A NUMERICAL APPROACH TO ROUGH-SURFACE SCATTERING BY THE PARABOLIC EQUATION METHOD

The parabolic equation method is an effective approach when the acoustic wave field is incident at low grazing angles onto a rough surface. The method consists of an integral equation and an integral, the first of which yields the surface field derivative. The main part of this paper is concerned with an approximation to this equation, valid when wavenumber times surface height is up to order unity. The approximation has several advantages. First, it allows a decomposition of the equation into deterministic and stochastic components. The stochastic part depends only locally upon the surface in certain regimes, and this can give rise to a great reduction in computational expense. Some basic statistical moments of the stochastic component are also considered. These are nonstationary, but for the incident field a simple stationary transformation is found, which can therefore be compared with Monte Carlo simulations using far fewer realizations. These results are demonstrated computationally. The final part of the paper describes the numerical implementation of the full parabolic equation method. Both of the integrals contain singularities, and these are treated semianalytically. © 1990, Acoustical Society of America. All rights reserved.