys flowing eastward into the Po plain (From north to south: Susa, Chisone, Pellice, Po, Varaita and Maira valleys;Figure 3b) with mean elevations of valley bottoms ranging from 400 to 600 m. Summit elevations reach over 2500 m in the massif, leading locally to ∼2000 m of relief. All valleys in the massif contained valley glaciers during Quaternary glaciations, the terminal moraines of which are located at the border of the Po Plain to the east of the massif [Carraro and Giardino, 2004]. The Susa valley has been glacially overdeepened and contains a complex Quaternary glacial, peri-glacial and post-glacial sedimentary record. The valley is also characterized by major deep-seated gravitational instabilities that were active in post-glacial times [Cadoppi et al., 2007].

[14] The area is affected by low-intensity upper-crustal seismicity (local magnitude: ML< 5). Most epicenters are located around the western border of the massif and define the north-south oriented Piemontais seismic arc. Focal mechanisms show transtensional and extensional solutions [Eva et al., 1998; Sue et al., 1999; R. Beucher et al., Complex arc dynamics in the South-Western Alps inferred from seismotectonics, to be submitted toTectonics, 2012], in agreement with structural evidence for recent extension, as indicated by Pliocene-Quaternary deposits displaced by north-south trending normal faults [Cadoppi et al., 2007].

3. Methods

3.1. Sample Collection and Treatment

[15] Samples were collected along roughly linear north-south transects in both massifs (Figure 3). Transects were designed to run perpendicular to the main drainage direction and parallel to the main faults, to prevent potential effects of localized exhumation along faults. Transect locations were chosen to allow sampling of a wide range of topographic wavelengths in areas characterized by the highest possible topographic relief. Sample elevations range from 1075 to 3163 m for the Pelvoux massif and from 380 to 1847 m for Dora-Maira (Figures 3 and 4 and Table 1). We aimed to sample at the most regular interval possible, as suggested by Braun [2002a], to optimize sampling for obtaining constraints on relief evolution; mean spacing between samples was ∼1.2 km for the Pelvoux transect and close to 2 km for the Dora-Maira transect, totaling 40- and 60-km long profiles, respectively.

Figure 4.

Thermochronological data along the Pelvoux and Dora-Maira transects. (a) Overall age-elevation relationship for all data from the transects, Pearson coefficients of correlation (r) are reported; (b) variation of age with distance along the transect. Open circles represent AFT data while black squares are AHe data. Discarded AHe data are shown as open squares with a cross; (c) topography and sampling locations along the profiles; dashed black line shows mean elevation; thin black lines are maximum and minimum elevation; shades of gray show probability distribution of elevation along transect box.

Table 1. New Apatite Fission-Track Data From the Pelvoux and Dora-Maira Massifsa
SampleElevation (m)Longitude (°E)Latitude (°N)LocationNρs (×106 cm−2)Nsρi (×106 cm−2)Niρd (×106 cm−2)NdP(χ2) (%)D (%)Age (Ma)±1σ (Ma)
  • a

    Age determinations for the Pelvoux massif were performed by E. Labrin with ζ= 346.6 ± 6.3 for glass dosimeter NBS962 while age determinations for the Dora-Maira massif were by R. Beucher withζ= 325.47 ± 10.06 for glass dosimeter IRMM-540; all ages are reported as central ages [Galbraith and Laslett, 1993]. N: number of grains counted; ρs: spontaneous track density; ρi: induced track density; ρd: dosimeter track density; Ns. Ni. Nd: number of tracks counted to determine the reported track densities; P(χ2): chi-square probability that the single grain ages represent one population;D: age dispersion reported as standard deviation of the mean. Samples from the Pelvoux massif are gneisses except for 2 southernmost samples (CH5, CH6), which are “Gres du Champsaur” sandstones. Samples from the Dora-Maira massif are all gneisses.

Pelvoux Massif
Dora-Maira Massif
DM211887.254845.0694Susa181.8371868.778886.0289 95496.05≪121±1.8
DM418477.249045.0159Chisone130.968906.3155876.0229 95498.69≪115±1.8
DM510617.246444.9646Chisone101.546779.1374556.029 95494.32≪117±2.1
DM611157.265844.9819Chisone130.977460.5952806.0189 95496.09≪116±2.6
DM96277.229144.9251Chisone102.06412912.2247646.0119 95472.09≪117±1.7
DM108507.211844.908Pellice209.6341 24147.9996 1836.0099 9540≪118±0.8
DM1114597.199444.8754Pellice92.88112111.4054796.0079 95466.65≪125±2.6
DM1210197.240244.847362.2366781.772456.0059 95496.51≪127±3.8
DM137917.219844.848551.553410.8792326.0029 95477.24≪117±3
DM141037.201844.7946323.50973418.1493 79669 95439.381418±0.9
DM154257.264444.8868Pellice81.319456.5372235.9999 95499.01≪120±3.3
DM1616477.170744.8301152.4911711.1327775.9979 95498.18≪121±1.9
DM1712687.169244.8215111.066497.0243235.9959 95492.17≪115±2.3
DM189147.161444.8177171.3171148.2827175.9939 95499.92≪116±1.6
DM207927.203544.769180.485193.0631205.9899 95487.56≪115±3.8
DM2114197.164944.7069Varaita131.362779.5185385.9919 95498.51≪114±1.8
DM2211327.179044.6919Varaita101.276577.2333235.9849 95480.98≪117±2.5
DM2310317.193344.6766Varaita311.5542786.6721 1945.9849 95431.284023±1.7
DM2712837.207044.5919Maira108.39139741.3021 9545.9729 95493.97≪120±1.3
DM296457.208544.7831154.19233327.6592 1975.5611 78694.49≪114±0.9
DM3015377.231244.746691.437625.4682365.5611 78697.93≪124±3.5
DM311687.244244.6229Varaita141.356988.8396395.5611 78618.661315±1.7
DM3213037.210044.5858Maira1913.1841 46265.5087 2645.5611 78650.78218±0.8
9013807.313645.1011Susa202.5721 12415.9476 9695.4114 3061.51313±0.2
9037807.265245.0883Susa200.029600.2324735.9714 69199.9≪123±0.3
9041077.268245.0843Susa200.1893860.8391 7125.9914 69199.9≪127±0.3
9063807.264745.1137Susa200.081360.4657895.9514 69196.5≪118±1.7
9071147.264345.1288Susa200.2764591.3492 2415.9814 69176.4≪121±1.2

[16] Samples from both massifs consist mainly of basement rocks (gneiss, schist and granite), except for the two southernmost samples from the Pelvoux massif (CH2 and CH3 in Table 1), which were collected from Eocene flysch (Champsaur sandstone). Samples were prepared for AFT thermochronology at the Grenoble laboratory following standard procedures (cf. Tricart et al. [2007]for details). All samples were dated using the external-detector andζ-calibration techniques [Hurford, 1990], using U-poor mica as an external detector and Durango and Fish Canyon Tuff apatite as age standards. Samples were irradiated in the P1 channel of the ORPHEE reactor at Saclay, France. Neutron fluences were monitored using NBS-962 and IRMM-540 glass dosimeters (cf.Table 1 for details). AFT data are reported as central ages [Galbraith and Laslett, 1993] ±1σ standard error in Table 1 and throughout the manuscript.

