Slow crack growth and aftershock sequences

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Abstract
We conducted a critical reexamination of Yamashita & Knopoff's (1987) models of aftershock occurrence, based on slow crack growth process. Such models assume that a time‐dependent process like slow crack growth, extensively documented at the sample scale, can be straightforwardly extrapolated to the field scale. If it is so, a question is rised : which model is the most consistent one with real data? We suggest here a possible way of discriminating between these models. The first model considers the slow growth of a main fracture surrounding small, locked asperities until slippage occurs. The second model considers the slow growth of satellite faults around the main fracture up to coalescence. By assuming power law distributions for the critical distances for quasistatic and dynamic crack growth, numerical simulations show that both models correctly predict Omori's law as well as the classical magnitude‐frequency law. Nevertheless, when looking further at the time distribution of aftershock magnitudes, it is shown that the results derived from the second model are inconsistent with usual observations since inverse sequence is predicted. Results derived from the first model are more realistic.

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