The antiplane shear, SH or scalar problem of scattering from an interface characterized by a narrow region of heterogeneity is considered. An approximate integral representation of the scattered wave fields in terms of a Green’s function for a reference problem, and the stress and momentum polarizations averaged through the thickness of the interface is derived. Providing certain material contrast parameters areO(1), the error in this expression is formallyO(kh)2, wherekis the wave number and 2his the thickness of the interface. To find the unknown polarizations we specialize to a model configuration that is periodic over a length scale much greater than the characteristic length scales of the heterogenities in the interface. This allows an exact formulation in terms of an infinite system of algebraic equations. Expressions modeling the reflection and transmission measured by a coaxial, confocal pair of transducers are then derived so that the effects of the transducer can be included in the modeling. These coefficients are calculated in terms of the solution of the algebraic system. Numerical results for several different model interfaces are presented.