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-plane 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 k that is roughly the ratio of available strain energy to energy release rate. For low values of k rupture does not occur because Griffith’s criterion is not satisfied. A bifurcation occurs when k is larger than a certain critical value, kc. For even larger values of k 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 k, sub-shear speeds for a narrow range of supercritical values of k, and super-shear speeds for k\1.3kc. Thus, there seems to be a certain universality in the behavior of seismic ruptures.