Dependence of earthquake stress drop on critical slip‐weakening distance

Abstract

Numerical simulations are conducted to investigate the dependence of the static stress drop of earthquakes on the critical slip‐weakening distance. A fault model in a two‐dimensional elastic medium is used, in which a locked zone (asperity) is assumed to exist between creeping zones. The presence of such a zone is commonly assumed for plate boundaries that have relatively low seismic coupling. Shear stress is concentrated at the edges of the locked zone and seismic rupture occurs when the strain energy release by rupture extension becomes sufficiently large to overcome the fracture energy. The static stress drop is calculated by taking the ratio of the average seismic slip to the length of seismic slip zone for the simulated earthquakes in the model, using various values for the normal stress applied to the fault and the characteristic slip distance of a rate‐ and state‐dependent friction law. The simulation results indicate that the static stress drop is proportional to the square root of the product of the critical slip‐weakening distance and the normal stress, when the seismic rupture starts near an edge of the locked zone. In contrast, when the seismic rupture starts near the center of the locked zone, the static stress drop increases linearly with normal stress and is independent of the critical slip‐weakening distance. These simulation results may explain the relatively small depth dependence, as well as the large scatter, in observations of the static stress drop.