基于FFT-MA谱模拟的快速随机反演方法研究
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摘要
虽然基于地质统计学的随机反演方法能够有效融合测井资料中的高频信息,但计算效率低,占用内存大,限制了它在实际资料中的应用.本文在保留传统随机反演方法优点的基础上,创造性地引入傅里叶滑动平均(Fast Fourier Transform-Moving Average,FFT-MA)谱模拟进行频率域的地质统计模拟,并利用逐步变形算法(Gradual Deformation Method,GDM)确保模拟结果与实际地震数据的匹配,构建了基于FFT-MA谱模拟的新的快速随机反演方法.与常规随机反演相比,新方法不仅分辨率高,而且能够使反演解得到快速收敛,有效提高计算效率,减少内存占用.模型试算获得了与理论模型吻合度较好的高分辨率反演结果.实际资料分析也表明新方法所得到的高分辨率反演结果能够对薄互储层进行良好的展示,为薄储层的识别提供高效可靠的技术支持.
Although the stochastic inversion based on geostatistics can effectively integrate high frequency information from well logs with higher resolution,however,it has low computational efficiency and too much memory consumption,which limits its application in real seismic data.The stochastic inversion is used to improve the operation efficiency of inversion and obtain highresolution inversion results.On the basis of the traditional stochastic inversion,a new method of stochastic inversion is proposed,i.e.the fast stochastic inversion based on fast Fourier transform-moving average(FFT-MA)spectrum simulation.This method is used to conduct geostatistical simulation in the frequency domain,and the gradual deformation updating method(GDM)can be used to accelerate the simulation convergence through continuous modification of the reservoir model until it matches the real seismic data.FFT-MA simulation is a spectrum simulation method which can perform fast simulation in the frequency domain by Fourier transform.Compared with the sequential Gaussian simulationalgorithm,the FFT-MA spectrum simulation can greatly improve the computational efficiency while has better simulation result.The conditioned FFT-MA spectrum simulation method can reconstruct the data which satisfy the specified covariance structure and grid size as well as the known well data.The GDM can get a series Gauss white noises realization which having the same mean and variance distribution.By changing the Gauss white noise,the FFT-MA disturbance simulation results will have all or part of the continuous modification.The synthetic seismic data can be obtained from the simulation results by forward modeling.Fast optimized stochastic inversion results will be obtained while the synthetic seismic data match well with the real seismic data.Compared with the conventional stochastic inversion,the fast stochastic inversion method can get high-resolution inversion result.Moreover,it can enhance the computational performance and reduce the memory consumption,and also accelerate the convergence process of the inversion.The model tests show that the proposed stochastic inversion method can obtain higher resolution of inversion results than the deterministic inversion method and match the model well.The analysis of the real data also shows that the high-resolution inversion result of the stochastic inversion method can have better exhibit thin interbedded reservoirs.The fast stochastic inversion method can get higher resolution of inversion result than deterministic inversion method and has faster computational efficiency than conventional stochastic inversion.The proposed method can be used in the identification of thin reservoirs.The proposed method is not affected by the sequential factors;therefore it can be parallel computed in the future research which will further improve the computational efficiency.
