Uniform distribution of points on a hypersphere for improving the resolution of stress tensor inversion

Abstract

Exhaustive grid search is a preferred method to determine the optimal solutions for stress tensor inversion because the object function can have multiple peaks. This study developed a uniform computational grid of normalised stress tensors. We designed the grid by using the reformulated parameter space, where normalised stress tensors correspond to points on the five-dimensional unit sphere. A computer-based procedure enabled us to arrange points on the sphere at approximately constant intervals. As a result, the new grid includes a greater number of triaxial stresses than axial stresses and their principal axes are uniformly distributed in physical space. An analysis of artificial fault-slip data using the multiple inverse method showed that the utilisation of the uniform grid enhanced the resolution in distinguishing stress tensors.