No. 967

Title:

Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks

Author(s):

Zhuang, Jiancang (Institute of Statistical Methametics);
Ogata, Yosihiko (Institute of Statistical Methametics)

Key words:

ETAS model, foreshock, earthquake, cluter.

Abstract:

    The space-time epidemic-type aftershock sequence (ETAS) model is a stochastic branching process in which earthquake activity is classified into background and clustering components and each earthquake triggers other earthquakes independently according to certain rules. This paper gives the probability distributions associated with the largest event in a cluster and their properties for all three cases when the process is subcritical, critical and supercritical. One of the direct uses of these probability distributions is to evaluate the probability of an earthquake to be a foreshocks and magnitude distributions of foreshocks and non-foreshock earthquakes. To verify these theoretical results, the JMA (Japan Meteorological Agency) earthquake catalog is analyzed, and we found no discrepancy between the analytic results and the inversion results by using the stochastic reconstruction method. We found that the proportion of foreshocks in background events is around 8%.