Higher order terms of the asymptotic ray theory series solution for the acoustic wave equation in 2, 3 and higher dimensions

P. F. Daley

Often referred to, but rarely derived in practice, are the transport equations for higher order terms in an Asymptotic Ray Theory (ART) solution method for hyperbolic (wave) equations. In most instances in the literature only the first term (zero order) term in the asymptotic series is used in the computation of dynamic (amplitude) quantities. Higher order terms in the series will be derived here in any number of dimensions, with the emphasis on the two and three dimensional cases, and compared with the exact solution. The type of medium propagation will be assumed to be an infinite space and the hyperbolic equation used will be the simple acoustic wave equation with a constant velocity - homogeneous medium. In addition, the summation of the series (i)-n will be presented for use in a solution which has been assumed to be high frequency.