David H. Berman
Dept. of Phys. and Astron., Univ. of Iowa, Iowa City, IA 52242
This is a continuation of a study of how to incorporate recently developed approximations for rough surface scattering into the description of propagation in a waveguide with rough boundaries and rough interior interfaces. Although reflection and transmission coefficients are not directly useful in variable sound-speed media, it is possible to derive from them an impedance operator that linearly relates pressures on either side of an interface to displacements on either side of the interface. This linear relationship can then be used in a variable sound-speed environment. It will be shown how the Green's function in a two-layered duct with a rough interior interface can be constructed from solutions for flat-surface Dirichlet and Neumann Green's functions. The averaged Green's function can be seen to be the Green's function for a two-layered duct with effective reflection and transmission coefficients across the mean interface separating the two layers. These effective reflection and transmission coefficients are not simply the mean reflection and transmission coefficients found at an interface separating two half-spaces; they include effects of multiple scattering between the boundaries of the waveguide. This work generalizes that discussed in D. H. Berman [J. Acoust. Soc. Am. 94, 1786(A) (1993)] where only reflection was treated.