Temporal Power-laws on Preseismic Activation and Aftershock Decay Affected by Transient Behavior of Rocks

A constitutive law for rock behaviors including the brittle, transient and steady-state behaviors is derived to recognize the temporal seismicity patterns on surface displacement or prior and subsequent to mainshocks, and formulated as the relaxation modulus (i.e., the ratio of stress to strain) following a temporal power-law relaxation. This constitutive law is transformable into the empirical power-law creep equation, and the exponent of the constitutive law is the valuables reflecting the fractal structures of rocks in response to the different deformation mechanisms. By the time-scale invariance in our law, the temporal seismicity pattern is recognized on the surface displacement owing to major large earthquake with many small events, on the power-law increase in the cumulative Benioff strain-release as the preseismic activation, and on the power-law aftershock decay represented by the modified Omori's law. The exponents of the temporal power-laws on the cumulative Benioff strain-release and the aftershock decay are linked to that of the constitutive law of rocks, and change coupled with the fractal structure of the crustal rocks.