A Variational Optimization Method for Solving Two Dimensional Magnetotelluric Inverse Problems

This article addresses a two-dimensional inverse problem of magnetotelluric sounding under the assumption of E-polarized electromagnetic fields. The main focus is on the construction of a forward numerical model based on the Helmholtz equation with a complex coefficient, and the recovery of electrical conductivity from boundary measurements. The second-order finite difference method is employed for numerical simulation, providing stable approximations of both the direct and the conjugate problems. The inverse problem is formulated as a minimization of a data misfit functional, and solved using Nesterov’s accelerated gradient descent method, which ensures fast convergence and robustness to noise. Numerical experiments are presented for a synthetic model featuring a smooth background conductivity and a localized anomaly. Comparison between the exact and reconstructed solutions demonstrates the high accuracy and efficiency of the proposed algorithm. The developed approach can serve as a foundation for constructing practical inversion schemes in geophysical exploration problems.