THE ROTATED PARABOLIC EQUATION AND SLOPING OCEAN BOTTOMS

A new approach for solving problems involving sloping ocean bottoms with the parabolic equation (PE) method is presented. In most implementations of the PE, range-dependent environments have been approximated as a sequence of range-independent regions. The PE, which has one range derivative, does not conserve both pressure and the normal component of particle velocity across boundaries between regions. For problems involving sloping ocean bottoms, this can lead to large errors for slopes of only a few degrees. The rotated PE, which marches parallel to the ocean bottom and has two normal derivatives, handles sloping interfaces properly. A benchmark solution for an upslope problem is presented to demonstrate the accuracy of the rotated PE. © 1990, Acoustical Society of America. All rights reserved.