•S; GEOMETRIC IMPLICATIONS OF SCATTERING ANGLES 



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gg In this section the general shape of the scattering functions will be discussed. In partic- 



(1 ular, the backscauering function will be shown to be underestimated because of the limited 



\"', slopes of the ice model. This topic is discussed first because it is important that the backscatter 



vj) functions of this report not be used for estimation or modeling purposes. A geometric discus- 



% -*. sion of the specular reflection function and the scattering curves will follow to explain some of 



s *«' the features of these curves. 



> BACKSCATTER 



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t>j£ Two notable features of such scattering curves as those of Fig. 4 and 6 are the null in 



S> the downward direction and the small ba<~kscattenng lobes. Both these features result from an 



ft/ interplay between the parabolic shape and the reflection coefficient. Figure 5 shows reflection 



and transmission losses for a water- : ce interface. These are computed by the method of Ewing, 



rJ5 Jardetsky, and Press (Ref. 4). Table 1 gives the acoustic parameters used. Computations of the 



Bj reflection loss for a wide range of these parameters are given by Maver, Behravesh. and Plona 



Cft (Ref. 5). Although the losses in Fig. 5 are plotted as functions of the phase velocity, an 



/S equivalent grazing angle scale is given at the top of the figure. 



|i As a result of the acoustic parameters chosen here, acoustic energy begins to penetrate 



■t the ice-water interface at a grazing angle of about 26 degrees. The next increase in grazing 



«.' angle of a few degrees finds almost all energy transmitted into the ice via the shear wave and 



£* almost none reflecting. At an angle of 45 degrees, less than 1% of the energy is reflected. A ray 



£y reflecting from a sloping surface is diverted by twice the slope of the surface. (Exact expres- 



'rA sions will be given later.) The rays scattered downward near 90 degrees have reflected from a 



slope near 45 degrees and hence suffered a large reflection loss. The nulls in the downward 



EC di r ection on the scattering curves are images of the null in the reflection coefficient, of Fig. 5. 



Near a grazing angle of 66 degrees the compressional wave in the ice is excited. From 

 this angle on to 90 degrees lO^e or more of the energy is reflected. Figure 5 shows good 

 v^ reflection coefficients starting at about 60 degrees. Such slopes will reflect at 120 to 180 degrees 



N or backscatter the energy. However, the parabolic ice keels used in this study have maximum 



jfcj slopes of 51.3 degrees. Therefore only a few of the rays of highest incident angles can reach 



ft/ these good reflectors for backscatter. 



PTo test the assumption that higher slope angles would produce more backscatter, a run 

 was made with keels of half width. This was a relatively simple test to make. The keels of set A 

 were reduced to half their width, with all other parameters remaining the same. This increases 

 the maximum slope angle from 51.3 to 68.2 degrees. This should permit many more rays to fall 

 into the preferred grazing-angle range. The additional 17 degrees should increase the backscat- 

 tered angular bins to angles about 34 degrees higher. Figure 9 shows the results, leaving little 

 doubt that the higher slope angles do control the backscatter and that if all slopes up to 90 de- 

 grees occurred in the model, the backscattered field would be continued completely around to 

 180 degrees. The accuracy of such a field would depend on the overall accuracy of the ice keel 

 model. 



Figure 9 shows that slopes above 51.3 degrees increase the backscattered field. How- 

 ever, the forward-scattered fields should not be accepted in the place of those of Fig. 6 because 

 the modeled keels do not have dimensions equal to the best estimates oi real ice keels. 



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