Michael D. Collins
Naval Res. Lab., Washington, DC 20375
William L. Siegmann
Rensselaer Polytech. Inst., Troy, NY 12180
The accuracy of a partial energy-conservation correction for the parabolic equation (PE) method is excellent for range-dependent ocean acoustics problems involving fluid sediments [M. D. Collins and E. K. Westwood, J. Acoust. Soc. Am. 89, 1068--1075 (1991)] but only fair for problems involving elastic sediments [M. D. Collins, J. Acoust. Soc. Am. 94, 975--982 (1993)]. A complete energy-conservation correction has been developed to improve accuracy for the elastic case. A range-dependent elastic waveguide is approximated by a sequence of range-independent regions. The complete energy-conservation correction involves matching energy flux across the vertical interfaces between the range-independent regions. The flux condition and the PE operator are used to obtain a nonlinear boundary value problem for the transmitted field that reduces to a linear boundary value problem for the fluid case. The flux integral is related to the inner product for the normal modes of the depth separated elastic wave equation. This fact is exploited to derive an efficient iteration formula for the elastic case.