Scaled mapping approach for treating sloping interfaces in range-dependent parabolic equation solutions, A

Abstract

An area of research in ocean acoustics is on solution techniques for environments with sloping seafloors. In these range-dependent environments the oceanic waveguide varies in the direction of propagation and exact analytic solutions do not exist. In order to enforce continuity conditions at the seaoor, the environment is approximated as a series of range-independent regions. An alternative to this approach, the mapping solution [M. D. Collins et al., JASA 107] applies a change of variables that results in a vertical translation of the environment and makes it easier to enforce ocean bottom interface conditions. An alternate mapping approach that uses a characteristic depth length scale is considered here. In contrast to the earlier mapping solution, the new approach uses a change of variables in which the depth variable is scaled relative to the depth of the bottom interface. The earlier approach distorted the surface, whereas the new mapping does not, which is a potential improvement. Along with the simplification of bottom interface conditions in both approaches, extra terms arising from the mapping are neglected. The new approach is implemented in a parabolic equation solution and is benchmarked against an existing solution. The accuracy of this new approach is established initially for problems involving fluid sediments.