Atmospheric sound propagation in a stratified moving media: Application of the semi analytic finite element method

This article presents a finite element based solution of the exact governing wave equation for a stratified inhomogeneous moving media. The model is applied to a two dimensional range independent problem in outdoor sound propagation in which the ground is treated as perfectly reflecting. The sound pressure field is expanded as a sum over eigenmodes propagating in the range direction, and the semi analytic finite element method is used to solve the governing eigenequation. This delivers faster solution times when compared to traditional finite element based methods while simultaneously accommodating continuous variations in fluid properties in the vertical direction. In principle, the method converges toward the exact solution and so delivers a benchmark method for range independent problems. The method is shown to provide excellent agreement with analytic solutions, and good convergence is demonstrated for more complex problems, including temperature inversions and logarithmic profiles for wind velocity. Finally, qualitative comparisons are made against infrasound predictions, including those obtained using wide angle parabolic equations. The method is shown to provide a focussed image of the sound pressure field over large distances, as well as to reproduce multiple turning points and ground interactions.