考量震波之群延時及相位譜特性之強地動模擬

Consider group delay time and phase spectrum characteristics of ground motion to simulate earthquake motion

凃雅瀞(Ya-Ching Tu)

指導教授 ： 羅俊雄

國立臺灣大學/工學院/土木工程學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201701120

摘要

進行強地動模擬研究時，相位是影響模擬結果的重要因素。因此，相位衍伸出的物理量-群延遲時間的研究是必要課題。本研究利用Meyer小波對強地動歷時進行離散小波轉換，將一筆強震資料解構成多筆包含不同頻寬的時間序列。經由傅立葉轉換以及群延遲時間的基本定義，可以計算單筆歷時經分解後的各成分波頻率對應的群延遲時間並進行統計分析。透過尋找符合不同頻寬下的群延遲時間機率分布狀態的機率密度函數，可以求得相對應的統計參數如:平均值及標準差。對所有測站特定頻寬下的群延遲時間平均值及標準差運用回歸分析研究，可以得到群延遲時間的平均值、標準差與測站震央距的相關性，並且決定回歸曲線的各個參數值。藉由選定的場址及經由統計分析獲得的回歸公式，即可以預測該場址不同頻寬的成分波群延遲時間的平均值及標準差並創造出多筆符合這樣的統計特性的群延遲時間。此時，為了將數據庫裡其他測站的群延時特性納入考量，我們利用卡爾曼濾波技術作為預測校正的工具以修正預測的每一個頻率對應的群延遲時間。將修正後單筆群延時資料進行積分運算，便可得每個頻率所對應的相位。結合不同頻率對應的傅立葉振幅及相位進行傅立葉逆傳換，便可模擬出單筆含有不同相位譜特性的強地動地表振動歷時。
最後，我們採用20160206美濃地震強地動資料，模擬特定測站的振動歷時，並與該測站的原始紀錄資料同時進行動力分析以比較兩者結構反應差異。藉此對我們發展的理論進行驗證。同時，也將討論不同地區或不同事件之間群延遲時間的平均值或標準差的差異。

關鍵字

強地動模擬 ； 相位譜 ； 群延遲時間 ； 卡爾曼濾波 ； 美濃地震 ； 甲仙地震

並列摘要

Modelling the phase of earthquake ground motion, particularly the group delay time, is required to investigate the ground motion simulation. In this study, the group delay time of each earthquake ground motion was investigated by using discrete wavelet transform (Meyer’s wavelet) on each compact support of a specific earthquake event. Through statistically analysis, the function form of probability density function of group delay time was assumed. The mean and standard deviation of group delay time on each decomposed component were developed for each layer of wavelet transform. With the regression analysis, the relationship between epicentral distance and group delay time were determined for the selected earthquake event. Through the decided regression coefficient and the given epicentral distance, the statistical parameters of group delay time can be predicted. Then, Kalman filter technique was implemented as a predictor-corrector of group delay time by considering nearby stations characteristics to update the estimated group delay time. Combining the simulated group delay time from statistical analysis and the selected site-specific amplitude the ground motion, the ground motion simulation can be generated.
Based on the ground motion data collected from 2016 Meinong earthquake, the developed algorithm on group delay time for ground motion simulation is examined. Finally, influence of structural response by using the concept of group delay time to simulate the ground motion (proposed by this research) and the original ground motion data (true recorded data) was discussed. Comparison on the estimated group delay time between different site condition and different seismic event was also discussed.

並列關鍵字

Earthquake motion simulation ； Phase spectrum ； Group delay time ； Kalman filter estimator ； Meinong earthquake ； Jiashian earthquake.

參考文獻

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