Global statistics of aftershocks following large earthquakes: independence of times and magnitudes

This paper considers the global statistics of times of largest aftershocks relative to the times of the corresponding main shocks. A large data set was used to show that the time-dependent distribution of largest aftershocks obeys a power law distribution. This is analogous to the Omori law for the sequence of all after- shocks. It is also shown that the times of the second, etc., largest aftershocks obey the same distribution. Thereby, we have confirmed the hypothesis that the times and magnitudes in an aftershock sequence are independent and make a good case for the Reasenberg-Jones representation of the aftershock process as a superposition of the Omori-Utsu law and the Gutenberg–Richter relation. Events that are smaller than the largest in an aftershock sequence show no delay relative to the largest event; this rejects the idea of the after- shock process as a direct failure cascade involving gradual transitions from larger to lesser scales, which imposes certain restrictions on the widely popular stochastic models of aftershock generation as branching processes. The above result is important in practice for prediction of aftershock activity and for assessing the hazard of large aftershocks.