28 



V. P. GORBATOVA 



The approximation method indicated can be used for reflecting bomidaries 

 mth the parameters shown in Table 1. 



Reflection from a layer with lower acoustic rigidity — For reflecting 

 boundaries with parameters as shown in Table 2, the magnitude of error 

 in determining the coefficient of reflection is given in Table 4, from which 

 it can be seen that when the angles at which the wave under consideration 

 strikes the reflecting boundary are not too great it is permissible to use 

 our approximate method of calculation. 



Table 4 



ANALYSIS OF THE INTENSITIES OF HEAD (REFRACTED) WAVES 

 A Two -Layered Medium 



The intensity of head waves in two -layered media is determined from the 

 formula 



c,rpp{p) 



7head = ^^ ^-^ (14) 



4:/r(Ao + 2/.o)|//-(r-roF^ 



The value of the multiplier Cq (see Fig. 2) depends shghtly on the values 

 of the parameter /q and is near to 2 when sin oCq < 0.9. The behaviour of 

 PPP (p) the coefficient of the head wave formation (see Fig. 4) — -will therefore 

 illustrate the dependence of the intensity of head waves in two-layered media 

 on the parameters of the interface at distances r, which are sufficiently 

 far from the point of emergence of the head wave, when we can set 

 /."(r-g'/^^A 



It can be seen from Fig. 4, moreover, that when y, A and a are fixed, 

 the intensity of the head wave increases in inverse proportion to the 

 difference in the longitudinal velocities at the refracting boundary. At 

 distances r'$>rQ the intensity of a refracted wave increases with reduced 

 sharpness of the refracting boundary just as the coefficient F^^ (p) grows. 

 At distances r comparable wdth Tq, when it is not possible to set yr (/" — /"o) = r^r 



