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

Abstract

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.

Crustal evolution of the early earth: The role of major impacts

“….7 .8 FRACTION OF EARTH COVERED BY BASINS volume of water and sea level has dropped from 2 to 1 km average depth (short dashed line). Impacts which produced basins 1000 km across also produced rim relief on those basins in excess of 1 km, if lunar cratering is any guide (Pike, 1967). Therefore the highest basin rims were above sea level when basins covered only 25% of the Earth's surface.…”

Schroeter's ratios for Martian craters: Radar results

“…(Only the ratios with the probable error lesser than the magnitude of the ratios themselves are considered here; N = 11.) Pike (1967) demonstrated that for the fresh crater Tycho (88 km), the Schroeter's ratio equals 1.99, rather than 0.80 predicted on the basis of Baldwin's (1963) work. Taken together, the quoted results, all resting on telescopic evidence, indicated that the diameter-dependent.…”

“…Application of any procedure that purports to monitor the crater degradation trends requires the knowledge of the initial crater geometry. In the case of the fresh simple craters whose linear dimensions are isometrically related (Pike, 1967) this is not a serious obstacle. For the present, let us adopt as a working hypothesis the notion that Croft's (1978) results for lunar craters hold for craters on all planetary surfaces.…”

Central peaks in lunar craters

“…1971, Pike, 1967). On the other hand, in a hypervelocity impact event a tremendous compressional wave is produced.…”

“…The prediction is that, with time, the crater floor will rise and the rim will sink until the entire structure approaches the original ground level (Danes, 1970 andPike, 1967 …”