3D frequency-domain airborne EM forward modelling using spectral element method with Gauss–Lobatto–Chebyshev polynomials

Abstract

ABSTRACTThe spectral element method (SEM) based on high-order complete orthogonal polynomials is an accurate and efficient numerical method for electromagnetic modelling due to its spectral accuracy and exponential convergence. The SEM combines the flexibility of the finite-element method and the high accuracy of the spectral method. In this paper, we introduce SEM into three-dimensional frequency-domain airborne electromagnetic forward modelling. Starting from Maxwell's equations, we obtain a vector Helmholtz equation for the electric field. We use the Galerkin method to discretise the Helmholtz equation, in which the curl-conforming Gauss–Lobatto–Chebyshev polynomials are used as basis functions. The GLC polynomials help to derive the analytical expressions of entries in the system matrix and thus guarantee the modelling accuracy. Finally, we use the direct solver MUMPS to solve for the electric field and calculate the magnetic field by interpolation. For numerical experiments, we first compare our results with the semi-analytical solutions of a homogeneous half-space to verify the accuracy of our algorithm. We then analyse the characteristics of SEM by assuming different orders of interpolation polynomials and meshes. We also compare our method with the finite element method and SEM based on Gauss–Lobatto–Legendre polynomials. The results show that SEM is an efficient and effective method for electromagnetic modelling, it can deliver very accurate results and is less sensitive to mesh quality than the finite element method.