Relative dating using cratering distribution dating karlek
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.
Indeed, Hartmann et al (2001) found just this situation in the Terra Meridiani hematite-rich area, which they identified as a very ancient surface recently exhumed within the last few tens of My, because of the paucity of small, sharp-rimmed, fresh craters -- an interpretation which appears consistent with observations from the 2004 Opportunity rover, which landed in this same general area on a sparsely cratered plain and found sulfate-rich sediments apparently eroding and leaving small, spherical hematite concretions which weathered out of the sediments as they eroded.
In general, however, in dating Martian units, we look for simpler situations where a relatively homogenous stratigraphic unit is identified, and which appears not to be contaminated by secondary-ejecta impact craters from any single, nearby, large fresh primary impact crater.
Another example is exhumation, which is common on Mars (Malin and Edgett 2000, 2001).
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.
For example, if a certain region has had some erosive episode that removed all craters between 125 m and 500 m in size, the log-differential plot would show a dramatic downturn in that size interval, but he cumulative plot would merely flatten out.
The cumulative plot produces an artificial smoothing of the data, which looks good, but comes at the expense of actual information-display about the data.
For example, bin divisions include 500 m, 707 m, 1 km, 1.4 km, 2 km, 2.8 km, and so on. In the text below, we will refer to three A branches of this size distribution.
Historically, the first branch recognized was the shallow branch, at diameters above about 1-2 km, recognized from craters counted on telescopic photos of the moon.We assume that in such a case, a gradual accumulation of primary impact craters and globally-averaged (or regionally-averaged) secondary ejecta craters will have built up a characteristic diameter distribution shape, sometimes called the "crater production function." Usually we count all visible craters and test to see if the size distribution fits the so-called A crater production function B the size distribution previously measured for accumulated primary and secondary impact craters, globally averaged in the absence of erosion/deposition processes.