Numerical Solution of the Inverse Scattering Problem for the Acoustic Equation in an Absorptive Layered Medium

Баев, А. В.

doi:10.1007/s10598-018-9390-9

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…This additional condition guarantees the uniqueness of determining m(x) and, consequently, from the given q(x). Therefore, instead of the problem of determining , , and in , it is convenient to consider the inverse problem of finding the coefficients , , and q(x) for (4) in the same domain based on information similar to (3), namely, (7) Here, and ε is fixed and arbitrarily small. Similar problems were considered in [10] for in the following cases:…”

Section: Mathematicsmentioning

confidence: 99%

“…x t y We use Theorem 1 to analyze the inverse problem of determining the coefficients in (4) based on data (7). We first note that these data uniquely specify the function for all and .…”

Section: R R X Y X T Y T T X Y Y S X S Y R φ( )mentioning

confidence: 99%

“…Recently, due to the spread of COVID-19 infection, the use of acoustic tomography methods has been proposed for diagnosing lung diseases as well. Computational modeling of acoustic tomography problems was carried out in [5][6][7][8][9] (see also numerous references therein). Below, we consider one of the possible variants for posing an acoustic tomography problem.…”

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confidence: 99%

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Ray Statement of the Acoustic Tomography Problem

Romanov

2022

Dokl. Math.

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The ray statement of the inverse problem of determining three unknown variable coefficients in the linear acoustic equation is studied. These coefficients are assumed to differ from given constants only inside some bounded domain. There are point pulse sources and acoustic receivers on the boundary of this domain. Acoustic signals are measured by a receiver near the moment of time at which the signal from a source arrives at the receiver. It is shown that this information makes it possible to uniquely determine all the three desired coefficients. Algorithmically, the original inverse problem splits into three subproblems solved successively. One of them is a well-known inverse kinematic problem (of determining the speed of sound), while the other two lead to the same integral geometry problem for a family of geodesic lines determined by the speed of sound.

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Section: Mathematicsmentioning

confidence: 99%

“…x t y We use Theorem 1 to analyze the inverse problem of determining the coefficients in (4) based on data (7). We first note that these data uniquely specify the function for all and .…”

Section: R R X Y X T Y T T X Y Y S X S Y R φ( )mentioning

confidence: 99%

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confidence: 99%

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Ray Statement of the Acoustic Tomography Problem

Romanov

2022

Dokl. Math.

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“…Numerical methods, suitable for solving the coefficient inverse problems for hyperbolic systems and equations, are usually divided into direct ones and iterative ones. Direct methods are based on the Gelfand-Levitan-Krein approach [25][26][27][28][29][30] and boundary control method [31,32]. It was shown that the discrete coefficients inverse problems equations, which arise in the Gelfand-Levitan-Krein approach and boundary control method, coincide [33,34].…”

Section: Introductionmentioning

confidence: 99%

A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations

2020

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We investigate the mathematical model of the 2D acoustic waves propagation in a heterogeneous domain. The hyperbolic first order system of partial differential equations is considered and solved by the Godunov method of the first order of approximation. This is a direct problem with appropriate initial and boundary conditions. We solve the coefficient inverse problem (IP) of recovering density. IP is reduced to an optimization problem, which is solved by the gradient descent method. The quality of the IP solution highly depends on the quantity of IP data and positions of receivers. We introduce a new approach for computing a gradient in the descent method in order to use as much IP data as possible on each iteration of descent.

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The Inverse Problem for the Nonhomogeneous Oscillation Equation on a Half-Line with a Boundary Condition of the Third Kind

Shcheglov

Andreyanova

2022

Comput Math Model

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Numerical Solution of the Inverse Scattering Problem for the Acoustic Equation in an Absorptive Layered Medium

Cited by 3 publications

References 5 publications

Ray Statement of the Acoustic Tomography Problem

Ray Statement of the Acoustic Tomography Problem

A Modification of Gradient Descent Method for Solving Coefficient Inverse Problem for Acoustics Equations

The Inverse Problem for the Nonhomogeneous Oscillation Equation on a Half-Line with a Boundary Condition of the Third Kind

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