I-l 



I. I^^ITRODUCTION 



A. PURPOSE AND SCOPE 



The purpose of this report is to survey our current understanding of 

 the effect of small random inhomogeneities on the propagation of acoustic waves 

 in the ocean. The inhomogeneities of interest to us are small in comparison to 

 the over-all dimensions of the medium: small compared to the ocean depth or 

 the depth of the principal ocean layers and small compared to the length of the 

 path of propagation. In particular, we have in mind such inhomogeneities as air 

 bubbles, marine organisms, surface roughness (as opposed to large-scale in- 

 homogeneities such as sea mounts) and the innumerable local fluctuations of tem- 

 perature, density and salinity which are commonly referred to as the ocean micro- 

 structure. In practice we invariably encounter very large numbers of inhomo- 

 geneities, located at random throughout the medium. Furthermore, some of 

 the inhomogeneities are of an indistinct or irregular shape. This is particularly 

 true of the patchy thermal structure and the irregular surface and bottom. 



The small inhomogeneities of the ocean affect a propagating sound 

 wave in a number of ways. To the extent that the inhomogeneities cause back- 

 scattering of the sound, they have the effect of attenuating the propagating wave 

 in the forward direction. Furthermore, the back- scattering causes the sound 

 to reverberate so that a pulse emitted over a short period of time is received 

 during a much extended interval. Finally, the slow variation in the propagation 

 constants of the medium causes the modulation of the phase and amplitude of 

 the propagating signal, which results on the one hand in fading, and on the other 

 in the incoherence of the signal as received by two different observers. The 

 scope of this report is, therefore, to outline the theoretical models which have 

 been developed to account for the above phenomena, and to compare the predic- 

 tions of the theory with the often scanty experimental data. 



We hope that the report may serve as a self-contained introduction to 

 the acoustic effects of small random inhomogeneities for those connected with 

 underwater sound propagation but not specialized in this particular field. At the 

 same time, we intend the report to pinpoint some of the strengths and deficiencies 

 in the present state of knowledge and to suggest topics in this general area de- 

 serving of further research. 



B. APPROACH 



We distinguish in our approach between strong and weak inhomogeneities, 

 A strong inhomogeneity corresponds to a radical change of the propagating char- 

 acteristics of the medium, e.g., an air bubble, a fish, or the transition from 



Arthur B.littleJnir. 



S-7001-0307 



