Modeling Bistatic Surface Scattering Strength Including a Forward Scattering Lobe with Shadowing Effects

Both the rough air-sea interface and entrapped air bubbles due to wave breaking scatter sound in all directions and contribute to so-called reverberation in active sonar. There are monostatic sonar systems where the source and receiver are at the same position, bistatic sonar systems where the source and receiver are separated, and multistatic sonar systems involving multiple sources and receivers at different positions. In monostatic situation, reverberation is mainly due to backscattering. In bistatic and multistatic situation, forward and out-of-plane scattering are significant contributors. The empirical Chapman-Harris formula is often used to predict surface backscattering strength in monostatic sonar. To better predict reverberation due to the sea surface in bistatic or multistatic sonar, a three-dimensional scattering formula that includes a forward scattering lobe will be desirable. Following the approach of earlier work, in this paper the separable form of backscattering models are extended by including an expression of forward scattering lobe obtained under the Kirchhoff approximation, taking into account shadowing effects. Comparison with another more sophisticated model shows that shadowing corrections are important at low grazing angles. The formula obtained here is simple and includes scattering effects from both the roughness of the sea surfaces and the sub-surface bubbles. It may be useful for modelling multistatic surface reverberations.