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Direct Method for Identification of Two Coefficients of Acoustic Equation

Author

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  • Nikita Novikov

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
    Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk, Russia
    Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia)

  • Maxim Shishlenin

    (Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
    Institute of Computational Mathematics and Mathematical Geophysics, 630090 Novosibirsk, Russia
    Department of Mathematics and Mechanics, Novosibirsk State University, 630090 Novosibirsk, Russia)

Abstract

We consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein approach, which allows us to obtain both functions by solving two sets of integral equations. The main advantage of the proposed approach is that the method does not use the multiple solution of direct problems, and thus has quite low CPU time requirements. We also consider the variation of the method for the 1D case, where the variation of the wave equation is considered. We illustrate the results with numerical experiments in the 1D and 2D case and study the efficiency and stability of the approach.

Suggested Citation

  • Nikita Novikov & Maxim Shishlenin, 2023. "Direct Method for Identification of Two Coefficients of Acoustic Equation," Mathematics, MDPI, vol. 11(13), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:13:p:3029-:d:1189215
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    References listed on IDEAS

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    1. Dmitriy Klyuchinskiy & Nikita Novikov & Maxim Shishlenin, 2021. "Recovering Density and Speed of Sound Coefficients in the 2D Hyperbolic System of Acoustic Equations of the First Order by a Finite Number of Observations," Mathematics, MDPI, vol. 9(2), pages 1-13, January.
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