学術雑誌論文 Genetic algorithm for fitting a mixed Bingham distribution to 3D orientations: a tool for the statistical and paleostress analyses of fracture orientations
混合ビンガム分布を三次元方向データにフィッティグする遺伝的アルゴリズム: 断裂系の統計解析と応力解析のための新しい方法

Yamaji, Atsushi

25 ( 1 )  , pp.72 - 83 , 2016-01 , wiley
ISSN:1038-4871
NII書誌ID(NCID):AA10848628
内容記述
Issue published online: 28 JAN 2016
The clustering of fracture orientations is important for tectonic studies and for geotechnical engineering. In this study, a real-coded genetic algorithm was adopted to fitting a mixed Bingham distribution to orientation data by maximizing the log-likelihood function of the distribution. The maximization is a difficult problem, because the function has multimodality and singularity. It was found that the algorithm was effective for this problem. Given the orientations of dilational fractures, the present method determines not only the stress axes and stress ratio of each of the fracture groups but also the maximum non-dimensionalized fluid pressure at the time of their formation. In addition, the software calculates the 95 % error ellipses of the concentration axes. The present method found that the orientations of ore veins of the Akenobe Mine, SW Japan, should be partitioned into three clusters. It is shown that two of the groups had distinctive Zn and Sn contents, and that the ore fluids had overpressures only slightly greater than the minimum principal stress at the time of the deposition of Zn- and Sn-rich veins.
混合ビンガム分布を最尤法で方向データにフィッティングする問題は,尤度関数が10次元を超える多次元の関数で,しかも多峰的関数であるために,非常に困難な問題である.今回開発した実数値遺伝的アルゴリズムは,この問題を効率的に解くことができる.岩脈群や鉱脈群に適用すると,各クラスターで3本の主応力軸と応力比が決まり,また,無次元化流体圧を制約することができる.認定すべきクラスター数もわかる.明延鉱山の鉱脈群に適用したところ,方向により3つのクラスターに分かれ,そのうち2つはZnが比較的豊富な鉱脈とSnが比較的豊富な鉱脈であった.つまり,応力の変化と鉱液の化学組成の変化が連動していた可能性がしめされた.
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http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/210377/1/iar.12135.pdf

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