Schroeter's rule and the modification of lunar crater impact morphology

The 1∶1 correspondence of crater rim volume to true crater volume allegedly observed for many lunar craters has been explained previously by the theories of explosive meteoritic impact. In fact, the equality occurs too infrequently to be of genetic significance. The ratio characteristically is about 0.4 to 0.8 for small, freshly formed lunar and terrestrial craters, but it is well over 1.0 in older and larger lunar craters. Most of the moon's craters are of explosive impact origin and acquire a specific, predictable shape governed by the law of allometric growth. Fresh crater dimensions and volumes are related by expressions of the form y = axb. Up to a diameter of 10 to 20 km, craters are stable landforms. Larger craters deform isostatically and are further modified by extrusive activity. Application of an allometric fresh crater shape model to Tycho suggests that even the most youthful appearing large lunar craters do not long retain their initial rim and true crater volumes, but that they begin to deform soon after impact.