Abstract：Affected by complex terrains in the work area,raw seismic data may be incomplete and irregular,and spatial aliasing is serious. When collecting data on uniform spatial grids,spatial aliasing is similar to the real spectra of missing seismic data. However,anti-aliasing reconstruction can't be realized based on Fourier transform and projection onto convex sets (POCS). To make up the missing linear events,first we pick up effective waves by dip-scanning in f-k frequency domain,and then establish a mask function and use it to the convex set projection algorithm to reconstruct the missing data. Numerical simulation has proved that the proposed method can reconstruct missing seismic data while effectively eliminating aliasing.
Naghizadeh M,Sacchi M D.Beyond alias hierarchical scale curvelet interpolation of regularly and irregularly sampled seismic data[J].Geophysics,2010,75(6):WB189-WB202.
[3]
罗大清,宋炜,吴律,等.加权方向校正及插值预测吸收边界条件的三维波动方程叠前数值模拟[J].石油地球物理勘探,1999,34(3):275-284.LUO Daqing,SONG Wei,WU Lü,et al.3-D wave equation prestack numerical simulation using the absorbing boundary condition that needs weighting-directional correction and interpolation prediction[J]. Oil Geophysical Prospecting,1999,34(3):275-284.
[4]
Ma J W.Three-dimensional irregular seismic data reconstruction via low-rank matrix completion[J]. Geophysics,2013,78(5):V181-V192.
[5]
Gao J,Sacchi M D,Chen X.A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions[J].Geophysics,2013,78(1):V21-V30.
[6]
Gao J J,Stanton A,Sacchi M D.Parallel matrix factorization algorithm and its application to 5D seismic reconstruction and denoising[J].Geophysics,2015,80(6):V173-V187.
[7]
张胤彬,张华,刘松.二维小波变换与中值滤波联合去噪方法研究[J].中国煤炭地质,2011,23(5):38-41.ZHANG Yinbin,ZHANG Hua,LIU Song.A study on 2D wavelet transform and median filtering jointed denoising method[J].Coal Geology of China,2011,23(5):38-41.
[8]
Chen Y,Ma J,Fomel S.Double sparsity dictionary for seismic noise attenuation[J].Geophysics,2016,81(2):V17-V30.
王清振,张金淼,姜秀娣,等.基于高维小波变换的高抗噪性边缘检测技术[J].石油地球物理勘探,2016,51(5):889-893.WANG Qingzhen,ZHANG Jinmiao,JIANG Xiudi,et al.A robust denoise edge detection method based on high-dimensional wavelet transform[J].Oil Geophysical Prospecting,2016,51(5):889-893.
[11]
徐彦凯,曹思远,何元.双曲Radon-ASVD方法压制叠前地震数据随机噪声[J].石油地球物理勘探,2017,52(3):451-457.XU Yankai,CAO Siyuan,HE Yuan.Prestack seismic random noise attenuation with a hyperbolic Radon-ASVD[J].Oil Geophysical Prospecting,2017,52(3):451-457.
[12]
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.
[13]
赵子越,李振春,张敏.利用压缩感知技术的离散正交S变换地震数据重建[J].石油地球物理勘探, 2020, 55(1):29-35.ZHAO Ziyue,LI Zhenchun,ZHANG Min. Seismic data reconstruction using discrete orthonormal S-transform based on compressive sensing[J].Oil Geophysical Prospecting,2020,55(1):29-35.
[14]
张华,刁塑,温建亮,等. 应用二维非均匀曲波变换压制地震随机噪声[J].石油地球物理勘探,2019,54(1):16-23.ZHANG Hua,DIAO Su,WEN Jianliang,et al. A random noise suppression with 2D non-uniform curvelet transform[J].Oil Geophysical Prospecting,2019,54(1):16-23.
[15]
Lu L.Application of local slant stack to trace interpolation[C].SEG Technical Program Expanded Abstracts,1985,4:560-562.
