12 



V, P. GORBATOVA 



In the main these simpHfications mean that the frequency rates of the 

 waves under consideration are determined not by accurate tables but simply 

 by a small number of typical graphs, which we shall give later. Further, 

 the assumption has been made that layers possessing a higher longitudinal 

 velocity have also a higher ratio of transverse velocity to longitudinal veloc- 

 ity and a greater density. This would appear to be true for most real media. 



The elastic properties of two neighbouring media (the ith and the i+lth) 

 are characterized by the following parameters: a— the ratio of the lower 

 longitudinal velocity to the higher; y— the ratio of the transverse velocity 

 to the longitudinal velocity in the layer where v is the smaller; Zl — the 

 ratio of the transverse velocity to the longitudinal velocity in a layer where- 

 V is the greater; cr— the ratio of the lower density to the higher. 



If Vi^ p < Vi + i^ p, 



V; 



oc = 



I, p 



^i+i, P 



^i,s 



XP 



A = 



'Vj+l, s 

 Vi+l,p 



Qi 



If Vi^ p > Vi+i^ p, 



Vi + l,p 



%p 



^f+1, s 

 Vi+1, p 



Vi,p 



a = 



Qi+i 



Qi+l 



That is, y <Zl, a <1,0, a< 1, on all occasions. 



The parameters a, y, A and a of adjacent layers, on whose boundaries 

 refraction occurs, are chosen within the following Hmits: 



0.3 < a < 0.9, 0.3 <y < 0.6, 0.4 <Zl < 0.6, 0.7 <(t < 1.0 



But the boundaries of adjacent layers characterized by the parameters 

 y = 0.3, A = 0.6 are excluded. For the ratio of transverse velocities in 

 the boundary media therefore we shall always assume: 0.3<(5<0.9, 



where 



a- 



Vi 



'' ■' , if ^iV p < ^f +1, p 

 , if % p > ^i+i, p 



'Vi+1, s 



Table 1 shows values for the parameters of adjacent layers on whose bound-^ 

 ary reflection occurs if the reflection takes place from the layer in which 

 the travel velocity of longitudinal waves is higher than in the layer 

 through which the wave has passed. If the reflection occurs from the layer 

 with the lower group velocity the values for the parameters will be found 

 in Table 2. 



