基于Lorenz规范条件下磁矢势和标势耦合方程的频率域电磁法三维正演

为了克服空气层和地表耦合以及避免一次场计算,开发适合不同类型场源、不同应用范围的频率域三维正演模拟统一平台,本文从麦克斯韦基本方程出发,推导基于Lorenz规范条件的磁矢势和标势耦合方程;通过将不同类型场源分解成一系列短导线(电性)源组合,采用交错网格采样和有限体积技术对方程进行离散得到对称大型稀疏线性方程组,并采用Jacobi迭代预处理QMR(Quasi-Minimum-Residual,拟最小残差)算法进行求解,我们成功实现不同类型场源、不同应用范围的频率域电磁法三维正演模拟.通过层状模型下大地电磁法以及有限长接地导线和大回线磁性源激发下的电磁场响应模拟,并与一维解析解对比验证算法的有效性.进而,我们利用该算法平台的模拟结果对典型地电模型在不同场源激发下频率域电磁法响应特征进行对比分析.本文算法研究及实现为建立频率域电磁法三维正反演统一框架打下基础.

A finite-volume solution to 3D frequency-domain electromagnetic modelling using Lorenz-gauged magnetic vector and scalar potentials

To eliminate the coupling between air and the earth and to avoid calculation of primary field, we develop a universal algorithm on forward modelling of the frequency-domain electromagnetic (EM) method for different source types and applications. We first present a magnetic vector and a scalar potential with Lorenz gauge based on Maxwell equation, then divide different sources into a lot of short wires. Next, we use staggered grids and the finite volume method to discrete the potential equations and implement the quasi-minimum-residual (QMR) iteration with Jacob to solve the large sparse and symmetrical linear equations system. Finally, we accomplish frequency-domain EM modelling for different source types and application areas. Through analyses and comparison of 1D and 3D MT, CSAMT and loop source responses, we demonstrate the efficiency and accuracy of the algorithm proposed in this study. Based on this, we analyze EM responses for different source types. The algorithm and numerical results presented in this paper build a framework for 3D frequency-domain EM forward modelling and inversion.