Please use this identifier to cite or link to this item: https://doi.org/10.1029/2011JB008447
Title: Quasi-hidden Markov model and its applications in cluster analysis of earthquake catalogs
Authors: Wu, Z. 
Issue Date: 2011
Citation: Wu, Z. (2011). Quasi-hidden Markov model and its applications in cluster analysis of earthquake catalogs. Journal of Geophysical Research B: Solid Earth 116 (12) : -. ScholarBank@NUS Repository. https://doi.org/10.1029/2011JB008447
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). Copyright 2011 by the American Geophysical Union.
Source Title: Journal of Geophysical Research B: Solid Earth
URI: http://scholarbank.nus.edu.sg/handle/10635/105318
ISSN: 01480227
DOI: 10.1029/2011JB008447
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