Planetary surface dating from crater size–frequency distribution measurements: Interpretation of small-area and low number counts

Abstract

Recent interest in the crater-dating of smaller and younger features of planetary surfaces has provoked questions about how far the method's validity extends. This work addresses the problem theoretically over a range of measurement scenarios, predicting the consequent statistical measurement uncertainty, and suggesting it should be the first criterion to determine usability. We map out the relationship between crater measurement area, observable crater diameters, measured age uncertainty, and the actual age of surface structures. Constraints on the range of possible measured ages arising from particular combinations of counting area and observable crater diameter are presented in a generalised form, with the intent to provide a reference for the choice and suitability for measurements of surfaces from different epochs. Additionally, several perhaps non-obvious aspects of evaluation of the chronology model, namely, the influence of the limits of the considered crater diameter interval, of varying the counting area at fixed crater density, of varying the counting area perimeter for a buffered count of a linear feature, and the logarithmic behaviour of the time-resolving ability of the method are described and demonstrated, likewise with the intent to support well-informed choices for actual crater-dating measurements.