A Volume Integral Equation Method for the Direct/Inverse Problem in Elastic Wave Scattering Phenomena

Touhei, Terumi

doi:10.5772/6843

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…In the porous media acoustics context (notably for applications dealing with the absorption of airborne sound) it has been found [100] that the effective (bulk) density of typical air-saturated porous materials can be complex, dispersive, and quite different (real part) from the density of air. Sometimes, theoretical studies of scattering are undertaken in a quite general setting (i.e., without assuming constant mass density), but the mass density is taken to be either continuously-varying [90] or constant in the final, numerical stage [32]. The reason for the latter assumption is (as was suggested in the preceding lines) that it is not easy to carry out the numerical calculations via the DI formulation when the mass density is not constant in Ω.…”

Section: Introductionmentioning

confidence: 99%

On the constant constitutive parameter (e.g., mass density) assumption in integral equation approaches to (acoustic) wave scattering

Wirgin

2019

Preprint

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In 2D acoustic and elastodynamic problems the spatial variability of a constitutive parameter such as the mass density makes it difficult to employ boundary integral and domain integral techniques to solve the forward and inverse wave scattering problems. The oft-employed method for avoiding this problem is to assume this constitutive parameter (which is chosen herein to be the mass density) to be spatially-invariant throughout all space. The reliability of this assumption is evaluated both theoretically and numerically and it is shown, in the example of a canonical-shaped scattering obstacle, that the scattered field can be obtained in the form of a series of powers of the mass density contrast (the latter vanishing for constant mass density). The first term of this series is the solution for the scattered field corresponding to the constant density assumption and it is shown that taking into account only two more terms in the series enables to correct for practically all the errors incurred by the constant mass density assumption for a wide range of the other constitutive parameters and frequencies. It is shown how to apply this result for obstacles of non-canonical shape.

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Section: Introductionmentioning

confidence: 99%

On the constant constitutive parameter (e.g., mass density) assumption in integral equation approaches to (acoustic) wave scattering

Wirgin

2019

Preprint

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“…Such simple models are often the outcome of certain assumptions and approximations in what is called the domain integral formulation (treated in depth in [94]) of the forward-scattering problem. These assumptions usually have to do with: 1) treating an elastic wave problem (in a solid or porous medium) as an acoustic wave problem [13,27,41,34,42,8] (in a so-called equivalent fluid), 2) treating a microscopically-inhomogeneous (e.g., porous) medium as a macroscopically-homogeneous (effective) medium [7,18,17,19,5,58,93], 3) treating the bioacoustic, marine acoustic, electromagnetic and geophysical problem as one in which the mass density, or another constitutive property, is constant everywhere (i.e., is the same and spatially-constant within the obstacle as well as in the host) [65,30,64,73,22,23,45,74,66,27,84,55,52,15,34,96,7,29,57,5,78,36,37,86,96], 4) treating a 3D problem as a 2.5D, 2D or even 1D problem [72,24,94] (and many other references) 5) treating the potato as a sphere...…”

Section: Introductionmentioning

confidence: 99%

Forward and inverse acoustic scattering problems involving the mass density

Wirgin¹

2019

Preprint

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This investigation is concerned with the 2D acoustic scattering problem of a plane wave propagating in a non-lossy fluid host and soliciting a linear, isotropic, macroscopically-homogeneous, lossy, flat-plane layer in which the mass density and wavespeed are different from those of the host. The focus is on the inverse problem of the retrieval of either the layer mass density or the real part of the layer wavespeed. The data is the transmitted pressure field, obtained by simulation (resolution of the forward problem) in exact, explicit form via separation of variables. Another form of this solution, which is exact and more explicit in terms of the mass-density contrast (between the host and layer), is obtained by a domain-integral method. A perturbation technique enables this solution to be cast as a series of powers of the mass density contrast, the first three terms of which are employed as the trial models in the treatment of the inverse problem. The aptitude of these models to retrieve the mass density contrast and real part of the layer wavespeed is demonstrated both theoretically and numerically.

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A Volume Integral Equation Method for the Direct/Inverse Problem in Elastic Wave Scattering Phenomena

Cited by 2 publications

References 11 publications

On the constant constitutive parameter (e.g., mass density) assumption in integral equation approaches to (acoustic) wave scattering

On the constant constitutive parameter (e.g., mass density) assumption in integral equation approaches to (acoustic) wave scattering

Forward and inverse acoustic scattering problems involving the mass density

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