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

<p>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 real fresh lunar craters, and we also make synthetic fresh lunar craters with these three outlines. This data repository includes: (1) shape files of all the crater outlines (.geojson), (2) power spectral densities of all the crater outlines (.txt and .pdf), and (3) python scripts (.py) to generate the synthetic crater outlines. Detailed descriptions of the uploaded files are shown below: </p>

<p>1. Shape files of all the crater outlines. Making use of the elevation data of the Moon, the rim crest, floor, and rim flank outlines of 104 fresh craters are vectorized. The rim crest is vectorized by tracking the highest elevations along the rim, the floor is traced as  the sharp transition between the steep crater wall and the flat crater floor, and the rim flank is outlined where the elevation of the ejecta reaches the background value.</p>

<p>2. Power spectral densities of all the crater outlines. The power spectral density is defined as <em>P</em>=[<em>F</em>(<em>r</em>(<em>θ</em>))]2/<em>L</em>, where <em>P</em> is the power that can be expanded either in the frequency domain or in the wavelength domain, <em>F</em> denotes the discrete Fourier transform, <em>L</em> is the length of the signal and is equal to 2π in this study as an outline should have a closed planar geometry, <em>r</em> represents radial distance of the outline, and <em>θ </em>is the arc angle of the outline. The power spectral densities of the rim crest, floor, and rim flank outlines of fresh lunar craters are shown here.</p>

<p>3. Python scripts to generate the synthetic crater outlines. In Monte Carlo landscape simulations on the evolution of lunar cratered terrains, the shapes of fresh craters are used as the initial condition. The nature of the Monte Carlo method requires that a large number of synthetic craters with random shapes need to be generated. In order for a landscape evolution model to be useful for understanding the topography of cratered terrains, each fresh synthetic crater should have similar properties in the wavelength domain as real craters, with some randomness in its shape in the spatial domain. A synthetic fresh lunar crater can thus be generated based on the power spectral densities of its crater outlines, whose shape only depends on its crater diameter.</p>