Geometric similitude of lunar and terrestrial craters.

Application of an elementary technique of dimensional analysis, that of testing for geometric similitude, suggests an impact genesis for most lunar craters. Geometrically similar phenomena fulfill four requirements: (1) log-log plots of paired descriptive variables are linear, (2) slopes of these plots equal ratios of the dimensions of the two variables, (3) intercepts of the plots are the same and (4) phenomena belong to the same general taxonomic group. Five topographic criteria are used to test lunar and terrestrial craters for geometric similitude: the variation of rim diameter with (1) interior depth, (2) exterior rim height, (3) exterior rim width and (4) rim crest circularity, and (5) variation of exterior rim height with crater depth. By all criteria, fresh bowl-shaped lunar craters between 10 m and 20 km in diameter are geometrically similar to fresh terrestrial meteorite craters and craters produced by chemical and nuclear explosives at shallow depths of burial. Most lunar craters exceeding 10-20 km in diameter fulfill only the last three criteria of similitude.