双感应测井资料自适应正则化反演
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摘要
为了准确获得地层真电阻率,确定地层侵入关系,将非线性反演理论与Morozov偏差原理结合,建立双感应测井(Dual-Induction Log)资料的自适应正则化全参数反演算法。首先根据Tikhonov正则化反演理论,将双感应测井资料反演问题变为含稳定泛函非线性目标函数极小化问题;再利用Gauss-Newton算法确定极小化解。在测井资料的最佳拟合迭代过程中,将Morozov偏差原理及Cholesky分解技术结合,建立一套自适应选择正则化因子方法;最后对大庆油田的实际测井资料进行反演处理。反演结论与试油结果表明,该算法在处理薄层、薄互层时能够取得更为满意的效果。
In order to determine the true resistivity of the formation,the formation of the intrusive relationship is determined,we present an adaptively regularized algorithm to simultaneously reconstruct all the model parameters from dual-induction log DIL data based on nonlinear inversion theory and Morozov discrepancy principle.We firstly adopt Tikhonov regularization inversion theory to transform the inversion problem into the minimization problem of non-quadratic objective function with the stabilizing functional defined on model space,and use Gauss-Newton method to obtain the minimization of objective function.Then,the combination of Morozov discrepancy principle and Cholesky decomposition is executed to propose an adaptive regularization factor choice strategy in order to obtain a stable inversion solution as well as to realize best fit of input data with modeling logs.Finally,the inversion results of piratical field logs measured from Daqing oilfield are compared with the test oil conclusion,the new inversion technique can produce more desired effect in thin reservoirs and thin interactive reservoirs application.
In order to determine the true resistivity of the formation,the formation of the intrusive relationship is determined,we present an adaptively regularized algorithm to simultaneously reconstruct all the model parameters from dual-induction log DIL data based on nonlinear inversion theory and Morozov discrepancy principle.We firstly adopt Tikhonov regularization inversion theory to transform the inversion problem into the minimization problem of non-quadratic objective function with the stabilizing functional defined on model space,and use Gauss-Newton method to obtain the minimization of objective function.Then,the combination of Morozov discrepancy principle and Cholesky decomposition is executed to propose an adaptive regularization factor choice strategy in order to obtain a stable inversion solution as well as to realize best fit of input data with modeling logs.Finally,the inversion results of piratical field logs measured from Daqing oilfield are compared with the test oil conclusion,the new inversion technique can produce more desired effect in thin reservoirs and thin interactive reservoirs application.
引文
[1]张建华,刘振华,仵杰.电法测井原理与应用[M].西安:西北大学出版社,2002.Zhang Jianhua,Liu Zhenhua,Wu Jie.Electrical logging principle and application[M].Xi'an:Northwestern University Press,2002.
[2]斯伦贝谢测井公司.测井解释原理与应用[M].北京:石油工业出版社,1991.Schlumberger Logging Company.Logging interpretation principle and application[M].Beijing:Petroleum Industry Press,1991.
[3]汪宏年,陶宏根,王桂萍,等.双感应测井资料的快速近似迭代反演[J].地球物理学报,2007,50(5):1614-1622.Wang Hongnian,Tao Honggen,Wang Guiping,et al.A fast approximate iterative inversion technique of dual induction logging data[J].Chinese Journal of Geophysics,2007,50(5):1614-1622.
[4]张玲玲.双感应测井资料的正反演理论及其在大庆油田的应用[D].长春:吉林大学,2007.Zhang Lingling.Numerical modeling and inversion of dual induction well logging data and their application in Daqing oilfield[D].Changchun:Jilin University,2007.
[5]陶宏根,李庆峰,王桂萍,等.双感应测井资料实用化快速近似迭代反演技术及其在大庆油田的应用[J].测井技术,2007,31(5):441-444.Tao Honggen,Li Qingfeng,Wang Guiping,et al.A practical fast iterative inversion technique of dual induction logging data and its application in Daqing oilfield[J].Well Logging Technology,2007,31(5):441-444.
