Spectral Analysis of the Morphology of Fresh Lunar Craters I: Rim Crest, Floor, and Rim Flank Outlines

The morphology of fresh lunar craters contains information about the physical properties of both the impactors and the lunar surface, and is therefore crucial to our knowledge of the impact cratering process. Spectral analysis is a powerful tool to study crater morphology, as it can reveal the topographic variation on different scales. In this study, we calculate the power spectral densities of the radial distance and elevation of the rim crest, floor, and rim flank outlines of fresh lunar craters. The resulting power spectral density can be decomposed into an average component and a natural variability component. For the average component, we derive the classic morphometric parameter-crater diameter relations that are consistent with previous studies. For the natural variability component, we find that in general the spectral power increases with wavelength, which can be fitted by a piecewise function with four breakpoints. Among the four breakpoints, the power of the third breakpoint (i.e., the degree-2 power) is of particular interest, as it determines the ellipticity of the outline. The power of the third breakpoint is found to have a diameter dependence with a peak at 20 km, which indicates that transitional craters are more elliptical than simple and complex craters. The diameter dependence of the power spectral density enables us to generate the synthetic outlines of a crater of a particular size, which can be used to develop a preliminary 3-dimensional shape model for fresh lunar craters that is useful for improving Monte Carlo modeling of cratered surfaces on the Moon.