Modeling Underwater Acoustic Scattering From Rough Surface

Scattering is a fundamental element on both multipath and reverberation researches. The incoherent scattering is described by small slope approximation (SSA) here for both sea surface and Biot medium on base of Kirchhoff approximation and perturbation method. The derivation of the SSA for surfaces subject to both the Dirichlet boundary condition and Biot medium is examined in detail here.The SSA T-matrix series, which can be interpreted as an expansion in a generalized surface slope, satisfies the appropriate reciprocity condition at each order and reduces to the standard perturbation series for small surface roughness. When the SSA T matrix is found to second order in generalized slope, it reduces to that of the Kirchhoff approximation as the frequency is increased. In this paper the accuracy of the SSA for the Dirichlet problem is investigated by comparison with exact results (Integration Equation Method). Numerical results for one-dimensional surfaces with a Gaussian roughness spectrum are demonstrated. Surfaces with rms slope angles up to (or nearly) 45°are considered.It is found that, for the numerous cases studied, the SSA results agree well with the exact results over a broad range of scattering angles. The range of scattering angles over which the SSA results are accurate depends on both the rms slope angle and the surface correlation length, as well as on the angle of incidence.A further study of Biot medium incoherent scattering is inspired by results described above. The lowest term of the sea bottom incoherent scattering is demonstrated in detail. Thus the small slope approximation of Voronovich is a promising method for modeling wave scattering from rough surfaces.