2.5维电磁响应的有限元模拟与波数取值研究

A STUDY ON THE 2.5-D ELECTROMAGNETIC MODELING BY THE FINITE ELEMENT METHOD AND THE WAVE NUMBER SELECTION

利用有限元法实现了任意方向偶极子源在二维介质中频率域电磁响应的数值模拟,研究了波数取值对模拟结果的影响。通过对构造走向的Fourier变换,将全三维电磁问题,转化为一系列二维问题,并在波数域求解,极大地减小了计算工作量,导出了波数域耦合适用于二维电性介质中任何方向电或磁偶极子响应计算的电磁场方程。针对每个给定的波数,上述耦合电磁场方程用等参有限元方法在x-z平面内求解。采用Fourier逆变换,将波数域解积分,得到空间域电磁场。针对电磁模拟计算中,源点的奇异性,采用具有一定面积的伪δ函数表达源电流分布,使数值解精度得以提高。另外,采用等参有限元,使地下复杂地质体得到准确表达。利用不同波数值对均匀介质与层状介质的模拟结果与解析解的对比,验证了算法的正确性与精度。利用层状介质模型的解析解与数值计算结果的对比,分析了波数的优化取值范围及取值点数对数值模拟结果的影响,考察了算法对非均匀介质的适应性。

A finite element method is developed for simulating frequency domain electromagnetic responses due to a dipole source in the presence of the 2-D conductivity structures. Computing costs are considerably minimized by reducing the full three-dimensional problem to a series of two-dimensional problem. This is accomplished by Fourier transforming the problem into y-wave number (Ky) domain, for the y-direction is parallel to the structural strike. In the Ky domain, two coupled partial differential equations for Hy and Ey has been derived. For the requisite number of Ky values, the coupled equations are solved by the finite element method on the isoparametric element on the x-z plane. Application of the inverse Fourier transform to the Ky domain solutions provide the electric and magnetic fields in real space. The formulations derived can be applied to general complex two dimensional structures containing either electric or magnetic dipole sources in any directions. In modeling of electromagnetic measurement, the singularity of the source point is circumvented by a pseudo-delta function to distribute a dipole source current, and the numeric accuracy is enhanced. Moreover, the suggested method employs an isoparametric finite-element to accommodate to the complex subsurface formation. A quantitative test of accuracy is presented which compares the finite element results to analytic solutions for a dipole source in homogeneous space and in layer medium for different wave number Ky. to validate the code. In addition, we use the layer model to determine the optimal range of the Ky values and study on the effects of the range of the wave number on the numeric results, and investigate on the adaptability of the code to the inhomogeneous medium.