The equilibrium size-frequency distribution of small craters reveals the effects of distal ejecta on lunar landscape morphology

Abstract

Small craters of the lunar maria are observed to be in a state of equilibrium, in which the rate of production of new craters is, on average, equal to the rate of destruction of old craters. Crater counts of multiple lunar terrains over decades consistently show that the equilibrium cumulative size-frequency distribution (SFD) per unit area of small craters of radius > is proportional #$ , and that the total crater density is a few percent of so-called geometric saturation, which is the maximum theoretical packing density of circular features. While it has long been known that the primary crater destruction mechanism for these small craters is steady diffusive degradation, there are few quantitative constraints on the processes that determine the degradation rate of meter to kilometer scale lunar surface features. Here we combine analytical modeling with a Monte Carlo landscape evolution code known as the Cratered Terrain Evolution Model to place constraints on which processes control the observed equilibrium size-frequency distribution for small craters. We find that the impacts by small distal ejecta fragments, distributed in spatially heterogeneous rays, is the largest contributor to the diffusive degradation which controls the equilibrium SFD of small craters. Other degradation or crater removal mechanisms, such cookie cutting, ejecta burial, seismic shaking, and micrometeoroid bombardment, likely contribute very little to the diffusive topographic degradation of the lunar maria at the meter scale and larger.

Thickness of Lunar Mare Basalts: New Results Based on Modeling the Degradation of Partially Buried Craters

“…Fassett and Thomson () investigated 13,657 small (0.8 ≤ D ≤ 5 km), unburied craters on lunar maria and determined κ 0 to be 5.5 m 2 /Myr, which is close to our value. The diameter dependence of topographic diffusivity has also been strongly supported by the study of mare crater degradation (0.8 ≤ D ≤ 5 km) where larger craters were found to have larger topographic diffusivities (Fassett et al, ), and the modeling of topographic degradation of craters ( D ≤ 100 m) at the Apollo 15 landing site where smaller craters were thought to have smaller topographic diffusivities (Minton et al, ). The partially buried craters used in this study cover a larger diameter range (3.7 ≤ D ≤ 45.3 km), which strongly supports the diameter dependence of the diffusivity that both we and they found.…”

“…The diameter dependence of topographic diffusivity has a strong theoretical basis (e.g., Howard, 2007;Minton et al, 2019;Soderblom, 1970;Xie et al, 2017). Soderblom (1970) was the first to investigate the crater degradation process by modeling the downslope movement of crater ejecta due to micrometeoroid bombardment.…”

Crater-ray formation through mutual collisions of hypervelocity-impact induced ejecta particles

“…The nature of the rays has been studied for a long time, and the origin of the brightness of the rays is fairly understood (e.g., Hawke et al, 2004). Another remarkable feature of crater rays, the spatial non-uniformity, is recently paid attention as a geologic process such that the spatially heterogeneous rays determine the rate of degradation of small craters (Minton et al, 2019). However, the mechanism of non-uniformity of crater-rays remains an unsolved problem; there are only a few studies investigating the mechanism for the generation of non-uniformities of the rays such as high-velocity detonation products in explosion cratering experiments analogous to the impact-induced vapor (Andrews, 1977), interaction of shock waves with old craters (Shuvalov, 2012), pattern formation through mutual collisions in granular media (Kadono et al, 2015), and, effect of the topography around the impact point (Sabuwala et al, 2018).…”

Degradation of Small Simple and Large Complex Lunar Craters: Not a Simple Scale Dependence

“…When the CSFD of crater populations in equilibrium is compared to a function of crater production (e.g., Neukum, 1983; Neukum et al, 2001), the obtained cumulative crater frequencies (Crater Analysis Techniques Working Group, 1979) typically do not follow a function of crater production but a power law of the form where a is a coefficient constant and b is the equilibrium slope. Lunar surface investigations suggest that the slope for populations of small simple craters ( D < 1 km) in equilibrium is relatively constant at b ~ − 2 (e.g., Gault, 1970; Hartmann, 1984; Hirabayashi et al, 2017; Minton et al, 2019; van der Bogert et al, 2017; Xiao & Werner, 2015).…”

“…It has been suggested that the slope of the production CSFD would also be maintained in equilibrium for production CSFDs that have both steep and shallow branches, such as is seen in the D > 20 km population of craters of the ancient lunar highlands (Chapman & McKinnon 1986; Richardson, 2009). However, Minton et al (2019) showed that even in the case of the steep sloped D < 100 m crater population of the mare, the equilibrium parameters a and b have a complicated dependence on how new craters of different sizes contribute to the degradation of old craters via process like distal secondary formation, and also on and how the visibility of craters to a human crater counter depends on size and accumulated degradation. These processes are poorly constrained for D > 20 km scale craters, and thus whether or not the lunar highlands are in a state of equilibrium and what an equilibrium CSFD looks like for the highlands remain open questions.…”