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



that many eigenrays exist for each source and receiver location. We 

 define an eigenray of order n as having n ray cycles between source 

 and receiver. To be more precise, we should talk of an eigenray 

 family consisting of four rays, each with slightly different travel 

 times, corresponding to rays which reach the receiver after traveling 

 n - 1, n, n + 1 upper half cycles and n lower half cycles. A ray 

 traveling n - 1 lower half cycles is said to be an eigenray of order 

 n - 1. 



The arrival time x, relative to the axial arrival time, of each 

 of the resolved arrivals of the shot records is plotted in Figure 3. 

 The vertical width of the bar is a measure of the spread in arrival 

 time (see Figure 2) due to the spread of the transmitted pulse as 

 well as diffraction along the ray path. Individual eigenrays can 

 actually be identified and tracked through successive shots. A given 

 eigenray arrives earlier as the receiving ship moves further away. 

 An eigenray of order n must have an increasing cycle length implying 

 that it travels through relatively fast sound-velocity regimes. 

 Calculations of eigenray arrival times for this sound-velocity profile 

 agree very well with the measured arrival times. 



It gradually became clear to us that the CHAIN 82 data exhibit 

 all the features of classic SOFAR propagation. We decided that we 

 ought to study the frequency arrival structure — the hope being that 

 we would observe mode dispersion. Actually, we expected nothing 

 dramatic because many modes were expected to be present between fre- 

 quencies of 100 to 300 Hz. 



The very first sonogram made with a graphic spectrum analyzer 

 showed us that we were very wrong. We were presented with simul- 

 taneously observable group-velocity profiles, characteristic of mode 

 dispersion, and resolved ray arrivals. Figure 4 shows several 



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