基于非均匀快速傅里叶变换的最小二乘反演地震数据重建
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摘要
不规则采样地震数据的重建是地震数据分析处理的重要问题.本文给出了一种基于非均匀快速傅里叶变换的最小二乘反演地震数据重建的方法,在最小二乘反演插值方程中,引入正则化功率谱约束项,通过非均匀快速傅里叶变换和修改周期图的方式,自适应迭代修改约束项,使待插值数据的频谱越来越接近真实的频谱,采用预条件共轭梯度法迭代求解,保证了解的稳定性和收敛速度.理论模型和实际地震数据插值试验证明了本文方法能够去除空间假频,速度快、插值效果好,具有实用价值.
Reconstruction of uneven seismic data is a crucial step of the analyzing and processing of the data. In this paper, a least squares inversion based on nonuniform fast Fourier transform is proposed, which can reconstruct both uneven and alias seismic data. The algorithm of nonuniform fast Fourier transform is used to do Fourier transform of uneven data. An adaptive DFT weighted norm regularization constraint is used during the reconstruction. The inverse problem is solved by the preconditioning conjugate gradient method, which makes the solutions stable and convergence quick. Experimental results on theoretical model and raw uneven seismic data show that the proposed method is fast, efficient and applicable.
Reconstruction of uneven seismic data is a crucial step of the analyzing and processing of the data. In this paper, a least squares inversion based on nonuniform fast Fourier transform is proposed, which can reconstruct both uneven and alias seismic data. The algorithm of nonuniform fast Fourier transform is used to do Fourier transform of uneven data. An adaptive DFT weighted norm regularization constraint is used during the reconstruction. The inverse problem is solved by the preconditioning conjugate gradient method, which makes the solutions stable and convergence quick. Experimental results on theoretical model and raw uneven seismic data show that the proposed method is fast, efficient and applicable.
引文
[1]Jakubowicz H.Wavefield reconstruction.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1994.1557~1560
[2]Larner K,Gibson B,Rothman D.Trace interpolation andthe design of seismic surveys.Geophysics,1981,46(4):407~409
[3]Lu L.Application of local slant-stack to trace interpolation.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1985.560~562
[4]King GA.Leong TK,Flinchbaugh B E.The role of interpolationin seismic resolution.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts.1984
[5]Monk D,McBeath R G,Wason C B.Interpolation of aliased seismic traces.US Patent,1993.5235556
[6]Claerbout J,Nichols D.Interpolation beyond aliasing by(t-x)domain in PEFs.53rdAnn.Internat.Mtg.,Eur.Assn.Geosci.Eng.,Expanded Abstracts,1991.1~10
[7]国九英,周兴元,俞寿朋.FX域等道距道内插.石油地球物理勘探,1996,31(1):28~34Guo J Y,Zhou X Y,Yu S P.Iso-interval trace interpolationinF-X domain.Oil Geophysical Prospecting(in Chinese),1996,31(1):28~34.
[8]国九英,周兴元.FK域等道距道内插.石油地球物理勘探,1996,31(2):211~218Guo J Y,Zhou X Y.Iso-interval trace interpolationinF-Kdomain.Oil Geophysical Prospecting(in Chinese),1996,31(2):211~218
[9]Spitz S.Seismic trace interpolation in thef-xdomain.Geophysics,1991,56(6):785~794
[10]Ji J.Interpolation using prediction-error filter simulation(PEFs).Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1993.1170~1173
[11]Soubaras R.Spatial interpolation of aliased seismic data.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1997.1167~1190
[12]Thorson J R,Claerbout J F.Velocity-stack and slant stackstochastic inversion.Geophysics,1985,50(12):2727~2741
[13]Kabir MMN,Verschuur D J.Restoration of missing offsets by parabolic Radon transform.Geophysical Prospecting,1995,43:347~368
[14]Ronen J.Wave equation trace interpolation.Geophysics,1987,52(7):973~984
[15]Chemingui N,Biondi B.Handling the irregular geometry in wide-azimuth surveys.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1999.32~35
[16]Pieprzak A W,McClean J W.Trace interpolation of severely aliased events.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1988.658~660
[17]Pieprzak A W,McClean J W.Interpolation of severely ali-ased events.US Patent,1990,4922465
[18]Liu B,Sacchi M.Minimum weighted norminterpolation of seismic data with adaptive weights.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,2001.1921~1924
[19]Wang Y H.Sparseness-constrained least-squares inversion:Application to seismic wave reconstruction.Geophysics,2003,68(5):1633~1638
[20]Trad D Q,Ulrych T J,Sacchi M D.Accurate interpolation with high-resolutiontime-variant Radontransforms.Geophysics,2002,67(4):644~656
