由於地震歷史資料的限制以及接收站的分布之不均，海底地震的地震參數往往難以精確描述，例如2006年屏東地震由於缺乏該地區之歷史資料與地面地震接收站的方位不良，正確的地震參數至今仍在分析與爭論中。另一方面，海嘯逆推法利用水靜力學模式直接對海嘯初始波形進行逆推，對於地震參數提供了不同的觀點。
海嘯波有著長週期的特型，在外海以線性淺水波方式傳播，因此該線性的特性提供了海嘯逆推的可能性。本研究發展一個新的逆推海嘯逆推方法：『微小海嘯源逆推法』。本研究先證明了微小海嘯源在不考慮頻散效應的影響下，單純使用線性淺水波方程式可以準確的逆推出初始海嘯源。接著本研究介紹在海嘯逆推方法中所使用的最小平方法，以及多站、多事件之逆推方法，並加入平滑(smoothing)的條件，以增進逆推結果。此外，本研究開發網格位移法，在有限的計算硬體資源下提升逆推解析度。
本研究並將所研發之微小海嘯源逆推法應用至馬尼拉海溝的北端之2006年屏東地震。本研究利用中央氣象局的潮位接收站資料對此地震所造成之海嘯進行探討，重現該海嘯源原始樣貌。結果顯示了微小海嘯源逆推法對於描繪地震所造成之地表垂直變位上有不錯的結果，該結果將有利於地震參數之決定。

With limited historical earthquake records and seismographs distributed in the deep ocean, the earthquake inversion suffers from the accuracy in determining the fault parameters, such as the strike, dip, and slip angles. One example is the 2006 Ping-Tung earthquake doublet. The seismologists are debating with the fault parameters still. On the other hand, using tsunami inversion which derived directly from the hydrostatic model might provide a different aspect for the fault parameter and tsunami source determinations. As a long wave with a long wave period, tsunami waves are pure linear shallow water waves in the offshore region. The linear behavior provides great opportunity for applying inverse method. In this study, a newly developed small tsunami source (STS) inverse method will be introduced. We first demonstrate that without considering the dispersion effect from the small tsunami source, the inverse method with linear shallow water wave theory is able to predict the tsunami source accurately. We then introduce the least square method for multi-gauge and multi-events inversions with a smoothing algorithm. Finally, a grid-shifting method is developed to increase the resolution of the tsunami source but without adding too much load on CPU.
The inverse method is then applied to the 2006 Ping-Tung earthquake doublet for validating the fault parameters. The earthquake focal center is located at the north bound of the Manila trench. With accuracy fault parameters, we can have a glance the trench structure. With abundant tidal gauge data provided by CWB in Taiwan, the detail of the tsunami source can be reconstructed. The result shows that the STS method is able to determine to fault parameters. The results will be shown on the full paper.

摘要 ................................................................................................................................................................. i
Abstract .......................................................................................................................................................... ii
Catalogue........................................................................................................................................................ iv
List of Figure ................................................................................................................................................... vi
LIST OF SYMBLES ........................................................................................................................................... viii
1. Introduction ................................................................................................................................................ 1
1-1 Introduction .............................................................................................................................................. 1
1-1-1 Tsunami inversion ................................................................................................................................ 1
1-1-2 2006 Ping-Tung earthquake doublet .................................................................................................... 2
1-1-3 Small unit source tsunami inverse method .......................................................................................... 3
1-1-4 Frequency dispersion ........................................................................................................................... 3
1-2 Scope of this Thesis ................................................................................................................................... 4
2. Algorithm .................................................................................................................................................... 5
2-1 Shallow Water Equation and COMCOT Numerical Model ......................................................................... 6
2-2 Tsunami Inverse Method ........................................................................................................................... 9
2-2-1 Least square method .......................................................................................................................... 10
2-2-2 Multi-gauge and Multi-event inversion .............................................................................................. 13
2-3 Smoothing .............................................................................................................................................. 14
2-4 Grid Shifting Method ............................................................................................................................... 17
3. Result and Discussion .................................................................................................................................24
3-1 Linear Superposition Test ........................................................................................................................ 24
3-2 A fictitious Tsunami Inversion .................................................................................................................. 40
3-3 2006 Pint-Tung Tsunami Inversion .......................................................................................................... 52
4. Conclusion and Feature Work .....................................................................................................................56
Reference ......................................................................................................................................................59

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