Analysis of Variance for Directions and Axes

Many data in structural geology consist of directions and axes. Different directional measurements are associated with different objects (foliation, lineation, strain-markers) and different events and times. Structural direction interrelate in a complex way. They depend on various external parameters such as paleostress and material properties. This contribution provides some ideas how to integrate these complex data into meaningful stochastic models, which allow to analyze the dependence of directions statistically. The central idea is the generalization of multivariate analysis of variance and multi-ple regression to directions and symmetric directions (e.g. axes). The generalization is based on a general distribution family for directions introduced by Beran and generalized linear models. The directions are rather described by their distribution than by their expected value as the analysis of variance for real variable does. The model works for 2D-directions, 2D-axes 3D-directions, 3D-axes and 3D-orientations. Possible independent variables are categorical and real values, physical tensors and further geometric objects such as directions and axis