Geodesic
Determination of the inhomogeneity parameters of an elastic ball anisotropic outer layer by the scattering of a plane sound wave
Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 350-367

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The problem of determining the type of inhomogeneity of the external anisotropic layer of an elastic ball from the scattered field of a plane sound wave is considered. It is assumed that the density and elastic moduli of the outer layer material are linear functions of the distance from the center of the ball. It is believed that the laws of dependency of all moduli of elasticity are identical. According to the acoustic pressure in the vicinity of the ball, it is required to determine the coefficients in the dependences for the density and elastic moduli. The problem of sound diffraction by a ball is solved by a numerical-analytical method. The scattered acoustic field and the field of elastic oscillations in the homogeneous part of the ball is represented by an expansion in terms of spherical harmonics. For the displacement and stress vector components in an inhomogeneous layer, a boundary value problem is numerically solved based on the equations of motion and boundary conditions on the layer surfaces. To determine the desired coefficients in the dependences of the density and elastic moduli of the outer layer, the observed pressure values are compared at a certain set of points on a spherical surface centered at the center of the ball and the calculated pressure values at these points. A variant of forming an indicator of the proximity of observed and calculated pressure values based on the division of observation points into groups is proposed. It is proposed to use the proximity indicator to identify the coefficients in the laws of density inhomogeneity and elastic moduli in the layer.
Keywords: sound scattering, plane sound wave, layered inhomogeneous elastic ball, transversally isotropic layer, numerical-analytical solution of the diffraction problem, coefficient inverse problem, proximity indicator. 
@article{CHEB_2022_23_4_a27,
     author = {S. A. Skobel'tsyn},
     title = {Determination of the inhomogeneity parameters of an elastic ball anisotropic outer layer by the scattering of a plane sound wave},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {350--367},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a27/}
}
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S. A. Skobel'tsyn. Determination of the inhomogeneity parameters of an elastic ball anisotropic outer layer by the scattering of a plane sound wave. Čebyševskij sbornik, Tome 23 (2022) no. 4, pp. 350-367. http://geodesic.mathdoc.fr/item/CHEB_2022_23_4_a27/