Asymptotic (in the geometric limit) phase errors associated with parabolic approximations to the one-way Helmholtz equation are investigated. In order to estimate the phase accuracy of various parabolic approximations, the canonical Hamiltonian formalism is used to derive ray equations. It is shown that among the class of parabolic approximations that allow the split-step Fourier algorithm to be used, the wide-angle c0-insensitive approximation [Tappert et al., J. Acoust. Soc. Am. 97, 2771-2782 (1995)] has full second- order accuracy. Other approximations in this class, such as the Thomson- Chapman and the Berman-Wright-Baer approximations, are shown to have second- order errors, as does the standard first-order parabolic approximation. Numerical calculations support the expectation that among this class of parabolic approximations the wide angle c0-insensitive approximation is superior.
ASJC Scopus subject areas
- Arts and Humanities (miscellaneous)
- Acoustics and Ultrasonics