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Solution of a Linear Coefficient Inverse Problem of Geophysics Based on Integral Equations

Solution of a Linear Coefficient Inverse Problem of Geophysics Based on Integral Equations —One of the promising modern trends in the development of the theory of solving inverse problems is the approach based on the idea of M.V. Klibanov (Beilina and Klibanov, 2012). In the cited work, the authors considered an inverse problem of identifying the objects with different dielectric properties using ground-penetrating radar method, which led to studying a nonlinear differential equation. This paper develops the idea of this approach leading to a linear matrix first-order partial differential equation. The solution of the linear inverse problem is presented for the case when the calculation formula for the field in the direct problem is the formula for the volumetric integral representation. The algorithm of this solution can be used to reconstruct physical properties of heterogeneous and anisotropic media for various geophysical methods. The results of computational experiments on the development of observation systems that simulate some practical cases are demonstrated. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Izvestiya, Physics of the Solid Earth" Springer Journals

Solution of a Linear Coefficient Inverse Problem of Geophysics Based on Integral Equations

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References (12)

Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2022. ISSN 1069-3513, Izvestiya, Physics of the Solid Earth, 2022, Vol. 58, No. 2, pp. 274–280. © Pleiades Publishing, Ltd., 2022. Russian Text © The Author(s), 2022, published in Fizika Zemli, 2022, No. 2, pp. 136–143.
ISSN
1069-3513
eISSN
1555-6506
DOI
10.1134/s106935132202001x
Publisher site
See Article on Publisher Site

Abstract

—One of the promising modern trends in the development of the theory of solving inverse problems is the approach based on the idea of M.V. Klibanov (Beilina and Klibanov, 2012). In the cited work, the authors considered an inverse problem of identifying the objects with different dielectric properties using ground-penetrating radar method, which led to studying a nonlinear differential equation. This paper develops the idea of this approach leading to a linear matrix first-order partial differential equation. The solution of the linear inverse problem is presented for the case when the calculation formula for the field in the direct problem is the formula for the volumetric integral representation. The algorithm of this solution can be used to reconstruct physical properties of heterogeneous and anisotropic media for various geophysical methods. The results of computational experiments on the development of observation systems that simulate some practical cases are demonstrated.

Journal

"Izvestiya, Physics of the Solid Earth"Springer Journals

Published: Apr 1, 2022

Keywords: linear coefficient inverse problem of geophysics; controlled sources; anisotropic, bianisotropic, elastic media

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