等间距地震道插值的傅里叶重建法
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摘要
地震采集过程中经常会碰到的大空间采样、坏道和数据分布不规则等问题,影响了地震处理及成像效果。针对上述问题,提出了一种改进插值方法,即扩大原来的空间距离长度,使空间波数采样变密,然后根据似二维F-K频谱图里取中间某一范围的频谱值,就可以去掉噪声和假频,振幅也可得到很好加强。理论和实际地震数据测试结果验证了修改后的方法插值效果好。
The problems of large spatial sampling,dead traces and irregular sampling often happen in seismic acquisition,which are suboptimal to process seismic data and obtain imaging results.Therefore,an improved interpolation method was proposed.Extending original length of spatial distance,thickening spatial and wavenumber sampling and taking out certain spectra by similar 2D F-K spectra can eliminate noise and alias,and also enhance the amplitude.The tests of synthetic models and real seismic data prove that good interpolation results can be obtained by the improved method.
The problems of large spatial sampling,dead traces and irregular sampling often happen in seismic acquisition,which are suboptimal to process seismic data and obtain imaging results.Therefore,an improved interpolation method was proposed.Extending original length of spatial distance,thickening spatial and wavenumber sampling and taking out certain spectra by similar 2D F-K spectra can eliminate noise and alias,and also enhance the amplitude.The tests of synthetic models and real seismic data prove that good interpolation results can be obtained by the improved method.
引文
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[4]TRAD D,ULRYCHT,SACCHI M.Latest views of thesparse radon transform[J].Geophysics,2003,68:386-399.
[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,2000,22:211-215.ZHOU Zhu-sheng,LU Jiang-nan.A fast and effectiveseismic trace interpolation method[J].Computing Techni-ques for Geophysical and Geochemical Exploration,2000,122(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 Jian-li,GUO Shu-xiang,YANG Chang-chun,etal.Seismic trace interpolation with generalized spectraldecomposition[J].Oil Geophysical Prospecting,2002,37(1):29-32.
[7]HINDRIKS K,DUIJNDAMA J W.Reconstruction of 3Dseismic signals irregularly sampled along two spatial coor-dinates[J].Geophysics,2000,65:253-263.
[8]ZWARTJES P M,GISOLF A.Fourier reconstruction withsparse inversion[J].Geophysical Prospecting,2007,55:199-221.
[9]ZWARTJES P M,DUIJNDAMA J W.Optimizing Recon-struction for Sparse Spatial Sampling[C/OL].70th AnnInternat Mtg,Soc Expl Geophys,2000 Technical ProgramExpanded Abstracts,Calgary,Canada,January,2000[2007-05-12].http://segdl.aip.org/dbt/SGA002162.pdf.
[10]ZWARTJES P M,SACCHI MD.Fourier reconstruction ofnon-uniformly sampled,aliased data[C/OL].74th AnnInternat Mtg,Soc Expl Geophys,2004 Technical ProgramExpanded Abstracts,Denver,USA,January,2004[2007-05-12].http://segdt.aip.org/dbt/SGA001997.pdf.
[11]SACCHI M D,ULRYCHTJ.Estimation of the discreteFourier transform:a linear inversion approach[J].Geo-physics,1996,61:1128-1136.
[12]FEICHTINGER H,GR CHENIG K,STROHMER T.Efficient numerical methods in non-uniform samplingtheory[J].Numerische Mathematik,1995,69:423-440.
[13]DUTTA,ROKHLIN V.Fast Fourier transforms for non-equispaced data[J].SIAMJ Sci Comput,1993,14:1368-1393.
[14]BEYLKIN G.On the fast Fourier transform of functionswith singularities[J].Applied and Computational Har-monic Analysis,1995,2:363-381.
[15]DUIJNDAM A J W,SCHONEWILLE M A.Non-uni-form fast Fourier transform[J].Geophysics,1999,64:539-551.
[16]AMUNDSEN L.Comparison of the least-squares criteri-on and the Cauchy criterion in frequency-wavenumberinversion[J].Geophysics,1991,56:2027-2035.
[17]HABER E.Numerical strategies for the solution of in-verse problems[D].Columbia:University of BritishColumbia,1997.
[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,2006,41:281-285.ZHANG Hong-mei,LIU Hong.Interpolation of poststackseismic traces based on sparse discreteτ-p transform[J].Oil Geophysical Prospecting,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.L Xiao-wei,CHEN Xiao-hong,DIAO Shun.Seismictrace interpolation by using L1 norm to calculate time-difference between traces[J].Oil Geophysical Prospec-ting,2003,38(6):618-622.
[4]TRAD D,ULRYCHT,SACCHI M.Latest views of thesparse radon transform[J].Geophysics,2003,68:386-399.
[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,2000,22:211-215.ZHOU Zhu-sheng,LU Jiang-nan.A fast and effectiveseismic trace interpolation method[J].Computing Techni-ques for Geophysical and Geochemical Exploration,2000,122(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 Jian-li,GUO Shu-xiang,YANG Chang-chun,etal.Seismic trace interpolation with generalized spectraldecomposition[J].Oil Geophysical Prospecting,2002,37(1):29-32.
[7]HINDRIKS K,DUIJNDAMA J W.Reconstruction of 3Dseismic signals irregularly sampled along two spatial coor-dinates[J].Geophysics,2000,65:253-263.
[8]ZWARTJES P M,GISOLF A.Fourier reconstruction withsparse inversion[J].Geophysical Prospecting,2007,55:199-221.
[9]ZWARTJES P M,DUIJNDAMA J W.Optimizing Recon-struction for Sparse Spatial Sampling[C/OL].70th AnnInternat Mtg,Soc Expl Geophys,2000 Technical ProgramExpanded Abstracts,Calgary,Canada,January,2000[2007-05-12].http://segdl.aip.org/dbt/SGA002162.pdf.
[10]ZWARTJES P M,SACCHI MD.Fourier reconstruction ofnon-uniformly sampled,aliased data[C/OL].74th AnnInternat Mtg,Soc Expl Geophys,2004 Technical ProgramExpanded Abstracts,Denver,USA,January,2004[2007-05-12].http://segdt.aip.org/dbt/SGA001997.pdf.
[11]SACCHI M D,ULRYCHTJ.Estimation of the discreteFourier transform:a linear inversion approach[J].Geo-physics,1996,61:1128-1136.
[12]FEICHTINGER H,GR CHENIG K,STROHMER T.Efficient numerical methods in non-uniform samplingtheory[J].Numerische Mathematik,1995,69:423-440.
[13]DUTTA,ROKHLIN V.Fast Fourier transforms for non-equispaced data[J].SIAMJ Sci Comput,1993,14:1368-1393.
[14]BEYLKIN G.On the fast Fourier transform of functionswith singularities[J].Applied and Computational Har-monic Analysis,1995,2:363-381.
[15]DUIJNDAM A J W,SCHONEWILLE M A.Non-uni-form fast Fourier transform[J].Geophysics,1999,64:539-551.
[16]AMUNDSEN L.Comparison of the least-squares criteri-on and the Cauchy criterion in frequency-wavenumberinversion[J].Geophysics,1991,56:2027-2035.
[17]HABER E.Numerical strategies for the solution of in-verse problems[D].Columbia:University of BritishColumbia,1997.
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