Detecting a layered ellipsoid solving a near-field inverse acoustic scattering problem

The scattering problem of time-harmonic acoustic plane waves by a two-layered object consisting of a penetrable triaxial ellipsoid with a soft confocal ellipsoidal core is considered. A low-frequency formulation of the direct scattering problem as well as a Rayleigh approximation is described. Consi...

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Bibliographic Details
Published in:Journal of applied mathematics and bioinformatics 2018-04, Vol.8 (2), p.29-46
Main Authors: Athanasiadis, C E, Athanasiadou, E S, Arkoudis, I
Format: Article
Language:English
Subjects:
Acoustic scattering
Acoustics
Angles (geometry)
Approximation
Ellipsoids
Euler angles
Inverse problems
Mathematical analysis
Needles
Plane waves
Rayleigh number
Scattering
Spheroids
Studies
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Summary:The scattering problem of time-harmonic acoustic plane waves by a two-layered object consisting of a penetrable triaxial ellipsoid with a soft confocal ellipsoidal core is considered. A low-frequency formulation of the direct scattering problem as well as a Rayleigh approximation is described. Considering near-field data, an inverse acoustic scattering problem is formulated and studied. A finite number of measurements of the leading order term of the scattered field in low-frequency approximation leads to specify the semi-axes of the ellipsoids. The orientation of the ellipsoids is obtained by using the Euler angles. Solving a near-field inverse acoustic scattering problem for the ellipsoids gives results that can also be used for spheroids, spheres, needles and discs, considering them as geometrically degenerate cases of the ellipsoid for appropriate values of the physical and geometrical parameters.
ISSN:1792-6939
1792-6939