[17] Selected samples from the Pelvoux transect were prepared for AHe analysis at the John de Laeter Center for Isotope Research, Perth, Australia. Apatite grains were handpicked and evaluated under a binocular microscope, with any grains displaying fluid or crystalline inclusions rejected from analysis. Photos of selected grains were recorded digitally and grain measurements taken for calculation of a geometric correction factor for α-particle ejection [Farley et al., 1996; Farley, 2002]. Individual crystals were sealed into platinum envelopes and inserted into wells in a copper planchette. Helium was thermally extracted from single crystals heated using a 1064 nm Nd-YAG laser.4He abundances were determined by isotope dilution using a pure 3He spike, calibrated daily against an independent 4He standard tank. The uncertainty in sample 4He measurement is <1%.

[18] Degassed apatite grains were digested in 25 μl of a 50% HNO3 solution spiked with 235U and 230Th for at least 12 h to allow the spike and sample isotopes to equilibrate. Procedural blanks were monitored through separate analyses of 25 μl of a standard solution spiked as the dissolved samples, and an unspiked reagent blank comprising 25 μl of HNO3. 250 μl of MilliQ water was added prior to analysis on an Agilent 7500CS mass spectrometer (TSW™ Analytical) at the University of Western Australia. U and Th isotope ratios were measured to a precision of <2%. Long-term monitoring of laboratory performance demonstrates a consistent AHe age precision of 2.5%, based on multiple age determinations of Durango apatite standard that produce an average age of 31.5 ± 0.8 (1σ) Ma. Errors on individual apatite ages are reported assuming a standard relative analytical error of 7%, which combines the errors in U, Th and He determinations as well as in the α-ejection correction, while reported sample-age errors correspond to the standard deviation (1σ) of the mean age weighted by the mass of the individual grains.

3.2. Spectral Analysis of Age-Elevation Relationships

[19] Surface topography in mountain belts is characterized by a wide distribution of wavelengths, ranging from narrow valleys to the scale of an entire massif, which contribute to the perturbation of the underlying thermal structure. As the magnitude of these thermal perturbations decreases exponentially with depth, the shapes of consecutively deeper (higher temperature) isotherms exhibit perturbations related to correspondingly longer wavelength topography: short-wavelength topography has a rather limited effect and only perturbs shallow isotherms while long-wavelength topography results in larger perturbations that penetrate more deeply (Figure 2).

[20] For a given thermochronological system, there exists a critical wavelength (λc) below which topography has little effect on the shape of the corresponding closure-temperature isotherm. As an example, for a sinusoidal topography with amplitude of 3 km and a mean geothermal gradient of 25°C km−1 (see below), a simple analytical solution [Mancktelow and Grasemann, 1997] shows that perturbation of the AFT closure isotherm (∼120°C) [e.g., Gallagher et al., 1998] by topography with wavelength less than 4 km is negligible (<2%). For wavelengths shorter than this critical value, the slope of the age-elevation relationship provides an accurate estimate of the exhumation rate. As a corollary, however, there is effectively no variation in age with elevation for wavelengths much greater thanλc, unless relief has changed since the rocks passed through the relevant closure-temperature isotherm (Figure 2). Analysis of the relationships between age and elevation at different topographic wavelengths through spectral analysis of thermochronological data sets can therefore, in theory, provide information on relief evolution and exhumation rates without requiring thermo-kinematic modeling of the data.

[21] We use classical spectral analysis [e.g., Jenkins and Watts, 1968] to calculate the frequency-response function of a system that has elevation as input and thermochronological (AFT) age as output, following the method proposed byBraun [2002a]. The function can be described in terms of a gain (G) and a phase (F), both functions of the wavelength of input topography (λ):

display math
display math

where C12 and Q12 are the real and imaginary parts of the cross spectrum, obtained from the real (Rz, Ra) and imaginary (Iz, Ia) parts of the smoothed spectral estimators of the input (elevation, z) and output (age, a) signals, respectively:

display math
display math

and C11 is the power spectrum of the input signal:

display math

These smoothed spectral estimators are in turn obtained from the Fourier transforms of the windowed input and output signals, applying a triangular “Bartlett” window [Jenkins and Watts, 1968] to the elevation and age profiles. To optimize the input parameters for this process, the sample ages from our study were linearly interpolated to provide 128 equally spaced data points prior to calculation of the Fourier transforms.

[22] The power spectra indicate how the amplitudes of the elevation and age signals are distributed at various topographic length scales. At short wavelengths, the gain estimate (GS) provides a good estimate of the inverse of exhumation rate. At long wavelengths, the gain estimate (GL) contains information on the relief change (R), over a time equal to the mean age of the input thermochronological data set (or the age of a sample located at the mean elevation of the area):

display math

where R is defined as the ratio between the relief amplitude (Δhi) at the time rocks passed through the closure-temperature isotherm and the present-day relief amplitude (Δh0):

display math

Note that we define Ras the inverse of the relief-change factorβ of Braun [2002a] for the sake of consistency with the Pecube modeling that will follow. According to this definition, for R = 0 the initial topography is a plateau (no relief); for 0 < R < 1 relief has grown from past to present; while for R > 1 relief has decreased from past to present. The phase term (Fλ) in turn, theoretically provides information about lateral changes in relief (i.e., valley migration) since the samples passed the closure-temperature isotherm.

[23] Applying the spectral method to real-world data requires estimating the associated uncertainty. We define two types of errors associated with the method: the “inherent” error is associated with non-perfect sampling of the topography and the interpolation of data sets onto regularly spaced points. It is directly related to the spectral power in the elevation and age signals at different wavelengths and can be estimated, for a series ofn points, by performing n/2 spectral analyses, the first including points 1 to n/2 and subsequent analyses using points 2 to (n/2 + 1), 3 to (n/2 + 2), etc. [Jenkins and Watts, 1968, p. 437].

[24] The second source of error is due to propagation of the uncertainty in the thermochronological ages and is more difficult to assess. We employ a Monte-Carlo approach for quantifying this error; each spectral analysis was performed 1000 times, picking each sample age randomly from a Gaussian distribution with that sample's analytical age as the mean and its 1σ error as the standard deviation. The resulting variation in spectral power and gain at different wavelengths provides an estimate of the uncertainty in the method arising from data quality.

3.3. Inversion of Thermochronological Data Sets

[25] The second inversion method [Braun and Robert, 2005; Herman et al., 2007; Valla et al., 2010a, 2012; Glotzbach et al., 2011] combines the three-dimensional thermo-kinematic modelPecube [Braun, 2003; Braun et al., 2012] with a scheme for parameter exploration based on the Neighborhood Algorithm [Sambridge, 1999a, 1999b]. The Pecube code predicts thermal histories and resulting thermochronological ages for an input exhumation and relief scenario. It allows modeling of complex scenarios of spatially and temporally varying exhumation rates, and permits surface topography to vary with time. Topographic changes are incorporated by applying the relief ratio R as defined above (equation (7)) [Valla et al., 2010a; van der Beek et al., 2010]. AFT and AHe ages are predicted from the modeled thermal histories of points located on the surface at the end of the model run, using age-prediction models based on the algorithms ofStephenson et al. [2006] and Farley [2000] for AFT and AHe, respectively.

