Testing of the foreshock hypothesis within an epidemic like description of seismicity

The epidemic type aftershock sequence (ETAS) model provides a good description of the post-seismic spatio-temporal clustering of seismicity and is also able to capture some features of the increase of seismic activity caused by foreshocks. Recent results, however, have shown that the number of foreshocks observed in instrumental catalogues is significantly much larger than the one predicted by the ETAS model. Here we show that it is possible to keep an epidemic description of post-seismic activity and, at the same time, to incorporate pre-seismic temporal clustering, related to foreshocks. Taking also into-account the short-term incompleteness of instrumental catalogues, we present a model which achieves very good description of the southern California seismicity both on the aftershock and on the foreshock side. Our results indicate that the existence of a preparatory phase anticipating main shocks represents the most plausible explanation for the occurrence of foreshocks.