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时频分析在地震资料处理中的应用
【作者】 周安；
【导师】 熊章强；
【作者基本信息】 中南大学 ， 地球探测与信息技术， 2010， 硕士
【摘要】 傅里叶变换反映的是信号或函数的整体特征,其不具备时间分辨率,随着信号分析的深入,傅里叶变换难以满足分析要求,不适合处理非平稳信号；短时傅里叶变换具有一定的局部分析能力,但其时频窗口固定不变,意味着其在时间域和频率域的分辨率是固定的,不具备自适应性；小波变换具有可变的时间和频率分辨率,具有较好的自适应性,但小波基的选择是关键；Wigner-Ville变换是二次变换,时频聚焦性较强,但是会产生交叉干扰项；Cohen类函数通过加入核函数在一定程度上抑制了交叉干扰项,但这是以降低一定的时频分辨率为代价的。本文比较了传统时频分析方法的优缺点,介绍了高阶谱时频分析方法,以及提出了改进的FX域EMD去噪方法。经验模态分解是比较新近提出的一种信号分解方法,它依据数据自身的时间尺度特征来进行信号分解,无需预先设定任何基函数。本文在Maiza Bekara的基础上,将FX域中的IMF1完全滤除,并滤除IMF2的高频噪声,这样可以达到更好的去噪目的。将其应用于井间地震数据去噪,提高了井间地震数据的信噪比。高阶谱分析的最大特点是：(1)高阶累积量具有对高斯有色噪声恒为零的特点,因而可用于提取高斯有色噪声中的非高斯信号；(2)高阶累积量含有系统的相位信息,因而可用于非最小相位系统辨识：(3)高阶统计量可用于检测和描述系统的非线性。这些性质是的高阶谱分析迅速成为现代随机信号分析与处理的一个重要工具。所以,高阶统计量对于处理非平稳信号非常适合,而地震信号正是这样的非平稳信号,因此能够很好的应用在地震资料处理中。
【Abstract】 Fourier Transformation, reflecting the unity features of the signals or functions, is not fit for processing the non-stationary signals. It doesn’t have time domain resolution. Short Time Fourier Transformation (STFT), added by a fixed time-frequency window, has a limited time-frequency resolution. It means that the time-domain resolution and frequency-domain resolution are fixed in STFT, so it’s not adaptive enough. Wavelet transformation, with a better adaptivity, has a flexible time-domain and frequency-domain resolution, but the wavelet basis is the key step. Wigner-Ville transform is a quadratic transformation, with a good time and frequency focusing, while it may generate crossing disturbances. Cohen class functions restrain the crossing disturbances to a certain extent by adding a kernel function while the resolution is decreased. The traditional time-frequency analysis methods are introduced in this paper. Their advantages and disadvantages will be summarized from the contrast of each other. Then high-order spectrum analysis method is introduced, and a method of improved EMD in the FX domain for noise attenuation is brought up.EMD is a signal decompose method, which decomposes the signals by the time-scale feature of itself, with no prestablishing any base functions. Based on Maiza Bekara, all the IMF1 and the high frequency of the IMF2 are filtered out so as to denoising the noise and reserving the useful information. Then it is used into the cross well seismic data to increase the SNR of the data.The evident features of high-order spectrum are:(1) the high-order cumulant is always be zero to Gauss colored noise, which can be used to pick up the non-Gauss signals from the Gauss colored noise; (2)the high-order cumulant contains the phase information, which can be used into the non-minimum phase system identification; (3) the high-order stastics can be used into detecting and describing the system’s nonlinear. Above all, high-order spectrum analysis method becomes an important tool to analysis and processes the modern random signals. Therefore, high-order statistics is very fit for processing the non-stationary signals, while the seismic signals are the non-stationary signals, so it can be useful in the seismic data.