基于MCMC的叠前地震反演方法研究
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摘要
马尔科夫链蒙特卡洛方法(MCMC)是一种启发式的全局寻优算法.它在贝叶斯框架下,利用已有资料进行约束,既可使最优解满足参数的统计特性,又通过融入的先验信息,提高解的精度;寻优过程可跳出局部最优,得到全局最优解.利用MCMC方法,可以得到大量来自于后验概率分布的样本,不仅可以得到每个未知参数的估计值,而且可以得到与之相关的各种不确定性信息.此外,由于算法并不是利用有单一最优解的目标函数,所以结果对初始值的依赖不强.通过对简单一维层状介质模型的处理,和实际资料的应用,说明利用基于Metropolis-Hastings算法的MCMC方法进行地震反演,通过对解空间的随机搜索能够得到较好的效果.
Markov Chain Monte Carlo method is a heuristic global optimization method.In the Bayesian framework,the optimal solution meets the statistical properties of the parameters with the constraints of data(eg.seismic data,well log);the accuracy of solution is improved with the prior information joined in;optimization process can jump out of local optimum,and ultimately obtain the global optimal solution.Using MCMC methods,we draw a large number of samples from the posterior distribution function.With these samples,we obtain not only the estimates of each unknown variable,but also various types of uncertainty information associated with the estimation.In addition,because of not making use of a objective functions with single optimal solution,the results obtained with MCMC method are independent of the choice of initial values. By testing a 1D layered model and the application of real seismic data in South China,shows the MCMC method based on Metropolis-Hastings algorithm is available and can obtain good results by random searching solution space.
Markov Chain Monte Carlo method is a heuristic global optimization method.In the Bayesian framework,the optimal solution meets the statistical properties of the parameters with the constraints of data(eg.seismic data,well log);the accuracy of solution is improved with the prior information joined in;optimization process can jump out of local optimum,and ultimately obtain the global optimal solution.Using MCMC methods,we draw a large number of samples from the posterior distribution function.With these samples,we obtain not only the estimates of each unknown variable,but also various types of uncertainty information associated with the estimation.In addition,because of not making use of a objective functions with single optimal solution,the results obtained with MCMC method are independent of the choice of initial values. By testing a 1D layered model and the application of real seismic data in South China,shows the MCMC method based on Metropolis-Hastings algorithm is available and can obtain good results by random searching solution space.
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):81-85 Wang J Y.Monte Carlo Method.Chinese Journal of Engineering Geophysics(in Chinese),2007,4(2):81-85
[2]杨培杰,印兴耀.基于支持向量机的叠前地震反演方法.中国石油大学学报(自然科学版),2008,32(1):37-41 Yang P J,Yin X Y.Prestack seismic inversion method based on support vector machine.Journal of the University of China University of Petroleum(Edition of Natural Science) (in Chinese),2008,32(1):37-41
[3]殷八斤,曾灏,杨在岩.AVO技术的理论与实践.北京:石油工业出版社,1995
[4]陈天胜,刘洋,魏修成.纵波和转换波联合AVO反演方法研究.中国石油大学学报(自然科学版),2006,30(1):33-37 Chen T S,Liu Y,Wei X C.Joint amplitude versus offset inversion of P-P and P-SV seismic data.Journal of China University of Petroleum(Edition of Natural Science )(in Chinese),2006,30(1):33-37
[5]沈凤,钱绍新,刘雯林等.AVO多参数反演在气层检测和储层定量研究中的应用.石油学报,1994,15(2):11-20 Shen F,Qian S X,Liu W L,et al.The application of AVO multiple parameter inversion in gas sand detection and reservoir quantitative examination.Acta Petrolei Sinica(in Chinese),1994,15(2),11-20
[6]Hampson D.AVO inversion,theory and practice.Geophysics, 1991,10(6):39-42
[7]王天禧.用平面波延拓方程进行地震数据的叠前速度反演.地球物理学报,1993,36(3):388-395 Wang T X.Prestack velocity inversion of seismic data using plane wavefield downward continuation.Chinese J.Geophys. (ActaGeophysica Sinica)(in Chinese),1993,36(3):388- 395
[8]岳碧波,彭真明,洪余刚等.基于粒子群优化算法的叠前角道集子波反演.地球物理学报,2009,52(12):3116-3123 Yue B B,Peng Z M,Hong Y G,et al.Wavelet inversion of pre-stack seismic angle-gather based on particle swarm optimization algorithm.Chinese J.Geophys.(in Chinese), 2009,52(12):3116-3123
[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):1876-1882 Yang P J,Yin X Y.Non-linear quadratic programming Bayesian prestack inversion.Chinese J.Geophys.(in Chinese), 2008,51(6):1876-1882
[10]路鹏飞,杨长春,郭爱华等.改进的模拟退火算法及其在叠前储层参数反演中的应用.地球物理学进展,2008,23(1): 104-109 Lu P F,Yang C C,Guo A H,et al.Modified simulated annealing algorithm and its application in pre-stack inversion of reservoir parameters.Progress in Geophysics,2008,23 (1):104-109
[11]黄伟传,杨长春,王彦飞.利用叠前地震数据预测裂缝储层的应用研究.地球物理学进展,2007,22(5):1602-1606 Huang W C,Yang C C.The application of pre-stack seismic data in predicting the fractured reservoir.Progress in Geophysics, 2007,22(5):1602-1606
[12]尚永生,杨长春,王真理等.塔里木盆地卡4区块AVO研究.地球物理学进展,2007,22(5):1408-1415 Shang Y S,Yang C C,Wang Z L,et al.AVO research in Ka-4 region of Tarim basin.Progress in Geophysics(in Chinese),2007,22(5):1408-1415
[13]Hammersley J M,Handscomb D C.Monte Carlo Methods. New York:Chapman and Hall,1964.
