基于LDPC矩阵采样方法的三维地震数据重构
|
摘要
按照以往的测量矩阵进行实际勘察无法较好地实现地震数据的重构,大多数矩阵设计复杂且元素多样,不符合实际标准。笔者将LDPC矩阵应用到地震勘探采样中,用较少的地震数据来重构完整的地震记录。采用K-SVD字典对数据进行稀疏变换,FISTA算法进行重构。对比以往的随机采样、离散均匀采样和jitter采样,LDPC矩阵更适合三维环境且恢复重构效果更好。对比重构数据的信噪比,三维模拟数据和实际数据都证实了LDPC矩阵信噪比值最高,重构出的数据效果最好。
The existing sampling matrices cannot realize good seismic data reconstruction results,and most of matrices are complicated and have different elements,which are not suitable for seismic prospecting.The authors applied LDPC matrix to seismic data acquisition,using less data to realize complete data reconstruction.The K-SVD dictionary was used for sparse transform,and FISTA reconstruction algorithm was used to recover original data.Compared with previous random sampling,discrete regular sampling and jitter sampling,the LDPC(Low Density Parity Check) matrix was more suitable in 3-D environment and achieved better performance.Comparing SNRs of reconstructed data of different methods,both 3-D simulated data and field data proved that LDPC matrix has the best SNR and performance.
The existing sampling matrices cannot realize good seismic data reconstruction results,and most of matrices are complicated and have different elements,which are not suitable for seismic prospecting.The authors applied LDPC matrix to seismic data acquisition,using less data to realize complete data reconstruction.The K-SVD dictionary was used for sparse transform,and FISTA reconstruction algorithm was used to recover original data.Compared with previous random sampling,discrete regular sampling and jitter sampling,the LDPC(Low Density Parity Check) matrix was more suitable in 3-D environment and achieved better performance.Comparing SNRs of reconstructed data of different methods,both 3-D simulated data and field data proved that LDPC matrix has the best SNR and performance.
引文
[1]Herrmann F J,Hennenfent G.Non-parametric seismic data recovery with curvelet frames[J].Geophysical Journal International,2008,173(1):233-248.
[2]Hennenfent G,Fenelon L,Herrmann F J.Nonequispaced curvelet transform for seismic data reconstruction:a sparsity-promoting approach[J].Geophysics,2010,75(6):WB203-WB210.
[3]李宇,韩立国,叶林,等.基于F-K域和Curvelet-中值滤波联合去噪的混采数据分离方法[J].世界地质,2017,36(2):609-615.LI Yu,HAN Li-guo,YE Lin,et al.Blended acquisition data separation method based on F-K domain and Curvelet-median filter joint denosing[J].Global Geology,2017,36(2):609-615.
[4]Labate D,Lim W Q,Kutyniok G,et al.Sparse multidimensional representation using shearlets[J].Optics&Photonics,2005,5914:59140U.
[5]Aharon M,Elad M,Bruckstein A.K-SVD:an algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311-4322.
[6]詹可军,宋建新.图像压缩感知中常用测量矩阵的性能比较[J].电视技术,2014,38(5):1-4.ZHAN Ke-jun,SONG Jian-xin.Performance comparison of commonly used measurement matrix in image compressed sensing[J].Video Engineering,2014,38(5):1-4.
[7]邓爱淘.基于LDPC码的压缩感知测量矩阵研究:博士学位论文[D].湘潭:湘潭大学,2015.DENG Ai-tao.Research on measurement matrix for compressed sensing based on LDPC code;doctor's degree thesis[D].Xiangtan:Xiangtan University,2015.
[8]钟菲.压缩感知理论在LDPC信道编码的应用研究:博士学位论文[D].长春:吉林大学,2013.ZHONG Fei.Application research of compressed sensing theory in LDPC channel coding:doctor's degree thesis[D].Changchun:Jilin University,2013.
[9]唐刚.基于压缩感知和稀疏表示的地震数据重建与去噪:博士学位论文[D].北京:清华大学,2010.TANG Gang.Seismic data reconstruction and denoising based on compressive sensing and sparse representation:doctor's degree thesis[D].Beijing:Tsinghua University,2010.
[10]刘文明.LDPC码编译码研究及应用:博士学位论文[D].武汉:华中科技大学,2006.LIU Wen-ming.Research on LDPC codes and applications:doctor's degree thesis[D].Wuhan:Huazhong University of Science and Technology,2006.
[11]Candès E J,Wakin M B.An introduction to compressive sampling[J].IEEE Signal Processing Magazine,2008,25(2):21-30.
[12]Donoho D L.Compressed sensing[J].IEEE Transactions on information theory,2006,52(4):1289-1306.
[13]周岩,韩立国,于江龙,等.稀疏反演求解基追踪降噪问题的地震谱分解方法[J].世界地质,2016,35(2):517-525.ZHOU Yan,HAN Li-guo,YU Jiang-long,et al.Using sparse inversion method solving basic pursuit denoising problem for seismic spectral decomposition[J].Global Geology,2016,35(2):517-525.
