Study on Pseudo-Spectral Method for TEM forwarding Modeling

The pseudo-spectral method, known for its high computational accuracy and speed, is particularly suitable for large-scale transient electromagnetic model calculations. This paper is based on the time-domain Maxwell's equations and employs Chebyshev polynomials to approximate the evolution operator, while using fast Fourier transforms to approximate spatial derivatives. The pseudo-spectral method is applied to calculate the three-dimensional transient electromagnetic response in both full-space and marine scenarios. By comparing with the analytical solutions of transient line source responses in a homogeneous medium in full-space, the correctness of the algorithm is validated. Analysis of models such as composite bodies and low-resistance body models in marine environments, reveals that the transient electromagnetic method exhibits high sensitivity to low-resistance bodies. The pseudo-spectral method effectively simulates the entire diffusion process of the electromagnetic field and its interaction with low-resistance bodies, providing rich time-domain information. The pseudo-spectral method holds promising potential for application, and further research incorporating the air-earth interface could significantly enhance its practical applicability.