Abstract
Unique solvability of systems of linear algebraic equations is studied to which many inverse 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 various dimensions that arise when processing magnetometric and gravimetric data from experimental observations are discussed. Conclusions are drawn about methods for constructing an optimal network of experimental observation points.
This is a preview of subscription content, log in via an institution to check access.
REFERENCES
A. M. Salnikov, I. E. Stepanova, N. V. Gudkova, and A. V. Batov, “Analytical modeling of the magnetic field of Mars from satellite data using modified S-approximations,” Dokl. Earth Sci. 499, 575–579 (2021).
D. V. Lukyanenko and A. G. Yagola, “Some methods for solving of 3D inverse problem of magnetometry,” Eurasian J. Math. Comp. Appl. 4 (3), 4–14 (2016).
I. I. Kolotov, D. V. Lukyanenko, I. E. Stepanova, et al., “Recovering the magnetic image of Mars from satellite observations,” J. Imaging 7 (11), 234 (2021).
V. N. Strakhov, Geophysics and Mathematics (Joint Institute of Physics of the Earth, RAS, Moscow, 1999) [in Russian].
V. N. Strakhov and I. E. Stepanova, “The S-approximation method and its application to gravity problems,” Izv., Phys. Solid Earth 38 (2), 91–107 (2002).
V. N. Strakhov and I. E. Stepanova, “Solution of gravity problems by the S-approximation method (regional version),” Izv., Phys. Solid Earth 38 (7), 535–544 (2002).
I. I. Kolotov, D. V. Lukyanenko, I. E. Stepanova, and A. G. Yagola, “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,” Comput. Math. Math. Phys. 63 (8), 1452–1465 (2023).
I. I. Kolotov, D. V. Lukyanenko, I. E. Stepanova, A. V. Shchepetilov, and A. G. Yagola, “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,” Comput. Math. Math. Phys. 63 (9), 1588–1599 (2023).
A. G. Yagola, I. E. Stepanova, Van Yanfei, and V. N. Titarenko, Inverse Problems and Methods of Their Solution: Applications to Geophysics (Binom, Moscow, 2014) [in Russian].
I. E. Stepanova, “On the S-approximation of the Earth’s gravity field,” Inv. Probl. Sci. Eng. 16, 535–544 (2008).
I. E. Stepanova, “On the S-approximation of the Earth’s gravity field. Regional version, " Inv. Probl. Sci. Eng. 17 (8), 1095–1111 (2009).
T. V. Gudkova, I. E. Stepanova, and A. V. Batov, “Density anomalies in subsurface layers of mars: model estimates for the site of the InSight mission seismometer,” Solar Syst. Res. 54, 15–19 (2020).
I. E. Stepanova, A. V. Shchepetilov, V. V. Pogorelov, and P. S. Mokhailov, “A structure-parametric approach to designing digital models of topography and gravitational field of the Earth using analytical S-approximations,” Geofiz. Prots. Biosfera 19 (2), 107–116 (2020).
V. V. Prasolov, Problems and Theorems of Linear Algebra (Fizmatlit, Moscow, 1996) [in Russian].
ACKNOWLEDGMENTS
We are grateful to A.S. Leonov for useful remarks and interest in this work.
Funding
This work was supported and carried out within the state assignment at the Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors of this work declare that they have no conflicts of interest.
Additional information
Translated by A. Klimontovich
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Stepanova, I.E., Lukyanenko, D.V., Kolotov, I.I. et al. On the Construction of an Optimal Network of Observation Points when Solving Inverse Linear Problems of Gravimetry and Magnetometry. Comput. Math. and Math. Phys. 64, 381–391 (2024). https://doi.org/10.1134/S0965542524030151
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542524030151