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

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.