基于L1/2正则化理论的地震稀疏反褶积  

Seismic sparse deconvolution based on L1/2 regularization

作　　者：康治梁 张雪冰 KANG Zhiliang;ZHANG Xuebing(College of Geophysics,Chengdu University of Technology,Chengdu 610059,China;Department of Physics,University of Toronto,Ontario M5S 1A7,Canada;School of Geomatics and Prospecting Engineering,Jilin Jianzhu University,Changchun 130118,China)

机构地区：[1]成都理工大学地球物理学院,四川成都610059 [2]加拿大多伦多大学物理学院,安大略多伦多,ON M5S 1A7 [3]吉林建筑大学测绘与勘查工程学院,吉林长春130118

出　　处：《石油物探》2019年第6期855-863,共9页Geophysical Prospecting For Petroleum

基　　金：吉林省科技厅优秀青年人才基金项目(20190103140JH);吉林省教育厅“十三五”科研规划项目(JJKH20180610KJ)共同资助~~

摘　　要：地震反褶积是一种重要的压缩地震子波、提高薄层纵向分辨率的地震数据处理方法。在层状地层的假设下,反射系数可视作稀疏的脉冲序列,所以地震反褶积可以描述为一个稀疏求解问题,L 1正则化被广泛用于解决稀疏问题,但近年来一些文献证明L 1正则化的稀疏表达能力不是最优的。针对这一问题,基于快速发展的L 1/2正则化理论,提出将L 1/2正则化作为反射系数的稀疏约束进行地震反褶积处理,并使用其特定的阈值迭代算法进行求解,对单道模型的测试证实了该方法对正则化参数和噪声有较好的适应能力。简单二维模型和Marmousi2模型数据的测试结果表明,基于该方法的反演结果能较好地拟合反射系数振幅,并且对噪声干扰的鲁棒性更强,能够更好地保护弱反射系数。实际数据应用结果表明,该方法能有效消除子波影响,较好地分辨出薄层结构和透镜体结构,为地震数据高分辨处理提供了有力工具。Seismic deconvolution is an important seismic processing method to eliminate the effect of seismic wavelets and improve the resolution of thin layers.Under the assumption of a layered-earth model,reflectivity is usually regarded as a sparse pulse sequence;the deconvolution problem can thus be modeled as a constrained sparsity problem.L 1 regularization is widely used to solve sparsity problems.Nevertheless,many recent practical applications showed L 1 regularization might not be the most effective method to address sparsity problems.Based on the well-developed L 1/2 regularization,a method was proposed which used L 1/2 regularization as the sparse constraint of a reflection coefficient for seismic deconvolution processing.A specific threshold iterative algorithm was used to solve the L 1/2 problem.Testing of a single-channel model demonstrated its adaptability to regularization parameters and noise.The tests on a simple 2D model and the Marmousi2 model showed that the method could invert the reflectivity coefficients,had better robustness to noise,and could protect against weak spikes.Field data tests showed that it could eliminate the effect of seismic wavelets,distinguish thin-layer and lenticular structures,and thereby provide a powerful tool for high-resolution processing of seismic data.

关 键 词：地震反演 稀疏性 L 1正则化 L 1/2正则化理论 非凸正则化 高分辨率 薄层识别 

分 类 号：P631[天文地球—地质矿产勘探]