基于三变量柯西分布先验约束的叠前三参数反演方法
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摘要
基于贝叶斯反演理论框架,本文引入褶积算子和Fatti近似正演算子,在对测井数据抽样统计建立协方差矩阵的基础上,采用三变量柯西先验分布对三参数反演过程进行正则化约束,在利用柯西分布长尾巴特征保护弱反射信息的同时考虑了三参数的统计相关特性,提高了反演结果的稳定性,最终通过反演得到了纵横波阻抗和密度三个物性参数。模型试算验证了方法的可行性和优越性,将该方法用于实际叠前地震道集数据,得到了较为准确的弹性参数,取得了很好的应用效果。
According to Bayesian inversion theory and with the help of convolution operator and Fatti approximation forward model operator,we utilize Trivariate Cauchy prior distribution to regularize the three term inversion problem based on covariance matrix by well log sampling statistics.The long tail property of the Cauchy distribution preserves weak reflection information and diminishes the statistical correlation between the three parameters,which makes the inverse problem more stable.Through the inversion process,we finally obtain P impedance,S impedance and density.The model test confirms the practicability and advantage of this method.The application of the method on real prestack seismic gathers shows that the inverted elastic parameters are reliable and results are good.
According to Bayesian inversion theory and with the help of convolution operator and Fatti approximation forward model operator,we utilize Trivariate Cauchy prior distribution to regularize the three term inversion problem based on covariance matrix by well log sampling statistics.The long tail property of the Cauchy distribution preserves weak reflection information and diminishes the statistical correlation between the three parameters,which makes the inverse problem more stable.Through the inversion process,we finally obtain P impedance,S impedance and density.The model test confirms the practicability and advantage of this method.The application of the method on real prestack seismic gathers shows that the inverted elastic parameters are reliable and results are good.
引文
[1]Downton J E.Seismic Parameter Estimation from AVOInversion[D].Calgary:University of Calgary,2005
[2]傅淑芳,朱仁益.地球物理反演问题.北京:地震出版社,1998
[3]Tarantola A.Inverse Problem theory and Methodsfor Model Parameter Estimation.Philadelphia:SI-AM,2005
[4]Smith G C,Gidlow P M.Weighted stacking for rockproperty estimation and detection of gas.GeophysicalProspecting,1987,35(8):993～1014
[5]Ulrych T J,Sacchi M D and Woodbury A.A Bayestour of inversion:A tutorial.Geophysics,2001,66(1):55～69
[6]Buland A,Omre H.Bayesian linearized AVO inver-sion.Geophysics,2003,68(3):185～198
[7]Downton J E,Lines L R.Constrained three parame-ter AVO inversion and uncertainty analysis.SEGTechnical Program Expanded Abstracts,2001,20:251～254
[8]陈建江,印兴耀.基于贝叶斯理论的AVO三参数波形反演.地球物理学报,2007,50(4):1251～1260Chen Jian-jiang,Yin Xing-yao.Three-parameterAVO waveform inversion based on Bayesian theorem.Chinese J Geophys,2007,50(4):1251～1260
[9]杨培杰,印兴耀.非线性二次规划贝叶斯叠前反演.地球物理学报,2008,51(6):1876～1882Yang Pei-jie,Yin Xing-yao.Non-linear quadric pro-gramming Bayesian prestack inversion.Chinese JGeophys,2008,51(6):1876～1882
[10]Wubshet M A.Regularization of the AVO Inver-sion Problem by Means of a Multivariate CauchyProbability Distribution.Alberta:University of Al-berta,2010
[11]Debski W,Tarantola A.Information on elastic pa-rameters obtained from the amplitudes of reflectedwaves.Geophysics,1995,60(5):1426～1436
[12]Fatti J L,Smith G C et al.Detection of gas in sand-stone reservoirs using AVO analysis:A 3-D seismiccase history using the Geostack technique.Geophy-sics,1994,59(9):1362～1376
[13]Castagna J P,Batzle M L,Eastwood R L.Relation-ships between compressional-wave and shear-wave ve-locities in clastic silicate rocks.Geophysics,1985,50(4):571～581
[14]Gardner G H F,Gardner L W and Gregory A R.Formation velocity and density:The diagnostic basicsfor stratigraphic traps.Geophysics,1974,39(6):770～780
[15]Potter C C,Dey A K and Stewart R R.Density pre-diction using P-and S-wave sonic velocities.CREWES Research Report(University of Calgary),1998,10:1～10
[2]傅淑芳,朱仁益.地球物理反演问题.北京:地震出版社,1998
[3]Tarantola A.Inverse Problem theory and Methodsfor Model Parameter Estimation.Philadelphia:SI-AM,2005
[4]Smith G C,Gidlow P M.Weighted stacking for rockproperty estimation and detection of gas.GeophysicalProspecting,1987,35(8):993～1014
[5]Ulrych T J,Sacchi M D and Woodbury A.A Bayestour of inversion:A tutorial.Geophysics,2001,66(1):55～69
[6]Buland A,Omre H.Bayesian linearized AVO inver-sion.Geophysics,2003,68(3):185～198
[7]Downton J E,Lines L R.Constrained three parame-ter AVO inversion and uncertainty analysis.SEGTechnical Program Expanded Abstracts,2001,20:251～254
[8]陈建江,印兴耀.基于贝叶斯理论的AVO三参数波形反演.地球物理学报,2007,50(4):1251～1260Chen Jian-jiang,Yin Xing-yao.Three-parameterAVO waveform inversion based on Bayesian theorem.Chinese J Geophys,2007,50(4):1251～1260
[9]杨培杰,印兴耀.非线性二次规划贝叶斯叠前反演.地球物理学报,2008,51(6):1876～1882Yang Pei-jie,Yin Xing-yao.Non-linear quadric pro-gramming Bayesian prestack inversion.Chinese JGeophys,2008,51(6):1876～1882
[10]Wubshet M A.Regularization of the AVO Inver-sion Problem by Means of a Multivariate CauchyProbability Distribution.Alberta:University of Al-berta,2010
[11]Debski W,Tarantola A.Information on elastic pa-rameters obtained from the amplitudes of reflectedwaves.Geophysics,1995,60(5):1426～1436
[12]Fatti J L,Smith G C et al.Detection of gas in sand-stone reservoirs using AVO analysis:A 3-D seismiccase history using the Geostack technique.Geophy-sics,1994,59(9):1362～1376
[13]Castagna J P,Batzle M L,Eastwood R L.Relation-ships between compressional-wave and shear-wave ve-locities in clastic silicate rocks.Geophysics,1985,50(4):571～581
[14]Gardner G H F,Gardner L W and Gregory A R.Formation velocity and density:The diagnostic basicsfor stratigraphic traps.Geophysics,1974,39(6):770～780
[15]Potter C C,Dey A K and Stewart R R.Density pre-diction using P-and S-wave sonic velocities.CREWES Research Report(University of Calgary),1998,10:1～10
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