A method of images for a penetrable acoustic waveguide

In this paper the complex-image approximation to the reflection coefficient for water over a seabed half-space is used to generate an image representation for a bounded acoustic waveguide with an underlying layered seabed. The images are true point sources; they have constant amplitudes which are raypath independent and, in the case of a Pekeris waveguide, frequency-independent. This image representation is ideal for constructing the Green's function kernel of the boundary integral equation method for target scattering in a waveguide. The singular behavior of the Green's function for an infinitesimal source/receiver separation, possibly with the target adjacent to one of the interfaces, is modeled correctly and the image expansion has a simple analytic form which can be analytically differentiated. The method is also accurate for significant source/receiver separations, which means that it can be used in the modeling of scattering from large-sized objects and can also be used as an efficient and accurate short-range propagation model for harmonic and broadband propagation in a penetrable waveguide.