Combinatoric-Variational Approach to Solving Inverse Problems in Geophysics Within the Framework of the Discrete Potential Theory. Complex Geological Environment

Inna Stepanova; Igor Kolotov

doi:10.2205/2025ES001000

VAK Russia 1.6 UDC 51 CSCSTI 37.01 Russian Classification of Professions by Education 05.00.00 Russian Library and Bibliographic Classification 26 Russian Trade and Bibliographic Classification 63 BISAC SCI UDC 55 UDC 550.34 UDC 550.383 CSCSTI 37.15 CSCSTI 37.25 CSCSTI 37.31 CSCSTI 38.01 CSCSTI 36.00 CSCSTI 37.00 CSCSTI 38.00 CSCSTI 39.00 CSCSTI 52.00

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COMBINATORIC-VARIATIONAL APPROACH TO SOLVING INVERSE PROBLEMS IN GEOPHYSICS WITHIN THE FRAMEWORK OF THE DISCRETE POTENTIAL THEORY. COMPLEX GEOLOGICAL ENVIRONMENT Combinatoric-Variational Approach to Solving Inverse Problems in Geophysics Within the Framework of the Discrete Potential Theory. Complex Geological Environment

АА Аа

Published in Russian Journal of Earth Sciences · Volume 25, Issue 3 · Pages 1–19 · Rubric: ORIGINAL ARTICLES

DOI: https://doi.org/10.2205/2025ES001000 · EDN: QYNSZG

Received: 09.10.2024 Accepted: 17.02.2025 Published: 24.03.2025

Authors

Inna Stepanova

ORCID

Igor Kolotov

ORCID

Inna Stepanova

Schmidt Institute of Physics of the Earth, Russian Academy of Sciences senior scientist · laboratory 102 · Russian Federation · Москва

ORCID

Igor Kolotov

Lomonosov Moscow State University Russian Federation

ORCID

ABSTRACT

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.

KEYWORDS

discrete potential, combinatoric approach, geological structure, integral representation

Funding

The work was carried out within the framework of the state assignment of the Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences.

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GOST

Stepanova I. E., Kolotov I. I. Combinatoric-Variational Approach to Solving Inverse Problems in Geophysics Within the Framework of the Discrete Potential Theory. Complex Geological Environment // Russian Journal of Earth Sciences. 2024. no. 3. pp. 1-19. DOI: https://doi.org/10.2205/2025ES001000. EDN: QYNSZG. (Date of access 23.10.2026).

MLA

Inna Stepanova, Kolotov I. I.. "Combinatoric-Variational Approach to Solving Inverse Problems in Geophysics Within the Framework of the Discrete Potential Theory. Complex Geological Environment." Russian Journal of Earth Sciences 25.3 (2024): 1-19. DOI: https://doi.org/10.2205/2025ES001000. EDN: QYNSZG.

APA

Stepanova I. E., Kolotov I. I. (2024). Combinatoric-Variational Approach to Solving Inverse Problems in Geophysics Within the Framework of the Discrete Potential Theory. Complex Geological Environment. Russian Journal of Earth Sciences, 25(3), 1-19. https://doi.org/10.2205/2025ES001000 EDN: QYNSZG.

Chicago

Inna Stepanova, Kolotov I. I.. "Combinatoric-Variational Approach to Solving Inverse Problems in Geophysics Within the Framework of the Discrete Potential Theory. Complex Geological Environment." Russian Journal of Earth Sciences 25, no. 3 (2024): 1-19. https://doi.org/10.2205/2025ES001000. EDN: QYNSZG.

WIKI

{{cite journal | author = Stepanova I. E., Kolotov I. I. | title = Combinatoric-Variational Approach to Solving Inverse Problems in Geophysics Within the Framework of the Discrete Potential Theory. Complex Geological Environment | journal = Russian Journal of Earth Sciences | year = 2024 | volume = 25 | issue = 3 | pages = 1-19 | doi = 10.2205/2025ES001000 }} EDN: QYNSZG

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