Computing effective reflection coefficients in layered media

Computations are presented which show that the effective reflection and transmission coefficients for a rough interface embedded in a layered medium can differ significantly from the mean reflection and transmission coefficients computed for the same rough interface when it separates two homogeneous half-spaces. These differences are large when the correlation length of the roughness is long compared to the skip distance of rays associated with normal modes in the layered medium. Otherwise, these differences may be generally neglected. However, increasing the rms roughness decreases the ratio of correlation length to skip distance at which the effect of the layering is important. The case of a Pekeris waveguide with a rough fluid–fluid interface and the case of a rough Dirichlet surface bounding an upwardly refracting medium are considered.