The second statistical approach preserves the identity of each profile while pro- 

 viding a measure of the distribution of positive and non-positive sound speed profiles. 

 Each profile is classified according to the above definition. See also Figure 2.3. 



Additional statistics are computed to provide information on the strength of the 

 observed gradients. For positive profiles the gradient from the absolute sound speed maxi- 

 mum to the shallower sound speed minimum is computed and tabulated. For non- 

 positive profiles, the gradient from the near surface maximum to the deeper absolute 

 minimum is computed. If the profile has a deeper positive gradient leg below the absolute 

 minimum, this value is computed also. With this statistical summary, we could determine 

 how many profile types are necessary to adequately represent the particular shallow water 

 site and season. With the aid of the gradient strength and depth information, suitable 

 representative profiles may be selected from the individual data subsets for acoustic 

 model inputs. 



To illustrate the division of a sample of sound speed profiles by the definition 

 illustrated in Figure 2.3, the profiles from the Lands End site, spring season, were 

 separated and replotted in Figure 2.4. Figure 2.4a shows the positive-gradient profiles 

 while Figure 2.4b shows the non-positive gradient profiles. 



2.3 Normal Mode Calculations 



Propagation loss calculations were made following procedures given by 

 D. F. Gordon in Reference 7. The normal mode program utilizes a multilayer (up to 12 

 layers) model of the shallow water channel. The bottom sediment layers are modeled in 

 the same manner as the layers in the water. Thus a liquid bottom is assumed and the 

 effect of shear waves is ignored. Each layer is characterized by five quantities: the 

 sound speed at the top and bottom of the layer, the sound speed gradient at the top of 

 the layer, the compressional wave absorption (equal to zero in the water) at the top and 

 the bottom of the layer and the density which is assumed constant in the layer. The 

 absorption loss in the water is computed from Thorp's equation (Reference 8) and is 

 added to the propagation loss at the end of the computation. The model can handle dis- 

 continuities in sound speed between water and sediment or between sediment layers or 

 between sediment and rock. 



Propagation loss as a function of frequency was calculated for a discrete frequency 

 range of 50 Hz to 4 kHz. The source depth was held constant at 25 meters and the 

 receiver depth was optimized, i.e., adjusted for maximum intensity. For example, see 

 Figure 4.4 where propagation loss for 275 and 500 Hz was plotted versus receiver depth 

 for the range of 100 km. The propagation loss was taken to be 75.8 dB and 83.5 dB at 

 275 and 500 Hz, respectively. A random phase addition of the mode contributions was 

 used in the calculations. A phased mode addition gives large spatial variation and would 

 be difficult to interpret at a given range. The random phase calculations are equivalent 

 to the results which would be obtained from phased mode theory by averaging over a 

 range interval centered at the fixed range. 



Shallow Water Normal Mode Model with Structured Bottom, D. F. Gordon, Paper IV-B, Shallow 

 Water Mobile Sonar Modeling Symposium, Naval Research Laboratory, 23-25 September 1975. 

 Analytic Description of the Low-Frequency Attenuation Coefficient, W. H. Thorp, J. Acoust. 

 Soc. Am., Vol 42, 1967, p. 270 (L). 



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