SEISMIC METHODS 



757 



3. The parameter p is equal to the quotient of the sine of the angle 

 of emergence divided by the velocity at the surface of the medium. That is, 



P = 



sm gp 



~~v7 



where ao is the angle of emergence of the refracted wave and Vq is the 

 velocity at the surface of the medium. (Compare p. 679.) 



When the velocity is a linear function (V=Vo+ah), the expression 

 for the travel-time becomes 



or 



T= 2\ 



a 1 ; 



Jpv, 



dh 



+ ah)^\-p^{Vo-\-ahy 



ds 



zy/l^^ 



(110)' 



where z is defined by the equation : z = p (Vo + ah). On carrying out the 

 indicated integration the expression for T becomes 



r=-f.o.[i 



+ Vi-^' 



^-vtsech-.];^^ 



or 



T= — sech-i/'Fo 

 a 



Similarly, 



_ 2 ( zdz _ 2 r "11 



JpVo 



or 



ap 



P'Vo' 



(111) 



(112) 



Equations 111 and 112 are the parametric equations of the travel-time 

 curve. The usual form of the equation of the travel-time curve may be 

 obtained by eliminating p from equations 111 and 112. From Equation 111, 



_1_ 



Vo 



sech 



aT 



* The expression for the travel-time given here differs from that given on p. 683 

 only in the value assigned to the upper limit in the integration. The value for the 

 upper limit used here follows directly from Equation 108. 