[6]汪宏年,陶宏根,王桂萍,等.从双感应测井录中提取原始视电导率的一种改进方法[J].测井技术,2007,31(3):236-240.Wang Hongnian,Tao Honggen,Wang Guiping,et al.An improved method to extract the original apparent conductivity from the dual induction log[J].Well Logging Technology,2007,31(3):236-240.
[7]姚东华,汪宏年,陶宏根等.水平层状介质中双侧向测井资料的迭代Tikhonov正则化反演[J].地球物理学报,2010,53(9):2227-2236.Yao Donghua,Wang Hongnian,Tao Honggen,et al.Iterative Tikhonov regularization inversion of bilateral normal logging data in horizontal layered media[J].Chinese Journal of Geophysics,2010,53(9):2227-2236.
[8]姚东华.双侧向测井资料迭代正则化反演与各向异性地层多分量感应测井数值仿真[D].长春:吉林大学,2010.Yao Donghua.Study the iterative regularization inversion of dual laterolog datum and the numerical simulation of multicomponent induction logging responses in general anisotropic formations[D].Changchun:Jilin University,2010.
[9]汪宏年,杨善德,常明澈.水平层状介质中侧向电阻率测井快速迭代反演与应用[J].地球物理进展,1998,13(4):97-107.Wang Hongnian,Yang Shande,Chang Mingche.The fast nonlinear inversion of laterolog for the horizontal layers and its application[J].Progress in Geophysics,1998,13(4):97-107.
[10]汪宏年,陶宏根,其木苏容,等.水平层状介质中双侧向资料的全参数正则化迭代反演与应用[J].地球物理学报,2002,45(增刊):387-399.Wang Hongnian,Tao Honggen,Chemid Surong.Regularized entire-parameter iterative inversion of dual laterolog in horizontally stratified media and its application.[J].Chinese Journal of Geophysics,2002,45(Suppl):387-399.
[11]Wang H N,Yang S D.A multiparameter iterative inversion of dual-laterolog in horizontally layered medium and its error analysis[J].IEEE Transactions on Geoscience and Remote Sensing,2002,40(2):482-493.
[12]肖庭延,于慎根,王彦飞.反问题的数值解法[M].北京:科学出版社,2006.Xiao Tingyan,Yu Shengen,Wang Yanfei.Numerical solution of the inverse problem[M].Beijing:Science Press,2006.
[13]王彦飞.反演问题的计算方法及其应用[M].北京:高等教育出版社,2007.Wang Yanfei.The calculation method and application of the inverse problem[M].Beijing:Higher Education Press,2007.
[14]Kirsch A.An introduction to the mathematical theory of inverse problem[M].New York:Springer Verlag,1996.
[15]Früauf F,Scherzer O,Leito A.Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators[J].SIAM Journal on Numerical Analysis,2005,43(2):767-786.
[16]Hansen P C,O'Leary D P.The use of the L-curve in the regularization of discrete ill-posed problems[J].SIAM Journal on Scientific Computing,1993,14(6):1487-1503.
[17]Burger M,Kaltenbacher B.Regularizing newton-kaczmarz methods for nonlinear ill-posed problems[J].SIAM Journal on Numerical Analysis,2007,44(1):153-182.
[18]Kaltenbacher B.Regularization by truncated Cholesky factorization:A comparison of four different approaches[J].Journal of Complexity,2007,23:225-244.
[19]Kaltenbacher B.Some Newton-type methods for the regularization of nonlinear ill-posed problems[J].Inverse Problems,1997,13:729-753.
[20]Haber E,Oldenburg D.A GCV based method for nonlinear ill-posed problems[J].Computational Geosciences,2000,4:41-63.
[21]Wang J J,Li G S.A Modified Tikhonov regularization method for solving ill-posed problems[J].Chinese Quarterly Journal of Mathematics,2000,15(2):98-101.
