Inversion of detrital zircon data to constrain spatially varying erosion rates

Landscapes evolve through surface processes that are often transient in space and time. To understand the underlying geomorphic processes, one must assess how erosion rates vary spatially. This can be done using provenance analysis. Here, we introduce a formal inversion method to derive erosion patterns using detrital zircon age data as fingerprints. Zircons are omnipresent in Earth’s crust and contain information about the time since (re)crystallization in their U/Th-Pb ratio. For each geological unit having undergone a specific tectonic or magmatic history, one can find a unique age-frequency signature. Hence, erosion and sedimentation of grains originating from diverse source areas lead to a mix of the varying age-frequency signatures in sediments found at the outlet of a catchment. Considering that the age signal is not altered during erosion-transportation-deposition events, and given that recent technological advances enable precise dating of large amounts of grains, U/Th-Pb zircon ages provide an appropriate fingerprinting tool. Our inversion approach relies on the least-squares method with a priori information and model covariance to deal with non-uniqueness. We show with synthetic and natural examples that we are able to retrieve erosion rate patterns of a catchment when the age distribution for each geological unit is well known. Furthermore, relying on the nested form of catchments and their subcatchments, we demonstrate that adding samples taken at the outlet of subcatchments improves the estimation of erosion rate patterns. We conclude that the least squares inverse model applied on detrital zircon data has great potential for investigating erosion rates.