18 V. P. GORBATOVA 



5. The values obtained for Cq {P^ -P/+i) [Pi+i -Pj)? ^^p (p) and Tq are inserted 

 in formula (2). 



Reflected Simple and Multiple Weaves 



The intensity of a simple wave reflected from the boundary of the nlth 

 and nth layers is determined from formula (3) 



p 

 sin (Xq 



(3) 



1 / ^ r V^ Attang,- _ hsdtan oco 1 

 V [ Z-j cos^ Xi cos^ ocq J 



i=0 



Similar formulae are given in Malinovskaia's work <^). 



The intensities of multiple waves are determined from formulae similar 

 to (3). Here again we must take into account all the refractions and reflec- 

 tions at the intermediate interfaces. Therefore if the multiple wave under 

 consideration intersects the interface between the iJth and i + lth layers 

 while it is travelling from above downwards m times and the same number 

 of times when it is travelling from below upwards, then the multiplier (P^ P,-+i) 

 (P,-^j^Pj) is repeated in the product U (P^Pi^y) {P^_^,■J^P■) also m times. If 

 the wave suffers n reflections from the given interface, the coefficient of 

 reflection corresponding to this boundary is raised to the nth power. We 

 introduce coefficients raised to the appropriate powers for reflection from 

 all the interfaces at wliich the wave under consideration suffers further 

 reflections. 



We sliall henceforward adopt the following notation : if the reflected wave 

 is travelHng in the mth layer and is reflected from its lower boundary, the 

 coefficient of reflection will be denoted by (P,„ P^) ; but if the reflection 

 takes place from the upper boundary of the mih layer the coefficient of 

 reflection will be denoted by (P„,/ P^>). 



In the sum > hi L each item is repeated as many times as the multiple 



-^-1 COS^ CCi 



wave under consideration passes through the ith layer. If this wave is 

 propagated from the shot point upwards and then is again reflected from the 



free surface and goes downwards, a further term, 2hsd ^-^ must be 



cos" a.i 



introduced into the sum ^2 ^^ tan a,- _ /,^^i^^ in formula (3) 



^—1 COS^ (Xi COS^ OCq 



