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研究生:羅雁文
研究生(外文):Yen-Wen Lo
論文名稱:強震後地震風險之統計分析
論文名稱(外文):Statistical analysis of the hazard of earthquakes after large earthquakes
指導教授:陳玉英陳玉英引用關係
指導教授(外文):Yuh-Ing Chen
學位類別:碩士
校院名稱:國立中央大學
系所名稱:統計研究所
學門:數學及統計學門
學類:統計學類
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:58
中文關鍵詞:餘震時空規模分布流病式餘震序列模式接受者操作特徵曲線尤登指數
外文關鍵詞:Spatial-temporal magnitude distributionETAS modelReceiver operating characteristic (ROC) curveYouden index
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強震及其伴隨的大規模餘震經常對人們的財產與生命帶來巨大的威脅,為了提供震後救災的重要資訊,本文進行強震後餘震的即時風險評估。傳統的RJ模式 (Reasenberg and Jones, 1989) 假設餘震發生的時間與其規模是互相獨立的,因應實務所需,Chen等人 (2015) 提出規模與時間相依的修正RJ模式,記作MRJ模式。因為一個大規模餘震可能引發一個新的餘震序列,本文將流病式餘震序列模式 (ETAS; Ogata,1988) 加以簡化得到SETAS模式,或引用Chen等人 (2015) 結果修正之,得到METAS模式。事實上,本文也將空間訊息納入SETAS及METAS模式發展為可以用來描述餘震空間時間及規模風險的模式。為了說明本文模式的應用,本文分析2011年3月11日發生於日本東部海域,芮氏規模9.0的地震,並且探討如何藉由模式進行強餘震的預測。最後,使用接受者操作特徵曲線及尤登指數評估上述餘震預測的效應。
Strong earthquakes and their large offspring usually cause the huge threat to people's property and lives. To provide information on the rescue work after the strong earthquakes, the immediate assessment of the risk of aftershocks is necessary. The traditional RJ model (Reasenberg and Jones, 1989) assumes that the time and magnitude of aftershocks are independent. For practical purpose, Chen et al. (2015) suggest the modified RJ model, in which the magnitude and time may be dependent. Since a large aftershock may initiate a new seismic sequence, the ETAS (epidemic type aftershock sequence) model (Ogata, 1988) is simplified to obtain the SETAS model. The SETAS model is also modified by using the results in Chen et al. (2015) to have the METAS model. In fact, the spatial information of the previous aftershocks is incorporated into the SETAS and METAS models. Therefore, in this paper, two models one obtained for describing the spatial-temporal-magnitude hazard of aftershocks. The application of the models proposed in this paper is illustrated based on the 5 years aftershocks after the 9.0 earthquake occurred on March 11, 2011, in Tohoku-Oki, Japan. The model-based prediction of future large aftershocks is also discussed. Finally, the efficiency of the prediction is evaluated by using the receiver operating characteristic (ROC) curve and Youden index.
摘要……………………………………………………………………………………………..i
Abstract……………………………………………………………………………………...…ii
致謝辭………………………………………………………………………………………...iii
Contents……………………………………………………………………………………….iv
Figure contents………………………………………………………………………………..v
Table contents………………………………………………………………………………vi
1. Introduction………………………………………………………………………………….1
2. Literature review…………………………………………………………………………….3
2.1 Time-magnitude distribution…………………………………………………………3
2.2 Space-time-magnitude distribution…………………………………………………6
2.3 Receiver operating characteristic (ROC) curve and Youden index………………9
3. Statistical models…………………………………………………………………………10
3.1 Simplified and modified time-magnitude distribution………………………………10
3.2 Simplified and modified space-time-magnitude distribution……………………….13
4. Data analysis……………………………………………………………………………….19
4.1 Time-magnitude distribution……………………………..……………………19
4.2 Space-time-magnitude distribution……………………………………………20
5. Conclusion and discussion…………...……………………………………………………22
References…………………………………………………………………………………….23
Appendix A…………………………………………………………………………………...25
Appendix B…………………………………………………………………………………...42

Chen, Y. I., Huang, C. S. and Liu, J. Y., 2015. Statistical analysis of earthquakes after the 1999 Mw 7.7 Chi-Chi, Taiwan, earthquake based on a modified Reasenberg-Jones model. Journal of Asian Earth Sciences, 114, 299-304.
Gutenberg, R. and C. F. Richter, 1944. Frequency of earthquakes in California. Bulletin of the Seismological Society of America, 34, 185-188.
Ogata, Y., 1983. Estimation of the parameters in the modified Omori formula for aftershock sequences by the maximum likelihood procedure. Journal of Physics of the Earth, 31, 115-124.
Ogata, Y., 1988. Statistical model for earthquake occurrences and residual analysis for point processes. Journal of the American Statistical Association, 83, 9-27.
Ogata, Y., 1998. Space-time point-process models for earthquake occurrences. Annals of the Institute of Statistical Mathematics, 50, 379-402.
Ogata, Y., and J. Zhuang, 2006. Space-time ETAS models and an improved extension. Tectonophysics, 413, 13-23.
Reasenberg, P. A. and L. M. Jones, 1989. Earthquake hazard after a mainshock in California. Science, 243, 1173-1176.
Reasenberg, P. A. and L. M. Jones, 1994. Earthquake aftershocks:update. Science, 265, 1251- 1252.
Swets, J., 1988. Measuring the accuracy of diagnostic systems. Science, 240, 1285-1293.
Utsu, T., 1971. Aftershock and earthquake statistic (III): analyses of the distribution of earthquakes in magnitude, time and space with special consideration to clustering characteristics of earthquake occurrence (1). Journal of the Faculty of Science, Hokkaido University Series VII. Geophysics, 3, 379-441
Utsu, T., Ogata, Y., Matsu’ura, R.S., 1995. The centenary of the Omori formula for a decay law of aftershock activity. Journal of Physics of the Earth, 30, 521-605.
Wiemer, S. and M. Wyss, 1997. Mapping the frequency-magnitude distribution in asperities: An improved technique to calculate recurrence times? Journal of Geophysical Research, 102, 15,115-15,128.
Wiemer, S. and K. Katsumata, 1999. Spatial variability of seismicity parameters in aftershock zones. Journal of Geophysical Research, 103, 13, 135-13, 151.
Wiemer, S. and M. Wyss, 2000. Minimum magnitude of completeness in earthquake catalogs: Examples from Alaska, the western US and Japan. Bulletin of the Seismological Society of America, 90, 859-869.
Youden, W. J., 1950. Index for rating diagnostic tests. Cancer, 3, 32-35.
Zhuang, J., Y. Ogata, and D. Vere-Jones, 2002. Stochastic declustering of space-time earthquake occurrences, Journal of the American Statistical Association, 97:458, 369-380.
Zhuang, J., Chang, C. P., Y. Ogata, and Chen, Y. I., 2005. A study on the background and clustering seismicity in the Taiwan region by using point process models. Journal of geophysical research, 110, B05S18, doi:10.1029.
Zhuang, J., 2011. Next-day earthquake forecasts for the Japan region generated by the ETAS model. Earth Planets Space, 63, 207-216.
Zhuang, J., 2012. Predictability study on the aftershock sequence following the 2011 Tohoku-Oki, Japan, earthquake: first results. Geophysical Journal International, doi: 10.1111/j.1365-246X.2012.05626.x.

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