Application of the operator expansion method to scattering of low frequency sound from the ocean surface

The operator expansion (OE) method, a new approximation for computing scattering from rough surfaces proposed by Milder (1991), is applied to the problem of low frequency (200 Hz) acoustic scattering from one-dimensional (1D) randomly rough surfaces used to model the ocean surface. The accuracy of the OE solution is determined through comparison with the exact solution obtained by solving an integral equation. Both methods compute scattering from a single deterministic surface; comparisons are presented for averages computed using 50 surface realizations. The OE solution is cast as a series which is found to be rapidly convergent and accurate over a wide range of incident and scattering angles. Alternative forms of the OE series solution also proposed by Milder prove to be more efficient than the standard series at obtaining an accurate solution. The authors´ numerical studies for 1D surface scattering indicate that rapid convergence of the OE solution is always associated with its accuracy; this behavior is expected to carry over to scattering from 2D surfaces, for which exact solutions are still very costly