石明+冯德山+李开鹏+王珣

摘 要：从Maxwell方程出发，开展了三维大地电磁场所满足的边值问题研究，利用加权余量法导出了三维大地电磁有限元方程.介绍了三维矢量有限元六面体网格剖分方式、插值基函数选取，推导了三维大地电磁矢量有限元正演的单元刚度系数矩阵及离散格式.编制了三维矢量有限元大地电磁正演的Matlab程序.三维COMMEMI 3D-1模型的视电阻率曲线与国际通用的标准测试数据能很好地拟合，验证了作者编写的矢量有限元正演程序的正确性.通过对高、低阻异常体的阻抗张量形态分析，说明张量阻抗等值线图能用以大致判断异常体特性，丰富了大地电磁响应特征的表达方式.

关键词：矢量有限元；大地电磁；正演模拟；张量阻抗

中图分类号：P631 文献标识码：A

文章编号：1674-2974（2016）10-0119-07

Abstract：Starting from the Maxwell equations， this article studied the boundary conditions of 3D MT. By using the weighted residual method， we derived the three-dimensional MT finite element equation. The three-dimensional vector finite element hexahedral meshing mode was introduced and the basis functions were selected. Then we derived the three-dimensional magnetotelluric vector finite element stiffness coefficient matrix and discrete format. A three-dimensional vector finite element magnetotelluric forward Matlab program was done. The apparent resistivity curve of the dimensional COMMEMI 3D-1 model matches the international standard test data， which proves the correctness of 3D magnetotelluric forward program. With the analysis of high and low resistivity anomalies， it shows that tensor impedance map can roughly determine the anomaly characteristics， which enriches the magnetotelluric response characteristics of expression.

Key words：vector finite element method；magnetotelluric； forward modeling； impedance tensor

大地电磁（MT）是以电离层激发的天然交变电磁场为场源，在地表观测相互正交的电场、磁场分量来获取地电构造信息的一种重要地球物理勘探方法[1].MT不需要庞大的发射源设备，只需采用比较轻便的接收设备，野外工作方便、成本低，被广泛应用于地壳和上地幔电性结构的研究，在石油天然气勘探、矿产资源勘探、工程与环境普查等领域，发挥着举足轻重的作用[2-9].可以预见，三维MT勘探技术是地球物理中深层领域的研究热点及今后MT的发展趋势，而三维MT正演是理解MT勘探物理现象并认识地质体电磁响应规律的有效手段，显然尤其重要.

尽管矢量FEM拥有诸多优点，但……