2008-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/672872摘要：本研究延續上一年度的計畫進度，希望建立高解析度的太平洋地區上部地函非均向性模型。 　　在上一年度的計畫(95WFA0102279)中，我們運用新的技術(詳見前述計畫報告中C012-1附件)建立了太平洋地區的剪力波速度(isotropic Vs)模型，現在我們將利用三分量的波形資料，以自由震盪理論為基礎的(normal-mode-based)非線性偶合理論(non-linear asymptotic coupling theory)建立太平洋地區上部地函剪力波速度非均向性的構造模型。 　　我們提出兩階段的側向參數化模型，以提高正演計算(forward computation)的精確性，並且於震波反演(inversion)時保有良好的靈活度。首先，以球諧波函數(spherical harmonics)作為參數化模型，球諧波函數在大圓路徑上可分解成正弦與餘弦函數，能提供運算核(kernels)所需的路徑積分擁有高效率與精確的解析解等優勢；接著，利用球諧波函數的正交特性，將球諧波函數為參數化模型的運算核，轉換到球面三球形(spherical triangular mesh)的節點(nodes)上。於轉換後，僅有約10~15%的節點具有效感應(effective sensitivity)，如此一來，便可大量降低反演時所需的運算量。 　　我們可以利用這個新的矩陣反演以格點為基底的單一尺度層析成像，以及以小波為基底的多尺度層析成像。換言之，此項新的技術利用單一的正演計算，卻可得到三種不同模型基底(model basis)之反演所需的偏微分矩陣(partial derivative matrices)。 <br> Abstract: To continue the study of our last proposal, we request support for another one year program to complete a high resolution model of seismic anisotropy of the Pacific upper mantle. In the last project (95WFA0102279), we have constructed an isotropic model for the Pacific region with the proposed new technique (For details, please see C012-1, the progress report of 95WFA0102279). We plan to move forward to the anisotropic case with three-component of waveform data in the time domain in the framework of normal-mode-based asymptotic coupling theory [Li and Romanowicz, 1995] for the upper mantle structure underneath the Pacific. In particular, we propose a two-step lateral model parameterization approach, by which both the accuracy in the forward computation and the flexibility in the inversion stage are achieved. In the first step, the model is parameterized in terms of spherical harmonics. Spherical harmonics can be simplified to cosine and sine functions in the great circle path connecting the source and receiver, allowing an efficient and accurate analytical solution for the path integral required in the computation of synthetics and partial derivatives. In the second step, partial derivative matrices w.r.t. spherical harmonics are mapped onto nodes of the spherical triangle meshes within the selected region. Taking advantage of the orthogonality of spherical harmonics, the above conversion is straightforward. After mapping, only about 10-15% of nodes receive effective sensitivities. As a result, the computation cost in the stage of inversion is significantly reduced. With the new matrices, we may utilize either the grid-based fixed-scale or the wavelet-based multi-scale inversion technique [eg.Chiao and Liang, 2003] for the regional tomography. The new approach allows us to obtain partial derivative matrices from three different model basis for the same data set, and only one forward computation is required.多尺度層析成像表面波震波非均向性multi-scale tomographysurface wavesseismic anisotropy