# Direct simulations of the stress redistribution in the scaling organization of fracture tectonics (SOFT) model

Abstract : A time-dependent stochastic process with three states (solid, broken and moving) is considered in a hierarchical system made of embedded cells of increasing levels. An earthquake of a given scale k is associated with the moving state of a cell of level k and results from the coherent self-organization of fractures of lower scales. A direct cascade of stress redistribution generates small-scale stress heterogeneities in the neighbourhood of the active fracture. An interesting feature of the model is that the size of the domain where stress redistribution takes place grows proportional to the length of the fracture. In the framework of the general model, inspired by the progress in the use of the renormalization techniques in approaching critical point phenomena, we independently study a fracturing' submodel and a friction' submodel. These submodels are two-state models that act on different timescales. In the friction' submodel, which comprises broken and moving states, the transitions between these two states are associated with stick-slip behaviour in a completely fractured fault zone. In the fracturing' submodel, which comprises solid and broken states, we model the brittle behaviour of rock material. In both models we obtain a spatio-temporal clustering of earthquakes, realistic aftershock sequences whose frequency decreases respect the modified Omori law, and a frequency-magnitude relationship that respects the Gutenberg-Richter law. We show that the model behaviour is controlled by the stress heterogeneity in the fault zone, we find evidence for a relationship between the periodicity of the largest earthquakes and the b-value, and we indicate how the different physical ingredients underlying each submodel can be gathered together in a more general model.
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### Citation

C. Narteau, P. Shebalin, M. Holschneider, J. -L. Le Mouël, C. J. Allègre. Direct simulations of the stress redistribution in the scaling organization of fracture tectonics (SOFT) model. Geophysical Journal International, Oxford University Press (OUP), 2000, 141, pp.115-135. ⟨10.1046/j.1365-246X.2000.00063.x⟩. ⟨insu-03596944⟩

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