Gregory J. Orris
U.S. Naval Res. Lab., Washington, DC 20375
The application of the Foldy--Wouthuysen transformation on the Helmholtz equation has been previously demonstrated [J. Acoust. Soc. Am. 96, 3343 (A) (1994)]. The result provides an asymptotic expansion for correction terms to the parabolic equation (PE). These terms include contributions from the coupling of the forward propagating and backward propagating solutions to the Helmholtz equation, caused by propagation through range-dependent media. The new correction terms have been found to depend on the curvature of the local index of refraction and can be calculated from available environmental parameters. A finite element PE (FEPE) has been modified to include these new correction terms. This new PE is used to model propagation of an acoustic field through an ocean with fluctuating sound-speed profiles caused by internal waves and other range-dependent oceanographic properties. The effects of these new terms and the circumstances under which they are expected to be most important are discussed, with special emphasis placed on global-scale propagation.