The statistical analysis of orthogonal orientation data

For three-dimensional directional data consisting of a sample of axes ($X_{i}$) together with a corresponding sample of perpendicular axes ($Z_{i}$), a least-squares procedure is proposed for finding the mean X axis and the mean Z axis. The criterion of best-fit used takes into account the implicit interdependence of the X and Z orientations and therefore yields mean X and Z directions which are themselves orthogonal. The method is applicable to many varieties of geological data which are of orthogonal type, e.g., "paired" field measurements of fold axes and normals to bedding planes