Abstract
Both earthquake size-distributions and aftershock decay rates obey power laws. Recent studies have demonstrated the sensibility of their parameters to faulting properties such as focal mechanism, rupture speed or fault complexity. The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour. Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear. We find that the event size-distribution obeys a power law only in the proximity of a critical volume fraction, whereas power-law aftershock decay rates are observed at all volume fractions accessible in the model. Then, we show that both the exponent of the event size-distribution and the time delay before the onset of the power-law aftershock decay rate are decreasing functions of the shear stress. These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.
Highlights
Where Mw is the moment magnitude and b a constant with a value around 1 along active fault zones
We have shown that these two fundamental laws of statistical seismology are relevant to avalanches in sheared granular matter, and they have common dependence on the level of stress
Concerning the GR law, which is commonly observed in a wide range of materials under different conditions from laboratory experiments to the field, we find scale invariance in the model only for a narrow range of volume fraction (φ ≃ 0 .644)
Summary
Where Mw is the moment magnitude and b a constant with a value around 1 along active fault zones. Narteau et al find that the time constant c in the MOL has the same dependence on the faulting mechanism[5] These two observations indicate that, under a simple assumption, b and c are decreasing functions of shear stress. Among them, sheared granular media[12,13,14,15,16,17,18,19] are simple representations of granular fault gouges (Fig. 1), which are commonly used in geophysics to analyse deformation of highly damaged rocks in fault zones[20,21,22] Both the energy and the stress can be defined in these models. The details of our numerical model are described in the Methods section
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