Wolff, Tatro, and Megehee 



described by a particular mathematical function. 



THE RAY TRACE PROGRAM 



In practice, the inputs to the program are temperature and 

 salinity as a function of depth for as many positions in x space as are 

 desired. The program utilizes Wilson's equation to convert these 

 variables to sound velocity. The only other variables which must be 

 specified initially are the source depth and the bottom depth. 



The program is capable of handling reflections at the air -sea and 

 sea-bottom interfaces and of accepting an irregular bottom profile. It 

 incorporates several options, such as terminating a ray after the first 

 convergence zone, or after a specified number of surface or bottom 

 reflections. 



Three types of output are available from this program. Figure 1 

 shows the printer output showing the values for all the computed 

 parameters at each time step. Figure 2 shows a condensed printer 

 output which shows only the initial point, the intermediate turning 

 points, and the end point of a ray. In this example, the terminate at 

 end of first convergence zone option has been utilized. Figure 3 

 shows a plotted output. This is plotted off-line on a CALCOMP 

 plotter. The upper box in this figure extends in depth from the 

 surface to 500 feet, and in range from zero to 7200 yards. It displays 

 the direct path sound field. The lower box covers the same depth 

 range, but the horizontal range is from 50,000 to 80,000 yards. The 

 sound which was all strongly refracted downward in the upper picture 

 is turned at depth and often returns to the surface at a considerable 

 range to form a convergence zone. The lower box displays the 

 convergence zone. From any of these three forms of output it is 

 possible to determine the range and width of the convergence zone, 

 and from the printer output the depth of water required for 

 convergence zone formation. 



The ray trace program has been described in detail by Ayres et al 

 (1966). 



EFFECT OF SOUND VELOCITY MICROSTRUCTURE 



Careful in-situ direct measurements of the sound velocity as a 

 function of depth by means of a velocimeter lowering indicate that 

 the sound velocity profile is not a smooth curve as it is often 

 depicted, but rather that it has a sort of perturbation superimposed 

 on it with an average wave length of approximately 10 meters and an 



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