应用二维非均匀曲波变换压制地震随机噪声
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摘要
由于野外地表条件及采集环境的影响,实际地震数据经常呈现不规则的空间采样,而常规的曲波变换去噪方法无法对非均匀空间采样的地震数据进行处理。为此,将非均匀快速傅里叶变换引入多尺度、多方向二维曲波变换,建立均匀曲波系数与空间非均匀采样地震数据之间的规则化反演算子,使用线性Bregman算法反演,在每次迭代过程中采用软阈值对曲波系数去噪,得到无噪声的均匀曲波系数,再进行常规二维曲波反变换,得到去噪后的地震数据。理论模型与实际资料的处理结果表明,该方法在将非均匀采样地震数据内插为均匀采样数据的同时,有效地压制了噪声干扰。
Real seismic data are often non-uniformly sampled due to limits of field acquisition environment and terrain conditions.But conventional curvelet-based denoising cannot process non-uniform sampled and noisy data.We first introduce the nonuniform fast Fourier transform(NFFT)in the multi-scale and multi-directional curvelet transform,and construct the regularized inversion of operator that takes the uniformly sampled curvelet coefficients to non-uniformly data.Then we use linearized Bregman method for the inversion calculation,and adopt soft thresholds to remove noise of the curvelet coefficients in each iteration,and get the noise free uniform curvelet coefficients.Finally we perform the conventional inverse fast discrete curvelet transform(FDCT)and get denoised seismic data.Tests on synthetic and real data reveal that the proposed method can better suppress random noise when it interpolates non-uniformly sampled data to uniformly sampled data.
Real seismic data are often non-uniformly sampled due to limits of field acquisition environment and terrain conditions.But conventional curvelet-based denoising cannot process non-uniform sampled and noisy data.We first introduce the nonuniform fast Fourier transform(NFFT)in the multi-scale and multi-directional curvelet transform,and construct the regularized inversion of operator that takes the uniformly sampled curvelet coefficients to non-uniformly data.Then we use linearized Bregman method for the inversion calculation,and adopt soft thresholds to remove noise of the curvelet coefficients in each iteration,and get the noise free uniform curvelet coefficients.Finally we perform the conventional inverse fast discrete curvelet transform(FDCT)and get denoised seismic data.Tests on synthetic and real data reveal that the proposed method can better suppress random noise when it interpolates non-uniformly sampled data to uniformly sampled data.
引文
[1] 田彦灿,王西文,彭更新,等.宽方位角地震资料噪声压制技术[J].石油地球物理勘探,2013,48(2):187-191.TIAN Yancan,WANG Xiwen,PENG Gengxin,et al.Noise attenuation technology on wide azimuth seismic data[J].Oil Geophysical Prospecting,2013,48(2):187-191.
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[3] 邱淑芳,刘西林,刘胜兰.一种基于PDE 与结构—纹理分解的图像去噪方法[J].东华理工大学学报,2013,36(1):90-94.QIU Shufang,LIU Xilin,LIU Shenglan.An image denoising method based on PDE and structure-texture[J].Journal of East China Institute of Technology,2013,36(1):90-94.
[4] Liu Y,Fomel S,Liu C.Signal and noise separation in prestack seismic data using velocity-dependent seislet transform[J].Geophysics,2015,80(6):WD117-WD128.
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[6] Chen Y,Ma J,Fomel S.Double-sparsity dictionary for seismic noise attenuation[J].Geophysics,2016,81(2):V17-V30.
[7] 何旭莉,刘素芹,仝兆岐.三维频率—波数域视速度去噪方法[J].中国石油大学学报,2010,34(4):62-66.HE Xuli,LIU Suqin,TONG Zhaoqi.3-D denoising method through visual speed in frequency-wavenumber domain[J].Journal of China University of Petroleum,2010,34(4):62-66.
[8] Liu Y,Liu N,and Liu C.Adaptive prediction filtering in t-x-y domain for random noise attenuation using regularized nonstationary autoregression[J].Geophysics,2015,80(1):V13-V21.
[9] 张华,陈小宏,杨海燕.地震信号去噪的最优小波基选取方法[J].石油地球物理勘探,2011,46(1):70-75.ZHANG Hua,CHEN Xiaohong,YANG Haiyan.Optimistic wavelet basis selection in seismic signal noise elimination[J].Oil Geophysical Prospecting,2011,46(1):70-75.
[10] 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] 宋维琪,刘太伟.地面微地震资料τ-p变换噪声压制[J].石油地球物理勘探,2015,50(1):48-53.SONG Weiqi,LIU Taiwei.Surface microseismic noise suppression with τ -p transform[J].Oil Geophysical Prospecting,2015,50(1):48-53.
[12] 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.
[13] 刘燕峰,邹少峰,居兴国.基于Contourlet变换的K-L变换地震随机噪声自适应衰减方法[J].石油物探,2017,56(5):676-683.LIU Yanfeng,ZOU Shaofeng,JU Xingguo.Seimic random noise self-adaptive attenuation method based on K-L transform in Contourlet domain[J].Geophysical Prospecting for Petroleum,2017,56(5):676-683.
