| 摘要: | 地動預估式 (Ground Motion Prediction Equation, GMPE) 是根據大量地震觀測資料所建立的經驗模型，用於預測如最大地表加速度等地動值，也是機率式地震危害度分析 (Probabilistic Seismic Hazard Analysis, PSHA) 的主要預測工具。現行多數地震危害度分析研究會採用多組GMPE，並透過邏輯樹方法加權整合各模型結果，作為最終評估依據。然而，由於邏輯樹中各分支權重多由專家判斷決定，PSHA邏輯樹分析常被批評結果過於主觀，缺乏客觀性。
本論文主要探討三個主題：(1) 利用台灣災害地震觀測資料，計算四種評分指標，對60組GMPE候選模型進行排序，篩選出適用於台灣的GMPE；(2) 提出一套客觀計算GMPE邏輯樹權重的新方法，使權重與各GMPE的發生機率成正比；(3) 建立一個以數學方法為基礎的GMPE，並與上述篩選出的最佳GMPE進行表現比較。
研究結果顯示，Cauzzi et al. [147] 所建立之GMPE，在各項指標下均能最佳擬合台灣5088筆地震觀測資料，可視為最適用於台灣地區的GMPE。以概似函數為排序指標時，可以客觀計算GMPE邏輯樹權重。此外，本研究建立的數學型GMPE，在預測台灣地震動方面，其表現與現有最佳GMPE相當。
需要強調的是，受到概似函數計算特性與大量樣本數影響，本研究提出的方法計算出的GMPE邏輯樹權重會出現極端分布，權重幾乎全部集中於單一模型。換言之，雖然以GMPE發生機率作為權重在理論上合理，但當樣本數較大時，實際結果往往過於極端。最後，本研究結論僅反映本次資料集下的最佳判斷，未來若有新資料並採用相同方法時，分析結果亦可能有所改變。;Ground Motion Prediction Equations (GMPEs) are empirical models developed with extensive earthquake observation data. They are used for predicting ground motion intensity measures, such as peak ground acceleration (PGA), and are the performance function for seismic hazard analysis, including probabilistic seismic hazard analysis (PSHA). On the other hand, most modern PSHA case studies use multiple GMPEs and integrate the individual outcomes with the so-called “logic-tree analyses” to obtain the weighted average as the (final) result. Nevertheless, the PSHA logic-tree analysis has been criticized for being subjective due to the logic-tree weights that are determined with subjective judgments.
This thesis focused on the three topics: 1) searching for suitable GMPEs for Taiwan, by ranking 60 GMPE candidates based on 4 indexes computed with strong-motion earthquake data recorded from damaging earthquakes in Taiwan; 2) proposing a new method to compute GMPE logic-tree weights objectively, which are proportional to the occurrence probability of the GMPEs; 3) developing a “math-based” GMPE and comparing its performance with the suitable ones.
The findings of the thesis are as follows: 1) the GMPE developed by Cauzzi et al. [147] is most suitable for Taiwan, with its predictions considered closest to the 5088 observations regardless of which index was adopted; 2) based on the likelihood functions, which is one of the indexes for model ranking, the GMPE logic-tree weights can be computed objectively; 3) the performance of the “math-based” GMPE is comparable to the most suitable GMPE recommended.
Nevertheless, it is noted that mainly due to the nature of likelihood function calculation and the relatively large sample size used in this study, the GMPE logic-tree weights computed with the proposed method are “unconventional” (almost 100% to 0). In other words, although the idea - GMPE logic-tree weights proportional to GMPE occurrence probability - is sound from the standpoints of probability, the result will be extreme in most cases (especially with a large sample size). Also, the findings of the study are the best judgments or inferences from the pool of observations used, and they will be altered when new data are used with the same methodology. |
