PORTER: SOFAR PROPAGATION OF WIDE-BAND SIGNALS TO LONG RANGES 



sonograms of shots at increasing ranges between 100 and 600 km. Shot 

 756 shows seven individually observable ray arrivals and four well- 

 defined mode dispersion curves. It was quickly realized that the 

 mode curves were not the first four, lowest order modes; the fre- 

 quencies were much too high for the observed arrival-time delays. 

 For example, mode m = 4 should arrive with frequencies of a few Hz 

 not 200 Hz as observed. The inevitable conclusion was that the mode- 

 dispersion curves (or group-velocity profiles) belonged to high-order 

 modes and that most of the high-order modes were among the missing. 



Where are they? It turns out that the modes actually observed 

 result from an interference mechanism. Figure 5 shows the upward 

 and downward traveling waves that combine to make the standing wave 

 we identify as the field of a single mode. These two waves interfere 

 constructively or destructively, depending on the depth z and the 

 sound-velocity profile. In other words, the receiver can be at a 

 null for a particular mode and then that mode will not appear in 

 the shot arrival. Constructive reinforcement depends on the receiver 

 depth, not the range. 



It can be shown for a bilinear profile that the modes that inter- 

 fere constructively are directly dependent on the skew of the sound- 

 velocity profile. The skew of the Mediterranean profile is 20 to 1. 

 As a consequence, only one out of every 2 modes interferes with 

 maximum constructive interference. In the North Atlantic the skew 

 is 6 to 1; one would expect 1 out of every 6 modes to interfere con- 

 structively. 



It is well known that a given frequency, for a given mode, 

 travels with a unique group velocity. Further, we have argued that 

 the modes actually received depend only on the receiver depth and 

 not the range. Thus, plots of arrival frequency versus fractional 



641 



