On the Uniqueness of Solutions to Systems of Linear Algebraic Equations Resulting from the Reduction of Linear Inverse Problems of Gravimetry and Magnetometry: a Local Case

I. I. Kolotov; Колотов И. И.; D. V. Lukyanenko; Лукьяненко Д. В.; I. E. Stepanova; Степанова И. Э.; A. G. Yagola; Ягола А. Г.

doi:10.31857/S0044466923080094

On the Uniqueness of Solutions to Systems of Linear Algebraic Equations Resulting from the Reduction of Linear Inverse Problems of Gravimetry and Magnetometry: a Local Case

Authors: Kolotov I.I.¹, Lukyanenko D.V.¹, Stepanova I.E.¹^,2, Yagola A.G.¹
Affiliations:
1. Faculty of Physics, Lomonosov Moscow State University
2. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences
Issue: Vol 63, No 8 (2023)
Pages: 1317-1331
Section: Partial Differential Equations
URL: https://ruspoj.com/0044-4669/article/view/664999
DOI: https://doi.org/10.31857/S0044466923080094
EDN: https://elibrary.ru/WSNXOD
ID: 664999

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Abstract

The paper considers issues of unique solvability of systems of linear algebraic equations to which many inverse problems of geophysics are reduced as a result of discretization. Examples of degenerate and nondegenerate systems of different dimensions arising from the interpretation of gravity and magnetometric data are given.

Keywords

degenerate systems of linear algebraic equations, integral representations, unique solvability

About the authors

I. I. Kolotov

Faculty of Physics, Lomonosov Moscow State University

Email: tet@ifz.ru
119992, Moscow, Russia

D. V. Lukyanenko

Faculty of Physics, Lomonosov Moscow State University

Email: tet@ifz.ru
119992, Moscow, Russia

I. E. Stepanova

Faculty of Physics, Lomonosov Moscow State University; Schmidt Institute of Physics of the Earth, Russian Academy of Sciences

Email: tet@ifz.ru
119992, Moscow, Russia; 123995, Moscow, Russia

A. G. Yagola

Faculty of Physics, Lomonosov Moscow State University

Author for correspondence.
Email: tet@ifz.ru
119992, Moscow, Russia

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