Crater Equilibrium State Characterization given Crater Production from a Single Power Law

Abstract

We generalize the crater equilibrium concept, a terminal state on a cratered surface where the balance of crater production and erasure apparently limits the crater population from further growth. Assuming the crater production consists of a single power law, our model identifies four classes of crater equilibrium. The first class is the most common state, where the power-law slope for the equilibrium size–frequency distribution is independent of the crater production slope power. The second class arises when there is efficient degradation of larger craters by smaller crater production, which results in dependence of the crater equilibrium slope power on the crater production slope power. The third class is another common state when a shallow production function causes a crater equilibrium state with a similarly shallow slope. This class results from the enhanced degradation of smaller craters by larger crater production. The fourth class is a combination of the second and third classes. We further compare the concept of geometric saturation, which has been widely used to quantify the level of crater equilibrium, and that of cookie-cutter saturation. We present a crucial update to the cookie-cutter saturation concept that brings models closer to the reality of crater accumulation over a range of sizes than the geometric saturation concept. Our model offers simpler analytical formulae for cookie-cutter saturation and proposes this concept as a more meaningful reference to argue the crater equilibrium level. Our work and earlier studies confirm the consistency of the crater equilibrium concepts, enabling deeper interpretations of crater equilibrium.