台灣地區強地動預估式之自然隨機誤差分析

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宋芝萱(Chih-Hsuan Sung) 查詢紙本館藏

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論文名稱

台灣地區強地動預估式之自然隨機誤差分析
(Aleatory Variability of Ground-motion Predition Equations Deduced from a Huge Dataset in Taiwan)

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摘要(中)

本研究建立適合台灣地區機率式地震危害度分析使用的強地動預估式，以中央氣象局的自由場強地動觀測網計畫之強震資料，篩選出地震矩規模大於4.0之150 個地殼地震，共計19,887筆強震資料進行分析。以混合效應模型(mixed-effect model)及最大概似法(maximum likelihood estimation)當作迴歸模型，透過非線性的迴歸分析來探討地動值與震源、路徑及場址間的關係，並以地震學理論為基礎建立預估式，考慮規模、地震波傳播距離、場址特性及震源機制等參數，完成適合台灣地區在各週期之地殼地震強地動預估式。
本研究利用變動視窗法(Spatial-correlation Mobile Window)、路徑玫瑰圖法(Pah Diagram)、半變異圖法(Semi-variogram)、CI法及震央距離法等方式進行事件間變異性與記錄間變異性的分析與拆解。在分析事件間變異性上，以變動視窗法最為合理，而紀錄間變異性的拆解則以路徑玫瑰圖有最好的結果，並且是唯一可以將路徑間變異性從紀錄間變異性中完整拆解出來的方法，也使的每筆強震紀錄都可以擁有各自的事件內自然隨機誤差。最後合併變動視窗法與路徑玫瑰圖法求得最小之單一路徑標準差σSP，可較總標準差σT降低約40%-55%。
另外也建立特定條件之強地動關係式，其中包含單站(single station)、單震源(single source)及單震源對陣列(single source to an array)的條件。結果發現，使用特定條件之預估式求得之單站標準差σSS、單一路徑標準差σSP及事件內的自然隨機變異性σ0皆比一般預估式的拆解更低。最後在機率式地震危害度分析中套用總標準差、單站標準差及單一路徑標準差，結果顯示只考慮自然隨機誤差的的危害度曲線(2475年再現期)，比過去只考慮總標準差評估出的強地動值降低約20%，再現期越長評估出的強地動值差異也越大。

摘要(英)

In this study, we use 19,887 records for 150 crustal earthquakes with moment magnitudes greater than 4.0 obtained from the Taiwan Strong-Motion Instrumentation Program network to build the Taiwan ground-motion prediction equations (GMPEs) for peak ground acceleration and spectral accelerations. The nonlinear regression analysis of ground-motion prediction model is the mixed-effect model with maximum likelihood method. Though this regression analysis to discuss the relationship of source, path, and site.
This paper describes the approaches for the presentation of the components of the error in ground-motion estimates for future earthquakes: (1) spatial-correlation mobile widow, (2)path diagram, (3) semi-variogram, (4) closeness index and (5) the distance of epicenter. Comparing the results with those obtained with the same data, but using the closeness index, semi-variogram and the distance of epicenter approaches, show that we get a lower path-to-path sigma with the combination of the spatial-correlation mobile window and the path diagram methods. For peak ground acceleration and spectral accelerations at periods of 0.3 s, 1.0 s, and 3.0 s, the path-to-path standard deviations obtained in the new approaches are 40%–55% smaller than the total standard deviation.
We also set up the ground-motion prediction equations for the single station, single source and single source to an array in this study. When we use these specific conditions GMPEs to analyze the variance, we can obtain the smaller single-station sigma, single-path sigma, and intra-event aleatory variability than general GMPEs. If we only use aleatory variability in PSHA, then the resultant hazard level would be 20% lower than the traditional one in 2475 year.

