起伏地形条件下大地电磁测深二维正反演研究及应用
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摘要
自20世纪70年代以来,复杂地表条件下的地球物理场数值模拟和反演成像问题一直受到研究者和工程师们的重视。尽管到目前为止与此有关的大多数问题还没有得到彻底的解决,但是已经取得了令人瞩目的进展。就复杂地表条件下的地球物理场数值模拟与反演成像来讲,目前的状态是进展与问题并存、机遇与挑战同在。起伏地形对大地电磁测深(MT)二维数据影响很大,如果不考虑起伏地形引起的大地电磁场畸变,将使大地电磁资料产生显著误差,其解释结果必然偏离实际构造,给实测资料的解释带来了相当大的困难,因此,起伏地形影响是山区开展工作必须着重考虑的问题。只有从正演理论上正确认识起伏地形的影响,才能在野外资料处理中给出正确的解释,而对于起伏地形条件下的二维正演问题来说,电磁场没有解析表达式,需要借助数值模拟方法；为了完全消除地形效应,实现带地形的二维反演是提高资料处理解释水平唯一途径。鉴于此,本文开展“起伏地形条件下MT二维正反演研究及应用”是非常必要的,具有重要的理论意义和现实意义。
首先,从电磁场满足的微分方程、边值问题和变分问题出发,实现了起伏地形下MT二维正演模拟的有限元计算算法。(1)研究了起伏地形的网格剖分,对传统方法进行了修正处理,从而使修正后的网格剖分更适合电磁场的分布规律；(2)讨论了大型稀疏复系数方程组的迭代解法。(3)为了验证起伏地形条件下MT二维正演算法的正确性,将二维正演模拟结果和一维正演计算的解析解进行对比,并对COMMEMI 2D-O测试模型进行了正演分析；(4)分析了山脊、山谷等起伏地形对MT响应的影响,得出了一些重要结论,为实际工作提供了理论指导作用。
其次,以最小二乘光滑约束反演算法为基础,分析了灵敏度矩阵的求解、反演方程组的迭代解法以及正则化因子的选取问题,实现了带地形的MT二维反演成像。通过理论模型试算,两种极化模式的反演结果都能真实地反映模型的地电参数,对于低阻异常体,TE极化模式的反演结果比TM极化模式显得更为敏感。另外,联合两种极化模式的数据同时进行反演的结果更能反映出模型的地电参数。
最后,对实测的V5-2000数据进行资料处理,分别从定性分析解释和反演定量解释两方面讨论MT的资料处理。
Since 1970s, most researchers have concentrated on numerical modeling and inversion of geophysical problem with complex geometry. So far, effort on many problems is still undergoing and some significant progress already has been made. Numerical modeling and inversion under complex situation are challenging and under development. The complex geometry brings significant impact in the magnetotelluric data, measuring at the surface. Without considering the complex geometry, sometimes it gives biased interpretation, likewise biased inverted structure and lead to difficulty in interpretation of the field data, therefore, in the fieldwork with complex fluctuation, the geometry impact should be taken into account seriously. It is import to theoretically modeling the problem with complex geometry and its impact on the modeling results, which in turn assists the interpretation of real measuring data. For 2-dimensional (2D) problem with complex geometry, no analytical solution exists, and numerical modeling is needed to solve it. The only way to eliminate the geometry effect is to fully consider the problem with geometry modeling. It is important to carry out the research of 2D forward modeling and inversion with topography either theoretically or pratically.
Firstly, based on the electromagnetic propagation equations, boundary problem and variational problem, finite element method are used to modeling 2D MT problem with complex geometry. The work has been done as follows:(1) Correction scheme according the distribution of electromagnetic fields are proposed to the traditional grid generation; (2) Brief discussion are forwarded in the solver of large sparse matrix with complex entries; (3) 2D Modeling results are compared with 1D results for validity and modeling analysis are carried out for COMMEMI 2D-0 model; (4) Some important results are made after the modeling of the impact of geometries (e.g., ridges and valleys), which give theoretical help in practice.
