| 电导率任意各向异性海洋可控源电磁三维矢量有限元数值模拟 |
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| 引用本文： | 李勇,吴小平,林品荣,韩思旭,李荡,刘卫强.电导率任意各向异性海洋可控源电磁三维矢量有限元数值模拟[J].地球物理学报,2017,60(5):1955-1978. |
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| 作者姓名： | 李勇 吴小平 林品荣 韩思旭 李荡 刘卫强 |
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| 作者单位： | 1. 中国科学技术大学地球和空间科学学院 地震与地球内部物理实验室, 合肥 230026;2. 中国地质科学院地球物理地球化学勘查研究所, 河北廊坊 065000;3. 国土资源部地球物理电磁法探测技术重点实验室, 河北廊坊 065000;4. 广东省核工业地质局二九三大队, 广州 510800 |
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| 基金项目： | 国家自然科学基金项目（41504063，41374076，41130420），国家重大科学仪器设备开发专项（2011YQ050060），国家高技术研究发展计划项目（2014AA06A610，2012AA09A201），中国地质科学院地球物理地球化学勘查研究所基本科研业务费专项资金（AS2013R02），国土资源部国土资源杰出青年科技人才培养计划和中国地质调查局青年地质英才计划联合资助. |
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| 摘 要： | 现有海洋可控源电磁三维数值模拟方法大多基于电导率各向同性介质理论,不能模拟海底地层电导率各向异性的实际情况.本文给出了电导率各向异性三维介质中电性源海洋可控源电磁二次电场的边值问题以及相应的变分问题,采用长方体单元对研究区域剖分,将场分量定义在剖分单元的边上,利用矢量有限单元法求解变分问题,实现了电导率任意各向异性海洋可控源电磁三维矢量有限元数值模拟.这个新的正演方法可以计算电导率任意各向异性三维地电模型的海洋可控源电磁响应,基于二次场矢量有限元法直接求解电磁场,避免了传统有限元方法可能遇到的伪解问题和难于处理电场法向分量不连续的问题,提高了数值模拟计算精度.一维电导率各向异性模型电磁场数值解与解析解吻合得相当好,无论在源附近还是远离源处相对误差均不超过1%.电导率各向异性二维模型的计算结果与已有文献采用的非结构有限元模拟结果十分吻合.三维地电模型数值模拟结果显示,电导率各向异性张量电导率主轴分量和欧拉角对不同装置海洋可控源电磁响应均有着明显的影响.
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| 关 键 词： | 海洋可控源电磁法 电导率任意各向异性 矢量有限元 三维正演 二次场 |
| 收稿时间： | 2016-08-28 |
Three-dimensional modeling of marine controlled-source electromagnetism using the vector finite element method for arbitrary anisotropic media |
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| LI Yong,WU Xiao-Ping,LIN Pin-Rong,HAN Si-Xu,LI Dang,LIU Wei-Qiang.Three-dimensional modeling of marine controlled-source electromagnetism using the vector finite element method for arbitrary anisotropic media[J].Chinese Journal of Geophysics,2017,60(5):1955-1978. |
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| Authors: | LI Yong WU Xiao-Ping LIN Pin-Rong HAN Si-Xu LI Dang LIU Wei-Qiang |
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| Abstract: | Arrangement of underground media fractures, preferred orientation of mineral grains and mineral composition bedding stratification are the factors leading to anisotropy of electrical conductivity for submarine layers. It has been proved by many researches that the influence of conductivity anisotropy should not be ignored, because it may result in false geological structures in marine electromagnetic data explanation. Up to now, most of available methods used in three-dimensional (3D) modeling of marine controlled-source electromagnetism (MCSEM) are based on the theory of isotropic media, which cannot simulate MCSEM response in real submarine anisotropic layers. In this paper, the MCSEM boundary value problem for the secondary electric field in 3D anisotropic media is put forward. Its corresponding variational equation is derived and then solved with the vector finite element method, in which a rectangular mesh is applied to dissect the computational region and the field component is defined on the edge of the rectangular element. Consequently, a vector finite element method for 3D MCSEM modeling is developed to calculate electromagnetic response in arbitrary anisotropic media. Meanwhile, secondary field formulation is used to remove source singularity. Our vector finite element method is able to deal with the discontinuity of the normal component of the electric field in 3D anisotropic media, and the vector basis functions are divergence-free which avoids the spurious solution, showing obvious advantage over the traditional nodal finite element method. The comparison between the analytical and numerical solutions of a layered anisotropic model shows high accuracy of our algorithm with less than one percent of relative error. The numerical solutions from our 3D vector finite element modeling also match well with the results from an available 2D unstructured finite element method for a 2D anisotropic conductivity model. A three-dimensional model is then simulated which shows that the principal axis anisotropy of the conductivity and Euler angle have significant impact on Inline and Broadside electromagnetic responses. |
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| Keywords: | Marine controlled-source electromagnetic method Conductivity arbitrary anisotropic medium Vector finite element method Three-dimensional modeling Secondary field |
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