[26] The Neighborhood Algorithm (NA) [Sambridge, 1999a, 1999b] performs a direct search in a multidimensional parameter space in order to find a minimum of the misfit function between observations and model predictions. We use the log likelihood function (logL) as an estimator of the misfit between predicted (pi) and observed (oi) ages [Glotzbach et al., 2011]:

display math

where n is the number of measured ages along the profiles and σi are the observational (1σ) errors. Note that we use the absolute value of logLso that the objective function is minimized for best fitting models, as required by the NA. During a second or appraisal stage, the model ensemble is resampled to provide Bayesian measures of marginal probability-density functions (PDFs) for all parameters, allowing quantitative assessment of the precision with which these parameters are resolved [Herman et al., 2010a; Valla et al., 2010a, 2012; Glotzbach et al., 2011]. We redirect the reader to a complete description of the NA in Sambridge [1999a, 1999b].

[27] A high-performance computing cluster was used to run a large number of forward models (∼5000 for each inversion in this study) in order to provide accurate estimates of parameter values, given the number of free parameters in these inversions. Convergence of the algorithm is assessed by looking at the evolution of misfit through time; convergence is expected when the misfit becomes stationary.

4. Results

4.1. Thermochronological Ages

4.1.1. Pelvoux Transect

[28] The 35 new AFT ages from the Pelvoux transect vary between 3.0 ± 0.4 Ma and 12.6 ± 1.0 Ma (Table 1 and Figure 4) and show little correlation with elevation (Pearson correlation coefficient r = 0.17; Figure 4a). Overall, AFT ages appear to increase toward the south, in particular in the southern 10 km of the profile (south of the Valgaudemar valley; Figure 4b). This trend suggests differential exhumation of the core of the massif with respect to its southern border during the last few million years, which may result from differential tectonic uplift or the isostatic response to accelerated erosion [Braun and Robert, 2005; Champagnac et al., 2007, 2008]. However, many other processes, including fluid circulation, may also lead to local perturbation of the closure isotherm and the above mentioned trend may in fact reflect a series of local perturbations of different origins. Although the two southernmost samples collected in the Champsaur sandstone (CH2 and CH3) have among the oldest ages in the transect, they do fit within the overall trend and nearby crystalline basement samples show similar ages. We therefore do not think these older ages are due to lithological effects. More detailed investigation would be needed to identify the origin of the age trend.

[29] On a smaller topographic wavelength, the transect crosses four major valleys: the Romanche, Vénéon, Valgaudemar and Drac, from north to south. Weighted linear regression of ages collected on the sidewalls of the Vénéon valley demonstrates a reasonably well-correlated age-elevation relationship (r = 0.53), the slope of which is 0.8 ± 0.5 km m.y.−1 between ∼5.7 Ma and ∼7.8 Ma (Figure 5a). The other valley profiles, however, do not display comparable age-elevation relationships.

Figure 5.

Age-elevation profiles for (a) the Vénéon valley, Pelvoux (samples V1 to V5); (b) the Chisone valley (samples DM9, DM10, DM11, DM15); (c) the Pellice valley (samples DM16, DM17, DM18, DM23, DM29) and (d) Monte Montoso, (samples: DM20, DM29, DM30) all in the Dora-Maira massif. Open circles with error bars are AFT ages; black squares in Figure 5a are AHe ages (open squares with crosses are discarded ages; see text for discussion). Continuous black line is best fit weighted linear regression; dashed line in Figure 5a is the regression through AHe ages. Slopes of age-elevation relationships with 1σ uncertainties are given, together with Pearsonian correlation coefficients.

[30] All except two samples from the Pelvoux transect are characterized by low age dispersions (D < 15% of relative standard deviation of true fission track ages); the exceptions being APT99–1 (D = 20%) and APT99–3 (D = 21%). Samples V10 and OL1 yielded a sufficient number of horizontal confined fission tracks to allow statistically meaningful measurement of fission track length (FTL) distributions. The mean FTL values and 1σ standard deviations of samples V10 and OL1 are 11.4 ± 0.2/1.5 μm and 12.5 ± 0.2/1.6 μm, respectively, consistent with moderate rates of cooling through the AFT partial annealing zone (PAZ).

[31] Thirteen samples from the Pelvoux transect were selected for AHe analysis. Three to five replicate single-grain measurements were performed for each sample, for a total of 45 single-grain ages. Unfortunately, only 8 out of 13 samples provided reproducible results and are reported inTable 2. The others are characterized by strongly discordant intrasample grain age distributions and are provided as supplementary material. Among the eight reproducible ages, four are older than the corresponding AFT ages (see Table 2for details). Samples from the nearby La Meije age-elevation profile analyzed previously displayed the same problematic behavior [van der Beek et al., 2010], which may be due to any of the following issues: (1) minute undetected inclusions that are rich in U-Th (e.g., zircon, monazite) and that are not dissolved during sample treatment [e.g.,Farley, 2002]; (2) He-implantation from surrounding U-Th-rich grains [Spiegel et al., 2009]; (3) mineral zoning leading to inappropriate α-correction [Hourigan et al., 2005; Vernon et al., 2009]; or (4) the effect of α-damage on He-diffusion kinetics [e.g.,Flowers et al., 2007; Gautheron et al., 2009]. Since strong zoning was not apparent in AFT analysis of these samples, all cooling ages are relatively young (<15 Ma) and U-concentrations do not exceed several tens of ppm, we consider mineral zoning orα-damage effects unlikely to play a strong role with these samples, and suspect that the aberrant AHe ages are due to either U-Th-rich inclusions or He-implantation. Due to the inherently destructive nature of (U-Th)/He analysis, a posteriori investigation of samples to further interrogate the root of the problematic behavior is not possible, and these aberrant analyses are not discussed further here.

Table 2. New Apatite (U-Th)/He Ages for the Pelvoux Massif
Samplea4He (ncc)238U (ng)232Th (ng)Raw He Age (Ma)FT FactorbCorr. He Age (Ma)c
  • a

    Ages in bold are mass-weighted mean age and are reported with associated 1σ standard deviation.

  • b

    Ages are corrected for α ejection following the method of Farley et al. [1996].

  • c

    Ages in parentheses are older than the apatite fission track age of the sample. These ages have not been used in the inversions.

  • d

    Uncertainties on single-grain age determinations are assumed to be 7% and are reported as absolute errors.

