基于Shearlet变换的自适应阈值地震数据去噪方法
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摘要
由于随机噪声的干扰,地震勘探的有效信号经常淹没其中难以识别,且在时间域难以分离随机噪声和有效信号。Shearlet变换是一种新的多尺度多方向时频分析方法,具有最优的稀疏表示能力、局部化特征和方向敏感性。Shearlet变换在去除随机噪声的同时,能够最大限度地保留有效信号,可以有效地提高地震数据的信噪比。针对传统的Shearlet变换阈值去噪方法不能随尺度和方向变化的不足,提出了随尺度和方向变化的自适应阈值,可以同时适应不同尺度和方向噪声水平的差异。利用Shearlet变换的自适应阈值算法与小波变换去噪方法,分别对理论和实际地震数据进行去噪。对比可知,Shearlet变换的自适应阈值算法具有更强的去噪能力,并能够最大限度地保留有效信号。
Due to the interference of stochastic noise,the effective signal of seismic exploration is usually covered and thus is difficult to be identified;meanwhile,it is difficult to distinguish the stochastic noise and effective signal in the time domain.As a new type of multi-scale and multi-directional time-frequency analysis method,Shearlet transform possesses the optimal sparse representation capacity,localization characteristics and directional sensibility.When the stochastic noise is removed by Shearlet transform,effective signals can be retained to the maximum degree,and the signal-to-noise ratio of seismic data can be effectively improved.Aiming at the deficiency in traditional Shearlet transform threshold de-noising method unable to change with the scale and direction,the adaptive threshold changing with the scale and direction is proposed,able to adapt to the difference in noise levels of different scales and directions.The adaptive threshold algorithm based on Shearlet transform and de-noising method based on wavelet transform can be used to de-noise the theoretical and actual seismic data respectively.It can be known by contrast that the adaptive threshold algorithm based on Shearlet transform has the stronger de-noising capacity,able to reserve the effective signal to the utmost extent.
Due to the interference of stochastic noise,the effective signal of seismic exploration is usually covered and thus is difficult to be identified;meanwhile,it is difficult to distinguish the stochastic noise and effective signal in the time domain.As a new type of multi-scale and multi-directional time-frequency analysis method,Shearlet transform possesses the optimal sparse representation capacity,localization characteristics and directional sensibility.When the stochastic noise is removed by Shearlet transform,effective signals can be retained to the maximum degree,and the signal-to-noise ratio of seismic data can be effectively improved.Aiming at the deficiency in traditional Shearlet transform threshold de-noising method unable to change with the scale and direction,the adaptive threshold changing with the scale and direction is proposed,able to adapt to the difference in noise levels of different scales and directions.The adaptive threshold algorithm based on Shearlet transform and de-noising method based on wavelet transform can be used to de-noise the theoretical and actual seismic data respectively.It can be known by contrast that the adaptive threshold algorithm based on Shearlet transform has the stronger de-noising capacity,able to reserve the effective signal to the utmost extent.
引文
[1]解吉高,刘春成,刘志斌,等.下刚果盆地北部中新统深水浊积岩储层及含油性地震预测[J].石油学报,2015,36(1):33-40.XIE Jigao,LIU Chuncheng,LIU Zhibin,et al.Seismic prediction of the reservoir and oil-bearing property of Miocene deep-water turbidite in northern Lower Congo Basin[J].Acta Petrolei Sini-ca,2015,36(1):33-40.
[2]陈志德,王成,刘国友,等.近地表Q值模型建立方法及其地震叠前补偿应用[J].石油学报,2015,36(2):188-196.CHEN Zhide,WANG Cheng,LIU Guoyou,et al.Modeling method of near-surface Q value and its seismic pre-stack compensation application[J].Acta Petrolei Sinica,2015,36(2):188-196.
[3]王姣,李红梅,李振春,等.基于GRNN振幅谱估计的井控提高地震分辨率技术[J].石油学报,2015,36(6):715-723.WANG Jiao,LI Hongmei,LI Zhenchun,et al.Well-controlled seismic resolution enhancement technology based on GRNN amplitude spectrum estimation[J].Acta Petrolei Sinica,2015,36(6):715-723.
