Gh. Brooke et al., A SLOPING BOUNDARY-CONDITION FOR EFFICIENT PE CALCULATIONS IN RANGE-DEPENDENT ACOUSTIC MEDIA, Journal of computational acoustics, 4(1), 1996, pp. 11-27
The traditional one-way parabolic equation (PE) formulation for range-
dependent layered acoustic media is modified to include effects associ
ated with the boundary conditions along a sloping interface. Essential
ly, the boundary condition for continuity of the normal displacement a
long a sloping interface is cast in an approximate form which does not
depend on range but does contain terms up to second order in the deri
vatives with respect to depth. The new sloping-boundary condition is t
hen applied along an ''equivalent'' horizontal interface within each r
ange-independent step of the PE. Numerical results obtained for standa
rd test cases indicate that the sloping-boundary condition, incorporat
ed into a one-way PE, maintains the efficiency yet improves the accura
cy of forward predictions.