### ASA 124th Meeting New Orleans 1992 October

## 3aUW7. Eliminating phase errors in parabolic equation propagation models
by perturbing the index of refraction.

**David H. Wood
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*Dept. of Comput. and Inform. Sci., Univ. of Delaware, Newark, DE 19716
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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 distorted phase factors using a
parabolic equation with the perturbed index are precisely the same as the
desired phase factors 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.