Although the stochastic inversion based on geostatistics can effectively integrate high frequency information from well logs with higher resolution,however,it has low computational efficiency and too much memory consumption,which limits its application in real seismic data.The stochastic inversion is used to improve the operation efficiency of inversion and obtain highresolution inversion results.On the basis of the traditional stochastic inversion,a new method of stochastic inversion is proposed,i.e.the fast stochastic inversion based on fast Fourier transform-moving average(FFT-MA)spectrum simulation.This method is used to conduct geostatistical simulation in the frequency domain,and the gradual deformation updating method(GDM)can be used to accelerate the simulation convergence through continuous modification of the reservoir model until it matches the real seismic data.FFT-MA simulation is a spectrum simulation method which can perform fast simulation in the frequency domain by Fourier transform.Compared with the sequential Gaussian simulationalgorithm,the FFT-MA spectrum simulation can greatly improve the computational efficiency while has better simulation result.The conditioned FFT-MA spectrum simulation method can reconstruct the data which satisfy the specified covariance structure and grid size as well as the known well data.The GDM can get a series Gauss white noises realization which having the same mean and variance distribution.By changing the Gauss white noise,the FFT-MA disturbance simulation results will have all or part of the continuous modification.The synthetic seismic data can be obtained from the simulation results by forward modeling.Fast optimized stochastic inversion results will be obtained while the synthetic seismic data match well with the real seismic data.Compared with the conventional stochastic inversion,the fast stochastic inversion method can get high-resolution inversion result.Moreover,it can enhance the computational performance and reduce the memory consumption,and also accelerate the convergence process of the inversion.The model tests show that the proposed stochastic inversion method can obtain higher resolution of inversion results than the deterministic inversion method and match the model well.The analysis of the real data also shows that the high-resolution inversion result of the stochastic inversion method can have better exhibit thin interbedded reservoirs.The fast stochastic inversion method can get higher resolution of inversion result than deterministic inversion method and has faster computational efficiency than conventional stochastic inversion.The proposed method can be used in the identification of thin reservoirs.The proposed method is not affected by the sequential factors;therefore it can be parallel computed in the future research which will further improve the computational efficiency.
引文
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Bosch M,Mukerji T,Gonzalez F E.2010.Seismic inversion forreservoir properties combining statistical rock physics andgeostatistics:A review.Geophysics,75(5):75A165-75A176.
Contreras A,Torres-Verdin C,Kvien K,et al.2005.AVAstochastic inversion of pre-stack seismic data and well logs for 3Dreservoir modeling.//EAGE 67th Conference and Exhibition.
Debeye H W,Sabbah E,Made P M.1996.Stochastic inversion.//66 Ann.Internat Mtg.,Soc.Expi.Geophys.ExpandedAbstracts,1212-1215.
Doyen P M.2007.Seismic Reservoir Characterization:An EarthModeling Perspective.Houten,The Netherlands:EuropeanAssociation of Geoscientists and Engineers,Publications.
Francis A.2005.Limitations of deterministic and advantages ofstochastic seismic inversion.CanadianSoc.Expi Geophys.Recorder,30(2):5-11.
Francis A M.2006a.Understanding stochastic inversion:Part 1.First Break,24(11):69-77.
Francis A M.2006b.Understanding stochastic inversion:Part 2.First Break,24(12):79-84.
Haas A,Dubrule O.1994.Geostatistical inversion—a sequentialmethod of stochastic reservoir modeling constrained by seismicdata.First Break,12(11):561-569.
Helgesen J,Magnus I,Prosser S,et al.2000.Comparison ofconstrained sparse spike and stochastic inversion for porosityprediction at Kristin field.The Leading Edge,19(4):400-407.
Hu L Y.2000.Gradual deformation and iterative calibration of Gaussianrelated stochastic models.Math.Geology,32(1):87-108.
Hu L Y,Ravalec-Dupin M L.2004.An improved gradualdeformation method for reconciling random and gradientsearches in stochastic optimizations.Math.Geol.,36(6):703-719.
Huang H D,Zhang R W,Wei S P.2009.Research on application ofseismic nonlinear random inversion to reservoir prediction in thethin sandstone of continental deposits.Acta Petrolei Sinica(inChinese),30(3):386-390.
Huang Z Y,Gan L D,Dai X F,et al.2012.Key parameteroptimization and analysis of stochastic seismic inversion.Applied Geophysics,9(1):49-56.
Moyen R,Doyen P M.2009.Reservoir connectivity uncertaintyfrom stochastic seismic inversion.//79th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2378-2381.
Oliver D S.1995.Moving averages for Gaussian simulation in twoand three dimensions.Math.Geol.,27(8):939-960.
Pardo-Igúzquiza E,Chica-Olmo M.1993.The Fourier integralmethod:An efficient spectral method for simulation of randomfields.Math.Geol.,25(2):177-217.
Ravalec M L,Noetinger B,Hu L Y.2000.The FFT movingaverage(FFT-MA)generator:An efficient numerical methodfor generating and conditioning Gaussian simulations.Math.Geol.,32(6):701-723.
