Random stress and earthquake statistics: time dependence

The inter earth quake time distribution is analysed on the assumption that those stresses that are not observed directly, change in a way that is describable by a random walk, i.e. as a Brownian motion. In this case, the time intervals between earthquake pairs has a power-law distribution with exponent -3/2. If tectonic stress loading is added to the Brownian motion, the interearthquake time distribution changes from a power-law to an almost Gaussian renewal distribution. The actual distribution depends on the ratio of the size of the random component to that of the tectonic component. We find that after about two days, tectonic stresses influence the temporal distribution of aftershocks, for main shocks with ML= 1.5. In the random regime the Omori law holds, while in the tectonic regime, an exponential distribution holds. The time of transition between random and tectonic effects increases with the size of the main shock.