[4]易远元,叶辉,邓爱居,等.三维地震速度场建立技术——以饶阳凹陷河间南地区为例[J].石油学报,2015,36(7):820-826.YI Yuanyuan,YE Hui,DENG Aiju,et al.3-D seismic velocity field building technology:a case study of southern Hejian area of Raoyang sag[J].Acta Petrolei Sinica,2015,36(7):820-826.
[5]崔永福,彭更新,吴国忱,等.孔洞型碳酸盐岩储层地震正演及叠前深度偏移[J].石油学报,2015,36(7):827-836.CUI Yongfu,PENG Gengxin,WU Guochen,et al.Seismic forward modeling and pre-stack depth migration of porous-type carbonate reservoirs[J].Acta Petrolei Sinica,2015,36(7):827-836.
[6]牛永效.基于频率及F-K域联合应用的地震波去噪技术研究[J].铁道标准设计,2017,61(2):47-49.NIU Yongxiao.Research on seismic data noise reduction based on combined application of frequency and F-K domain filter[J].Railway Standard Design,2017,61(2):47-49.
[7]LIU Guochang,CHEN Xiaohong,DU Jing,et al.Random noise attenuation using f-x regularized nonstationary autoregression[J].Geophysics,2012,77(2):V61-V69.
[8]贾春梅,姜国庆,刘志成,等.频域稀疏双曲Radon变换去噪方法[J].物探与化探,2016,40(3):527-533.JIA Chunmei,JIANG Guoqing,LIU Zhicheng,et al.Denoising method based on sparse hyperbolic Radon transform in the frequency domain[J].Geophysical&Geochemical Exploration,2016,40(3):527-533.
[9]HU Yue,WANG Limin,CHENG Feng,et al.Ground-roll noise extraction and suppression using high-resolution linear Radon transform[J].Journal of Applied Geophysics,2016,128:8-17.
[10]包乾宗,高静怀,陈文超.面波压制的Ridgelet域方法[J].地球物理学报,2007,50(4):1210-1215.BAO Qianzong,GAO Jinghuai,CHEN Wenchao.Ridgelet domain method of ground-roll suppression[J].Chinese Journal of Geophysics,2007,50(4):1210-1215.
[11]金丹,程建远,王保利,等.基于Curvelet变换的地震资料弱信号识别及去噪方法[J].煤炭学报,2016,41(2):332-337.JIN Dan,CHENG Jianyuan,WANG Baoli,et al.Seismic weak signal identification and noise elimination based on Curvelet domain[J].Journal of China Coal Society,2016,41(2):332-337.
[12]WANG Deli,TONG Zhongfei,TANG Chen,et al.An iterative curvelet thresholding algorithm for seismic random noise attenuation[J].Applied Geophysics,2010,7(4):315-324.
[13]MORTEZANEJAD R,GHOLAMI A.Optimization of wavelet-and curvelet-based denoising algorithms by multivariate SURE and GCV[J].Journal of Geophysics and Engineering,2016,13(3):378-390.
[14]姚振岸,孙成禹,石小磊,等.基于曲波变换和各向异性扩散滤波的联合去噪技术[J].石油学报,2016,37(4):490-498.YAO Zhen'an,SUN Chengyu,SHI Xiaolei,et al.A combined denoising method based on Curvelet transform and anisotropic diffusion filtering[J].Acta Petrolei Sinica,2016,37(4):490-498.
[15]赵娴.基于Contourlet变换二维TFPF压制地震勘探随机噪声[D].长春:吉林大学,2016.ZHAO Xian.2-D TFPF based on Contourlet transform for seismic random noise attenuation[D].Changchun:Jilin University,2016.
[16]唐飞.基于Contourlet变换和Shearlet变换的图像去噪算法研究[D].湘潭:湘潭大学,2014.TANG Fei.Research on image denoising methods based on Contourlet transform and Shearlet transform[D].Xiangtan:Xiangtan University,2014.
[17]GUO Kanghui,LABATE D.Optimally sparse multidimensional representation using shearlets[J].SIAM Journal on Mathematical Analysis,2007,39(1):298-318.
[18]GUO Kanghui,LABATE D,LIM W Q,et al.Wavelets with composite dilations[J].Electronic Research Announcements of the American Mathematical Society,2004,10(9):78-87.
[19]GUO Kanghui,LABATE D,LIM W Q,et al.Wavelets with composite dilations and their MRA properties[J].Applied and Computational Harmonic Analysis,2006,20(2):202-236.
