On the Theory of Sound Propagation in a Velocity Gradient Near an Impedance Boundary

lntrod uctionAlthough several numerical methods including Fast Field.Parabolic Equation and Normal Mode Solutions are available for predicting outdoor sound propagation over a flat nite impedance ground.ray trace methods offer greatest convenience both in terms of computation and physical insight.Traditional ray trace methods cannot allow properly for interaction with the ground.On the Other hand a heuristic modi cation of the classical Weyl-Van der Pol formulation of the total eld in the presence of the ground has been advocated for incorporation in ray tracing codes.By using a WKB method of approximation a closed form solution to propagation in an am sound velocity gradient has been obtained.In the limit of zero gradient the solution reduces to the standard form for a homogeneous atmosphere.If the velocity gradient is linear then it is shown that the solution may be reconciled with the Airy function form for propagation with upward refraction and the normal mode solution for downward refraction.