On the use of stair steps to approximate bathymetry changes in ocean acoustic models

Stair-step discretization criteria have been established for accurately representing smoothly varying bathymetry in numerical models. It is shown that the strictest criterion applies to backscatter calculations, where the horizontal stair-step size must be a small fraction of an acoustic wavelength (Δx⩽λ/4). The forward scatter problem—assuming that backscatter is weak—can be accurately solved with an order-of-magnitude larger step sizes. A coupled-mode approach is used to illustrate solution convergence by computing backscattering from a single bottom facet as well as backscattering in the benchmark wedge used for checking ocean acoustic models in the 1987 benchmark session of the Acoustical Society of America (ASA). Published field solutions for the ASA wedge are used to illustrate forward scatter results.