TAPPERT: SELECTED APPLICATIONS OF THE PARABOLIC-EQUATION METHOD IN 

 UNDERWATER ACOUSTICS 



Dr. S. N. Marshall (Naval Research Laboratory) : I am getting 

 back to times for computation again. Can you tell me whether you 

 use software or hardware FFTs and what your computation time in long 

 runs is? 



Dr. Tappert: Yes. I use software FFTs, but coded in FORTRAN. 

 At AESD they have a Compass-coded FFT. The difference is about 

 50 percent. You can in principle achieve gains of an order of magni- 

 tude by using hardware FFTs. 



On a machine like the UNIVAC 1108 or IBM 370/165, without the 

 fluctuations in the ocean, it takes roughly the same amount of machine 

 time to compute the acoustic field as it takes the acoustic field 

 to advance, which is roughly one mile per second, so if you are going 

 100 miles, it takes roughly 100 seconds. 



Dr. R. M. Fitzgerald (Naval Research Laboratory) : Regarding the 

 approximation in small angle for the parabolic-equation method, I 

 think you can show that the approximation is one in which the angles 

 are restricted to a small cone but the direction of the cone is 

 arbitrary. 



Dr. Tappert: That is very true. Yes. 



Dr. Fitzgerald: And in that way you can overcome the limitation 

 now that you cannot treat steep rays. You do it by using separate 

 cones and linearly superimposing the results. 



Dr. Tappert: The problem I had in trying to work that out is 

 how you superimpose. You certainly can take a cone of angles that 

 is not oriented horizontally. For example, if you want to do the 

 bottom bounce experiment, you take a cone going down and then it is 



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