Oriented Odyssey of the lunar scars: Directional distribution of lunar craters

Abstract

We study the global spatial distribution of lunar impact craters using directional statistics on the sphere. Crater coordinates are mapped to unit vectors and modeled via mixtures of von Mises–Fisher (vMF) distributions. Model selection using information criteria supports a four-component vMF mixture, indicating clear multimodality in crater-density structure. A goodness-of-fit comparison finds no statistical evidence that a more general Kent model is needed for these data. Using the fitted spherical density, we construct low-density maps and identify candidate regions with comparatively reduced crater occurrence, with emphasis on polar latitudes relevant to future landing and volatile-prospecting missions. Our framework provides a reproducible, geometry-aware method for summarizing crater anisotropy and translating statistical density estimates into mission-planning layers.