Physical interpretation of moment tensor and the energetics of shear faulting

Abstract

Moment tensor is a basic concept of source representation in seismology, established in the 1970s. On the basis of theoretical consideration to the equation of motion in continuum mechanics, we clarified the physical meaning of the Backus-Mulcahy moment tensor and derived a fundamental equation that the moment tensor of a seismic event is mathematically equivalent to the volume integral of coseismic static stress changes over the whole region. This equation provides new perspectives on the interaction between the inelastic source process and the elastic process in the surrounding region. As an example, we applied it to the energetics of shear faulting and obtained a quantitative relation between the work done for shear faulting and the static change in elastic strain energy in the surrounding region. With this energy equation, we elucidated the theoretical background of the Wallace-Bott hypothesis; that is, when the level of background tectonic stress is much higher than coseismic stress changes, the most probable orientation of slip on a given fault is parallel to the maximum resolved shear stress there in the sense of the efficiency of shear-strain energy release in the surrounding region.