Three-dimensional spontaneous rupture propagation and implications for the earthquake source mechanism

Abstract

We consider spontaneous cracks spreading out areally over a fault plane in an infinite medium as a realistic earthquake source model. The boundary integral equation technique described in Das is used to determine the displacements and stresses everywhere on the crack plane. For faults spreading out symmetrically in all four quadrants over infinite planes of constant yield strength, we find that the terminal rupture velocity VIIICR in the direction of purely anti-plane rupture is given by VIIICR < β. In the purely in-plane direction of rupture propagation, we find the terminal rupture velocity VIICR to be given by VIICR < α or VIICR < 0.5α, depending on the yield strength. We also find that crack propagation in the purely antiplane direction does not influence crack propagation in the purely in-plane direction and vice versa. For infinitely long shear cracks of finite width, the slip at a point is found to grow more slowly after the arrival of a shear wave diffracted from the nearer crack edge. The slip virtually ceases after the shear arrival from the further crack edge. This implies that for such faults the slip is controlled by the fault width. For a rectangular fault in an infinite medium, our final dynamic solution is in closer agreement with the static elliptical crack solution of Eshelby than with the static rectangular ‘dislocation model’ solution of Chinnery. We find the relationship between the average slip ū and average dynamic stress drop τe on such a rectangular fault of half-width W to be τe=Cμ(ū/W), where c ∼ 0.7. The slip at an interior point is again controlled by the fault width for faults that are much longer than wide so that the slip may stop in the region where the fault initiated before the completion of the rupture process. This implies that two rectangular faults of varying lengths but of the same width have the same slip for the same average stress drop, a fact clearly contradicted by observations that fault slip increases with earthquake size for great earthquakes occurring along the same fault. This contradiction is resolved if stress drops are also bigger for bigger earthquakes.