Finally, attenuation of shear waves in the ice is omitted. This may very well add a 

 decibel or more loss to paths through the ice, changing the angular scattering diagram. This 

 effect and others upon the reflection coefficient at the ice plate might reduce the specular 

 reflection coefficient, which depends upon reflection from the plate. 



CONCLUSIONS 



A collection of ice keels has been modeled by parabolas that have distributions of size 

 and spacing that match estimates of real keels. Rays representing a plane wave have been scat- 

 tered from this set of keels, with resultant scattering angles and specular reflection coefficients. 



The reflection-transmission characteristics of the water-ice interface are shown to be 

 important in determining the angles into which energy is scattered. The particular geometric 

 properties of the parabolas also have a strong effect on the estimated scattering angles. This is 

 particularly true of backscatter. which is underestimated by the parabolic shapes. 



Specular reflection coefficients from the keels are estimated by computing the ratio of 

 shadowed surface to total surface. 



For grazing angles up to 20 degrees, transmission through the keels accounts for more 

 scattered energy than reflection from ihe keel. Below 20 degrees, this transmission is 

 predominantly by shear waves rather than compressional waves. 



RECOMMENDATIONS 



The ray theory program utilized here permits keel shapes to be approximated by 

 several parabolic or straight-line segments, although only a single parabolic segment per keel 

 was used here. Such compound shapes could more nearly model real keels. Because the shapes 

 used here lead to defective estimates of backscatter, the use of compound shapes is particularly 

 indicated for keel backscatter estimations. 



Before more appropriate keel shapes are generated, much information is needed about 

 detailed keel shape and structure. If keels tend to remain collections of independent ice blocks 

 or slabs throughout their life, then the current analysis, which is based on solid ice shapes, has 

 very limited validity. If keels do solidify and if their shape is modified by local melting and 

 freezing, then a solid ice model can be appropriate. Clearly, a great deal of observed 

 information on shapes and slopes is needed to produce random model shapes that match 

 readily. Upsounder echo traces might serve as sources of this needed information. 



If acoustic paths through ice keels are important, as the current analysis indicates, then 

 the internal elastic-acoustic properties and degree of homogeneity of keels is important. Of 

 particular importance are the sound speed and the attenuation of the two wave types, shear 

 and compressional. A systematic study of the ice in keels is needed. 



Acoustic experiments performed in the vicinity of a well-observed keel could reveal 

 much about the acoustic properties of keels. The basic requirements are receivers at several 

 depths, both in front of and behind the keel, and a variable source angle. The ability to 

 separate mullipath arrivals would also be useful. 



16 



