eprintid: 1278 rev_number: 15 eprint_status: archive userid: 2 dir: disk0/00/00/12/78 datestamp: 2015-02-16 14:36:05 lastmod: 2017-02-08 12:21:44 status_changed: 2015-04-27 12:10:36 type: article metadata_visibility: show creators_name: Wu, Zhengxiao corp_creators: Department of Statistics and Applied Probability, National University of Singapore, Singapore title: Quasi-hidden Markov model and its applications in cluster analysis of earthquake catalogs ispublished: pub subjects: MP2_3 divisions: EPOS-P full_text_status: none abstract: We identify a broad class of models, quasi ‐ hidden Markov models (QHMMs), which include hidden Markov models (HMMs) as special cases. Applying the QHMM framework, this paper studies how an earthquake cluster propagates statistically. Two QHMMs are used to describe two different propagating patterns. The “mother ‐ and ‐ kids” model regards the first shock in an earthquake cluster as “mother” and the aftershocks as “kids,” which occur in a neighborhood centered by the mother. In the “domino” model, however, the next aftershock strikes in a neighborhood centered by the most recent previous earthquake in the cluster, and therefore aftershocks act like dominoes. As the likelihood of QHMMs can be efficiently computed via the forward algorithm, likelihood ‐ based model selection criteria can be calculated to compare these two models. We demonstrate this procedure using data from the central New Zealand region. For this data set, the mother ‐ and ‐ kids model yields a higher likelihood as well as smaller AIC and BIC. In other words, in the aforementioned area the next aftershock is more likely to occur near the first shock than near the latest aftershock in the cluster. This provides an answer, though not entirely satisfactorily, to the question “where will the next aftershock be?” . The asymptotic consistency of the model selection procedure in the paper is duly established, namely that, when the number of the observations goes to infinity, with probability one the procedure picks out the model with the smaller deviation from the true model (in terms of relative entropy rate). date: 2011-12-24 date_type: published publication: Journal of Geophysical Research volume: 116 number: B12 publisher: American Geophysical Union id_number: doi:10.1029/2011JB008447 refereed: TRUE issn: 0148-0227 official_url: http://dx.doi.org/10.1029/2011JB008447 access_IS-EPOS: limited owner: Publisher citation: Wu, Zhengxiao (2011) Quasi-hidden Markov model and its applications in cluster analysis of earthquake catalogs. Journal of Geophysical Research, 116 (B12). DOI: https://doi.org/10.1029/2011JB008447