Towards accurate modelling of rock surface exposure dating using luminescence to estimate post-exposure erosion rate

Abstract

Depth-dependent luminescence in the top few millimetres of rock surface emerges as a potential tool to estimate rock surface exposure age and post-exposure erosion rate. It relies on the principle that the luminescence depth profile (LDP) propagates deeper with the time of sunlight exposure and moves to shallower depth with the erosion rate. The propagation of LDP is generally assumed to follow the first-order kinetic (FOK) model, except for a few recent studies. The FOK model predicts an exponential decay of infrared stimulated luminescence (IRSL) signal with light exposure time, which rarely corroborates experimental observation; IRSL signal decay is much slower than exponential decay. The faster decay of IRSL, predicted by the FOK model, results in faster propagation of LDP and thus always underestimates the exposure age and translates into a higher erosion rate. Interestingly, the slower-than-exponential decay of the IRSL signal can be better explained by general order kinetics (GOK). Thus, recent studies on rock surface luminescence dating have employed the GOK model. However, the GOK model is yet to be explored to predict post-exposure erosion rates. Here, we apply the GOK model and theoretically demonstrate the impact of the order of kinetics on the calibration and propagation of LDP in the presence of erosion and how the LDP's transient to steady state transition depends on the order of kinetics. We have performed a series of synthetic tests to assess the impact of selecting an incorrect model on the prediction of erosion rate. Finally, using the revised rate equation, the erosion rates are recalculated for natural samples (data available in the literature: Lehmann et al. (2019b)) and the impact of GOK on the predicted erosion rate is discussed.