基于自适应加密的三维全电流RMT有限元-无限元耦合正演

Radio-magnetotelluric (RMT) is an important method for shallow subsurface exploration. In order to understand the features of three-dimensional (3D) RMT responses and the effects of displacement current on RMT data, this project will develop a high-precision 3D RMT numerical simulation program, taking into account multiple factors, such as topography, the three-dimensional geo-electric structure with dual parameter of resistivity and permittivity. Research aspects will also contain fast forward modeling with high-precision, which based on an adaptive mesh refinement algorithm and the finite element-infinite element couple method. First, we will derive the boundary value problem for the 3D RMT total electric field problem with consideration of the displacement currents. Then we employ an unstructured tetrahedron grid to subdivide the target area, adopt posterior error estimators to calculate the element errors, and then adaptively refine the meshes. Thus, a high accuracy calculation for electromagnetic response will be realized with the optimal mesh discretization strategy. After that, an unstructured triangular prism is used for the discretization of the boundary area. We then can construct the finite element infinite element coupling equations, and solve the equations to obtain the electric fields. Finally, we will study the effect of displacement current on the RMT responses with the calculation and analysis of typical models. This project can help to understand the characteristics of RMT responses, which can effectively improve the quality of analysis and interpretation of RMT data.

射线大地电磁法（radio-magnetotelluric，RMT）是浅地表勘探的重要手段之一。为深入认识三维RMT响应的特征及位移电流的影响机制，本项目拟开发高精度的全电流三维RMT数值模拟程序，综合考虑起伏地形、电阻率及介电常数双参数三维地电结构，开展基于自适应网格加密算法和有限元-无限元耦合技术的快速高精度正演研究。首先，推导全电流三维RMT电场总场边值问题；然后采用非结构四面体网格对目标区域进行离散，并通过后验误差估计算法，对网格进行自适应加密，从而基于最优的网格划分实现高精度的电磁响应计算；之后，以非结构三棱柱体对目标区域边界离散，采用有限元-无限元耦合技术，构建耦合方程组，求解方程组获得电场值；最后，通过典型模型计算及分析，研究多因素控制下的RMT位移电流影响机制。本项目将深入认识RMT响应的数据特征，提高RMT实测资料的分析与解释水平。

射频大地电磁法(Radio-magnetotelluric, RMT)是百米内浅地表电磁勘探的重要手段之一。由于勘探频段为10k-300kHz，其电磁场传播同时受地下电阻率和介电常数两种电性参数共同作用。传统准静态条件下的电磁场数值模拟软件严重制约RMT正演模拟精度，阻碍了后续反演解译准确性。为此，本项目针对RMT三维全电流电磁响应快速高精度计算开展了以下工作：（1）综合考虑起伏地形、三维地电结构、电阻率及介电常数双参数等因素，构建了同时考虑位移电流与传导电流的全电流电磁场边值问题，结合后验误差估计算法，开发了Linux系统下基于Fortran语言的三维RMT自适应矢量有限元模拟软件。（2）设计了满足RMT电磁场衰减规律的无限元形函数，提出了有限元-无限元耦合技术，采用非结构四面体网格进行测区离散及有限元分析，利用三棱柱无限元网格处理测区外的截断边界，大大减少方程组未知量，实现了三维RMT快速高精度正演计算。（3）将项目所开发软件应用于几种典型RMT模型数值计算，深入认识了RMT响应的数据特征及多因素控制下的位移电流影响规律，证明了所开发正演算法的高效性和准确性。项目成果对推动RMT三维正反演技术的发展、提高RMT实测资料的分析与解释水平具有重要的理论及实际意义。

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