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



factor M. Somewhat less obviously, all modes constructively interfere 

 when r/h(0) is an integer, that is, when there is an integer number of 

 ray cycles between source and receiver. Since is a function of the 

 group velocity (because of the resonance condition) , the signal is 

 reinforced only for those arrival times that correspond to the recep- 

 tion of an eigenray. 



Figure 9 shows the received signal structure when an impulse is 

 transmitted. There are resolved arrivals corresponding to individual 

 eigenrays. Each arrival has a spectrum determined by those modes for 

 which the interference factor is greatest. 



The previous analysis holds with slight modification if a dis- 

 persive pulse is transmitted. From Figure 10, if a is rapidly varying 

 the arrival time is a sum of the channel plus the pulse dispersion. 

 To illustrate the effect of pulse dispersion, consider a linear FM 

 pulse from to 400 Hz with a time spread of 1 sec received at 300 km. 

 The pulse sweeps up with higher frequencies transmitted later. Since 

 higher frequencies are delayed due to channel dispersion, the net 

 effect of the swept pulse is to increase the dispersion. The left 

 side of Figure 11 is the dispersion curves for the CHAIN 82 profile; 

 the right side is the resulting dispersion curves for the FM trans- 

 mitted pulse. 



PROPAGATION LOSS FOR WIDE-BAND SOFAR TRANSMISSIONS 



All of this suggests that simplifications can be achieved in the 

 calculation of wide-band transmission loss. Intuitively, if the 

 received signal bunches into energy packets that are resolved in time 

 and frequency, the total energy is the sum of the energy of the 

 individual packets. More precisely, we have shown that the received 

 energy is the sum of the energies transmitted in each mode and 



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