[16]
李国发.f-k域与f-x域联合实现道内插[J].石油地球物理勘探,1995,30(5):693-701.LI Guofa.Joint trace interpolation in f-k and f-x domains[J].Oil Geophysical Prospecting,1995,30(5):693-701.
[17]
崔兴福,刘东奇,张关泉.小波变换实现地震道内插[J].石油地球物理勘探,2003,38(1):93-97.CUI Xingfu,LIU Dongqi,ZHANG Guanquan.Seismic trace interpolation based on wavelet transform[J].Oil Geophysical Prospecting,2003,38(1):93-97.
[18]
孟小红,郭良辉,张致付,等.基于非均匀快速傅里叶变换的最小二乘反演地震数据重建[J].地球物理学报,2008,51(1):235-241.MENG Xiaohong,GUO Lianghui,ZHANG Zhifu,et al.Reconstruction of seismic data with least squares inversion based on nonuniform fast Fourier transform[J].Chinese Journal of Geophysics,2008,51(1):235-241.
[19]
刘财,李鹏,刘洋,等.基于seislet变换的反假频迭代数据插值方法[J].地球物理学报,2013,56(5):1619-1627.LIU Cai,LI Peng,LIU Yang,et al.Iterative data interpolation beyond aliasing using seislet transform[J].Chinese Journal of Geophysics,2013, 56(5):1619-1627.
[20]
石颖,张振,王建民.地震数据反假频规则化方法研究[J].地球物理学进展,2013,28(1):250-256.SHI Ying,ZHANG Zhen,WANG Jianmin,et al. Investigation on anti-aliasing regularization approach for seismic data[J].Progress in Geophysics,2013,28(1):250-256.
[21]
高建军,陈小宏,李景叶.不规则地震数据的抗假频重建方法[J].石油地球物理勘探,2010,45(3):326-331.GAO Jianjun,CHEN Xiaohong,LI Jingye.Studies on anti-aliasing reconstruction method for irregular seismic data[J].Oil Geophysical Prospecting,2010,45(3):326-331.
[22]
刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究[J].地球物理学报,2004,47(2):299-305.LIU Xiwu,LIU Hong,LIU Bin.A study on algorithm for reconstruction of de-alias uneven seismic data[J]. Chinese Journal of Geophysics,2004,47(2):299-305.
[23]
黄小刚,王一博,刘伊克,等.半径-斜率域加权反假频地震数据重建[J].地球物理学报,2014,57(7):2278-2290.HUANG Xiaogang,WANG Yibo,LIU Yike,et al.Weighted anti-alias seismic data reconstruction in R-P domain[J].Chinese Journal of Geophysics,2014,57(7):2278-2290.
[24]
Zhang H,Diao S,Yang H Y,et al.Reconstruction of 3D non-uniformly sampled seismic data along two spatial coordinates using non-equispaced curvelet transform[J].Exploration Geophysics,2018,49(6):906-921.
[25]
Abma R,Kabir N.3D interpolation of irregular data with a POCS algorithm[J].Geophysics,2016,71(6):E91-E97.
[26]
张红梅,刘洪.基于稀疏离散τ-p变换的非均匀地震道重建[J].石油物探,2006,45(2):141-145.ZHANG Hongmei,LIU Hong.Non-uniform seismic trace reconstruction based on discrete and sparse τ-p transform[J].Geophysical Prospecting for Petroleum,2006,45(2):141-145.
[27]
Naghizadeh M.Seismic data interpolation and denoising in the frequency-wavenumber domain[J].Geophysics,2012,77(2):V71-V80.
[28]
张华,陈小宏.基于jitter采样和曲波变换的三维地震数据重建[J].地球物理学报,2013,56(5):1637-1649.ZHANG Hua,CHEN Xiaohong.Seismic data reconstruction based on jittered sampling and curvelet transform[J].Chinese Journal of Geophysics,2013,56(5):1637-1649.
