### ASA 125th Meeting Ottawa 1993 May

## 2aAO3. New results for the elastic parabolic equation.

**Michael D. Collins
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*Naval Research Laboratory, Washington, DC 20375
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New results are presented for the elastic parabolic equation (PE).
Galerkin's method is applied to handle solid--solid interfaces efficiently.
Rayleigh and Stoneley waves are handled with the elastic PE for the first time.
Conversion formulas that are local in range are derived for obtaining
quantities such as the horizontal displacement and the shear potential from the
dependent variables of the nonstandard formulation of elasticity that is used
with the elastic PE. The two-way elastic PE is implemented for problems
involving realistic boundary and interface conditions and is applied to solve
reverberation problems. The self-starter is generalized to problems involving a
source in a solid layer. The energy-conserving PE is generalized to elastic
media. The elastic PE is applied to problems involving the propagation of an
interface wave up a sloping bottom and the cutoff of modes and coupling into
shear-wave beams in the sediment. The latter problem is analogous to an
acoustic problem that was solved by Jensen and Kuperman [``Sound propagation in
a wedge-shaped ocean with a penetrable bottom,'' J. Acoust. Soc. Am. 67,
1564--1566 (1980)].