Can spatial statistics help decipher impact crater saturation?

Abstract

Impact crater saturation equilibrium is a state where a surface is so densely cratered that a new crater cannot form without removing older craters and the observed crater density is in (quasi-)equilibrium. Whether densely cratered surfaces throughout the solar system are saturated for large, kilometer-sized craters has been debated for decades. This work explores if spatial statistics can provide insight if these crater distributions are in saturation equilibrium. The supposition is that crater distributions become more spatially uniform (more evenly spaced) as they reach saturation (Squyres et al.). A numerical simulation of crater saturation is combined with observations of cratered terrains throughout the solar system to assess the utility of using spatial statistics. The numerical simulations examine spatial statistics and saturation equilibrium for crater distributions for various input population size-frequency distribution (SFD) slopes, along with a range in the effective crater erasure size, effectiveness of smaller craters erasing the rims of larger craters, and the amount of rim needed to recognize a crater. Simulations show that saturated terrains do become more spatially uniform, and that the degree of uniformity appears to be most dependent on the input SFD slope. When simulation results are compared to observed crater distributions, I find that large, kilometer-sized craters on densely cratered terrains throughout the solar system are likely in saturation equilibrium.