[21]DuijndamA,Schonewille M.Nonuniform Fast Fourier Transform.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1997.1135~1138
[22]孟小红,胡朝顺,刘海英等.利用非均匀快速傅里叶变换进行地球物理数据插值.长春科技大学学报,2000,30(增刊):150~153Meng X H,Hu C S,Liu HY,et al.The application of unouniform fast fourier transformtointerpolation of geophysical data.Journal of Changchun UniversityofScience and Technology(in Chinese),2000,30(Suppl.):150~153
[23]李冰,刘洪,李幼铭.三维地震数据离散光滑插值的共轭梯度法.地球物理学报,2002,45(5):691~699Li B,Liu H,Li Y M.3-Dseismic data discrete smoothinterpolation using conjugate gradient.Chinese J.Geophys.(in Chinese),2002,45(5):691~699
[24]刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究.地球物理学报,2004,47(2):299~305Liu X W,Liu H,Liu B.Astudy on algorithmfor preconstruction of de-alias uneven seismic data.Chinese J.Geophys.(in Chinese),2004,47(2):299~305
[25]DuijndamAJ W,Schonewille M A.Nonuniform fast Fourier transform.Geophysics,1999,64(2):539~551
[2]Larner K,Gibson B,Rothman D.Trace interpolation andthe design of seismic surveys.Geophysics,1981,46(4):407~409
[3]Lu L.Application of local slant-stack to trace interpolation.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1985.560~562
[4]King GA.Leong TK,Flinchbaugh B E.The role of interpolationin seismic resolution.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts.1984
[5]Monk D,McBeath R G,Wason C B.Interpolation of aliased seismic traces.US Patent,1993.5235556
[6]Claerbout J,Nichols D.Interpolation beyond aliasing by(t-x)domain in PEFs.53rdAnn.Internat.Mtg.,Eur.Assn.Geosci.Eng.,Expanded Abstracts,1991.1~10
[7]国九英,周兴元,俞寿朋.FX域等道距道内插.石油地球物理勘探,1996,31(1):28~34Guo J Y,Zhou X Y,Yu S P.Iso-interval trace interpolationinF-X domain.Oil Geophysical Prospecting(in Chinese),1996,31(1):28~34.
[8]国九英,周兴元.FK域等道距道内插.石油地球物理勘探,1996,31(2):211~218Guo J Y,Zhou X Y.Iso-interval trace interpolationinF-Kdomain.Oil Geophysical Prospecting(in Chinese),1996,31(2):211~218
[9]Spitz S.Seismic trace interpolation in thef-xdomain.Geophysics,1991,56(6):785~794
[10]Ji J.Interpolation using prediction-error filter simulation(PEFs).Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1993.1170~1173
[11]Soubaras R.Spatial interpolation of aliased seismic data.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1997.1167~1190
[12]Thorson J R,Claerbout J F.Velocity-stack and slant stackstochastic inversion.Geophysics,1985,50(12):2727~2741
[13]Kabir MMN,Verschuur D J.Restoration of missing offsets by parabolic Radon transform.Geophysical Prospecting,1995,43:347~368
[14]Ronen J.Wave equation trace interpolation.Geophysics,1987,52(7):973~984
[15]Chemingui N,Biondi B.Handling the irregular geometry in wide-azimuth surveys.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1999.32~35
[16]Pieprzak A W,McClean J W.Trace interpolation of severely aliased events.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1988.658~660
[17]Pieprzak A W,McClean J W.Interpolation of severely ali-ased events.US Patent,1990,4922465
[18]Liu B,Sacchi M.Minimum weighted norminterpolation of seismic data with adaptive weights.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,2001.1921~1924
[19]Wang Y H.Sparseness-constrained least-squares inversion:Application to seismic wave reconstruction.Geophysics,2003,68(5):1633~1638
[20]Trad D Q,Ulrych T J,Sacchi M D.Accurate interpolation with high-resolutiontime-variant Radontransforms.Geophysics,2002,67(4):644~656
[21]DuijndamA,Schonewille M.Nonuniform Fast Fourier Transform.Soc.Explor.Geophys.Ann.Internat.Mtg.,Expanded Abstracts,1997.1135~1138
[22]孟小红,胡朝顺,刘海英等.利用非均匀快速傅里叶变换进行地球物理数据插值.长春科技大学学报,2000,30(增刊):150~153Meng X H,Hu C S,Liu HY,et al.The application of unouniform fast fourier transformtointerpolation of geophysical data.Journal of Changchun UniversityofScience and Technology(in Chinese),2000,30(Suppl.):150~153
[23]李冰,刘洪,李幼铭.三维地震数据离散光滑插值的共轭梯度法.地球物理学报,2002,45(5):691~699Li B,Liu H,Li Y M.3-Dseismic data discrete smoothinterpolation using conjugate gradient.Chinese J.Geophys.(in Chinese),2002,45(5):691~699
[24]刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究.地球物理学报,2004,47(2):299~305Liu X W,Liu H,Liu B.Astudy on algorithmfor preconstruction of de-alias uneven seismic data.Chinese J.Geophys.(in Chinese),2004,47(2):299~305
[25]DuijndamAJ W,Schonewille M A.Nonuniform fast Fourier transform.Geophysics,1999,64(2):539~551
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