Foreshock Rates from Aftershock Abundance

Abstract

The question whether foreshocks behave like mainshocks that happen to have larger aftershocks is important for the understanding of earthquake nucleation and the modeling of earthquake clustering. Many models, including the short-term earthquake probability (STEP) model, for forecasting short-term earthquake hazard in California, and the epidemic-type aftershock sequence (ETAS) model, for the description of earthquake clustering, imply that all earthquakes of magnitude M , including foreshocks, can trigger earthquakes according to a magnitude dependent triggering ability 10 αM . The magnitudes of the triggered earthquakes are proportional to 10- bM , according to the Gutenberg–Richter relation for the magnitude-frequency distribution, and therefore can be larger than the magnitude of the initiating event. However, numerous studies observe a lower foreshock occurrence than predicted from aftershock models. In this article we show that, for homogeneous earthquake catalogs and a consistent definition of foreshocks and aftershocks, foreshock rates can be predicted from aftershock characteristics. For Southern California the probability that the initiating event of an earthquake cluster in the magnitude range 2.0–4.5 is followed by at least one larger event within one day is around 4%. This agrees well with corresponding data from the global centroid moment tensor (CMT) catalog where the probability that the initiating earthquake of a cluster is followed by at least one larger event within 30 days is around 3%. These foreshock rates are significantly lower than previously reported, and we discuss possible reasons for this.