基于压缩感知理论与傅立叶变换的地震数据重建(英文)
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摘要
传统的地震勘探数据采样必须遵循奈奎斯特采样定理,而本文基于新发展的压缩感知理论,在突破传统采样定理限制的基础上,利用随机欠采样方法将传统规则欠采样所带来的互相干假频转化成较低幅度的不相干噪声,从而将数据重建问题转为更简单的去噪问题。在数据重建过程中引入凸集投影算法(POCS),采用指数规律衰减的阈值参数,在每次迭代过程中,改变以往从时间到空间都需要进行正反变换的做法,提出只对地震数据空间方向进行正反变换,从而可以减少内存空间,提高运算速度,并且也分析了本文POCS算法的抗噪声与反假频能力,同时我们也对二维和三维地震数据重建进行了比较。理论模型和实际数据表明本文方法效果明显,这对于指导复杂地区数据采集、缺失地震道重建及降低勘探成本方面具有重要的实用价值。
Traditional seismic data sampling follows the Nyquist sampling theorem.In this paper,we introduce the theory of compressive sensing(CS),breaking through the limitations of the traditional Nyquist sampling theorem,rendering the coherent aliases of regular undersampling into harmless incoherent random noise using random undersampling,and effectively turning the reconstruction problem into a much simpler denoising problem.We introduce the projections onto convex sets(POCS) algorithm in the data reconstruction process,apply the exponential decay threshold parameter in the iterations,and modify the traditional reconstruction process that performs forward and reverse transforms in the time and space domain.We propose a new method that uses forward and reverse transforms in the space domain.The proposed method uses less computer memory and improves computational speed.We also analyze the antinoise and anti-aliasing ability of the proposed method,and compare the 2D and 3D data reconstruction.Theoretical models and real data show that the proposed method is effective and of practical importance,as it can reconstruct missing traces and reduce the exploration cost of complex data acquisition.
Traditional seismic data sampling follows the Nyquist sampling theorem.In this paper,we introduce the theory of compressive sensing(CS),breaking through the limitations of the traditional Nyquist sampling theorem,rendering the coherent aliases of regular undersampling into harmless incoherent random noise using random undersampling,and effectively turning the reconstruction problem into a much simpler denoising problem.We introduce the projections onto convex sets(POCS) algorithm in the data reconstruction process,apply the exponential decay threshold parameter in the iterations,and modify the traditional reconstruction process that performs forward and reverse transforms in the time and space domain.We propose a new method that uses forward and reverse transforms in the space domain.The proposed method uses less computer memory and improves computational speed.We also analyze the antinoise and anti-aliasing ability of the proposed method,and compare the 2D and 3D data reconstruction.Theoretical models and real data show that the proposed method is effective and of practical importance,as it can reconstruct missing traces and reduce the exploration cost of complex data acquisition.
引文
Abma,R.,and Kabir,N.,2006,3D interpolation of irregulardata with a POCS algorithm: Geophysics,71(5),91-97.
Bregman,L.,1965,The method of successive projectionfor finding a common point of convex sets: Soviet Math,6(3),688-692.
Candès,E.,Demanet,L.,Donoho,D.,et al.,2006,Fastdiscrete curvelet transforms: SIAM Multiscale Modelingand Simulation,5(1),861-899.
Donoho,D.,L.,2006,Compressed sensing: IEEETransactions on information Theory.52(4),1289-1306.
Gao,J.J.,Chen,X.H.,and Li,J.Y.,2011,Thereconstruction method for irregular seismic data: OilGeophysical prospecting (in Chinese),46(1),40-46.
Gao,J.J.,Chen,X.H.,Li,J.Y.,et a1.,2010,Irregularseismic data reconstruction based on exponentialthreshold model of POCS method: Applied Geophysics,7(3),229-238.
Galloway,E.,and Sacchi,M.,2007,POCS method forseismic data reconstruction of irregularly sampled data:CSPG Conference,Calgary,Canada,555.
Herrmann,F.J.,2010,Randomized sampling andsparsity: Getting more information from fewer samples:Geophysics,173-187.
Hennenfent,G.,Fenelon,L.,and Herrmann,F.J.,2010,Nonequispaced curvelet transform for seismic datareconstruction: A sparsity-promoting approach:Geophysics,75(6),203-210.
Hennenfent,G.,and Herrmann,F.J.,2008,Simply denoise:wavefield reconstruction via jittered under-sampling:Geophysics 73(3),19-28.
Jin,S.,2010,5D seismic data regularization by a dampedleast-norm Fourier inversion: Geophysics,75(6),103-111.
Ma,J.W.,Tang,G.,and Tang,W.,2010,Recovery ofincomplete seismic data based on Curvelet transform and compressed sensing: Chinese Geophysical Year Meeting(in Chinese).ChangSha,656-659.
Kreimer,N.,and Sacchi,M.,2012,A tensor higher-ordersingular value decomposition for prestack seismic datanoise reduction and interpolation: Geophysics 77(3),113-122.
Liu,B.,2004,Multi-dimensional reconstruction of seismicdata: Ph.D.Thesis,University of Alberta,Canada,1-15.
Naghizadeh,M.,and Sacchi,M.D.,2010a,Beyond aliashierarchical scale curvelet interpolation of regularly andirregularly sampled seismic data: Geophysics,75(6),189-202.
