本研究利用時空聚焦(聚合)理論及波形逆推法結合互逆格林函數，提出一個決定海嘯初始水位之方法。海嘯與地震息息相關，現行海嘯數值模式中均依賴斷層參數與半彈性理論計算海嘯初始水位；但實際上，海底斷層參數獲得不易，故海嘯初始水位甚難被準確決定；另一方面，雖經由地震波可以推測斷層參數，但是由於地層是不均勻的介質，因此，利用地震波決定所需之斷層參數仍有相當大之改進空間。對於海嘯模擬而言，若能得知海嘯初始水位，可藉此推估對應之斷層參數。由於海嘯在大洋中之傳遞是一種線性行為，傳遞過程受大洋之地形影響及非線性效應甚微，故滿足線性淺水方程式及可逆性之要求；但在實務中，用來量測水位之潮位站均佈設於近岸，受淺化效應之影響，線性系統之可逆性並無法直接應用於近岸區。因此，本研究整體逆推程序分為兩部份：利用變係數KdV及聚合理論將近岸潮位站之水位資料逆推至水深大於50m以上之線性區，並將逆推結果與模式比對以確認波形逆推之準確性；第二部份根據線性系統之可逆性，使用最小平方法與最小平方QR分解法重現海嘯初始波源，並與模式的海嘯初始波源進行比對均有相當穩合的結果，該結果將有利於斷層參數之決定。

In this study, the method of deciding the water level of the initial tsunami is proposed by using spatial-temporal focusing (Coalescence) theory and waveform inversion reciprocal with Green function. Tsunami and earthquake are so closely bonded that the current tsunami numerical model is dependent on the parameters of the fault and the initial tsunami water level by calculating the theory of
half flexibility. But in fact, it is not easy to have the parameters of seabed fault so that the initial tsunami water level is very hard to get a accurate value. On the other hand, although the parameters of fault can be speculated by seismic waves, because ground is uneven medium, therefore, it is still a lot of improvement to get the parameters of fault by using seismic waves. For the tsunami simulation, if you have the value of the initial tsunami water level, the fault parameters can be estimated.Since the propagation of tsunami in the ocean is a linear behavior, the propagating process is affected by the topography of the ocean and the nonlinear effect
so minimal that it is to satisfy the linear shallow water equations and the requirement of reversibility;However, in fact, the values of the water level measured by the tide stations on the coast are influenced by the shoaling effect so that the reversibility of linear system can not be directly applied to Coastal areas.Therefore, the overall Inversion procedure on this study consists of two parts; the first one is that the usage of variable
coefficient Korteweg-de Vries (vKdV) equation and the Coalescence theory inverses the data gathered by the Coastal tide stations to the water level data where the depth is more than 50m on the linear region, and compares the above results with the stimulation and confirms the accuracy of the inversed waveform;The second one is that according to the reversibility of the linear system the use of least squares and least squares QR- decomposition (LSQR) method reproduce the initial tsunami wave source that compares with the initial tsunami wave source by stimulating and has a very good conformity. The seismic parameters can be easily decided by the above results.

第一章 緒論 1
1.1 前言 1
1.2 研究動機與目的 2
1.3 文線回顧 2
1.4 研究方法 4
1.5 本文內容 5
第二章 相關理論簡介及說明 6
2.1 海嘯與地震之關係 6
2.2 傳統海嘯波源驅動模式及海嘯初始水位 9
2.3 海嘯數值模式與互逆格林函數 13
2.3.1海嘯數值模式 13
2.3.2 互逆格林函數 15
2.4 海嘯於近岸之傳遞行為與KdV方程式 17
2.4.1 淺水方程的數值模型 17
2.4.2 孤立波與KdV方程式 18
2.5 變係數KdV方程式與聚合理論 24
2.5.1 變係數KdV方程式 24
2.5.2 聚合理論 27
2.5.3 數值方法 29
2.6 逆推法與最小平方法 30
2.7 最小平方QR分解法 31
第三章 非線性頻散波形逆推之數值試驗 33
3.1 聚合理論逆推程序 33
3.2 聚合理論逆推波形試驗 34
3.2.1 模擬平坦底床之孤立波 35
3.2.2 模擬平坦底床之N形波 36
3.2.3模擬先平底後斜坡底床之孤立波 36
3.2.4 模擬先平底後斜坡底床之N形波 37
3.3 座標轉換試驗與其驗證 37
3.3.1 以平坦底床之餘弦波驗證座標轉換 38
3.3.2 以真實底床之餘弦波驗證座標轉換 39
3.3.3 以平坦底床之孤立波驗證座標轉換 39
3.3.4 以真實底床之孤立波驗證座標轉換 40
3.4 小結 41
第四章 利用海嘯模式進行逆推驗證 51
4.1 南亞海嘯簡介 51
4.2 斷層參數及地形設定 52
4.3 參數設定與演算流程 53
4.3.1 Arugam站 54
4.3.2 Goadu站 55
4.4 利用海嘯逆推法進行逆推模擬 55
4.5 海嘯波源逆推結果 61
第五章 結論與建議 72
5.1 結論 72
5.2 建議 73
參考書目 75

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