一种有效的地震道插值方法
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摘要
地震处理中重要的环节之一是地震道插值技术.野外采集过程中常会碰到大空间采样、坏道和数据分布不规则等问题.为满足地震数据处理精度要求,需进行地震道插值,提高成像效果.本文针对Zwartjes的基于非二次模型权函数稀疏反演傅里叶插值(FRSI)法存在的问题,如不规则地震道插值时不能去掉产生的噪声、假频及插值道振幅弱,等距道插值时不能准确插值,效果差,提出了改进方法,即扩大原有距离,使波数采样变密,依据似二维f-k频谱图,取中间某一范围频谱值,去除假频和噪声,以提高振幅能量.理论与实际测试验证了修改后的方法插值效果更好.
One of the important links in seismic processes is seismic trace interpolation technique.There are many problems often happened in seismic acquisition such as large spatial sampling,dead traces and irregular sampling etc.To meet accuracy requirements of seismic data processing,it need be interpolated to improve imaging results.Zwartjes etc present a method of Fourier reconstruction with sparse inversion(FRSI) based on non-quadratic model weight function,which cannot remove alias and noise and improve weakly the amplitude of interpolated traces with unequal group interval data,and cannot interpolate correctly seismic traces with equal group interval data.Therefore,the paper proposes an improved method.Extending original length,thickening spatial and wavenumber sampling and taking out certain spectra by similar f-k spectra can eliminate alias and noise and enhance the amplitude energy.Tests of synthetic models and real seismic data proved that the modified method interpolated better.
One of the important links in seismic processes is seismic trace interpolation technique.There are many problems often happened in seismic acquisition such as large spatial sampling,dead traces and irregular sampling etc.To meet accuracy requirements of seismic data processing,it need be interpolated to improve imaging results.Zwartjes etc present a method of Fourier reconstruction with sparse inversion(FRSI) based on non-quadratic model weight function,which cannot remove alias and noise and improve weakly the amplitude of interpolated traces with unequal group interval data,and cannot interpolate correctly seismic traces with equal group interval data.Therefore,the paper proposes an improved method.Extending original length,thickening spatial and wavenumber sampling and taking out certain spectra by similar f-k spectra can eliminate alias and noise and enhance the amplitude energy.Tests of synthetic models and real seismic data proved that the modified method interpolated better.
引文
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[2]张红梅,刘洪.基于稀疏离散τ-p变换的叠后地震道内插[J].石油地球物理勘探,2006,41(3):281-285.Zhang H M,Liu H.Interpolation of poststack seismic tracesbased on sparse discreteτ-p transform[J].Oil GeophysicalProspecting(in Chinese),2006,41(3):281-285.
[3]吕小伟,陈小宏,刁顺.利用L1范数求取道间时差技术进行地震道插值[J].石油地球物理勘探,2003,38(6):618-622.Lv X W,Chen X H,Diao S.Seismic trace interpolation byusing L1norm to calculate time-difference between traces[J].Oil Geophysical Prospecting(in Chinese),2003,38(6):618-622.
[4]Larner K,Gibson B,Rothman D.Trace interpolation and thedesign of seismic survey[J].Geophysics,1981,46(4):407-409.
[5]周竹生,陆江南.一种快速有效的地震道空间内插方法[J].物探化探计算技术,2000,22(3):211-215.Zhou Z S,Lu J N.A fast and effective seismic traceinterpolation method[J].Computing Techniques forGeophysical and Geochemical Exploration(in Chinese),2000,22(3):211-215.
[6]王建立,郭树祥,杨长春,等.广义谱分解地震道内插方法[J].石油地球物理勘探,2002,37(1):29-38.Wang J L,Guo S X,Yang C C,et al.Seismic traceinterpolation with generalized spectral decomposition[J].OilGeophysical Prospecting(in Chinese),2002,37(1):29-38.
[7]Trad D,Ulrych T,Sacchi M.Latest views of the sparse Radontransform[J].Geophysics,2003,68:386-399.
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[11]Hindriks K.Duijndam A.J.W.Reconstruction of 3Dseismicsignals irregularly sampled along two spatial coordinates[J].Geophysics,2000,65:253-263.
[12]Zwartjes P,Gisolf A.Fourier reconstruction with sparse inversion[J].Geophysical Prospecting,2007,55(2):199-221.
[13]Zwartjes P M,Duijndam A J W.Optimizing Reconstructionfor sparse spatial sampling[C].//70th Ann.Internat.Mtg.,Soc.Expl.Geophys.,2000,2162-2165.
[14]Zwartjes P M,Sacchi M D.Fourier reconstruction of non-uniformly sampled,aliased data[C].//74th AnnualInternational Meeting,Soc.Expl.Geophys.,2004.
[15]Sacchi M D,Ulrych T J.Estimation of the discrete Fouriertransform:a linear inversion approach[J].Geophysics,1996,61(4):1128-1136.
[16]Feichtinger H G,Gr?chenig K H,Strohmer T.Efficientnumerical methods in non-uniform sampling theory[J].Numerische Mathematik,1995,69:423-440.
[17]Beylkin G.On the fast Fourier transform of functions withsingularities[J].Appl.Comp.Harm.Anal.,1995,2(4):363-381.
[18]Dutt A,Rokhlin V.Fast Fourier transforms for nonequispaceddata[J].SIAM Journal on Scientific Computing,1993,14(6):1368-1393.
[19]高建军,陈小宏,王芳芳,等.不规则地震道数据规则化重建方法研究[J].地球物理学进展,2011,26(3):983-991.Gao J J,Chen X H,Wang F F,et al.Study on regularizedreconstruction of uneven seismic traces[J].Progress inGeophysics(in Chinese),2011,26(3):983-991.
