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Distribution of slopes on a cratered planetary surface: Theory and preliminary applications

1969; American Geophysical Union; Volume: 74; Issue: 22 Linguagem: Inglês

10.1029/jb074i022p05253

2156-2202

Allan H. Marcus,

Aeolian processes and effects

The distribution of slopes over any finite span on a surface excavated by primary impact craters is derived from a representation of the surface as a ‘moving average’ of impact events. The cumulants are always positive, and they are large for typical mare crater densities. In some cases the distribution can be approximated by a rapidly convergent Gram-Charlier type A series. The slope distribution has a much higher peak near zero slope and also has much heavier tails than a Gaussian distribution with the same variance. Under some conditions the slopes have approximately a symmetric stable distribution law with characteristic exponent one unit smaller than the crater diameter population index. Observations of slopes in Mare Cognitum are in good agreement with theory, if the validity of the photoclinometric data and the model can be accepted.