Topographical Features of the Lunar Surface Unveiled Through Spherical Geodesic Triangulation Analysis Method of DEM Roughness at Equal Spatial Scales

Abstract

This study introduces an innovative method using equal spherical geodesic triangulation to uniformly sample the digital elevation model (DEM) of the lunar surface, ensuring an even distribution of elevation data. Utilizing spherical spline fitting, we have proposed new methods for calculating slope angles and aspects. An equilateral triangular grid serves as the computational framework to compute the Hurst exponent at various spatial scales, elucidating the lunar surface's 2D spatial characteristics. Elevation statistics indicate that the relatively small areas of lunar maria dominate the peak values of the lunar elevation statistics. This phenomenon is attributed to the early tectonic processes associated with maria. At the kilometer scale, most lunar slopes angle ranges from $0°$ to $10°$. Meanwhile, at scales from kilometers to several kilometers, slope aspects predominantly exhibit a north–south (NS) orientation. However, this anisotropy is most likely an artefact resulting from satellite data acquisition and DEM processing. We computed 2D Hurst exponents at scales ranging from several kilometers to tens of kilometers. These Hurst exponents demonstrate high resolution in identifying ejecta boundaries of impact craters. These insights contribute to a more comprehensive understanding of the Moon's complex geological history and surface morphology.