[20]李雪聪,刘伊克,常旭,等.基于F-K偏移和反偏移的地震道插值方法研究[J].地球物理学进展,2009,24(6):2020-2029.Li X C,Liu Y K,Chang X,et al.Interpolation for seismictraces based on F-K migration and demigration[J].Progressin Geophysics(in Chinese).2009,24(6):2020-2029.
[21]王立明,刘保华,王揆洋,等.间距地震道插值的傅立叶重建法[J].中国石油大学学报(自然科学版),2008,32(6):51-56.Wang L M,Liu B H,Wang K Y.Interpolating equal groupinterval seismic traces by Fourier reconstruction[J].Journalof China University of Petroleum(Edition of Natural Science)(in Chinese),2008,32(6):51-56.
[2]张红梅,刘洪.基于稀疏离散τ-p变换的叠后地震道内插[J].石油地球物理勘探,2006,41(3):281-285.Zhang H M,Liu H.Interpolation of poststack seismic tracesbased on sparse discreteτ-p transform[J].Oil GeophysicalProspecting(in Chinese),2006,41(3):281-285.
[3]吕小伟,陈小宏,刁顺.利用L1范数求取道间时差技术进行地震道插值[J].石油地球物理勘探,2003,38(6):618-622.Lv X W,Chen X H,Diao S.Seismic trace interpolation byusing L1norm to calculate time-difference between traces[J].Oil Geophysical Prospecting(in Chinese),2003,38(6):618-622.
[4]Larner K,Gibson B,Rothman D.Trace interpolation and thedesign of seismic survey[J].Geophysics,1981,46(4):407-409.
[5]周竹生,陆江南.一种快速有效的地震道空间内插方法[J].物探化探计算技术,2000,22(3):211-215.Zhou Z S,Lu J N.A fast and effective seismic traceinterpolation method[J].Computing Techniques forGeophysical and Geochemical Exploration(in Chinese),2000,22(3):211-215.
[6]王建立,郭树祥,杨长春,等.广义谱分解地震道内插方法[J].石油地球物理勘探,2002,37(1):29-38.Wang J L,Guo S X,Yang C C,et al.Seismic traceinterpolation with generalized spectral decomposition[J].OilGeophysical Prospecting(in Chinese),2002,37(1):29-38.
[7]Trad D,Ulrych T,Sacchi M.Latest views of the sparse Radontransform[J].Geophysics,2003,68:386-399.
[8]Amundsen L.Comparison of the least-squares criterion andthe Cauchy criterion in frequency-wavenumber inversion[J].Geophysics,1991,56(12):2027-2035.
[9]Duijndam A J W,Schonewille M A.Non-uniform fast Fouriertransform[J].Geophysics,1999,64:539-551.
[10]Duijndam A J W,Schonewille M A,Hindriks C O H.Reconstruction of band-limited signals,irregularly sampledalong one spatial direction[J].Geophysics,1999,64(2):524-538.
[11]Hindriks K.Duijndam A.J.W.Reconstruction of 3Dseismicsignals irregularly sampled along two spatial coordinates[J].Geophysics,2000,65:253-263.
[12]Zwartjes P,Gisolf A.Fourier reconstruction with sparse inversion[J].Geophysical Prospecting,2007,55(2):199-221.
[13]Zwartjes P M,Duijndam A J W.Optimizing Reconstructionfor sparse spatial sampling[C].//70th Ann.Internat.Mtg.,Soc.Expl.Geophys.,2000,2162-2165.
[14]Zwartjes P M,Sacchi M D.Fourier reconstruction of non-uniformly sampled,aliased data[C].//74th AnnualInternational Meeting,Soc.Expl.Geophys.,2004.
[15]Sacchi M D,Ulrych T J.Estimation of the discrete Fouriertransform:a linear inversion approach[J].Geophysics,1996,61(4):1128-1136.
[16]Feichtinger H G,Gr?chenig K H,Strohmer T.Efficientnumerical methods in non-uniform sampling theory[J].Numerische Mathematik,1995,69:423-440.
[17]Beylkin G.On the fast Fourier transform of functions withsingularities[J].Appl.Comp.Harm.Anal.,1995,2(4):363-381.
[18]Dutt A,Rokhlin V.Fast Fourier transforms for nonequispaceddata[J].SIAM Journal on Scientific Computing,1993,14(6):1368-1393.
[19]高建军,陈小宏,王芳芳,等.不规则地震道数据规则化重建方法研究[J].地球物理学进展,2011,26(3):983-991.Gao J J,Chen X H,Wang F F,et al.Study on regularizedreconstruction of uneven seismic traces[J].Progress inGeophysics(in Chinese),2011,26(3):983-991.
[20]李雪聪,刘伊克,常旭,等.基于F-K偏移和反偏移的地震道插值方法研究[J].地球物理学进展,2009,24(6):2020-2029.Li X C,Liu Y K,Chang X,et al.Interpolation for seismictraces based on F-K migration and demigration[J].Progressin Geophysics(in Chinese).2009,24(6):2020-2029.
[21]王立明,刘保华,王揆洋,等.间距地震道插值的傅立叶重建法[J].中国石油大学学报(自然科学版),2008,32(6):51-56.Wang L M,Liu B H,Wang K Y.Interpolating equal groupinterval seismic traces by Fourier reconstruction[J].Journalof China University of Petroleum(Edition of Natural Science)(in Chinese),2008,32(6):51-56.
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