Ravalec-Dupin M L,Noetinger B.2002.Optimization with thegradual deformation method.Math.Geol.,34(2):125-142.
Sams M,Saussus D.2008.Comparison of uncertainty estimatesfrom deterministic and geostatistical inversion.//78th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1486-1490.
Sams M S,Atkins D,Siad N,et al.1999.Stochastic inversion forhigh resolution reservoir characterisation in the central Sumatrabasin.//Society of Petroleum Engineers Asia Pacific ImprovedOil Recovery Conference,257-260.
Sams M S,Saussus D.2010.Comparison of lithology and net payuncertainty between deterministic and geostatistical inversionworkflows.First Break,28(2):35-44.
Sancevero S S,Remacre A Z,Portugal R S,et al.2005.Comparingdeterministic and stochastic seismic inversion for thin-bedreservoir characterization in a turbidite synthetic reference modelof Campos basin,Brazil.The Leading Edge,24(11):1168-1172.
Srivastava R P,Sen M K.2010.Stochastic inversion of prestackseismic data using fractal-based initial models.Geophysics,75(3):R47-R59.
Yang K,Ai D F,Geng J H.2012.A new geostatistical inversionand reservoir modeling technique constrained by well-log,crosshole and surface seismic data.Chinese J.Geophys.(inChinese),55(8):2695-2704,doi:10.6038/j.issn.0001-5733.2012.08.022.
Yang X C,Li X F,Zhang M G.2001.Process and Mathematicalbasis of investigations of seismic inversion.Process inGeophysics(in Chinese),16(4):96-109,doi:10.3969/j.issn.1004-2903.2001.04.013.
Zhang S X,Zhang F C,Li S P,et al.2010.Detailed prediction ofthin reservoir in Andian area of Biyang Depression.GeophysicalProspecting for Petroleum(in Chinese),49(1):34-41.
黄捍东,张如伟,魏世平.2009.地震非线性随机反演方法在陆相薄砂岩储层预测中的应用.石油学报,30(3):386-390.
杨锴,艾迪飞,耿建华.2012.测井、井间地震与地面地震数据联合约束下的地质统计学随机建模方法研究.地球物理学报,55(8):2695-2704,doi:10.6038/j.issn.0001-5733.2012.08.022.
杨晓春,李小凡,张美根.2001.地震波反演方法研究的某些进展及其数学基础.地球物理学进展,16(4):96-109,doi:10.3969/j.issn.1004-2903.2001.04.013.
张世鑫,张繁昌,李少鹏等.2010.泌阳凹陷安店区块薄储层精细预测.石油物探,49(1):34-41.
Bosch M,Mukerji T,Gonzalez F E.2010.Seismic inversion forreservoir properties combining statistical rock physics andgeostatistics:A review.Geophysics,75(5):75A165-75A176.
Contreras A,Torres-Verdin C,Kvien K,et al.2005.AVAstochastic inversion of pre-stack seismic data and well logs for 3Dreservoir modeling.//EAGE 67th Conference and Exhibition.
Debeye H W,Sabbah E,Made P M.1996.Stochastic inversion.//66 Ann.Internat Mtg.,Soc.Expi.Geophys.ExpandedAbstracts,1212-1215.
Doyen P M.2007.Seismic Reservoir Characterization:An EarthModeling Perspective.Houten,The Netherlands:EuropeanAssociation of Geoscientists and Engineers,Publications.
Francis A.2005.Limitations of deterministic and advantages ofstochastic seismic inversion.CanadianSoc.Expi Geophys.Recorder,30(2):5-11.
Francis A M.2006a.Understanding stochastic inversion:Part 1.First Break,24(11):69-77.
Francis A M.2006b.Understanding stochastic inversion:Part 2.First Break,24(12):79-84.
Haas A,Dubrule O.1994.Geostatistical inversion—a sequentialmethod of stochastic reservoir modeling constrained by seismicdata.First Break,12(11):561-569.
Helgesen J,Magnus I,Prosser S,et al.2000.Comparison ofconstrained sparse spike and stochastic inversion for porosityprediction at Kristin field.The Leading Edge,19(4):400-407.
