### ASA 127th Meeting M.I.T. 1994 June 6-10

## 3aUW7. A complete energy-conservation correction for the elastic parabolic
equation.

**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.