基于谱元法的频率域三维海洋可控源电磁正演模拟

高精度、快速有效的正演模拟算法是三维电磁正反演的前提.为了提高海洋电磁三维数值模拟的精度和效率，本文提出利用基于Gauss-Lobatto-Chebyshev（GLC）基函数的谱元法进行海洋可控源三维电磁正演模拟.谱元法结合有限元法和谱方法的优点.我们通过应用伽辽金加权残差法离散二次电场矢量亥姆赫兹方程，在单元内选择混合阶GLC多项式的张量积作为高阶矢量插值基函数，在求解大型稀疏线性方程组时利用直接求解器进行快速求解，从而实现了三维海洋可控源电磁快速高精度正演模拟.一维和三维模型正演结果验证了本文算法的有效性和准确性.典型模型的数值结果表明谱元法是一种有效的三维海洋可控源电磁正演数值方法，能在稀疏网格剖分情况下获得精确的海洋电磁正演模拟响应.

Spectral element method for 3D frequency-domain marine controlled-source electromagnetic forward modeling

Marine controlled-source electromagnetic (MCSEM) method is an important predrill reservoir appraisal method to reduce exploration risk in detecting sub-seafloor hydrocarbon reservoirs. Most 3D forward modelings for MCSEM are based on conventional numerical methods like finite-difference and finite-element method. In this paper, we introduce spectral element method (SEM) based on Gauss-Lobatto-Chebyshev (GLC) polynomials for 3D frequency-domain MCSEM.
SEM is an accurate and efficient electromagnetic modeling methods due to its spectral accuracy and exponential convergence. The method combines the flexibility of finite-element method with the accuracy of spectral method by a simple application of spectral method to each element. Staring from the Maxwell's equations, we obtain a vector Helmholtz equation of electric field. Then we use Galerkin weighted residual method to discretize the vector Helmholtz equation, in which the curl-conforming Gauss-Lobatto-Chebyshev (GLC) polynomials are chosen as basis functions. As a kind of high-order complete orthogonal polynomials, the GLC polynomials have the characteristic of exponential convergence with the order and can derive the matrix elements analytically, which improves the modeling accuracy. Finally, we use the direct solver MUMPS to solve the final system of equations to speed up the modeling process. For numerical experiments, we first simulate responses of a 3-layer model and compare our SEM results with open-source software to check the accuracy of our SEM algorithm. After that, we analyze efficiency of SEM by comparing with finite-difference method. Finally, we apply SEM for typical 3D models and analyze the MCSEM responses. Numerical results show that SEM is an efficient and effective method for MSCEM modeling, and it can deliver very accurate results even with coarse meshes.