REFRACTED AND REFLECTED LONGITUDINAL WAVES 39 



tance slightly more quickly than in media where t'o, p< ^i, p- ^^ ^^^ 

 bedding depth Hq of the boundary increases the waves reflected from it will 

 dampen more slowly with increase of r. At distances r = JiqI^, the intensity 

 of reflected waves when Hq ^ h^^ is not less than 0.8 of the intensity above 

 the shot point when hf^f^hg^ is not less than 0.5. 



(b) Doubly Reflected Waves — The intensity of doubly reflected waves 

 above the shot point is equal to 



2 (oo % p - ^1 ^1, p) ^ 1 



47r (Aq + 2//o) Vq^ p {qq vq, p + Qi v^^ p) ^ ^h^ -hgd 



This does not depend on the value of the transverse -svave velocity and 

 takes on higher values the greater the discontinuity in the acoustic rigidities 

 at the interface, the shallower the depth of the bed ^o ^^^ the greater h^^. 



The ratio between the intensities of doubly and singly reflected waves 

 above a shot point is equal to 



y double _ go^'0,p~gl^l, p ^hp — hsd ^ 

 y single ?0 ^'0, p + ^1 ^1, p ^ho-hsd 



when the shot depth varies from hg^<^hQ to h^^p=ihQ this hes within the 

 limits 



^0 ^0, p — Q\ ^1, p ! ydouble }^ 



Qo^'0,p+Qi^l,p I ysingle 2 



?0^0,p-^l^^l, p 



Qo^o.p + Qi^hP 



The doubly reflected wave diminishes more slowly than the single re- 

 flected wave -with growth of ;■. The rate at which it diminishes also depends 

 on Avhether the two -layered medium is characterized by the inequahty 

 Vq < Vj^ or Vq p^- v^^ and on the values of the transverse velocities of 

 the waves. The effect of a change in the transverse velocity on the rate at 

 which the intensity of the doubly reflected waves is damped can be the 

 same as in the case of singly reflected waves. 



Figure 11 shows curves for the damping of intensity of doubly reflected 

 waves with distance for media where Vq^ p < v^^p (continuous Hues) deter- 

 mined by the parameter A = ^i, s 1% p i^^ 'which the rate of damping also 



mainly depends) and for media where v^^ p > ^i, p I dotted lines characterized 



11 ^1 s 1 ^ ^0, 



by the parameters y = — '- — and Zi = 



^l,P ^0, p; 



Since doubly reflected waves diminish ^nth. distance more slowly than 

 single echoes, the question arises whether they become more intense, at 

 some distance from the shot point, than such single echoes. We shall not 



