An energy-conserving parabolic equation for elastic media

Abstract

The accuracy of the parabolic equation (PE) method is improved for range‐dependent elastic media. The energy‐conserving elastic PE is a generalization of the energy‐conserving acoustic PE. A range‐dependent waveguide is approximated by a sequence of range‐independent regions. A linear approximation is derived for the nonlinear condition corresponding to conservation of compressional energy flux at the vertical interfaces between range‐independent regions. The rotated elastic PE is applied to generate reference solutions for demonstrating accuracy. The energy‐conserving elastic PE is applied to solve problems involving the propagation of an interface wave along a sloping ocean bottom and a problem involving mode cutoff and coupling into shear wave beams in the ocean bottom. The latter problem is analogous to a cutoff problem that was first solved with the acoustic PE [F. B. Jensen and W. A. Kuperman, J. Acoust. Soc. Am. 67, 1564–1566 (1980)].