Ill- 68 



Tlien (III-41) reduces to 



I(t) 



Ec 

 4r^ 



1 1 



/ 



m(r cos e )b (9) sin 6 d 9 



(III- 45) 



where r = ct/2 and m(r cos 9) = m(r, 9, cp) if we assume that the scattering 

 properties are layered horizontally and choose the vertical direction as the polar 

 axis. Machlup then assumed b(9) = cos 9 and was able to carry through the 

 analysis to solve for m in terms of I and the other parameters to obtain peak 

 values of m ranging from 10"®m'^ to 10~®m~^. Figure III-28 shows a graph 

 of m versus depth, based on measurements of 15-kc components of the explosive 

 sound. Further details, together with an excellent bibliography, are given by 

 Her sey and Backus (Ref. III-15). 



DEPTH (m) 

 300 400 600 800 1000 



m^VOLUME 

 SCATTERING 

 COEFFICIENT 



l._l i., 





J — , 



1 1 



1 1 









A 





r^ 



^ 



^ 



n 



\ 



' 









\ 











\ 



0.1 0.2 0.3 0.4 0.6 0.8 1.0 2.0 



TIME AFTER SHOCK WAVE (sec) 



FIGURE III- 28 VARIATION OF VOLUME SCATTERING 



CROSS SECTIONS (AFTER HERSEY AND 

 BACKUS) 



D. SCATTERING FROM THE SEA SURFACE 



Scattering from the irregularities of the sea surface plays a dominant 

 part in the propagation characteristics of the ocean. Unfortunately, however, a 

 realistic description of the ocean surface makes the analysis of sound scattering 



artbur Sl.lUtlcJnc-. 



S-7001-0307 



