Use of equivalency in estimating the historical size distribution of impact craters |
| |
Authors: | WW Mullins |
| |
Institution: | Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, USA |
| |
Abstract: | A previous analysis of a stochastic model of lunar-type impact cratering is extended to utilize geological age data by defining a more general statistic to be the number of equivalent whole craters of original diameter di and age ≤t in an observational area A; each crater is taken to be equivalent to the fraction of its rim (or area) that is in A and not occluded by later craters. By integration of a new gain-loss differential equation, a generalization of the previous basic equation is obtained that relates the expected value to the process functions specifying the size distribution and flux of craters (primary or secondary) as they form. The results are specialized to the plausible case in which the cratered body can be subdivided into geological provinces of increasing ages t1, t2, …, ti … and the size probability distribution can be approximated as constant within each of the periods ti+1 - ti. It is shown that use of the permits, in principle, a reconstruction of the historical values of the process functions and correctly compensates for the effect of overlap by removing the false bias favoring large craters that results from the usual method of crater counting. Possible generalizations of the gain-loss equation are indicated. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|