高分辨率Radon变换方法及其在地震信号处理中的应用
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摘要
Radon变换方法在地震资料处理中广泛采用,在地震同相轴识别和估计方面具有良好效果.无论是倾斜叠加,还是广义Radon变换方法,一般采用最小二乘反演方法实现.目前,在提高反演算法的效率和分辨率方面仍值得研究.本文从倾斜叠加的定义出发,阐明Radon变换分辨率问题的来源和解决办法.采用最小二乘反演方法研究高分辨率抛物线Radon变换和双曲Radon变换时,给出稀疏约束预条件共轭梯度法求解的高分辨率Radon变换的实现方法,同阻尼最小二乘方法相比,分辨率和精度明显提高,文中给出了模型算例.根据有效波和多次波NMO后剩余时差不同,采用高分辨率抛物线和双曲Radon变换可以压制多次波,分别给出了方法原理,最后给出应用实例.研究表明,稀疏约束预条件共轭梯度法可以有效实现高分辨率Radon变换;数值算例表明,算法计算效率和精度较高,可以更好地实现多次波压制.
Radon transformation is employed commonly in seismic data processing, especially in the events identification and estimation. The least square inversion scheme is the most ordinary method to implement the Radon transform, both for slant stack and for general Radon transform. Although many and many study have been made, there are a lot of works needed doing in enhancing the transform revolution and the computation efficiency. In this paper ,Parabolic Radon Transform (PRT) and Hyperbolic Radon Transform(HRT) have been studied by least square inversion .In the implementation of the methods, sparse constraint preconditions conjugate gradient method has been applied for enhancing the resolution. Compared to the damped least square method, the sparse constraint preconditions conjugate gradient method has advantages. This is proved by a synthetic model. On base of the difference of residual move-out between the primary and the multiple reflections, the multiple could be suppressed by Radon transform. The principals and the schemes of the method are presented in the paper with a real example. It shows that the sparse constraint precondition conjugate gradient method is proper for enhancing the Radon transform resolution , the efficiency and the accuracy are very well, and by the algorithm multiple can be suppressed better.
Radon transformation is employed commonly in seismic data processing, especially in the events identification and estimation. The least square inversion scheme is the most ordinary method to implement the Radon transform, both for slant stack and for general Radon transform. Although many and many study have been made, there are a lot of works needed doing in enhancing the transform revolution and the computation efficiency. In this paper ,Parabolic Radon Transform (PRT) and Hyperbolic Radon Transform(HRT) have been studied by least square inversion .In the implementation of the methods, sparse constraint preconditions conjugate gradient method has been applied for enhancing the resolution. Compared to the damped least square method, the sparse constraint preconditions conjugate gradient method has advantages. This is proved by a synthetic model. On base of the difference of residual move-out between the primary and the multiple reflections, the multiple could be suppressed by Radon transform. The principals and the schemes of the method are presented in the paper with a real example. It shows that the sparse constraint precondition conjugate gradient method is proper for enhancing the Radon transform resolution , the efficiency and the accuracy are very well, and by the algorithm multiple can be suppressed better.
引文
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[2] PhinneyRA,ChowdhuryKR,FrazerLN.Transformationandanalysisofrecordsections[J].J.Geophys.Res.,1981,86(3):359～377.
[3] DurraniTS,BissetD.TheRadontransformanditsproperties[J].Geophysics,1984,49(11):1180～1187.
[4] ChapmanCH.GeneralizedRadontransformsandslantstacks[J].Geophys.J.Roy.Astr.Soc.,1981,54(4):481～518.
[5] ThorsonJR,ClaerboutJF.Velocity-stackandslantstackstochasticinversion[J].Geophysics,1985,50(12):2727～2741.
[6] BeylkinG.Discreteradontransform[J].IEEETrans.Acoust.,Speech,SignalProcessing,1987,35(2):162～172.
[7] KostovC.Toeplitzstructureinslant-stackinversion[A].In:60thAnnualInternat.Mtg.,Soc.Expl.Geophys.,1990,ExpandedAbstracts[C].1618～1621.
[8] FosterJD,MosherCC.SuppressionofmultiplesreflectionusingtheRadontransform[J].Geophysics,1992,57(3),386～395.
[9] ZhouB,GreenhalghSA.Linearandparabolicτ-previsited[J].Geophysics,1994,59(8):1133～1149.
[10] YilmazO,TanerMT.Discreteplane wavedecompositionbyleast meansquare errormethod[J].Geophysics,1994,59(6):973～982.
[11] HampsonD.Inversevelocitystackingformultipleelimination[J].J.Can.Soc.Expl.Geophys.,1986,22(1):44～55.
[12] SacchiMD,UlrychTJ.High-resolutionvelocitygathersandoffsetspacereconstruction[J].Geophysics,1995,60(4):1169～1177.
[13] CaryPW.ThesimplestdiscreteRadontransform[A].In:68thAnnualInternat.Mtg.,Soc.Expl.Geophys.,ExpandedAbstracts[C].1998,1999～2002.
[14] TradDQ,UlrychTJ,SacchiMD.Accurateinterpolationwithhigh resolutiontime variantRadontransforms[J].Geophysics,2002,67(4):644～656.
[15] Weglein,A.B.,Multipleattenuation:anoverviewofrecentadvancesandtheroadahead[J].TheLeadingEdge,1999,18(1):40～44.
[16] HuntL,CaryP,UphamW.AnimprovedRadonTransformforshortperiodmultipleattenuation[A].In:CSEG23rdAnnualMtg.,ExpandedAbstracts[C].1996,58～59.
[17] 牛滨华,孙春岩,张中杰,等.多项式Radon变换[J].地球物理学报,2001,44(2):263～271.
[18] 朱生旺,魏修成,李锋,等.用抛物线Radon变换稀疏解分离和压制多次波[J].石油地球物理勘探,2002,37(2):110～115.
[19] 刘喜武,刘洪,刘彬.反假频非均匀地震数据重建方法研究[J].地球物理学报,2004,47(2):121～127.
[20] 高静怀,陈文超,李幼铭,等.广义S变换与薄互层地震响应分析[J].地球物理学报,2003,46(4):526～532.
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