Fracture mechanics rupture model of earthquakes and an estimate of ambient shear stress

Abstract

A model of the earthquake rupture process has been proposed in the light of fracture mechanics. In this model, the earthquake dislocation is not the elastic displacement on the faulting surface, rather it is an inelastic displacement at the tip of the crack. Every point on the crack surface always undergoes a process of stress rise from a low initial value, i.e. ambient shear stress τ o to the higher value and finally to the yielding strength during rupture. At the instant of fracture, a main dislocation at the tip of the crack generates a strong elastic wave radiating from the tip of the crack. Therefore the earthquake dislocation should be related to inelastic displacement at the tip of the crack, but not be related to elastic displacement on the crack surface. Thus, the resulting earthquake dislocation D is proportional to ambient shear stress τ o 2, not τ o . A set of relations between source parameters and τ o has been built. They are different from the equations usually used for estimating stress drop. Based on our rupture model and our scaling law model, two equations for estimating ambient shear stress from body wave magnitude m b, maximum spectral magnitude m f and seismic moment log( M o ) have been derived.