基于广义高斯分布的地震盲反褶积方法研究  

Seismic blind deconvolution method based on generalized Gaussian distribution

作　　者：李海山 吴国忱[1] 印兴耀[1] 

机构地区：[1]中国石油大学(华东)地球科学与技术学院,青岛266555

出　　处：《地球物理学进展》2012年第3期936-944,共9页Progress in Geophysics

基　　金：国家自然基金项目(40739908);国家油气重大专项(2008zx05014-001-010hz)联合资助

摘　　要：Bussgang算法是针对褶积盲源分离问题提出的,本文将其用于地震盲反褶积处理.由于广义高斯概率密度函数具有逼近任意概率密度函数的能力,从反射系数序列的统计特征出发,引入广义高斯分布来体现反射系数序列超高斯分布特征.依据反射系数序列的统计特征和Bussgang算法原理,建立以Kullback-Leibler距离为非高斯性度量的目标函数,并导出算法中涉及到的无记忆非线性函数,最终实现了地震盲反褶积.模型试算和实际资料处理结果表明,该方法能较好地适应非最小相位系统,能够同时实现地震子波和反射系数估计,有效地提高地震资料分辨率.Deconvolution is an effective and essential method to improve seismic resolution, Traditional deconvolution techniques assume that the wavelet is minimum phase and the reflection eoeffieients have a white Gaussian noise distribution. The assumption of a Gaussian distribution means that recovery of the true phase of the wavelet is impossible; however, a non-Gaussian distribution in theory allows recovery of the phase. It is generally recognized that primary reflection coefficients typically have a non-Gaussian amplitude distribution, and the purpose of deconvolution is to recover the non-Gaussian distribution feature of the reflectivity. Blind deconvolution differs from conventional deconvolution in that the reflection coefficients have a non-Gaussian amplitude distribution and we do not make a priori assumption about the wavelet phase. Bussgang algorithm was proposed for convolutive blind source separation problem, in this paper, it was applied to seismic blind deconvolution process. Because the generalized Gaussian probability density function has the capacity for approximating any probability density function, in accordance with the statistical characteristics of the reflectivity, it was introduced in to reflect the super-Gaussian distribution characteristics of the reflectivity. On the basis of the statistical characteristics of the reflectivity and the principle of Bussgang algorithm, a corresponding objective function which utilizing Kullback-Leibler distance as non- Gaussian measure was established, and then, the memoryless nonlinearity involved in Bussgang algorithm was derived, finally, the seismic blind deconvolution technique based on generalized Gaussian distribution was realized. The results of model test showed that the conventional deconvolution methods, such as spiking deconvolution, estimate the wavelet characteristics from the autocorrelation, unfortunately, there is no information about the phase of the wavelet in the autocorrelation, so the deconvolution result is incorrect. However, testing re

关 键 词：广义高斯分布 地震盲反褶积 Bussgang算法 Kullback-Leibler散度 混合相位子波 

分 类 号：P315[天文地球—地震学] P631[天文地球—固体地球物理学]