Residual Strain Mechanism of Aftershocks and Exponents of the Modified Omori's Law

Abstract

The rate of aftershocks caused by residual stresses left after a major seismic event or material failure is considered. It is assumed that the local (or “micro” with respect to the scale of the major event) failures registered as aftershocks are produced by static fatigue (delayed fracture). The key point is that the post failure unloading leaves residual strain; the latter induces stresses proportional to the effective (average) moduli. The moduli decay with accumulated microfailures (microcracks or defects or sliding zones), which explains the aftershock rate decay observed by the (modified) Omori's law. It is found that the value of Omori's exponent, p, reveals one of three types of effective moduli decay with the number of aftershocks: p = 1 (the original Omori's law) corresponds to the exponential reduction of the effective moduli, typical for isotropic distribution of accumulated microcracks or sliding zones; p < 1 (the modified Omori's law) corresponds to the power law reduction of the effective moduli, typical for parallel sliding zones; p > 1 (the modified Omori's law) corresponds to the emergence of critical number of defects. This can be indicative of approaching critical event, that is, major seismic event or failure.