[22]Neubauer A.Tikhonov regularisation for non-linear ill-posed problems:Optimal convergence rates and finite-dimensional approximation[J].Inverse Problems,1989,5:541-557.
[23]Honerkamp J,Weese J.Tikhonovs regularization method for ill-posed problems[J].Continuum Mechanics and Thermodynamics,1990,2:17-30.
[24]Lu S,Pereverzev S V,Ramlau R.An analysis of Tikhonov regularization for nonlinear ill-posed problems under a general smoothness assumption[J].Inverse Problems,2007,23:217-230.
[25]Bokmann C,Pornsawad P.Iterative Runge-Kutta-type methods for nonlinear ill-posed problems[J].Inverse Problems,2008,24,doi:10.1088/0266-5611/24/2/025002.
[26]Scherzer O,Linz.The use of Morozov'discrepancy principle for Tikhonov regularization for solving non-inear ill-osed problems[J].Computing,1993,51:45-60.
[27]Bonesky T.Morozov's discrepancy principle and Tikhonov-type functionals[J].Inverse Problems,2009,25,doi:10.1088/0266-5611/25/1/01501528.
[28]Routh P S,Oldenburg D W.Inversion of controlled source audio-frequency magnetotellurics data for a horizontally layered earth[J].Geophysics,1999,64(6):1689-1697.
[2]斯伦贝谢测井公司.测井解释原理与应用[M].北京:石油工业出版社,1991.Schlumberger Logging Company.Logging interpretation principle and application[M].Beijing:Petroleum Industry Press,1991.
[3]汪宏年,陶宏根,王桂萍,等.双感应测井资料的快速近似迭代反演[J].地球物理学报,2007,50(5):1614-1622.Wang Hongnian,Tao Honggen,Wang Guiping,et al.A fast approximate iterative inversion technique of dual induction logging data[J].Chinese Journal of Geophysics,2007,50(5):1614-1622.
[4]张玲玲.双感应测井资料的正反演理论及其在大庆油田的应用[D].长春:吉林大学,2007.Zhang Lingling.Numerical modeling and inversion of dual induction well logging data and their application in Daqing oilfield[D].Changchun:Jilin University,2007.
[5]陶宏根,李庆峰,王桂萍,等.双感应测井资料实用化快速近似迭代反演技术及其在大庆油田的应用[J].测井技术,2007,31(5):441-444.Tao Honggen,Li Qingfeng,Wang Guiping,et al.A practical fast iterative inversion technique of dual induction logging data and its application in Daqing oilfield[J].Well Logging Technology,2007,31(5):441-444.
[6]汪宏年,陶宏根,王桂萍,等.从双感应测井录中提取原始视电导率的一种改进方法[J].测井技术,2007,31(3):236-240.Wang Hongnian,Tao Honggen,Wang Guiping,et al.An improved method to extract the original apparent conductivity from the dual induction log[J].Well Logging Technology,2007,31(3):236-240.
[7]姚东华,汪宏年,陶宏根等.水平层状介质中双侧向测井资料的迭代Tikhonov正则化反演[J].地球物理学报,2010,53(9):2227-2236.Yao Donghua,Wang Hongnian,Tao Honggen,et al.Iterative Tikhonov regularization inversion of bilateral normal logging data in horizontal layered media[J].Chinese Journal of Geophysics,2010,53(9):2227-2236.
[8]姚东华.双侧向测井资料迭代正则化反演与各向异性地层多分量感应测井数值仿真[D].长春:吉林大学,2010.Yao Donghua.Study the iterative regularization inversion of dual laterolog datum and the numerical simulation of multicomponent induction logging responses in general anisotropic formations[D].Changchun:Jilin University,2010.
[9]汪宏年,杨善德,常明澈.水平层状介质中侧向电阻率测井快速迭代反演与应用[J].地球物理进展,1998,13(4):97-107.Wang Hongnian,Yang Shande,Chang Mingche.The fast nonlinear inversion of laterolog for the horizontal layers and its application[J].Progress in Geophysics,1998,13(4):97-107.
