Statistical analysis of crater
distribution compared to geologic units on Mars
Fox, Odysseusand Kraal, Erin, 2014,
Statistical analysis of crater distribution compared to geologic
units on Mars: Geological Society of America Abstracts with
Programs, Northeastern Section - 49th Annual Meeting Lancaster,
PA, (23–25 March), v. 46, no. 2.
This study examines the spatial pattern of impact craters within
defined geologic units on Mars. Impact cratering on a planet is a
stochastic process, evenly distributing craters around the planet.
Therefore the spatial pattern within a given age range should follow
a random Poisson distribution. The Χ2 goodness of fit analysis was
used to determine if impact craters on similarly aged surfaces of
Mars are, in fact, randomly distributed.
Using a published geological map, three formations (the Ridged
Plains Material (Hprg) formation, the Cratered Plateau Material
(Nplc) formation and the Cratered Plains Material (Apc) formation)
with different relative ages were evaluated. Within each age
formation, crater density was measured using a collective minimum
surface area of 106 km2. In order to achieve this area, multiple
areas of the same age/formation were sometimes combined together.
For each formation the area was divided into 100 cells of equal size
(1.7° dimensions measuring 100 km per side) and the number of
craters in each bin was determined using a published database of
Martian craters.
This observed crater distribution was compared to the generated
Poisson distribution for expected crater impacts. The Χ2 Goodness of
Fit analysis determined whether the observed data deviate from the
Poisson expectations. Only the crater distribution in the younger
Apc formation does not exceed the Χ2 Goodness of Fit Test at the
P< 0.05 level (α= one d.f.) In this analysis, the Null Hypothesis
(i.e., random distribution of impact craters) is rejected for the
two older geological formations (Hprg and Nplc) but it cannot be
rejected for the younger Apc geological formation. It is possible
that as the younger formation ages and accumulates additional
impacts, a non-random pattern of impact craters may emerge, or the
distribution may be associated with crater preservation rather than
formation. To test this new hypothesis we will analyze a younger
aged formation, Smooth Plains Material (Aps).
Statistical analysis of crater
distribution compared to geologic units on Mars