REFRACTED AND REFLECTED LONGITUDINAL WAVES 31 



the head wave is excited. All the other parameters of the medium %vill 

 be regarded as unchanged. 



We shall find, for example, the variation in the intensity of a head wave 

 excited in the nth. horizon of the medium (see Fig. 1) with v^ = 6000 m/s. 

 if the longitudinal velocity in the ith layer adapts from 1540 to 

 5150 m/s. 



When v^^ ^ in formula (2) changes, the quantity Tq (the abscissa of the point 

 of emergence of the head wave under consideration) and the value of the 

 coefficient of refraction at the upper and lower boundaries (that is the ex- 

 pressions (P,._iP,) (P,.P,._i) and (PiP,.+i)(P.+jP.)) of the ith layer will also 

 change. 



We shall regard the intensities as being determined at such distances r 

 from Tq that we can assume l//-(r— /(,)''' ?« r^. Then, when v^ varies and all 

 the other parameters of the structure of the medium remain unchanged, 

 the intensity of the head waves will vary proportionately to the product of 

 the coefficients of refraction [(P^.^P,-) (P.P._j)] [(P,Pi+i)(P,+iPi)], allowance 

 having been made for the refraction of the wave at the boundaries of the 

 ith layer. The curves in Fig. 8a therefore, where the value 



is plotted against ''^ illustrate the variations in the intensity of the head 



V 



n,p 



-'i-f 1, p 



waves with gro'v\1;h of v^ . The curve determined by the parameter b = 



Vi 



= 0.35 characterizes the change in intensity of the head wave excited in 

 the ith layer of the medium with v^ = 6000 m/s and f,_j — 1800 m/s 

 when Vj^ ^ varies within the range 1540 — 5150 m/s. The curves for cases where 



the values of the parameter b = — — — show how the intensity of the head 



waves excited in the nth layers would vary with variation in v^ , if the medium 

 under consideration were characterized by some other difference in the 



velocities v,_j and v^+i^p smd by the same value '~^'P = 0.3. 



If a medium with a different ratio of ^/-i^p/i'n^p were considered then differ- 

 ent curves would be obtained. Fig. 86 shows the l(P,_iPj)(PjP,_i)] [(^,-P,+i) 

 (Pj+iPj)] curves for the same parameters b = f,_jp/z;,.,.j p, but for a ratio 

 «^/-i,p/Vp = 0-175. 



For a medium which differs from the one discussed above only in having 

 a different value for the velocity y,_j^p (^^i_i^p= 1500 m/s), the intensity of 



