【作者】 徐云霞；

【导师】 王山山；

【作者基本信息】 成都理工大学 ， 应用地球物理， 2010， 硕士

【摘要】 对信号的传统分析方法是傅里叶变换,但是对地震信号这种典型的非平稳信号而言,传统的傅里叶变换不能达到分析要求,需要进行时频联合域分析。目前时频分析技术已被广泛应用于时变滤波去噪、检测地层变化特征、提高地震资料分辨率等物探领域中。本研究主要通过对连续小波变换和逆谱分解进行研究以形成高精度时频分析方法,并将该方法运用于理论试算和实际资料处理中。在连续小波变换中,有三个非常重要的参数:小波函数、尺度范围及变换所选择的尺度步长。对信号采用不同的小波函数进行分析,将得到不同精度的时频分析结果;尺度与频率对应,较好的选择尺度的分析范围能够更准确的分析信号频率;变换尺度步长的选择对能否较好的分析信号的局部特征有重要影响;小波变换的结果是时间-尺度域结果,不能从变换域直接得到信号的频率信息;同时对信号的分析要满足能对信号实现的重构,分析才具有实际意义。因此本文对小波函数的选择、变换尺度范围的确定和变换时所采用的尺度步长进行了深入研究;研究了尺度与频率的对应关系,通过这种关系可以直接得到对应的频率信息;对连续小波变换的重构问题进行研究,保证用小波变换进行资料处理时具备一定的实际意义。逆谱分解是基于连续小波反变换和约束条件的,小波函数的选择和约束条件对分解结果的精度有重要影响。逆谱分解的分析结果相对其他时频分析方法如短时傅里叶变换、小波变换而言具有更高的精度。在逆谱分解方法中,本文主要研究了L1、L2和稀疏脉冲三种约束条件对分析结果的影响,通过理论模型试算得出三种约束的分析精度是逐渐升高的,其中稀疏脉冲约束(sparse spike)具有最高的精度。本文在对高精度时频分析方法理论研究成功的基础上,将该方法的研究运用于实际资料处理和解释中,在分频资料解释和高分辨率处理中均取得较好的应用效果。更多还原

【Abstract】 The traditional analysis method of signal is Fourier transform, but to the typical non-stationary signal such as seismic signal, this method can’t reach the requirement, it is need to use time and frequency domain to analysis. As the widely use of time-frequency analysis method in petroleum exploration, it’s researched by many people.This research mainly through continuous wavelet transform and inverse spectral decomposition research to form high-precision time-frequency analysis method, then use these methods in theoretical calculation and practical data processing.In CWT, there are three important parameters: wavelet function, the space of scale and the step. Adopting different wavelet function to analyse the signal will get different resolution results; The scale is related to frequency, the much better choice of the scale range the better frequency results will be obtained; The choice of step is related to the partial feature of the signal. The result of wavelet transform is time-scale range, we can’t obtain the information of frequency directly in the transform result; Also analysis the signal need to meet the reconstruction to let it has a practical significance. So I had studied the inverse problem about wavelet transform to certain the data processing has practical significance.The inverse spectral decomposition is based on inverse wavelet transform and constraint condition. The choice of wavelet function and constraint condition has important influence to the decomposition result. Compared with other methods such as short time Fourier transform and continuous wavelet transform this method has better time and frequency resolution. In inverse spectral decomposition, the paper mainly studied the influence of constraint condition. In theoretical models mainly used three constraints condition minimum L2 norm, minimum L1 norm and sparse spike or minimum support constraint. The accuracy of these constraints is raised, and the sparse spike has the best accuracy.This paper use accuracy time-frequency to the processing and processing of real seismic data base on the successful research of high precision time-frequency methods, and have a good application effect in frequency data interpretation and high resolution processing.更多还原