Three-dimensional magnetotelluric modelling in a mixed space-wavenumber domain

A new three-dimensional (3D) magnetotelluric (MT) modelling scheme in a mixed space-wavenumber domain is presented. The modelling scheme is based on using two-dimensional Fourier transform along two horizontal directions to solve a vector-scalar potential formula derived from Maxwell’s equations based on the primary-secondary potential separation. The derived one-dimensional (1D) governing equations in a mixed space-wavenumber domain are solved by using finite element method (FEM) together with a chasing method, and then two-dimensional (2D) inverse Fourier transform is used to recover the final solution of the electromagnetic fields in the 3D spatial domain. An iterative scheme is applied to approximate the true solution by repeating above steps since the governing equations cannot be directly solved due to an unusual primary-secondary potential field separation used. Nevertheless, the new method is capable of reducing the memory requirement and computational time in the mixed domain, and the 1D governing equations are highly parallel among different wavenumbers. For each of the 1D equations, the two- or four-node Gaussian quadrature rule can be utilized in both horizontal directions for Gauss Fast Fourier Transform. It is worth mentioning that the linear matrix equation to be solved is a fixed bandwidth system, and the chasing method is more efficient and convenient than solvers with preconditioners for the 1D matrix equations. The reliability and efficiency of the newly proposed method are verified with three synthetic 3D models by comparisons with a classical integral equation solution, an adaptive FEM solution, and a nonadaptive FEM solution. The proposed algorithm will be utilized in electrical resistivity tomography and controlled-source electromagnetic methods in future studies.