面向目标自适应有限元法的带地形三维大地电磁各向异性正演模拟

doi:10.6038/cjg2018L0068

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摘要传统三维大地电磁各向异性模拟均是基于规则六面体网格，计算精度有限且较难拟合复杂地质条件.本文采用面向目标自适应非结构矢量有限元法，对三维大地电磁各向异性介质进行模拟.首先从电场双旋度方程出发，利用伽辽金方法建立变分方程；然后利用电流密度连续性条件构建适合大地电磁各向异性问题的加权后验误差估计方法，实现面向目标的网格自适应正演；最后通过典型算例分析各向异性对网格自适应和大地电磁响应的影响特征以及各向异性的识别方法.本文算法能够高精度地拟合起伏地表和任意各向异性介质，适用于分析复杂地电条件大地电磁响应特征，为提高大地电磁资料解释水平提供了理论基础.

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关键词 ：大地电磁, 矢量非结构有限元, 电性各向异性, 面向目标自适应

Abstract：Traditional 3D MT data interpretations are based on an isotropic model that is sometimes inappropriate, because it has been well established that electrical anisotropy is widely present in the deep earth. The MT anisotropic modelling is generally worked on structured meshes that has a limited accuracy but cannot model complex geology. We present a goal-oriented adaptive unstructured finite-element method for accurately and efficiently simulating 3D anisotropic MT responses. This is largely different from the traditional 3D MT modelling, like finite-difference or integral equation method that uses artificially refined grids. The accuracy of the latter methods are severely influenced by the quality of mesh, especially for complex geology and topography.
We use Galerkin method to discretize the electric field vector wave equation for obtaining the final finite-element equation. Once the electric field is solved, the magnetic field can be calculated via Faraday's law. By solving two polarization modes with source parallel to the x-and y-axes respectively, we can get the impedance tensor. For the adaptive strategy, we use the continuity of normal current to evaluate the posterior error, while the weighting coefficient of the posterior error is obtained by solving a dual problem of the forward problem. Besides, we use a convergence rule to determine which receiver will be used in the next refinement iteration.
We check the accuracy of our algorithm against the analytical solutions for a layered anisotropic earth. Further, we study the anisotropic effect on the adaptive meshes and MT responses by models with anisotropic bodies embedded in a half-space. At last, we study the MT responses for an anisotropic body located under a trapezoid hill. The numerical experiments show that our algorithm is an effective tool for modelling 3D anisotropic MT soundings with topography. The numerical results demonstrate that:1) Anisotropy influences the adaptive meshes differently based on the resistivity contrasts in different directions; 2) The influences of topography on MT responses depends on the polarization mode, while the anisotropy influences the MT responses depending on the direction of anisotropic principal axes and polarization; 3) Anisotropy is resolvable from the distribution of the apparent resistivities by polar plots. Our study aims to provide foundations for the interpretation of 3D MT data on the conditions of topography and anisotropy.

Key words： Magnetotelluric (MT) Unstructured vector finite-element method Electrical anisotropy Goal-oriented adaptive method

收稿日期: 2017-01-24

PACS:

P631

基金资助:国家自然科学基金重点项目（41530320），面上项目（41274121），国家重点研发计划（2017YFC0601900，2016YFC0303100），中国科学院先导专项（XDA14020102），吉林大学高层次科技创新团队建设项目资金（JLUSTIRT）和中央高校基本科研业务费专项资金联合资助.

通讯作者: 殷长春,男,1965年生,教授,国家"千人计划"特聘专家,主要从事电磁勘探理论,特别是航空和海洋电磁方面的研究.E-mail:yinchangchun@jlu.edu.cn E-mail: yinchangchun@jlu.edu.cn

作者简介: 曹晓月,男,1990年生,博士生,主要从事大地电磁正反演研究.E-mail:caoxy_em@163.com

链接本文:

http://www.geophy.cn//CN/10.6038/cjg2018L0068 或 http://www.geophy.cn//CN/Y2018/V61/I6/2618

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