基于压缩感知的L1范数谱投影梯度算法地震数据重建
|
摘要
随着油气勘探的发展,采集的数据规模与复杂度越来越大,对这些数据进行重建的精度与效率影响到后续地震资料的处理效果。常用于地震数据重建的压缩感知理论与重建算法各有精度与效率的优势,因此对于大规模、复杂地震数据,综合考虑重建精度与计算时间,提出了一种基于压缩感知理论和L1范数谱投影梯度算法(SPGL1)的地震数据重建方法。首先根据地震数据的缺失情况选择采样矩阵,然后在contourlet域中采用L1范数谱投影梯度算法重建缺失的稀疏系数,最后进行contourlet反变换实现地震数据的重建。合成地震数据实验结果表明,基于压缩感知和L1范数谱投影梯度算法重建的地震数据精度较好,计算效率高。通过实际地震资料处理,对比了相同稀疏变换基情况下常用的贪婪算法中的正交匹配追踪(OMP)、梯度投影稀疏重建算法(GPSR)及L1范数谱投影梯度算法(SPGL1)的应用效果,发现基于压缩感知的L1范数谱投影梯度算法鲁棒性较好,受噪声影响小,重建精度高,并且兼顾了计算效率的需求。
With the development of oil and gas exploration,the scale and complexity of collected data are increasing.The reconstruction of seismic missing data is essential for subsequent data processing.Reconstruction algorithms based on compressive sensing are accurate and efficient.Here,we proposed a seismic data reconstruction method,based on a spectral projection gradient L1 algorithm(SPGL1) and on compressive sensing,which can be applied to large-scale and complex seismic data.First,a sampling matrix was selected according to the missing data.Then,the missing sparse coefficients were reconstructed using the SPGL1 in the contourlet domain.Finally,the contourlet inverse transform was used to reconstruct the seismic data.Tests on synthetic and field data demonstrated the superiority of the proposed method over traditional methods:it provided higher accuracy and efficiency.Based on the contourlet transform,we could conclude that the SPGL1 is more robust than OMP and the gradient projection algorithm GPSR in the processing of noisy data.
With the development of oil and gas exploration,the scale and complexity of collected data are increasing.The reconstruction of seismic missing data is essential for subsequent data processing.Reconstruction algorithms based on compressive sensing are accurate and efficient.Here,we proposed a seismic data reconstruction method,based on a spectral projection gradient L1 algorithm(SPGL1) and on compressive sensing,which can be applied to large-scale and complex seismic data.First,a sampling matrix was selected according to the missing data.Then,the missing sparse coefficients were reconstructed using the SPGL1 in the contourlet domain.Finally,the contourlet inverse transform was used to reconstruct the seismic data.Tests on synthetic and field data demonstrated the superiority of the proposed method over traditional methods:it provided higher accuracy and efficiency.Based on the contourlet transform,we could conclude that the SPGL1 is more robust than OMP and the gradient projection algorithm GPSR in the processing of noisy data.
引文
[1] SPITZ S.Seismic trace interpolation in the F-X domain[J].Geophysics,1991,56(6):785-794
[2] NAGHIZADEH M,SACCHI M D.Multistep autoregressive reconstruction of seismic records[J].Geophysics,2007,72(6):111-118
[3] CHEMINGUI N,BIONDI B.Handling the irregular geometry in wide-azimuth surveys[J].Expanded Abstracts of 69th Annual Internat SEG Mtg,1999:32-35
[4] RONEN J.Wave-equation trace interpolation[J].Geophysics,1987,52(7):973-984
[5] 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):674-681,693CHEN Z B,WANG L Z,SONG Y,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
[6] 王升超,韩立国,巩向博.基于各向异性Radon变换的叠前地震数据重建[J].石油物探,2016,55(6):808-815 WANG S H,HAN L G,GONG X B.Prestack seismic data reconstruction by anisotropic Radon transform[J].Geophysical Prospecting for Petroleum,2016,55(6):808-815
[7] 白兰淑,刘伊克,卢回忆,等.基于压缩感知的Curvelet域联合迭代地震数据重建[J].地球物理学报,2014,57(9):2937-2945BAI L S,LIU Y K,LU H Y,et al.Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing[J].Chinese Journal of Geophysics,2014,57(9):2937-2945
[8] 张良,韩立国,刘争光,等.基于压缩感知和Contourlet变换的地震数据重建方法[J].石油物探,2017,56(6):804-811ZHANG L,HAN L G,LIU Z G,et al.Seismic data reconstruction based on compressed sensing and contourlet transform[J].Geophysical Prospecting for Petroleum,2017,56(6):804-811
[9] 王华忠,冯波,王雄文,等.压缩感知及其在地震勘探中的应用[J].石油物探,2016,55(4):467-474WANG H Z,FENG B,WANG X W,et al.Compressed sensing and its application in seismic exploration[J].Geophysical Prospecting for Petroleum,2016,55(4):467-474
