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

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

Matematičeskoe modelirovanie, Tome 36 (2024) no. 1, pp. 41-58.

Résumé

Typical three-dimensional inverse problems of magnetic prospecting are considered, namely: 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 their 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 aposteriori 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 found solutions are tested in solving model inverse problems and used in the processing of experimental data.

Détail

Keywords: magnetic prospecting, theree-dimensional inverse ill-posed problems, fast solution algorithm, a-posteriori error estimate.

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