V10.10.5180.6781.87⋅10−16.330.739(8.57 ± 0.60)d
V10.21.0841.6972.75⋅10−15.430.786(6.91 ± 0.48)
V10.30.0800.1531.19⋅10−24.540.735(6.18 ± 0.28)
V10.40.2230.2791.77⋅10−26.960.781(8.92 ± 0.34)
V10 (Vénéon, Elevation = 1720 m)  (7.50 ± 1.14)
V9.10.1700.7991.83⋅10−11.790.7742.31 ± 0.16
V9.20.1500.2605.11⋅10−24.870.7996.09 ± 0.43
V9.30.1950.5021.01⋅10−13.280.8104.05 ± 0.28
V9 (Vénéon, Elevation = 1715 m)  3.49 ± 1.55
V5.10.2200.6246.50⋅10−23.040.7194.24 ± 0.30
V5.20.1320.4484.19⋅10−22.540.7383.44 ± 0.24
V5.30.1870.6221.40⋅10−12.510.7183.50 ± 0.24
V5 (Vénéon, Elevation = 1420 m)  3.74 ± 0.37
V4.10.8941.6221.98⋅10−14.740.8295.72 ± 0.40
V4.20.7581.6266.30⋅10−24.090.8095.06 ± 0.35
V4.32.2946.1361.26⋅10−13.300.8353.94 ± 0.28
V4 (Vénéon, Elevation = 1270 m)  4.69 ± 0.69
V3.10.7211.0444.02⋅10−15.570.822(6.78 ± 0.47)
V3.20.5641.1334.94⋅10−13.970.7785.10 ± 0.36
V3 (Vénéon, Elevation = 1805 m)  (6.02 ± 0.84)
V20.3630.9134.16⋅10−23.480.7494.65 ± 0.33
2A-2.10.3020.4751.13⋅10−35.630.706(7.97 ± 0.27)
2A-2.30.0250.0381.30⋅10−35.800.733(7.92 ± 0.73)
2A-2.40.0550.0859.32⋅10−35.580.704(7.93 ± 0.45)
2A-2 (Les Deux-Alpes, Elevation = 2800 m)  (7.95 ± 0.73)
VA3.10.6290.7229.82⋅10−37.690.798(9.64 ± 0.35)
VA3.20.3710.4744.39⋅10−36.920.784(8.83 ± 0.34)
VA3.30.2560.2833.19⋅10−38.000.728(11.00 ± 0.42)
VA3.40.5310.5622.08⋅10−28.290.792(10.47 ± 0.38)
VA3 (Valgaudemar, Elevation = 1500 m)  (9.92 ± 0.83)

[32] Samples that provided replicable and geologically reasonable AHe ages (Table 2) are mostly concentrated in the Vénéon valley. Here, AHe ages vary between 3.5 ± 1.5 Ma and 8.0 ± 0.7 Ma (Table 2). Sample ages from the north flank of the valley show a reasonable correlation (r = −0.43) with elevation, although with a lower slope than the AFT data (0.37 ± 0.26 km m.y.−1 between ∼3.7 and ∼8.0 Ma; Figure 5a). The only sample from the Valgaudemar valley further south that provided an interpretable AHe age is VA3, for which the 9.9 ± 0.8 Ma age overlaps with the corresponding AFT age.

4.1.2. Dora-Maira Transect

[33] Data for the Dora-Maira transect are reported inTable 1 and plotted in Figure 4. They comprise 23 new and 5 previously published AFT ages [Tricart et al., 2007]. AFT ages show a relatively wide range between 13.1 ± 0.2 Ma and 27.3 ± 0.3 Ma, with no clear relationship with elevation (r= 0.10). All samples dated are characterized by low age dispersions (D < 5% of relative standard deviation of true fission track ages); however, in several samples apatite quality was such that only a few grains could be dated, which renders the dispersion statistics less reliable. Because of the less-than-optimal apatite quality of samples from the Dora-Maira massif, which showed low U-Th content, numerous inclusions and uneven shapes, and the initial, somewhat disappointing results on Pelvoux samples (cf. above), no AHe dating was attempted on the Dora-Maira samples.

[34] Sampling through three of the traversed valleys establishes several apparent age-elevation relationships at short wavelengths. In the Val Chisone (Figure 5b), four samples are aligned along an elevation profile for which weighted linear regression provides an exhumation rate of 0.14 ± 0.07 km m.y.−1 (r = 0.8) between 16.5 and 24.6 Ma. This estimation is confirmed along the Val Pellice (0.14 ± 0.04 km m.y.−1) and the Montoso (0.09 ± 0.04 km m.y.−1) profiles, which both provide comparable age-elevation relationships with correlation coefficients of 0.8 and 1.0 for similar time ranges. These results are in accord with previous estimates from the northern part of the massif [Cadoppi et al., 2002; Malusà et al., 2005; Tricart et al., 2007], which suggested a mean age-elevation gradient of 0.1 km m.y.−1 in the Susa valley. No clear longitudinal trend is apparent in the data, suggesting relatively homogeneous exhumation of the massif between its northern and southern part.

4.2. Spectral Analysis Results

[35] Computed age and elevation power spectra and gain functions for both massifs are shown in Figure 6. The power spectra provide information on the relative strength of the input (elevation profile) and output (age profile) signals as a function of wavelength: a strong signal will result in a lower “inherent” error on the gain estimate. Thus, the power spectrum allows assessment of the resolution of the data at different wavelengths, thereby identifying better and less resolved windows in the gain spectrum.

Figure 6.

Spectral analysis of the AFT data sets for the Pelvoux and Dora-Maira massifs: (a) Elevation and age profiles interpolated from the AFT age-elevation data set. The mean value has been subtracted from both profiles; AFT ages are shown with error bars. (b) Power spectra of the elevation (thick black line) and age (shaded lines) profiles; for the ages 1000 profiles are randomly generated from the age distributions assuming a Gaussian error distribution (only a sample of these is shown; see text for discussion). (c) Phase shift between age and elevation spectra. (d) The real part of the gain function between age and elevation calculated fromequation (1); error bars show the “inherent” error in the gain function calculated following Jenkins and Watts [1968]; shaded lines show gain function calculated from 1000 randomly generated age profiles in Figure 6a. Vertical dashed lines delimit short- and long-wavelength domains used to estimate exhumation rate and relief change; thick horizontal black lines show mean gain value within these domains; red line indicates inverse of exhumation rate determined from age-elevation relationships (shaded region denotes uncertainty). See text for further discussion.

4.2.1. Pelvoux Transect

[36] The observed increase in ages toward the south (Figure 4b) may influence the spectral analysis by introducing spurious correlations between age and elevation at long wavelengths. We can “correct” the ages by subtracting the best fit linear trend from the data, so as not to impose this long-wavelength trend, assuming that its origin is related to differential cooling/exhumation that occurred after the samples passed through the apatite closure isotherm. Performing this correction for the Pelvoux transect AFT ages slightly improves the correlation between age and elevation (r= 0.26), but spectral analyses undertaken on both the raw and the trend-corrected data did not reveal any significant differences. Other nonlinear corrections could be used to remove the trend but, in the absence of geological justifications and given our objective to test the spectral analysis method, we only discuss the results using the raw data so as not to introduce any bias in the data set.

[37] The elevation power spectrum shows maximum values for wavelengths between 10 and 20 km (Figure 6b), which is clearly the dominant wavelength in the topography (Figure 6a). The age profile is better resolved at wavelengths around 6 km, as shown by its power spectrum. At short wavelengths (below 2 km), both power spectra are close to zero, implying limited resolution of the data. As a consequence, the calculated gain function appears noisy at these short wavelengths. This is probably due to the relatively coarse and irregular sampling intervals at this scale, notwithstanding our attempt to sample tightly and regularly, as well as the noise in the age data expressed by the irregular age-elevation relationships obtained in three of the four main valleys. Gain values appear to decrease between 2 and ∼5 km wavelengths and include some negative values. The “inherent” noise in the data is larger for wavelengths ≤5 km than the noise introduced by the uncertainty in AFT ages. Finally, at the longest wavelengths analyzed, the gain function seems to stabilize at a value around zero and becomes less noisy. At these wavelengths, the uncertainties due to the age errors are larger than those due to the inherent noise, although both are small.

