A generalized impedance method for application of the parabolic approximation to underwater acoustics

The parabolic equation (PE) has become an important computational tool for approximating underwater acoustic path losses in inhomogeneous environments. The numerical solution of this equation is performed on a grid over the propagation medium which includes the water column, and has also included a homogeneous ‘‘false bottom’’ below the actual ocean bottom. This situation is viewed as one in which the propagation medium can be divided into a horizontally inhomogeneous upper layer and a horizontally homogeneous lower layer. The pressure field in the latter layer is found using standard techniques valid for homogeneous media, and in the former layer is found using an implicit finite difference scheme. These fields and their normal derivatives are matched along the interface between the layers. The result is referred to as a generalized impedance boundary condition (GIBC), which serves to eliminate the need for a false bottom. Predictions obtained using the standard parabolic equation and a completely homoge...