https://scholars.lib.ntu.edu.tw/handle/123456789/45088
標題: | 多重尺度震波走時層析成像 | 作者: | 喬凌雲 | 關鍵字: | 層析成像;複尺度分析;自然正規因子;尺度-位置之同時標定;球面小波;continuous inverse problem;seismic tomography;multiresolution analysis;space-scale localization;spherical wavelets | 公開日期: | 2001 | 出版社: | 臺北市:國立臺灣大學海洋研究所 | 摘要: | 震波走時層析成像的本質是連續地球物理逆 推問題,但是由於波線趨近之下,此一逆推問題之 資料算核(data kernel)在垂直波線方向之頻譜寬 度無法界定,因此使得Gram 矩陣(由資料算核之內 積組成)無法正常計算。為進行這類型的研究,勢必 對於想要推估之速度模型預先執行有限參數化。傳 統上這種有限參數化以球諧函數和箱型函數為 主。近年來,由於震波走時資料之大量累積,各種 容納高自由度之地球層析成像模型似乎具有愈益 提高之解析度,也似乎提供愈益細緻的地球內部構 造。但是由於這些層析成像模型彼此之間有相當程 度的歧異,使得現階段之震波走時資料到底對於地 球內部構造具有何種程度之解析能力成為需要釐 清之課題。近年來,對於有限參數化所可能導致的 映頻效應已經有較佳的掌握,但是基於不同基底函 數之參數化以及不同型式的正規化 (regularization)方式對於層析成像模型的影響 雖為許多研究致力的方向,但目前累積的共識仍以 經驗為主。我們相信參數化與正規化的一個核心問 題未受應得之評估,即特定參數化所選擇基底函數 之尺度-位置可同時標定的程度。利用近年來快速 發展之複尺度分析,將球面小波基底函數成功應用 於震波走時層析成像,我們發現這種參數化方式不 但易於計算,而且所獲致結果較諸傳統的球諧函數 和箱型函數具有低數十倍的模型變量(model variance)。且由於此一參數化方式本身即已具自 然正規化之功能,不須借助額外無法驗證之先驗條 件來設計正規化之運作,因此提供由資料本身所真 正具有之解析能力。本計劃成功發展此一參數化方 式之相關理論以及演算法則並將之利用於不同型 式的層析成像問題以及其他的連續地球物理逆推 問題。在利用Sd-SKS 差異走時描繪核幔邊界的研 究上有極佳之表現。 Seismic travel time tomography is commonly discretized by a truncated expansion of the pursued model in terms of chosen basis functions. The robustness of the resulting Earth model as well as whether parameterization affects the actual resolving power of a given data set have long been seriously debated. From the perspective of the model resolution, however, there is one important aspect of the parameterization issue of seismic tomography that has yet to be systematically explored, that is, the space-frequency localization of a chosen parameterization. In fact, the two most common parameterizations tend to enforce resolution in each of their own particular domains. Namely, the parameterization in terms of spherical harmonics with global support tends to emphasize spectral resolution while sacrificing the spatial resolution, whereas the compactly supported pixels tend to behave conversely. Some of the significant discrepancies among tomographic models are very likely to be manifestations of this effect, when dealing with data set with non-uniform sampling. With an example of the tomographic inversion for the lateral shear wave heterogeneity of the D” layer using S-SKS travel times, we demonstrate an alternative parameterization in terms of the multi-resolution representation of the pursued model function. Unlike previous attempts of multi-scale inversion that invoke pixels with variable sizes, or overlay several layers of tessellation with different grid intervals, our formulation invokes the biorthogonal generalized Harr wavelets on the sphere. We show that the multi-resolution representation can be very easily constructed from an existing blocks-based discretization. A natural scale hierarchy of the pursued model structure constrained by the resolving power of the given sampling is embedded within the obtained solution. It provides a natural regularization scheme based on the actual ray-paths sampling and is thus free from a priori prejudices intrinsic to most regularization schemes. Unlike solutions obtained through spherical harmonics or spherical blocks, that tend to collapse structures onto ray-paths, our parameterization imposes regionally varying Nyquist limits, that is, the robustly resolvable local wavelength bands within the obtained solution |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/14781 | 其他識別: | 892611M002043 | Rights: | 國立臺灣大學海洋研究所 |
顯示於: | 海洋研究所 |
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