Roger M. Oba
Naval Res. Lab., Stennis Space Center, MS 39529-5004
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.]