Power spectral densities of the floor, rim crest, and rim flank outlines of fresh lunar craters

The morphology of fresh lunar craters encodes information about the physical properties of the lunar surface and is crucial to our understanding of the impact cratering process. Early studies of lunar crater morphology were conducted in the spatial domain by measuring the morphometric parameters, such as crater depth and rim height. However, the simple crater morphology models derived from these early studies made the assumption that the crater shape is axisymmetric, with well-defined features, and therefore they failed to capture the detailed texture of a cratered surface, especially one dominated by complex craters. In comparison to the studies in the spatial domain, spectral analysis in the frequency or wavelength domain is a more powerful tool to study the crater morphology, as it can reveal trends in the topographic variation of craters at different scales that are not as readily apparent in the spatial domain.

In this study, we calculate and present the power spectral densities (PSDs) of the floor, rim crest, and rim flank outlines of fresh lunar craters by using the latest topographic data of the Moon. The obtained PSD is first decomposed into an average component with a wavelength of positive infinity (i.e., a frequency of zero) and noise components with wavelengths of 1, 1/2, …, 1/N of the outline perimeter. Based on the average component, we derive the average depth and rim height of the crater, which agree well with those measured in the spatial domain. For the noise components, our results show that their power increases with wavelength, which can be fit by a piecewise function with four breakpoints. Among the four breakpoints, the third breakpoint at the wavelength of half of the outline perimeter is of particular interest, as its power determines the ellipticity of the outline.

Comparing the PSDs of the three outlines for different sized craters, we find that: (1) the power of the third breakpoint of the rim crest has a clear dependence on the crater diameter, where a distinct smaller slope is found for craters larger than the simple-to-complex transition of 20 km, indicating that complex craters are less elliptical than simple craters; and that (2) the power of the third breakpoint of the rim crest is lower than those of the floor and rim flank, which indicates that the rim crest is less elliptical than the floor and rim flank.

In the end, we demonstrate how to synthesize the floor, rim crest, and rim flank outlines of a fresh lunar crater based on their PSDs, which can contribute to developing a more realistic, three-dimensional shape model for fresh lunar craters in a landscape evolution model.