基于阈值约束的协克里金法联合反演重力与重力梯度数据
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摘要
常规协克里金方法反演重力或重力梯度数据具有抗噪性好、加入先验信息容易等优点,其反演的地下密度分布能够识别异常体中心位置,还原异常体基本形态,但反演图像光滑,分辨率低,这是由于常规方法估计的密度协方差矩阵全局发散、平稳.为了通过协克里金方法获得聚焦的密度分布需要改善密度协方差矩阵的性质.首先,本文推导了理论密度协方差公式,其性质表明,当理论模型聚焦分布时,其密度协方差矩阵是非平稳且聚焦分布的.为了打破常规协方差矩阵全局平稳、发散的特征,本文设置密度阈值处理协方差矩阵,通过不断更新协方差矩阵来迭代实现协克里金反演,最终得到相对聚焦的反演结果.用本文方法处理重力与重力梯度数据恢复两种密度模型,均得到了与正演模型匹配的反演结果;再将方法运用于文顿盐丘的实际测量重力与重力梯度数据,反演结果与已知的地质情况匹配较好.
The conventional Cokriging inversion of gravity and gravity gradient data has the advantages of good anti-noise performance and being easy to add prior information.And this method can identify the position of the anomaly body and to restore its basic shape.But the inversion image of this approach is smooth and its resolution is low which are due to the density covariance matrix estimated by the conventional method are of global divergence and stationary.So the performance of the density covariance matrix has to be improved for getting focusing density distribution by the Cokriging inversion.Firstly,this paper deduces the theoretical formula of density covariance matrix,which proves that the density covariance matrix is nonstationary and focused when the theoretical model is compact.In order to break the global stationary and divergence of the conventional covariance matrix,we set a density threshold to deal with the covariance matrix and update the covariance matrix to iteratively perform Cokriginginversion until the focused results are obtained.Then we set two kinds of forward models to testify our methods,showing the recovered models match with the forward models.Finally we use our method to process the gravity and gravity gradient data from the Vinton salt dome,and the inversion results are in good agreement with the known geological structures.
The conventional Cokriging inversion of gravity and gravity gradient data has the advantages of good anti-noise performance and being easy to add prior information.And this method can identify the position of the anomaly body and to restore its basic shape.But the inversion image of this approach is smooth and its resolution is low which are due to the density covariance matrix estimated by the conventional method are of global divergence and stationary.So the performance of the density covariance matrix has to be improved for getting focusing density distribution by the Cokriging inversion.Firstly,this paper deduces the theoretical formula of density covariance matrix,which proves that the density covariance matrix is nonstationary and focused when the theoretical model is compact.In order to break the global stationary and divergence of the conventional covariance matrix,we set a density threshold to deal with the covariance matrix and update the covariance matrix to iteratively perform Cokriginginversion until the focused results are obtained.Then we set two kinds of forward models to testify our methods,showing the recovered models match with the forward models.Finally we use our method to process the gravity and gravity gradient data from the Vinton salt dome,and the inversion results are in good agreement with the known geological structures.
引文
Asli M,Marcotte D,Chouteau M.2000.Direct inversion of gravity data by Cokriging.∥Proceedings of the 6th International Geostatistics Congress-Geostat 2000.Marshalltown:Geostatistical Association of South Africa,64-73.
Chasseriau P,Chouteau M.2003.3D gravity inversion using a model of parameter covariance.Journal of Applied Geophysics,52(1):59-74.
Coker M O,Bhattacharya J P,Marfurt K J.2007.Fracture Patterns within mudstones on the flanks of a salt dome:syneresis or slumping?Gulf Coast Association of Geological Societies Transaction,57:125-137.
Ennen C.2012.Mapping gas-charged fault blocks around the Vinton Salt Dome,Louisiana using gravity gradiometry data[Master’s thesis].Houston:University of Houston.
Fedi M,Hansen P C,Paoletti V.2005.Analysis of depth resolution in potential-field inversion.Geophysics,70(6):A1-A11.
Gallardo L A,Meju M A.2003.Characterization of heterogeneous near-surface materials by joint 2Dinversion of dc resistivity and seismic data.Geophysical Research Letters,30(13):1658.
Gao J,Zhang H J.2016.Two-dimensional joint inversion of seismic velocity and electrical resistivity using seismic travel times and full channel electrical measurements based on alternating crossgradient structural constraint.ChineseJournalofGeophysics(in Chinese),59(11):4310-4322,doi:10.6038/cjg20161131.
Gao X H,Huang D N.2017.Research on 3Dfocusing inversion of gravity gradient tensor data based on a conjugate gradient algorithm.Chinese Journal of Geophysics(in Chinese),60(4):1571-1583,doi:10.6038/cjg20170429.
Geng M X,Huang D N,Yang Q J,et al.2014.3Dinversion of airborne gravity-gradiometry data using Cokriging.Geophysics,79(4):G37-G47.
Geng M X,Huang D N,Yu P,et al.2016.Three-dimensional constrained inversion of full tensor gradiometer data based on Cokriging method.Chinese Journal of Geophysics(in Chinese),59(5):1849-1860,doi:10.6038/cjg20160528.
