STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



DISCUSSION 



Dr. F. D. Tappert (New York University) : Have you examined the 

 question of what happens to these branch cuts when you make the para- 

 bolic approximation? 



Dr. Stickler: Not directly, but I think that your restriction 

 of parabolic method to low angles of incidence roughly corresponds to 

 reflecting the integration around the branches. Physically that can 

 be interpreted as integration over the faster phase velocities, which 

 in turn correspond to the higher modes . 



Dr. Tappert: The parabolic equation does have a continuous part 

 to the spectrum and I wonder where it comes from? From the Helmholtz 

 equation? It's not a proper mode so it must be either a branch-cut 

 contribution or a leaky mode . 



Dr. Stickler: You mean the spectriam of your parabolic operation 

 has a continuous mode? 



Dr. Tappert: Yes. It may be in the integration along the 

 semicircular — 



Dr. Stickler: I'm not sure there is a one-to-one correspondence. 

 I don ' t know . 



Dr. R. R. Goodman (Naval Research Laboratory) : When doing these 

 computations one should be aware that the experimentalists can put more 

 than one hydrophone in the water and one can do some interesting space 

 and time correlations to look at some of the realities of these various 

 contributions . I think this is an important point because one can then 

 begin to design an experiment to look for the types of things you are 

 talking about. 



Dr. F. M. Labianca (Bell Telephone Laboratories) : I tend to 



agree that there is a continuous spectriim for the parabolic equation, 



but let me clarify one thing. Are you referring to the case where there 



is no range dependence in sound speed? In other words, where separa- 

 tion of variables applies? 



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