STATISTICAL ANALYSIS OF CRATER DISTRIBUTION COMPARED TO GEOLOGIC UNITS ON MARS

This study examines the spatial pattern of impact craters within defined geologic units on Mars. Impact cratering on a planet is a stochastic process, evenly distributing craters around the planet. Therefore the spatial pattern within a given age range should follow a random Poisson distribution. The Χ² goodness of fit analysis was used to determine if impact craters on similarly aged surfaces of Mars are, in fact, randomly distributed.

Using a published geological map, three formations (the Ridged Plains Material (Hprg) formation, the Cratered Plateau Material (Nplc) formation and the Cratered Plains Material (Apc) formation) with different relative ages were evaluated. Within each age formation, crater density was measured using a collective minimum surface area of 10⁶ km². In order to achieve this area, multiple areas of the same age/formation were sometimes combined together. For each formation the area was divided into 100 cells of equal size (1.7° dimensions measuring 100 km per side) and the number of craters in each bin was determined using a published database of Martian craters.

This observed crater distribution was compared to the generated Poisson distribution for expected crater impacts. The Χ² Goodness of Fit analysis determined whether the observed data deviate from the Poisson expectations. Only the crater distribution in the younger Apc formation does not exceed the Χ² Goodness of Fit Test at the P< 0.05 level (α= one d.f.) In this analysis, the Null Hypothesis (i.e., random distribution of impact craters) is rejected for the two older geological formations (Hprg and Nplc) but it cannot be rejected for the younger Apc geological formation. It is possible that as the younger formation ages and accumulates additional impacts, a non-random pattern of impact craters may emerge, or the distribution may be associated with crater preservation rather than formation. To test this new hypothesis we will analyze a younger aged formation, Smooth Plains Material (Aps).