abstract

We present a theoretical model, based on fracture mechanics concepts, of the behavior of an earthquake source prior to the occurrence of the earthquake, to understand under what conditions precursory slip may occur on a fault and to determine realistic initial conditions for the dynamic problem of faulting. We consider a two-dimensional fault consisting of in-plane periodic shear cracks and unbroken zones in an infinite, homogeneous elastic medium. Between the cracks of length 2a and the unbroken zones are “intermediate” zones in which the stress drop occurs when a “critical shear displacement” (CSD) is reached (Panasyuk-Dugdale model) at the crack tip. The unbroken zones can also be interpreted in terms of friction as regions where the stress is lower than the static frictional stress, so that our model can be interpreted from the point of view of fracture or friction. Let the period of this system be 2d. As the load at infinity is slowly increased, the intermediate zones grow quasi-statically with a small amount of associated slip in the broken regions of the fault plane. It is found that when the cracks are very small or very large or the CSD is large, the intermediate zones will coalesce before the CSD is reached, i.e., the entire fault is ruptured and additional preseismic slip occurs. The initial conditions for dynamic rupture occurring at a later time on the fault is then a stress condition. Thus, for the initial stages of the dynamic problem (not studied here) one need not solve a mixed boundary value problem but only the much simpler stress boundary problem. The rupture velocity of the dynamic rupture on such a fault which is entirely broken, may have any value up to the P-wave velocity, in principle. The average slip on the fault at the point of coalescence increases with crack size from zero at zero crack length up to a/d ≃ 0.67 and then decreases to zero at a/d = 1. The displacement distribution on the crack and the shear stress distribution around the crack as a function of increasing load and increasing crack size a/d are studied. It is shown that strain accumulation occurs not only at the ends of a Griffith crack but also in broad regions off the crack in the normal direction. Corresponding to the unbroken zone, there is a similar zone but of strain release off the crack. This zone becomes more and more pronounced for large cracks and high loads. For very long cracks, the increase in shear stress off the crack becomes very very small but the decrease off the initially unbroken zone becomes very pronounced. Interaction between cracks is correctly accounted for in our method.

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