基于广义高斯分布和非凸L_p范数正则化的地震稀疏盲反褶积  

Seismic sparse blind deconvolution based on generalized Gaussian distribution and non-convex L_p norm regularization

作　　者：曹静杰 

机构地区：[1]河北地质大学,河北石家庄050031

出　　处：《石油地球物理勘探》2016年第3期428-433,413,共6页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目(41204075);河北省自然科学基金项目(D2014403007);河北省普通高校青年拔尖人才项目(BJ2014049)资助

摘　　要：由于在大多数情形下反射系数的概率分布服从广义高斯分布,可由Lp范数作为度量(0.7<p<1.3),且当p<1时,广义高斯分布对弱反射信息的保留比修正柯西分布更好。为此,基于反射系数广义高斯分布的假设,从贝叶斯稀疏反演理论出发,建立了非凸Lp范数正则化的盲反褶积模型。在求解时通过交替松弛策略使反射系数和子波同步趋于真实解。为了稳定地求解反射系数,将非凸Lp范数(0<p<1)正则化模型转变为一个重赋权最小二乘问题求解。数值试验表明,该方法能够较好地提取子波和反射系数,有效地提高地震数据的纵向分辨率。Since reflection coefficients obey the generalized Gaussian distribution in most cases,the L_p(0.7<p<1.3)norm can be chosen as a measurement of sparsity.And the generalized Gaussian distribution keeps weak reflection information better than the modified Cauchy distribution when p<1.Based on the assumption of the reflection-coefficient generalized Gaussian distribution,a non-convex L_p norm regularized blind deconvolution model is build according to the Bayesian sparse inversion theory.True solutions of reflection coefficients and wavelets can be simultaneously obtained with the alternative relaxation strategy.In order to get stable solutions,the non-convex L_p(0<p<1)norm regularized problem is transformed to a re-weighted least-squares problem.Numerical tests show that the proposed approach can extract wavelets and reflection coefficients and efficiently improve the vertical resolution.

关 键 词：盲反褶积 L_p范数 预条件共轭梯度法 非凸正则化 

分 类 号：P631[天文地球—地质矿产勘探]