基于压缩感知和稀疏反演的地震数据低频补偿
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摘要
目前波形反演是地下速度成像技术研究的热点,但地震采集数据低频能量的缺失制约着波形反演的效果。笔者基于压缩感知理论和稀疏约束反演技术,提出了一种地震数据低频补偿方法。第一步,利用反射系数的稀疏性,根据压缩感知概念,构造L1范数约束的稀疏反演问题,在Fourier域通过有限带宽重构全带宽频谱,实现对地震数据全带宽拓频。这个过程借助快速迭代阈值法求解反问题。第二步,截取拓频后数据的低频能量和原数据的高频能量构成最终的低频补偿地震数据。模拟数据例子和实际数据例子证明了该方法能够有效地对10 Hz以下的频率进行补偿。
Full waveform inversion(FWI) is a hot topic in the subsurface velocity imaging.However,the lack of effective low frequency energy in seismic data restricts the performance of FWI.A method about low frequency information compensation of seismic based on compressed sensing theory and sparse inversion technique is proposed in this paper.A L1 norm constrained sparse inversion problem is first constructed according to the sparsity of reflectivity and the theory of compressed sensing.This inversion equation can be effectively solved by Fast Iterative Thresholding Algorithm(FISTA) and the full frequency components are then reconstructed in the Fourier domain with band-limited seismic dada.The low frequency components form the reconstructed data and high frequency components of the original data are reasonably combined to obtain the final low frequency compensated data.Synthetic and real data examples are tested to demonstrate the performance of the proposed method.
Full waveform inversion(FWI) is a hot topic in the subsurface velocity imaging.However,the lack of effective low frequency energy in seismic data restricts the performance of FWI.A method about low frequency information compensation of seismic based on compressed sensing theory and sparse inversion technique is proposed in this paper.A L1 norm constrained sparse inversion problem is first constructed according to the sparsity of reflectivity and the theory of compressed sensing.This inversion equation can be effectively solved by Fast Iterative Thresholding Algorithm(FISTA) and the full frequency components are then reconstructed in the Fourier domain with band-limited seismic dada.The low frequency components form the reconstructed data and high frequency components of the original data are reasonably combined to obtain the final low frequency compensated data.Synthetic and real data examples are tested to demonstrate the performance of the proposed method.
引文
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[8]韩红平,陈如山.压缩感知中信号重构算法的研究[D].南京:南京邮电大学,2012.Han Hongping,Chen Rushan.Research on Signal Recon-struction Algorithm of Compressive Sense[D].Nanjing:Nanjing University of Posts and Telecommunications,2012.
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[11]Scales J,Gersztenkorn A.Robust Methods in InverseTheory[J].Inverse Problems,1998,4(4):1071–1091.
[12]Malioutov D,Cetin M,Willsky A.Homotopy Continua-tion for Sparse Signal Representation[J].Acoustics,Speech,and Signal Processing,2005,735(5):733-736.
[13]Beck A,Teboulle M.A Fast Iterative Shrinkage-Thre-sholding Algorithm for Linear Inverse Problems[J].SI-AM Journal Imaging Sciences,2009,2(1):183-202.
[14]Han L,Han L.Seismic Spectral Decomposition and De-noising with In-Crowd Algorithm[C]//SEG TechnicalProgram Expanded Abstracts.Las Vegas:SEG,2012.
[15]Van den Berg E,Friedlander M P.Probing the ParetoFrontier for Basis Pursuit Solutions[J].SIAM Journalon Scientific Computing,2008,31(2):890-912.
[2]Virieux J,Operto S.An Overview of Full-Waveform In-version in Exploration Geophysics[J].Geophysics,2009,74(6):1-26.
[3]罗有春.提高地震勘探分辨率方法理论与应用研究:反褶积[D].成都:成都理工大学,2009.Luo Youchun.Improve the Method and Applied Researchof Seismic Survey Resolution:Deconvolution[D].Chengdu:Chengdu University of Technology,2009.
[4]乐友喜,王经才,屠世杰.约束L1模反褶积[J].石油地球物理勘探,1997,32(2):171-180.Yue Youxi,Wang Jingcai,Tu Shijie.Restrained L1 Mo-dulo Deconvolution[J].Oil Geophysical Prospecting,1997,32(2):171-180.
[5]Economou N,Vafidis A.Spectral Balancing GPR DataUsing Time-Variant Band-with in the t-f Domain[J].Geophysics,2010,75(3):19-27.
[6]陈学华,贺震华,黄德济.时频域高分辨地震层序识别[J].吉林大学学报:地球科学版,2008,38(1):152-155.Chen Xuehua,He Zhenhua,Huang Deji.Seismic Se-quence Identifying with High Resolution in Time-Frequen-cy Domain[J].Journal of Jilin University:Earth ScienceEdition,2008,38(1):152-155.
[7]赵淑红,朱光明.用小波变换谱均衡法提高地震资料的分辨率[J].西安科技大学学报,2007,27(2):255-259.Zhao Shuhong,Zhu Guangming.Using Combined Methodof Wavelet Transform and Spectrum Equalization to Im-prove Seismic Data Resolution[J].Journal of Xi'an Uni-versity of Science Technology,2007,27(2):255-259.
[8]韩红平,陈如山.压缩感知中信号重构算法的研究[D].南京:南京邮电大学,2012.Han Hongping,Chen Rushan.Research on Signal Recon-struction Algorithm of Compressive Sense[D].Nanjing:Nanjing University of Posts and Telecommunications,2012.
[9]Baraniuk G R.Compressive Sensing[J].IEEE SignalProcessing Magazine,2007,52(4):118-124.
[10]Candès E J,Wakin M B.An Introduction to Compres-sive Sampling[J].IEEE Signal Processing Magazine,2008,25(2):21-30.
[11]Scales J,Gersztenkorn A.Robust Methods in InverseTheory[J].Inverse Problems,1998,4(4):1071–1091.
[12]Malioutov D,Cetin M,Willsky A.Homotopy Continua-tion for Sparse Signal Representation[J].Acoustics,Speech,and Signal Processing,2005,735(5):733-736.
[13]Beck A,Teboulle M.A Fast Iterative Shrinkage-Thre-sholding Algorithm for Linear Inverse Problems[J].SI-AM Journal Imaging Sciences,2009,2(1):183-202.
[14]Han L,Han L.Seismic Spectral Decomposition and De-noising with In-Crowd Algorithm[C]//SEG TechnicalProgram Expanded Abstracts.Las Vegas:SEG,2012.
[15]Van den Berg E,Friedlander M P.Probing the ParetoFrontier for Basis Pursuit Solutions[J].SIAM Journalon Scientific Computing,2008,31(2):890-912.
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