[14] Ramesh N,Domimique G,Mohamed T,et al.Coherent and random noise attenuation using the curvelet transform[J].The Leading Edge,2008,27(2):240-248.
[15] 刘洋,SERGEY F,刘财,等.高阶seislet变换及其在随机噪声消除中的应用[J].地球物理学报,2009,52(8):2142-2151.LIU Yang,Sergey F,LIU Cai,et al.High-order seislet transform and its application of random noise attenuation[J].Chinese Journal of Geophysics,2009,52(8):2142-2151.
[16] 张广智,常德宽,王一惠,等.基于稀疏冗余表示的三维地震数据随机噪声压制[J].石油地球物理勘探,2015,50(4):600-606.ZHANG Guangzhi,CHANG Dekuan,WANG Yihui,et al.3D seismic random noise suppression with spare and redundant representation[J].Oil Geophysical Prospecting,2015,50(4):600-606.
[17] Lari H H,Gholami A.Curvelet-TV regularized Bregman iteration for seismic random noise attenuation[J].Journal of Applied Geophysics,2014,109(2):233-241.
[18] 张之涵,孙成禹,姚永强,等.三维曲波变换在地震资料去噪处理中的应用研究[J].石油物探,2014,53(4):421-430.ZHANG Zhihan,SUN Chengyu,YAO Yongqiang,et al.Research on the application of 3D curvelet transform to seismic data denoising[J].Geophysical Prospecting for Petroleum,2014,53(4):421-430.
[19] 彭才,常智,朱仕军.基于曲波变换的地震数据去噪方法[J].石油物探,2008,47(5):461-464.PENG Cai,CHANG Zhi,ZHU Shijun.Noise elimination method based on curvelet transform[J].Geophysical Prospecting for Petroleum,2008,47(5):461-464.
[20] Neelamani R,Baumstein A I,Gillard D G,et al.Coherent and random noise attenuation using the curvelet transform[J].The Leading Edge,2008,27(2):240-248.
[21] Zhang H,Chen X H,Zhang L Y.3D simultaneous seismic data reconstruction and noise suppression based on the curvelet transform[J].Applied Geophy-sics,2017,14(1):87-95.
[22] Hennenfent G,Fenelon L,Herrmann F J.Nonequi-spaced curvelet transform for seismic data reconstruction:A sparsity-promoting approach[J].Geophysics,2010,75(6):WB203-WB210.
[23] Candès E,Demanet L,Donoho D,et al.Fast discrete curvelet transforms[J].SIAM Multiscale Modeling and Simulation,2006,5(1):861-899.
[24] Bregman L M.The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming[J].USSR Computational Mathematics and Mathematical Physics,1967,7(3):200-217.
[25] Yin W,Osher S,Goldfarb D,et al.Bregman iterative algorithms for L1-minimization with applications to compressed sensing[J].SIAM Journal on Imaging Sciences,2008,1(1):143-168.
[26] Lorenz D A,Sch?pfer F,Wenger S.The linearized Bregman method via split feasibility problems:analysis and generalizations[J].SIAM Journal on Imaging Sciences,2013,7(7):1237-1262.
[27] 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.
[28] Górszczyk A,Adamczyk A,Malinowski M.Application of curvelet denoising to 2D and 3D seismic data-practical considerations[J].Journal of Applied Geophysics,2014,105(3):78-94.
[29] Herrmann F J.Randomized sampling and sparsity:Getting more information from fewer samples[J].Geophysics,2010,75(6):WB173-WB187.
[2] 刘志刚,谢言光,陈峰.地震数据处理中噪声衰减方法的探讨[J].石油地球物理勘探,2009,44(增刊1):67-71.LIU Zhigang,XIE Yanguang,CHEN Feng.Discussion on noise attenuation methods in seismic data pro-cessing[J].Oil Geophysical Prospecting,2009,44(S1):67-71.
[3] 邱淑芳,刘西林,刘胜兰.一种基于PDE 与结构—纹理分解的图像去噪方法[J].东华理工大学学报,2013,36(1):90-94.QIU Shufang,LIU Xilin,LIU Shenglan.An image denoising method based on PDE and structure-texture[J].Journal of East China Institute of Technology,2013,36(1):90-94.
[4] Liu Y,Fomel S,Liu C.Signal and noise separation in prestack seismic data using velocity-dependent seislet transform[J].Geophysics,2015,80(6):WD117-WD128.
[5] 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):38-42.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):38-42.
[6] Chen Y,Ma J,Fomel S.Double-sparsity dictionary for seismic noise attenuation[J].Geophysics,2016,81(2):V17-V30.
[7] 何旭莉,刘素芹,仝兆岐.三维频率—波数域视速度去噪方法[J].中国石油大学学报,2010,34(4):62-66.HE Xuli,LIU Suqin,TONG Zhaoqi.3-D denoising method through visual speed in frequency-wavenumber domain[J].Journal of China University of Petroleum,2010,34(4):62-66.
