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



arrival time (delay from the axial arrival divided by the axial 

 arrival time) for all shots should group along the same dispersion 

 curves. Note that the fractional arrival time is directly proportional 

 to the group velocity. Figure 6 is a plot of the arrival frequencies 

 for seven shots at ranges from 100 km to 600 km. The curves drawn 

 through the symbols are not fits to the data; they are calculated 

 group-velocity profiles for those modes predicted to have maximum 

 constructive interference. The horizontal axis is fractional arrival 

 time . 



The theoretical curves are calculated only for wholly refracted 



-2 

 modes. All energy arriving earlier than t = - 0.65 x lo is felt 



to be surface reflected. We feel that there is observed surface 



reflected energy on only three pulses. 



MODE EXPANSIONS AND THE WKB APPROXIMATION 



One of the more dramatic of the phenomena observed in these 

 sonograms is the simultaneous appearance of resolved modes and rays . 

 Nowhere in the literature do references to this combined behavior 

 appear. There is evidence of lower order modes at long ranges in the 

 Arctic, and there is also evidence of resolved arrivals in most of 

 the early papers on SOFAR propagation. However, the mode and ray 

 viewpoints are thought to be separate. That is, one can observe 

 either modes or rays but not both together. We have seen that both 

 phenomena appear together and are observable, at least in the Mediter- 

 ranean, with the appropriate spectrum analysis. 



We have developed a simple theory based on the WKB approximation 



and combined with a stationary phase integration over the spectrum of 



the transmitted pulse. The results are summarized in Figures 7 and 8. 



The spectrum of the received signal is a sum over the normal modes $ . 

 •^ m 



643 



