an error of approximately + 0.2°C. 



It is immediately clear (Figure 1) that these profiles may 

 be very complex. A few scattered points are not sufficient to give an 

 accurate picture of the profile. The shape of the profiles obtained with 

 a small error in temperature measurement or depth location may be indeter- 

 minate. The absolute values of velocity may differ by only a fraction of 

 a percent but the sign of the velocity gradient in the surface duct may 

 differ. 



When the velocity profile is known, much can be easily predicted. 

 The application of Snell's law allows one to trace sound rays through the 

 ocean represented by the profile. Useful ranges and so-called "shadow 

 zones" may be distinguished. The velocity gradient, — — , determines the 



T c dv . . „_. ,_, , . .. dv . 



curvature of rays. If -j— is positive, the rays curve upward; if -r— is 



dz : 



negative, the rays curve downward. Since ranges and acoustic travel times 

 for active sonar are relatively short, the prediction of target range does 

 not require high accuracy in the absolute value of v(z) , provided that the 

 path taken by the sound is known approximately; the sign of -r— (i.e., 

 whether the gradient is positive or negative) is most important to deter- 

 mine the probable path. 



In Appendix A, Figures A-l, A-2, and A. 3 are rays plots produced 

 by a computer which show the bending for positive, negative, and zero 

 curvature conditions. Simple graphical techniques have been worked out and 

 prepared for use by sonar operators. 



In order for convergence zone operation to be possible, what 

 is known as a "velocity excess" must exist. Velocity excess is the dif- 

 ference between the velocity at the bottom of the ocean and the velocity 

 at the bottom of the layer depth. A rule of thumb is that the velocity 



8 



3rtbur ai.lUttleJnr. 



