Direct and Inverse Medium Scattering in a Three-Dimensional Homogeneous Planar Waveguide

Source abstract

Time-harmonic acoustic waves in an ocean of finite height are modeled by the Helmholtz equation inside a layer with suitable boundary conditions. Scattering in this geometry features phenomena unknown in free space: resonances might occur at special frequencies, and wave fields consist of partly evanescent modes. Inverse scattering in waveguides hence needs to cope with energy loss and limited aperture data due to the planar geometry. In this paper, we analyze direct wave scattering in a three-dimensional planar waveguide and show that resonance frequencies do not exist for a certain class of bounded penetrable scatterers. More important, we propose the factorization method for solving inverse scattering problems in the three-dimensional waveguide. This fast inversion method requires near-field data for special incident fields, and we rigorously show how to generate this data from standard point sources. Finally, we discuss our theoretical results in light of numerical examples.