An estimate of the accuracy of the Kirchhoff approximation in acoustic wave scattering from rough surfaces

Abstract

The author constructs a variational principle for the scattering coefficient of an acoustic wave incident onto a rough surface. The surface is taken to obey Dirichlet boundary conditions and has a roughness described statistically. Substitution of the acoustic Kirchhoff approximation into this variational principle, as a trial field, leads to a comparison of the results obtained using the Helmholtz scattering formula and the variational approach. They use the results obtained from this comparison to give an estimate of the accuracy of the former method. They conclude that the Helmholtz/Kirchhoff method gives a result equal to the 'optimum' available result, when using this form of trial field, for the special cases of specular and back-scattered signals from a smooth defect. The inclusion of roughness decreases the accuracy of the Helmholtz/Kirchhoff method and a better estimate of the true scattering coefficient is obtained using the variational principle.