Magnetotelluric method: theoretical deduction, analytical solutions and numerical modeling in a one-dimensional Earth

Método magnetotelúrico: dedução teórica, soluções analíticas e modelagem numérica em uma Terra 1D

Abstract

The magnetotelluric (MT) method is a passive geophysical technique that uses natural variations in electromagnetic fields to investigate the Earth’s subsurface resistivity structure. This article has a didactic objective: to guide students of physics and geophysics, at any level, through the theoretical foundations and mathematical derivations underlying the 1D MT method. Starting from Maxwell’s curl equations in the frequency domain, we derive wave-like differential equations for the electric and magnetic field components in a conductive medium. These equations lead to analytical solutions that describe the attenuation and phase shift of electromagnetic waves as they propagate through layered Earth models. From these results, we deduce expressions for the MT impedance and phase. The step-by-step presentation is complemented by simple computational implementations in Python for 1D models, enabling readers to connect the theoretical concepts with practical applications. By presenting the methodology in a clear and structured way, this work aims to support students and educators in developing a deeper understanding of the magnetotelluric method and its role in subsurface exploration.

Keywords:
Geophysics; Geophysical Method; Magnetotelluric Method; Maxwell Equations; Forward Modeling