A Variety of Aftershock Decays in the Rate- and State-Friction Model Due to the Effect of Secondary Aftershocks: Implications Derived from an Analysis of Real Aftershock Sequences

The model based on rate- and state-dependent friction law reproduces the temporal decay of an aftershock sequence with the p value of the Omori–Utsu law equal to 1, if we simply assume a constant stress rate over time. However, because p values vary in real aftershock sequences, this model requires some modification. This study examined the effect of secondary aftershocks on the variety of the p value. A large aftershock causes a stepwise stress increase in the aftershock area, and the expected seismicity rate derived from the friction law also increases abruptly. These multiple increases in the seismicity rate during its decay following a mainshock could cause variation in the apparent p value. In this study, a model incorporating this idea is applied to two aftershock sequences observed in Japan and is shown to substantially modify the modeling of aftershock activity.