Robust multichannel predictive deconvolution based on the alternating split Bregman iteration algorithm
Li Zhongxiao1,2, Li Zhenchun1,2
1. School of Geosciences, China University of Petroleum(East China), Qingdao, Shandong 266580, China;
2. Laboratory for Marine Mineral Resources, Qingdao National Laboratory for Marine Science and Technology, Qingdao, Shandong 266071, China
Abstract：This paper introduces the L1 norm minimization constraint of primaries into the multichannel predictive deconvolution and proposes a robust multichannel predictive deconvolution based on the alternating split Bregman iteration algorithm.The proposed method utilizes the proximity operator to solve the optimization problem of the L1 norm minimization.Moreover,since the proposed method only needs the matrix inversion once during the whole iteration procedure,it has low computational complexity.This paper introduces the mathematical model of the multichannel predictive deconvolution,then gives the optimization problem of the robust multichannel predictive deconvolution,and elaborates the iteration steps of the alternating split Bregman iteration algorithm for solving the optimization problem.Compared with the robust multichannel predictive deconvolution method based on the iterative reweighted least squares algorithm,the proposed method can improve the computation efficiency while achieving similar accuracy.Moreover,compared with the multichannel predictive deconvolution method based on the least squares and the robust single channel predictive deconvolution method based on the alternating split Bregman iteration algorithm,the proposed method can better balance primary preservation and multiple removal.In addition,the proposed method utilizes the advantage of the multichannel predictive deconvolution and can better accommodate the fluctuant change of the sea floor than the single channel predictive deconvolution.Tests on synthetic and real data demonstrate that the proposed method can effectively suppress water layer multiples while preserving primaries in the case that the water layer multiples exhibit periodicity.Additionally,the proposed method has high computational efficiency.However,it is hard to judge intuitively multiple removal effects if the periodicity of water layer multiples is not satisfied well.
Zhu Weiqiang,Wang Yanchun,Mo Yangang et al.A method to reduce sea bottom reverberations based on predictive deconvolution.Marine Geology Frontiers,2011,27(11):66-69.
[5]
Porsani M J,Ursin B.Direct multichannel predictive deconvolution.Geophysics,2007,72(2):H11-H27.
[6]
Liu Zhipeng,Zhao Wei,Zhu Zhenyu.Multiple attenuation using multichannel predictive deconvolution in radial domain.SEG Technical Program Expanded Abstracts,2012,1-5.
[7]
Taner M T.Long period sea-floor multiples and their suppression.Geophysical Prospecting,1980,28(1):30-48.
[8]
Guitton A,Verschuur D J.Adaptive subtraction of multiples using the L1-norm.Geophysical Prospecting,2004,52(1):27-38.
[9]
Liu Jun,Lu Wenkai.An improved predictive deconvolution based on maximization of non-Gaussianity.Applied Geophysics,2008,5(3):189-196.
Wu Yinting,Liu Yike,Chang Xu et al.An improved matching method based on L1-norm for multiple elimination and application in deepwater basin of South China Sea.Chinese Journal of Geophysics,2012,55(3):1007-1016.
Jing Hongliang,Shi Ying,Li Ying et al.Surface-related multiple adaptive subtraction method based on L1/L2 norm.OGP,2015,50(4):619-625.
[12]
Liu Lei,Lu Wenkai.A fast L1 linear estimator and its application on predictive deconvolution.IEEE Geoscience and Remote Sensing Letters,2015,12(5):1056-1060.
[13]
Chen S S,Donoho D L,Saunders M A.Atomic decomposition by basis pursuit.SIAM Journal on Scientific Computing,1998,20(1):33-61.
[14]
Mallat S,Zhang Zhifeng.Matching pursuits with time-frequency dictionaries.IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
[15]
Natarajan B K.Sparse approximate solutions to linear systems.SIMA Journal on Computing,1995,24(2):227-234.
[16]
Scales J A,Gersztenkorn A.Robust method in inverse theory.Inverse Problems,1988,4(4):1071-1091.
[17]
Trad D,Ulrych T J,Sacchi M D.Latest views of the sparse Radon transform.Geophysics,2003,68(1):386-399.
[18]
Li Zhongxiao,Lu Wenkai.Adaptive multiple subtraction based on 3D blind separation of convolved mixtures.Geophysics,2013,78(6):V251-V266.
[19]
Goldstein T,Osher S.The split Bregman method for L1 regularized problems.SIAM Journal on Imaging Science,2009,2(2):323-343.
[20]
Gholami A,Sacchi M D.A fast and automatic sparse deconvolution in the presence of outliers.IEEE Transactions on Geoscience and Remote Sensing,2012,50(10):4105-4116.
[21]
Gou Fuyan,Liu Cai,Liu Yang et al.Complex seismic wavefield interpolation based on the Bregman iteration method in the sparse transform domain.Applied Geophysics,2014,11(3):277-288.
[22]
Wiggins J W.Attenuation of complex water-bottom multiples by wave-equation-based prediction and subtraction.Geophysics,1988,53(12):1527-1539.
[23]
Sacchi M D,Ulrych T J.High-resolution velocity gathers and offset space reconstruction.Geophysics,1995,60(4):1169-1177.
