SPHERICAL-LINEAR REGRESSION FOR SPATIAL FABRIC ANALYSIS

A new method of spherical-linear regression is presented that allows modeling of the trend of rock fabrics in geographic space. A single formulation permits various trend models with different degrees of freedom and different numbers of parameters estimated. The most restrictive model allows estimation of a constant trend, i.e. no spatial variability in fabric orientation. One relaxation step provides a way to account for a great circle path of mean fabric orientation in space. Further relaxation allows the evaluation of a small circle trend model. A more complex and flexible trend model is available, however its geological applicability is questionable. Unlike existing methods, this new approach doesn't require non-bijective transformations that lead to problems with interpretation of modeling results. This method was used to analyze a dataset of foliations, beddings, fold axes and lineations from an Early Proterozoic metamorphic belt in the Baltic shield. The technique allowed the quantification of fine scale variations in the mean fabric orientation of the region, which were used to develop a new deformation model for this area.