[10] 张岩,任伟建,唐国维.基于波原子域的地震数据压缩感知重建[J].地球物理学进展,2017,32(5):2152-2161ZHANG Y,REN W J,TANG G W.Compressed sensing reconstruction of seismic data based on wave atoms domain[J].Progress in Geophysics,2017,32(5):2152-2161
[11] MALLAT S G,ZHANG Z F.Matching pursuit with time-frequency dictionary[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415
[12] TROPP J A,GILBERT A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2007,53(12):4655-4666
[13] 宋维琪,李艳清,刘磊.独立分量分析与压缩感知微地震弱信号提取方法[J].石油地球物理勘探,2017,52(5):984-989,1041SONG W Q,LI Y Q,LIU L.Microseismic weak signal extraction based on the independent component analysis and compressive sensing[J].Oil Geophysical Prospecting,2017,52(5):984-989,1041
[14] GILBERT A C,STRAUSS M J,TROPP J A,et al.One sketch for all:fast algorithms for compressed sensing[C]//Proceedings of the 39th Annual ACM Symposium on Theory of Computing.New York:Association for Computing Machiner,2007:237-246
[15] MISHALI M,ELDAR Y C,DOUNAEVSKY O,et al.Xampling:analog to digital at sub-Nyquist rates[J].IET Circuits,Devices & Systems,2011,5(1):8-20
[16] CHEN S S,SAUNDERS M A,DONOHO D L.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,1998,20(1):33-61
[17] DAUBECHIES I,DEFRISE M,MOL C D.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57(12):1412-1457
[18] CAND E J,ROMBERG J,TAO T.Robust uncertainty principles:exact signal reconstruction from highly incomplete Fourier information[J].IEEE Transation on Information Theory,2006,52(2):489-509
[19] MARIO A T F,ROBERT D N,STEPHEN J W.Gradient projection for sparse reconstruction:application to compressed sensing and other inverse problems[J].IEEE Journal of Selected Topics in Signal Processing,2007,1(4):586-597
[20] BIRGIN G E,MARTINEZ J M,RAYDAN M.Nonmonotone spectral projected gradient methods on convex sets[J].SIAM Journal on Optimization,2000,10(4):1196-1211
[21] BERG E V D,FRIEDLANDER M.Sparse optimization with least-squares constraints[J].SIAM Journal on Optimization,2011,21(4);1201-1229
[22] BERG E V D,FRIEDLANDER M.Probing the pareto frontier for basis pursuit solutions[J].SIAM Journal on Scientific Computing,2008,30(2):890-912
[23] BARANIUK R G.Compressive sensing[J].IEEE Signal Processing Magazine,2007,24(4):118-121
[24] 周亚同,刘志峰,张志伟.形态分量分析框架下基于DCT与曲波字典组合的地震信号重建[J].石油物探,2015,54(5):560-568 ZHOU Y T,LIU Z F,ZHANG Z W.Seismic signal reconstruction under the morphological component analysis framework combined with discrete cosine transform (DCT) and curvelet dictionary[J].Geophysical Prospecting for Petroleum,2015,54(5):560-568
[25] DO M N.The contourlet transform:an efficient directional multiresolution image representation[J].IEEE Fransactions on Image Processing,2005,14(12):2091-2106
[26] 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 Y F,ZOU S F,JV X G.Seismic random noise self-adaptive attenuation method based on K-L transform in the contourlet-domain[J].Geophysical Prospecting for Petroleum,2017,56(5):676-683
[27] 郑雪辰,包乾宗,孔啸,等.地震数据重建的谱投影梯度算法中的参数选取[J].石油物探,2018,57(1):58-64ZHENG X C,BAO Q Z,KONG X,et al.Parameter selection of spectral projection gradient algorithm for seismic data reconstruction[J].Geophysical Prospecting for Petroleum,2018,57(1):58-64
[2] NAGHIZADEH M,SACCHI M D.Multistep autoregressive reconstruction of seismic records[J].Geophysics,2007,72(6):111-118
[3] CHEMINGUI N,BIONDI B.Handling the irregular geometry in wide-azimuth surveys[J].Expanded Abstracts of 69th Annual Internat SEG Mtg,1999:32-35
[4] RONEN J.Wave-equation trace interpolation[J].Geophysics,1987,52(7):973-984
[5] 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):674-681,693CHEN Z B,WANG L Z,SONG Y,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
[6] 王升超,韩立国,巩向博.基于各向异性Radon变换的叠前地震数据重建[J].石油物探,2016,55(6):808-815 WANG S H,HAN L G,GONG X B.Prestack seismic data reconstruction by anisotropic Radon transform[J].Geophysical Prospecting for Petroleum,2016,55(6):808-815