Hu L Y.2000.Gradual deformation and iterative calibration of Gaussianrelated stochastic models.Math.Geology,32(1):87-108.
Hu L Y,Ravalec-Dupin M L.2004.An improved gradualdeformation method for reconciling random and gradientsearches in stochastic optimizations.Math.Geol.,36(6):703-719.
Huang H D,Zhang R W,Wei S P.2009.Research on application ofseismic nonlinear random inversion to reservoir prediction in thethin sandstone of continental deposits.Acta Petrolei Sinica(inChinese),30(3):386-390.
Huang Z Y,Gan L D,Dai X F,et al.2012.Key parameteroptimization and analysis of stochastic seismic inversion.Applied Geophysics,9(1):49-56.
Moyen R,Doyen P M.2009.Reservoir connectivity uncertaintyfrom stochastic seismic inversion.//79th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,2378-2381.
Oliver D S.1995.Moving averages for Gaussian simulation in twoand three dimensions.Math.Geol.,27(8):939-960.
Pardo-Igúzquiza E,Chica-Olmo M.1993.The Fourier integralmethod:An efficient spectral method for simulation of randomfields.Math.Geol.,25(2):177-217.
Ravalec M L,Noetinger B,Hu L Y.2000.The FFT movingaverage(FFT-MA)generator:An efficient numerical methodfor generating and conditioning Gaussian simulations.Math.Geol.,32(6):701-723.
Ravalec-Dupin M L,Noetinger B.2002.Optimization with thegradual deformation method.Math.Geol.,34(2):125-142.
Sams M,Saussus D.2008.Comparison of uncertainty estimatesfrom deterministic and geostatistical inversion.//78th Ann.Internat Mtg.,Soc.Expi.Geophys..Expanded Abstracts,1486-1490.
Sams M S,Atkins D,Siad N,et al.1999.Stochastic inversion forhigh resolution reservoir characterisation in the central Sumatrabasin.//Society of Petroleum Engineers Asia Pacific ImprovedOil Recovery Conference,257-260.
Sams M S,Saussus D.2010.Comparison of lithology and net payuncertainty between deterministic and geostatistical inversionworkflows.First Break,28(2):35-44.
Sancevero S S,Remacre A Z,Portugal R S,et al.2005.Comparingdeterministic and stochastic seismic inversion for thin-bedreservoir characterization in a turbidite synthetic reference modelof Campos basin,Brazil.The Leading Edge,24(11):1168-1172.
Srivastava R P,Sen M K.2010.Stochastic inversion of prestackseismic data using fractal-based initial models.Geophysics,75(3):R47-R59.
Yang K,Ai D F,Geng J H.2012.A new geostatistical inversionand reservoir modeling technique constrained by well-log,crosshole and surface seismic data.Chinese J.Geophys.(inChinese),55(8):2695-2704,doi:10.6038/j.issn.0001-5733.2012.08.022.
Yang X C,Li X F,Zhang M G.2001.Process and Mathematicalbasis of investigations of seismic inversion.Process inGeophysics(in Chinese),16(4):96-109,doi:10.3969/j.issn.1004-2903.2001.04.013.
Zhang S X,Zhang F C,Li S P,et al.2010.Detailed prediction ofthin reservoir in Andian area of Biyang Depression.GeophysicalProspecting for Petroleum(in Chinese),49(1):34-41.
黄捍东,张如伟,魏世平.2009.地震非线性随机反演方法在陆相薄砂岩储层预测中的应用.石油学报,30(3):386-390.
杨锴,艾迪飞,耿建华.2012.测井、井间地震与地面地震数据联合约束下的地质统计学随机建模方法研究.地球物理学报,55(8):2695-2704,doi:10.6038/j.issn.0001-5733.2012.08.022.
杨晓春,李小凡,张美根.2001.地震波反演方法研究的某些进展及其数学基础.地球物理学进展,16(4):96-109,doi:10.3969/j.issn.1004-2903.2001.04.013.
张世鑫,张繁昌,李少鹏等.2010.泌阳凹陷安店区块薄储层精细预测.石油物探,49(1):34-41.
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