3D Forward Modeling for Frequency AEM by Vector Finite Element
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摘要: 目前有限元技术的开发及在电磁勘查技术中的应用已日趋成熟.然而，有限元正演模拟主要集中于地面和海洋电磁，航空电磁三维有限元模拟尚没有受到足够重视.以前人工作为基础，利用结构化网格实现了航空电磁系统的三维矢量有限元正演模拟.从二次场双旋度矢量非齐次亥姆霍兹方程出发，应用广义变分原理推导出变分方程，并采用六面体单元剖分，将场置于单元棱边上，对每个单元应用线性插值，最后合成含有稀疏矩阵的线性方程组.针对航空电磁多源性问题，利用MUMPS(multifrontal massively parallel sparse direct solver)直接求解器进行求解，在保证精度的前提下大幅度提高计算速度.利用单个异常体模型检验算法的精度和软件的稳定性，进而通过典型地电模型的模拟验证算法的有效性.对不同地下电性结构正演模拟结果进行对比分析，进一步研究了覆盖层和垂直接触带等典型构造对航空电磁响应的影响特征.Abstract: The finite-element method and application in EM exploration are well-developed. However, applications of the technology are focused mostly on ground and marine EM. Little attention has been put on airborne EM. Based on the previous research, we work on three-dimensional (3D) modeling for airborne systems by vector finite-element. We apply double-curl inhomogeneous vector Helmholtz equation for the second field and obtain the variational equations by using the generalized variational principle. By dividing the model domain into hexahedral elements and putting the field on the edge, we use linear interpolation for each element and put them together to set up the linear equations. For the multiple-source problem of AEM, we use the MUMPS solver that could achieve satisfying results both on speed and accuracy. We test the stability of our algorithm on a single abnormal body model first and check the practicability of the algorithm by simulating on typical geoelectrical models. The model results show that the overburden and the vertical contacting zone have great influence on the AEM responses.
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Key words:
- airborne EM /
- vector finite element /
- vertical magnetic dipole /
- fast solver /
- electric prospecting
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图 2 三维矢量有限元单个异常体模型
Fig. 2. A single abnormal body model for 3D vector FE
图 3 本文结果与Newman and Alumbaugh (1995)的IE模拟结果对比
a, b.单个异常体模型的响应；c, d.各自响应的相对误差
Fig. 3. Comparison of FE results from this paper with those from Newman and Alumbaugh (1995)
图 4 不同频率(900 Hz, 5 000 Hz和23 000 Hz)和不同埋深(20 m, 30 m和50 m)的单个异常体航空电磁响应
Fig. 4. AEM responses for a single abnormal body in the earth for different frequencies (900 Hz, 5 000 Hz and 23 000 Hz) and different buried depths (20 m, 30 m and 50 m)
图 6 覆盖层下多个异常体的航空电磁响应
Fig. 6. AEM responses for multiple abnormal bodies under the overburden
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