[8] Liu Y,Liu N,and Liu C.Adaptive prediction filtering in t-x-y domain for random noise attenuation using regularized nonstationary autoregression[J].Geophysics,2015,80(1):V13-V21.
[9] 张华,陈小宏,杨海燕.地震信号去噪的最优小波基选取方法[J].石油地球物理勘探,2011,46(1):70-75.ZHANG Hua,CHEN Xiaohong,YANG Haiyan.Optimistic wavelet basis selection in seismic signal noise elimination[J].Oil Geophysical Prospecting,2011,46(1):70-75.
[10] 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] 宋维琪,刘太伟.地面微地震资料τ-p变换噪声压制[J].石油地球物理勘探,2015,50(1):48-53.SONG Weiqi,LIU Taiwei.Surface microseismic noise suppression with τ -p transform[J].Oil Geophysical Prospecting,2015,50(1):48-53.
[12] 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.
[13] 刘燕峰,邹少峰,居兴国.基于Contourlet变换的K-L变换地震随机噪声自适应衰减方法[J].石油物探,2017,56(5):676-683.LIU Yanfeng,ZOU Shaofeng,JU Xingguo.Seimic random noise self-adaptive attenuation method based on K-L transform in Contourlet domain[J].Geophysical Prospecting for Petroleum,2017,56(5):676-683.
[14] Ramesh N,Domimique G,Mohamed T,et al.Coherent and random noise attenuation using the curvelet transform[J].The Leading Edge,2008,27(2):240-248.
[15] 刘洋,SERGEY F,刘财,等.高阶seislet变换及其在随机噪声消除中的应用[J].地球物理学报,2009,52(8):2142-2151.LIU Yang,Sergey F,LIU Cai,et al.High-order seislet transform and its application of random noise attenuation[J].Chinese Journal of Geophysics,2009,52(8):2142-2151.
[16] 张广智,常德宽,王一惠,等.基于稀疏冗余表示的三维地震数据随机噪声压制[J].石油地球物理勘探,2015,50(4):600-606.ZHANG Guangzhi,CHANG Dekuan,WANG Yihui,et al.3D seismic random noise suppression with spare and redundant representation[J].Oil Geophysical Prospecting,2015,50(4):600-606.
[17] Lari H H,Gholami A.Curvelet-TV regularized Bregman iteration for seismic random noise attenuation[J].Journal of Applied Geophysics,2014,109(2):233-241.
[18] 张之涵,孙成禹,姚永强,等.三维曲波变换在地震资料去噪处理中的应用研究[J].石油物探,2014,53(4):421-430.ZHANG Zhihan,SUN Chengyu,YAO Yongqiang,et al.Research on the application of 3D curvelet transform to seismic data denoising[J].Geophysical Prospecting for Petroleum,2014,53(4):421-430.
[19] 彭才,常智,朱仕军.基于曲波变换的地震数据去噪方法[J].石油物探,2008,47(5):461-464.PENG Cai,CHANG Zhi,ZHU Shijun.Noise elimination method based on curvelet transform[J].Geophysical Prospecting for Petroleum,2008,47(5):461-464.
[20] Neelamani R,Baumstein A I,Gillard D G,et al.Coherent and random noise attenuation using the curvelet transform[J].The Leading Edge,2008,27(2):240-248.
[21] Zhang H,Chen X H,Zhang L Y.3D simultaneous seismic data reconstruction and noise suppression based on the curvelet transform[J].Applied Geophy-sics,2017,14(1):87-95.
[22] Hennenfent G,Fenelon L,Herrmann F J.Nonequi-spaced curvelet transform for seismic data reconstruction:A sparsity-promoting approach[J].Geophysics,2010,75(6):WB203-WB210.
[23] Candès E,Demanet L,Donoho D,et al.Fast discrete curvelet transforms[J].SIAM Multiscale Modeling and Simulation,2006,5(1):861-899.
[24] Bregman L M.The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming[J].USSR Computational Mathematics and Mathematical Physics,1967,7(3):200-217.
[25] Yin W,Osher S,Goldfarb D,et al.Bregman iterative algorithms for L1-minimization with applications to compressed sensing[J].SIAM Journal on Imaging Sciences,2008,1(1):143-168.
[26] Lorenz D A,Sch?pfer F,Wenger S.The linearized Bregman method via split feasibility problems:analysis and generalizations[J].SIAM Journal on Imaging Sciences,2013,7(7):1237-1262.
[27] 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.
[28] Górszczyk A,Adamczyk A,Malinowski M.Application of curvelet denoising to 2D and 3D seismic data-practical considerations[J].Journal of Applied Geophysics,2014,105(3):78-94.
[29] Herrmann F J.Randomized sampling and sparsity:Getting more information from fewer samples[J].Geophysics,2010,75(6):WB173-WB187.