698 



EXPLORATION GEOPHYSICS 



(62) 



Application of this correction to the observed move-out time gives the 

 move-out that would be obtained by a conventional split-spread placed 

 symmetrically about a shot-point midway between the actual shot-point 

 and the center of the end-shot spread. 



Reduction of the observed reflection time T to the effective split-spread 

 time Tg is obtained by the application of the following equation : 



r, = — log^ 

 a 



[cosh{-f}W 



sinh' 



aT 

 2 



2Fi ; J 



(63) 



By using the corrected values of the reflection and move-out times, the 

 results may be calculated in the conventional manner as given for split- 

 spreads, and the positions of the reflection may be plotted with reference 

 to a point midway between the shot-point location and the center of the 

 end-spread. 



Cross Spreads I\ot at Right Angles. — The conventional vector resolu- 

 tion of the trigonometric functions of the cross components of dip requires 



that the two component set-ups be placed 

 at right angles. Occasionally a set-up loca- 

 tion will be found in which this cannot be 

 done, but the seismometers can be set up at 

 an angle that differs from 90° by an angle 

 <^. This situation may be treated by correct- 

 X ing one of the observed move-out times to a 

 normal move-out for a right-angle posi- 

 tion for the measured component. 



Consider the X and Y axes to repre- 

 sent the normal spread directions. Let the 

 ■X^ axis represent the abnormal spread di- 

 rection making an angle <f> with the normal 

 X-axis, as shown in Figure 429. 



Fig. 429. — Rotation of spread. 



or 



The reflection time T is a function oi x and 3;. Therefore, 



9^' 'dx -dx' -dy d^' 



— — r = — — cos <f> + — — sm (b 



(64) 



(65) 



Replacing the derivatives by the measured move-out times and spread 



