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应用地球物理  2018, Vol. 15 Issue (3-4): 536-544    DOI: 10.1007/s11770-018-0706-5
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基于有限元-积分方程的三维可控源电磁法混合正演模拟
周峰1,汤井田1,任政勇1,张志勇2,陈煌1,皇祥宇1,钟乙源1
1. 中南大学地球科学与信息物理学院,湖南长沙 410083
2. 东华理工大学地球物理与测控技术学院,江西南昌 330013
A hybrid finite-element and integral-equation method for forward modeling of 3D controlled-source electromagnetic induction
Zhou Feng1, Tang Jing-Tian1, Ren Zheng-Yong1, Zhang Zhi-Yong2, Chen Huang1, Huang Xiang-Yu1, and Zhong Yi-Yuan1
1. School of Geosciences and Infophysics of Central South University, Changsha 410083, China.
2. School of Geophysics and Measurement-control Technology, East China Institute of Technology, Nanchang 330013, China.
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摘要 本文基于非结构化四面体网格研究了矢量有限元与积分方程相结合的三维可控场源频率域电磁正演模拟算法。为了避免数值计算处理场源奇异性的困难,研究工作采用二次场算法,以水平层状介质为背景,由快速汉克尔积分求解一次场。将矢量有限元外边界二次场通过并矢格林函数映射到内部边单元,利用积分方程法无截断边界效应的特点,减少有限元截断边界的影响,同时有效减小求解区域;采用电、磁并矢格林函数进行数据后处理,降低由非结构化网格求解梯度不准确带来的数值误差,从而进一步提高电磁场的求解精度。最后,通过与块状异常体以及圆盘模型的公开结果进行对比,验证了本文算法的精度和效率,并利用研发算法进行了带地形模型试算,分析了可控源电磁法各分量的地形影响特征。
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关键词可控源电磁法   有限元-积分方程混合算法   矢量形函数   非结构化网格     
Abstract: We have developed a hybrid solver that combines the finite-element and integral-equation method for 3D CSEM modeling based on unstructured meshes. To avoid the source singularity, the secondary field is used in the modeling framework. The primary electromagnetic field from an electric dipole source in a layered medium is calculated based on the magnetic vector potential method. The inhomogeneities of the computational region are discretized by a vector-based finite-element mesh with boundaries at finite distance from the inhomogeneities by using the dyadic Green’s function, reducing the truncation boundary effect and the solution region. The electric and magnetic Green’s function is used in data postprocessing to reduce the numerical errors owing to inaccurate gradients because of unstructured meshes; thus, the electromagnetic field is more accurately calculated. Finally, the proposed algorithm is applied to a block and a disc model, and we assess the topography effect on the field components.
Key wordsCSEM   FEM   IE   hybrid algorithm   mesh   
收稿日期: 2018-07-25;
基金资助:

本研究由国家自然科学基金委(编号:41830107和41574120)和中南大学博士生自主探索创新项目(编号:2016zzts086)联合资助。

引用本文:   
. 基于有限元-积分方程的三维可控源电磁法混合正演模拟[J]. 应用地球物理, 2018, 15(3-4): 536-544.
. A hybrid finite-element and integral-equation method for forward modeling of 3D controlled-source electromagnetic induction[J]. APPLIED GEOPHYSICS, 2018, 15(3-4): 536-544.
 
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