Acoustic wave scattering from a randomly rough surface

Acoustic wave scattering from a randomly rough surface is studied using a multiple scattering analysis. Assuming the surface asperities to be small, approximate boundary conditions are used to derive a pair of coupled integral equations for the velocity potentials. The Dyson equation is next derived on introducing symbolic operators. Using the bilocal approximation the Dyson equation is solved, thereby obtaining explicit expressions for the coherent reflection and transmission coefficients. The analysis is similarly carried on further to compute the incoherent intensity by using the ladder approximation, and hence an expression for the scattering coefficient is obtained.