[10]汪宏年,陶宏根,其木苏容,等.水平层状介质中双侧向资料的全参数正则化迭代反演与应用[J].地球物理学报,2002,45(增刊):387-399.Wang Hongnian,Tao Honggen,Chemid Surong.Regularized entire-parameter iterative inversion of dual laterolog in horizontally stratified media and its application.[J].Chinese Journal of Geophysics,2002,45(Suppl):387-399.
[11]Wang H N,Yang S D.A multiparameter iterative inversion of dual-laterolog in horizontally layered medium and its error analysis[J].IEEE Transactions on Geoscience and Remote Sensing,2002,40(2):482-493.
[12]肖庭延,于慎根,王彦飞.反问题的数值解法[M].北京:科学出版社,2006.Xiao Tingyan,Yu Shengen,Wang Yanfei.Numerical solution of the inverse problem[M].Beijing:Science Press,2006.
[13]王彦飞.反演问题的计算方法及其应用[M].北京:高等教育出版社,2007.Wang Yanfei.The calculation method and application of the inverse problem[M].Beijing:Higher Education Press,2007.
[14]Kirsch A.An introduction to the mathematical theory of inverse problem[M].New York:Springer Verlag,1996.
[15]Früauf F,Scherzer O,Leito A.Analysis of regularization methods for the solution of ill-posed problems involving discontinuous operators[J].SIAM Journal on Numerical Analysis,2005,43(2):767-786.
[16]Hansen P C,O'Leary D P.The use of the L-curve in the regularization of discrete ill-posed problems[J].SIAM Journal on Scientific Computing,1993,14(6):1487-1503.
[17]Burger M,Kaltenbacher B.Regularizing newton-kaczmarz methods for nonlinear ill-posed problems[J].SIAM Journal on Numerical Analysis,2007,44(1):153-182.
[18]Kaltenbacher B.Regularization by truncated Cholesky factorization:A comparison of four different approaches[J].Journal of Complexity,2007,23:225-244.
[19]Kaltenbacher B.Some Newton-type methods for the regularization of nonlinear ill-posed problems[J].Inverse Problems,1997,13:729-753.
[20]Haber E,Oldenburg D.A GCV based method for nonlinear ill-posed problems[J].Computational Geosciences,2000,4:41-63.
[21]Wang J J,Li G S.A Modified Tikhonov regularization method for solving ill-posed problems[J].Chinese Quarterly Journal of Mathematics,2000,15(2):98-101.
[22]Neubauer A.Tikhonov regularisation for non-linear ill-posed problems:Optimal convergence rates and finite-dimensional approximation[J].Inverse Problems,1989,5:541-557.
[23]Honerkamp J,Weese J.Tikhonovs regularization method for ill-posed problems[J].Continuum Mechanics and Thermodynamics,1990,2:17-30.
[24]Lu S,Pereverzev S V,Ramlau R.An analysis of Tikhonov regularization for nonlinear ill-posed problems under a general smoothness assumption[J].Inverse Problems,2007,23:217-230.
[25]Bokmann C,Pornsawad P.Iterative Runge-Kutta-type methods for nonlinear ill-posed problems[J].Inverse Problems,2008,24,doi:10.1088/0266-5611/24/2/025002.
[26]Scherzer O,Linz.The use of Morozov'discrepancy principle for Tikhonov regularization for solving non-inear ill-osed problems[J].Computing,1993,51:45-60.
[27]Bonesky T.Morozov's discrepancy principle and Tikhonov-type functionals[J].Inverse Problems,2009,25,doi:10.1088/0266-5611/25/1/01501528.
[28]Routh P S,Oldenburg D W.Inversion of controlled source audio-frequency magnetotellurics data for a horizontally layered earth[J].Geophysics,1999,64(6):1689-1697.