Chrono-morphologic surface- a parameter to quantify craters' heterogeneity and its applicability on Mars

Abstract

On any solid planetary surface, crater populations in any given region show variations in their geomorphology related to their initial formation conditions and to their post-formation modifications. This ubiqutous and random distribution of craters in time and space defines a universal cratering characteristic- the craters heterogeneity, that is present regardless of the existence of an atmosphere and related constraints on craters evolution. On Mars, of which chronology is calibrated upon an airless body- the Moon- evidence shows that craters modifications are related to the environmental constraints over main geologic eras; nonetheless, an overall evaluation of the heterogeneity remains elusive. Here, we develop a new mathematical construct, the “chrono-morphologic surface” that considers the ensemble of craters in a surface unit or region as a whole, including the size of craters, their subsequent modifications, and area upon which craters spread to estimate the heterogeneity of craters in relation to their entropic state. Crater heterogeneity parameter, that is calculated using this construct is checked for consistency and syncronicity at different locations, at different spatial scales, and for a variety of geologic and morphologic units across Mars. Regardless of the initial constraints of craters formation and evolution, we observed a natural logarithmic decrease of heterogeneity values across Mars that is also consistent at all spatial scales and in agreement with the existing chrono-stratigraphies that we analyzed. We suggest that this technique provides a more accurate determination of the evolution stages of Martian craters and, as such, has the potential to provide a new framework upon which interpretations of Mars' past geological and environmental history can be revisited.