{"title":"Modeling the Solution of the Acoustic Inverse Problem of Scattering for a Three-Dimensional Nonstationary Medium","authors":"A. B. Bakushinsky, A. S. Leonov","doi":"10.1134/s1063771023601401","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>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.</p>","PeriodicalId":455,"journal":{"name":"Acoustical Physics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acoustical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s1063771023601401","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Acoustical Physics is an international peer reviewed journal published with the participation of the Russian Academy of Sciences. It covers theoretical and experimental aspects of basic and applied acoustics: classical problems of linear acoustics and wave theory; nonlinear acoustics; physical acoustics; ocean acoustics and hydroacoustics; atmospheric and aeroacoustics; acoustics of structurally inhomogeneous solids; geological acoustics; acoustical ecology, noise and vibration; chamber acoustics, musical acoustics; acoustic signals processing, computer simulations; acoustics of living systems, biomedical acoustics; physical principles of engineering acoustics. The journal publishes critical reviews, original articles, short communications, and letters to the editor. It covers theoretical and experimental aspects of basic and applied acoustics. The journal welcomes manuscripts from all countries in the English or Russian language.
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