基于广义S变换的时频分析方法及其应用
发布时间：2019-06-28 11:39
【摘要】：针对地震勘探中实际地震信号时变非平稳的特点,本文从传统傅里叶变换出发,阐述了从信号频谱分析到信号时频分析跨越的必要性。然后分类论述地震数据处理解释中常用的时频分析方法,并通过模型试算验证不同方法的适用性和缺陷。在理论上,针对常用线性类时频分析方法,基于函数空间的内积理论,将短时傅里叶变换(STFT)、连续小波变换(CWT)、S变换(ST)、广义S变换(GST)统一到同一形式下,并结合窗口和基函数概念,对比说明不同方法的时间、频率分辨率问题以及内在联系。在三大类时频分析方法中,线性类和双线性类时频分析方法,在达到信号于各数域投影的目的中都应用到了窗函数,对于线性类时频分析方法,窗函数的作用是实现时间局部性,其选择遵循海森伯格不确定性原理；对于双线性类时频分析方法,窗函数的作用是抑制交叉项,其选择存在抑制交叉项与尽可能维持最初时间、频率分辨率的矛盾。对于自适应时频分析方法,自适应核时频分析方法仍存在窗口问题,即模糊域中为抑制交叉项而产生的核函数问题。另外,基于匹配追踪的时频分析方法以及希尔伯特-黄变换(HHT)则从不同的角度,实现了信号的自适应分解,摆脱了窗口存在下的时间分辨率和频率分辨率相互牵制的束缚,但是,它们的算法实现相对复杂,并且存在对应的缺陷。本文重点由常见线性类时频分析方法出发,分别实现并对比了短时傅里叶变换(STFT)、连续小波变换(CWT)、魏格纳-威利分布(WVD)及广义S变换(GST)等几种时频分析方法。从理论和模型试算中验证了广义S变换的优越性,并得出窗口意义下的时频分辨能力并不是指单一的时间分辨率或频率分辨率的高低,而是指窗口对信号局部特点的适应性,也即时间分辨率与频率分辨率实现合理分配所体现出的窗的灵活性。最后,将广义S变换(GST)用于实际地震资料的属性提取及解释。首先对时频分析下的属性做简要说明,然后,经模型试算得出时频属性与地质属性的对应关系,最后将模型研究所得结论用于实际地震资料解释。
[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.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.4
本文编号：2507272
[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.
【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P631.4
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