Eliminating phase errors in parabolic equation propagation models by perturbing the index of refraction

Abstract

For a fixed index of refraction, solutions of a parabolic equation consist of local normal modes added together using phase factors that are distortions of those of the Helmholtz equation. A method is presented for perturbing the index of refraction in such a way that the distortedphasefactors using a parabolic equation with the perturbed index are precisely the same as the desiredphasefactors that would have been obtained from the Helmholtz equation with the original index of refraction. The phase errors of numerous types of parabolic equations can be be eliminated in this way because the analytic form of the distortion of the phase factors follows from whatever formula has been used to approximate a certain square root. In addition, the perturbation of the index of refraction can be efficiently updated at each range step in a range-dependent environment.