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

作者: Kolotov I.I.¹, Lukyanenko D.V.¹, Stepanova I.E.¹^,2, Yagola A.G.¹
隶属关系:
1. Faculty of Physics, Lomonosov Moscow State University
2. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences
期: 卷 63, 编号 8 (2023)
页面: 1317-1331
栏目: Partial Differential Equations
URL: https://ter-arkhiv.ru/0044-4669/article/view/664999
DOI: https://doi.org/10.31857/S0044466923080094
EDN: https://elibrary.ru/WSNXOD
ID: 664999

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详细

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.

关键词

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

作者简介

I. Kolotov

Faculty of Physics, Lomonosov Moscow State University

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

D. Lukyanenko

Faculty of Physics, Lomonosov Moscow State University

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

I. 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. Yagola

Faculty of Physics, Lomonosov Moscow State University

编辑信件的主要联系方式.
Email: tet@ifz.ru
119992, Moscow, Russia

参考

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Kolotov I.I., Lukyanenko D.V., Stepanova I.E. et al. Recovering the magnetic image of Mars from satellite observations / // Journal of Imaging. 2021. V. 7. № 11. P. 234.
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Степанова И.Э., Щепетилов А.В., Погорелов В.В., Михайлов П.С. Структурно-параметрический подход при построении цифровых моделей рельефа и гравитационного поля Земли с использованием аналитических S-аппроксимаций // Геофизические процессы и биосфера. 2020. Т. 19. № 2. С. 107–116.