DOI: 10.4231/93zk-pv90
title: Online repository for 2D power spectral analysis of fresh lunar impact craters

description: &lt;p&gt;The morphology of fresh lunar craters provides important clues about how craters of different sizes form, and is used as a baseline for understanding how craters evolve over time. Topographic spectral analysis is a powerful tool to study the morphology of lunar craters, as it can quantify the topographic variation of individual crater morphologic features at different length scales. In our work, we aim to calculate the 2D power spectral densities of surface elevations of three morphologic features from 104 fresh lunar craters larger than 1 km in diameter, including the continuous ejecta, wall, and floor.&lt;/p&gt;

&lt;p&gt;This data repository includes: (1) a spreadsheet of all the crater features (1. crater_2d_psd_results.xlsx), (2) shape files of all the crater features (2. shape_files.zip), (3) surface elevations of all the crater features (3. elevation_matrices.zip), (4) power spectral densities of all the crater features (4. power_spectral_densities.zip), (5) python scripts to reconstruct a matrix with random noises with a Gaussian distribution (5. python_gaussian_reconstruction.zip), and (6) python scripts to generate shape models of synthetic craters (6. python_synthetic_craters.zip). Detailed descriptions of the uploaded files are shown below: &lt;/p&gt;

&lt;p&gt;1. A spreadsheet of all the crater features, including the crater name, diameter, age, location, and the coefficients obtained when fitting the power spectral density.&lt;/p&gt;

&lt;p&gt;2. Shape files of all the crater features. 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. The continuous ejecta is enclosed by the rim flank and rim crest outlines, the wall is enclosed by the rim crest and floor outlines, and the floor is enclosed by the floor outline.&lt;/p&gt;

&lt;p&gt;3. Surface elevations of all the crater features. The surface elevations of the continuous ejecta, wall, and floor are all defined in a matrix. In the elevation matrices of the continuous ejecta and wall, the x-axis is the arc angle of each pixel, and the y-axis is the radial distance between the pixel and the crater center. In the elevation matrix of the floor, the x- and y-axes are the distances between the pixel and the crater center along the east-west and north-south directions.&lt;/p&gt;

&lt;p&gt;4. Power spectral densities of all the crater features. The power spectral density is defined as &lt;em&gt;P&lt;/em&gt;=[&lt;em&gt;F&lt;/em&gt;(&lt;i&gt;h&lt;/i&gt;))]^2/&lt;i&gt;S&lt;/i&gt;, where &lt;em&gt;P&lt;/em&gt; is the power spectral density, &lt;em&gt;F&lt;/em&gt; denotes the discrete Fourier transform, &lt;em&gt;S&lt;/em&gt; is the surface area of the feature, and &lt;i&gt;h&lt;/i&gt; represents the elevation matrix. The power spectral densities of the continuous ejecta, wall, and floor of fresh lunar craters are documented here.&lt;/p&gt;

&lt;p&gt;5. Python scripts to reconstruct a matrix with random noises with a Gaussian distribution. To validate the broad applicability of using power spectral density to reconstruct the original elevation matrix, we present an example where a completely random matrix of Gaussian noises is reconstructed from its power spectral density. The difference between the original and reconstructed matrices is extremely small (&lt;10^(-13)), showing that the original matrix is successfully reconstructed from its power spectral density.&lt;/p&gt;

&lt;p&gt;6. Python scripts to generate shape models of synthetic craters. 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 wavenumber 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 morphologic features, whose shape only depends on its crater diameter.&lt;/p&gt;
description: This repository includes the spreadsheet, shape files, surface elevations, and power spectral densities of all the selected crater units as well as python scripts to generate synthetic craters and to reconstruct Gaussian random noises.