Self‐Similar Initial Morphology of Lunar Simple Craters With Implications for Formation and Degradation Process

Abstract Impact craters dominate the lunar surface and morphology‐based dating typically assumes that their initial profiles correspond to the average shape of fresh craters. However, the selected fresh craters may have experienced degradation, and their relationships with impact conditions remain poorly understood. In this study, we present 1,349 numerical simulations of simple crater formations across a wide range of impact conditions (impact velocities of 6–20 km/s and projectile radii of 100–1,000 m). The results show that shapes of simple craters (<15 km in diameter) are self‐similar when described by dimensionless coordinates (normalized by crater radius and depth); however, the depth‐to‐diameter ratio is not constant, revealing a key deviation from the simplification assumed in previous studies. Instead, the depth‐to‐diameter ratio fluctuates within defined, size‐dependent bounds (e.g., to for above impact conditions). We further find that the derived crater diameters are consistent with π‐scaling laws established from laboratory sand experiments, and the crater depths and volumes are notably underestimated by these scaling laws. Additionally, the inherent variations in initial crater morphology due to varied impact conditions introduce an uncertainty of approximately ±17% when estimating ages based on crater morphology degradation. Our results also indicate that if the average crater profile derived from these numerical simulations is used as the initial profile, the resulting crater ages differ by 28% from those obtained using observed profiles of fresh craters. These findings provide crucial guidance for refining techniques to estimate crater ages from their degradation state, thereby offering critical constraints on planetary surface geological processes.