42 V. P. GORBATOVA 



reflected from this boundary will be greater in inverse proportion to the 

 thickness of the layers which have the higher velocities and in direct pro- 

 portion to the thickness of the layers which have the lower velocities. The 

 more the velocity of the ith. layer differs from that in the layer where the 

 shot is fired, the greater ^vi\\ be the influence which a change in the thiclaiess 

 of this layer exerts on the intensity of waves reflected from interfaces lying 

 at greater depths. 



(c) From formula (11) we can easily obtain expressions for the intensity 

 ratio of multiple echoes above a shot point, when the reflection occurs at 



the boundary of the n — lth. and nth layers and the free surface. 



n-l 



2h; — - — , we shall have the following formula 



1=0 



for the intensity ratio of waves reflected k and k — 1 times: 



^ = -J^ ^n m Pi + l) iPi+1 Pd]v {Pn-lPn-l)v, (18) 



Jk ^ — -L 1=0 



where [{P-P-_^_^) (P^-^^ Pj)]^ and (P„_iP„_i)„ are determined from formulas 

 (12) and (13), and k is the number of times the wave is reflected. 



As can be seen from (18) the greatest difference in the intensities above 

 the shot point is found to occur between single and double echoes. The 

 greater the number of reflections the smaller the difference between the 

 intensities of waves reflected a neighbouring number of times. 



For such multiple echoes where the second reflection has taken place 

 from the free surface, we can easily obtain from (18) the following expres- 

 sion: 



jl {k-l)ik+l) 



^k-ijk+l 



k' 



(19) 



where j\ is the intensity above the shot point of a wave reflected k times; 

 //f-i is the intensity above the shot point for a wave reflected k~^ times; Jh^-^ 

 is the intensity above the shot point for a wave reflected k -{- 1 times. 



For example, for the intensity of a a single ^vaye j\, a double echo yg ^^^ 

 a triple echo 73 we have 



•'2 ^ r-- 



= 0.75 



7173 



The ratio (19) does not depend only on the values of the transverse velo- 

 cities but also on the longitudinal velocities. This is true for any type of effect 

 ^vhen any component of displacerrsgnt is being recorded above the point 

 of disturbance. 



