STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



Bartberger (1973) uses the same numerical integration scheme, 

 but he determines the proper as well as improper modes. He sums the 

 proper modes plus a finite number of the improper modes. 



2 

 Pedersen and Gordon (1965) consider a profile in which c (z) 



approaches zero as 1/z and, hence, as mentioned above, is one in which 



there are no proper modes. They partition the sound speed in the 



upper portion of the sovind-speed profile into layers such that the 



square of the index of refraction can be approximated by a straight 



line and the density by a constant. They determine and sum a finite 



number of improper modes. 



Kutschale (1970) partitions the sound-speed profile into layers 

 such that in each layer the sound speed and density can be approxi- 

 mated by a constant. He allows for shear in any layer. He determines 

 and sums the proper modes and evaluates the EJP branch integrals. 



Beisner (1974) uses a "shooting" technique to determine the 

 proper modes and wavenumbers , and he sums the proper modes . 



Deavenport and Beard (see Spofford, 1973) model the profile as 

 an Epstein layer. The depth function can then be expressed in terms 

 of hypergeometric functions. They determine and siam the proper modes. 



Leiberger uses WKB techniques to determine the proper modes . 

 This work is described briefly by Spofford (1973) . 



Fitzgerald (see Spofford, 1973) partitions the sound-speed 



profile in layers in the same manner as Pedersen and Gordon, but he 



2 

 terminates in a layer in which c (z) ->■ - «> as z ^ ■». He sums a 



finite number of the trapped modes. 



Stickler (1975) partitions the sound speed into layers such that 

 in each layer the sound speed can be approximated by a straight line 



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