Estimating exhumation rate and relief evolution by spectral analysis of age–elevation datasets

Age–elevation relationships have been used widely to constrain the rate of rock exhumation in a range of tectonic environments (Wagner et al., 1977; Morley et al., 1980; Benjamin et al., 1987; Gleadow and Fitzgerald, 1987; House et al., 1997; Batt et al., 2000). In order to avoid complications arising from the thermal perturbation caused by finite-amplitude surface topography (Stüwe et al., 1994), the variation of thermochronometric ages with elevation is usually sampled along near-vertical profiles. It has been shown (House et al., 1998), however, that information pertaining to the evolution of surface landforms through time is also contained in the variation of ages with elevation at a larger length scale. For example, the spatial distribution of (U–Th)/He apatite ages across deeply incised valleys has been used to argue for the antiquity of the present-day drainage system of the Sierra Nevada, California (House et al., 1998, 2001). This low-temperature, chronometric method (Rutherford, 1907; Zeitler et al., 1987) was recently shown to have the potential to constrain the rate of surface landform evolution in response to more or less rapid changes in tectonic or climatic environment (Farley et al., 1996; Wolf et al., 1996). However, the interpretation of age data derived from such a low-temperature ( 70 C) thermochronometer is difficult and relies on the knowledge of usually poorly constrained local parameters, notably, the geothermal gradient (House et al., 1998, 2001). Here, a new method to interpret thermochronometric data is proposed that does not suffer from this drawback.