A Chebyshev pseudo-spectral approach for simulating magnetotelluric TM-mode responses on 2D structures

Abstract We introduce a Chebyshev pseudo-spectral (CPS) approach for 2D TM-mode magnetotelluric modelling, which was the first applied on the magnetotellric data in 2D model. In this method, 2D partial differential equations are solved using the Chebyshev differentiation matrix over the Gauss-Chebysev-Lobatto points. In order to test computational efficiency and its accuracy, we compare the simulatation of this method to the analytical solution and finite element (FE) and finite difference (FD) methods. The comparison of CPS numerical solution and corresponding analytical solution on a homogeneous half-space model and a layered model show that the CPS approach can provide an accurate modelling result. The discrete nodes for modelling were also analyzed on two models, which suggest that a few nodes can produce modelling results with a high accuracy. Especially for 2D and 3D modelling problems, the reduction in the number of nodes can improve the computational efficiency significantly. However, the CPS approach will lead to an unsymmetrical and non-sparse matrix, which is not favored by the iterative solver. We further compare the numerical result of the CPS method to the FD method and the averaged numerical solutions of the COMMEMI on the COMMEMI 2D-1 model. We find the numerical result of CPS method is closer to the averaged numerical solutions of the COMMEMI than that of observed by the FD. Finally, a realistic smooth model is considered to compare the modelling results using the CPS method to the published data. All these comparison results suggest that the CPS method can not only give a high accuracy for modelling results and also provide more detail information. Especially, a few nodes can be required in this method relative to the FD and FE method, which can decrease the relative errors. We then deduce that CPS method might be an alternative approach to simulate the magnetotelluric responses in 2D structures.