Solution of the Optimization Problem of Magnetotelluric Sounding in Quaternions by the Differential Evolution Method

Abstract

The article discusses the application of quaternion Fourier transforms and quaternion algebra to transform Maxwell’s equations. This makes it possible to present the problem of magnetotelluric sensing (MTS) in a more convenient form for research. Studies of the inverse MTS problem for multi-layer regions are presented using the differential evolution method, which demonstrates high convergence. For single-layer regions, a new method for solving inverse problems based on minimizing the quadratic functional using conjugate optimization methods is considered. Numerical results obtained using special Python libraries are presented, with analysis and conclusions.

Keywords

• Maxwell’s equation
• electric field
• magnetic field
• quaternions
• magnetotelluric sounding