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



eigenray. Contrast this with narrow-band propagation loss where the 

 modes must be combined coherently. Those using mode theory have 

 generally observed that incoherent mode summation is a better fit to 

 data measured with shots, a result that confirms wide-band theory. 



Software has been developed to calculate the loss. The program 

 is based on the WKB approximation to the normal modes, and the sta- 

 tionary phase approximation to the propagation integral. Loss esti- 

 mation proceeds first by estimating the eigenrays for a given range. 

 This is done by calculating the cycle length and requiring that there 

 be an integer number of cycles between source and receiver. Then the 

 resonance condition and group velocity relation are combined to 

 determine the received frequency for each mode. The interference 

 factor M is then calculated to find the energy distribution among the 

 modes . 



The main difficulty with the method is that the WKB solution 

 diverges near ray turning points. Thus, as we vary the source and 

 receiver depths, we observe a rapidly varying and erroneous propaga- 

 tion loss. We have attempted to correct this by applying a diffrac- 

 tion correction, based on Airy functions, to the field of each mode 

 when z is near the turning point. 



Figures 12 and 13 show propagation loss as a function of depth 



for two ranges at 100 Hz. Figure 12 is for the sound velocity pro- 



2 

 file measured on CHAIN 82, while Figure 13 is the N - bilinear 



approximation to that profile. The diffraction correction signifi- 

 cantly smooths the loss curves for both profiles. This is expected 



because the introduction of diffraction reduces the effect of the WKB 



2 

 turning points. It should also be noted that the N - bilinear loss 



curve is significantly smoother than that for the actual CHAIN 82 



profile. This is a consequence of the changing slope of dc/dz of 



the actual data. 



652 



