FITZGERALD: CONVERGENCE ZONE DEPENDENCE ON FREQUENCY 



Such a region corresponds to the shadow region for the associated ray. 

 The argument of the exponential describing the decay of the eigenfunc- 

 tion in the shadow region is proportional to frequency. The lower the 

 frequency, the farther the wave function extends into the shadow region. 

 This is simply a statement that diffraction effects become more sig- 

 nificant at lower frequencies. In the experiment to be described, the 

 diffraction effects at 13.89 Hz appear sufficient to markedly change 

 the character of the transmission-loss curve from that of 111.1 Hz. 



In Figure 1, the pressure is rewritten on the second line in 

 terms of phase and amplitude by using trigometric identities. The 

 transmission loss depends on the amplitude which is the square-bracketed 

 term. In this term we again have the geometric spreading factor, 

 1/r, and an interference summation. Considering the double summation 

 in the amplitude, we note that the convergence zone phenomenon is due 

 to the existence of a set of modes which have the property that 



m m+1 A 



where X, the convergence zone interval {'^ 65 km) , is independent of m. 

 Because the interference effects depend as well on the modal excita- 

 tions, P , we shall also be looking at the products, P P 



m ^ m m+i 



Figure 2 shows a simplified sound speed profile that is typical 

 of the North Atlantic in the sense that it exhibits a thermocline, a 

 SOFAR axis and a depth excess. This profile was used to compute the 

 modal parameters in Figure 3 . 



Figure 3 shows calculations of modal parameters for the profile 

 of Figure 2 for frequencies 13.89 Hz and 111.1 Hz. The lower fre- 

 quency points are marked with an X. The higher frequency points are 

 marked with a circle. Source depths are 104 m (13.89 Hz) and 21 m 



669 



