AN ENERGY-CONSERVING PARABOLIC EQUATION INCORPORATING RANGE REFRACTION

A new parabolic equation (PE) is presented that is independent of k0 and capable of handling relatively large range variations in the index of refraction. This equation is similar to, and ostensibly simpler than, an earlier range refraction PE (RAREPE). The modified range refraction parabolic equation (MOREPE) is obtained by a transformation approach, and operator and multiscale formalisms are described to validate the equation. Principal properties of MOREPE are developed, including energy conservation and possession of the correct (Helmholtz) rays in the high-frequency, small-angle limit. Exact solutions with range variation in sound speed are presented to illustrate differences between standard PE (SPE) and MOREPE. Propagation examples in range-independent environments demonstrate close agreement between MOREPE and SPE, while examples with strong range dependence exhibit significant differences between the two equations in their predictions of acoustic intensity. Analytical and numerical comparisons of solutions to the one-way Helmholtz equation (HE1), MOREPE, and SPE demonstrate the increased accuracy of MOREPE over SPE in range-dependent environments.