Determination of regional stress tensors from fault-slip data

Stress tensors are regularly determined from fault-slip and/or earthquake focal mechanism data in structural geology and seismotectonics. The inverse problem is non-linear, unless empirical rules of rupture and friction are employed. All the methods used to date to determine the stress tensor to this non-linear inverse problem are of a local nature, and thus cannot guarantee that the global optimal stress tensor has been obtained. We apply a hybrid global optimization method to find the global optimal stress tensor. Although the inverse problem is non-linear, the effect of non-linearity on the biases of stress tensors has not been investigated. We will examine the biases of inverted stress tensors and their effect on the principal orientations of stress and the shape parameter of the stress ellipsoid. The biases of stress parameters have been shown to be comparable with the estimated stress parameters numerically. We compare the accuracy of the four stress parameters, with and without taking the errors in fault planes into account. If the errors in fault planes are not taken into account, the stress parameters are too optimistically estimated by a factor of 4 to 9 in the example. We will also mathematically reformulate the assumption that the directions of maximum shear stress represent those of slips on fault planes as two functionally independent but equivalent constraints of equality. The new formulation is computationally more effective and provides a correct method for calculating the accuracy of stress parameters.