Geodesic
"Fast" algorithm for solving some three-dimensional inverse problems of magnetometry
Matematičeskoe modelirovanie, Tome 36 (2024) no. 1, pp. 41-58

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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.
Keywords: magnetic prospecting, theree-dimensional inverse ill-posed problems, fast solution algorithm, a-posteriori error estimate. 
@article{MM_2024_36_1_a3,
     author = {A. S. Leonov and D. V. Lukyanenko and A. G. Yagola},
     title = {"Fast" algorithm for solving some three-dimensional inverse problems of magnetometry},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {41--58},
     publisher = {mathdoc},
     volume = {36},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2024_36_1_a3/}
}
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A. S. Leonov; D. V. Lukyanenko; A. G. Yagola. "Fast" algorithm for solving some three-dimensional inverse problems of magnetometry. Matematičeskoe modelirovanie, Tome 36 (2024) no. 1, pp. 41-58. http://geodesic.mathdoc.fr/item/MM_2024_36_1_a3/