Title

太平洋地區上部地函多重尺度之表面波層析成像

Translated Titles

Multi-scale Waveform Tomography of the Pacific Upper Mantle Using Surface Wave Data

DOI

10.6342/NTU.2008.02543

Authors

許雅婷

Key Words

波形震波層析成像 ; 太平洋上部地函 ; 多重尺度有限參數法 ; 球諧函數 ; 非線性漸進耦合理論 ; waveform tomography ; the Pacific upper mantle ; multi-scale parameterization ; spherical harmonics ; NACT

PublicationName

臺灣大學地質科學研究所學位論文

Volume or Term/Year and Month of Publication

2008年

Academic Degree Category

碩士

Advisor

龔源成

Content Language

繁體中文

Chinese Abstract

受限於地震大多發生在特定位置及測站幾乎處於大陸區塊,波線資料分佈不甚均勻,為此,模型的參數化方式很有可能是影響速度構造反演結果的原因之一。本研究的震波波形反演 (waveform tomography) 以兩階段的參數化轉換,結合多重尺度 (multi-scale) 的逆推解析,讓區域性的解析尺度端其資料密度自然決定,以解決上述震波資料不均衍生的種種問題。首先,在正演計算 (forward computation) 的部分採用以normal mode理論為基礎的非線性漸進耦合理論 (non-linear asymptotic coupling theory, NACT),此階段,我們以球諧函數 (spherical harmonics) 為模型基底,球諧函數在大圓路徑上可分解成數組正弦 (sine) 與餘弦 (cosine) 函數,提供高效率與精確的路徑積分解析解。但是隨著預設解析尺度越精細 (即求解到越高階),以球諧函數為基底的模型參數量將正比於 ,反演的運算效率因此大為減弱。在不降低解析尺度的前提下,參數化的第二階段,我們將球諧函數展開後的敏感度算核 (sensitivity kernel) 轉化到局部節點 (node) 上,轉換後的區域性基底僅有10-15%的節點具有有效感應 (effective sensitivity),大大減少反演所需的參數量。藉由兩階段的模型參數化,我們得以在保有不同階段參數化基底的條件下,於逆推反演時持有模型的靈活度,透過此轉化後的區域性偏導數矩陣,求得以節點為基底的單一尺度解析亦或以球面小波為基底的多重尺度解析。本研究方法將首次應用於太平洋上部地函,環太平洋地震帶及其周圍測站提供的充足跨洋傳波路徑,使得本區實為表面波研究的不二選區。比較單一尺度模型與多重尺度模型可以發現,其皆可再進一步改善對大尺度構造已有一定解析能力的初始三維全球模型 (SAW642AN) 額外近25%的擬合程度。另一方面,兩種模型解相似度極高,可能原因有:(1)配合NACT使用的資料權重配予會適度平緩資料密度不勻的問題,無法發揮多重尺度解析固有的優勢。(2)以NACT求得的敏感度算核為一在側向無寬度的二維運算核,但在有限的球諧函數參數化下,其於側向將擁有一定寬度,致使模型側向較平滑。往後我們將納入非均向性 (anisotropy) 的考量與更完善的地殼修正,並簡化過於人為操造的權重配給,在多重尺度有限參數化的逆推方式下,因應資料本身於空間中帶有的有效訊息,對速度構造提供更具體的解釋。

English Abstract

Owing to the abundant circum-Pacific earthquakes and seismic stations, the coverage density of trans-Pacific minor-arc surface waves is highest among the globe, making the region an excellent candidate for the high resolution surface waves tomography. We invert long period waveform of Rayleigh waves 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 initial 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 and therefore forward synthetics. 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 the 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 Kuo, 2001] 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. We present the tomographic results, compare models derived from different model parameterizations, and discuss how the tomographic features are influenced by model parameterizations.

Topic Category 基礎與應用科學 > 地球科學與地質學
理學院 > 地質科學研究所
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