Earthquakes as multiscale dynamic ruptures with heterogeneous fracture surface energy

摘要

We propose a model of the wide-scale growth of dynamic rupture during an earthquake, based on our multiscale simulation of a planar crack in a three-dimensional homogeneous elastic space. A simple slip-weakening law governs the fracture/friction processes, and its characteristic parameters, slip-weakening distance and fracture surface energy, have multiscale heterogeneous distributions. We consider a set of randomly distributed circular patches, whose diameter is proportional to the fracture surface energy. Each patch represents an asperity between irregular fault surfaces, and the size-number relation of the patches obeys power law statistics. We assess rupture propagation from a small instability using a boundary integral equation method with a renormalization technique. Although most events stop shortly after their initiation, some grow, triggering neighboring patches of similar size. Small and large events show statistically self-similar properties of rupture growth and stop spontaneously without requiring a special stopping mechanism. The rupture velocity locally exceeds the shear wave speed but globally remains subshear speed due to the increase of the average fracture energy as the rupture grows. The relation between size and frequency of events is a power law, which is explained by the triggering probability between patches. As a consequence of statistically self-similar random triggering growth, we observe a distinct “main phase” in seismic waves similar to those of natural earthquakes, but we cannot estimate the final size of the event from the initial part of the seismic waves. If this is true for the real earthquakes, predicting the size of a future earthquake would be quite difficult.