The Green`s function for an acoustic, half-space impedance problem Part II: Analysis of the slowly varying and the plane wave component

We show that the acoustic Green`s function for a half-space impedance problem in arbitrary spatial dimension d can be written as a sum of two terms, each of which is the product of an exponential function with the eikonal in the argument and a slowly varying function. We introduce the notion of families of slowly varying functions to formulate this statement as a theorem and present its proof.