Fast algorithm for solving some three-dimensional inverse problems of magnetometry

Leonov, A.S.; Lukyanenko, D.V.; Yagola, A.G.

Авторы: Leonov A.S., Lukyanenko D.V., Yagola A.G.
Журнал: Mathematical Models and Computer Simulations
Том: 16
Номер: 3
Год издания: 2024
Первая страница: 352
Последняя страница: 363
DOI: 10.1134/S2070048224700030
Аннотация: 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 thesolution 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.
Добавил в систему: Лукьяненко Дмитрий Витальевич

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Fast algorithm for solving some three-dimensional inverse problems of magnetometryстатья

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