In a recent article the author gave a general theory of scattering by thin layers included in a continuous matrix. Such layers may be thought of as plates, shells, coatings, or interface layers depending on the particular physical context. It was shown that, in the general case, the scattering may be described in terms of the stress and momentum polarizations in the layer and that when the latter
... [Show full abstract] is thin compared with the wavelength of the incident sound, the through-thickness average polarizations satisfy certain boundary integral equations. In this article we develop the theory in the context of imperfect interfaces such as those which may occur in adhesive and diffusion bonds. The advantage of this approach is that it can account for general inhomogeneities and interfacial roughness provided that the root mean square thickness is small compared with the wavelength.