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Modeling the Solution of the Acoustic Inverse Problem of Scattering for a Three-Dimensional Nonstationary Medium

  • ACOUSTIC SIGNALS PROCESSING. COMPUTER SIMULATION
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Abstract

The inverse problem of acoustic sounding of a three-dimensional nonstationary medium is considered, based on the Cauchy problem for the wave equation with a sound speed coefficient depending on the spatial coordinates and time. The data in the inverse problem are measurements of time-dependent acoustic pressure in some spatial domain. Using these data, it is necessary to determine the positions of local acoustic inhomogeneities (spatial sound speed distributions), which change over time. A special idealized sounding model is used, in which, in particular, it is assumed that the spatial sound speed distribution changes little in the interval between source time pulses. With such a model, the inverse problem is reduced to solving three-dimensional Fredholm linear integral equations for each sounding time interval. Using these solutions, the spatial sound speed distributions are calculated in each sounding time interval. When a special (plane-layer) geometric scheme for the location of the observation and sounding domains is included in the sounding scheme, the inverse problem can be reduced to solving systems of one-dimensional linear Fredholm integral equations, which are solved by well-known methods for regularizing ill-posed problems. This makes it possible to solve the three-dimensional inverse problem of determining the nonstationary sound speed distribution in the sounded medium on a personal computer of average performance for fairly detailed spatial grids in a few minutes. The efficiency of the corresponding algorithm for solving a three-dimensional nonstationary inverse sounding problem in the case of moving local acoustic inhomogeneities is illustrated by solving a number of model problems.

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Funding

The study was supported by the Russian Science Foundation (project no. 22-71-10070) for the first author and the Program for Improving the Competitiveness of the National Research Nuclear University MEPhI (project 02.a03.21.0005 of August 27, 2013) for the second. The main results of sections 1–3 were obtained through a grant from the Russian Science Foundation.

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Authors and Affiliations

  1. Institute of System Analysis, Federal Research Center Institute Computer Science and Control, Russian Academy of Sciences, 117312, Moscow, Russia

    A. B. Bakushinsky

  2. Mari State University, Republic of Mary El, 424000, Yoshkar-Ola, Russia

    A. B. Bakushinsky

  3. National Research Nuclear University MEPhI, 115409, Moscow, Russia

    A. S. Leonov

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  1. A. B. Bakushinsky
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  2. A. S. Leonov
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Correspondence to A. S. Leonov.

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Bakushinsky, A.B., Leonov, A.S. Modeling the Solution of the Acoustic Inverse Problem of Scattering for a Three-Dimensional Nonstationary Medium. Acoust. Phys. 70, 153–164 (2024). https://doi.org/10.1134/S1063771023601401

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  • DOI: https://doi.org/10.1134/S1063771023601401

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