Eikonal approximation and the parabolic equation

Abstract

We discuss two aspects of the general problem of sound propagation in an ocean characterized by a range-dependent profile. We first consider a normal-mode formalism for describing a situation in which the eikonal approximation can be applied in the horizontal plane. The difficulty with this approach is shown to be an ordering in the geometric optics path-length parameter due to mode coupling. By example we indicate how this difficulty can be overcome. We then use the formalism to discuss the approximations which make up the parabolic equation method. The parabolic equation is derived by assuming the eikonal approximation in the horizontal plane and a degenerate spectrum approximation. The degeneracy approximation is reflected in a stationary phase approximation to an integral representation for the pressure field. We then derive improved equations by relaxing these assumptions. We relax the degeneracy assumption by considering an improved stationary-phase approximation and we relax the eikonal assumption by considering the ’’supereikonal’’ approximation. Subject Classification: [43]30.20, [43]30.25, [43]30.50.