基于混合阶矢量基函数的海洋可控源电磁三维谱元法数值模拟

在前人工作的基础上,本文推导了电导率任意各向异性介质的海洋可控源电磁三维谱元法正演方程.采用一次场/二次场分离算法结合混合阶矢量基函数,可以有效避免源点的奇异性的影响,从而提高数值解的精度.采用任意六面体单元离散研究区域,有利于模拟复杂地形和地电结构.利用不完全LU分解的Induced Dimension Reduction(IDR(s))迭代算法求解线性方程组,有效地提高了求解的效率.设计典型的地电模型进行正演计算,并将计算结果与有限元解进行对比,对比结果表明本文提出的基于混合阶矢量基函数的海洋可控源电磁三维谱元数值模拟算法是正确的、有效的.本文算法具有良好的通用性,可推广用于电导率呈任意各向异性的陆地电磁、井中电磁等数值模拟研究.

3D modeling of marine CSEM using the spectral element method based on mixed-order vector basis function

Based on previous work, this work uses a 3-D spectral-element method to solve controlled-source Electromagnetic (EM) induction problems in a general anisotropy conducting medium. In this approach, an algorithm for primary/secondary field separation coupled with a mix-order vector basis function was employed to enhance the accuracy of solution. The sparse system of spectral element equations is solved by using an Induced Dimension Reduction (IDR(s)) method with an incomplete LU preconditioner and the efficiency of the solution is improved effectively. We have applied this developed algorithm to compute a typical MCSEM response over a 3D model of a hydrocarbon reservoir located in both isotropic and general anisotropic media. Comparison of the numerical results from our method and FEM solutions shows that the algorithm proposed in this study is correct and effective, and can be extended to other EM induction problems such as borehole EM and airborne EM modeling.