SEISMIC METHODS 761 



In terms of the new variables (/I'and L), the travel-time equations for 

 down dip shooting and up dip shooting are : 



^=^(^^ + s^^W^-]^j +2/jcoseVpr-2-y^ 

 and 



respectively. 



If h' is replaced by its equivalent, h+L tan 6, the expression for T' 

 becomes identical with that for T. This is to be expected because the 

 refracted path for up dip shooting is the same as that for down dip shooting. 

 In practice, however, the values of V\ obtained at the two shot-points may 

 not be exactly the same and therefore the check times for the reversed 

 paths may not be identical. In this case, the travel-time curves are adjusted 

 before computing V2 and 6 so as to make the travel-times T and T' identical. 



V2 and 6 may be obtained from the slopes of the line segments cor- 

 responding to the refracted paths. That is, V2 and 6 may be obtained from 

 the relations 



1T7 = slope 



r 2 (down dip) 



7777 = slope = 



y 2 (up dip) 



The values of V2' and V2" {apparent velocities) and Vi are obtained 

 from the field curve directly or from the adjusted field curve, depending 

 on whether Vi is the same at the two shot-points or not, 



A more practical method makes use of the relationship that the sine of 

 the angle of emergence is equal to the product of the velocity in the surface 

 layer by the slope of the travel-time curve. This relationship may be de- 

 rived from Equation 116 by making use of the relation r^z^r- = sin (a + 6). 



V2 

 Thus 



slope = rry [cOS Q Sin (a + ^) + slu Q COS (a + ^) ] 



(down dip) r\ 



But 



