STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



and environments involving sloping bottoms. Perturbation techniques 

 can be used to extend normal-mode theory to less restrictive environ- 

 ments . 



Fortunately, in many areas this is an adequate model, and normal- 

 mode theory has proved successful in explaining various acoustic 

 phenomena. In those environments where this is not true, other 

 methods must be employed. All these alternative methods involve 

 approximations, some of which cannot be listed directly. The validity 

 of some of these approximations can be tested by comparison with the 

 "exact" normal-mode representation. These comparisons are certainly 

 necessary, and they usually yield considerable insight into the nature 

 of the approximations as well as suggest methods for improving them. 



This paper has two points of focus: (1) the physical interpreta- 

 tion of the concept and techniques of normal-mode expansions, and 

 (2) the description of those features of the expansion that are the 

 result of the assumption that the depth coordinate is semi-infinite. 

 Expanding slightly on this second point, consider the case of an 

 acoustic wave guide of finite cross section with perfectly reflecting 

 walls. The normal-mode expansion of the pressure field for this case 

 consists of an infinite, discrete sum of normal modes. If one of 

 these wave-guide walls is moved to infinity, then the normal-mode 

 expansion must be modified, depending upon the behavior of the sound 

 speed at infinity. Physically, this modification accounts for the 

 energy that can now be propagated to infinity in this new direction. 

 The principal effect on the normal-mode expansion is that, in general, 

 the representation consists of a sum of trapped or proper modes plus 

 an integral superposition of modes. 



This feature depends on the nature of sound speed as the depth 

 coordinate approaches infinity. If the sound speed is constant 



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