d 



n 



HORTON: THE EFFECT OF ROUGH INTERFACES ON SIGNALS 

 THAT PENETRATE THE BOTTOM 



WATER 



Y- 



SEDIMENT 



-A 



'1 • 



Q 



THE HELMHOLTZ INTEGRAL FOR POINTS P AND Q BELOW jd IS 



(p) =iw 



4n/ 



= t - * f I -^ 



(ii; 



NOW 



3n 



9 and 



8z 



+ — TT— = — ;r— = + 1 k COS 6 G, 



dn dz-, o e 



SO 



(P) 



4n 



9(t) 



+ -^ + i kn cos G 

 9z, " e 



i^ 



Gd^(12; 



IF * IS LOCALLY A PLANE WAVE WITH ANGLE OF 



INCIDENCE, e , IT WILL BE REFRACTED INTO THE BOTTOM 

 w 



WITH REFRACTION ANGLE 



B' 



Figure 10. HELMHOLTZ AND GREEN'S FUNCTIONS 



289 



