Moskva, Moscow, Russian Federation
UDK 51 Математика
UDK 55 Геология. Геологические и геофизические науки
UDK 550.34 Сейсмология
UDK 550.383 Главное магнитное поле Земли
GRNTI 37.01 Общие вопросы геофизики
GRNTI 37.15 Геомагнетизм и высокие слои атмосферы
GRNTI 37.25 Океанология
GRNTI 37.31 Физика Земли
GRNTI 38.01 Общие вопросы геологии
GRNTI 36.00 ГЕОДЕЗИЯ. КАРТОГРАФИЯ
GRNTI 37.00 ГЕОФИЗИКА
GRNTI 38.00 ГЕОЛОГИЯ
GRNTI 39.00 ГЕОГРАФИЯ
GRNTI 52.00 ГОРНОЕ ДЕЛО
OKSO 05.00.00 Науки о Земле
BBK 26 Науки о Земле
TBK 63 Науки о Земле. Экология
BISAC SCI SCIENCE
Variational-combinatoric approach is used when solving linear and nonlinear inverse problems of geophysics within the framework of discrete potential. The acquired data about physical fields and their sources are of discrete character. Combinatoric methods of discrete mathematics allow us to organize some selective choice of the information on the physical field elements. Analytical approximations are built only by means of verified data which can be recognized as useful signal, not as an arbitrary or systematic noise.
discrete potential, combinatoric approach, geological structure, integral representation
1. Arsanukaev Z. Z. Calculation of spatial elements of anomalous fields based on the theory of discrete gravitational fields // Izvestiya, Physics of the Solid Earth. — 2004. — Vol. 40, no. 11. — P. 935–955. — EDN: https://elibrary.ru/GUVETJ. EDN: https://elibrary.ru/OXLZFV
2. Raevsky D. N., Stepanova I. E. On the solution of inverse problems of gravimetry by the modified method of Sapproximations // Izvestiya, Physics of the Solid Earth. — 2015. — Vol. 51, no. 2. — P. 207–218. — DOI:https://doi.org/10.1134/s1069351315020081. DOI: https://doi.org/10.7868/S000233371502009X; EDN: https://elibrary.ru/TJFERF
3. Samarsky A. A., Nikolaev E. S. Methods for solving grid equations. — Moscow : Nauka, 1978. — P. 592. — (In Russian).
4. Sachkov V. N. Combinatorial methods of discrete mathematics. — Moscow : Nauka, 1977. — P. 320. — (In Russian).
5. Strakhov V. N. On the equivalence in the inverse problem of gravimetry at variable mass density // Doklady Akademii Nauk SSSR. — 1977. — Vol. 236, no. 2. — P. 329–331. — (In Russian).
6. Strakhov V. N., Stepanova I. E., Grichuk L. V. Theory of Discrete Gravitational Potential and Its Use in Gravimetry // «Theoretical and Practical Issues of Geological Interpretation of Gravitational, Magnetic and Electric Fields», Proceedings of the International Conference. — Voronezh : Voronezh State University, 1996. — P. 49–71. — (In Russian).
7. Tikhonov A. N., Goncharsky A. V., Stepanov V. V., et al. Numerical methods for solving ill-posed problems. — Moscow : Nauka, 1990. — P. 230. — (In Russian).
8. 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. — 2020. — Vol. 54, no. 1. — P. 15–19. — DOI:https://doi.org/10.1134/S0038094620010037. EDN: https://elibrary.ru/ORTHUR
9. Stepanova I. E., Kolotov I. I. Solution of the Interpretation Tomography Problem in Geophysics under the Linear Integral Representation Method and Theories of Discrete Gravity and the Magnetic Potential // Doklady Earth Sciences. — 2024a. — Vol. 516, no. 1. — P. 835–843. — DOI:https://doi.org/10.1134/s1028334x24600907. EDN: https://elibrary.ru/EWNDQS
10. Stepanova I. E., Kolotov I. I. The Combinatorial-Variational Approach to Solving Linear and Nonlinear Inverse Problems in Geophysics // Doklady Earth Sciences. — 2024b. — Vol. 518, no. 1. — P. 1534–1545. — DOI:https://doi.org/10.1134/S1028334X24602499. EDN: https://elibrary.ru/HBZGAQ
11. Stepanova I. E., Strakhov V. N. Solution of gravity problems by the S-approximation method (regional version) // Izvestiya, Physics of the Solid Earth. — 2002a. — Vol. 38, no. 7. — P. 535–544. — EDN: https://elibrary.ru/LHCHST.
12. Stepanova I. E., Strakhov V. N. The S-approximation method and its application to gravity problems // Izvestiya, Physics of the Solid Earth. — 2002b. — Vol. 38, no. 2. — P. 91–107. — EDN: https://elibrary.ru/LHLKQT
