基于谱元法的广域电磁法三维正演模拟

为了提高广域电磁法三维正演精度和效率, 本文提出采用基于Gauss-Lobatto-Legendre(GLL)多项式的谱元法进行广域电磁法三维正演模拟.首先从麦克斯韦方程组出发, 推导了二次场满足的电场双旋度控制方程, 利用伽辽金加权残差法将微分形式的边值问题转换为积分弱形式, 再通过单元剖分和高阶正交基函数插值对全域问题进行离散, 最后通过求解大型线性方程组得到全局的数值解.层状介质模型验证了算法的正确性和精度, 三维地电模型分析了算法稳定性以及广域电磁法响应特征.研究表明谱元法是进行广域电磁法三维正演模拟的有效方法, 具有高精度、低网格依赖性等优势.

Spectral element method for 3D wide field electromagnetic method forward modeling

In order to improve the accuracy and efficiency of 3D wide field electromagnetic method forward modeling, this paper introduce the spectral element method based on Gauss-Lobatto-Legendre(GLL) polynomial for 3D forward modeling. Based on Maxwell's equations, the electric field curl-curl control equation satisfied by secondary field is derived. The boundary value problem in differential form is transformed into integral weak form by using Galerkin weighted residual method. Then the global problem is discretized by element subdivision and high-order orthogonal basis function interpolation. Finally, the global numerical solution is obtained by solving large-scale linear equations. The layered medium model verifies the correctness and accuracy of the algorithm, and the 3D geoelectric model analyzes the stability of the algorithm and characteristic of wide field electromagnetic response. The results show that the spectral element method is an effective method for wide field electromagnetic forward modeling. Compared with the traditional numerical methods, it has the advantages of high accuracy and low grid dependence.