Effective reflection coefficients for the mean acoustic field between two rough interfaces

A formalism is presented which demonstrates that the mean Green's function for the acoustic field between two rough interfaces can be expressed as a Green's function associated with two flat interfaces with effective reflection coefficients. This result incorporates all orders of the fluctuations in the half-space scattering amplitudes associated with each interface considered separately. From the mean Green's function modal attenuations can be found. To lowest order in the surface height fluctuations it is shown that it is not sufficient to use mean half-space scattering amplitudes as effective reflection coefficients. The formalism is designed to provide approximations for the Green's function in layered media which are based on previously developed approximations for half-space scattering amplitudes.