平成18（2006）年度　一般研究１実施報告書

課題番号	18−共研−1019	専門分類	6
研究課題名	地震活動と前駆的現象組み込んだ統計的点過程モデルの研究
フリガナ 代表者氏名	オガタ　ヨシヒコ 尾形　良彦	ローマ字	Yosihiko Ogata
所属機関	統計数理研究所
所属部局	モデリング研究系
職　　名	教授
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研究目的と成果（経過）の概要

Aims of Research: Using point process to model the occurrence process of earthquake and find reliable precursory phenomena for earthquake forecasts

Achievements:
1. Foreshocks. Using the stochastic reconstruction techniques introduced by Zhuang et al. (2004, Journal of Geophysical Research, Vol 109, B50301), we analyzed the earthquake data from Japan, New Zealand and Southern California. We define foreshocks as background events that trigger at least one larger event, directly or indirectly. We found that the proportion of foreshocks in the background events is much less than their corresponding event in the triggered events. This is caused by the difference between background earthquakes and triggered earthquakes, i.e., a background event triggers less number of events than a triggered event of the same magnitude.
2. Probability forecasting by using space-time ETAS model. This is a collaborative project with UCLA and SCEC (Southern California Earthquake Center) on software implementation of using ETAS model for earthquake probability forecast. The ETAS module (Version 1.0.0) in the SCEC CSEP project has been implemented and can be used in practice.
3. On Neyman-Scott model. A Neyman-Scott point process is the cluster members produced from unobserved cluster centers that from a Poisson process. This model can be used as the phenomena accompanying the occurrence of large earthquakes. Our study gives the methodologies for estimating the stochastic intensity of cluster centers (earthquakes) from the partial observed information of the accompanying phenomena in a given time window.
4. Filtering theory of the self-similar ETAS model. Self-similar ETAS model is an extension of the ETAS model in which the magnitude threshold is not necessary. However, the likelihood of this model requires all the events, observable and unobservable, to be known. Our filtering theory gives the stochastic intensity of the occurrence of earthquakes conditioning on only the observable events. This theory makes the likelihood based inference on self-similar model possible.

当該研究に関する情報源（論文発表、学会発表、プレプリント、ホームページ等）

論文発表:
1. Zhuang, J. (2006). Second-order residual analysis of spatiotemporal point processes and applications in model evaluation, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 68 (4), 635-653. doi: 10.1111/j.1467-9868.2006.00559.x.
2. Zhuang, J. and Ogata, Y. (2006). Properties of the probability distribution associated with the largest event in an earthquake cluster and their implications to foreshocks, Physical Review, E. 73, 046134. doi: 10.1103/PhysRevE.73.046134 .
学会発表:
1. Zhuang, J. and Ogata, Y. (2006). Probability distributions associated foreshocks implied by clustering models for earthquake occurrences, 2006 Western Pacific Geophysics Meeting, Beijing International Convention Center, Beijing, China, July 2006.
2. Zhuang, J., Vere-Jones, D., Ogata, Y., Ma, L. and Guan, H. (2006). Statistical modelling (tests) of the relationship between precursory phenomena and earthquake occurrences, 2006 Western Pacific Geophysics Meeting, Beijing International Convention Center, Beijing, China, July 2006.
3. Zhuang, J., Savage, M. K., Christophersen, A., Jackson, D. D., Vere-Jones, D. and Ogata, Y. (2006). Foreshock probabilities, 2006 SCEC Meeting, Palm Springs, California, USA, Sep. 2006.
4. Zhuang, J. and Jackson, D. D. (2006). Foreshocks probabilities in Southern California explained by clustering models, 2006 American Geophysical Union Fall Meeting, S13A-0213, San Francisco, USA, December, 2006.
プレプリント:
1. Zhuang, J. (2007). Likelihood based detection of cluster centers for Neyman-Scott point processes, Submitted to Journal of American Statistical Association.
2. Zhuang, J. (2007). Filtering theory for a partially observation self-similar point process, Submitted to Annual of Applied Probability.
3. Zhuang, J., Savage, M. K., Christophersen, A., Jackson, D. D., Vere-Jones, D. and Ogata, Y. (2007). Differences between background and dependent seismicity: their influences on foreshock probabilities and implications in earthquake forecasts, In preparation.

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研究参加者一覧
氏名	所属機関
庄　建倉	University of California, Los Angeles