NORMAL MODES IN OCEAN ACOUSTICS 



D. C. Stickler 



Applied Research Laboratory 

 Pennsylvania State University 



The utility of using normal-mode theory to explain acoustic 

 phenomena when dealing with underwater acoustic problems has 

 been established. Pekeris used it to predict the results 

 of shallow -water transmission of explosive charges. This 

 report discusses applications of normal-mode expansions and 

 the role of the discrete and continuous spectrum, it provides 

 a physical interpretation, describes the effect of both proper 

 and improper or leaky modes, describes the differences arising 

 from the branch -cut choices, and considers the effect of shear 

 waves on the pressure field. 



Several working computer programs based on normal-mode theory 

 are compared both by a general description of their capa- 

 bilities and by their specific treatment of the discrete and 

 continuous spectral contributions. 



BACKGROUND 



During World War II C. L. Pekeris became the first to apply 

 normal-mode theory to problems in underwater acoustics. Since that 

 time this technique has been employed to explain various acoustic 

 phenomena. The elementary model used by Pekeris will be used here 

 to describe some of the properties of normal-mode expansions. 



To apply normal-mode theory in underwater acoustics it is nec- 

 essary to assume that the acoustic parameters depend on the depth 

 coordinate alone. This means, in particular, that both the longi- 

 tudinal and shear speeds and the density depend only on depth and 

 that the ocean-surface and ocean-bottom interface are flat and 

 orthogonal to the depth coordinate. Specifically, this excludes 

 sound-speed profiles that depend upon either range or azimuth 



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