TAPPERT: SELECTED APPLICATIONS OF THE PARABOLIC-EQUATION METHOD IN 

 UNDERWATER ACOUSTICS 



For example, if you only want transmission loss, it doesn't 

 really matter whether you have an error in the phase. But if you 

 want to do beamforming with the complex signal, then you need accurate 

 phase information as well. 



There is no universal simple answer to your question. We have to 

 make more computer runs, compare with more data, and do more analysis 

 before we fully understand all the limits of the method. It is a 

 flexible method. It is not just one simple formula that you do once 

 and for all. There are ways to improve and extend and refine this 

 parabolic-equation method. 



Dr. H. Weinberg (New London Laboratory, Naval Underwater Systems 

 Center) : If I understand correctly, you use a virtual source to take 

 into account the free surface. Would it be easy to take into account 

 surface loss or its equivalent? 



Dr. Tapper t: One would think so, and I have struggled hard to 

 find a way to do it, but with the algorithm that I described it seems 

 to be difficult to relax the flat-surface boundary condition. 



Dr. Weinberg: I don't see why it is more difficult for you to 

 treat the free surface than some sort of boundary condition. Is that 

 because of the algorithm you chose? 



Dr. Tappert: It is because of the Past Fourier Transforms. With 

 other algorithms it would be easier to introduce surface losses and 

 surface scattering. And I really do encourage others to look into 

 other algorithms. There is nothing magic about this one. I am con- 

 vinced that it is unusually efficient and effective and accurate, but 

 again it would be worth knowing just how much better it is than other 

 possible numerical algorithms. 



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