Studying the Global Spatial Randomness of Impact Craters on Mercury, Venus, and the Moon With Geodesic Neighborhood Relationships

Impact crater records on planetary surfaces are often analyzed for their spatial randomness. Generalized approaches such as the mean second closest neighbor distance (M2CND) and standard deviation of adjacent area (SDAA) are available via a software tool but do not take the influence of the planetary curvature into account in the current implementation. As a result, the measurements are affected by map distortion effects and can lead to wrong interpretations. This is particularly critical for investigations of global data sets as the level of distortion typically increases with increasing distance from the map projection center. Therefore, we present geodesic solutions to the M2CND and SDAA statistics that can be implemented in future software tools. We apply the improved methods to conduct spatial randomness analyses on global crater data sets on Mercury, Venus, and the Moon and compare the results to known crater population variations and surface evolution scenarios. On Mercury, we find that the emplacement of smooth plain deposits strongly contributed to a global clustering of craters and that a random distribution of Mercury's basins is not rejected. On Venus, the randomness analyses show that craters are largely randomly distributed across all sizes but where local nonrandom distributions due to lower crater densities in regions of recent volcanic activity may appear. On the Moon, the global clustering of craters is more pronounced than on Mercury due to mare volcanism and the Orientale impact event. Furthermore, a random distribution of lunar basins is not rejected.Plain Language Summary: The arrangement of craters on a planetary surface can be random or nonrandom. A nonrandom arrangement, such as clustered or ordered, can indicate geologic or cratering‐related processes. There are generalized approaches to quantify the arrangement of craters available via a software tool. The randomness calculations in this tool rely on the spatial relationships between craters and are determined in a two‐dimensional map projection. This is problematic because two‐dimensional representations do not take the influence of a curved planetary surface into account. Thus, measuring the spatial arrangement of craters is prone to errors. We revise the given approaches by implementing improved computations and measure the global spatial arrangement of craters on Mercury, Venus, and the Moon. On Mercury, we observe that the smooth plains' emplacement largely causes global clustering and that the distribution of basins cannot be distinguished from a random population. On Venus, craters across all sizes are largely in a random arrangement. However, nonrandomly distributed populations may occur due to local volcanic activity. On the Moon, we observe that the emplacement of lunar maria and the Orientale impact strongly influenced the global clustering of craters. Furthermore, the arrangement of lunar basins is similar to a random distribution.Key Points: We improve approaches to quantify the spatial randomness of impact craters by applying geodesic methods. We apply these methods to analyze the global spatial randomness of impact crater populations on Mercury, Venus, and the Moon. We use the results to investigate known crater population variations and surface evolution scenarios on Mercury, Venus, and the Moon.Deutsche Forschungsgemeinschaft (DFG) http://dx.doi.org/10.13039/501100001659Deutsches Zentrum für Luft‐ und Raumfahrt (DLR) http://dx.doi.org/10.13039/50110000294