Planetary surface dating from crater size-frequency distribution measurements: Spatial randomness and clustering

We describe a quantitative procedure to measure the degree of clustering in an observed crater population relative to a series of randomly distributed populations. We split the population by according to crater size to be able to identify clustering at different scales, and find that a clustering analysis based on the mean 2nd-closest neighbour distance measure more closely corresponds to visual interpretations of the spatial configuration than the mean closest neighbour distance. Standard deviation of adjacent area is found in certain cases to be an even more sensitive measure. The technique is demonstrated for two sites on Mars. We were able to make use of a case where the spatial distribution was 'less clustered than random' to reveal the transition between a crater population superimposed on a lava flow and that belonging to an underlying unit. In general, this type of analysis may give a better insight into the post-formation modification of studied units, enabling a more precise classification of which sizes of craters derive from the original accumulation population and which from areas resurfaced by later modification events, consequentially improving the accuracy of dating resurfacing events. Clustering analysis is thus an additional tool for understanding the structure of a crater population and the effects causing an observed population to differ from an ideal one. (C) 2011 Elsevier Inc. All rights reserved.