Extension of the Rotated Elastic Parabolic Equation to Beach and Island Propagation

Improvements in the capability of handling sloping interfaces and boundaries with the parabolic equation method have been an active area of research. Recent progress in accurately treating range-dependent seismoacoustic problems has involved coordinate transformation techniques. The variable-rotated parabolic equation is among recent advances in this area. The solution rotates the coordinate axes to achieve greater accuracy in the presence of range-dependent bathymetry. At points of slope change the rotated solution interpolates and extrapolates the field into adjacent regions. This approach is extended to solve problems involving variable topography (above-ocean-surface sediments) by accounting for the transition and boundary conditions at the water/solid/air interfaces. It is applied to range-dependent problems of sound transmission up a beach and through an island. The method is benchmarked for accuracy against a finite-element solution.