Seismic random noise attenuation based on variational mode decomposition
FANG Jiangxiong1,2, WEN Zhiping2, GU Huaqi3, LIU Jun2, ZHANG Hua2
1. Nuclear Technology Application Engineering Research Center, Ministry of Education, East China University of Technology, Nanchang, Jiangxi 330013, China;
2. School of Geophysics and Measurement-control Technology, East China University of Technology, Nanchang, Jiangxi 330013, China;
3. Jiangxi Fundamental Geographic Information Center, Nanchang, Jiangxi 330209, China
Abstract：The empirical mode decomposition (EMD) method usually has heavy computational burdens and low resolution in recursive iterative sifting process.To deal with these problems a globally adaptive variational mode decomposition (VMD) method in the frequency domain is proposed.Different from the EMD recursive iterative sifting mode,the VMD decomposition process can be transformed to solving the optimization problem of the variational functional,which is constrained with the minimum sum of the estimated bandwidth of each band-limited intrinsic mode function (BIMF) component.By introducing an augmented Lagrange function to build the unconstrained term,the alternate direction method of multipliers (ADMM) is used to seek the optimal solution of the variational functional to achieve the signal decomposition.During the iterative process,the center frequency and bandwidth of each component are constantly updated,all BIMF components are obtained at one time with higher time efficiency than EMD.Each modal component has band-limited characteristics in the frequency spectrum to achieve high resolution and adaptive splitting of the signal band.Finally,tests on theoretical model and field data show that the proposed VMD method has not only excellent noise-attenuation and amplitude-preservation performances,but also high computational efficiency,which can meet the processing requirements of high-dimensional and massive seismic data.
Chen K,Sacchi M D.Robust f-x projection filtering for simultaneous random and erratic seismic noise attenuation[J].Geophysical Prospecting,2017,65(3):650-668.
[2]
李宇,韩立国,叶林,等.基于F-K域和Curvelet-中值滤波联合去噪的混采数据分离方法[J].世界地质,2017,36(2):609-615.LI Yu,HAN Liguo,YE Lin,et al.Blended acquisition data separation method based on F-K domain and Curvelet-median filter joint denoising[J].Global Geo-logy,2017,36(2):609-615.
[3]
Mao J,Gao J,Chen W.On the denoising method of prestack seismic data in wavelet domain[J].Chinese Journal of Geophysics,2006,25(1):1155-1163.
[4]
勾福岩,刘财,刘洋,等.基于OC-Seislet变换的海洋涌浪噪声衰减方法[J].吉林大学学报(地球科学版),2015,45(3):962-970.GOU Fuyan,LIU Cai,LIU Yang,et al.Swell noise attenuation methods based on OC-Seislet transform[J].Journal of Jilin University (Earth Science Edition),2015,45(3):962-970.
[5]
张华,陈小宏,李红星,等.曲波变换三维地震数据去噪技术[J].石油地球物理勘探,2017,52(2):226-232.ZHANG Hua,CHEN Xiaohong,LI Hongxing,et al.3D seismic data de-noising approach based on Curvelet transform[J].Oil Geophysical Prospecting,2017,52(2):226-232.
[6]
张岩,任伟建,唐国维.利用多道相似组稀疏表示方法压制随机噪声[J].石油地球物理勘探,2017,52(3):442-450.ZHANG Yan,REN Weijian,TANG Guowei.Random noise suppression based on sparse representation of multi-trace similarity group[J].Oil Geophysical Prospecting,2017,52(3):442-450.
[7]
邵婕,孙成禹,唐杰,等.基于字典训练的小波域稀疏表示微地震去噪方法[J].石油地球物理勘探,2016,51(2):254-260.SHAO Jie,SUN Chengyu,TANG Jie,et al.Micro-seismic data denoising based on sparse representations over learned dictionary in the wavelet domain[J].Oil Geophysical Prospecting,2016,51(2):254-260.
Liu W,Cao S,Chen Y,et al.An effective approach to attenuate random noise based on compressive sensing and curvelet transform[J].Journal of Geophysics & Engineering,2016,13(2):135-145.
[10]
Cheng J,Sacchi M D.Separation and reconstruction of simultaneous source data via iterative rank reduction[J].Geophysics,2015,80(4):57-66.
[11]
Zhang D,Zhou Y,Chen H,et al.Hybrid rank-sparsity constraint model for simultaneous reconstruction and denoising of 3D seismic data[J].Geophysics,2017,82(5):V351-V367.
[12]
Zhou Y T,Shi C J,Chen H M,et al.Spike-like blending noise attenuation using structural low-rank decomposition[J].IEEE Geoscience & Remote Sensing Letters,2017,14(9):1633-1637.
[13]
Chen Y K,Zhou Y T,Chen W,et al.Empirical low-rank approximation for seismic noise attenuation[J].IEEE Transactions on Geoscience & Remote Sensing,2017,55(8):4696-4711.
[14]
颜中辉,栾锡武,王赟,等.基于经验模态分解的分数维地震随机噪声衰减方法[J].地球物理学报,2017,60(7):2845-2857.YAN Zhonghui,LUAN Xiwu,WANG Yun et al.Seismic random noise attenuation based on empirical mode decomposition of fractal dimension[J].Chinese Journal of Geophysics,2017,60(7):2845-2857.
[15]
Chen W,Chen Y,Liu W.Ground roll attenuation using improved complete ensemble empirical mode de-composition[J].Journal of Seismic Exploration,2016,25(5):485-495.
[16]
Chen W,Xie J Y,Zu S H,et al.Multiple-reflection noise attenuation using adaptive randomized-order empirical mode decomposition[J].IEEE Geoscience and Remote Sensing Letters,2017,14(1):18-22.
[17]
Huang N E,Zheng S,Long S R,et al.The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis[C].Proceedings Mathematical Physical & EngineeringSciences,1998,454(1971):903-995.
[18]
Wu Z,Huang N E.Ensemble empirical mode decomposition:a noise-assisted data analysis method[J].Advances in Adaptive Data Analysis,2009,1(1):1-41.
[19]
Torres M E,Colominas M A,Schlotthauer G,et al.A complete ensemble empirical mode decomposition with adaptive noise[C].IEEE international Conference on Acoustics,Speech and Signal Processing (ICASSP),2011:4144-4147.
[20]
Dragomiretskiy K.Variational Methods in Signal Decomposition and Image Processing[D].UCLA,University of California,Los Angeles,2015.
[21]
Hestenes M R.Multiplier and gradient methods[J].Journal of Optimization Theory & Applications,1969,4(5):303-320.
[22]
Powell M J D.A method for nonlinear constraints in minimization problems[J].Optimization,1969,5(6):283-298.
[23]
Mallat S G,Zhang Z.Matching pursuits with time-frequency dictionaries[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415.
Wang Z,Bovik A C,Sheikh H R,et al.Image quality assessment:from error visibility to structural simila-rity[J].IEEE Transactions on Image Processing,2004,13(4):600-612.
