MELLEN: SOUND PROPAGATION IN A RANDOM MEDIUM 



to get a best match. Obviously, I was going to select either 10, 15 or 

 20 depending on the standard deviation of the data points from the 

 trend curve. However, the standard deviation for those three values 

 of N ranged only from 1.1 to 1.4 dB. I decided that was not a very 

 sensitive test. There was a more sensitive test: The match for N=20 

 had a negative value of a I 



If one is going to use 10 log R + aR as a transmission loss law, 

 you'd better be sure that all significant components of the energy are 

 being attenuated at the same rate, because that is a fundamental 

 assumption behind the law. A good example where it fails is the 

 classical shallow-water, isospeed theory where the modal attenuated 

 coefficient is quadratic in the mode number; this leads to transmission 

 loss varying as 15 log R + aR. This example illustrates the fact that 

 the slope of transmission loss curve with range is strongly affected 

 by differential attenuation of the different components. 



In our massaging of the data in the Gulf of Maine at 1 kHz we 

 found that this kind of differentially attenuated energy was at least 

 as important as the ducted energy out to ranges of something like 40 

 kyd. That was the transition range where they were about equally 

 important. 



Now, the trouble is, if you start out at 40 kyd in order to be 

 sure that most of the energy is ducted and not differentially attenua- 

 ted, you've got only a factor of four on range before you start 

 running into noise or land as the case might be. You can't make a 

 very sensitive test of scope with the available data given the normal 

 scatter of points from any trend curve. Based on my personal experi- 

 ence I would be very skeptical about assuming 10 log R in cases 

 such as that. 



Dr. Mellen: We have an initial spherical spreading region 

 while the sound channel is being set up. After that we have a mode 



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