Abstract
The distribution of depths of lunar craters can be predicted by a model which takes into account the formation, obliteration, filling, and isostatic readjustment of craters. These theoretical studies suggest more efficient ways of estimating the initial depth-diameter relationship, assuming that the deepest craters are the most recent. The estimated initial depth H( χ) of continental craters of diameter χ (larger than 15 km) is H( χ) = 1.0 χ 0.40 and for craters in the maria is H( χ) = 0.75 χ 0.50, where H( χ) and χ are in kilometers. As the difference is not significant, there is no reason to believe that many craters in the continents and maria have had different modes of origin. If the crater-forming and crater-filling rates are exponentially decreasing functions of time, and if isostatic readjustment of craters can be neglected, then the distribution of H( χ) − Y is a truncated Weibull distribution, where Y is the observed depth of a crater of diameter χ. This distribution gives good fits to empirical crater depth distributions based on extensive unpublished data of G. Fielder. The crater-filling mean lifetime is about 1.5 times as long on the continents, and 1.7 times as long on the maria, as the crater-forming mean lifetime. This implies that crater-filling mechanisms on the Moon were of longer duration than crater-forming mechanisms, especially on the maria. It is also possible to obtain some information about the underlying distribution of crater diameter χ. If the meteoroidal impact hypothesis were correct, this distribution would be an inverse power law with index γ>, and should be the same on continents and maria. From the data we estimate γ = 2.18 on the continents but γ = 2.66 on the maria. Because of very large uncertainties in the estimates this discrepancy is not significant. The available statistical data are still not adequate to establish the validity or otherwise of the impact hypothesis.
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