起伏地形电偶源2.5维有限元数值模拟
来源期刊：中国有色金属学报2013年第9期
论文作者：张继锋 智庆全 李 貅 冯 兵
文章页码：2540 - 2551
关键词：电偶源；等参单元；起伏地形；数值模拟
Key words：electric dipole source; isoparametric element; ridge terrain; numerical simulation
摘 要：地形的起伏严重影响着电磁场分布，在实际资料处理中，研究地形起伏对电磁场的畸变规律可使电磁勘探解释更加准确可信。采用任意四边形网格剖分求解区域，实现起伏地形2.5维电偶源有限元正演算法，推导波数域电磁场耦合微分方程，通过基于等参单元的双二次插值将连续函数的微分离散化；采用一维非零元素紧缩存储，利用大规模稀疏矩阵并行求解器PARDISO求解，得到电偶源激发下二维地电断面的波数域电磁场响应。然后通过选取适当的波数进行傅里叶反变换，获取空间域电磁场响应，对正演中的关键问题，如波数的选择、场源参数的选取以及辅助场的计算等进行了分析和研究，为提高正演计算的精度和速度提供了理论保证。验证该算法的正确性和高效性，分别对山丘和山谷等典型地形进行了数值计算，分析起伏地形的电磁场响应规律。
Abstract: The topography seriously affects the distribution of electromagnetic field, and the study on distortion law of topography for the electromagnetic field can make the electromagnetic interpretation more accurate and reliable in the actual data processing work. The electric dipole source electromagnetic field finite element algorithm of 2.5D rugged topography was studied by using arbitrary quadrilateral mesh generation for computational domain. Firstly, the electromagnetic coupled differential equations in wave number domain was deduced, and continuous function was discretized based on the isoparametric element of interpolation, the wave number domain electromagnetic response is obtained for the two dimensional geoelectric section by a nonzero element compact storage and large-scale parallel sparse matrix solver PARDISO. The electromagnetic field space response is got by choosing appropriate wave number of the inverse Fourier transform. The forward key problems, such as the selection of wave number, source selection and the auxiliary field solution, were analyzed and studied, which provide a theoretical guarantee for improving the computation precision and speed. The correctness and high efficient of the algorithm were verified. Finally, the electromagnetic response characteristics of the trapezoidal hill and valley were analyzed.
张继锋，智庆全，李 貅，冯 兵
(长安大学 地质工程与测绘学院，西安 710054)
摘 要：地形的起伏严重影响着电磁场分布，在实际资料处理中，研究地形起伏对电磁场的畸变规律可使电磁勘探解释更加准确可信。采用任意四边形网格剖分求解区域，实现起伏地形2.5维电偶源有限元正演算法，推导波数域电磁场耦合微分方程，通过基于等参单元的双二次插值将连续函数的微分离散化；采用一维非零元素紧缩存储，利用大规模稀疏矩阵并行求解器PARDISO求解，得到电偶源激发下二维地电断面的波数域电磁场响应。然后通过选取适当的波数进行傅里叶反变换，获取空间域电磁场响应，对正演中的关键问题，如波数的选择、场源参数的选取以及辅助场的计算等进行了分析和研究，为提高正演计算的精度和速度提供了理论保证。验证该算法的正确性和高效性，分别对山丘和山谷等典型地形进行了数值计算，分析起伏地形的电磁场响应规律。
关键词：电偶源；等参单元；起伏地形；数值模拟
ZHANG Ji-feng, ZHI Qing-quan, LI Xiu, FENG Bing
(School of Geology Engineering and Geomatics, Chang’an University, Xi’an 710054, China)
Abstract:The topography seriously affects the distribution of electromagnetic field, and the study on distortion law of topography for the electromagnetic field can make the electromagnetic interpretation more accurate and reliable in the actual data processing work. The electric dipole source electromagnetic field finite element algorithm of 2.5D rugged topography was studied by using arbitrary quadrilateral mesh generation for computational domain. Firstly, the electromagnetic coupled differential equations in wave number domain was deduced, and continuous function was discretized based on the isoparametric element of interpolation, the wave number domain electromagnetic response is obtained for the two dimensional geoelectric section by a nonzero element compact storage and large-scale parallel sparse matrix solver PARDISO. The electromagnetic field space response is got by choosing appropriate wave number of the inverse Fourier transform. The forward key problems, such as the selection of wave number, source selection and the auxiliary field solution, were analyzed and studied, which provide a theoretical guarantee for improving the computation precision and speed. The correctness and high efficient of the algorithm were verified. Finally, the electromagnetic response characteristics of the trapezoidal hill and valley were analyzed.
Key words:electric dipole source; isoparametric element; ridge terrain; numerical simulation
