A mapping approach for handling sloping interfaces

A mapping approach for handling sloping interfaces in parabolic equation solutions is developed and tested. At each range, the medium is rigidly translated vertically so that a sloping interface becomes horizontal. To simplify the approach, the slope is assumed to be small and the extra terms that arise in the wave equation under the mapping are neglected. The effects of these terms can be approximately accounted for by applying a leading-order correction to the phase. The mapping introduces variations in topography, which are relatively easy to handle for the case of a pressure-release boundary condition. The accuracy of the approach is demonstrated for problems involving fluid sediments. The approach should also be accurate for problems involving elastic sediments and should be useful for solving three-dimensional problems involving variable topography.