Paleostress analysis of heterogeneous fault-slip data: The Gauss method

We describe the Gauss method for reconstructing paleostress tensors from heterogeneous fault-slip data. We define compatibility measure and compatibility function, which verify the compatibility of a given stress tensor with observed fault-slip data. In order to constrain inversion results to mechanically acceptable solutions, we additionally consider the ratio between the normal and shear stress on the fault plane, since it is assumed that the results of paleostress inversion should be in agreement with the Amontonʹs Law. The optimal solution for stress tensors that activated the observed faults is found by searching for the global and highest local maxima of the object function F defined as a sum of compatibility functions for all fault-slip data. We verify the reliability of the method both by mathematical means and by numerical tests, and analyse its effectiveness in the case of large dispersion of angular misfit between the direction of slip and shear stress along the faults.