Modern methods of analysis for three-dimensional orientational data

Structural geology studies commonly include data about orientations of objects in space. By “orientation” we mean not just a single direction, such as a foliation pole or the long axis of an ellipsoid, but a complete three-dimensional orientation of a body such as a foliation-lineation pair, a fold, an ellipsoid, etc. Over the past four decades, researchers in various fields have developed theory and algorithms for dealing with such data. In this paper, we explain how to apply orientation statistics to common geologic data types. We review plotting systems, measures of location and dispersion, inference (confidence/credible regions and hypothesis tests) for population means, and regression. We pay special attention to methods that work for small sample sizes and widely dispersed data. Our original contributions include a concept of Kamb contouring for orientations, a technique for handling anisotropy in confidence/credible regions, and large-scale numerical experiments on the performance of various inference methods. We conclude with a detailed study of foliation-lineations from the western Idaho shear zone, using statistical results to argue that the data are not consistent with a published model for them.