Fast two-step interpolation algorithm for seismic data
MA Zechuan1, LI Yong1,2, CHEN Lixin1, CHEN Jie1, WANG Pengfei1, LI Xuemei1
1. School of Geophysics, Chengdu University of Technology, Chengdu, Sichuan 610059, China; 2. State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation(Chengdu University of Technology), Chengdu, Sichuan 610059, China;
Abstract：In order to improve interpolation efficiency and choose an optimal interpolation scheme,based on the analysis formula of convex set projection (POCS) algorithm and iterative threshold (IST) algorithm,fast iterative shrinking threshold (FIST) algorithm and fast convex set projection (FPOCS) algorithm are developed.The basic idea is that the interpolation results from the previous step and the interpolation results from the first two steps are linearly combined with the linear operator to get the iterative contraction operator,and the interpolation algorithm is used for interpolation.Then a new quality control criterion is introduced to improve the computational efficiency and accuracy.IST,POCS,FIST and FPOCS algorithms are used to interpolate the incomplete seismic data of the four-layer seismic model and Marmousi model established by Seismic Lab,and the best threshold strategy is selected and finally verified by actual seismic data.The results show that the signal-to-noise ratio from an exponentially declining thre-shold is higher than those from a constant threshold,a linearly declining threshold and a data-driven threshold.Combined with termination criterion,when the maximum iterations are 35 to 50,a better interpolation effect can be obtained.
童思友,高航,刘锐,等.基于Shearlet变换的自适应地震资料随机噪声压制[J].石油地球物理勘探,2019,54(4):744-750.TONG Siyou,GAO Hang,LIU Rui,et al.Seismic random noise adaptive suppression based on Shearlet transform[J].Oil Geophysical Prospecting,2019,54(4):744-750.
[2]
Curry W.Interpolation with Prediction-Error Filters and Training Data[D].Stanford University,2008.
Gao J J,Chen X H,Li J Y,et al.Irregular seismic data reconstruction based on exponential threshold model of POCS method[J].Applied Geophysics,2010,7(3):229-238.
[5]
Gao J J,Sacchi M D,Chen X H.Convergence improvement and noise attenuation considerations for POCS reconstruction[C].Extended Abstracts of 73rd EAGE Conference & Exhibition,2011,2214-4609.
[6]
Spitz S.Seismic trace interpolation in the F-X domain[J].Geophysics,1991,56(6):785-794.
[7]
Wang Y H.Seismic trace interpolation in the f-x-y domain[J].Geophysics,2002,67(4):1232-1239.
[8]
Sacchi M D,Ulrych T J,Walker C J,et al.Interpolation and extrapolation using a high-resolution discrete Fourier transform[J].IEEE Transactions on Signal Processing,1998,46(1):31-38.
[9]
Abma R,Kabir N.3D interpolation of irregular data with a POCS algorithm[J].Geophysics,2006,71(6):E91-E97.
[10]
温睿,刘国昌,冉扬.压缩感知地震数据重建中的三个关键因素分析[J].石油地球物理勘探,2018,53(4):682-693.WEN Rui,LIU Guochang,RAN Yang.Three key factors in seismic data reconstruction based on compressive sensing[J].Oil Geophysical Prospecting,2018,53(4):682-693.
[11]
Menke W.Applications of the POCS inversion method to interpolating topography and other geophysical fields[J].Geophysical Research Letters,1991,18(3):435-438.
[12]
刘红喜,孙凯,孙宏彬,等.具有边缘保持特性的POCS超分辨率图像重建方法[J].吉林大学学报(信息科学版),2015,33(6):620-624.LIU Hongxi,SUN Kai,SUN Hongbin,et al.Super-resolution image reconstruction of POCS with edge preserving[J].Journal of Jilin University(Information Science Edition),2015,33(6):620-624.
[13]
王本锋,李景叶,陈小宏,等.基于Curvelet变换与POCS方法的三维数字岩心重建[J].地球物理学报,2015,58(6):2069-2078.WANG Benfeng,LI Jingye,CHEN Xiaohong,et al.Curvelet-based 3D reconstruction of digital cores using the POCS method[J].Chinese Journal of Geophysics,2015,58(6):2069-2078.
[14]
王本锋,陈小宏,耿建华.地震数据POCS插值重建中的一种新型质量控制准则[J].石油物探,2019,58(1):71-77.WANG Benfeng,CHEN Xiaohong,GENG Jianhua.A novel quality control criterion in the POCS interpolation of seismic data[J].Geophysical Prospecting for Petroleum,2019,58(1):71-77.
[15]
Herrmann F J,Hennenfent G.Non-parametric seismic data recovery with Curvelet frames[J].Geophysical Journal of the Royal Astronomical,2008,173(1):233-248.
[16]
Beck A,Teboulle M.A fast iterative shrinkage-thre-sholding algorithm for linear inverse problems[J].SIAM Journal on Imaging Sciences,2009,2(1):183-202.
[17]
Gao J J,Stanton A,Naghizadeh M,et al.Convergence improvement and noise attenuation considerations for beyond alias projection onto convex sets reconstruction[J].Geophysical Prospecting,2013,61(S1):138-151.
[18]
Donoho D.Compressed sensing[J].IEEE Transac-tions on Information Theory,2006,52(4):1289-1306.
[19]
陈祖斌,王丽芝,宋杨,等.基于压缩感知的小波域地震数据实时压缩与高精度重构[J].石油地球物理勘探,2018,53(4):674-681,693.CHEN Zubin,WANG Lizhi,SONG Yang,et al.Seismic data real-time compression and high-precision reconstruction in the wavelet domain based on the compressed sensing[J].Oil Geophysical Prospecting,2018,53(4):674-681,693.
[20]
Candes E.Compressive sampling[C].Proceedings of the International Congress of Mathematicians,2006,1433-1452.
[21]
Candes E J,Tao T.Near-optimal signal recovery from random projections:universal encoding strategies[J].IEEE Tansactions on Information Theory,2006,52(12):5406-5425.
[22]
薛亚茹,王敏,陈小宏.基于SL0的高分辨率Radon变换及数据重建[J].石油地球物理勘探,2018,53(1):1-7.XUE Yaru,WANG Min,CHEN Xiaohong.High re-solution Radon transform based on SL0 and its application in data reconstruction[J].Oil Geophysical Prospecting,2018,53(1):1-7.
[23]
Michael E,Peyman M,Ron R.Analysis versus syn-thesis in signal priors[J].Inverse Problems,2007,23(3):947-968.
[24]
Figueiredo M A T,Nowak R D.An EM algorithm for wavelet-based image restoration[J].IEEE transactions on Image Processing,2003,12(8):906-916.
[25]
Daubechies I,Defrise M,Christine D M.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57(11):1413-1457.
