Statistical Geomorphology of the Lunar Surface
When the lunar crater area density (number of craters per unit area) is contoured on the lunar surface, it is evident that lunar craters are not distributed at random. The terra-mare dichotomy is clearly indicated and, in addition, the terrae themselves display nesting and parallelism of the contours. A mathematical “nesting index” is defined, which varies from zero for a random set of contours to 1 for a perfect bull's eye. For the whole front face of the moon, the nesting index is as high as 0.90. When only the southern terrae are considered, the nesting index is as high as 0.83. Also, there are systematic relationships between the classes of craters (degree of erosion) and crater density. As a result of these observations, the following working hypothesis is proposed. Two independent erosional processes operate on the lunar surface. The first is continuous and reduces craters from class 1 to class 2 to finally class 3 and sometimes class 4. The second process is discontinuous and produces craters of class 5 and occasionally class 4.

Barring interference from the discontinuous process, a newly formed crater will remain in class 1 for the length of time necessary for the crater density of that area to increase by a value, k In practice k ranges from 6 to 24 craters per 58 × 103km2. It can be shown that such a process is described by a line of slope —1 when the logarithm of the percentage of class 1 craters is plotted versus the logarithm of the density of craters. The position along this line of slope —1 of any lunar area is defined as the geomorphic index. The distribution and location of this index suggest the presence of two types of processes of rejuvenation on the lunar surface. The first, and most evident, is mare flooding, which is able to completely bury the majority of craters of an area or reduce them to class 4 or 5. For the case of the maria it is likely that the geomorphologic indices are closely related to time indices, that is, geomorphologically younger maria were the most recent to be formed. The probable order of formation of the mare surfaces is presented.

The second process of rejuvenation operated on the terrae. It can be shown that rejuvenation progressively decreases as one goes from a mare shore toward the center of the terrae. The hypothesis is presented that mare-producing impacts rejuvenate the environs of the impact locus by seismic waves and ballistic sedimentation.

Rejuvenation can also explain the nesting indices of the crater density contours, previously described.