[7] 白兰淑,刘伊克,卢回忆,等.基于压缩感知的Curvelet域联合迭代地震数据重建[J].地球物理学报,2014,57(9):2937-2945BAI L S,LIU Y K,LU H Y,et al.Curvelet-domain joint iterative seismic data reconstruction based on compressed sensing[J].Chinese Journal of Geophysics,2014,57(9):2937-2945
[8] 张良,韩立国,刘争光,等.基于压缩感知和Contourlet变换的地震数据重建方法[J].石油物探,2017,56(6):804-811ZHANG L,HAN L G,LIU Z G,et al.Seismic data reconstruction based on compressed sensing and contourlet transform[J].Geophysical Prospecting for Petroleum,2017,56(6):804-811
[9] 王华忠,冯波,王雄文,等.压缩感知及其在地震勘探中的应用[J].石油物探,2016,55(4):467-474WANG H Z,FENG B,WANG X W,et al.Compressed sensing and its application in seismic exploration[J].Geophysical Prospecting for Petroleum,2016,55(4):467-474
[10] 张岩,任伟建,唐国维.基于波原子域的地震数据压缩感知重建[J].地球物理学进展,2017,32(5):2152-2161ZHANG Y,REN W J,TANG G W.Compressed sensing reconstruction of seismic data based on wave atoms domain[J].Progress in Geophysics,2017,32(5):2152-2161
[11] MALLAT S G,ZHANG Z F.Matching pursuit with time-frequency dictionary[J].IEEE Transactions on Signal Processing,1993,41(12):3397-3415
[12] TROPP J A,GILBERT A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2007,53(12):4655-4666
[13] 宋维琪,李艳清,刘磊.独立分量分析与压缩感知微地震弱信号提取方法[J].石油地球物理勘探,2017,52(5):984-989,1041SONG W Q,LI Y Q,LIU L.Microseismic weak signal extraction based on the independent component analysis and compressive sensing[J].Oil Geophysical Prospecting,2017,52(5):984-989,1041
[14] GILBERT A C,STRAUSS M J,TROPP J A,et al.One sketch for all:fast algorithms for compressed sensing[C]//Proceedings of the 39th Annual ACM Symposium on Theory of Computing.New York:Association for Computing Machiner,2007:237-246
[15] MISHALI M,ELDAR Y C,DOUNAEVSKY O,et al.Xampling:analog to digital at sub-Nyquist rates[J].IET Circuits,Devices & Systems,2011,5(1):8-20
[16] CHEN S S,SAUNDERS M A,DONOHO D L.Atomic decomposition by basis pursuit[J].SIAM Journal on Scientific Computing,1998,20(1):33-61
[17] DAUBECHIES I,DEFRISE M,MOL C D.An iterative thresholding algorithm for linear inverse problems with a sparsity constraint[J].Communications on Pure and Applied Mathematics,2004,57(12):1412-1457
[18] CAND E J,ROMBERG J,TAO T.Robust uncertainty principles:exact signal reconstruction from highly incomplete Fourier information[J].IEEE Transation on Information Theory,2006,52(2):489-509
[19] MARIO A T F,ROBERT D N,STEPHEN J W.Gradient projection for sparse reconstruction:application to compressed sensing and other inverse problems[J].IEEE Journal of Selected Topics in Signal Processing,2007,1(4):586-597
[20] BIRGIN G E,MARTINEZ J M,RAYDAN M.Nonmonotone spectral projected gradient methods on convex sets[J].SIAM Journal on Optimization,2000,10(4):1196-1211
[21] BERG E V D,FRIEDLANDER M.Sparse optimization with least-squares constraints[J].SIAM Journal on Optimization,2011,21(4);1201-1229
[22] BERG E V D,FRIEDLANDER M.Probing the pareto frontier for basis pursuit solutions[J].SIAM Journal on Scientific Computing,2008,30(2):890-912
[23] BARANIUK R G.Compressive sensing[J].IEEE Signal Processing Magazine,2007,24(4):118-121
[24] 周亚同,刘志峰,张志伟.形态分量分析框架下基于DCT与曲波字典组合的地震信号重建[J].石油物探,2015,54(5):560-568 ZHOU Y T,LIU Z F,ZHANG Z W.Seismic signal reconstruction under the morphological component analysis framework combined with discrete cosine transform (DCT) and curvelet dictionary[J].Geophysical Prospecting for Petroleum,2015,54(5):560-568
[25] DO M N.The contourlet transform:an efficient directional multiresolution image representation[J].IEEE Fransactions on Image Processing,2005,14(12):2091-2106
[26] 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 Y F,ZOU S F,JV X G.Seismic random noise self-adaptive attenuation method based on K-L transform in the contourlet-domain[J].Geophysical Prospecting for Petroleum,2017,56(5):676-683
[27] 郑雪辰,包乾宗,孔啸,等.地震数据重建的谱投影梯度算法中的参数选取[J].石油物探,2018,57(1):58-64ZHENG X C,BAO Q Z,KONG X,et al.Parameter selection of spectral projection gradient algorithm for seismic data reconstruction[J].Geophysical Prospecting for Petroleum,2018,57(1):58-64