ROTATION STATISTICS FOR GEOLOGIC DATA

Geologic data -- directions, orientations, ellipsoids, tensors, etc. -- are often geometric in nature. Analysis of such data requires methods beyond those taught in elementary statistics courses. In particular, rotation statistics is required for the analysis of three-dimensional orientational data such as foliation-lineation pairs, slickensides, and paleomagnetic rotations. In this presentation, we survey a variety of rotation statistics techniques and apply them to geological problems.

We describe a novel system for visualizing rotational data in three dimensions. In contrast to two-dimensional plots, which necessarily obscure relationships among rotational data, our plot has a better chance of revealing important trends such as clusters and outliers. The plot has an equal-volume property and thus represents densities accurately. We demonstrate Kamb contouring of rotational data.

We compare several methods for quantifying the mean, spread, and anisotropy of spread of a set of rotational data. We also summarize techniques for regression and cluster analysis. These tools are applied to paleomagnetic data from the Troodos ophiolite, Cyprus.

Finally, we describe hypothesis testing and the construction of confidence/credible regions. We compare bootstrapping and Markov chain Monte Carlo (MCMC) approaches. These techniques are applied to a foliation-lineation dataset from the western Idaho shear zone, USA.