TAPPERT: SELECTED APPLICATIONS OF THE PARABOLIC-EQUATION METHOD IN 

 UNDERWATER ACOUSTICS 



Tappert, F. D. , in Lectures in Applied Mathematics, Vol. 15, (ed.) 

 A. C. Newell, Amer. Math. Soc . , Providence, R. I., 215-216, 1974. 



, J. Acous. Soc. Amer., 55 :S34 (1974) 



Tappert, F. D. , and I. M. Besieris, Proa. Inter. Symp. on Electro- 

 magnetic Wave Theory, Tbilisi, USSR, Sept. 1971. 



Tappert, F. D. , and R. H. Hardin, in AESD Tech. Note 73-05, (ed.) 

 C. W. Spofford, ONR, Arlington, Va., Nov. 1973. 



, , Proc. Eighth Inter. Congress on Acoustics, 



London 1974, p. 452. 

 Tappert, F. D. , and C. N. Judice, Phys. Rev. Lett., 29:1308 (1972). 



DISCUSSION 



Dr. J. B. Hersey (Office of Naval Research) : First of all, I 

 think our speaker is to be congratulated on an absolutely brilliant 

 performance. I have been very excited to see some of the nagging 

 problems of ocean acoustics, not necessarily finally solved but yield- 

 ing some very, very intriguing and encouraging results. Congratula- 

 tions, sir. 



Dr. Tappert: Thank you. 



Mr. E. D. Garabed (Naval Air Development Center) : You mentioned 

 that in this parabolic-equation method there was a limitation on 

 angles that it can be used for. Can you give me some idea as to what 

 that angular limitation is, in degrees? 



Dr. Tappert: Roughly a 5 percent error at 20 degrees is intro- 

 duced in the ray periods or modal phase velocities. The significance 

 of this error really depends on what you want to measure, or what you 

 want to get out of the calculation. Some things are computed more 

 accurately than others. 



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