A Fourier approach for estimating and correcting the topographic perturbation of low-temperature thermochronological data

• Numerically derived dependence of thermochronological data on topography
• Method to find most promising sample sites to estimate palaeo-topography
• Method to correct exhumation rates derived from non-vertical age–elevation profiles

Thermochronology is a unique tool to reconstruct the long-term exhumation history of outcropping rocks. Pronounced (palaeo-) topography can markedly perturb near-surface isotherms, which can result in erroneous exhumation histories derived from age–elevation relationships but also offers the possibility to reconstruct palaeo-topography. Here we use a synthetic dataset to illustrate the complex non-linear relationships between the degree of topographic perturbation of thermochronological ages on one hand, and exhumation rate, geothermal gradient, and topographic wavelength and relief on the other. The dataset reveals that, in theory, relief changes can be retrieved for wavelengths as low as 5 km, and wavelength changes are possible to detect for relief as low as 0.5 km. In addition, the data attest that even in regions characterised by very slow exhumation rates (e.g. 0.03 km/Ma), changes in palaeo-topography can be successfully retrieved. Coupling of this dataset with a Fast Fourier Transform (FFT) algorithm to decompose complex 2D topography into sinusoidal functions allows a rapid and accurate estimation of the topographic perturbation and resulting thermochronological ages assuming steady-state exhumation. This coupled method was successfully implemented to (i) predict most promising sample sites for the estimation of palaeo-topography and (ii) correct exhumation rates derived from non-vertical age–elevation profiles.