A near-field inverse scattering problem for an elastic ellipsoid

The scattering problem of time-harmonic elastic waves from a triaxial rigid ellipsoidal obstacle is considered. The direct scattering problem is formulated. A method using near-field data for solving the corresponding inverse scattering problem in order to specify the size and the orientation of the ellipsoid is described. A matrix with elements given in terms of measurements of the leading low-frequency coefficient of the scattered field is constructed. The eigenvalues of this measurement matrix provide information for the semi-axes of the ellipsoid whereas the eigenvectors together with a rotation matrix whose elements are given in terms of the Euler angles are used to specify the orientation of the ellipsoid. Corresponding results for geometrically degenerate cases of the ellipsoid such as spheroids, spheres, needles and disks are obtained for appropriate values of the geometrical parameters. (C) 2019 Elsevier B.V. All rights reserved.