-^tt^en,^ 



10 20 30 



Ray Angle Ideg) 



Figure 1 2. Locus of potnts along the wave front from which rays 

 of a given grazing angle strike the keel at designated angles. 



I 



between these limiting rays increases by only 0.4 m from a ray angle of to 30 degrees. The 

 maximum slope of 51.3 degrees occurs where the keel meets the surface, so the ray reaching 

 this point is the boundary between the direct rays and the surface reflected rays. As can be seen 

 from the 5 1 . 3-degree line in Fig. 1 2, as the grazing angle increases, a growing proportion of the 

 wave front intersects the keel directly and a decreasing portion intersects the keel after 

 reflection from the surface. The proportion would reach zero if the figure were extended to a 

 ray angle of 51.3 dtgrees. 



The slope of 26 degrees is of interest because, as was discussed earlier, at grazing angles 

 of 26 to 60 degrees the rays are largely transmitted into the ice. The locations of rays that 

 intersect the keel where its slope, or cV is 26 degrees are labeled 26-degree slopes on the figure. 

 However, of more interest are the rays for which 6 * <b is 26 degrees. This is the true dividing 

 line between reflected and transmitted fiys. Rays with this property are shown by dashed lines 

 in the figure. Note that only about 15^ of the rays are perfectly reflected. Most of the rest meet 

 the keel at angles that favor transmission through the keel h, a shear wave. However, at an 

 incident angle above 60 degrees there is a more even split between reflected and transmitted 

 rays. The wedge between the lines labeled "51.3-deg slope" and "60-deg incident angle" repre- 

 sents these rays, which comprise more than half the wave front at ray angles above 25 degrees. 

 The reflected energy from these rays will be directed backward to the backscattered region. 



The direction that a reflected ray leaves the keel. d n is given by 6 * 26. Figure 13 shows 

 these reflected angles for an incident wave front of 20 degrees. The line labeled "slope angle" is 

 the slope on the keel and is equivalent to the angles along the 20-degree abscissa in Fig. 12. The 

 reflected angle is then twice this slope plus 20 degrees for the direct rays on the right side of the 

 figure. At a wave front location of -2.2 m, the rays become surface-reflected, and 9 is 



13 



