The Diffraction of an Acoustic Wave by an Embedded Quarter-Space

The subject of this paper is the diffraction of a plane harmonicwave when it falls upon a quarter-space with different transmissionproperties from the rest of unbounded space. A matching procedureallows asymptotic expressions for the field on the two planeinterfaces to be calculated in a fairly simple way. In orderto obtain these expressions, certain assumptions are made aboutthe asymptotic form of the field on the interface. These assumptionsare plausible and lead to consistent results. We begin with the problem of wave propagation in two weldedquarter-spaces due to excitation on the plane boundary. Thisproblem has an exact solution and provides an illustration ofthe method of matching asymptotic fields (not the method ofmatched asymptotic expansions). We then move on to the problemof a plane wave normally incident on our embedded quarter-spaceand derive exact expressions for the asymptotic field on theinterfaces. Finally, we include an analysis of oblique incidence.