Modeling and Prediction of Aftershock Activity

We provide an overview of the basic models of the aftershock processes and advanced methods used to predict postseismic hazard. We consider both the physical mechanisms for aftershock generation and models of aftershocks and time-dependent models of aftershock processes. In particular, we provide a validation of the aftershock process using a superposition of the Gutenberg–Richter and Omori–Utsu laws. We show that the key role in assessment of postseismic hazard is earthquake productivity, which characterizes the ability of earthquakes to produce subsequent shocks. We discuss the recently established exponential law of earthquake productivity and show that the exponential form is invariant under variations in magnitude and focus depth. Being in discordance with the popular epidemic type aftershock sequence (ETAS) model, the law makes it possible to build a corrected model. We study versions of theoretical validation for the Båth law, which specifies the mean difference between the magnitudes of the main shock and the largest aftershock. We consider also the time-dependent Båth law. We provide a detailed review of modern approaches and methods for dealing with the estimation of the magnitude of the largest aftershock. As well, we review the problem of estimating the duration of aftershocks with magnitudes equal to or greater than a specified value, the hazardous period.