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

## 3pUW11. Range/depth dependence of long-range reverberation in shallow
water.

**Ji-Xun Zhou
**

**
Xue-Zhen Zhang
**

**
Peter H. Rogers
**

**
**
*School of Mech. Eng., Georgia Inst. of Technol., Atlanta, GA 30332
*

*
*
Using an angular power spectrum method can greatly simplify some
calculations for shallow water sound transmission, long-range reverberation,
and their spatial coherence. The method is based on normal mode and ray-mode
analogies and originally appeared in Chinese papers that are not available in
English [J. X. Zhou, Acta Acust. Sin. 5, 86--99 (1980) and Acta Oceano. Sin. 1,
212--217 (1979)]. The average field intensity is calculated by summing the
power spectrum of local plane waves for all normal modes propagating in
different directions. In this presentation, analytical expressions for
range/depth dependences of the propagation, long-range reverberation, and
echo-reverberation ratio are given for two cases: a linear negative gradient
layer and a Pekeris model. The results will be compared with some experimental
data. At small grazing angles the bottom equivalent scattering coefficient is
expressed as M((theta),(phi))=(mu) sin[sup m] (theta) sin[sup n] (phi). The
range dependence of echo-reverberation ratio (ER) in the three-half law region
(r[sup -3/2]) for the Pekeris model can be expressed as ER(r)~r[sup (m+n-2)].
It will decrease or increase with increasing distance. For Lambert's scattering
law (m=n=1), ER should be independent of the distance. In a linear negative
gradient shallow water, ER(r,z;z[sub 0])~F(z,z[sub 0])/r. An analytical
expression of the depth distribution function F(z,z[sub 0]) will be given.
[Work supported by ONR.]