1-2 



water to air at the surface. A weak inhomogeneity, on the other hand, corre- 

 sponds to a slight change of the propagation characteristics of the medium, and 

 is typified by the small but ubiquitous fluctuations of temperature, salinity, 

 density and velocity. 



All the theoretical methods employed to attack wave propagation in an 

 inhomogeneous medium must take recourse to a number of mathematical and 

 physical approximations in order to handle an otherwise too formidable problem. 

 Thus, the analysis is generally confined to one type of inhomogeneity at a time, 

 and ignores any interaction between different kinds of inhomogeneities . In the 

 case of strong inhomogeneities, the approximation is usually to regularize the 

 geometry of the individual scatterers. For example, air bubbles and marine 

 organisms are taken to be spherical in shape, and ocean surface waves might 

 even be regarded as sinusoidal. For weak inhomogeneities, on the other hand, 

 a convenient approximation scheme is furnished by the fact that the changes in 

 the relative propagation characteristics are very small compared to unity, so 

 that the magnitude of these relative changes can be used as a small parameter 

 in a perturbation theory. 



It is therefore natural to divide the subject matter of this report into 

 two parts: strong inhomogeneities; and weak inhomogeneities. Tlie notation used 

 is summarized in Appendix C. 



C. GENERAL CONCLUSIONS 



The inhomogeneities of the ocean affect a passing sound wave in a man- 

 ner which can be qualitatively understood by the theory outlined in this report. 

 Quantitative predictions are still somewhat less accurate than we would expect 

 possible when our present understanding of the scattering mechanisms is incor- 

 porated fully in the scattering calculations. 



The theoretical investigations to date have attempted to cope with the 

 formidable mathematical problems encountered by making numerous analytical 

 approximations. We believe that the time is ripe to place much greater emphasis 

 on numerical computation based directly on our physical understanding of the 

 scattering process without the many rough analytical approximations required 

 for a completely theoretical development. Especially in the areas of scattering 

 by the surface (Section HID) and by the micro- structure of the index of refrac- 

 tion (Chapter IV) we would expect that an imaginative program of numerical cal- 

 culation would be able to improve considerably our current ability to predict 

 sound scattering in the ocean. 



We recommend, therefore, that some study be devoted to the design 

 of efficient numerical procedures for carrying out these calculations, having as 

 its ultimate objective a computer program capable of tracing the long-distance 

 propagation of a sound wave subject to surface and volume scattering. 



arthur ffl.littlfjnf. 



S-7001-0307 