[38] The perturbation of the ∼120°C closure isotherm of the AFT system depends on its depth below the surface, which depends on the geothermal gradient and the exhumation/advection rate. Surprisingly few reliable estimates of the geothermal gradient are available in the Alps. In our model, crustal thickness, basal temperature and crustal heat production (Table 3) are set to obtain a stable (i.e., in the absence of advection) and spatially uniform geothermal gradient of ∼25°C km−1, based on modeling results by Glotzbach et al. [2011] for the Mont Blanc massif. We justify our choice of a spatially uniform and stable geothermal gradient in the absence of data available to constrain its value or any spatial variations therein. Perturbation of the 120°C isotherm scales positively with geothermal gradient; i.e., it will be larger for any topographic wavelength if the geothermal gradient is higher. For the exhumation rates of ∼0.8 km m. y.−1 (Figure 5a) and the geothermal gradient cited above, noticeable perturbation (>10% of the topography amplitude) of the 120°C isotherm occurs for topographic wavelengths >7 km [Mancktelow and Grasemann, 1997] and we take this as the cutoff value between “short” and “long” wavelengths.

Table 3. Fixed Parameter Values Used in Pecube/NA Inversions
Parameter (Unit)Value
Crustal density (kg m−3)2700
Sublithospheric mantle density (kg m−3)3200
Equivalent elastic thickness (km)20
Young's modulus (Pa)1.1011
Poisson ratio0.25
Crustal thickness (km)20
Thermal diffusivity (km2 m.y.−1)25
Basal crustal temperature (°C)520
Sea-level temperature (°C)15
Atmospheric lapse rate (°C km−1)6
Crustal heat production (°C m.y.−1)0

[39] The inverse of the exhumation rate deduced from the age-elevation profile of the Vénéon valley (0.8 ± 0.5 km m.y−1; Figure 5a) suggests an expected gain value at short wavelength (GS) of 1.2−0.5+2.6 m.y. km−1. This value is within the inherent noise of the gain function at wavelength less than 2 km. For comparison, we calculated a weighted mean value and standard error of the gain function for λ < 2 km: GS = 2.2 ± 1.2 (1σ) m.y. km−1. The exhumation rate derived from this value is 0.4−0.1+0.6 km m.y.−1. Thus, the spectral analysis only constrains exhumation rates to be between 0.3 and 1.0 km m.y.−1, which is consistent with the exhumation rates inferred from the age-elevation profile along the Vénéon valley (Figure 5a) as well as with the rates of 0.6 ± 0.3 km m.y.−1 (since 5.5 Ma) obtained by van der Beek et al. [2010]from inverse modeling of an age-elevation data set at La Meije peak, just east of our profile.

[40] The long-wavelength gain (GL; λ > 7 km) was similarly estimated at 0.07 ± 0.04 m.y. km−1. From the mean GS and GL and equation (6), we can estimate the relief evolution of the massif since a time corresponding to the mean age of the data set. The computed relief ratio, R = 0.9 ± 0.6 (1σ) is affected by a high uncertainty, which reflects the uncertainty in the gain function. Using the GSvalue calculated from the age-elevation profile, leads to a similar estimate of the relief ratio (R = 0.9 ± 0.7). The high associated uncertainty on these values does not provide much insight into the evolution of relief since ∼8 Ma (the mean AFT age of the data set). However, considering an average exhumation rate of 0.8 km m.y.−1 and average topographic amplitude of 3000 m, the AFT isotherm should be conformal to topography only for wavelength greater than 30 km. For the shorter wavelengths assessed here (7–20 km), the gain value is overestimated and the relief development parameter (R) therefore underestimated. This may suggest that R > 1 and relief has thus decreased. Finally, the phase estimate (Figure 6c) is close to 0 for all λ > 2 km (and very noisy for shorter wavelengths), suggesting little lateral migration of topography.

4.2.2. Dora-Maira Transect

[41] Both the age and the elevation power spectra reveal a strong signal for wavelengths greater than 10 km (Figure 6) and appear reasonably well resolved at wavelengths between 3 and 10 km. The two signals present roughly the same distribution of power as a function of wavelength, underlining an overall (anti-) correlation of ages and elevations at all wavelengths. Again, there is little power in both signals at wavelengths below 3 km, implying poor resolution at short wavelengths. Using a similar approach as for the Pelvoux transect, but assuming an exhumation rate of 0.1 km m.y.−1, we estimate the critical wavelengths for no (<2%) and significant (>10%) perturbation of the AFT closure isotherm to be 3 and 10 km, respectively.

[42] The gain function computed for the Dora-Maira massif presents a higher noise level than for the Pelvoux, due to more irregular spacing of samples and larger errors on individual AFT ages along the transect. For the exhumation rate deduced from the age-elevation profiles (0.12 ± 0.02 km m.y.−1; Figures 5b–5d), the expected value of the gain function at short wavelengths is 8.3−1.2+1.7 m.y. km−1, roughly consistent with the weighted-average short-wavelength gain (λ < 3 km; GS = 6.2 ± 4.7 m.y. km−1, E = 0.16−0.1+0.5 km m.y−1). The weighted-average gain at wavelengths >10 km (GL) is not very tightly constrained at 1.4 ± 9.7 m.y. km−1, which leads to a crude estimate for R = 0.8 ± 5.5 (1σ). Using the value expected from the age-elevation profile, we obtain an estimate for R = 0.8 ± 5.9. As for the Pelvoux massif, spectral analysis of the Dora-Maira transect thus does not reveal clear variations in relief over the last 18 Ma (the mean AFT age of samples from Dora Maira), although the estimated meanR-value may suggest relief growth, again taking into account that we probably underestimate the amount of relief change. Finally, phase changes are close to zero for all wavelengths except the shortest, where they are very noisy, again suggesting little if any lateral migration of topography.

4.2.3. Synthesis

[43] The exhumation rates inferred from the spectral analyses, although associated with large relative errors, are consistent with independent estimates for exhumation rates in both massifs. Variations in relief are difficult to assess from these analyses and the results tend to suggest only minor relief change in both massifs, with a possible increase in Dora Maira and decrease in the Pelvoux. As discussed earlier, however, an inherent limitation of the spectral approach is that it only provides averaged denudation rates and relief changes since the mean time of closure of the samples in the data set (the mean thermochronological age of the data).

4.3. Inversion Results

[44] In order to test the predictions of the spectral analyses, we search for best fit exhumation rates and relief evolution scenarios from Pecube-NA inversions. Fixed thermal and kinematic input parameters used in ourPecube modeling are given in Table 3; these are similar to those used previously in modeling thermochronology data from the Pelvoux massif [van der Beek et al., 2010] and imply a stable geothermal gradient of 25°C km−1. Simulations were run for 15 m.y. for the Pelvoux and 30 m.y. for the Dora-Maira transects, respectively, in order to allow modeling the oldest AFT ages. The AFT ages and associated 1σ standard deviation were used as observational constraints for both transects, while the Pelvoux inversion also incorporated the 4 AHe ages that are younger than their corresponding AFT ages (Table 2).

