Common dependence on stress for the two fundamental laws of statistical seismology

Two of the long-standing relationships of statistical seismology are power laws: the Gutenberg–Richter relation describing the earthquake frequency–magnitude distribution, and the Omori–Utsu law characterizing the temporal decay of aftershock rate following a main shock. Recently, the effect of stress on the slope (the b value) of the earthquake frequency–magnitude distribution was determined by investigations of the faulting-style dependence of the b value. In a similar manner, we study here aftershock sequences according to the faulting style of their main shocks. We show that the time delay before the onset of the power-law aftershock decay rate (the c value) is on average shorter for thrust main shocks than for normal fault earthquakes, taking intermediate values for strike-slip events. These similar dependences on the faulting style indicate that both of the fundamental power laws are governed by the state of stress. Focal mechanisms are known for only 2 per cent of aftershocks. Therefore, c and b values are independent estimates and can be used as new tools to infer the stress field, which remains difficult to measure directly.

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