A Variational Optimization Method for Solving Two Dimensional Magnetotelluric Inverse Problems

Tleulesova A.M. Temirbekov N.M. Dauletbay M.N. Temirbekov A.N. Turlybek Z.G. Tugenbayeva Z.S. Kasenov S.E.
September 2025 Multidisciplinary Digital Publishing Institute (MDPI)

Mathematics
2025 #13 Issue 18

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.

Helmholtz equation , inverse problem , magnetotelluric sounding , Nesterov method , numerical solution

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Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, Al-Farabi Avenue 71, Almaty, 050040, Kazakhstan
National Engineering Academy of the Republic of Kazakhstan, Almaty, 050060, Kazakhstan
Natural Scientific and Pedagogical Higher School, Mukhtar Auezov South Kazakhstan University, Tauke Khan Ave 5, Shymkent, 160012, Kazakhstan

Faculty of Mechanics and Mathematics
National Engineering Academy of the Republic of Kazakhstan
Natural Scientific and Pedagogical Higher School

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