Circular statistics for the analysis of directional geological data

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  • Arai Hiroyoshi
    Department of Earth Sciences, School of Education, Waseda University

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  • 地質学における方向データ解析法：円周データの統計学
  • チシツガク ニ オケル ホウコウ データ カイセキホウ : エンシュウ データ ノ トウケイガク

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Abstract

Geological data such as the strike of bedding, paleocurrent directions, paleomagnetic directions, and the trend of mineral lineations are directional data defined by an angle from a reference direction. The main characteristic of such data is circularity in any reference direction (i.e. 0°=360°), which creates problems when analyzing the data statistically. In this regard, only directional statistics are adequate for dealing with directional data. This paper introduces the fundamental theory of circular statistics, a form of directional statistics that is restricted to data on a circumference, and presents practical methods with which to analyze circular data, including their graphical representation, descriptive statistics, the characteristics of circular uniform and von Mises distributions, tests of goodness-of-fit, and single- and multi-sample statistical tests. In addition, statistical software is considered with which to analyze circular data.

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