FREQUENCY DISTRIBUTION MODELING OF DEPTH-DIAMETER RATIOS OF SMALL (D < 200 M) LUNAR CRATERS

Small lunar craters (SLC; diameter < 200 m) are the dominant impact features on the lunar surface and also the least studied historically. Images from recent lunar missions (e.g. Lunar Reconnaissance Orbiter (LRO), Kaguya) [1,2] are now providing information that will lead to a deeper understanding of the impact cratering processes of small craters.

The final size of craters correlates to impactor size, velocity and the target material of the lunar surface. As such, for small craters, the depths are shallow as found from recent studies and hence their structure records the regolith character (depth (d), material) at the target location. Morphology of SLC is critical to our understanding of the regolith because such craters are relatively rapidly degraded and have a transient existence in a geologic time-scale. A recent study [3] with crater diameters (D) in the range 20 m to 200 m shows that the cluster density of observations shrink as depth-to-diameter (d/D) ratios decrease. If the representative crater dataset conforms to the true crater-size frequency distribution then the frequency distribution (specifically the cumulative distribution function (CDF)) can lead to an understanding of the degradation rate for SLCs as exemplified in another recent study [4]. In this work we obtain the CDF for the Apollo lunar landing sites for small craters and also examine the relationship of CDF to slope for the craters. LROC Narrow Angle Camera (NAC) DEMs are used for this analysis to obtain values of d, D, and slope.

The probability distribution function (PDF) for d/D in not expected to be uniform but a bell-shaped distribution. Consequently, the CDF for such a distribution will be of sigmoid nature and thus can be expressed as a smooth generalized logistic function (GLF). This CDF model can be fitted by regression and the CDF parameters can provide interesting insights to the degradation process. We contest, that unlike arbitrary empirical models, the GLF model proposed here better describes the inherent dynamics of the crater population modification.

References:

[1] Robinson, M. S., et al., Space Science Reviews 150.1-4 (2010): 81-124.

[2] Haruyama, Junichi, et al., Earth Planets and Space 60.4 (2008): 243.

[3] Mahanti, P., et al. LPSC Abstract#1584, 2014.

[4] Basilevsky, A. T., et al., Planetary and Space Science 92 (2014): 77-87.