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:
- Faculty of Physics, Lomonosov Moscow State University
- Schmidt Institute of Physics of the Earth, Russian Academy of Sciences
- Issue: Vol 63, No 8 (2023)
- Pages: 1317-1331
- Section: УРАВНЕНИЯ В ЧАСТНЫХ ПРОИЗВОДНЫХ
- URL: https://journals.rcsi.science/0044-4669/article/view/136199
- DOI: https://doi.org/10.31857/S0044466923080094
- EDN: https://elibrary.ru/WSNXOD
- ID: 136199
Cite item
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.
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
References
- Salnikov A.M., Stepanova I.E., Gudkova T.V., Batov A.V. Analytical modeling of the magnetic field of Mars from satellite data using modified S-approximations / // Doklady Earth Sciences. 2021. V. 499. P. 575–579.
- Lukyanenko D.V., Yagola A.G. Some methods for solving of 3D inverse problem of magnetometry // Eurasian Journal of Mathematical and Computer Applications. 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 / // Journal of Imaging. 2021. V. 7. № 11. P. 234.
- 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.
- Страхов В.Н., Степанова И.Э. Метод S-аппроксимаций и его использование при решении задач гравиметрии (региональный вариант) // Физика Земли. 2002. № 7. С. 3–12.
- Ягола А.Г., Степанова И.Э., Ван Янфей, Титаренко В.Н. Обратные задачи и методы их решения. Приложения к геофизике. М.: Бином, 2014. 214 с.
- Кошляков Н.С., Глинер Э.Б., Смирнов М.М. Основные дифференциальные уравнения математической физики. М.: Физматгиз, 1962. 767 с.
- Stepanova I.E. On the S-approximation of the Earth’s gravity field // Inverse Problems in Science and Engineering. 2008. V. 16. № 5. P. 535–544.
- Stepanova I.E. On the S-approximation of the Earth’s gravity field. Regional version // Inverse Problems in Science and Engineering. 2009. V. 16. № 5. P. 1095–1111.
- Stepanova I.E., Shchepetilov A.V., Mikhailov P. S. Analytical Models of the Physical Fields of the Earth in Regional Version with Ellipticity // Izvestiya, Physics of the Solid Earth. 2022. V. 58. № 3. P. 406–419.
- 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 Research volume. 2020. V. 54. P. 15–19.
- 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.