Spherical Orientation Data:Tensors

Abstract

This text first introduced us to the study of univariate observations, those documented by a single magnitude value. Fortunately, in their initial training, geologists mostly deal with measurements that are univariate and scalar, such as rock density or a chemical abundance. Our discussions progressed to bivariate observations, described by two scalar values (x-y), and then to multivariate observations, each of which required three or more values for its description. From Chapter 9 onward, complexity was incremented with a new dimension, quite literally. Orientation became an issue in sampling. Although it is disregarded in almost all introductory statistics courses, even the novice earth scientist must become adept at managing orientation data, usually without formal study. Our introduction to orientation data concerned axes,directions and unit vectors. Orientation distribution replaced our introductory obsession with frequency distributions along a line (Chaps. 2–8). Although true vectors possess an associated magnitude, the arguments mostly concern the orientation distribution.