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Grazing Ray Angle in Water ideg) 



Figure 14 Refraction angle at watc-ice interface for the water 

 wave and ice shear wave. 



The final scattering function for a single keel is the convolution of the angles of Fig. 13 

 with the reflection losses of Fig. 5. However, the transmission losses of Fig. 5 contain ray- 

 spreading terms that must be removed, since equal intervals along the s scale of Fig. 12 

 represent equal energy, and spreading effects are built in. 



MODEL SHORTCOMINGS 



The models used here fail to represent reality in many ways. Some of their 

 shortcomings are listed here. The results of limitations on slope angles were discussed in the 

 section on backscatter. Perhaps the next most noticeable shortcoming is the absence of 

 reflection from the far sides of the keels. These reflections might add significantly to the 

 backscatters ng strengths of the keels. In a pure ray construction treatment, as used here, one 

 must terminate internal reflections at some number or level. Here, they were terminated at 

 zero. 



A third important shortcoming is the absence of an ice plate which could alter ray 

 paths. This shortcoming does not cause serious angular dislocations though, because the 

 transmission coefficient is such that rays directed into the ice plate will readily pass back into 

 the water. A nonfiat upper ice surface, however, will disturb ray paths. 



15 



