  Several methods for handling sloping fluid-solid interfaces with the elastic
parabolic equation are tested. A single-scattering approach that is modified
for the fluid-solid case is accurate for some problems but breaks down when the
contrast across the interface is sufficiently large and when there is a Scholte
wave. An approximate condition for conserving energy breaks down when a Scholte
wave propagates along a sloping interface but otherwise performs well for a
large class of problems involving gradual slopes, a wide range of sediment
parameters, and ice cover. An approach based on treating part of the fluid
layer as a solid with low shear speed handles Scholte waves and a wide range of
sediment parameters accurately, but this approach needs further development.
The variable rotated parabolic equation is not effective for problems involving
frequent or continuous changes in slope, but it provides a high level of
accuracy for most of the test cases, which have regions of constant slope.
Approaches based on a coordinate mapping and on using a film of solid material
with low shear speed on the rises of the stair steps that approximate a sloping
interface are also tested and found to produce accurate results for some cases.
