It is shown that phase errors associated with the standard parabolic wave equation can be eliminated in a range-independent environment by appropriately transforming the environment. Solutions to the standard parabolic equation (PE) in the transformed environment are close to solutions to the Helmholtz equation in the original environment in the sense that ray and asymptotic mode contributions to the PE wave fields have no phase errors relative to their Helmholtz equation counterparts. Although phase errors are eliminated in the PE wave fields, complete asymptotic equivalence to the Helmholtz equation wave fields is not attained. Ray- and mode-based wave-field expansions are used to illustrate similarities and differences between PE and Helmholtz equation wave fields. Numerical simulations show excellent agreement between PE wave fields in the transformed environment and mode-based solutions to the Helmholtz equation in the true environment.
ASJC Scopus subject areas
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics