【摘要】：針對地震勘探中實際地震信號時變非平穩(wěn)的特點,本文從傳統(tǒng)傅里葉變換出發(fā),闡述了從信號頻譜分析到信號時頻分析跨越的必要性。然后分類論述地震數(shù)據(jù)處理解釋中常用的時頻分析方法,并通過模型試算驗證不同方法的適用性和缺陷。在理論上,針對常用線性類時頻分析方法,基于函數(shù)空間的內積理論,將短時傅里葉變換(STFT)、連續(xù)小波變換(CWT)、S變換(ST)、廣義S變換(GST)統(tǒng)一到同一形式下,并結合窗口和基函數(shù)概念,對比說明不同方法的時間、頻率分辨率問題以及內在聯(lián)系。在三大類時頻分析方法中,線性類和雙線性類時頻分析方法,在達到信號于各數(shù)域投影的目的中都應用到了窗函數(shù),對于線性類時頻分析方法,窗函數(shù)的作用是實現(xiàn)時間局部性,其選擇遵循海森伯格不確定性原理；對于雙線性類時頻分析方法,窗函數(shù)的作用是抑制交叉項,其選擇存在抑制交叉項與盡可能維持最初時間、頻率分辨率的矛盾。對于自適應時頻分析方法,自適應核時頻分析方法仍存在窗口問題,即模糊域中為抑制交叉項而產生的核函數(shù)問題。另外,基于匹配追蹤的時頻分析方法以及希爾伯特-黃變換(HHT)則從不同的角度,實現(xiàn)了信號的自適應分解,擺脫了窗口存在下的時間分辨率和頻率分辨率相互牽制的束縛,但是,它們的算法實現(xiàn)相對復雜,并且存在對應的缺陷。本文重點由常見線性類時頻分析方法出發(fā),分別實現(xiàn)并對比了短時傅里葉變換(STFT)、連續(xù)小波變換(CWT)、魏格納-威利分布(WVD)及廣義S變換(GST)等幾種時頻分析方法。從理論和模型試算中驗證了廣義S變換的優(yōu)越性,并得出窗口意義下的時頻分辨能力并不是指單一的時間分辨率或頻率分辨率的高低,而是指窗口對信號局部特點的適應性,也即時間分辨率與頻率分辨率實現(xiàn)合理分配所體現(xiàn)出的窗的靈活性。最后,將廣義S變換(GST)用于實際地震資料的屬性提取及解釋。首先對時頻分析下的屬性做簡要說明,然后,經模型試算得出時頻屬性與地質屬性的對應關系,最后將模型研究所得結論用于實際地震資料解釋。
[Abstract]:In view of the fact that the actual seismic signal is time-varying and non-stationary in seismic exploration, this paper expounds the necessity of crossing from signal spectrum analysis to signal time-frequency analysis based on the traditional Fourier transform. Then the time-frequency analysis methods commonly used in seismic data processing and interpretation are classified and discussed, and the applicability and defects of different methods are verified by model trial calculation. In theory, aiming at the commonly used linear time-frequency analysis methods, based on the inner product theory of function space, the short-time Fourier transform (STFT), continuous wavelet transform (CWT), S transform (ST), generalized S transform (GST) is unified into the same form, and combined with the concepts of window and basis function, the time and frequency resolution of different methods and their internal relations are compared and explained. Among the three kinds of time-frequency analysis methods, linear class and bilinear time-frequency analysis methods are applied to window function in achieving the purpose of signal projection in each number domain. for linear time-frequency analysis method, the function of window function is to realize time localization, and its choice follows Heisenberg uncertainty principle. For bilinear time-frequency analysis method, the function of window function is to suppress the cross term, and there is a contradiction between suppressing the cross term and maintaining the initial time and frequency resolution as much as possible. For the adaptive time-frequency analysis method, there is still a window problem in the adaptive kernel time-frequency analysis method, that is, the kernel function problem caused by suppressing the cross term in the fuzzy domain. In addition, the time-frequency analysis method based on matching tracking and Albert-Huang transform (HHT) realize the adaptive decomposition of the signal from different angles, and get rid of the constraint of time resolution and frequency resolution in the presence of windows. However, their algorithms are relatively complex and have corresponding defects. In this paper, based on the common linear time-frequency analysis methods, several time-frequency analysis methods, such as short-time Fourier transform (STFT), continuous wavelet transform (CWT), Wigner-Willie distribution (WVD) and generalized S transform (GST), are implemented and compared respectively. The superiority of the generalized S transform is verified from the theoretical and model calculations, and it is concluded that the time-frequency resolution in the sense of window does not refer to the single time resolution or frequency resolution, but to the adaptability of the window to the local characteristics of the signal, that is, the flexibility of the window reflected in the reasonable distribution of time resolution and frequency resolution. Finally, the generalized S transform (GST) is applied to the attribute extraction and interpretation of practical seismic data. Firstly, the attributes under time-frequency analysis are briefly explained, and then the corresponding relationship between time-frequency attributes and geological attributes is obtained by model trial calculation. Finally, the conclusions of the model are applied to the interpretation of actual seismic data.
【學位授予單位】：吉林大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：P631.4

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