利用MCMC方法估算地震参数
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摘要
本文介绍了用MCMC(马尔可夫链蒙特卡洛)方法估计地震参数的基本原理及应用。首先利用MCMC方法生成马尔可夫链,然后对链进行统计分析,得到未知参数的估计值。在运用Metropolis-Hastings算法生成马尔可夫链时,可随着迭代次数的增加逐渐减小其游走的步长,以确保迭代初期较早收敛到真值附近,迭代后期在真值附近能得到精度较高的估计值。模型试算结果表明:反演结果与理论模型基本吻合,实际资料的应用效果也证明了算法的有效性。
This paper introduces the basic theory and applications of Markov Chain Monte Carlo(MCMC) method for estimating seismic parameters.By making statistical analysis of the chains which are generated by MCMC,the estimates of unknown parameters are obtained.The algorithm for chain generation is Metropolis-Hastings algorithm,and the step length in proposal distribution function decreases as the number of iterations goes up,which ensure the speed to converge at the beginning and the precision of the estimation.The application of both synthetic data and real data shows the MCMC method for elastic parameter estimation is feasibly and effective.
This paper introduces the basic theory and applications of Markov Chain Monte Carlo(MCMC) method for estimating seismic parameters.By making statistical analysis of the chains which are generated by MCMC,the estimates of unknown parameters are obtained.The algorithm for chain generation is Metropolis-Hastings algorithm,and the step length in proposal distribution function decreases as the number of iterations goes up,which ensure the speed to converge at the beginning and the precision of the estimation.The application of both synthetic data and real data shows the MCMC method for elastic parameter estimation is feasibly and effective.
引文
[1]王家映.地球物理资料非线性反演方法讲座(二)蒙特卡洛法.工程地球物理学报,2007,4(2):81~85Wang Jia-ying.Monte Carlo Method.Chinese Jour-nal of Engineering Geophysics,2007,4(2):81~85
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[4]Press F.Earth models obtained by Monte Carlo in-version.J Geophys Res,1968,73(16):5223~5234
[5]Tarantola A.Inverse Problem Theory.New York:Elsevier Sci,1987
[6]Grandis H,Menvielle M and Roussignol M.Bayesianinversion with Markov chains-I the magnetotelluricone-dimensional case.Geophys J Int,1999,138(3):757~768
[7]Malinverno A and Leaney S.A Monte Carlo methodto quantify uncertainty in the inversion of zero-offsetVSP data.SEG Technical Program Expanded Ab-stracts,2000,19:2393~2396
[8]Malinverno A.Parsimonious Bayesian Markov chainMonte Carlo inversion in a nonlinear geophysicalproblem.Geophys J Int,2002,151(3):675~688
[9]Chen Jin-song.Joint inversion of seismic AVO andEM data for gas saturation estimation using a sam-pling-based stochastic model.SEG Technical Pro-gram Expanded Abstracts,2004,23:236~239
[10]Chen Jin-song.A Bayesian model for gas saturationestimation using marine seismic AVA and CSEM da-ta.Geophysics,2007,72(2):85~95
[11]王辉,张玉芬.基于模型的叠前数据多参数非线性反演.岩性油气藏,2008,20(2):108~113Wang Hui,Zhang Yu-fen.Model-based multi-param-eters non-linear inversion method in prestack domain.Lithologic Reservoirs,2008,20(2):108~113
[12]Hong Tian-cong and Mrinal K Sen.A new MCMC al-gorithm for seismic waveform inversion.Geophys JInt,2009,177(1):14~32
[13]赵琪.MCMC方法研究[博士论文].山东济南:山东大学,2007,11~18
[14]Sheldon M Ross著;王兆军等译.统计模拟(第四版).北京:人民邮电出版社,2007:203~206
[15]朱嵩.基于贝叶斯推理的环境水力学反问题研究[博士论文].浙江杭州:浙江大学,2008,63~90
[2]Hammersley J M and Handscomb D C.Monte CarloMethods.New York:Chapman and Hall,1964
[3]Keilis-Borok V I and Yanovskaya T B.Inverse problemsof seismology.Geophys J,1967,13(1~3):223~234
[4]Press F.Earth models obtained by Monte Carlo in-version.J Geophys Res,1968,73(16):5223~5234
[5]Tarantola A.Inverse Problem Theory.New York:Elsevier Sci,1987
[6]Grandis H,Menvielle M and Roussignol M.Bayesianinversion with Markov chains-I the magnetotelluricone-dimensional case.Geophys J Int,1999,138(3):757~768
[7]Malinverno A and Leaney S.A Monte Carlo methodto quantify uncertainty in the inversion of zero-offsetVSP data.SEG Technical Program Expanded Ab-stracts,2000,19:2393~2396
[8]Malinverno A.Parsimonious Bayesian Markov chainMonte Carlo inversion in a nonlinear geophysicalproblem.Geophys J Int,2002,151(3):675~688
[9]Chen Jin-song.Joint inversion of seismic AVO andEM data for gas saturation estimation using a sam-pling-based stochastic model.SEG Technical Pro-gram Expanded Abstracts,2004,23:236~239
[10]Chen Jin-song.A Bayesian model for gas saturationestimation using marine seismic AVA and CSEM da-ta.Geophysics,2007,72(2):85~95
[11]王辉,张玉芬.基于模型的叠前数据多参数非线性反演.岩性油气藏,2008,20(2):108~113Wang Hui,Zhang Yu-fen.Model-based multi-param-eters non-linear inversion method in prestack domain.Lithologic Reservoirs,2008,20(2):108~113
[12]Hong Tian-cong and Mrinal K Sen.A new MCMC al-gorithm for seismic waveform inversion.Geophys JInt,2009,177(1):14~32
[13]赵琪.MCMC方法研究[博士论文].山东济南:山东大学,2007,11~18
[14]Sheldon M Ross著;王兆军等译.统计模拟(第四版).北京:人民邮电出版社,2007:203~206
[15]朱嵩.基于贝叶斯推理的环境水力学反问题研究[博士论文].浙江杭州:浙江大学,2008,63~90
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