Penetration of a quasi‐statically slipping crack into a seismogenic zone of heterogeneous fracture resistance

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Abstract
This paper is concerned with some aspects of nonuniform stressing above a deep creeping portion of a fault zone prior to a large crust‐breaking earthquake. The model that we use involves a slipping crack, representing the deeper, more stably sliding portions of the fault zone, which penetrates upward from depth and is blocked in the lower region of the seismogenic zone. When conditions are uniform along strike, the upward penetration at the crack front is by mode III in strike‐slip fault zones but by mode II in thrust or normal fault zones. Two major results are reported. First, we analyze approximately, via a linear perturbation formulation, how a tectonic crack front encounters and ultimately shears through arrays of localized “asperities” that are distributed parallel to the crack front and have a toughness which is greater than that of adjoining segments of the fault zone. Using a fast Fourier transform based numerical procedure to simulate crack penetration into asperities, we find a notable difference between mode II and mode III crack fronts in that the former penetrates approximately twice as far between the asperities as the latter under the same loading level. This is interesting because observations of slip distribution in large earthquakes suggest that there is a significant aseismic component to the total slip budget in subduction zone earthquakes, which in contrast does not seem to be present in strike‐slip zone earthquakes, and also that the surface slip distribution in continental dip‐slip faulting is typically much more irregular than for strike‐slip faulting. In a simulation involving multiple rows of periodic asperities we note that the more deeply penetrating mode II crack front contacts more asperities simultaneously while breaking them at different load levels compared to the less flexible mode III crack front, which simply breaks one row of asperities and jumps (unstably) to the next. The second major result concerns whether a straight crack front in the lithosphere along a strike‐slip fault zone is configurationally stable, that is, whether the crack front will tend to remain straight as the crack penetrates upward from depth. It is found that for infinitesimal perturbations of the straight front beyond a critical wavelength, of the order of the crustal lithosphere thickness, the stress intensity factor is higher at the most advanced portions of the crack front rather than at the least advanced; the opposite is true at shorter wavelengths. When resistance to crack growth is essentially uniform over the fault plane, this means that the straight crack front is configurationally unstable at long wavelengths. The issue of configurational stability is related to the concept of fault segmentation, which is based on the observation that fault zones, particularly long ones, do not rupture along their entire length during a single earthquake. Effect of a vertical gradient of fracture resistance is discussed in the appendix, where it is shown that a significant upward gradient of resistance to crack growth may completely stabilize the straight crack configuration.

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