Statistics
Scientific paper
Sep 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008dps....40.0905r&link_type=abstract
American Astronomical Society, DPS meeting #40, #9.05; Bulletin of the American Astronomical Society, Vol. 40, p.400
Statistics
Scientific paper
The problem of when crater saturation and equilibrium conditions exist and how these are affected by the shape of the impactor population (which produced the craters) has been a long standing issue, particularly with regard to interpreting the lunar cratering record. In this work, I present a modern approach to this old problem, using a three-dimensional, cratered terrain evolution model, which includes: (1) a general solution to the crater size scaling laws, containing both gravity and strength terms; (2) a general solution to the ejecta velocity scaling laws, used to compute ejecta production and distribution under conditions of both gravity and strength; (3) the effects of crater super-positioning, with a dynamic crater-size range of three orders of magnitude (1024); (4) downslope regolith motion and scarp degradation, when unstable slope conditions exist; and (5) the effects of impact-induced 'seismic shaking' on existing crater morphology and regolith distribution. Crater statistics are computed automatically after each model time step, along with displays for shaded relief, topography, and ejecta distribution. This modeling shows that where (on an R-plot) the condition of crater saturation or equilibrium occurs is highly dependant upon the shape of the impactor population. In general, steeply sloped (< -2 cumulative power law) impactor populations produce classic 'empirical saturation' conditions at equilibrium, while shallow sloped (> -2 cumulative power law) impactor populations produce a 'quasi equilibrium' condition below the classic empirical saturation levels. When the impactor population varies in slope as a function of size, the resulting crater population will continue to reflect the shape of the impactor population, even after saturation / equilibrium conditions have been achieved. This feature allows the shape of an impactor population to be determined, even after final saturation / equilibrium crater counts have been reached.
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