[45] In order to maintain consistency between the spectral analysis and the numerical inversions, we only invert for simple scenarios including three free parameters: exhumation rate (E), relief change (R) and a relief-change timescale (τ). The latter controls the way in which relief (Δh) evolves through time [Braun and Robert, 2005]:

display math

where Δh0is the present-day relief,t is time since the onset of the model run and tfis the total model run-time. Note thatτ can be either positive or negative; if τ is close to zero, relief variation will be linear through time; if τ is strongly positive, relief change will take place rapidly at the onset of the model run and if τis strongly negative, relief change will take place rapidly close to the present-day. Also note that the current implementation differs somewhat from the definition initially proposed byBraun and Robert [2005], in order to allow a smooth variation in the style of relief change with τ. We let these parameters vary between 0 and 1 km m.y.−1 for E, 0 and 2 for R and −1000 m.y. and 1000 m.y. for τ.We refrain from using more sophisticated scenarios which include more than one phase of exhumation and relief change for two reasons: first, this simple scenario allows direct comparison of inversion results with average exhumation rates and relief change since the samples crossed the closure isotherm obtained by the spectral method; second, there is likely little resolution in more complex two- or three-phase models when constrained with AFT data only [Valla et al., 2010a; van der Beek et al., 2010].

[46] Inversion results are reported in Figures 7 and 8 (for Pelvoux and Dora Maira, respectively) as scatterplots of fit as a function of input parameter values, with associated Bayesian estimates of parameter resolution shown as normalized marginal probability density function (PDFs). Optimal parameter fits and their uncertainty estimates are also reported and compared with spectral analysis results in Figure 10.

Figure 7.

(a) Scatterplots and 1D marginal posterior probability-density functions of parameter values showing results of NA inversion of the Pelvoux data set (including AFT and AHe ages). Each dot corresponds to a forward model; its color is proportional to the log likelihood of the predicted ages (equation (8)). Each diagram is the projection of parameter combinations onto a two-dimensional space defined by two of the three parameters explored (Exhumation rateE; relief factor R; relief-change timescaleτ); horizontal and vertical scales define the intervals for given parameters. Maximum-likelihood model is represented by a star. (b) Evolution of misfit as a function of model index used to evaluate the convergence of the Neighborhood Algorithm. (c) Plot of predicted (maximum-likelihood model) and observed ages along the profile. The red line represents predicted AFT ages and the blue line predicted AHe ages. The dark gray line is the absolute difference between predicted and observed AFT ages. (d) Plot of predicted versus observed ages for the maximum-likelihood model. In Figures 7c and 7d, white dots represent AFT ages while black squares are AHe ages (discarded AHe data are shown as white squares with a cross).

Figure 8.

(a) Scatterplots and 1D marginal posterior probability-density functions of parameter values showing results of NA inversion of the Dora-Maira data set. Each dot corresponds to a forward model; its color is proportional to the log likelihood of the predicted ages (equation (8)). Each diagram is the projection of parameter combinations onto a two-dimensional space defined by two of the three parameters explored (Exhumation rateE; relief factor R; relief-change timescaleτ); horizontal and vertical scales define the intervals for given parameters. Maximum-likelihood model is represented by a star. (b) Evolution of misfit as a function of model index used to evaluate the convergence of the Neighborhood Algorithm. (c) Plot of predicted (maximum-likelihood model) and observed ages along the profile. The red line represents predicted AFT ages and the blue line predicted AHe ages. The dark gray line is the absolute difference between predicted and observed AFT ages. (d) Plot of predicted versus observed AFT ages for the maximum-likelihood model.

4.3.1. Pelvoux

[47] The inversion converges well for both exhumation rate and relief factor, leading to optimal values of E = 0.82 ± 0.02 km m.y.−1 and R = 1.96 ± 0.04. The timescale of relief change is less well constrained (τ = −642 ± 210 m.y.), although optimal models, with log likelihoods above −230, clearly tend toward negative τ-values (Figures 7 and 9). The predicted ages and observations are plotted along the transect on Figure 7c. This allows a rapid assessment of the degree to which observed ages are reproduced, which appears satisfactory in the northern part of the transect but clearly less so in the middle and southern parts. Overall, the predicted AFT ages show significantly less scatter than the observed ages, while the AHe ages included in the models are well reproduced (Figure 7d).

Figure 9.

Relief-change timescale (τ) in the Dora-Maira and Pelvoux massifs.τ ranges from −1000 to +1000 m.y.: if τ is close to zero, relief variation will be linear through time; if τ is strongly positive, relief change will take place rapidly at the onset of the model run and if τis strongly negative, relief change will take place rapidly close to the present-day (shaded lines). Relief has been normalized by present-day mean topography. Bold lines represent maximum-likelihood model given by the inversion method, with 1σ standard deviation.

[48] The preferred R-value of ∼2, together with negativeτ-values, suggests a significant decrease in relief late in the model history (Figure 9), in contrast to the inferred limited relief change predicted by the spectral analysis. We note, however, that reasonably fitting scenarios can also be found that include an increase in relief, although this should have occurred early in the history (associated with positive τ-values, cf.Figures 7 and 9) The spectral analysis and inversion methods do provide consistent estimates for exhumation rate, with the inversion providing a much better constrained value.

4.3.2. Dora-Maira

[49] As for the Pelvoux inversion, exhumation rate is well constrained in the Dora-Maira transect, with a preferred value ofE = 0.19 ± 0.02 km m.y.−1. The results for the relief factor are less well constrained (R = 0.64 ± 0.30) but tend to support values of R < 1, i.e., relief increase. The timescale for relief change shows scattered results; although most optimal models prefer negative values (τ = −392 ± 249, m.y. cf. Figures 8 and 9), we note that models also provide reasonable fits to the data for positive τ-values, often combined with very lowR. Comparison of observations with predictions provided by a model combining the optimal parameter values shows that misfit is evenly distributed along the profile. The absolute residual ranges between 0 and 10 m.y. (mean ≈ 5 m.y.) and, as for the Pelvoux transect, there is less variation in predicted than in observed AFT ages.

[50] Overall, both R and τappear less well constrained for Dora Maira than for the Pelvoux. However, inferred values for both exhumation rate and relief change are consistent between the spectral analysis and the thermo-kinematic inversion for Dora Maira (Figure 10).

Figure 10.

Comparison of exhumation rates and relief development (parameterized by E, R, and τ) for the Pelvoux and Dora-Maira massifs estimated from spectral analysis (SA) and thermo-kinematicPecube inversion (PI). Optimal parameter values are shown as dashed lines, with 1σ uncertainties as boxes.

