Sound propagation over inhomogeneous ground including a sound velocity profile

The atmospheric profile whose sound speed varies linearly with height is simple in concept, but leads to complications when solving for the sound pressure. Its effects are commonly approximated by a similar profile whose squared refractive index is a linear function of height. In this paper, the validity of the approximation has been examined for sound propagation above an impedance ground and a computational approximation is given. The method relies upon a family of radiation boundary conditions for the wave equation derived by truncating a summation function approximation of a corresponding plane wave reflection coefficient representation. It is demonstrated how these boundary conditions can be formulated in terms of a finite element approach. Numerical examples illustrate results with four coefficients included at the upper fictitious boundary conditions for the case of sound propagation above a grass-strip and sound propagation over the grass-strip with an atmospheric profile.