基于贝叶斯理论的振幅随偏移距变化三参数同步反演
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摘要
受多种因素的影响,常规叠后地震道波阻抗反演不能得到可靠的波阻抗及其他岩性信息,而叠前波阻抗反演却可以得到比常规叠后波阻抗反演更丰富、更有效的岩性信息。为此建立了振幅随偏移距变化(AVO)波阻抗反演公式的一阶差分模型及褶积模型,推导了基于贝叶斯理论的AVO波阻抗反演公式,给出了采用Huber分布作为模型参数的先验分布及测井数据的参数协方差矩阵作为约束条件的实现方法,并利用共轭梯度法计算了纵、横波阻抗及密度。结果表明,利用该方法可提高叠前反演问题的稳定性和反演结果的可靠性,反演得到的纵、横波阻抗及密度可用来进一步计算流体及孔隙度等信息,为岩性及含油气性解释提供可靠依据。
Routine post-stack seismic trace inversion techniques affected by many factors can not get reliable impedance or other lithologic information.However,more abundant and more effective lithologic information can be obtained from pre-stack data inversion than that obtained from ordinary post-stack impedance inversion.The one order differential model and convolutional model of impedance formula of amplitude versus offset(AVO) inversion were established.Impedance inversion formula from AVO was derived based on Bayesian framework.Methods of using Huber function as prior model parameter distribution and covariance matrix from well log as constrains were developed.The P-wave impedance,S-wave impedance and density were calculated by the conjugate gradient algorithm.The numerical results show that the robustness of noise interference and the reliability of inverted result are improved by the method,and the inverted P-wave impedance,S-wave impedance and density are calculated to obtain more reliable information of fluids and porosity,which can provide reliable foundation for lithologic and oil-bearing interpretation.
Routine post-stack seismic trace inversion techniques affected by many factors can not get reliable impedance or other lithologic information.However,more abundant and more effective lithologic information can be obtained from pre-stack data inversion than that obtained from ordinary post-stack impedance inversion.The one order differential model and convolutional model of impedance formula of amplitude versus offset(AVO) inversion were established.Impedance inversion formula from AVO was derived based on Bayesian framework.Methods of using Huber function as prior model parameter distribution and covariance matrix from well log as constrains were developed.The P-wave impedance,S-wave impedance and density were calculated by the conjugate gradient algorithm.The numerical results show that the robustness of noise interference and the reliability of inverted result are improved by the method,and the inverted P-wave impedance,S-wave impedance and density are calculated to obtain more reliable information of fluids and porosity,which can provide reliable foundation for lithologic and oil-bearing interpretation.
引文
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[3]HAMPSON D,RUSSELL B.Simultaneous inversion ofpre-stack seismic data[C]//75th Annual InternationalMeeting,SEG,Expanded Abstracts,2005:1633-1638.
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[11]SMITHG C,GIDLOW P M.Weighted stacking for rockproperty estimation and detection of gas[J].GeophysicalProspecting,1987,35:993-1014.
[12]CASTAGNA J P,BATZLE ML,EASTWOOD R L.Re-lationships between compressional wave and shear wavevelocities in clastic silicate rocks[J].Geophysics,1985,50:571-581.
[13]GREENBERG ML,CASTAGNAJ P.Shear-wave veloci-ty estimation in porous rocks:theoretical formulation pre-liminary verification and applications[J].GeophysicalProspecing,1992,40:195-210.
[14]GARDNER L W,GREGORY A R.Formation velocityand density——the diagnostic basics for stratigraphictraps[J].Geophysics,1974,39:770-780.
[2]BULAND A,MORE H.Bayesian linearized AVO inver-sion[J].Geophysics,2003,68:185-198.
[3]HAMPSON D,RUSSELL B.Simultaneous inversion ofpre-stack seismic data[C]//75th Annual InternationalMeeting,SEG,Expanded Abstracts,2005:1633-1638.
[4]SIMMONS J L,BACKUS MM.Waveform-based AVO in-version and AVO prediction error[J].Geophysics,1996,61:1575-1588.
[5]HUBER P J.Robust statistical procedures[M].Philadel-phia:SIAM,1977.
[6]GIDLOW P M,SMITHG C,VAIL P J.Hydrocarbon de-tection using fluid factor traces,a case study:how usefulis AVO analysis[C]//Joint SEG/EAEG Summer Re-search Workshop,Technical Program and Abstracts,1992:78-89.
[7]AKI,RICHARDS P G.定量地震学——理论和方法(第一卷)[M].李钦祖,邹其嘉,译.北京:地震出版社,1987:146-168.
[8]DEBSKI W,TARANTOLA A.Information on elastic pa-rameters obtained from the amplitudes of reflected waves[J].Geophysics,1995,60:1426-1436.
[9]傅淑芳,朱仁益.地球物理反演问题[M].北京:地震出版社,1997.
[10]OLDENBURG D W,SCHEUER T,LEVY S.Recoveryof the acoustic impedance from refection seismograms[J].Geophysics,1983,48:1318-1337.
[11]SMITHG C,GIDLOW P M.Weighted stacking for rockproperty estimation and detection of gas[J].GeophysicalProspecting,1987,35:993-1014.
[12]CASTAGNA J P,BATZLE ML,EASTWOOD R L.Re-lationships between compressional wave and shear wavevelocities in clastic silicate rocks[J].Geophysics,1985,50:571-581.
[13]GREENBERG ML,CASTAGNAJ P.Shear-wave veloci-ty estimation in porous rocks:theoretical formulation pre-liminary verification and applications[J].GeophysicalProspecing,1992,40:195-210.
[14]GARDNER L W,GREGORY A R.Formation velocityand density——the diagnostic basics for stratigraphictraps[J].Geophysics,1974,39:770-780.
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