Asian Journal of Pure and Applied Mathematics

This paper introduces the one-dimensional (1D) forward solving of the magnetotelluric (MT) sounding problem through the concept of the grid adaptation approach, and it displays a numerical solution. Conventional uniform grid techniques have commonly found difficulty in both properly resolving sharp resistivity contrasts and high conductive layers and skinny conducting layers without high computational expenses. To overcome these shortcomings, a dynamic grid refinement method was proposed that focuses on grid nodes where the solution may be particularly sensitive and where the gradients of resistivity may be large. Operating the governing equations on both uniform and adaptive meshes in the finite difference discretisation scheme, the overall performance of the methods has been compared systematically. The findings illustrated that the adaptive grid refinement strategy really enhanced the accuracy of solutions, decreased computation time, and converged rapidly in comparison to the uniform grid technique. These complex, multi-layered conductivity models were easily able to be handled, and the frequency-varying skin depth was well-represented by the adaptive method throughout a wide frequency range. Variations of resistivity contrasts were also examined, whereby the adaptive grid was able to deliver significant improvements in terms of accuracy, especially in medium- and high-contrast environments. Besides, a tendency to convergence analysis and visualization using one-dimensional, two-dimensional, and three-dimensional diagrams confirmed the excellent use of the adaptive grid approach in modeling the responses of MT. The adaptive model is a computationally efficient and robust method of forward MT modelling and is best adapted to realistic geophysical situations. The further development of the approach will be directed to higher-dimensional MT issues and solving equations with real field data and inverse modelling.