On the Uniqueness of Solution to Systems of Linear Algebraic Equations to Which the Inverse Problems of Gravimetry and Magnetometry Are Reduced: A Regional Variant

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

doi:10.31857/S0044466923090119

On the Uniqueness of Solution to Systems of Linear Algebraic Equations to Which the Inverse Problems of Gravimetry and Magnetometry Are Reduced: A Regional Variant

Authors: Kolotov I.I.¹, Lukyanenko D.V.¹, Stepanova I.E.¹^,2, Shchepetilov A.V.³, 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
3. Faculty of Physics, Moscow State University
Issue: Vol 63, No 9 (2023)
Pages: 1446-1457
Section: General numerical methods
URL: https://freezetech.ru/0044-4669/article/view/664980
DOI: https://doi.org/10.31857/S0044466923090119
EDN: https://elibrary.ru/JJFWYJ
ID: 664980

Cite item

Full Text

Open Access
Restricted Access

Access granted
Restricted Access

Subscription Access

Abstract

Conditions for the unique solvability of systems of linear algebraic equations to which many inverse problems of gravitational and magnetic exploration are reduced are considered. The mathematical statements of inverse problems take into account the sphericity of the Earth.

Keywords

solvability, singular systems, integral representations

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. V. Shchepetilov

Faculty of Physics, Moscow State University

Email: tet@ifz.ru
119991 Russia , Moscow

A. G. Yagola

Faculty of Physics, Lomonosov Moscow State University

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

References

Страхов В.Н. Геофизика и математика. М.: ОИФЗ РАН, 1999. 64 с.
Страхов В.Н., Степанова И.Э. Метод S-аппроксимаций и его использование при решении задач гравиметрии (локальный вариант) // Физика Земли. 2002. № 2. С. 3–19.
Степанова И.Э. Апробация методики S-аппроксимаций на материалах детальной гравиметрической и магнитометрических съемок // Геофиз. журнал. 2007. Т. 28. № 1. С. 97–105.
Stepanova I.E. On the S-approximation of the Earth’s gravity field. Regional version // Inverse Problem. Sci. and Engineer. 2009. V 17. № 8. P. 1095–1111.
Gudkova T.V., Stepanova I.E., Batov A.V. Density anomalies in subsurface layers of mars: model estimates for the site of the InSight mission seismometer // Solar System Res. 2020. V. 54. P. 15–19.
Кошляков Н.С., Глинер Э.Б., Смирнов М.М. Основные дифференциальные уравнения математической физики. М.: Физматгиз, 1962. 767 с.
Лаврентьев М.А., Люстерник Л.А. Курс вариационного исчисления. М.–Л.: Гостоптехиздат, 1950.
Lukyanenko D.V., Yagola A.G. Some methods for solving of 3D inverse problem of magnetometry // Eurasian J. Math. and Comp. Appl. 2016. V. 4. № 3. P. 4–14.
Kolotov I.I., Lukyanenko D.V., Stepanova I.E., et al. Recovering the magnetic image of Mars from satellite observations // J. of Imaging. 2021. V. 7. № 11. P. 234.
Тихонов А.Н., Гончарский А.В., Степанов В.В., Ягола А.Г. Численные методы решения некорректных задач. М.: Наука, 1990. 230 с.
Ягола А.Г., Степанова И.Э., Ван Янфей, Титаренко В.Н. Обратные задачи и методы их решения. Приложения к геофизике. М.: Бином. Лаборатория знаний, 2014. 214 с.