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Small Crater Degradation at the Apollo Landing Sites - Characterizing Differences in Degradation Rates

Introduction: Small lunar craters (SLC; 30 m ≤ D ≤ 300 m) form [1] and modify the local regolith and topography. Smaller craters, which form more frequently than larger craters, also typically experience higher degradation rates [2, 3, 4]. As a surface ages, smaller craters (size range 40 ≤ D ≤ 80 m analyzed here) form a steady state population such that the craters disappear at the same rate as others of the same diameter are formed [5, 6]. At equilibrium, by expressing a very small change in the cumulative population (N ) as a product of the slope of the cumulative population vs. d D and the small change in d D , the average degradation rate for the population can be inferred [7]. Here, N is a function of and is the number of craters than a given D. The degradation rate for SLCs is found to vary over the crater lifetime [7, 8] such that stages of crater evolution (from fresh to obliterated) occur over progressively longer intervals. It is hypothesized that differences in the target properties can significantly affect degradation rate. In this work, we compare depth-to-diameter ratios ( d D ) and crater degradation computed from d D statistics at six Apollo landing sites to identify effects of evolving target properties and possible impact/seismic disturbances (inferred from existing morphology). Methods: SLCs were first identified manually from NAC ortho-photo mosaics, the digital terrain model (DTM) and a derived slope map for the six sites: Apollo 11 (A11), Apollo 12 (A12), Apollo 14 (A14), Apollo 15 (A15), Apollo 16 (A16) and Apollo 17 (A17). Flat geologic units were then chosen (Figure 1) with slopes (< 5◦) to minimize slope effects from pre-existing target topography on the slow impact-induced degradation process. Crater size-frequency distributions (CSFD) were then used to identify a common size range (40m80m) exhibiting equilibrium. Depth (d) and diameter (D) measurements for this size range were extracted automatically [9] from NAC DTMs followed by computation of d D . The degradation rate and fractional evolution time (P0) are obtained from d D . P0 is a ratio of the number of craters with d D ≤ 0.1 and total number of craters ( d D ≥ 0.04), expressed as a percentage (Table 1). Under the first order assumption that existing/observed concentration (population density) above a particular d D is proportional to the fractional evolution time spent up to at that d D , this is equal to the fraction of total evolution time that the equilibrium population spends with d D higher than 0.1. Considering that d D ≥ 0.1 indicates fresher craters, this represents the fractional time spent by the population at equilibrium as fresh craters. Figure 1: SLCs at flat areas within the Apollo sites