[14]Grandis H,Menvielle M,Roussignol M.Bayesian inversion with Markov chains-I The magnetotelluric one-dimensional case.Geophys.J.Int.,1999,138(3),757-768
[15]Malinverno A,Leaney S.A Monte Carlo method to quantify uncertainty in the inversion of zero-offset VSP data.In:SEG 70th Annual Meeting,Calgary,Alberta,2000
[16]Chen J S.Joint inversion of seismic AVO and EM data for gas saturation estimation using a sampling-based stochastic model.In:SEG 74th Annual Meeting,Denver,Colorado, 2004
[17]Chen J S,Hoversten G M,Vasco D,et al.A Bayesian model for gas saturation estimation using marine seismic AVA and CSEM data.Geophysics,2007,72(2):85-95
[18]Hong T C,Sen M K.A new MCMC algorithm for seismic ??waveform inversion and corresponding uncertainty analysis. Geophys.J.Int.,2009,177(1):14-32
[19]Wang D Y,Zhang G Z.AVO simultaneous inversion using Markov Chain Monte Carlo.In:SEG 80th Annual Meeting, Denver,Colorado,2010
[20]Keilis-Borok V I,Yanovskaya T B.Inverse problems of seismology.Geophys.J.,1967,13(1/3):223-234
[21]Press F.Earth models obtained by Monte Carlo inversion.J. Geophys.Res.,1968,73(16):5223-5234
[22]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):108-113 Wang H,Zhang Y F.Model-based multi-parameters nonlinear inversion method in prestack domain.Lithologic Reservoirs(in Chinese),2008,20(2):108-113
[23]Malinverno A.Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem.Geophys. J.Int.,2002,151(3):675-688
[24]Tarantola A.Inverse Problem Theory.New York:Elsevier Sci,1987
[25]赵琪.MCMC方法研究.山东:山东大学[博士论文], 2007.11-18
[26]Ross S M.统计模拟.王兆军等译.第四版.北京:人民邮电出版社,2007.203-206
[27]朱嵩.基于贝叶斯推理的环境水力学反问题研究.浙江:浙江大学[博士论文],2008.63-90
[28]Fatti J L,Smith G C,Vail P J,et al.Detection of gas in sandstone reservoirs using AVO analysis;A 3-D seismic case history using the Geostack technique.Geophysics,1994,59 (9):1362-1376.
[29]郑晓东.Zoeppritz方程的近似及其应用.石油地球物理勘探,1991,26(2):129-144
[30]Castagna]P,Batzle M L,Eastwood R L.Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks.Geophysics,1985,50(4):571-581
[31]马中高,解吉高.岩石的纵、横波速度与密度的规律研究.地球物理学进展,2005,20(4),905-910 Ma Z G,Xie J G.Relationship among compressional wave, shear wave velocities and density of rocks.Progress in Geophysics,2005,20(4),905-910
[2]杨培杰,印兴耀.基于支持向量机的叠前地震反演方法.中国石油大学学报(自然科学版),2008,32(1):37-41 Yang P J,Yin X Y.Prestack seismic inversion method based on support vector machine.Journal of the University of China University of Petroleum(Edition of Natural Science) (in Chinese),2008,32(1):37-41
[3]殷八斤,曾灏,杨在岩.AVO技术的理论与实践.北京:石油工业出版社,1995
[4]陈天胜,刘洋,魏修成.纵波和转换波联合AVO反演方法研究.中国石油大学学报(自然科学版),2006,30(1):33-37 Chen T S,Liu Y,Wei X C.Joint amplitude versus offset inversion of P-P and P-SV seismic data.Journal of China University of Petroleum(Edition of Natural Science )(in Chinese),2006,30(1):33-37
[5]沈凤,钱绍新,刘雯林等.AVO多参数反演在气层检测和储层定量研究中的应用.石油学报,1994,15(2):11-20 Shen F,Qian S X,Liu W L,et al.The application of AVO multiple parameter inversion in gas sand detection and reservoir quantitative examination.Acta Petrolei Sinica(in Chinese),1994,15(2),11-20
[6]Hampson D.AVO inversion,theory and practice.Geophysics, 1991,10(6):39-42
[7]王天禧.用平面波延拓方程进行地震数据的叠前速度反演.地球物理学报,1993,36(3):388-395 Wang T X.Prestack velocity inversion of seismic data using plane wavefield downward continuation.Chinese J.Geophys. (ActaGeophysica Sinica)(in Chinese),1993,36(3):388- 395
