本徵振盪理論地震圖的推導與實踐 — 台灣南部之表面波層析成像

本徵振盪理論 (normal mode theory) 是地震學上發展十分完整的理論之一。由於它同時兼具計算上的效率與理論本身的準確性，是使我們了解地震波在球對稱（側向均勻）地球模型中傳播特性的重要工具。藉由地震所激發的能量，此理論已被廣泛用於探討地球本身的共振頻率，也提供我們對其內部的震波結構（如Ｐ波、Ｓ波速度及密度）有更進一步的研究。本論文同時著重本徵振盪理論及其應用兩方面。首先，我們利用廣義球諧函數 (generalized spherical harmonics) 及座標轉換，重新推導在球對稱模型中空間上任一點的理論地震位移，因為其質點運動可表示成地球本徵振盪的線性疊加 (normal mode summation)。相較於利用一般球諧函數 (ordinary spherical harmonics) 展開的表示式，新的表達式更為精簡。透過理論地震圖在不同模型下的比較，我們能夠直觀的探討地球本身重力 (self-gravitation)、衰減 (attenuation)、徑向非均向性 (radial anisotropy) 對於震波形的影響。應用方面，我們發展了以小波 (wavelet) 為基礎的測量表面波相速度 (phase velocity) 的方法。由於本徵振盪理論不僅提供理論合成波形，也能夠計算其所對應的相速度值，透過它能驗證我們發展的量測方法是否準確。再者，將此方法應用在台灣南部的臨時寬頻測站，進而得到此區域地殼及上部地函的剪力波速度構造，藉此了解現今活躍的造山運動所影響地殼變形的程度。這是第一個由遠震表面波所逆推的台灣區域非一維構造。與近震體波走時 (local body-wave traveltime) 求得的模型相較，兩者的速度構造相近。但在西部下部地殼以下，我們的模型有相對較好的解析能力。我們推測北港高區附近變形前緣下方深度20-40公里的高速異常，應是岩漿底侵 (magmatic underplating) 而形成的部份下部地殼。形成機制可能與南海張裂造成被動大陸邊緣的拉張活動有關。相較於中央山脈下方已增厚的地殼，此近乎完整的高速區，暗示弧陸碰撞 (arc-continent collision) 所造成的下地殼變形還侷限在側向距離縫合帶~50公里以內的區域。我們的速度模型，為解釋因板塊碰撞撞而引起的造山運動及其它更早期的構造演化，提供了新的可靠的地震學依據。

關鍵字

本徵振盪理論地震圖；表面波層析成像；相速度；小波；弧陸碰撞

並列摘要

Normal mode theory, which compromises accuracy and efficiency in computation, allows us to investigate wave propagations in a spherically symmetric earth model. This theory has been widely used in exploring the resonant frequencies of the Earth excited by large earthquakes, and is able to provide insights into seismic structures of the Earth. In this thesis, we focus on synthetic waveforms expressed by normal-mode summation as well as application to surface-wave tomography. A new derivation of displacement in response to seismic sources in terms of the modal summation of the Earth is presented. Starting from the well-known formal expression of normal-mode summation, we obtain the explicit expressions of displacements by means of generalized spherical harmonics and coordinate transformation. Moreover, numerical experiments of normal-mode synthetics are conducted to investigate the influences of self-gravitation, attenuation, radial anisotropy, density and P-wave speed on seismic waveforms. We develop a wavelet-based measurement of surface-wave phase velocities and then apply this method to a linear temporary array with ~140 km span in southern Taiwan to obtain shear-wave speed structures in the crust and uppermost mantle. Synthetic tests using waveforms in both spherically symmetric and 3D heterogeneous models verify the reliability of our measurement approach. Our seismic images reveal similar features in the crust to those constrained by local body-wave travel-time tomography, while yielding more robust features down to the depth of 70 km. Our model particularly improves the resolution beneath western Taiwan, where the lower crust is characterized by high seismic speed. This feature is probably pertain to magmatic underplating as a consequence of the opening of the South China Sea and has remained unscathed during arc-continent collision. Our tomography model provides new reliable seismological evidence for the tectonic evolution of Taiwan as a result of the convergence between Eurasian and Philippine Sea Plates.

並列關鍵字

normal-mode synthetic seismograms ； surface-wave tomography ； phase velocity ； wavelet ； arc-continent collision

參考文獻

Al-Attar, D. & Woodhouse, J.H., 2008. Calculation of seismic displacement fields in self-gravitating earth models-applications of minors vectors and symplectic structure, Geophys. J. Int., 175, 1176-1208.

Bao, H., Bielak, J., Ghattas, O., Kallivokas, L.F., O’Hallaron, D.R., Shewchuk, J.R. & Xu, J., 1998. Large-scale simulation of elastic wave propagation in heterogeneous media on parallel computers, Comput. Methods Appl. Mech. Eng., 152, 85–102.

Bautista, B.C., Bautista, M.L.P., Oike, K., Wu, F.T. & Punongbayan, R.S., 2001. A new insight on the geometry of subducting slabs in northern Luzon, Philippines, Tectonophysics, 339, 279-310.

Bielak, J., Loukakis, K., Hisada, Y. & Yoshimura, C., 2003. Domain reduction method for three-dimensional earthquake modeling in localized regions. Part I: Theory. Bull. Seism. Soc. Am. 93, 817-824.

Boore, D.M., 1972. Finite-difference methods for seismic wave propagation in hetergeneous materials, in: Methods in Computational Physics, pp.1-37, ed. Bolt, B.A., Academic Press, New York, NY.

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本徵振盪理論地震圖的推導與實踐 — 台灣南部之表面波層析成像

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