Ozkan,M.,Tekalp,M.,and Sezan,M.,1994,POCS basedrestoration of space-varying blurred images: IEEETransactions on Image Processing,3(4),450-454.
Trad,D.,Ulryeh,T.,and Sacchi,M.,2003,Latest view ofsparse Radon transform: Geophysics,68(1),386-399.
Trad,D.O.,2009,Five-dimensional interpolation:Recovering from acquisition constraints: Geophysics,74(6),123-132.
Tang,G.,and Yang,H.Z.,2010,Seismic data compressionand reconstruction based oil Poisson Disk sampling:Chinese J.Geophys.(in Chinese),53(9),2181-2188.
Tang,G.,2010.Seismic Data Reconstruction andDenoising based on Compressive Sensing and SparseRepresentation: Ph.D.thesis,Tsinghua University (inChinese),62-65.
Vassallo,M.,A.Ozbek,K.Ozdemir.,and K.Eggenberger.,2010,Crossline wavefield reconstruction frommulticomponent streamer data: Part 1-Multichannelinterpolation by matching pursuit (MIMAP) using pressureand its crossline gradient: Geophysics,75(6),53-67.
Wang,J.F.,Ng,M.,and Perz,M.,2010,Seismic datainterpolation by greedy local Radon transform: Geophysics,75(6),225-234.
Xu,S.,Zhang,Y.,Pham,D.,and Lambare,G.,2005,Antileakage Fourier transform for seismic data regularization:Geophysics,70(4),87-95.
Bregman,L.,1965,The method of successive projectionfor finding a common point of convex sets: Soviet Math,6(3),688-692.
Candès,E.,Demanet,L.,Donoho,D.,et al.,2006,Fastdiscrete curvelet transforms: SIAM Multiscale Modelingand Simulation,5(1),861-899.
Donoho,D.,L.,2006,Compressed sensing: IEEETransactions on information Theory.52(4),1289-1306.
Gao,J.J.,Chen,X.H.,and Li,J.Y.,2011,Thereconstruction method for irregular seismic data: OilGeophysical prospecting (in Chinese),46(1),40-46.
Gao,J.J.,Chen,X.H.,Li,J.Y.,et a1.,2010,Irregularseismic data reconstruction based on exponentialthreshold model of POCS method: Applied Geophysics,7(3),229-238.
Galloway,E.,and Sacchi,M.,2007,POCS method forseismic data reconstruction of irregularly sampled data:CSPG Conference,Calgary,Canada,555.
Herrmann,F.J.,2010,Randomized sampling andsparsity: Getting more information from fewer samples:Geophysics,173-187.
Hennenfent,G.,Fenelon,L.,and Herrmann,F.J.,2010,Nonequispaced curvelet transform for seismic datareconstruction: A sparsity-promoting approach:Geophysics,75(6),203-210.
Hennenfent,G.,and Herrmann,F.J.,2008,Simply denoise:wavefield reconstruction via jittered under-sampling:Geophysics 73(3),19-28.
Jin,S.,2010,5D seismic data regularization by a dampedleast-norm Fourier inversion: Geophysics,75(6),103-111.
Ma,J.W.,Tang,G.,and Tang,W.,2010,Recovery ofincomplete seismic data based on Curvelet transform and compressed sensing: Chinese Geophysical Year Meeting(in Chinese).ChangSha,656-659.
Kreimer,N.,and Sacchi,M.,2012,A tensor higher-ordersingular value decomposition for prestack seismic datanoise reduction and interpolation: Geophysics 77(3),113-122.
Liu,B.,2004,Multi-dimensional reconstruction of seismicdata: Ph.D.Thesis,University of Alberta,Canada,1-15.
Naghizadeh,M.,and Sacchi,M.D.,2010a,Beyond aliashierarchical scale curvelet interpolation of regularly andirregularly sampled seismic data: Geophysics,75(6),189-202.
Ozkan,M.,Tekalp,M.,and Sezan,M.,1994,POCS basedrestoration of space-varying blurred images: IEEETransactions on Image Processing,3(4),450-454.
Trad,D.,Ulryeh,T.,and Sacchi,M.,2003,Latest view ofsparse Radon transform: Geophysics,68(1),386-399.
Trad,D.O.,2009,Five-dimensional interpolation:Recovering from acquisition constraints: Geophysics,74(6),123-132.
Tang,G.,and Yang,H.Z.,2010,Seismic data compressionand reconstruction based oil Poisson Disk sampling:Chinese J.Geophys.(in Chinese),53(9),2181-2188.
Tang,G.,2010.Seismic Data Reconstruction andDenoising based on Compressive Sensing and SparseRepresentation: Ph.D.thesis,Tsinghua University (inChinese),62-65.
Vassallo,M.,A.Ozbek,K.Ozdemir.,and K.Eggenberger.,2010,Crossline wavefield reconstruction frommulticomponent streamer data: Part 1-Multichannelinterpolation by matching pursuit (MIMAP) using pressureand its crossline gradient: Geophysics,75(6),53-67.
Wang,J.F.,Ng,M.,and Perz,M.,2010,Seismic datainterpolation by greedy local Radon transform: Geophysics,75(6),225-234.
Xu,S.,Zhang,Y.,Pham,D.,and Lambare,G.,2005,Antileakage Fourier transform for seismic data regularization:Geophysics,70(4),87-95.
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