利用極值理論探討最大可能地震規模:以台灣為例

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顧凱文(Kai-Wen Ku) 查詢紙本館藏

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土木工程學系

論文名稱

利用極值理論探討最大可能地震規模:以台灣為例
(Using extreme value theory to estimate the maximum credible earthquake in Taiwan)

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摘要(中)

台灣位於歐亞板塊與菲律賓海板塊之邊界上，由於板塊擠壓之緣故導致地震頻繁，有鑑於此，為了達到防災及減災之目的，在建築設計時需將地震因素納入考量，以降低地震所帶來的損傷及危害。
本文之研究目的為使用極值理論（Extreme Value Theory）來預估台灣各地區之最大可能規模，而預估最大可能規模主要分為定值方法（deterministic procedure）及機率性方法（probabilistic procedure），在過去經常使用定值方法來預估最大可能規模，其常用之預估方式為歷史紀錄之最大地震規模加0.5（此0.5為一個主觀的數值）或使用經驗公式，然而其存在著較高的不確定性因素，因此本研究選擇使用機率性方法中的極值理論，其採用數學統計之方式來預估最大可能規模，相較於定值方法而言，較為客觀。
本研究將台灣從1978年至2017年之地震歷史資料使用統計分析方法中之韋伯分佈（Weibull distribution）進行建模，其中使用卡方檢驗（Chi-square test）來分析韋伯分佈理論值與歷史觀察值間之擬合狀況，並搭配極值理論來分析台灣各區域之最大可能規模，最後將極值理論（極值理論中不同時間週期及不同的機率分佈）所預測之最大可能規模與定值方法中之歷史最大規模加0.3或加0.5所預估之規模值進行比較分析。
相對於加0.3法及加0.5法而言，本研究之極值理論可以直接評估各時間及不同百分位數下之規模，且其考慮到時間因素，而加0.3法及加0.5法未考慮時間因子，因此，本研究之極值理論應用於預測地震規模上較為客觀且實際。

摘要(英)

Taiwan is located in the boundary of the Eurasian Plate and Philippine Sea Plate. Because of the plate extrusion, there is high seismicity rate over the past few years. Therefore, in order to achieve the purpose of disaster prevention and mitigation, seismic factors should be taken into account in the design of the building to reduce the damage and harm caused by the earthquake.
The purpose of this paper is to apply the Extreme Value Theory（EVT）to estimate the maximum credible magnitude of each seismic zone in Taiwan. The estimated maximum credible magnitude mainly included the deterministic procedure and probabilistic procedure. In the past, the deterministic procedure was often used to estimate the maximum credible magnitude. The commonly used method is the largest earthquake magnitude of the historical record plus 0.5. However, it is a subjective value, so there is high uncertainty. The extreme value analysis used in this study is a probabilistic procedure. The probabilistic procedure is more objective compared with the deterministic procedure because it used a more objective method to estimate the maximum credible magnitude.
This study collected the seismic data from 1978 to 2017 and used the Weibull distribution to model the observation. Furthermore, this study used the Chi-square test to test the hypothesis if the observation follows the Weibull distribution. Finally, the maximum credible magnitude calculated by the EVT（different time periods and different tail of probability distributions in extreme value theory）is compared with the value evaluated by the methods of maximum historical magnitude plus 0.3 and plus 0.5 in the deterministic procedure.
Compared with the plus 0.3 method and the plus 0.5 method, EVT can directly evaluate the different time periods and the magnitude of different percentiles. The most important is that the extreme value theory takes the time factor into account. While the traditional plus 0.3 method and the plus 0.5 method do not. Therefore, using EVT is more objective and practical for predicting the magnitude of earthquakes.

關鍵字(中)

★ 極值理論
★ 韋伯分布
★ 截斷分布
★ 最大可能規模
★ 卡方檢驗

關鍵字(英)

論文目次

摘要 I
Abstract II
目錄 V
圖目錄 VII
表目錄 X
第一章緒論 1
1-1 研究動機 1
1-2 研究目的 2
第二章文獻回顧 3
2-1 極值理論（Extreme Value Theory） 3
2-2 韋伯分佈（Weibull distribution） 4
2-3 截斷分佈（Truncated distribution） 4
2-4 卡方檢驗（Chi-square test） 5
2-5 最大極限規模（Ultimate maximum magnitude） 6
2-6 最大可能規模（Maximum credible magnitude） 6
第三章研究方法 14
3-1 資料建立 14
3-1-1 台灣地震資料來源 14
3-1-2 資料之輸入 14
3-1-3 模型之選用 15
3-2 使用Excel建立韋伯分佈 16
3-3 極值理論之分析 18
3-3-1 極值分佈之建立 18
3-3-2 極值分佈之應用 18
第四章結果討論 25
4-1 韋伯分佈之建立 25
4-2 探討不同百分位數下之預測規模 25
4-2-1 百分位數為90%時之最大可能規模 25
4-2-2 百分位數為70%時之最大可能規模 26
4-2-3 百分位數為50%時之最大可能規模 26
4-3 與定值方法作比較 27
4-3-1歷史最大規模 27
4-3-2歷史最大規模加0.3（加0.3法） 27
4-3-3歷史最大規模加0.5（加0.5法） 28
第五章結論與建議 57
5-1結論 57
5-2建議 58
參考文獻 60

參考文獻

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指導教授

王瑞斌

審核日期

2019-7-24

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