[8]岳碧波,彭真明,洪余刚等.基于粒子群优化算法的叠前角道集子波反演.地球物理学报,2009,52(12):3116-3123 Yue B B,Peng Z M,Hong Y G,et al.Wavelet inversion of pre-stack seismic angle-gather based on particle swarm optimization algorithm.Chinese J.Geophys.(in Chinese), 2009,52(12):3116-3123
[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):1876-1882 Yang P J,Yin X Y.Non-linear quadratic programming Bayesian prestack inversion.Chinese J.Geophys.(in Chinese), 2008,51(6):1876-1882
[10]路鹏飞,杨长春,郭爱华等.改进的模拟退火算法及其在叠前储层参数反演中的应用.地球物理学进展,2008,23(1): 104-109 Lu P F,Yang C C,Guo A H,et al.Modified simulated annealing algorithm and its application in pre-stack inversion of reservoir parameters.Progress in Geophysics,2008,23 (1):104-109
[11]黄伟传,杨长春,王彦飞.利用叠前地震数据预测裂缝储层的应用研究.地球物理学进展,2007,22(5):1602-1606 Huang W C,Yang C C.The application of pre-stack seismic data in predicting the fractured reservoir.Progress in Geophysics, 2007,22(5):1602-1606
[12]尚永生,杨长春,王真理等.塔里木盆地卡4区块AVO研究.地球物理学进展,2007,22(5):1408-1415 Shang Y S,Yang C C,Wang Z L,et al.AVO research in Ka-4 region of Tarim basin.Progress in Geophysics(in Chinese),2007,22(5):1408-1415
[13]Hammersley J M,Handscomb D C.Monte Carlo Methods. New York:Chapman and Hall,1964.
[14]Grandis H,Menvielle M,Roussignol M.Bayesian inversion with Markov chains-I The magnetotelluric one-dimensional case.Geophys.J.Int.,1999,138(3),757-768
[15]Malinverno A,Leaney S.A Monte Carlo method to quantify uncertainty in the inversion of zero-offset VSP data.In:SEG 70th Annual Meeting,Calgary,Alberta,2000
[16]Chen J S.Joint inversion of seismic AVO and EM data for gas saturation estimation using a sampling-based stochastic model.In:SEG 74th Annual Meeting,Denver,Colorado, 2004
[17]Chen J S,Hoversten G M,Vasco D,et al.A Bayesian model for gas saturation estimation using marine seismic AVA and CSEM data.Geophysics,2007,72(2):85-95
[18]Hong T C,Sen M K.A new MCMC algorithm for seismic ??waveform inversion and corresponding uncertainty analysis. Geophys.J.Int.,2009,177(1):14-32
[19]Wang D Y,Zhang G Z.AVO simultaneous inversion using Markov Chain Monte Carlo.In:SEG 80th Annual Meeting, Denver,Colorado,2010
[20]Keilis-Borok V I,Yanovskaya T B.Inverse problems of seismology.Geophys.J.,1967,13(1/3):223-234
[21]Press F.Earth models obtained by Monte Carlo inversion.J. Geophys.Res.,1968,73(16):5223-5234
[22]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):108-113 Wang H,Zhang Y F.Model-based multi-parameters nonlinear inversion method in prestack domain.Lithologic Reservoirs(in Chinese),2008,20(2):108-113
[23]Malinverno A.Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem.Geophys. J.Int.,2002,151(3):675-688
[24]Tarantola A.Inverse Problem Theory.New York:Elsevier Sci,1987
[25]赵琪.MCMC方法研究.山东:山东大学[博士论文], 2007.11-18
[26]Ross S M.统计模拟.王兆军等译.第四版.北京:人民邮电出版社,2007.203-206
[27]朱嵩.基于贝叶斯推理的环境水力学反问题研究.浙江:浙江大学[博士论文],2008.63-90
[28]Fatti J L,Smith G C,Vail P J,et al.Detection of gas in sandstone reservoirs using AVO analysis;A 3-D seismic case history using the Geostack technique.Geophysics,1994,59 (9):1362-1376.
[29]郑晓东.Zoeppritz方程的近似及其应用.石油地球物理勘探,1991,26(2):129-144
[30]Castagna]P,Batzle M L,Eastwood R L.Relationships between compressional-wave and shear-wave velocities in clastic silicate rocks.Geophysics,1985,50(4):571-581
[31]马中高,解吉高.岩石的纵、横波速度与密度的规律研究.地球物理学进展,2005,20(4),905-910 Ma Z G,Xie J G.Relationship among compressional wave, shear wave velocities and density of rocks.Progress in Geophysics,2005,20(4),905-910
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