5. Discussion

5.1. Methodology: Spectral Analysis Versus Thermo-kinematic Inversion

[51] Although spectral analysis appears to represent a promising method for the assessment of mean relief evolution over a given period of time, our study highlights some of the difficulties that arise when dealing with natural data. These difficulties concern in particular sampling logistics (the need to obtain closely and regularly spaced data) as well as uncertainties in individual sample ages. For the Dora-Maira transect, relatively high age errors propagate into errors in the estimated gain function that exceed the “inherent” error in the analysis due to non-perfect sampling of the topography. In contrast, the lower age errors for the Pelvoux data resulted in gain estimates for which the resolution is limited by the inherent error. The spacing between samples obviously controls the inherent error, particularly at short wavelengths, resulting in better resolution as this spacing becomes smaller. On the other hand, age errors affect gain values at all wavelengths. This difference between the two transects underscores the necessity of carefully preparing the sampling strategy according to the expected ages and potential precision. Note that the absolute rather than the relative age errors will determine the resolution of the spectral analysis. As older thermochronological ages are usually associated with higher absolute age errors, attention should to be paid to sample quality to ensure optimal constraints on gain estimates. In contrast, as young ages generally are associated with lower absolute errors, the limiting factor to control is the spacing between samples.

[52] Comparison between results from the spectral analysis and numerical inversion methods (Figure 10) demonstrates consistent estimates of exhumation rate, although the numerical inversions obtain much better precision on these estimates. Both methods also predict rates that are consistent with previous estimates obtained independently along age-elevation profiles in the Pelvoux [van der Beek et al., 2010] and Dora-Maira [Tricart et al., 2007] massifs. The results for relief development are more difficult to compare, due to the large uncertainties on spectral gain estimates. Both methods provide consistent results for the Dora-Maira massif, suggesting moderate increase in relief over the last 18 m.y. For the Pelvoux, in contrast, the numerical inversion suggests significant relief decrease while the spectral analysis does not resolve relief development. This outcome highlights the limited resolving power of “classical” AFT and AHe data to constrain relief development even in these high-relief mountain environments. Using numerical inversions,Valla et al. [2010a]have shown recently that AFT data alone sampled along local age-elevation profiles are insufficient to provide quantitative constraints on the regional exhumation and relief history; multiple thermochronology data (AFT, AHe, track-length data) are required, but even these can provide significant constraints only in optimal circumstances, where the rate of relief change is 2–3 times higher than the background exhumation rate. Moreover, the limited quality of our AHe data set highlights potential difficulties that arise when aiming to apply multiple-thermochronometers strategies. In a follow-up study,Valla et al. [2011a] have shown that data collected along transects, such as presented here, have more potential to independently resolve exhumation rates and relief development, as possibly demonstrated by the higher resolution obtained on the R parameter in this study compared to van der Beek et al. [2010], who used a local age-elevation profile. However,Valla et al. [2011a]also showed that using spatially distributed data collected more or less randomly along valley bottoms, combined with one or more age-elevation profiles, leads to the most accurate and precise predictions, especially when combining AFT, AHe and track-length data.

[53] From a general point of view, investigating the evolution of relief using thermochronology at the scale of a massif presents inherent difficulties. Both spectral analysis and thermo-kinematic inversions assume spatially uniform rock-uplift rates throughout the massif. From the overall age-elevation relationships for each transect presented in this study (Figure 4) we suspect that, at such a scale, the thermochronological ages are likely to be affected by local factors within each valley and (inferred) rock-uplift rates vary spatially. Thus, application of thermo-kinematic models or spectral analyses would require extracting both the regional and local components of exhumation to provide reliable estimates of relief evolution. This requires detailed study of local factors likely to affect the thermochronological ages and the age-elevation relationship (local tectonics, fluid circulation etc.), which may prove difficult in practice. A more general consequence is that quantification of relief evolution is more likely to be successful in stable contexts where tectonic activity is known to have been insignificant over a long period and where relief change is therefore climatically driven. The second assumption implicit in both techniques is that relief evolution is consistent over the entire massif. The comparison between the deeply carved glacial Susa valley and the other, much less glacially influenced, valleys of the Dora-Maira massif shows that a single massif can present variable relief development. When considering strategies to address relief development, one must therefore assess the scale at which the relief change has occurred. Changes in relief due to glacial valley carving are expected to occur at relatively short wavelengths (5–10 km). Spectral analysis cannot be used at such a local scale since the method explicitly compares short- and long-wavelength age-elevation relationships, based on the assumption that closure isotherms should be conformal to the long-wavelength topography. Similarly, thermo-kinematic models are limited by the closure temperature of the considered system(s): the ability to resolve relief evolution at the valley scale will strongly depend on the ratio between exhumation rate and the expected amplitude of relief change [Valla et al., 2010a].

[54] Given the logistical challenge of sampling a dense and evenly spaced long transect through a mountain belt (as an example, sampling the two transects presented here took about a month of full-time equivalent work for 1 person – even in these relatively accessible Alpine massifs), a more efficient strategy might be to concentrate on obtaining spatially distributed data, using multiple thermochronometers per sample and prioritizing data quality. Selecting samples based on expected data quality could, however, inherently bias the data set due to limited availability of promising lithologies. Furthermore, the assumption that both exhumation and relief evolution are spatially constant over the massif seems to be difficult to fulfill; therefore, models should be limited to quantification of local relief evolution. Such an approach has recently been applied byValla et al. [2011b, 2012], who used high-resolution4He/3He thermochronometry to derive cooling paths between ∼100°C and surface temperatures on individual samples, and compared cooling paths between samples collected at different elevations along a valley-ridge transect to infer recent relief change in the Swiss Alps.

5.2. Regional Implications

[55] The spectral analysis and inversion methods support a mean exhumation rate of ∼0.8 km m.y.−1since ∼8 Ma in the Pelvoux massif, whereas data from the Dora-Maira massif are consistent with slower mean exhumation rates of <0.2 km m.y.−1 since ∼18 Ma. This discrepancy between the two massifs fits within the established regional pattern of exhumation rates [Vernon et al., 2008] and is compatible with the Neogene tectonic history of the western Alps, during which the external massifs experienced transpressive to transcurrent deformation, whereas the core of the belt has undergone extension [Selverstone, 2005; Sue et al., 2007].

[56] Our current analysis only resolves a mean exhumation rate since the Middle Miocene for the Pelvoux massif and therefore does not allow commenting on temporal variations in exhumation rate, in particular a possible transient Late Miocene increase in exhumation rates followed by a decrease during the Pliocene, as recorded in the age-elevation profile studies byvan der Beek et al. [2010] and suggested in other external crystalline massifs (i.e., Argentera [Bigot-Cormier et al., 2006], Mont Blanc [Glotzbach et al., 2008, 2011], Aar [Vernon et al., 2009; Valla et al., 2012]). We note, however, that both the steep AFT age-elevation gradient combined with relatively old ages (leading to a zero-age intercept at >4 km below the valley bottom) and the less steep AHe age-elevation gradient observed in the Vénéon age-elevation profile (Figure 5a) both suggest a decrease in exhumation rates since ∼6 Ma, consistent with the studies cited above.

