A numerical treatment of rough surface scattering for the parabolic wave equation

Abstract

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. Numerical PERUSE (PE Rough Surface) results for rough surface scattering in surface ducts are analyzed by resolving them in depth into the virtual modes of Labianca [J. Acoust. Soc. Am. 53, 1137–1147 (1973)]. The resulting modal intensities are then plotted as a function of range, and decay rates are estimated for each mode. Comparison with simple Rayleigh theory shows no obvious correlation; it appears that there is significant mode coupling due to the rough surface.