Epidemic type aftershock sequence exponential productivity

Abstract

Studying the hierarchical structure of the aftershock sequence of the three largest earthquakes of the last decade, we show that the number of offspring events counted in a fixed magnitude band with respect to the magnitude of the parent events follows an exponential distribution. Such an exponential productivity law is coherent with the exponential decays inferred from largest earthquakes worldwide. Epidemic Type Aftershock Sequences (ETAS) are the most popular stochastic models of seismicity and they are all based on a Poisson distribution of the earthquake productivity with a pronounced non-zero mode. We construct here an alternative model incorporating an exponential productivity law. For the three aftershock sequences. we estimate parameters of both models using aftershocks occuring during the first 2 days. We simulate a set of synthetic earthquake catalogues for both models and compare the average cumulated number of events with respect to time. In all cases, the ETAS model overestimates the number of events in the interval from 2 to 365 days. For the same time period, the exponential ETAS model gives a satisfactory cumulative number of events. We conclude that exponential distribution of the earthquake productivity seems to be an important property of the seismic relaxation process.