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Criticality of Rupture Dynamics in 3-D

Raul Madariaga, & Kim B. Olsen

Published December 2000, SCEC Contribution #529

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

Madariaga, R., & Olsen, K. B. (2000). Criticality of Rupture Dynamics in 3-D. Pure and Applied Geophysics, 157(11-12), 1981-2001. doi: 10.1007/PL00001071.