AVO反演的不确定性分析
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摘要
叠前地震数据反演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,但叠前数据体的噪声及其它因素严重影响了AVO反演的稳定性,如何评估AVO反演结果的可靠性显得尤为重要.本文从贝叶斯理论出发,假定均匀先验分布、高斯噪音分布,推出不确定性分析方程,利用协方差矩阵中的方差描述反演问题的不确定性,模型研究显示反演不确定性与叠前信噪比、纵横波速度比、覆盖次数及反演采用的角度范围相关,方法预测的反演误差可定量解释反演结果的可靠性,为解释人员提供有效的质量监控手段.
More abundant and effective lithologic information can be obtained from inversion of pre-stack data in comparison with from ordinary post-stack impedance inversion.The noise and other factors of pre-stack data can heavily influence the stability of the inversion problem.So it is very important to predict the reliability of AVO estimates.Based on Bayesian theorem,it is initially assumed that the prior probability distributions are uniform and the noise is independent and Gaussian.In this case,the uncertainty analysis equation can be obtained.The variance in parameter covariance matrix can be used to investigate the uncertainty in the problem.The modeling studys show that the uncertainty of AVO inversion is a function of the prestack noise,the ratio of the P-to S-wave velocity,the fold and the range of angle available for inversion.The predicted errors by the method give interpreters tools to help quantify the reliability of their AVO interpretation.
More abundant and effective lithologic information can be obtained from inversion of pre-stack data in comparison with from ordinary post-stack impedance inversion.The noise and other factors of pre-stack data can heavily influence the stability of the inversion problem.So it is very important to predict the reliability of AVO estimates.Based on Bayesian theorem,it is initially assumed that the prior probability distributions are uniform and the noise is independent and Gaussian.In this case,the uncertainty analysis equation can be obtained.The variance in parameter covariance matrix can be used to investigate the uncertainty in the problem.The modeling studys show that the uncertainty of AVO inversion is a function of the prestack noise,the ratio of the P-to S-wave velocity,the fold and the range of angle available for inversion.The predicted errors by the method give interpreters tools to help quantify the reliability of their AVO interpretation.
引文
[1] Tarantola A.Inverse problem theory,methods for data fitting and model parameter estimation[M].Elsevier Science Publishers,1987．
[2] 彭真明,李亚林,魏文阁,等.粒子滤波非线性AVO反演方法[J].地球物理学报,2008,51(4) :1218-1225． Peng Z M,Li Y L,Wei W G,etal.Nonlinear AVO inversion using particle filter[J].Chinese J.Geophys.(in Chinese),2008,51(4) :1218-1225．
[3] 杨迪琨,胡祥云.含噪声数据反演的概率描述[J].地球物理学报,2008 ,51 (3) :901-907． Yang D K,Hu X Y.Inversion of noisy data by probilistic methodology[J].Chinese J.Geophys.(in Chinese),2008,51(3) :901-907．
[4] Riedel M,Dosso S E,Beran L.Uncertainty estimation for amplitude variation with offset(AVO)inversion[J].Geophysics,2003,68:1485-1496．
[5] Houck R T.Quantifying the uncertainty in an AVO interpretation[J].Geophysics,2002,67:117-125．
[6] Loures L,Moraes F.Reservoir porosity inference[J].72nd Ann Internat Mtg Soc of Expl Geophys,2002,1809-1812．
[7] Shuey R T.A simplification of the Zoeppritz equations[J].Geophysics,1985,50:609-614．
[8] Gidlow P M,Smith G C,Vail P J.Hydrocarbon detection using fluid factor traces,a case study:How useful is AVO analysis[J].Joint SEG/EAEG summer research workshop,Technical Program and Abstracts,1992,78-89．
[9] Smith G C,Gidlow P M.Weighted stacking for rock property estimation and detection of gas[J].Geophysical Prospecting,1987,35:993-1014．
[10] Gardner L W,Gregory A R.Formation velocity and density-The diagnostic basics for stratigraphic traps[J].Geophysics,1974,39:770-780．
[11] Aki K I,Richards P G.Quantitative seismology:theory and methods[J].W H Freeman and Co Cambridge,1980:144-154．
[12] Downton J,Lines L.Constrained three parameter AVO inversion and uncertainty analysis[J].71st Ann Internat Mtg Soc of Expl Geophys,2001,251-254．
[13] Sivia D S.DataAnalysis:A Bayesian tutorial[M].Oxford University Press,1996．
[2] 彭真明,李亚林,魏文阁,等.粒子滤波非线性AVO反演方法[J].地球物理学报,2008,51(4) :1218-1225． Peng Z M,Li Y L,Wei W G,etal.Nonlinear AVO inversion using particle filter[J].Chinese J.Geophys.(in Chinese),2008,51(4) :1218-1225．
[3] 杨迪琨,胡祥云.含噪声数据反演的概率描述[J].地球物理学报,2008 ,51 (3) :901-907． Yang D K,Hu X Y.Inversion of noisy data by probilistic methodology[J].Chinese J.Geophys.(in Chinese),2008,51(3) :901-907．
[4] Riedel M,Dosso S E,Beran L.Uncertainty estimation for amplitude variation with offset(AVO)inversion[J].Geophysics,2003,68:1485-1496．
[5] Houck R T.Quantifying the uncertainty in an AVO interpretation[J].Geophysics,2002,67:117-125．
[6] Loures L,Moraes F.Reservoir porosity inference[J].72nd Ann Internat Mtg Soc of Expl Geophys,2002,1809-1812．
[7] Shuey R T.A simplification of the Zoeppritz equations[J].Geophysics,1985,50:609-614．
[8] Gidlow P M,Smith G C,Vail P J.Hydrocarbon detection using fluid factor traces,a case study:How useful is AVO analysis[J].Joint SEG/EAEG summer research workshop,Technical Program and Abstracts,1992,78-89．
[9] Smith G C,Gidlow P M.Weighted stacking for rock property estimation and detection of gas[J].Geophysical Prospecting,1987,35:993-1014．
[10] Gardner L W,Gregory A R.Formation velocity and density-The diagnostic basics for stratigraphic traps[J].Geophysics,1974,39:770-780．
[11] Aki K I,Richards P G.Quantitative seismology:theory and methods[J].W H Freeman and Co Cambridge,1980:144-154．
[12] Downton J,Lines L.Constrained three parameter AVO inversion and uncertainty analysis[J].71st Ann Internat Mtg Soc of Expl Geophys,2001,251-254．
[13] Sivia D S.DataAnalysis:A Bayesian tutorial[M].Oxford University Press,1996．
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