The problem of bulk wave insonification of a uniform membrane under specified conditions of compressible fluid-loading is considered. Specific attention is paid to the acoustic response within a wavelength or so of the boundary and a uniform asymptotic description is obtained from a multiple scales analysis. A crucial feature of this analysis is the identification of boundary points, possibly complex, about which the reflection process is non-regular. Posing and solving a suitable inner diffraction problem then reveals that this is related to the excitation of a surface wave at such points. The inner analysis predicts not only the amplitude and phase of this contribution, but also the portion of the boundary that the surface wave occupies. It is demonstrated that this domain is a region of the complex extension of the boundary and that rays emitted from this domain intersect the physical plane, yielding the acoustic radiation that accompanies the surface wave. Knowledge of this radiation pattern then permits a new geometrical interpretation of the far-field spatial cut-off phenomenon associated with such radiation. It also extends existing theories of surface ray excitation and propagation by offering a method by which regions of existence of complex surface rays, propagating within the complex extension of the physical boundary, can be determined. This is shown to be intimately related to the effects of Stokes' phenomenon upon the diffraction solution local to the point of surface ray excitation.