Generalization of the rotated parabolic equation to variable slopes

The parabolic equation method is very efficient for solving range-dependent propagation problems. This approach is also accurate when range dependence is treated properly. This problem was resolved for fluid media by applying energy-conservation [J. Acoust. Soc. Am. 89, 1058–1075 (1991)] and single-scattering [J. Acoust. Soc. Am. 91, 1357–1368 (1992)] corrections. Since these corrections were less successful for problems involving elastic layers, other approaches such as mapping [J. Acoust. Soc. Am. 107, 1937–1942 (2000)] and rotating [J. Acoust. Soc. Am. 87, 1035–1037 (1990)] coordinates were investigated. In this presentation, the rotated parabolic equation solution is generalized to problems involving variable slope. The medium is divided into a series of regions with constant slope. When changes in slope are encountered, the field is propagated beyond the change and then used to interpolate and extrapolate onto a computational grid that is rotated relative to the previous grid. This approach is implemented and tested for the fluid problem. It should also be applicable to the elastic problem, but it will be necessary to apply a change of variables each time the slope changes since the dependent variables are the tangential and normal displacements. [Work supported by ONR.]