On the Unique Solvability of Inverse Problems of Magnetometry and Gravimetry

Inna Stepanova (), Dmitry Lukyanenko, Igor Kolotov, Alexey Shchepetilov and Anatoly Yagola
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Inna Stepanova: Schmidt Insitute of Physics of Earth, Russian Academy of Sciences, Moscow 123995, Russia
Dmitry Lukyanenko: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Igor Kolotov: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Alexey Shchepetilov: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia
Anatoly Yagola: Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia

Mathematics, 2023, vol. 11, issue 14, 1-19

Abstract: This article deals with the question of the unique solvability of systems of linear algebraic equations, to the solution of which many inverse problems of geophysics are reduced as a result of discretization when applying the methods of integral equations or integral representations. Examples are given of degenerate and nondegenerate systems of different dimensions that arise in the processing of magnetometric and gravimetric data from experimental observations. Conclusions are drawn about the methods for constructing the optimal grid of experimental observation points.

Keywords: degenerate system; integral representations; unique solvability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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