基于压缩感知理论的缺失地震数据重构方法
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摘要
压缩感知是一种新的理论,它打破常规尼奎斯特-香农采样定理的制约,利用信号的稀疏特性或可压缩特性,用较少的数据即可重构恢复完整的信号。建立了基于压缩感知理论的缺失地震数据重构模型。首先在与稀疏变换不相关的测量矩阵基础上引入一种约束矩阵,使地震数据的缺失满足或接近高斯随机分布;随机缺失的地震数据变换到稀疏域会产生很多与有效信号不相干的随机噪声,接着通过一种新的自适应阈值迭代算法可以很好地消除稀疏系数中的随机噪声干扰,经过逆稀疏变换即得到重构后的地震数据。Marmousi 2模型测试及实际地震资料处理均验证了该方法的可行性和有效性。重构缺失地震数据取得了较好的效果。
Compressive sensing(CS) is a new kind of theory which breaks the limitation of the conventional Nyquist-Shannon sampling theorem and recovers the complete signal from few data by using the sparse or compressed characteristics of the signal.With the theory of CS,a seismic data recovery model is built in this paper.Based on the measure matrix which is incoherent with the sparsifying basis,a kind of restrained matrix is proposed as to achieve the effects of seismic missing data with gaussian random distribution or nearly gaussian random distribution and hence the sparsifying coefficient of the aliasing seismic data will contain many random noises which is uncorrelated with the effective signal.The full data can be reconstructed from a new adaptive iterative threshold solution and an inverse sparse transform.From the test of the synthetic seismic data and Marmousi 2 model,we verified the availability and feasibility of our method.
Compressive sensing(CS) is a new kind of theory which breaks the limitation of the conventional Nyquist-Shannon sampling theorem and recovers the complete signal from few data by using the sparse or compressed characteristics of the signal.With the theory of CS,a seismic data recovery model is built in this paper.Based on the measure matrix which is incoherent with the sparsifying basis,a kind of restrained matrix is proposed as to achieve the effects of seismic missing data with gaussian random distribution or nearly gaussian random distribution and hence the sparsifying coefficient of the aliasing seismic data will contain many random noises which is uncorrelated with the effective signal.The full data can be reconstructed from a new adaptive iterative threshold solution and an inverse sparse transform.From the test of the synthetic seismic data and Marmousi 2 model,we verified the availability and feasibility of our method.
引文
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[2]孙大明,邵维.高分辨率三维地震采集技术研究[J].吉林大学学报:地球科学版,2002,32(4):395-398.Sun Daming,Shao Wei.Research on AcquisitionTechnology on High Resolution 3-D Seismic[J].Jour-nal of Jilin University:Earth Science Edition,2002,32(4):395-398.
[3]Ronen J.Wave Equation Trace Interpolation[J].Geo-physics,1987,52(7):973-984.
[4]Chemingui N,Biondi B.Handing the Irregular Geo-metry in Wide-Azimuth Surveys[C]//SEG Interna-tional Exposition and 66th Annual Meeting.[S.l.]:SEG,1996:32-35.
[5]Spitz S.Seismic Trace Interpolation in the f-x Domain[J].Geophysics,1991,56(6):785-794.
[6]Naghizadeh M,Sacchi M.f-x Adaptive Seismic TraceInterpolation[J].Geophysics,2009,74(1):v9-v16.
[7]Yang L,Sergey F.Trace Interpolation Beyond Alias-ing Using Regularized Nonstationary Autoregression[J].SEG Expanded Abstracts,2010,29:3662.
[8]Kabir N,Verschuur J.Restoration of Missing Offsetsby Parabolic Radon Transform[J].Geophys Prosp,1995,43(4):347-368.
[9]高建军,陈小宏,李景叶,等.基于非均匀Fourier变换的地震数据重建方法研究[J].地球物理学进展,2009,24(5):1741-1747.Gao Jianjun,Chen Xiaohong,Li Jingye,et al.Studyon Reconstruction of Seismic Data Based on Nonuni-form Fourier Transform[J].Progress in Geophysics,2009,24(5):1741-1747.
[10]Naghizadeh M,Sacchi M.Beyond Alias HierarchicalScale Curvelet Interpolation of Regularly and Irregu-larly Sampled Seismic Data[J].Geophysics,2009,75:189-202.
[11]Naghizadeh M,Sacchi M.Hierarchical Scale CurveletInterpolation of Aliased Seismic Data[C]//SEG Inter-national Exposition and 80th Annual Meeting.[S.l.]:SEG,2010.
[12]Herrmann J,Hennenfent G.Non-Parametric SeismicData Recovery with Curvelet Frames[J].GeophysicalJournal International,2008,173(1):1-5.
[13]Baraniuk R.A Lecture on Compressive Sensing[J].IEEE Signal Processing Magazine,2007,24(4):118-121.
[14]Donoho D.Compressed Sensing[J].IEEE Trans onInformation Theory,2006,52(4):1289-1306.
[15]Donoho D,Tsaig Y.Extensions of CompressedSensing[J].Signal Processing,2006,86(3):533-548.
[16]Hennenfent G,Herrmann J.Random Sampling:New Insights into the Reconstruction of Coarsely-Sampled Wavefields[C]//SEG International Exposi-tion and 77th Annual Meeting.[S.l.]:SEG,2007.
[17]Candès E J,Tao T.Near Optimal Signal Recoveryfrom Random Projections:Universal EncodingStrategies[J].IEEE Transactions on InformationTheory,2006,52(12),5406-5425.
[18]Candès E J,Donoho D L.New Tight Frames of Cur-velets and Optimal Representations of objects withPiecewise c2 Singularities[J].Comm on Pure and Ap-pl Math,2004,57(2):219-216.
[19]吴爱弟,赵秀玲.基于曲波变换的地震信号去噪方法[J].中国石油大学学报,2010,34(3):30-33.Wu Aidi,Zhao Xiuling.Seismic Signal DenoisingMethod Based on Curvelet Transform[J].Journal ofChina University of Petroleum,2010,34(3):30-33.
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