Age dating crater counting
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.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.
The problem is that we now count from D = 11 m up to multi-km sizes and the size distribution is much steeper at small sizes (power laws with slopes up to -3.____).(Even the major review of Martian cratering studies in 1992 by Strom et al.did not include discussion of crater counts below diameters of a few km, although some Viking images resolved craters of a few hundred meters in size.) Upper ~ 4 km above the Amazonian/Hesperian boundary, and 16 km for early Hesperian to early Noachian.This has been identified with the mix of asteroidal and cometary interplanetary fragments, and such craters are called A primary craters, connoting that they originate from cosmic debris falling from the sky at high speed.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.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.
Malin and Edgett (2001, 2003), thinking in terms of dating the underlying process, asserted that such processes render Martian crater counts more or less useless for dating.
This plots crater counts relative to an artificial -2 power law distribution (N = k D.
It was introduced when the counters were dealing primarily with craters larger than 1 km, which roughly fit a -2 power law (more accurately, it is a -1.80 power law).
As discussed by Hartmann (1966) the crater numbers can date the actual formation age of a surface in an ideal case, such as a broad lava flow which forms a one-time eruptive event.
The flow accumulates craters and the crater numbers date the time of formation.
On the contrary, such a situation can give extremely valuable estimates of the timescale of the exhumation processes, not to mention the timescale of exposure of the original underlying surface (which in turn is a lower limit to its age).