[20]冯成祥.一类双正交Shearlet多尺度分析与离散Shearlet变换[D].杭州:浙江工业大学,2012.FENG Chengxiang.A kind of Biorthogonal Shearlet multiscale analysis and discrete Shearlet transformation[D].Hangzhou:Zhejiang University of Technology,2012.
[21]刘成明,王德利.基于贝叶斯理论的Shearlet域一次波与多次波分离[J].石油学报,2016,37(4):483-489.LIU Chengming,WANG Deli.Primary and multiple separation in Shearlet domain based on Bayesian theory[J].Acta Petrolei Sinica,2016,37(4):483-489.
[22]岳彦刚,石智,张卓.基于Shearlet变换的图像边缘检测[J].计算机应用与软件,2014,31(4):227-230.YUE Yan'gang,SHI Zhi,ZHANG Zhuo.Image edge detection algorithm based on Shearlet transform[J].Computer Applications and Software,2014,31(4):227-230.
[23]刘俊良,雷琳,周石琳.非下采样形态学Shearlet变换:提高结构细节捕捉的图像表示新方法[J].信号处理,2014,30(2):163-171.LIU Junliang,LEI Lin,ZHOU Shilin.Non-subsampled morphological Shearlet transform algorithm:a new image representation to promote structural details capturing[J].Journal of Signal Processing,2014,30(2):163-171.
[24]YUAN Min,YANG Bingxin,MA Yide,et al.Compressed sensing MRI reconstruction from highly undersampled k-space data using nonsubsampled Shearlet transform sparsity prior[J].Mathematical Problems in Engineering,2015,2015:615439.
[25]ZHOU Shichong,SHI Jun,ZHU Jie,et al.Shearlet-based texture feature extraction for classification of breast tumor in ultrasound image[J].Biomedical Signal Processing and Control,2013,8(6):688-696.
[26]LIU Shuaiqi,SHI Mingzhu,ZHU Zhihui,et al.Image fusion based on complex-shearlet domain with guided filtering[J].Multidimensional Systems and Signal Processing,2017,28(1):207-224.
[27]SHAHDOOSTI H R,KHAYAT O.Image denoising using sparse representation classification and non-subsampled shearlet transform[J].Signal,Image and Video Processing,2016,10(6):1081-1087.
[28]KONG Dehui,PENG Zhenming,FAN Hongyi,et al.Seismic random noise attenuation using directional total variation in the Shearlet domain[J].Journal of Seismic Exploration,2016,25(4):321-338.
[29]KONG Dehui,PENG Zhenming.Seismic random noise attenuation using shearlet and total generalized variation[J].Journal of Geophysics and Engineering,2015,12(6):1024-1035.
[30]GAO Guorong.Image denoising by non-subsampled shearlet domain multivariate model and its method noise thresholding[J].Optik-International Journal for Light and Electron Optics,2013,124(22):5756-5760.
[31]刘成明,王德利,王通,等.基于Shearlet变换的地震随机噪声压制[J].石油学报,2014,35(4):692-699.LIU Chengming,WANG Deli,WANG Tong,et al.Random seismic noise attenuation based on the Shearlet transform[J].Acta Petrolei Sinica,2014,35(4):692-699.
[32]YANG Chengli,LIU Peiyong,YIN Guofu,et al.Crack detection in magnetic tile images using nonsubsampled shearlet transform and envelope gray level gradient[J].Optics&Laser Technology,2017,90:7-17.
[33]WANG Xiangyang,LIU Yu'nan,XU Huan,et al.Blind optimum detector for robust image watermarking in nonsubsampled shearlet Domain[J].Information Sciences,2016,372:634-654.
[34]张超.微弱地震信号时频消噪算法研究[D].长春:吉林大学,2016.ZHANG Chao.Research on weak seismic signal denoising by using time-frequency algorithm[D].Changchun:Jilin University,2016.
[2]陈志德,王成,刘国友,等.近地表Q值模型建立方法及其地震叠前补偿应用[J].石油学报,2015,36(2):188-196.CHEN Zhide,WANG Cheng,LIU Guoyou,et al.Modeling method of near-surface Q value and its seismic pre-stack compensation application[J].Acta Petrolei Sinica,2015,36(2):188-196.
