Relative dating using cratering distribution
For example a surface may be covered by a few hundred meters of mobile sand dunes; the numbers of craters of diameter D and depth d would give a mean characteristic age of topographic features of the scale of D,d.
Smaller craters in mobile dunes would disappear faster and have lower mean ages.
An isochron is defined as a size distribution of all craters created, as described above, over a specified period of years, such as 100 My or 1 Gy.
The diagram we use to plot craters combines ease of use, maximum sensitivity to possible crater losses at particular sizes, and mathematical convenience (since, by mathematical coincidence, it has the same slope as a plot of cumulative number of craters vs. This diagram divides the D range into log intervals with base /2. Figure 1 gives a schematic representation of the shape of a well-preserved, or A production, size distribution on this type of plot.
Much later, the surface may be exhumed, as documented in various cases by Malin and Edgett.
In an ideal case, such a surface might then show vestiges of the degraded original craters (indicating the duration of exposure of the first surface) and a second population of fresh, small, sharp-rimmed craters formed since the recent exhumation event.
The first papers on diameter distributions of craters, meteoroids, and asteroids, fitted those distributions to power laws of the form N = k D and typically found b ~ -2 for lunar craters.
Departures from the -2 power law were regarded as diagnostic.
Tanaka (1986, Table 2) defined crater density limits to the Amazonian, Hesperian, and Noachian relative-age eras, based on the previous work of Scott and Carr (1978) and Condit (1978), for the purpose of stratigraphic mapping of Mars.
That work parallels the development of terrestrial geology, in defining stratigraphy and relative time intervals long before the absolute time intervals could be measured.
In this sense, the derived age is a size-dependent Acrater retention [email protected] B the survival time of craters of given size.
It is not quite a formation age in the sense of the lava flow age, but conveys tremendous information about the erosion/deposition/resurfacing environment of Mars.