Criticality of rupture dynamics in 3-D

We study the propagation of seismic ruptures along a fault surface using a fourth-order finite difference program. When prestress is uniform, rupture propagation is simple but presents essential differences with the circular self-similar shear crack models of Kostrov. The best known is that rupture can only start from a finite initial patch (or asperity). The other is that the rupture front becomes elongated in the in-plant direction. Finally, if the initial stress is sufficiently high, the rupture front in the in-plane direction becomes super-shear and the rupture front develops a couple of "ears" in the in-plane direction. We show that we can understand these features in terms of single nondimensional parameter kappa that is roughly the ratio of available strain energy to energy release rate. For low values of kappa rupture does not occur because Griffith's criterion is not satisfied. A bifurcation occurs when kappa is larger than a certain critical value, kappa (c). For even larger values of kappa rupture jumps to super-shear speeds. We then carefully study spontaneous rupture propagation along a long strike-slip fault and along a rectangular asperity. As for the simple uniform fault, we observe three regimes: no rupture for subcritical values of kappa, sub-shear speeds for a narrow range of supercritical values of kappa, and super-shear speeds for kappa > 1.3 kappa (c). Thus, there seems to be a certain universality in the behavior of seismic ruptures.