[3]王姣,李红梅,李振春,等.基于GRNN振幅谱估计的井控提高地震分辨率技术[J].石油学报,2015,36(6):715-723.WANG Jiao,LI Hongmei,LI Zhenchun,et al.Well-controlled seismic resolution enhancement technology based on GRNN amplitude spectrum estimation[J].Acta Petrolei Sinica,2015,36(6):715-723.
[4]易远元,叶辉,邓爱居,等.三维地震速度场建立技术——以饶阳凹陷河间南地区为例[J].石油学报,2015,36(7):820-826.YI Yuanyuan,YE Hui,DENG Aiju,et al.3-D seismic velocity field building technology:a case study of southern Hejian area of Raoyang sag[J].Acta Petrolei Sinica,2015,36(7):820-826.
[5]崔永福,彭更新,吴国忱,等.孔洞型碳酸盐岩储层地震正演及叠前深度偏移[J].石油学报,2015,36(7):827-836.CUI Yongfu,PENG Gengxin,WU Guochen,et al.Seismic forward modeling and pre-stack depth migration of porous-type carbonate reservoirs[J].Acta Petrolei Sinica,2015,36(7):827-836.
[6]牛永效.基于频率及F-K域联合应用的地震波去噪技术研究[J].铁道标准设计,2017,61(2):47-49.NIU Yongxiao.Research on seismic data noise reduction based on combined application of frequency and F-K domain filter[J].Railway Standard Design,2017,61(2):47-49.
[7]LIU Guochang,CHEN Xiaohong,DU Jing,et al.Random noise attenuation using f-x regularized nonstationary autoregression[J].Geophysics,2012,77(2):V61-V69.
[8]贾春梅,姜国庆,刘志成,等.频域稀疏双曲Radon变换去噪方法[J].物探与化探,2016,40(3):527-533.JIA Chunmei,JIANG Guoqing,LIU Zhicheng,et al.Denoising method based on sparse hyperbolic Radon transform in the frequency domain[J].Geophysical&Geochemical Exploration,2016,40(3):527-533.
[9]HU Yue,WANG Limin,CHENG Feng,et al.Ground-roll noise extraction and suppression using high-resolution linear Radon transform[J].Journal of Applied Geophysics,2016,128:8-17.
[10]包乾宗,高静怀,陈文超.面波压制的Ridgelet域方法[J].地球物理学报,2007,50(4):1210-1215.BAO Qianzong,GAO Jinghuai,CHEN Wenchao.Ridgelet domain method of ground-roll suppression[J].Chinese Journal of Geophysics,2007,50(4):1210-1215.
[11]金丹,程建远,王保利,等.基于Curvelet变换的地震资料弱信号识别及去噪方法[J].煤炭学报,2016,41(2):332-337.JIN Dan,CHENG Jianyuan,WANG Baoli,et al.Seismic weak signal identification and noise elimination based on Curvelet domain[J].Journal of China Coal Society,2016,41(2):332-337.
[12]WANG Deli,TONG Zhongfei,TANG Chen,et al.An iterative curvelet thresholding algorithm for seismic random noise attenuation[J].Applied Geophysics,2010,7(4):315-324.
[13]MORTEZANEJAD R,GHOLAMI A.Optimization of wavelet-and curvelet-based denoising algorithms by multivariate SURE and GCV[J].Journal of Geophysics and Engineering,2016,13(3):378-390.
[14]姚振岸,孙成禹,石小磊,等.基于曲波变换和各向异性扩散滤波的联合去噪技术[J].石油学报,2016,37(4):490-498.YAO Zhen'an,SUN Chengyu,SHI Xiaolei,et al.A combined denoising method based on Curvelet transform and anisotropic diffusion filtering[J].Acta Petrolei Sinica,2016,37(4):490-498.
[15]赵娴.基于Contourlet变换二维TFPF压制地震勘探随机噪声[D].长春:吉林大学,2016.ZHAO Xian.2-D TFPF based on Contourlet transform for seismic random noise attenuation[D].Changchun:Jilin University,2016.
[16]唐飞.基于Contourlet变换和Shearlet变换的图像去噪算法研究[D].湘潭:湘潭大学,2014.TANG Fei.Research on image denoising methods based on Contourlet transform and Shearlet transform[D].Xiangtan:Xiangtan University,2014.
[17]GUO Kanghui,LABATE D.Optimally sparse multidimensional representation using shearlets[J].SIAM Journal on Mathematical Analysis,2007,39(1):298-318.
