STICKLER: NORMAL MODES IN OCEAN ACOUSTICS 



Dr. Tapper t: Yes. 



Dr. Labianca: I agree there is a continuous spectrum in that 

 case because the depth dependence is going to be exactly the same, 

 you know, just straight separation of variables on the Helmholtz 

 equation. 



Mr. A. O. Sykes (Office of Naval Research) : Would you clarify 

 Figure 9 for me? There seem to be two groups of normal-mode models 

 which give different results. Can you comment on that? 



Dr. Stickler: Typically, it is, of course, much easier to only 

 sum the modes that are involved. Carrying out the numerical integra- 

 tion for the branch-cut integral is a much more expensive proposition 

 and so usually the branch -cut integrals are neglected or dismissed as 

 not important at long range. Many times that is the case. 



If I had used calculated or summed proper modes, then I would 

 have made the prediction labelled "ARL discrete." Bartberger summed 

 the proper and a finite number of the improper modes. They fell on 

 the other curve. 



When I added to the discrete contribution the contribution of 

 the Ewing, Jardesky, Press type branch, then the transmission is 

 given by the curve, "ARL discrete plus continuous." 



Mr. Sykes: Is the point that some of the improper modes have a 

 finite contribution which really should be included and so you think 

 that the upper curve is the better estimate? 



Dr. Stickler: Yes, the upper curve is a better estimate. 

 Figure 9 illustrates several points. First, as I mentioned earlier, a 

 sum of the improper modes is not always a good approximation to the 

 Ewing, Jardesky, Press type branch. And it also illustrates that the 

 Ewing, Jardesky, Press type branch cannot be neglected in some 

 examples. 



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