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; p1 (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.
Plain Language Summary After an earthquake or a major failure, aftershocks (seismic or acoustic pulses) are observed. The aftershock rate rapidly decreases with time, which is expressed by modified Omori's law. It is believed that one of the mechanisms of aftershocks is the accumulation of cracks generated by the residual stress left after the major event. We argue that it is the residual strain that is left after the major event; the stress causing aftershock is proportional to strain and to the material elastic modulus (stiffness). The latter decreases with accumulated cracks, which creates the reduction of the rate of crack accumulation that is the rate of aftershocks. We analyze the proposed mechanism and demonstrate that the law of decrease of elastic moduli with aftershocks is controlled by the modified Omori's law.