[14]Baraniuk R G.Compressive sensing[lecture notes][J].IEEE Signal Processing Magazine,2007,24(4):118-121.
[15]Candès E J.The restricted isometry property and its implications for compressed sensing[J].Comptes Rendus Mathematique,2008,346(9/10):589-592.
[16]Candes E J,Plan Y.A probabilistic and RIPless theory of compressed sensing[J].IEEE Transactions on Information Theory,2011,57(11):7235-7254.
[17]CAI Rui,ZHAO Qun,SHE De-ping et al.Bernoullibased random undersampling schemes for 2D seismic data regularization[J].Applied Geophysics,2014(3):321-330,351-352.
[18]Perez D O,Velis D R,Sacchi M D.High-resolution prestack seismic inversion using a hybrid FISTA leastsquares strategy[J].Geophysics,2013,78(5):R185-R195.
[2]Hennenfent G,Fenelon L,Herrmann F J.Nonequispaced curvelet transform for seismic data reconstruction:a sparsity-promoting approach[J].Geophysics,2010,75(6):WB203-WB210.
[3]李宇,韩立国,叶林,等.基于F-K域和Curvelet-中值滤波联合去噪的混采数据分离方法[J].世界地质,2017,36(2):609-615.LI Yu,HAN Li-guo,YE Lin,et al.Blended acquisition data separation method based on F-K domain and Curvelet-median filter joint denosing[J].Global Geology,2017,36(2):609-615.
[4]Labate D,Lim W Q,Kutyniok G,et al.Sparse multidimensional representation using shearlets[J].Optics&Photonics,2005,5914:59140U.
[5]Aharon M,Elad M,Bruckstein A.K-SVD:an algorithm for designing overcomplete dictionaries for sparse representation[J].IEEE Transactions on Signal Processing,2006,54(11):4311-4322.
[6]詹可军,宋建新.图像压缩感知中常用测量矩阵的性能比较[J].电视技术,2014,38(5):1-4.ZHAN Ke-jun,SONG Jian-xin.Performance comparison of commonly used measurement matrix in image compressed sensing[J].Video Engineering,2014,38(5):1-4.
[7]邓爱淘.基于LDPC码的压缩感知测量矩阵研究:博士学位论文[D].湘潭:湘潭大学,2015.DENG Ai-tao.Research on measurement matrix for compressed sensing based on LDPC code;doctor's degree thesis[D].Xiangtan:Xiangtan University,2015.
[8]钟菲.压缩感知理论在LDPC信道编码的应用研究:博士学位论文[D].长春:吉林大学,2013.ZHONG Fei.Application research of compressed sensing theory in LDPC channel coding:doctor's degree thesis[D].Changchun:Jilin University,2013.
[9]唐刚.基于压缩感知和稀疏表示的地震数据重建与去噪:博士学位论文[D].北京:清华大学,2010.TANG Gang.Seismic data reconstruction and denoising based on compressive sensing and sparse representation:doctor's degree thesis[D].Beijing:Tsinghua University,2010.
[10]刘文明.LDPC码编译码研究及应用:博士学位论文[D].武汉:华中科技大学,2006.LIU Wen-ming.Research on LDPC codes and applications:doctor's degree thesis[D].Wuhan:Huazhong University of Science and Technology,2006.
[11]Candès E J,Wakin M B.An introduction to compressive sampling[J].IEEE Signal Processing Magazine,2008,25(2):21-30.
[12]Donoho D L.Compressed sensing[J].IEEE Transactions on information theory,2006,52(4):1289-1306.
[13]周岩,韩立国,于江龙,等.稀疏反演求解基追踪降噪问题的地震谱分解方法[J].世界地质,2016,35(2):517-525.ZHOU Yan,HAN Li-guo,YU Jiang-long,et al.Using sparse inversion method solving basic pursuit denoising problem for seismic spectral decomposition[J].Global Geology,2016,35(2):517-525.
[14]Baraniuk R G.Compressive sensing[lecture notes][J].IEEE Signal Processing Magazine,2007,24(4):118-121.
[15]Candès E J.The restricted isometry property and its implications for compressed sensing[J].Comptes Rendus Mathematique,2008,346(9/10):589-592.
[16]Candes E J,Plan Y.A probabilistic and RIPless theory of compressed sensing[J].IEEE Transactions on Information Theory,2011,57(11):7235-7254.
[17]CAI Rui,ZHAO Qun,SHE De-ping et al.Bernoullibased random undersampling schemes for 2D seismic data regularization[J].Applied Geophysics,2014(3):321-330,351-352.
[18]Perez D O,Velis D R,Sacchi M D.High-resolution prestack seismic inversion using a hybrid FISTA leastsquares strategy[J].Geophysics,2013,78(5):R185-R195.