### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 5aUW3. A numerical method for random two-way propagation in the Helmholtz
equation.

**Roger M. Oba
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*Naval Res. Lab., Stennis Space Center, MS 39529-5004
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Consider a strongly stratified ocean with randomness for which numerical
computation of average complex pressure with two-way propagation is to be made.
Let depth dependence be piecewise continuously differentiable and sediment be
modeled by a fluid bottom. Within a fixed range interval, model uncertainty by
an ensemble dependence upon some parameter in a continuously differentiable
way, and the range dependence to be piecewise constant over independent
intervals. For a single frequency source at a known depth, analysis for one
element of the ensemble proceeds via the Helmholtz equation in radial symmetry
and satisfies an outward radiation condition at large range. A previously
developed modification for finite length range intervals in finite depth of the
Kohler--Papanicolaou coupled mode equations in the forward scattering
approximation [R. M. Oba, Acoust. Lett. 16, 56--61 (1992)] computes the
transmission loss and phase for the average solutions for one-way propagation.
This paper presents a reformulation of this method to two-way propagation of
average solutions. This analysis will also show the development and computation
of averaged scattering type operators. [Work supported by Naval Research
Laboratory and ONR.]