大地电磁测深与地震初至波走时交叉梯度反演
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摘要
在地球物理勘探过程中,观测数据有限且存在误差,导致反演结果存在非唯一解。为了解决非唯一性问题,笔者研究了交叉梯度数学理论,实现了用交叉梯度约束2D大地电磁和地震初至波走时的联合反演,并建立了2个模型。通过各自模型实验和不同模型间的对比,证明了交叉梯度联合反演比单独反演修复几何形态和物性参数的效果好,且交叉梯度与岩石物性无关;利用得到的交叉梯度图进一步证明了联合反演模型相似度高,也从交叉绘图中得到联合反演的物性关系更好的结论,反向证明了联合反演的正确性。
In the process of geophysical exploration,observation data are limited and errors exist,leading to the presence of non-unique inversion results.In order to solve the problem of non-uniqueness,the authors study the mathematical theory of cross-gradient,and achieve the joint inversion of 2D magnetotelluric and first-arrival wave seismic traveltime with cross-gradient.At the same time,we establish two models.Through test of each model and comparison between the two models,it is proven not only that the result of the cross-gradient joint inversion is better than the single inversion in remediation on geometry and physical property parameters,but also that the cross-gradient is independent from the petro-physical properties.Further,the cross-gradient figure evidences the high similarity of the joint inversion models,and the cross-plot of joint inversion presents a better correlation with physical properties.These,in turn,prove the validity of the joint inversion.
In the process of geophysical exploration,observation data are limited and errors exist,leading to the presence of non-unique inversion results.In order to solve the problem of non-uniqueness,the authors study the mathematical theory of cross-gradient,and achieve the joint inversion of 2D magnetotelluric and first-arrival wave seismic traveltime with cross-gradient.At the same time,we establish two models.Through test of each model and comparison between the two models,it is proven not only that the result of the cross-gradient joint inversion is better than the single inversion in remediation on geometry and physical property parameters,but also that the cross-gradient is independent from the petro-physical properties.Further,the cross-gradient figure evidences the high similarity of the joint inversion models,and the cross-plot of joint inversion presents a better correlation with physical properties.These,in turn,prove the validity of the joint inversion.
引文
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[14]Wannamaker P E,Stodt J A,Rijo L.A Stable Finite Element Solution for Two-Dimensional Magnetotelluric Modeling[J].Geophys J R,1987,88:277-296.
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[16]朴英哲,李桐林,刘永亮,等.在大地电磁二维Occam反演中求取拉格朗日算子方法的改进[J].吉林大学学报:地球科学版,2014,44(2):660-667.Pak Yongchol,Li Tonglin,Liu Yongliang,et al.Improvement of Choosing Lagrange Multiplier on MT2DOccam Inversion[J].Journal of Jilin University:Earth Science Edition,2014,44(2):660-667.
[17]de Groot-Hedlin C D,Constable S C.Occam’s Inversion to Generate Smooth,Two-Dimensional Models from Magnetotelluric Data[J].Geophysics,1990,93:1613-1624.
[18]Constable S C,Parker K L,Constable C G.Occam’s Inversion a Practical Algorithm for Generating Smooth Models from EM Sounding Data[J].Geophysics,1987,52:289-300.
[2]于鹏,王家林,吴健生,等.地球物理联合反演的研究现状和分析[J].勘探地球物理进展,2006,29(2):87-93.Yu Peng,Wang Jialin,Wu Jiansheng,et al.Research Status and Analysis of Joint Inversion[J].Progress in Exploration Geophysics,2006,29(2):87-93.
[3]Heincke B,Hobbs R.Joint Inversion of MT,Gravity and Seismic Data Applied to Sub-Basalt Imaging[C]//Annual Meeting.New Orleans:SEG,2006:784-787.
[4]Colombo D,Stefano M D.Geophysical Modeling via Simultaneous Joint Inversion of Seismic Gravity,and Electromagnetic Data:Application to Prestack Depth Imaging[J].The Leading Edge,2007,26(3):326-331.
[5]Haber E,Oldenburg D.Joint Inversion:A Structural Approach Inverse Problems[J].IOP Science,1997,13:63-77.
[6]Zhang J,Morgan F D.Joint Seismic and Electrical Tomography[C]//Symposium on the Application of Geophysics to Engineering and Environmental Problems.[S.l.]:SEG,1997:391-396.
[7]Gallardo L A,Meju M A.Characterization of Heterogeneous Near-Surface Materials by Joint 2DInversion of DC Resistivity and Seismic Data[J].Geophysical Research Letters,2003,30(13):1658-1661.
[8]彭淼,谭捍东,姜枚,等.基于交叉梯度耦合的大地电磁与地震走时资料三维联合反演[J].地球物理学报,2013,56(8):2728-2738.Peng Miao,Tan Handong,Jiang Mei,et al.ThreeDimension Joint Inversion Magnetotelluric and Seismic Travel Time Data with Cross-Gradient Constraints[J].Chinese Journal of Geophysics,2013,56(8):2728-2738.
[9]王俊,孟小红,陈朝曦,等.交叉梯度理论及其在地球物理联合反演中的应用[J].地球物理学进展,2013,28(4):2094-2103.Wang Jun,Meng Xiaohong,Chen Zhaoxi,et al.The Theory of Cross-Gradient and Its Application in Geophysical Joint Inversion[J].Progress in Geophysics,2013,28(4):2094-2103.
[10]Gallardo L A,Meju M A.Joint Two-Dimensional DC Resistivity and Seismic Travel Time Inversion with Cross-Gradients Constraints[J].Jouranl of Geophsical Research,2004,109:3311.
[11]Vidale J.Finite-Difference Calculation of Travel-Times in Three Dimenisons[J].Geophysics,1990,55:521-526.
[12]Zelt C A,Barton P J.Three-Dimensional Seismic Refraction Tomography:A Comparison of Two Methods Applied to Data from the Faeroe Basin[J].Geophys Res,1998,103:7187-7210.
[13]刘小军,王家林,于鹏,等.基于二次场的二维大地电磁有限元法数值模拟[J].同济大学学报:自然科学版,2007,35(8):1113-1117.Liu Xiaojun,Wang Jialin,Yu Peng,et al.Numerical Simulation of Two-Dimensional Magnetotelluric Secondary Field Based on the Finite Element Method[J].Journal of Tongji University:Natural Science,2007,35(8):1113-1117.
[14]Wannamaker P E,Stodt J A,Rijo L.A Stable Finite Element Solution for Two-Dimensional Magnetotelluric Modeling[J].Geophys J R,1987,88:277-296.
[15]de Lugao P P,Wannamaker P E.Calculating the Two-Dimensional Magnetotlluric Jacobian in Finite Elements Using ReciProcity[J].Geophys J,1996,127:806-810.
[16]朴英哲,李桐林,刘永亮,等.在大地电磁二维Occam反演中求取拉格朗日算子方法的改进[J].吉林大学学报:地球科学版,2014,44(2):660-667.Pak Yongchol,Li Tonglin,Liu Yongliang,et al.Improvement of Choosing Lagrange Multiplier on MT2DOccam Inversion[J].Journal of Jilin University:Earth Science Edition,2014,44(2):660-667.
[17]de Groot-Hedlin C D,Constable S C.Occam’s Inversion to Generate Smooth,Two-Dimensional Models from Magnetotelluric Data[J].Geophysics,1990,93:1613-1624.
[18]Constable S C,Parker K L,Constable C G.Occam’s Inversion a Practical Algorithm for Generating Smooth Models from EM Sounding Data[J].Geophysics,1987,52:289-300.
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