On the construction of an optimal network of observation points when solving inverse lin-ear problems of gravimetry and magnetometry

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Resumo

Unique solvability of systems of linear algebraic equations is studied to which many in-verse problems of geophysics are reduced as a result of discretization after applying the method of integral equations or integral representations. Examples of singular and nonsingular systems of vari-ous dimensions that arise when processing magnetometric and gravimetric data from experimental observations are discussed. Conclusions are drawn about methods for constructing an optimal net-work of experimental observation points.

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Sobre autores

I. Stepanova

Moscow State University

Autor responsável pela correspondência
Email: tet@ifz.ru
Rússia, Leninskiye Gory, Moscow, 119991

D. Lukyanenko

Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: tet@ifz.ru
Rússia, ul. Bolshaya Gruzinskaya, 10, build. 1, Moscow, 123995

I. Kolotov

Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: tet@ifz.ru
Rússia, ul. Bolshaya Gruzinskaya, 10, build. 1, Moscow, 123995

A. Shchepetilov

Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: tet@ifz.ru
Rússia, ul. Bolshaya Gruzinskaya, 10, build. 1, Moscow, 123995

A. Yagola

Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: tet@ifz.ru
Rússia, ul. Bolshaya Gruzinskaya, 10, build. 1, Moscow, 123995

A. Levashov

Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: tet@ifz.ru
Rússia, ul. Bolshaya Gruzinskaya, 10, build. 1, Moscow, 123995

Bibliografia

  1. 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. Vol. 499. P. 575–579.
  2. Lukyanenko D.V., Yagola A.G. Some methods for solving of 3D inverse problem of magnetometry // Eurasian Journal of Mathematical and Computer Applications. 2016. Vol. 4. No 3. P. 4–14.
  3. Kolotov I.I, Lukyanenko D.V., Stepanova I.E., Yagola A.G., Wang Y. Recovering the magnetic image of Mars from satellite observations // J.of Imaging. 2021. Vol. 7. No 11. P. 234.
  4. Страхов В.Н. Геофизика и математика. М.: ОИФЗ РАН, 1999. 64 с.
  5. Страхов В.Н., Степанова И.Э. Метод S- аппроксимаций и его использование при решении задач гравиметрии (локальный вариант) // Физ. Земли. 2002. № 2. C. 3–19.
  6. Страхов В.Н., Степанова И.Э. Метод S- аппроксимаций и его использование при решении задач гравиметрии (региональный вариант) // Физ. Земли. 2002. № 7. C. 3–12.
  7. Kolotov I.I., Lukyanenko D.V., Stepanova I.E., Yagola A.G. 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 // Computational Mathematics and Mathematical Physics, издательство Pleiades Publishing, Ltd (Road Town, United Kingdom). 2023. V. 63. No 9. P. 1588–1599.
  8. Kolotov I.I., Lukyanenko D.V., Stepanova I.E., Shchepetilov A.V., Yagola A.G. 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 // Computational Mathematics and Mathematical Physics, издательство Pleiades Publishing, Ltd (Road Town, United Kingdom). 2023. V. 63. No 8. P. 1452–1465.
  9. 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.
  10. Stepanova I.E. On the S-approximation of the Earth’s gravity field // Inverse Problems in Science and Engng. 2008. Vol. 16. No 5. P. 535–544.
  11. Stepanova I.E. On the S-approximation of the Earth’s gravity field. Regional version // Inverse Problems in Science and Engng. 2009. Vol. 16. No 5. P. 1095–1111.
  12. 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. Vol. 54. P. 15–19.
  13. 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. C. 107–116.
  14. Прасолов В.В. Задачи и теоремы линейной алгебры. М.: Физматлит. 1996, 302 с.

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2. Fig. 1. Projections of the locations of two groups of observation points on a horizontal plane.

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3. Fig.2. Schematic representation of the process of adding a point to the optimal network.

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