[18]GUO Kanghui,LABATE D,LIM W Q,et al.Wavelets with composite dilations[J].Electronic Research Announcements of the American Mathematical Society,2004,10(9):78-87.
[19]GUO Kanghui,LABATE D,LIM W Q,et al.Wavelets with composite dilations and their MRA properties[J].Applied and Computational Harmonic Analysis,2006,20(2):202-236.
[20]冯成祥.一类双正交Shearlet多尺度分析与离散Shearlet变换[D].杭州:浙江工业大学,2012.FENG Chengxiang.A kind of Biorthogonal Shearlet multiscale analysis and discrete Shearlet transformation[D].Hangzhou:Zhejiang University of Technology,2012.
[21]刘成明,王德利.基于贝叶斯理论的Shearlet域一次波与多次波分离[J].石油学报,2016,37(4):483-489.LIU Chengming,WANG Deli.Primary and multiple separation in Shearlet domain based on Bayesian theory[J].Acta Petrolei Sinica,2016,37(4):483-489.
[22]岳彦刚,石智,张卓.基于Shearlet变换的图像边缘检测[J].计算机应用与软件,2014,31(4):227-230.YUE Yan'gang,SHI Zhi,ZHANG Zhuo.Image edge detection algorithm based on Shearlet transform[J].Computer Applications and Software,2014,31(4):227-230.
[23]刘俊良,雷琳,周石琳.非下采样形态学Shearlet变换:提高结构细节捕捉的图像表示新方法[J].信号处理,2014,30(2):163-171.LIU Junliang,LEI Lin,ZHOU Shilin.Non-subsampled morphological Shearlet transform algorithm:a new image representation to promote structural details capturing[J].Journal of Signal Processing,2014,30(2):163-171.
[24]YUAN Min,YANG Bingxin,MA Yide,et al.Compressed sensing MRI reconstruction from highly undersampled k-space data using nonsubsampled Shearlet transform sparsity prior[J].Mathematical Problems in Engineering,2015,2015:615439.
[25]ZHOU Shichong,SHI Jun,ZHU Jie,et al.Shearlet-based texture feature extraction for classification of breast tumor in ultrasound image[J].Biomedical Signal Processing and Control,2013,8(6):688-696.
[26]LIU Shuaiqi,SHI Mingzhu,ZHU Zhihui,et al.Image fusion based on complex-shearlet domain with guided filtering[J].Multidimensional Systems and Signal Processing,2017,28(1):207-224.
[27]SHAHDOOSTI H R,KHAYAT O.Image denoising using sparse representation classification and non-subsampled shearlet transform[J].Signal,Image and Video Processing,2016,10(6):1081-1087.
[28]KONG Dehui,PENG Zhenming,FAN Hongyi,et al.Seismic random noise attenuation using directional total variation in the Shearlet domain[J].Journal of Seismic Exploration,2016,25(4):321-338.
[29]KONG Dehui,PENG Zhenming.Seismic random noise attenuation using shearlet and total generalized variation[J].Journal of Geophysics and Engineering,2015,12(6):1024-1035.
[30]GAO Guorong.Image denoising by non-subsampled shearlet domain multivariate model and its method noise thresholding[J].Optik-International Journal for Light and Electron Optics,2013,124(22):5756-5760.
[31]刘成明,王德利,王通,等.基于Shearlet变换的地震随机噪声压制[J].石油学报,2014,35(4):692-699.LIU Chengming,WANG Deli,WANG Tong,et al.Random seismic noise attenuation based on the Shearlet transform[J].Acta Petrolei Sinica,2014,35(4):692-699.
[32]YANG Chengli,LIU Peiyong,YIN Guofu,et al.Crack detection in magnetic tile images using nonsubsampled shearlet transform and envelope gray level gradient[J].Optics&Laser Technology,2017,90:7-17.
[33]WANG Xiangyang,LIU Yu'nan,XU Huan,et al.Blind optimum detector for robust image watermarking in nonsubsampled shearlet Domain[J].Information Sciences,2016,372:634-654.
[34]张超.微弱地震信号时频消噪算法研究[D].长春:吉林大学,2016.ZHANG Chao.Research on weak seismic signal denoising by using time-frequency algorithm[D].Changchun:Jilin University,2016.