(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hu, Guanghui; Lu, Yulong; Zhang, Bo
This paper is concerned with the inverse scattering of time-harmonic
elastic waves from rigid periodic structures. We establish the factorization
method to identify an unknown grating surface from knowledge of the scattered
compressional or shear waves measured on a line above the scattering surface.
Near-field operators are factorized by selecting appropriate incident waves
derived from quasi-periodic half-space Green’s tensor to the Navier
equation. The factorization method gives rise to a uniqueness result for the
inverse scattering problem by utilizing only the compressional or shear
components of the scattered field corresponding to all quasi-periodic
incident plane waves with a common phase-shift. A number of computational
examples are provided to show the accuracy of the inversion algorithms, with
an emphasis placed on comparing reconstructions from the scattered near-field
and those from its compressional and shear components.
