Acoustic scattering from a ‘‘Pierson–Moskowitz’’ sea surface

Abstract

The validity of the Kirchhoff and perturbation approximations for scattering from ‘‘Pierson–Moskowitz’’ sea surfaces has been examined through comparison with exact results obtained by solving an integral equation. The height of the surfaces used varies in only one direction. All results are for an acoustic frequency of 200 Hz and for incident grazing angles of 10°–20°. The Kirchhoff approximation accurately predicts incoherent scattering near the specular direction. First-order perturbation theory yields bistatic backscattering levels that are 1–3 dB low for the examples studied. When the scattering cross section is calculated to order (kh)4 using perturbation theory, the accuracy for bistatic backscattering is excellent, even when kh is as large as 1.79. Here k is the acoustic wave number and h is the root-mean-square (rms) surface height. An easily evaluated approximation to the scattering cross section to order (kh)4 has also been obtained. The Kirchhoff approximation for the coherent reflection loss is more accurate than second-order perturbation theory when the reflection loss exceeds about 1 dB. For lower losses, the perturbation result is more accurate. The composite-roughness model has been examined for monostatic backscattering. The model is accurate at a grazing angle of 20° but predicts a scattering level that is higher than the exact result at a grazing angle of 10°.