SCALED IMPACT SIGNATURES ON THE MOON - INVESTIGATING FRESH SIMPLE CRATER SHAPES

Fresh impact crater shapes are references for quantifying morphological changes observed in older craters due to impacts and surface processes over geologic time [1,2,3]. However, a reference fresh crater shape is not readily available for craters of various sizes. Craters formed and identified during recent/ ongoing lunar missions [4] are not large enough to make reliable topographic measurements, and only a small percentage of existing craters are very fresh. Quantifying measurable changes in crater topography is thus dependent on models for fresh impact crater shapes and scaling rules. Morphological features in impact craters scale with size (D; diameter), and often expressed as power laws relating measurements of crater features (e.g., depth, rim-height) to D [5]. While the features are derived from the shape, the full crater shape (elevation profile) cannot be inferred from the features, which are sampled only at specific locations on the crater profile.

In this work, we show that with some approximations and within size limits of 800 m to 5 km, the overall crater shape profile scales with diameter and can be predicted/ estimated, advancing our knowledge of the initial reference crater shape. We obtain this approximation by using a standardized crater profile representation using Chebyshev coefficients [6]. The individual Chebyshev coefficients each represent a component of the overall crater shape, and most lunar craters can be mathematically approximated with only the first 17 Chebyshev coefficients. We also analyze the scaling behavior at critical points (center, mid-wall, rim) on the crater elevation shape profile and investigate differences between existing scaling laws and those obtained from predicted fresh crater shapes.

References: [1]Head, J. W. (1975),The Moon, 12(3), 299-329. [2]Craddock, R. A., & Howard, A. D. (2000), Journal of Geophysical Research: Planets, 105(E8), 20387-20401.[3] Fassett, C. I., & Thomson, B. J. (2014), Journal of Geophysical Research: Planets, 119(10), 2255-2271. [4] Speyerer, E.J., et al., Nature 538.7624 (2016): 215. [5] Pike, R.J. Impact and explosion cratering: Planetary and terrestrial implications. 1977. [6]Mahanti, P., Robinson, M. S., Humm, D. C., & Stopar, J. D. (2014), Icarus, 241, 114-129.