Use of equivalency in estimating the historical size distribution of impact craters

Details Use of equivalency in estimating the historical size distribution of impact craters Use of equivalency in estimating the historical size distribution of impact craters

Mar 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978icar...33..624m&link_type=abstract

Icarus, vol. 33, Mar. 1978, p. 624-629.

Mathematics

Probability

Cratering, Equivalence, Impact Damage, Meteorite Craters, Size Determination, Chronology, Mathematical Models, Probability Distribution Functions, Stochastic Processes, Craters, Abundance, Meteoroid Impacts, Impacts, Ages, Crater Formation, Distribution, History, Size Distribution

Scientific paper

A previous analysis of a stochastic model dealing specifically with compensation for the effect of crater overlap is extended to allow for the incorporation of certain geological age data in calculations for reconstructing the history of impact cratering on an astronomical body from the present generally overlapping pattern of craters. The extension is obtained by deriving a gain-loss differential equation. It is demonstrated that the false bias favoring large craters, which arises from the usual method of counting craters in an overlapping crater field, is properly compensated or removed by counting equivalent craters on an area or arc basis. The results are shown to apply most readily to the case where the cratered body can be subdivided into several geological provinces of increasing ages t1, t2, . . ., tk, such that the k-th province contains no craters older than tk, and the probability distribution regulating the size of craters of age t is the same in all provinces and can be approximated as independent of time within each of the periods t1, t2 t1, . . ., tk+1 - t sub k.

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