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On the Unique Solvability of Inverse Problems of Magnetometry and Gravimetry

Author

Listed:
  • Inna Stepanova

    (Schmidt Insitute of Physics of Earth, Russian Academy of Sciences, Moscow 123995, Russia)

  • Dmitry Lukyanenko

    (Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Igor Kolotov

    (Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Alexey Shchepetilov

    (Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

  • Anatoly Yagola

    (Department of Mathematics, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia)

Abstract

This article deals with the question of the unique solvability of systems of linear algebraic equations, to the solution of which many inverse problems of geophysics are reduced as a result of discretization when applying the methods of integral equations or integral representations. Examples are given of degenerate and nondegenerate systems of different dimensions that arise in the processing of magnetometric and gravimetric data from experimental observations. Conclusions are drawn about the methods for constructing the optimal grid of experimental observation points.

Suggested Citation

  • Inna Stepanova & Dmitry Lukyanenko & Igor Kolotov & Alexey Shchepetilov & Anatoly Yagola, 2023. "On the Unique Solvability of Inverse Problems of Magnetometry and Gravimetry," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3230-:d:1200074
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