A coupled mode solution for acoustic propagation in a waveguide with stepwise depth variations of a penetrable bottom

A coupled mode solution is formulated for the problem of acoustic propagation in a cylindrically symmetric ocean divided, in range, into a finite number of adjoining Pekeris waveguides of differing water depths. Attenuation is included in the bottom and the problem is discretized by assigning a pressure release boundary condition at a depth which is sufficiently far removed to prevent significant energy from returning to the water. This formulation includes backscatter from the depth variations of the water column and full coupling between a finite number of modes propagating in the water column and in the bottom. Numerical results based on an implementation of this solution are presented.