Does Mars Have a Pristine, -2 Cumulative Power Law Distribution for Craters >5 Km in Diameter?

Introduction. Crater densities have been instrumental in determining relative ages of surfaces on Mars and other cratered planetary bodies. Fundamental to this technique has been the cumulative bombardment of the surface over time of projectiles supplied from the population of Mars-crossing asteroids and comets. Diameters of craters are a function of impact energy determined by the velocity and mass of the projectiles [e.g., 1]. Accumulation of craters over time eventually results in a statistically defined crater size-frequency production function (PF). For larger crater diameters, larger surfaces and greater time spans are needed to accrue sufficient craters to precisely define the PF. For craters > 5 km in diameter on Mars, this requirement generally limits meaningful counts to surfaces Early Amazonian and older and covering > 10 to 10 km, depending on crater density. Results for the form of the PF range significantly, particularly in the ~2 to 20 km diameter size range for intermediate age surfaces on Mars. Results by Tanaka [2] suggested a -2.0 cumulative PF power-law slope between 1 and 5 km diameter and a -1.8 slope between 5 and 16 km diameter. The Hartmann PF [3] as calculated from his lunar PF by Ivanov [1] yields a slope of -1.72 for the 1 to 32 km diameter range. The Neukum PF [3] shows a much smaller slope of ~-1.2 in the ~6 to 14 km size range, steepening at larger and smaller diameters. At larger diameters, the Neukum PF steepens to ~-2.5 and the Hartmann to -2.2 [1]. Frey [4] finds a slope of -2 for combined large craters and quasi-circular depressions inferred to be craters at diameters >25 km; the slope in this case might be related to saturation. These discrepancies result in significant uncertainty in the interpretation of relative ages for a host of surfaces and geologic units. Complicating these results is the relative degree to which crater obliteration processes may have affected the data used to define the PF. Crater counts of Vastitas units. Geologic mapping of the northern plains of Mars has defined the boundaries of two widespread, contemporaneous units tentatively named the Vastitas marginal and interior units [56]. Possibly the two units represent different morphologic manifestations of the same deposits. This is a revision of the previous global mapping, for which the units were variously mapped as members of the Vastitas Borealis and Arcadia Formations [7]. The new map proposes that the base of the Amazonian Period now be defined by the timing of formation of the Vastitas units. These units have been suggested to be the result of a plains-filling ocean [e.g., 8]. However, morphologies within the unit, including thumbprint terrain, sinuous valleys with medial ridges, and polygonal fractures, indicate that the units have been heavily modified, in association with or soon following their formation [e.g., 5]. Crater counts for the Vastitas units have been performed by merging the present version of the crater database of Barlow [9] with the mapping. We include counts of pristine only and all craters (Figure 1, Table 1). The non-pristine craters are the heavily modified ghost craters that are nearly rimless, flat-floored, and lack preserved ejecta morphologies [10]. We find that the pristine crater distribution follows a –2 power law slope between 5 and 16 km diameter (Table 1). The slope is not constant but steepens slightly with increasing diameter. Werner et al. [11] find even steeper distributions (~-2.2 to -2.3) for counts within parts of the Vastitas units where polygonal terrain is present. The general consistency of the crater counts across varying elevation and latitude ranges that we have tabulated indicates that the Vastitas units essentially reflect the same distribution and relative age throughout.