SCALED IMPACT SIGNATURES ON THE MOON - INVESTIGATING FRESH SIMPLE CRATER SHAPES
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 . 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: Head, J. W. (1975),The Moon, 12(3), 299-329. Craddock, R. A., & Howard, A. D. (2000), Journal of Geophysical Research: Planets, 105(E8), 20387-20401. Fassett, C. I., & Thomson, B. J. (2014), Journal of Geophysical Research: Planets, 119(10), 2255-2271.  Speyerer, E.J., et al., Nature 538.7624 (2016): 215.  Pike, R.J. Impact and explosion cratering: Planetary and terrestrial implications. 1977. Mahanti, P., Robinson, M. S., Humm, D. C., & Stopar, J. D. (2014), Icarus, 241, 114-129.