34 V. P. GORBATOVA 



The head waves emerge towards points on the ground surface at angles 

 such that shi ocq < 0.9 for which, as can he seen from Fig. 2, we can take 

 Cq !^ 2. Then the variation in the head wave intensity value with variation 

 of v^ will depend solely on the behaviour of the multiphers /"^^(p) and 



(PiP'i+diPi+iPi)- 



As v^ diminishes, the discontinuity in the longitudinal velocities at 



the principal refracting boundary will diminish and the coefficient r^^{p) 



and the angles of incidence on to the intermediate interfaces mil increase, 



while all the coefficients of refraction at these interfaces will decrease. 



We shall now see how the intensity of head waves PqP-J^^P^Pq in 

 a three -layer medium changes as v^ p changes. As can be seen from Fig. 4, 

 the coefficient r^^(p) for boundaries of layers characterized by the parameters 

 y = A = 0.6, a = 1.0 increases least rapidly as the sharpness of the refracting 

 boundary diminishes. 



Fig. 9 shows curves for the variation in head wave intensity in three- 

 layered media with change in the boundary velocity t^g p ^^ the interface 

 of layers characterized by the parameters y = A = 0.6, a = 1.0. The 

 intermediate interfaces examined have an upper layer to lower layer longitu- 

 dinal wave velocity ratio within the limits 0.3 < agi = — — < 1/0.3 and 



a density ratio equal to unity. The parameter of each of these curves is the 



ratio t^o,pK,p = Sr 



As can be seen from the figure, the intensity of the head wave PqP^PJP^Pq 

 increases as the difference between the velocities v^ „ and v, „ decreases. 

 For three -layered media for which ^o p -^ '^i p "^ ^2 p *^^^ remains true 

 so long as Vq does not approach v^ 'Xh.aX is, so long as v^ <,0.9v^p. 

 With further diminution of v^p the intensity of head waves diminishes 

 despite the concomitant diminution in the values of v^ and v^ . 



If the adjacent layers are characterized by other parameters, y. A, a, 

 the intensity of a refracted wave formed on their boundary will increase 

 with diminution of the discontinuity in the values of the longitudinal velocities 

 at this boundary more rapidly than is shown in Fig. 9. A variation in a at 

 the intermediate interface does not entail changes in the course of the curves 

 shown but only alters their vertical scale. 



Accordingly, we may conclude that in three-layered media with the 

 parameters indicated at the start the intensity of the head waves PqPxP^PxPq 

 will increase as the difference in the values of the longitudinal velocities 

 v^p and v^ decreases. Indeed the intensity of such waves will decrease 

 only for media where Vq v-^p when the value oi v^^p approaches VQp, or 

 in other words when the difference between v^ „ and v^ „ decreases. 



