基于电场、磁场分离的瞬变电磁2.5维正演算法

熊彬; 阮百尧

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基于电场、磁场分离的瞬变电磁2.5维正演算法

首发时间：2009-07-13

熊彬 ¹ 阮百尧 ²

1、中南大学信息物理工程学院
2、桂林理工大学

摘要：研究和提出了一种新的基于电场、磁场分离的瞬变电磁2.5维正演计算方法。传统的人工源电磁法正演多是通过求解耦合的电磁场所满足的边值问题，从而获得频率域或时间域电磁场数值解。该算法利用矢量的旋度和散度运算规则，由三维电磁场分离出沿地质构造走向的电场和磁场分量，并设地下导电性分布沿走向无变化，对分离出来的电磁场分量取走向方向的傅氏变换，进而得到二维地电断面拉氏傅氏域中独立电磁场所满足的边值问题。文中首先介绍了时间域电磁场基本方程和独立电磁场所满足的拉氏傅氏域方程，然后通过Galerkin方法获得大型稀疏对称线性方程组，进而运用有限单元法求解拉氏傅氏域电磁场分量的数值近似解。较之于传统算法而言，该方法的主要优势在于所需求解的稀疏线性方程组规模被大幅度削减，譬如，有限元网格节点总数为n，传统方法的方程组规模就为2n×2n，本文算法的则为n×n，仅为前者的四分之一。为了验证所提方法的可行性和有效性，文后对回线激发源条件下几例典型模型进行了模拟计算。结果表明，该方法计算速度较之耦合电磁场的有明显提高。

关键词：瞬变电磁法电磁场分离 2.5维正演

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2.5-D forward algorithm for transient electromagnetic method based on the independent electric and magnetic fields

Xiong Bin ¹ Ruan Baiyao ²

1、School of Info-Physics and Geomatics Engineering, Central South University
2、Guilin University of Technology

Abstract：A new forward algorithm for 2.5-D transient electromagnetic method (TEM) based on the independent electric and magnetic fields has been developed. In modeling controlled source electromagnetic data, the conventional scheme is usually to solve the boundary value problem of the coupled EM field, thereby obtaining the frequency domain or time domain numerical solution. Based on the operation rule of curl and divergence, the present modeling method transforms the governing Maxwell equations into Laplace domain and then expands them in component format. Applying the Fourier transform to the components in the invariant conductivity direction (or strike direction), we obtain 2.5-D TEM boundary value problem in the Laplace and along-strike spatial Fourier domain. Firstly, the EM fundamental equations in time domain and the independent EM equations in Laplace and Fourier domains are introduced in this paper. Then, the Galerkin method is used to derive the finite-element equations. Finally, we get the EM components numerical solutions in Laplace and Fourier domains by the finite element method. Compared with the conventional algorithm, the present scheme can reduce the size of the global system matrix to the utmost extent. For example, if n is the total number of the FEM nodes, the equation sizes of the conventional and the present are 2n×2n and n×n, respectively, that is to say, the present is only one fourth of the former. In order to illustrate the feasibility and usefulness of the present algorithm, several typical examples of the transient electromagnetic fields produced by loop sources at air-earth interface are presented. The results of three numerical experiments show that the computation speed of the present scheme is increased obviously.

Keywords： Transient electromagnetic method Independent EM field 2.5-D forward

基金：

1. 国家高技术研究发展计划项目,高等学校博士学科点专项科研基金新教师项目,湖南省自然科学基金（2007AA06Z134,20070533104,07JJ6118）

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熊彬，阮百尧. 基于电场、磁场分离的瞬变电磁2.5维正演算法[EB/OL]. 北京：中国科技论文在线 [2009-07-13]. https://www.paper.edu.cn/releasepaper/content/200907-288.

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论文编号	200907-288
论文题目	基于电场、磁场分离的瞬变电磁2.5维正演算法
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