Coupled-mode field computations for media with locally reacting irregular boundaries

Coupled-mode methods have been used in underwater acoustics to compute three-dimensional sound propagation and scattering. Significant computational simplifications are possible for media with a lateral variation restricted to cylindrically symmetric anomalies, such as seamounts, and also for media which are invariant in one of the horizontal directions. Typically, the upper and lower depth boundaries of the medium have then been horizontal and flat. This paper generalizes the discrete coupled-mode method with a reflection- (or scattering-) matrix formulation to media with irregular and locally reacting boundaries. Horizontal and vertical segments thereby approximate a sloping boundary. Incorporation of the boundary conditions in a correct way necessitates modifications of the basic equation systems. Additional coupling matrices appear, involving integration of normal-mode products over the depth increments for adjacent regions of the medium. The paper includes three computational examples. One is from underwater acoustics with an island that rises above the sea level. The other two are from atmospheric acoustics with sound propagation over a locally reacting irregular ground surface. Using nonlinear optimization, it is possible to select a suitable artificial absorbing medium termination for a mode representation of the field.