94 S. D. Shushakov 



In the upper part of Fig. 10 we show the damping of a double wave at higher 

 frequencies than in the lower part of the same figure. 



The relationships we have indicated are also connected with the depth 

 of the reflecting boundary. If this depth is reduced the path of a multiple 

 reflection is reduced (the more multiples there are, the smaller it becomes) 

 to a greater extent than the path of a single reflection. At the same time, 

 the angles of incidence increase at shallow depths more rapidly with distance 

 from the source than they do at great depths, and become bigger in proportion 

 to the number of multiples. Therefore the intensity of a reflected wave with 

 a large number of multiples grows as the depth diminishes, to a greater 

 extent than does a reflected wave with a small number of multiples. 



The relationships indicated are more pronounced when the angles of 

 incidence at the lower reflecting boundaries are small in comparison with 

 those at the upper reflecting boundaries, and less pronounced when these 

 angles are large. Moreover, the intensity of a multiple reflection in the 

 direction of a rise of the lower reflecting boundary is characterized by having 

 a more distinct peak than the intensity of a single wave; whereas in the 

 direction of a dip in this boundary the intensity is characterized by monotonic 

 and sharper damping. At the same time, the intensity of waves with a large 

 number of multiples becomes greater in the direction of a dip in the lower 

 reflecting boundary, in inverse ratio to the number of multiples, at considerably 

 greater distances from the source than it does in the direction of a rise. 



Some Features of Multiple Waves which have their first Reflections 

 above the Excitation point — Records of waves obtained by well-shooting, 

 where the first reflection occurs above the shot point, can be more inten- 

 sive than records of direct waves. The reflection coefficient from the 

 base of the low-velocity zone is roughly equal to 0.6-0.8 (16,5). The 

 amplitude of the vibrations for a spherical direct wave is. 



A, 



^,- 110_ -aSa 



where Aq is some constant, S^ is the path length and a is the absorption 

 coefficient for one unit of path. 

 For a reflected wave 



Ar- ^^ e , 



where K is the reflection coefficient and S^. the length of path. Hence 



K=4^e'^^'r-s,). (6) 



