36 V. P. GORBATOVA 



at which the head wave is produced, the more uniformly will it weaken 

 waves from this boundary with differences Vf^. We can therefore assume that 

 in multi-layered media with layered velocities which increase with depth 

 the intensity of the head waves produced at interfaces where the difference 

 in velocity is slight mil be fully comparable Avith the wave intensity which 

 would be found with these velocities and densities of the covering layer, 

 but with a much bigger discontinuity in the velocities of longitudinal Avaves 

 at the interface where the head wave is formed. We consider the para- 

 meters y, A, a at this boundary to be unchanged. 



If the overburden contains one layer with a high velocity which is less than 

 or equal to 0.9 t;^ then even under the most favourable conditions of the 

 intensity of the primary waves from the underlying layers will diminish by 

 a factor of not inore than 0.45 as the jump in longitudinal velocities in these 

 horizons is reduced (within the limits 0.3—0.9) and provided y, A and 

 a remain unchanged. 



The conclusion we have reached here has been made on the assumptions 

 indicated at the beginning of this section (that is we are assuming that the 

 intensities of the primary waves are being compared at distances from r^^ 



such that we can regard K '■('' — /"o)^^* ^ ^^ and that the head waves are 

 emerging towards points on the ground surface at angles such that sincco<0.9). 

 But as we can show, these assumptions are not so important. 



If for example we make the comparison at a distance r compai'able with Iq 

 then the intensity of the head waves will increase still more rapidly as the 

 discontinuity in longitudinal velocities at the reflecting boundary diminishes 

 than at fairly great distances from Tq. When there are weathered zones 

 present the angles at which the Avaves emerge at the ground surface are 

 small and, of course, satisfy the inequality sincfQ < 0.9. If the longitudinal 

 velocity alone varies in the nth. layer on the boundary of which the wave 

 under consideration is formed, while the transverse velocity remains constant, 

 then, as can be seen from Fig. 4, the diminution in the discontinuity 

 in longitudinal velocities at this boundary will be accompanied by a still 

 more rapid increase in the intensity of the head waves formed at it than 

 in the case we considered above, where we assumed that the ratio v^^ Jv^^ ^^ 

 remained constant. The principal conclusion reached here still holds good. 

 Intensive head waves can be observed coming from refracting boundaries 

 where the difference in velocities is slight. Head waves formed at a weak 

 interface lying above a boundary where the discontinuity in velocities is 

 great can of course be a good deal more intense than waves formed at a sharper 

 boundary lying underneath. It is also possible for refracted waves formed 

 at deeper boundaries, Avhere the difference in velocities is slight, to be more 