Gloaguen E,Marcotte D,Chouteau M,et al.2005.Borehole radar velocity inversion using Cokriging and cosimulation.Journal of Applied Geophysics,57(4):242-259.
Higdon D,Swall J,Kern J.1999.Non-stationary spatial modeling.∥Proceedings of the Bayesian Statistics 6.Proceedings of the Sixth Valencia International Meeting.Oxford:Oxford Univ.Press,761-768.
Last B J,Kubik K.1983.Compact gravity inversion.Geophysics,48(6):713-721.
Li Y G,Oldenburg D W.1996.3-D inversion of magnetic data.Geophysics,61(2):394-408.
Li Y G,Oldenburg D W.1998.3-D inversion of gravity data.Geophysics,63(1):109-119.
Lin W,Zhdanov M S.2018.Joint multinary inversion of gravity and magnetic data using Gramian constraints.Geophysical Journal International,215(3):1540-1557.
Myers D E.1982.Matrix formulation of co-kriging.Journal of the International Association for Mathematical Geology,14(3):249-257.
Qin P B,Huang D N.2016.Integrated gravity and gravity gradient data focusing inversion.Chinese Journal of Geophysics(in Chinese),59(6):2203-2224,doi:10.6038/cjg20160624.
Shamsipour P,Marcotte D,Chouteau M,et al.2010.3Dstochastic inversion of gravity data using Cokriging and cosimulation.Geophysics,75(1):I1-I10.
Shamsipour P,Chouteau M,Marcotte D.2011.3D stochastic inversion of magnetic data.Journal of Applied Geophysics,73(4):336-347.
Shamsipour P,Marcotte D,Chouteau M,et al.2013.3Dstochastic
gravity inversion using nonstationary covariances.Geophysics,78(2):G15-G24.
Sun J,Li Y.2015.Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering.Geophysics,80(4):ID1-ID18.
Yin C C,Sun S Y,Gao X H,et al.2018.3Djoint inversion of magnetotelluric and gravity data based on local correlation constraints.Chinese Journal of Geophysics(in Chinese),61(1):358-367,doi:10.6038/cjg2018K0765.
Yu P,Wang J L,Wu J S,et al.2007.Constrained joint inversion of gravity and seismic data using the simulated annealing algorithm.Chinese Journal of Geophysics(in Chinese),50(2):529-538,doi:10.3321/j.issn:0001-5733.2007.02.026.
Zhdanov M S.2002.Geophysical Inverse Theory and Regularization Problems.Amsterdam:Elsevier.
Zhdanov M S.2009.New advances in regularized inversion of gravity and electromagnetic data.Geophysical Prospecting,57(4):463-478.
Zhdanov M S,Gribenko A,Wilson G.2012.Generalized joint inversion of multimodal geophysical data using Gramian constraints.Geophysical Research Letters,39(9).
高级,张海江.2016.基于交叉梯度交替结构约束的二维地震走时与全通道直流电阻率联合反演.地球物理学报,59(11):4310-4322,doi:10.6038/cjg20161131.
高秀鹤,黄大年.2017.基于共轭梯度算法的重力梯度数据三维聚焦反演研究.地球物理学报,60(4):1571-1583,doi:10.6038/cjg20170429.
耿美霞,黄大年,于平等.2016.基于协同克里金方法的重力梯度全张量三维约束反演.地球物理学报,59(5):1849-1860,doi:10.6038/cjg20160528.
秦朋波,黄大年.2016.重力和重力梯度数据联合聚焦反演方法.地球物理学报,59(6):2203-2224,doi:10.6038/cjg20160624.
殷长春,孙思源,高秀鹤等.2018.基于局部相关性约束的三维大地电磁数据和重力数据的联合反演.地球物理学报,61(1):358-367,doi:10.6038/cjg2018K0765.
于鹏,王家林,吴健生等.2007.重力与地震资料的模拟退火约束联合反演.地球物理学报,50(2):529-538,doi:10.3321/j.issn:0001-5733.2007.02.026.
Chasseriau P,Chouteau M.2003.3D gravity inversion using a model of parameter covariance.Journal of Applied Geophysics,52(1):59-74.
Coker M O,Bhattacharya J P,Marfurt K J.2007.Fracture Patterns within mudstones on the flanks of a salt dome:syneresis or slumping?Gulf Coast Association of Geological Societies Transaction,57:125-137.
Ennen C.2012.Mapping gas-charged fault blocks around the Vinton Salt Dome,Louisiana using gravity gradiometry data[Master’s thesis].Houston:University of Houston.
Fedi M,Hansen P C,Paoletti V.2005.Analysis of depth resolution in potential-field inversion.Geophysics,70(6):A1-A11.
Gallardo L A,Meju M A.2003.Characterization of heterogeneous near-surface materials by joint 2Dinversion of dc resistivity and seismic data.Geophysical Research Letters,30(13):1658.
