Mixture of a seismicity model based on the rate-and-state friction and ETAS model

Abstract:

Currently the ETAS model [Ogata, 1988, JASA] is considered to be a standard model of seismicity. However, because the ETAS model is a purely statistical one, the physics-based seismicity model derived from the rate-and-state friction (hereafter referred to as Dieterich model) [Dieterich, 1994, JGR] is frequently examined. However, the original version of the Dieterich model has several problems in the application to real earthquake sequences and therefore modifications have been conducted in previous studies.

Iwata [2015, Pageoph] is one of such studies and shows that the Dieterich model is significantly improved as a result of the inclusion of the effect of secondary aftershocks (i.e., aftershocks caused by previous aftershocks). However, still the performance of the ETAS model is superior to that of the improved Dieterich model. For further improvement, the mixture of the Dieterich and ETAS models is examined in this study.

To achieve the mixture, the seismicity rate is represented as a sum of the ETAS and Dieterich models of which weights are given as k and 1-k, respectively. This mixture model is applied to the aftershock sequences of the 1995 Kobe and 2004 Mid-Niigata sequences which have been analyzed in Iwata [2015]. Additionally, the sequence of the Matsushiro earthquake swarm in central Japan 1965-1970 is also analyzed. The value of k and parameters of the ETAS and Dieterich models are estimated by means of the maximum likelihood method, and the model performances are assessed on the basis of AIC. For the two aftershock sequences, the AIC values of the ETAS model are around 3-9 smaller (i.e., better) than those of the mixture model. On the contrary, for the Matsushiro swarm, the AIC value of the mixture model is 5.8 smaller than that of the ETAS model, indicating that the mixture of the two models results in significant improvement of the seismicity model.