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Rupture Dynamics in 3-D: a review

Raul Madariaga, Sophie Peyrat, & Kim B. Olsen

Published 2001, SCEC Contribution #534

We review some recent results on the propagation of seismic ruptures along a planar fault surface subject to a friction law that contains a finite length scale and therefore has a well defined fracture energy flow. For this study we use the new fourth-order finite-difference method developed by Olsen, Archuleta and Madariaga. We look first at the rupture of an unbounded fault plane starting from a single circular asperity. Rupture propagation is simple but presents substantial differences with the self-similar shear crack model of Kostrov: the most important being that ruptures do not have circular symmetry because rupture resistance can never be uniform around the edge of the rupture front.

We study the non-linear parameterization of this problem and show that there is a simple non-dimensional parameter kappa that controls the overall properties of rupture propagation. This number generalizes previous studies in 2D and 3D by Andrews, Das and Aki, Day, Burridge and many others. We demonstrate for several models that the rupture process has a bifurcation point at a critical value (kappa=kappa_c), so that for values of kappa less than critical rupture does not grow, while for values barely above critical ruptures grow indefinitely at sub-Rayleigh or sub-shear speeds. For values of kappa larger than 1.5 kappa_c an additional bifurcation occurs: rupture in the in-plane direction becomes super-shear and the rupture front develops a couple of “ears” in the in-plane direction. Finally we study a realistic stress distribution derived from the inversion of the accelerograms
of the Landers earthquake. This earthquake started from a critical patch that was probably a few km in radius and then rupture evolved under the control of stress and strength heterogeneities. We find that rupture in Landers occurred for a value of kappa that was barely above critical, which is the reason rupture was sub-shear on the average. In the presence of stress or strength
heterogeneity, rupture propagation becomes very complex and it propagates only in those regions where preexisting stress is high over relatively broad zones. Thus, rupture is a sort of ercolation process controlled by the local ratio of available energy to energy release rate.

Madariaga, R., Peyrat, S., & Olsen, K. B. (2001). Rupture Dynamics in 3-D: a review. Annali di Geofisica, in Problems in Geophysics for the New Millenium, a collection of papers in honour of Adam Dziewonski, 89-110.