基于有限体积法的二维大地电磁各向异性数值模拟

Two-dimensional magnetotelluric anisotropic forward modeling using finite-volume method

为了计算带任意地形的各向异性介质中二维大地电磁响应,本文在非结构化网格的基础上,采用有限体积法,开发了二维大地电磁各向异性正演模拟的新算法.首先,从Maxwell方程出发,推导二维各向异性介质中大地电磁场的边值问题;然后,采用三角网格自动生成技术对求解区域进行非结构化网格剖分,进而构建节点中心控制体积单元,利用有限体积方法,得到求解边值问题的大型稀疏线性方程组;最后,利用Pardiso精确地计算了大地电磁响应值.三个各向异性模型的计算结果表明,本文开发的有限体积算法,不仅能够高精度求解带任意地形的大地电磁电导率各向异性问题,而且对于同一模型,该方法的计算消耗和精度都与有限单元法相当.因此,有限体积法是处理电磁法各向异性问题的一种有效方法.

In order to calculate the two-dimensional magnetotelluric response in anisotropic media with arbitrary topography,we develop a finite-volume approach for this problem.Firstly,based on the energy compensation principle and divergence theorem,the energy compensation equations for two-dimensional magnetotelluric problem with anisotropic conductivity structures are derived from Maxwell′s equations.Then,a triangular grid is used to discretize the two-dimensional conductivity model so that arbitrarily complex cases with topography can be greatly dealt with.The node-centered finite-volume algorithm is used to derive the final system of linear equations.PARDISO,a high-performance parallel solver,is chosen to achieve accurate electrical field and magnetic field efficiently.Finally,three models with anisotropic conductivity structures are used to test our proposed approach.The results show that not only can finite-volume method be used to accurately solve magnetotelluric anisotropic problems,but it also can be used to model the complex cases with arbitrarily surface topography by using unstructured grids.