GArcmB

Tectonic Study Group

Kyoto University

Program Package ver. 1.2

The goodness of fit of a mixed Bingham distribution is evaluated by the function, L(X ), where X denotes the distribution. The best partition of orientation data into clusters is denoted by the maximal point of this function. However, it is a tough problem to find the point, because the function has a number of local maxima. To make matters worse, the maxima point have to be searched for in a high dimensional space. The value of this function arrives at the global maximum of L(X ) or at its vicinity in a successful run, but at a local maximum of the function in an unsuccessful run.

• Yamaji, A., Sato, K. and Tonai, S. (2010) Stochastic modeling for the stress inversion of vein orientations: Paleostress analysis of Pliocene epithermal veins in southwestern Kyushu, Japan. Journal of Structural Geology 32, 1137-1146, doi:10.1016/j.jsg.2010.07.001 [Manuscript (Open File)].
• Yamaji, A. and Sato, K. (2011) Clustering of fracture orientations using a mixed Bingham distribution and its application to paleostress analysis from dike or vein orientations. Journal of Structural Geology 33, 1148-1157, doi:10.1016/j.jsg.2011.05.006 [Manuscript (Open File)].
• Yamaji, A. (2016) Genetic algorithm for fitting a mixed Bingham distribution to 3D orientations: a tool for the statistical and paleostress analyses of fracture orientations. Island Arc 25, 72-83, doi:10.1111/iar.12135 [This article is available freely from the journal's homepage].

Run1 Run5 (AVI animations)

The author thanks his colleagues and students for the comments on the early versions of the software. Publication of the software was financially supported by JSPS KAKENHI Grant Number 15H02141.

Atsushi Yamaji
Division of Earth and Planetary Sciences, Kyoto University

Examples of successful and unsuccessful runs (Delta g = 100)

Explanation

GArcmB is the freeware for the fuzzy clustering of 3D orientations and for the paleostress analysis of dilational fractures such as dikes and mineral veins. The software searches for the mixed Bingham distribution that best fits a set of orientation data through the real coded genetic algorithm. The number of clusters and that of stresses are evaluated by using Bayesian information criterion. The software runs on 64-bit operating systems (Windows, Mac and Linux).

Run2 Run3 Run4 (AVI animations)