Skip to main content
Log in

Solution of the Interpretation Tomography Problem in Geophysics under the Linear Integral Representation Method and Theories of Discrete Gravity and the Magnetic Potential

  • GEOPHYSICS
  • Published:
Doklady Earth Sciences Aims and scope Submit manuscript

Abstract

A fundamentally new approach to solving inverse problems in geophysics based on the linear integral representation method and the theories of discrete gravity and the magnetic potential is proposed. This approach makes it possible to reconstruct the continuously distributed masses with a relatively high accuracy from the heterogeneous data at some grid points.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

Similar content being viewed by others

REFERENCES

  1. V. N. Strakhov, I. E. Stepanova, and L. V. Grichuk, in Proc. Int. Conf. “Geological Interpretation of Gravity, Magnetic and Electromagnetic Fields: Theory and Practice” (Voronezh State Univ., Voronezh, 1996), pp. 49–71 [in Russian].

  2. Z. Z. Arsanukaev, Izv., Phys. Solid Earth 40 (11), 935–956 (2004).

    Google Scholar 

  3. V. N. Strakhov and I. E. Stepanova, Izv., Phys. Solid Earth 38 (2), 91–108 (2002).

    Google Scholar 

  4. V. N. Strakhov and I. E. Stepanova, Izv., Phys. Solid Earth 38 (7), 535–545 (2002).

    Google Scholar 

  5. I. E. Stepanova, I. A. Kerimov, and A. G. Yagola, Izv., Phys. Solid Earth 55 (2), 218–231 (2019).

    Article  Google Scholar 

  6. D. N. Raevskiy and I. E. Stepanova, Izv., Phys. Solid Earth 51 (2), 197–207 (2015).

    Article  Google Scholar 

  7. N. S. Koshlyakov, E. B. Gliner, and M. M. Smirnov, The Main Difference Equations for Mathematical Physics (Fizmatgiz, Moscow, 1962) [in Russian].

    Google Scholar 

  8. M. A. Lavrent’ev and L. A. Lyusternik, Course of Various Calculus (Gostoptekhizdat, Moscow, 1950) [in Russian].

    Google Scholar 

  9. A. N. Tikhonov, A. V. Goncharskii, V. V. Stepanov, and A. G. Yagola, Numerical Methods for Solving Some Problems (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  10. I. I. Kolotov, D. V. Lukyanenko, I. E. Stepanova, A. V. Shchepetilov, and A. G. Yagola, Comput. Math. Math. Phys. 63 (9), 1588–1599 (2023).

    Article  MathSciNet  Google Scholar 

  11. I. I. Kolotov, D. V. Lukyanenko, I. E. Stepanova, and A. G. Yagola, Comput. Math. Math. Phys. 63 (8), 1452–1465 (2023).

    Article  MathSciNet  Google Scholar 

  12. V. N. Strakhov, Dokl. Akad. Nauk SSSR 236 (2), 329–331 (1977).

    ADS  Google Scholar 

  13. MESSENGER Mission: Magnetometer (MAG) Instrument. https://pds-ppi.igpp.ucla.edu/search/view/?f=yes&id =pds://PPI/mess-mag-calibrated/data/mbf/2011.

  14. T. Gudkova, I. Stepanova, and A. Batov, Solar Syst. Res. 54, 15–19 (2020). https://doi.org/10.1134/S0038094620010037

    Article  ADS  Google Scholar 

Download references

Funding

This work was carried out under a State Assignment of the Schmidt Institute of Physics of the Earth, Russian Academy of Sciences.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. E. Stepanova.

Ethics declarations

The authors of this work declare that they have no conflicts of interest.

Additional information

Translated by E. Maslennikova

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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. Dokl. Earth Sc. (2024). https://doi.org/10.1134/S1028334X24600907

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1134/S1028334X24600907

Keywords:

Navigation