fr)^ 



X (a^ I 6(T - constant 



along a horizontal ray tube. 



A computer program based on the consideration above was written to proceed 

 in two stages. The first determines the eigenvalues and normalized eigenfunc- 

 tions at each point of a rectangular grid in the horizontal plane. Then, during 

 the second part, a set of horizontal ray tracing equations is integrated for each 

 eigenvalue, and the contributions of individual modes are combined to obtain 

 the total field. 



As in ordinary ray programs, only the leading term of the asymptotic ex- 

 pansion of each mode is foxmd. The ejq)ansion then reduces to that derived by 

 Pierce almost 10 years ago. -'•^ 



The program predicted propagation loss along a 1500-nmi track extending 

 northward from 27° 30'N, 157° 50'W to 52° 30'N, 157° 50'W. Eleven equidistant 

 velocity-depth profiles obtained from the measured data displayed in figure 12 

 were entered into the computer program. Note that the SO FAR axis rises from 

 a depth of 795 m at 27° 30'N to about 50 m at 52° 30'N. Lack of relevant data 

 prevented the inclusion of any dependence of sound speed or bottom depth upon 

 longitude. 



Figure 13 displays propagation losses from dynamite charges detonated 

 500 ft below sea level along the track to a 2500-ft receiver depth situated at 

 27° 30'N. The top graph represents observational data, while the middle graph 

 shows computed results. The two are superimposed in the bottom graph. The 

 figure displays an interesting feature. The propagation loss decreases with in- 

 creasing range beyond 42°N. This decrease may be explained by the fact that 

 the receiver is only 124 ft away from the SOFAR axis, where the signal is 

 strongly affected by the amplitude of the few lowest modes, as shown in figure 14. 

 As the source ship moved north, the source approached the SOFAR axis causing 

 the amplitude of these modes (figure 15) to increase to such an extent that even- 

 tually the loss due to horizontal spreading was overcome and the total propaga- 

 tion loss decreased. 



The 10, 800-ft receiver depth of figure 16 is well below the turning points 

 of the first few modes, and so the signal there is dominated by the higher modes. 

 The amplitudes of these modes are not greatly affected when the source approaches 

 the SOFAR axis; therefore, for this receiver, cylindrical spreading dominates 

 the entire track. 



115 