Secondly, the 2D inversion was carried out with least square method with smooth constraint, in which the calculation of sensitivity matrix and iterative solver of the inversion equations and the choice of the tradeoff parameter are analyzed. From the results, the inversion of TM and TE reflects the true geo-electrical structure and TE mode is much more sensitive to the low resistivity structure than TM mode. The hybrid inversion of both polarization data gives better interpretation for the geo-electrical structure.
Lastly, the inversion was implemented for V5-2000 field data and discussed from the qualitative analysis interpretation and quantitative interpretation of inversion.
首先,从电磁场满足的微分方程、边值问题和变分问题出发,实现了起伏地形下MT二维正演模拟的有限元计算算法。(1)研究了起伏地形的网格剖分,对传统方法进行了修正处理,从而使修正后的网格剖分更适合电磁场的分布规律；(2)讨论了大型稀疏复系数方程组的迭代解法。(3)为了验证起伏地形条件下MT二维正演算法的正确性,将二维正演模拟结果和一维正演计算的解析解进行对比,并对COMMEMI 2D-O测试模型进行了正演分析；(4)分析了山脊、山谷等起伏地形对MT响应的影响,得出了一些重要结论,为实际工作提供了理论指导作用。
其次,以最小二乘光滑约束反演算法为基础,分析了灵敏度矩阵的求解、反演方程组的迭代解法以及正则化因子的选取问题,实现了带地形的MT二维反演成像。通过理论模型试算,两种极化模式的反演结果都能真实地反映模型的地电参数,对于低阻异常体,TE极化模式的反演结果比TM极化模式显得更为敏感。另外,联合两种极化模式的数据同时进行反演的结果更能反映出模型的地电参数。
最后,对实测的V5-2000数据进行资料处理,分别从定性分析解释和反演定量解释两方面讨论MT的资料处理。
Since 1970s, most researchers have concentrated on numerical modeling and inversion of geophysical problem with complex geometry. So far, effort on many problems is still undergoing and some significant progress already has been made. Numerical modeling and inversion under complex situation are challenging and under development. The complex geometry brings significant impact in the magnetotelluric data, measuring at the surface. Without considering the complex geometry, sometimes it gives biased interpretation, likewise biased inverted structure and lead to difficulty in interpretation of the field data, therefore, in the fieldwork with complex fluctuation, the geometry impact should be taken into account seriously. It is import to theoretically modeling the problem with complex geometry and its impact on the modeling results, which in turn assists the interpretation of real measuring data. For 2-dimensional (2D) problem with complex geometry, no analytical solution exists, and numerical modeling is needed to solve it. The only way to eliminate the geometry effect is to fully consider the problem with geometry modeling. It is important to carry out the research of 2D forward modeling and inversion with topography either theoretically or pratically.
Firstly, based on the electromagnetic propagation equations, boundary problem and variational problem, finite element method are used to modeling 2D MT problem with complex geometry. The work has been done as follows:(1) Correction scheme according the distribution of electromagnetic fields are proposed to the traditional grid generation; (2) Brief discussion are forwarded in the solver of large sparse matrix with complex entries; (3) 2D Modeling results are compared with 1D results for validity and modeling analysis are carried out for COMMEMI 2D-0 model; (4) Some important results are made after the modeling of the impact of geometries (e.g., ridges and valleys), which give theoretical help in practice.
Secondly, the 2D inversion was carried out with least square method with smooth constraint, in which the calculation of sensitivity matrix and iterative solver of the inversion equations and the choice of the tradeoff parameter are analyzed. From the results, the inversion of TM and TE reflects the true geo-electrical structure and TE mode is much more sensitive to the low resistivity structure than TM mode. The hybrid inversion of both polarization data gives better interpretation for the geo-electrical structure.
Lastly, the inversion was implemented for V5-2000 field data and discussed from the qualitative analysis interpretation and quantitative interpretation of inversion.
引文
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