{"title":"Fast Algorithm for Solving Some Three-Dimensional Inverse Problems of Magnetometry","authors":"A. S. Leonov, D. V. Lukyanenko, A. G. Yagola","doi":"10.1134/s2070048224700030","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":38050,"journal":{"name":"Mathematical Models and Computer Simulations","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Models and Computer Simulations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s2070048224700030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Mathematical Models and Computer Simulations is a journal that publishes high-quality and original articles at the forefront of development of mathematical models, numerical methods, computer-assisted studies in science and engineering with the potential for impact across the sciences, and construction of massively parallel codes for supercomputers. The problem-oriented papers are devoted to various problems including industrial mathematics, numerical simulation in multiscale and multiphysics, materials science, chemistry, economics, social, and life sciences.
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