Cosmogenic nuclide concentrations in episodically eroding surfaces: Theoretical results

The buildup of cosmogenic nuclides in an eroding surface can be used to infer erosion rates and exposure ages. This situation is often modelled by assuming that the erosion rate is constant in time. In many cases, however, the erosion is episodic: surface denudation occurs by the spalling off of slabs of rock at discrete times. We consider a stochastic model of such exfoliation processes, and compute the expected behavior of the cosmogenic nuclide concentration. We also consider a nonstochastic model, in which the exfoliation events occur at regularly spaced intervals. These two models represent extreme end members of the episodic spallation scenarios: in the first, the spallation events are uncorrelated in time, while in the second they are tightly correlated. Understanding how the nuclide concentration is related to the timing and the magnitude of these events is important in making geologic inferences.