STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



as the depth coordinate becomes infinite, then the representation 

 consists of a finite sum of "trapped" modes (there may be none) plus 

 an integral superposition which can sometimes be approximated by a 

 sum of "leaky" modes. If the sound speed approaches zero sufficiently 

 rapidly as the depth coordinate approaches infinity, there are no 

 trapped modes, only an integral superposition that, as above, can be 

 approximated in some situations as a sum of leaky modes. Finally, 

 if the square of the index of refraction approaches minus infinity 

 as the depth coordinate approaches infinity, then no energy can be 

 propagated to infinity, and the representation is an infinite sum 

 of trapped modes. 



Note that in the first two examples acoustic energy can be 

 propagated to infinity. This is reflected in the fact that the con- 

 tinuous superposition of modes is present, while in the last it is 

 not. 



This paper attempts to develop a more precise meaning and to 

 provide a physical interpretation for these terms. The basic point 

 is that the nature of the representation depends on how the sound- 

 speed profile is terminated. Furthermore, it should be pointed out 

 that, while in some circumstances one termination is to be preferred 

 over another, in general, each can be valid and useful. 



This paper consists of two parts: a general description of 

 normal-mode expansions, and a brief summary of some of the programs 

 in underwater acoustics. 



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