### ASA 129th Meeting - Washington, DC - 1995 May 30 .. Jun 06

## 2pUW2. Combined volume and surface scattering in a channel using a modal
formulation.

**Shimshon Frankenthal
**
M. J. Beran

**
**
*Dept. of Elec. Eng., Catholic Univ. of America, Cardinal Station,
Washington, DC 20064
*

*
*
In previous work, a modal approach was used to study random volume
scattering in a shallow channel [M. J. Beran and S. Frankenthal,
3203--3211 (1992)]. Here, the way to include the effects of a rough channel
surface in the formulation is shown. To include the effects of a rough surface,
the modes are taken to be dependent on the range and transverse coordinates in
addition to the depth coordinate. The propagation is studied in terms of the
ensemble-averaged two-point coherence function and the equation governing the
coherence function is derived. In order to insure energy conservation when the
generalized modal field equations are simplified, the parabolic approximation
is replaced by a method which includes both forward and backward propagating
fields. The two-point coherence function is expressed as the sum over both
self-modal and cross-modal coherence functions. The difference between the
equations governing the self-modal coherence functions and the cross-modal
coherence functions is considered. A numerical example which uses typical
shallow water parameters is presented. Figures portray how the mode energies
are transferred between the modes as the acoustical field propagates. [This
work was partially supported by ONR.]