[57] The AFT ages from the Dora-Maira transect are consistent with those found in the Susa and Val d'Aosta valleys to the north [Cadoppi et al., 2002; Malusà et al., 2005; Tricart et al., 2007] and confirm the contrast with younger ages found westward within the Viso ophiolites and the “Schistes Lustrés” Complex [Schwartz et al., 2007], which overlie the massif along a contact that has been interpreted as an extensional detachment. However, as previously pointed out by Tricart et al. [2007], the diachronous age pattern is inconsistent with late-stage exhumation of the massif along this western ductile shear zone, suggesting that this structural configuration was emplaced early in the history of the massif, at temperatures well above the AFT closure temperature.

[58] Although our analysis was not designed to resolve potential temporal variations in exhumation rate, it appears that the data do not require such variations and are consistent with continuous slow denudation of the Dora-Maira massif throughout Neogene-Quaternary times. From the provenance analysis of sediment filling the Ligurian molasse basin to the east,Carrapa [2002]showed that incision into the basement nappes of the Dora-Maira massif likely occurred during the last 10 m.y. The late arrival of basement pebbles probably reflects erosion of overlying sedimentary nappes before ∼10 Ma. It appears that erosion through the sedimentary cover and into the crystalline core of the massif was not associated with significant changes in exhumation rate, in contrast to the suggestion that the inferred Pliocene decrease in exhumation rates in the External Crystalline Massifs is due to the erosion level reaching basement [van der Beek et al., 2010; Glotzbach et al., 2011].

[59] The relief history for the Pelvoux massif remains equivocal. The current data do not support a potential increase in relief associated with glacial valley carving in the massif, as strongly suggested by the geomorphology [Champagnac et al., 2007; van der Beek and Bourbon, 2008] and unambiguously recorded by low-temperature thermochronometers in the Mont-Blanc massif [Glotzbach et al., 2011] and Rhône Valley [Valla et al., 2011b], ∼200 km to the northeast. Although the numerical inversion predicts an apparently well-constrained late-stage decrease in relief that would have taken place in the last 1–1.5 Ma (Figure 9), we hesitate to place much emphasis on this outcome, as it is not confirmed by the spectral analysis. Also, as we modeled the exhumation history using a temporally and spatially constant exhumation rate, the inferred relief decrease could be an artifact; i.e., the model could try to reproduce the steep age-elevation profile by decreasing relief and thus increasing exhumation on mountain peaks with respect to valley bottoms. However, we do not exclude that this late-stage relief decrease is real and could speculate it is associated with large-scale glacial erosion around the Equilibrium Line Altitude (ELA) in a “glacial-buzzsaw” type scenario [cf.Mitchell and Montgomery, 2006; Egholm et al., 2009]. Within the Pelvoux massif, the modal elevation and local slope minima occur between at elevations between the modern ELA and that inferred for the most extensive glaciation [van der Beek and Bourbon, 2008]. These observations suggests that efficient cirque retreat and periglacial processes [Delunel et al., 2010] may have preferentially eroded the topography and limited relief development around the ELA.

[60] In contrast, our analyses suggest a moderate increase in relief for the Dora Maira massif during Neogene times. We cannot place tight constraints on the timing of relief increase, although the numerical inversions would suggest it occurred during Late Pliocene-Quaternary times (Figure 9) and is thus possibly associated with Quaternary glaciations. The difference in late-stage relief development between the Pelvoux and Dora-Maira massifs could thus be due to different degrees of glaciation; whereas the Dora Maira massif featured individual valley glaciers [Carraro and Giardino, 2004] that would have deepened the valleys without affecting higher-elevation regions, the Pelvoux massif was characterized by a regional ice-dome [van der Beek and Bourbon, 2008; Delunel, 2010] that would have allowed efficient glacial erosion through cirque retreat at higher elevations. Incision of the valleys might have been episodic and limited to extensive glaciations while erosion by cirque glaciers or periglacial processes would have been active even at times of less extensive glaciation.

[61] The phase estimates from the spectral analysis suggest that in both massifs, relief evolution took place without significant lateral shifts in valley locations, consistent with the inferred pre-Quaternary drainage pattern in the Pelvoux [Montjuvent, 1974, 1978] and with the occurrence of individual valley glaciers in the Dora-Maira massif. This style of relief development contrasts with that inferred for the Coast Mountains of British Columbia (Canada), where similar modeling of thermochronology data sets suggests that glacial erosion strongly modified the map-view valley pattern [Ehlers et al., 2006; Olen et al., 2012].

[62] As previously pointed out by Valla et al. [2010a], our study reveals that the relatively high closure temperatures of the AFT (and AHe) thermochronological systems only partially record the relief history of Alpine mountain belts, leading to a general under-estimation of relief changes in current thermochronological studies. This apparent problem could be overcome by future application of thermochronological systems that are sensitive to lower temperatures, such as4He/3He [Shuster et al., 2005; Valla et al., 2011b] or OSL [Herman et al., 2010b] thermochronometry.

6. Conclusions

[63] We have sampled thermochronological age-elevation relationships along two transects located in two crystalline massifs of the western Alps that present different tectonic histories. Analyses were performed using spectral analysis and thermo-kinematic inversion to test how thermochronological data sets can constrain exhumation and relief histories. Our results show that, although the spectral method provides consistent estimates of exhumation rates with respect to numerical inversions and local age-elevation relationships, these are associated with large uncertainties due to imperfect sampling and analytical errors. Given the logistical challenge of sampling dense thermochronological age transects, we suggest that a more efficient approach may be to sample spatially distributed data, using multiple thermochronometers per sample and prioritizing data quality.

[64] The Pelvoux transect suggests a mean exhumation rate of ∼0.8 km m.y.−1since Middle Miocene times, in accord with previous estimates. The Dora-Maira transect reveals a much slower mean exhumation rate of <0.2 km m.y.−1for the last ∼20 m.y. The data do not unambiguously constrain relief development for either massif: the data from the Dora-Maria massif suggest moderate Pliocene-Quaternary relief increase whereas the results from the Pelvoux are inconclusive but could imply relief decrease since ∼1–1.5 Ma. We attribute this lack of resolution of the relief history to the relatively high closure temperature of the AFT system, which formed the basis for most of these analyses. We therefore suggest favoring multiple thermochronometer studies including newly developed very-low-closure temperature systems to explore recent relief development in mountain belts. We also suggest that quantification of relief evolution can only be assessed at a relatively local scale where one can assume exhumation rate and relief evolution to be uniform.


[65] This project was financed by the INSU-CNRS “Reliefs de la Terre” program (Pelvoux samples) and the Agence Nationale de la Recherche (ANR-08-BLAN-0303-01 “Erosion and Relief Development in the Western Alps”; Dora-Maira samples). R.B. was supported by a PhD grant from the French Ministry for Research and Higher Education. We thank the “Parc National des Ecrins” for granting permission to sample in the Pelvoux massif. Computations were performed on R2D2, the high performance cluster maintained by the CIMENT project (Calcul Intensif/Modélisation/Expérimentation Numérique et Technologique) at Université Joseph Fourier. P.v.d.B. thanks Matthias Bernet, Frédéric Herman, Max Rohrman and Leo Zijerveld for assistance with sampling the Pelvoux transect. We thank Francis Coeur and François Senebier for sample preparation. Constructive comments by Rebecca Flowers, Jeff Benowitz and two anonymous reviewers, as well as by Associate Editor Simon Brocklehurst and Editor Alex Densmore, considerably improved the manuscript.