Ray scattering functions were derived as follows. A number of rays were launched at 

 the same angle, but at successive ranges to simulate a plane wave directed at the keel set at a 

 javen angle of incidence. Usually 300 rays were used. Rays leaving the keel set and crossing a 

 given receiver depth are sorted into angular bins. Any reflection of transmission losses at 

 boundaries alters the intensities of the accumulated rays. Spreading loss is accounted for by the 

 collection into angular bins. Rays are equally spaced along the plane wave front and therefore 

 represent equal energy. The sum cf ay contributions in any bin is a measure of relative 

 intensity. 



Two scattering processes are allowed in the computations: reflection at the ice-water 

 interface and refraction through the keel. Refraction is permitted at both the ihear and 

 compressional speed n the ice. However, few rays strike the keels at sufficiently large grazing 

 angles for transmission at the compressional speed, so shear wave paths through the keels 

 predominate. Edge-diffracted rays were included in Ref. I. But since their contribution to the 

 field is small, they are not included here. 



The computer program used here requires a non-zero sound speed gradient, so the rays 

 will have curvature. Since our purpose here is to determine the scattering properties of the set 

 of keels, we prefer straight line rays. 1 he curvature is minimized by using a small gradient and 

 r>v placing source and receiver depths ;ust below the keels. These depths were usually 10 or 

 20 m. depending on the deepest keels in the set. A sound-speed gradient of 0.0002 sec"' was 

 used in all compulsions here. 



The reflection and transmission properties of ice can be computed following Ewing, 

 Jardetsky, and Press (Ref. 4). The acoustic parameters required are the sound speed in the 

 water, the shear and compressional sound speeds in the ice. and the density of water and ice. 

 Table 1 shows the values of these parameters used here. These are typical observed values for 

 Arctic sea ice. The shear speed vanes over a large range of values, depending on the condition 

 of the ice. Observed values easily vary from 1400 to 2200 m s. 



Table I . Typical acoustic parameters in Arctic sea ice and water. 



Parameter Value 



So nd speed in water W40 m s 



Com prrssic r,al sound speed in ice 3600 m s 



Shear ci nd speed in ice 1600 m s 



Water densiry 1026 kg m 3 



Ice density 920 kg m 3 



