| New parabolic equation methods are developed for modeling seismo-acoustic wave propagation in environments that involve complex range and depth dependence and variable topography.; The parabolic equation method is very efficient for solving range-dependent ocean acoustics and seismology problems. The approach is also accurate when range dependence is treated properly. This problem has been resolved for fluid media by applying energy-conservation and single-scattering corrections. These corrections have been less successful for problems involving elastic layers.; The development of an accurate and efficient elastic parabolic equation has proven to be more difficult than the development of the acoustic parabolic equation. Important unresolved problems remain in this area, including improving accuracy for range-dependent problems. Progress has been made through other approaches based on coordinate transformations such as mapping and rotating coordinates. These approaches provide improved accuracy, but do not fully resolve the problem.; Another key issue for the elastic problem is to handle depth dependence effectively. Progress in this area has been made with an improved formulation of the elastic parabolic equation that handles layering more effectively. The improved formulation uses the range derivative of the horizontal displacement and the vertical displacement as the dependent variables. In this formulation, solid-solid interfaces are treated effectively using Galerkin's method.; In this work, coordinate transformation techniques are applied to problems involving sloping fluid-solid interfaces, which is considered the most important unresolved issue in the development of parabolic equations. By combining the approaches that handle sloping interfaces accurately and the improved formulation, the first precise parabolic equation solutions are developed for this class of problem. Solutions are applied to classes of range-dependent problems that have never been solved before, such as modeling a Scholte (interface) wave along a sloping ocean bottom and its transition into a Rayleigh (boundary) wave beyond the shoreline. |
