HANNA: DESIGN OF TRANSMISSION LOSS EXPERIMENTS 



To estimate this effect, a wave model which properly treats 

 caustic fields (the parabolic equation model mentioned earlier) was 

 run, including both the bottom-interacting and refracted fields, 

 and averaged in frequency over 1/3-octave at 35 Hz. The results of 

 these calculations are shown in Figure 15 with the rms sum, again, as 

 the estimated transmission loss. The inferred reflectivity is shown 

 at the top of the figure; it follows the earlier 35 Hz curve down to 

 about 5 degrees, below which it goes even further into negative values 

 than before. The significant point here is that even if the proper 

 summation of the bottom- interacting paths were used as the estimated 

 transmission loss, negative reflectivity losses would be obtained at 

 low grazing angles because of the refracted contribution to the field. 

 The effect of the refracted field will depend upon frequency, geometry 

 and depth excess. 



To summarize the analysis at this point, it has been shown that 

 certain features of the low frequency bottom loss measurements made 

 by NOO and NADC, especially apparent negative bottom losses, could 

 be induced by 1) an over-simplified transmission loss model, and 

 2) inseparable bottom-interacting and refracted fields at ranges 

 corresponding to low grazing angles. 



Bottom- reflected paths 



So far the attention has focused on the model for propagation in 

 the water. Consider for a moment the diagram of Figure 16 which shows 

 not only a path refracting through the bottom, but one reflecting from 

 the boundary as well (some of the NOO data show the presence of both 

 paths) . In general, if the incident amplitude is A and that of the 

 reflected path is aA, then the amplitude of the reflected path is 

 (1 - a) A (neglecting reflection back into the bottom of the emerging 

 refracted ray). When these paths recombine in the water, their 



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