反假频非均匀地震数据重建方法研究
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摘要
研究基于Fourier变换的数据重建方法 ,既能进行非均匀采样数据重建 ,又可以去除空间假频 .将不规则采样数据重建问题归结为信息重建的地球物理反演问题 ,采用最小二乘方法从观测的稀疏或不规则数据反演模型空间完全信息 .在求解信息重建反演问题时 ,引入DFT 加权范数规则化策略 ,采用预条件共轭梯度法 (PCG)求解 ,保证解的稳定性和收敛速度 .处理线性同相轴假频问题时 ,根据采样定理 ,引入线性预测方法 ,采用Yule Walker方程由带限信号的无假频低频功率谱预测高频功率谱 ,达到反假频目的 .本文研究了均匀采样数据内插 ,非均匀采样数据重建 ,非均匀分布高频信息重建等方面问题 ,数值试验取得较好效果 .
Spacial trace interpolation is one of the most important issues in seismic data processing. In this paper, a novel Fourier transform based algorithm is proposed, which can reconstruct both uneven and alias seismic data. We formulate band-limited data reconstruction as a minimum norm least squares (LS) type problem where an adaptive DFT-weighted norm regularization term is used. The inverse problem is solved by the pre-conditional conjugate gradient method, which makes the solutions stable and convergence quick. Based on the assumption that seismic data are consisted of finite linear events, and from sampling theorem, alias events can be attenuated via LS weight predicted linearly from low frequency. Three application issues are discussed on even gap trace interpolation, uneven gap filling, and high frequency trace reconstruction from low frequency data trace constrained by few high frequency traces. Both synthetic and real data numerical examples show the proposed method is valid, efficient and applicable.
Spacial trace interpolation is one of the most important issues in seismic data processing. In this paper, a novel Fourier transform based algorithm is proposed, which can reconstruct both uneven and alias seismic data. We formulate band-limited data reconstruction as a minimum norm least squares (LS) type problem where an adaptive DFT-weighted norm regularization term is used. The inverse problem is solved by the pre-conditional conjugate gradient method, which makes the solutions stable and convergence quick. Based on the assumption that seismic data are consisted of finite linear events, and from sampling theorem, alias events can be attenuated via LS weight predicted linearly from low frequency. Three application issues are discussed on even gap trace interpolation, uneven gap filling, and high frequency trace reconstruction from low frequency data trace constrained by few high frequency traces. Both synthetic and real data numerical examples show the proposed method is valid, efficient and applicable.
引文
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[19] LiuB ,SacchiMD .MinimumDFT weightednorminterpolationofseismicdatausingFFT .CSEGGeophysicsExpandedAbstract,2002.118～123
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[23] 国九英,周兴元,俞寿朋.f k域等道距道内插.石油地球物理勘探,1996,32(2):211～218GuoJY ,ZhouXY ,YuSP .Seismictraceinterpolationwithequalspaceinthef kdomain.OilGeophysicalProspecting(inChinese),1996,32(2):211～218
[24] 王建立,郭树祥,杨长春等.广义谱分解地震道内插方法.石油地球物理勘探,2002,37(1):29～32WangJL ,GuoSX ,YangCC ,etal.Seismictraceinterpolationwithgeneralizedspectraldecomposition.OilGeophysicalProspecting(inChinese),2002,37(1):29～32
[2] LarnerK ,GibsonB ,RothmanD .Traceinterpolationandthedesignofseismicsurveys.Geophysics,1981,46(4):407～409
[3] LuL .Applicationoflocalslant stacktotraceinterpolation.55thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstracts,1985.560～562
[4] KingGA ,LeongTK ,FlinchbaughBE .Theroleofinterpolationinseismicresolution.54thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstracts,1984.766～767
[5] SchonewilleMA ,DuijndamAJW .DecompositionofsignalandnoiseforsparselysampleddatausingamixedFourierRadontransform.66thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstract,1996.1438～1441
[6] SpitzS .Traceinterpolationbeyondaliasingandwithoutpicking.59thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstracts,1989.1121～1122
[7] SpitzS .Seismictraceinterpolationinthef xdomain.Geophysics,1991,56(6):785～794
[8] JiJ.Interpolationusingprediction errorfiltersimulation(PEFs).63rdAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAb stracts,1993.1170～1173
[9] ManinM ,SpitzS .Wavefieldde aliasingforacquisitionconfigurationsleadingtocoarsesampling.65thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstracts,1995.930～932
[10] PorsaniJM .Seismictraceinterpolationusinghalf steppredictionfil ters.Geophysics,1999,64(5):1461～1467
[11] SoubarasR .Spatialinterpolationofaliasedseismicdata.67thAnn.Internat.Mtg.,Soc.Exp.Geophys.ExpandedAbstracts,1997.1167～1190
[12] ClaerboutJ ,NicholsD .Interpolationbeyondaliasingby(t x)doma inPEFs.53rdAnn.Internat.Mtg.,Eur.Assn.Geosci.Eng.Ex pandedAbstracts,1991.1～10
[13] PieprzakAW ,McCleanJW .Traceinterpolationofseverelyaliasedevents.58thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstracts,1988.658～660
[14] GuoJ,ZhouX ,YangH .Efficientf kdomainseismictraceinterpo lationforspatiallyaliaseddata.66thAnn.Internat.Mtg.,Soc.Ex pl.Geophys.ExpandedAbstracts,1996.1457～1460
[15] G櫣l櫣nayN,ChambersRE .Un aliasedf kdomaintraceinterpolation(UFKI).66thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstracts,1996.1461～1464
[16] G櫣l櫣nayN,ChambersRE .Generalizedf kdomaintraceinterpola tion.67thAnn.Internat.Mtg.,Soc.Expl.Geophys.ExpandedAbstracts,1997.1100～1103
[17] RonenJ .Waveequationtraceinterpolation.Geophysics,1987,52(7):973～984
[18] DuijndamAJW ,SchonewilleM ,HindriksK .Reconstructionofseismicsignals,irregularlysampledalongonspatialcoordinate.Geo physics,1999,64(2):524～538
[19] LiuB ,SacchiMD .MinimumDFT weightednorminterpolationofseismicdatausingFFT .CSEGGeophysicsExpandedAbstract,2002.118～123
[20] 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):691～699LiB ,LiuH ,LiYM .ConjugategradientalgorithmforDSIto3Dseismicdata.ChineseJ .Geophys.(inChinese),2002,45(5):691～699
[21] CabreraSD ,ThomasWP .Extrapolationandspectrumestimationwithiterativeweightednormmodification.IEEETrans.SignalPro cessing,1991,39(4):842～850
[22] 国九英,周兴元,俞寿朋.f x域等道距道内插.石油地球物理勘探,1996,32(1):28～34GuoJY ,ZhouXY ,YuSP .Seismictraceinterpolationwithequalspaceinthef xdomain.OilGeophysicalProspecting(inChinese),1996,32(1):28～34
[23] 国九英,周兴元,俞寿朋.f k域等道距道内插.石油地球物理勘探,1996,32(2):211～218GuoJY ,ZhouXY ,YuSP .Seismictraceinterpolationwithequalspaceinthef kdomain.OilGeophysicalProspecting(inChinese),1996,32(2):211～218
[24] 王建立,郭树祥,杨长春等.广义谱分解地震道内插方法.石油地球物理勘探,2002,37(1):29～32WangJL ,GuoSX ,YangCC ,etal.Seismictraceinterpolationwithgeneralizedspectraldecomposition.OilGeophysicalProspecting(inChinese),2002,37(1):29～32
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