Fast Algorithm for Solving Some Three-Dimensional Inverse Problems of Magnetometry

• Published in: Mathematical models and computer simulations 2024, Vol.16 (3), p.352-363
• Main Authors: Leonov, A. S., Lukyanenko, D. V., Yagola, A. G.
• Format: Article
• Language: English
• Subjects: Algorithms; Computation; Inverse problems; Magnetic dipoles; Magnetic induction; Magnetic measurement; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Personal computers; Regularization; Regularization methods; Simulation and Modeling; Tensors
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048224700030

Typical three-dimensional inverse problems of magnetic prospecting are considered: determination of the vector density of magnetic dipoles in the studied area of the Earth’s crust from the components of the vector (and/or gradient tensor) of magnetic induction measured on the surface. These problems, being, as a rule, ill-posed, can be solved by standard regularization methods. However, for such a solution on sufficiently detailed grids, significant computing resources (computing clusters, supercomputers, etc.) are required to solve the problem in minutes. The article proposes a new, fast regularizing algorithm for solving such three-dimensional problems, which makes it possible to obtain an approximate solution on a personal computer of average performance in tens of seconds or in a few minutes. In addition, the approach used allows us to calculate an a posteriori error estimate of the found solution in a comparable time, and this makes it possible to evaluate the quality of the solution when interpreting the results. Algorithms for solving the inverse problem and a posteriori error estimation for the solutions found are tested in solving model inverse problems and used in the processing of experimental data.