關鍵字(中)

★ 強地動預估式
★ 路徑效應
★ 標準差
★ 單站
★ 機率式地震危害度分析

關鍵字(英)

★ GMPE
★ path effect
★ sigma
★ single station
★ PSHA

論文目次

中文摘要 i
Abstract ii
致謝 iii
目錄 v
表目錄 ix
圖目錄 xi
符號說明 xviii
第一章緒論 1
1-1 研究動機與目的 1
1-2 文獻回顧 2
1-2-1 GMPE相關研究－採用更多的參數 3
1-2-2 殘餘值分析、場址項固定及變異數拆解之研究 8
1-3 研究流程與內容 12
第二章資料蒐集與處理 13
2-1 強震資料蒐集 13
2-1-1資料挑選規則 13
2-1-2 規模參數 13
2-1-3 震源機制參數 14
2-1-4 測站場址參數 14
2-1-5 地動參數建立 15
2-2 強震資料處理 15
2-3 相關研究之強地動資料比較 16
第三章研究方法 29
3-1 衰減模型之優化 29
3-1-1 考慮規模與距離項 29
3-1-2 增加場址項 30
3-1-3 增加震源機制項 30
3-1-4 規模平方項 31
3-1-5 挑選本研究之預估式雛型 31
3-2 預估式迴歸分析方法 32
3-2-1 最大概似法 32
3-2-2 混合效應模型 36
3-3 殘餘值分析 39
3-4 變異數拆解 40
3-4-1 變異數拆解流程 40
3-4-2 路徑相似指數(CI index) 42
3-4-3 震央距離法 42
3-4-4 半變異圖法(Semi-variogram) 43
3-4-5 變動視窗法(Spatial-correlation mobile-window method) 43
3-4-6 路徑玫瑰圖(Path diagram) 44
3-5 特定條件之變異數拆解 49
3-5-1 單一測站強地動預估式 49
3-5-2 單一地震強地動預估式 50
3-5-3 單震源對陣列之強地動預估式 50
第四章地殼震源強地動預估式建立 58
4-1 本研究之預估式分析 58
4-2 國內外預估式之比較 61
第五章殘餘值分析及變異數拆解結果 67
5-1 殘差值分析 67
5-2 事件間變異性拆解 73
5-2-1 變動視窗法(Spatial-correlation mobile-window method) 73
5-2-2 震央距離法 74
5-2-3 半變異圖法(Semi-variogram) 74
5-2-4 三種方法之比較 75
5-3 紀錄間變異性拆解 81
5-3-1 路徑玫瑰圖(Path diagram) 81
5-3-2 路徑相似性參數(CI index) 82
5-3-3 半變異圖法(Semi-variogram) 83
5-3-4 三種方法之比較 83
5-4 國內外變異性拆解之比較 90
5-4-1 事件間變異數的拆解 90
5-4-2 紀錄間變異數的拆解 91
5-4-3 單一測站標準差與單一路徑標準差 91
第六章特定條件之變異數拆解 95
6-1 單一測站強地動預估式 95
6-1-1 單站之殘餘值與變異數分析 96
6-1-2 變動視窗法 97
6-1-3 半變異圖法 97
6-2 單一震源強地動預估式 108
6-2-1 單震源之殘餘值與變異數分析 108
6-2-2 變動視窗法 109
6-2-3 半變異圖法 109
6-3 單震源對陣列之強地動預估式 119
6-3-1 單震源對陣列之殘餘值與變異數分析 119
6-3-2 半變異圖法 120
6-3-3 變動視窗法 120
第七章討論 125
7-1 路徑玫瑰圖法與CI法 125
7-2 單站之路徑效應與自然的隨機變異性 129
7-3 非彈性衰減 133
7-4 變動視窗法與半變異圖法 135
7-5 特定條件之變異數 137
7-6 自然的隨機誤差與知識的不確定性 139
7-7 地震危害度分析之應用 141
第八章結論與建議 143
參考文獻 145
附錄A 156
附錄B 166
附錄C 183
附錄D 200
附錄E 224
附錄F 233
附錄G 250

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指導教授

李錫堤(Chyi-Tyi Lee)

審核日期

2016-10-3

推文