Stress inversion meets plasticity theory: A review of the theories of fault-slip analysis from the perspective of the deviatoric stress-strain space

Abstract

The mechanical behavior of materials is not affected by our choice of a coordinate system. Thus, the description of the behavior should not be affected by this choice. This is known as the principle of coordinate invariance, and is important not only for plasticity theory but for theoretical investigations in structural geology. The deviatoric stress-strain space, which fulfills the principle, is shown to be useful for the formulation of stress inversion. Problems in the inversion schemes of fault data are transformed into geometrical problems so that we can solve the problems using geometrical interpretations. In addition, the formulation gives the good basis for defining the classes of dissimilarities between reduced stress tensors that are the solutions of the inversion. We redefine the classes, here, from the standpoint of probability. It is demonstrated finally that the violation of the principle spoils the accuracy and resolution of the inversion.