【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.更多还原

【Abstract】 Deconvolution is an effective and essential method to improve seismic resolution.Traditional deconvolution techniques assume that the wavelet is minimum phase and the reflection coefficients 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 results showed that the deconvolution method in this paper can be better adapt to non-minimum phase systems,the seismic wavelet and reflectivity can be estimated at the same time,the phase of wavelet can be correctly recovered,and the method is robust in the presence of noise.Then,the method was used to process the field data,in contrast with the spiking deconvolution result,the blind deconvolution technique not only improved the resolution of the profile,the phase axis superimposed together were separated,but also highlights the weak reflection information between the strong reflection axis.As an effective means to improve seismic resolution,the blind deconvolution technique can broaden the effective band of seismic records,and will play an important role in seismic exploration and exploitation.更多还原