Distances for the solutions of stress tensor inversion in relation to misfit angles that accompany the solutions.

The misfit angles between observed and theoretical slip directions are important in evaluating the reliability of the solution to a stress tensor inversion. The distance between stress tensors is also essential for evaluating the resolution of a method of separating stresses from heterogeneous fault-slip data. Here, we define ‘angular stress distance’ for this purpose. This new method has the attribute of improved distance measurements compared with existing methods. The value of angular stress distance is equivalent to a number of important properties. First, the distance between the correct and optimal stresses for a data set approximates the mean misfit angle. Secondly, when we evaluate the dispersion of reduced stress tensors obtained via a bootstrap or other resampling technique, the value of the dispersion evaluated with the mean distance of the tensors from the optimal solution is approximately equal to the noise level of the data. Thirdly, the distance is equal to the Lode angle difference of the stresses if they have common principal orientations. We demonstrate that stresses cannot share common principal axes if their distance is greater than a certain threshold value. The relationships among the distances that have been proposed for reduced stress tensors are also discussed. [ABSTRACT FROM AUTHOR]