102 T. I. Oblogina 



to the path KB. The fronts of the head waves EG and CB will touch the 

 front of the diffracted wave at E and C respectively. Note that after diffraction 

 there are two head waves for the one head wave before dijffraction (dashed 

 hne): the wave CB which we have referred to above, and a wave DN, the 

 front of which is parallel to the dashed-line front and touches the front of 

 the diffracted wave at D. We may also note the further wave AL excited 

 on the path MA by the front GA. 



Writing down the equations for the wave hodographs along the longitudinal 

 profile r = H, we obtain 



^f 



+ H'; (1) 



for the diffracted wave KCDEF: 



1 H ,_. 



t-. = — :\- -1 cos oci ; (z) 



for the head wave DN; 



for the head wave EG; 



, 1 H ,„> 



t-, == X ^ cos oc-i ; (o) 



V-, Vc 



to — -X -] COS OCo , {f*>) 



V2 Vq 



for the head wave CB 



where oci = arc sin — , oco — arc sin — — the critical angles. 



Figure 1, b shows hodographs for Iq, t-^, t^ and t^ waves. In the sector 

 of the profile which lies above the contact we observe a diffracted wave t^, 

 the hyperbolic hodograph of which touches the hodographs of the head 

 waves t-^, t^ and 1^2 (the wave t'-^ has a negative apparent velocity). As we 

 see, when v-^ is greater than v^^^ the diffracted wave emerges into the first 

 onsets in the sector of the profile 



Ax = H(tdn 0C2 — tan (Xi) = Hvq 



We shall now examine a case when v^ is smaller than v^ and the system 

 of a head and a shear wave moves as before from left to right; in other 



