Topographic Diffusion Revisited: Small Crater Lifetime on the Moon and Implications for Volatile Exploration

Crater degradation and erosion control the lifetime of craters in the meter-to-kilometer diameter range on the lunar surface. A consequence of this crater degradation process is that meter-scale craters survive for a comparatively short time on the lunar surface in geologic terms. Here, we derive crater lifetimes for craters of <∼200 m in diameter by analyzing existing functional expressions for crater population equilibrium and production. These lifetimes allow us to constrain the topographic degradation needed at different scales to explain when craters become undetectable on equilibrium surfaces. We show how topographic degradation can be treated as a process of anomalous (scale-dependent) topographic diffusion and find large differences in effective diffusivities at different scales, consistent with a wide range of evidence besides equilibrium behavior. Understanding the range of morphology of meter-scale craters is particularly relevant for future exploration of the lunar surface with rovers. We illustrate expectations for the d/D distribution of small lunar craters on surfaces with negligible regional-scale slopes. Our results imply that if volatiles are found in preserved <4 m craters and were delivered after crater formation, the volatiles must have been emplaced in the last ∼50 Ma. Given the rates of surface evolution we infer, the most likely emplacement time for any volatiles discovered at or near the surface in the interior of fresh, small craters may be much younger than this upper limit.