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[1] The hidden Markov model (HMM) and related algorithms provide a powerful framework for statistical inference on partially observed stochastic processes. HMMs have been successfully implemented in many disciplines, though not as widely applied as they should be in earthquake modeling. In this article, a simple HMM earthquake occurrence model is proposed. Its performance in declustering is compared with the epidemic-type aftershock sequence model, using a data set of the central and western regions of Japan. The earthquake clusters and the single earthquakes separated using our model show some interesting geophysical differences. In particular, the log-linear Gutenberg-Richter frequency-magnitude law (G-R law) for the earthquake clusters is significantly different from that for the single earthquakes.

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A general dynamical cluster identification framework including both modeling and computation is developed. The earthquake declustering problem is studied to demonstrate how this framework applies.A stochastic model is proposed for earthquake occurrences that considers the sequence of occurrences as composed of two parts: earthquake clusters and single earthquakes. We suggest that earthquake clusters contain a "mother quake" and her "offspring." Applying the filtering techniques, we use the solution of filtering equations as criteria for declustering. A procedure for calculating maximum likelihood estimations (MLE's) and the most likely cluster sequence is also presented.