Some properties on far-field pattern of scattering by penetrable obstacle in ocean waveguide

This paper is concerned with the properties of propagation far-field patterns corresponding to the scattering of time harmonic acoustic waves by a bounded penetrable obstacle in an ocean waveguide.The sets of solutions to the transmission problem are constructed such that the restriction of these solutions to the boundary of the penetrable obstacle is dense in a Hilbert space.Then conditions under which a set of propagation far-field patterns is complete in a Hilbert space are determined.These properties are important in investigating inverse transmission problems in an ocean waveguide.