HANNA: DESIGN OF TRANSMISSION LOSS EXPERIMENTS 



periodicity in the spectrum corresponding to each pairwise time delay 

 in the time history. (It will become apparent shortly that, depending 

 upon the desired characterization of the transmission loss, it is 

 necessary to anticipate the relative time history of arrivals and, 

 thereby, the general structure of the spectrum of the impulse 

 response.) Further elaboration of the model to include such features 

 as frequency dependent absorption and frequency .independent phase 

 shifts (such as produced by caustics) will cause details of the 

 spectrum to change; however, the basic periodicities induced by the 

 travel-time differences will remain. It is these periodicities which 

 will drive our later concerns. 



SOME COMPLICATIONS 



Limitations of Impulsive Sources 



The desire to measure the spectrum of the impulse response be- 

 tween any two points runs rapidly into some practical difficulties. 

 To measure a spectrum, such as shown in Figure 1, requires a source 

 of energy with a flat, featureless spectrum over the frequency domain 

 of interest. In general, such sources can only be approximated, 

 often poorly. The most widely used impulsive source in Navy measure- 

 ment work is the explosive charge. However, because of the presence 

 of bubble pulses, these explosives themselves have a rich spectrum 

 which may rival that of the ocean's impulse response. 



Examples of these spectra for 1.8-pound charges of TNT detonated 

 at 60 and 800 feet are shown in Figures 2 and 3, respectively. In 

 Figure 2 the rapid ('^^6 Hz) variation is the bubble pulse frequency 

 while the slower ('\^80 Hz) variation is caused by the surface-reflected 

 arrival. (Both spectra shown in Figures 2 and 3 are low-pass filtered 

 at 300 Hz.) It is quite possible to produce a 6 Hz period in the 



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