How to promote earthquake ruptures: different nucleation strategies in a dynamic model with slip–weakening friction

Abstract

The introduction of the linear slip–weakening friction law permits the solution of the elasto–dynamic equation for a rupture which develops on a fault, by removing the singularity in the components of stress tensor, thereby ensuring a finite energy flux at the crack tip. With this governing model, largely used by seismologists, it is possible to simulate a single earthquake event but, in absence of remote tectonic loading, it requires the introduction of an artificial procedure to initiate the rupture, i.e, to reach the failure stress point. In this paper, by studying the dynamic rupture propagation and the solutions on the fault and on the free surface, we systematically compare three conceptually and algorithmically different nucleation strategies widely adopted in the literature: the imposition of an initially constant rupture speed, the introduction of a shear stress asperity, and the perturbation to the initial particle velocity field. Our results show that, contrarily to supershear ruptures which tend to “forget” their origins, subshear ruptures are quite sensitive to the adopted nucleation procedure, which can bias the runaway rupture. We confirm that that the most gradual transition from imposed nucleation and spontaneous propagation is obtained by initially forcing the rupture to expand at a properly chosen, constant speed (0.75 times the Rayleigh speed). We also numerically demonstrate that a valid alternative to this strategy is an appropriately smoothed, elliptical shear stress asperity. Moreover, we evaluate the optimal size of the nucleation patch where the procedure is applied; our simulations indicate that its size has to equal the critical distance of Day (1982) in case of supershear ruptures and to exceed it in case of subshear ruptures.