Gao J,Zhang H J.2016.Two-dimensional joint inversion of seismic velocity and electrical resistivity using seismic travel times and full channel electrical measurements based on alternating crossgradient structural constraint.ChineseJournalofGeophysics(in Chinese),59(11):4310-4322,doi:10.6038/cjg20161131.
Gao X H,Huang D N.2017.Research on 3Dfocusing inversion of gravity gradient tensor data based on a conjugate gradient algorithm.Chinese Journal of Geophysics(in Chinese),60(4):1571-1583,doi:10.6038/cjg20170429.
Geng M X,Huang D N,Yang Q J,et al.2014.3Dinversion of airborne gravity-gradiometry data using Cokriging.Geophysics,79(4):G37-G47.
Geng M X,Huang D N,Yu P,et al.2016.Three-dimensional constrained inversion of full tensor gradiometer data based on Cokriging method.Chinese Journal of Geophysics(in Chinese),59(5):1849-1860,doi:10.6038/cjg20160528.
Gloaguen E,Marcotte D,Chouteau M,et al.2005.Borehole radar velocity inversion using Cokriging and cosimulation.Journal of Applied Geophysics,57(4):242-259.
Higdon D,Swall J,Kern J.1999.Non-stationary spatial modeling.∥Proceedings of the Bayesian Statistics 6.Proceedings of the Sixth Valencia International Meeting.Oxford:Oxford Univ.Press,761-768.
Last B J,Kubik K.1983.Compact gravity inversion.Geophysics,48(6):713-721.
Li Y G,Oldenburg D W.1996.3-D inversion of magnetic data.Geophysics,61(2):394-408.
Li Y G,Oldenburg D W.1998.3-D inversion of gravity data.Geophysics,63(1):109-119.
Lin W,Zhdanov M S.2018.Joint multinary inversion of gravity and magnetic data using Gramian constraints.Geophysical Journal International,215(3):1540-1557.
Myers D E.1982.Matrix formulation of co-kriging.Journal of the International Association for Mathematical Geology,14(3):249-257.
Qin P B,Huang D N.2016.Integrated gravity and gravity gradient data focusing inversion.Chinese Journal of Geophysics(in Chinese),59(6):2203-2224,doi:10.6038/cjg20160624.
Shamsipour P,Marcotte D,Chouteau M,et al.2010.3Dstochastic inversion of gravity data using Cokriging and cosimulation.Geophysics,75(1):I1-I10.
Shamsipour P,Chouteau M,Marcotte D.2011.3D stochastic inversion of magnetic data.Journal of Applied Geophysics,73(4):336-347.
Shamsipour P,Marcotte D,Chouteau M,et al.2013.3Dstochastic
gravity inversion using nonstationary covariances.Geophysics,78(2):G15-G24.
Sun J,Li Y.2015.Multidomain petrophysically constrained inversion and geology differentiation using guided fuzzy c-means clustering.Geophysics,80(4):ID1-ID18.
Yin C C,Sun S Y,Gao X H,et al.2018.3Djoint inversion of magnetotelluric and gravity data based on local correlation constraints.Chinese Journal of Geophysics(in Chinese),61(1):358-367,doi:10.6038/cjg2018K0765.
Yu P,Wang J L,Wu J S,et al.2007.Constrained joint inversion of gravity and seismic data using the simulated annealing algorithm.Chinese Journal of Geophysics(in Chinese),50(2):529-538,doi:10.3321/j.issn:0001-5733.2007.02.026.
Zhdanov M S.2002.Geophysical Inverse Theory and Regularization Problems.Amsterdam:Elsevier.
Zhdanov M S.2009.New advances in regularized inversion of gravity and electromagnetic data.Geophysical Prospecting,57(4):463-478.
Zhdanov M S,Gribenko A,Wilson G.2012.Generalized joint inversion of multimodal geophysical data using Gramian constraints.Geophysical Research Letters,39(9).
高级,张海江.2016.基于交叉梯度交替结构约束的二维地震走时与全通道直流电阻率联合反演.地球物理学报,59(11):4310-4322,doi:10.6038/cjg20161131.
高秀鹤,黄大年.2017.基于共轭梯度算法的重力梯度数据三维聚焦反演研究.地球物理学报,60(4):1571-1583,doi:10.6038/cjg20170429.
耿美霞,黄大年,于平等.2016.基于协同克里金方法的重力梯度全张量三维约束反演.地球物理学报,59(5):1849-1860,doi:10.6038/cjg20160528.
秦朋波,黄大年.2016.重力和重力梯度数据联合聚焦反演方法.地球物理学报,59(6):2203-2224,doi:10.6038/cjg20160624.
殷长春,孙思源,高秀鹤等.2018.基于局部相关性约束的三维大地电磁数据和重力数据的联合反演.地球物理学报,61(1):358-367,doi:10.6038/cjg2018K0765.
于鹏,王家林,吴健生等.2007.重力与地震资料的模拟退火约束联合反演.地球物理学报,50(2):529-538,doi:10.3321/j.issn:0001-5733.2007.02.026.