REFRACTED AND REFLECTED LONGITUDINAL WAVES IS 



Multiple reflected waves are examined at a distance from the points of 

 emergence of like reflected -refracted waves. We evaluate the distance with 



the help of inequalities similar to (1), where only in the term > — ' — - — - 



■^-J cos"a/ 



is each of the items repeated as many times as the multiple wave under 



consideration passes through the iih layer. 



METHODS FOR CALCULATING INTENSITIES 

 Head Waves 



The intensity of a head wave propagated in a medium (Fig, 1) from the 

 n — 1th and nth boundaries of the layers is determined by the expression 



c,''n\PiPi^^){Pi^^p,)rpp{p) 



t" = /n\ 



Jhead— . /^ ^ m/-/ xa; ' ^"^^ 



where Cq is some multiplier dependent on the properties of the zero layer* 



r^^ (p) is the coefficient of the head wave formation at the boundary of 

 the Tilth, and nth layers; 



r is the distance between shot point and the observation point along the 

 free surface; 



Tq is the abscissa of the point of origin of the head wave under consid- 

 eration ; 



Aq, and //q are the Lame constants for the layer where the shot is fired; 



(P-P-^-^ (Pi+iPi) are the coefficients of refraction in the intensities when 

 the wave is passing through the boundary bet\veen the iih and the j+lth 

 layers from above to below and from below to above. 



n-2 



In the product IJ (P^P^j^^ (Pi+i^i) i^ formula (2) the coefficients of 

 i = o 

 refraction of the wave under consideration at all the intermediate interfaces 



are taken into account. 



The coefficients of refraction, the coefficients of head wave formation, 

 and also the multipher Cq depend both on the properties of the interfaces 

 themselves and also on the angle at which the primary wave under consider- 

 ation strikes these boundaries. Values for these coefficients are given in 

 the detailed tables compiled by the team of mathematicians headed by 

 Petrashen' at the Leningrad Section of the Institute of Mathematics. Using 

 these tables to determine the quantities mentioned we have compiled graphs 



* The advisability of using this Hes in the fact that if the calculations are suffciently 

 approximate, we can assume that Cq = 2 when sin OCq < 0.9. 



