PERUSE: a numerical treatment of rough surface scattering for the parabolic wave equation

Scattering of underwater acoustic signals from real ocean surfaces often does not fit into any of the classical theoretical approaches to the problem. Thus the need for a numerical approach is clear. A novel method is presented that uses a sequence of conformal mappings to locally flatten successive segments of the surface, which is assumed piecewise linear and frozen in time. Each conformal mapping preserves the elliptic form of the reduced wave equation, so that in each transformed space the parabolic approximation can be made and the solution advanced one range step using the split-step Fourier algorithm. This PERUSE (PE RoUgh SurfacE) numerical method is validated by exhibiting classically predicted Bragg angle peaks for single scatter of a plane wave from a sinusoidal surface. For multiple rough surface scattering in surface ducts, PERUSE results are analyzed by resolution in depth into the virtual modes of Labianca [J. Acoust. Soc. Am. 53, 1137–1147 (1973)]. The resulting modal intensities are then plotted as functions of range, and decay rates are estimated for each mode. Comparison with a classical ray-based scattering theory shows no obvious correlation; it appears that there is significant mode coupling due to the rough surface.