An explicit factorization of the Green's function for an acoustic half-space problem with impedance boundary conditions into an oscillatory exponential and a slowly varying function

In this paper, new representations of the Green’s function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms that appear also in the case of Dirichlet or Neumann boundary conditions, the remaining part of the Green’s function is factored into an oscillatory complex exponential function (with the product of the wavenumber and the eikonal as argument) and a remaining function which is slowly varying and hence allows for efficient polynomial approximation; b) the representation is given uniformly for all parameters by a single formula which consists of the product of two analytic functions.