A non-extensive statistics of the fault-population at the Valles Marineris extensional province, Mars.

A non extensive statistical physics approach is formulated and tested for the fault length distribution in the Valles Marineris extensional province, Mars. The approach is composed of the following parts: (1) the Tsallis entropy Sq (defined as Sq = kB(1 − ∑ i = 1Wpiq)/(q − 1), (2) maximization of the Tsallis entropy under appropriate constraints, (3) derivation of the cumulative distribution function (CDF) of the fault length population. In testing the model a non-extensive q parameter equal to 1.10 for independent, non-interacting faults and q = 1.75 for linked faults are estimated. The latter supports the conclusion that the fault system in the Valles Marineris extensional province, Mars, is a sub-extensive one and verifies with statistical physics terms the geological criteria introduced by Schultz (2000) to classify the faults in independent and linked, respectively.

Research Highlights
► Analysis of the faults' length distribution in Mars.
► Applicability of the universal non extensive entropy principle.
► Demonstration of subextensivity of Mars' faults system.
► Nonextensive q-statistics origin of fault classification in linked and independent subsets.