2004-10-012024-05-15https://scholars.lib.ntu.edu.tw/handle/123456789/665770摘要：本研究將利用地球的模態疊加法之第一階擾動理論，並改善其應用計算在三維地球的長週期地震波之精確 度。對模態間在三維地球的偶合效應之計算，為簡化計算過程，傳統的模態疊加技術僅考量連接震源及接收站之間的大圓路徑下之構造, 本研究將利用數值積分的方式將全球的三維構造列入計算範圍.為提高數值積分運算的使用效率，本研究將利用球諧波函數建構地球的三維構造，且將計算過程分成兩個步驟。首先，我們利用數值積分計算模態間相對於任一震矩張量及任一在特定座標下的球諧波函數之偶合效應，並將結果列表存放。接著，對於任何給定的地球三維構造模型，我們可將其模型函數旋轉到該特定座標。如此，則前步驟的結果即可如”格林函數”般應用於模擬地震波動之計算。雖然以上第一步驟之計算量將隨著模態的角序數(angular order)之增加而提高，但其計算結果卻可應用於任一地球三維構造模型及任一震源及接收站的組合。本研究之結果將可改善目前的震波全球構造造影，協助我們推估更可靠的地球三維構造。<br> Abstract: We request support for a one year program to develop a new technique for the computation of synthetic seismic waveforms. With the formulism of the first order normal mode perturbation theory, this study aims to improve the accuracy of long-period synthetic seismic waveforms in a 3D Earth model. Unlike the traditional normal mode summation based approaches, in which the coupling effects among modes are calculated only along the great-circle path (e.g., along the same branch, path-average approximation; or across different branches, non-linear asymptotic theory), this new technique takes into account the complete global 3D effects by numerical integrations. To compromise the time-consuming numerical integrations, spherical harmonics are used as model coefficients, and the procedure will be implemented in two steps. First, the coupling effects among modes from each source moment tensor and spherical harmonics of a particular geometry are computed and stored as a table file. Second, for any given 3D Earth model, the model coefficients are rotated (Euler rotation) to the desired geometry in which the tabled file can be directly used as “green’s function”, and the computation of synthetics is then straightforward. While the numerical cost in the first step is expensive for modes with large angular orders, its resulting table file can be applied to any combination of seismic sources, receivers and any 3D Earth model. The proposed new technique will benefit the global seismic tomography, leading to more reliable seismological constraints to the Earth structure. In particular, it’s potentially very useful for seismic attenuation tomography, as the inclusion of off-great-circle path effects brings a more precise estimate in amplitudes of seismic waveforms due to the 3D elastic structure, which must be removed to accurately account for anelastic effects.合成地震波地球的模態疊加法震波造影synthetic seismogramnormal mode summationseismic tomography