TAPPERT: SELECTED APPLICATIONS OF THE PARABOLIC-EQUATION METHOD IN 

 UNDERWATER ACOUSTICS 



frequencies, the cusped and smooth caustics near the surface are com- 

 plicated by surface image interference of the diffraction field. Note 

 the high degree of correspondence between the field contours at 200 

 Hertz and the illuminated regions according to the ray trajectories 

 of Figure 10. 



The third example is for the so-called canonical sound-speed 

 profile of Walter Munk (1974) . In this case (Figure 15) , the source 

 is on the axis and a high-loss bottom is placed at the reciprocal 

 depth of the surface to eliminate RSR paths. The two focal regions 

 on the axis reflect the basic asymmetry of the profile. 



The fourth example illustrates effects associated with a range- 

 dependent sound-speed profile. The entire field is shown in Figures 

 16 and 17 for the first and second 80-mile segments, respectively. 

 The profile at the source (again on the axis) persists for the first 

 60 miles, at which point the axis is rapidly moved up, resulting in 

 a concentration of energy near the surface. At a range of 120 miles, 

 the profile rapidly changes back to the original profile, shifting 

 the surface-concentrated energy deeper and leading to a continuous 

 shadow-zone near the surface. Invoking acoustic reciprocity, for a 

 shallow source moving away from an axis-depth receiver, the inter- 

 mittent convergence-zone behavior of the signal would change to nearly 

 continuous reception from 60 to 120 miles and then essentially no 

 reception beyond. This behavior is a direct result of the strong 

 horizontal gradients which an adiabatic normal-mode approach could 

 not treat. 



The following examples illustrate effects associated with range- 

 variable bathymetry. Figure 18 displays the field contours for a 

 high-reflectivity shoaling bottom where initially refracted energy 



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