The symbols jtt and 72 represent the normalized minimum and maximum sound- 

 velocity profiles, respectively. In- Figure U(f), the factor Q, which is also 

 normalized is a complex term that represents, in part, the derivative of 

 sonar range with respect to source angle. The <j[> . and tan<^ . parameters in 

 Figure h(d) and U(e) are valid for any i"'^'^ point in the sound velocity pro- 

 file. The geometrical apreading loss is computed as the product of term.s 

 involving tan<^^, Q, a simple ratio of sound velocities, and a constant. In 

 each graph of Figure h the curves denoted by y^ and J2 can be computed with 

 standard ray theory techniques. 



Three observations concerning Figure h can be rigorously proven: 



(1) Any profile between ?i^ and ?2 ^^ Figure 3 will generate a/i. 

 versus v curve between y-j^ and 72 in Figure U(a)j 



(2) Every curve in Figure I4. is either monotonically increasing or 

 decreasing. 



(3) The values of the acoustic parameters in Figxire U(b) through 

 h(f ) must lie between the y-]_ and y2 curves. 



These three observations will now be used to compute the extreme values of 

 each acoustic-parameter. In Figure U(a) the sonar range (normalized) is held 

 fixed at fi y^. Corresponding to ^ j^. is an interval of v values (Snell's in- 

 dex) between v 2 and v x» This interval of v values contains every v that 

 can possibly produce the sonar range fi j^, when the profile varies from P]_ 

 to P2, as in Figure 3. This interval of v values can now be used in con- 

 junction with the curves in the remaining graphs to delineate the shaded 

 regions in Figure Ii(b) through U(f). 



The extreme values of each parameter can now be computed by combining the 

 profile and the v value that corresponds to the upper and lower corners of 

 the shaded regions. The extreme values of the acoustic parameters not ex- 

 plicitly depicted in Figure h can be easily obtained from the above computa- 

 tions. 



FEATURES OF THE NElif TECHNIQUE 



The technique just described for predicting the bottom-reflected sound 

 field has the following essential features. 



(1) No computations need be performed by the user of the prediction 

 system. 



(2) All quantities can be indexed by area, bottom depth, and soimd 

 velocity at the source. Historical data corresponding to the 

 oceanographic province, and the remaining two indices can easily 

 be determined during operations. It is estimated that one 

 volume can be used to graphically depict the acoustic parameters 

 associated with regions as large, or larger, than the North 

 American Basin. 



53 



