Minimum effective area for high resolution crater counting of martian terrains

The acquisition of high-resolution imagery for the surface of Mars has enabled mapping of spatially limited (order of <103 km2) landforms such as alluvial fans, deltas, and lacustrine deposits that are targets for exploration due to their association with liquid water. It is essential for our understanding of the planet's geologic and climate history therefore to place these landforms within the global chronostratigraphic context. Here, we analyze both the statistical variability in the cratering pattern as well as the influence of small crater resurfacing on crater counting small landforms. We identified and counted craters (diameter (D) > 200 m) on four type terrains using Mars Reconnaissance Orbiter (MRO) Context Camera (CTX) imagery that span the Noachian, Hesperian, and Amazonian epochs. The counts from each location include a region covering 10,000 km2, ten 1000 km2 subsets of that larger area, and approximately one hundred 100 km2 samples. The data demonstrate significant variation in the crater size frequency and derived model ages across a single terrain type for the 100 km2 samples. The crater size frequency at this area scale varies across a single, uniform geologic unit by up to a factor of 2-3 on the four different terrains. At 1000 km2, the local pattern variations that are relevant at the 100 km2 scale become less important and the age variations are tighter. In all four terrain cases, the 10,000 km2 and 1000 km2 samples capture distinct crater populations (km-sized craters) that formed before and after resurfacing event(s). However, due to the relatively high mean distance between km-sized craters, the 100 km2 size area samples more commonly than not exclude a statistically significant sample at the kilometer size range, masking important information about the pre-resurfacing history of the terrain. We therefore suggest that due to the effect of pattern variability in cratering over 100 km2 and the susceptibility of smaller craters to resurfacing, crater counts derived from small area samples are suspect to major uncertainties.