David H. Berman
Dept. of Phys. and Astron., Univ. of Iowa, Iowa City, IA 52242
There are now a number of good approximations for plane-wave scattering from rough interfaces separating two half-spaces. This work will describe how these approximations can be used when there are two or more rough interfaces. The technique to be developed is based on matching approximate scattering states, expressed in terms of half-space scattering amplitudes, across source planes. Boundary conditions at interfaces are satisfied by the scattering states. It will be shown how the resulting description can be renormalized so that the mean field is described in terms of effective reflection coefficients at the interfaces, which are distinct from coherent half-space scattering amplitudes. It will also be shown that the method of smoothing gives a first-order approximation to a fully renormalized mean field. Expressions for effective modal attentuations will also be derived.