SEISMIC METHODS 697 



but a few of the more important will be discussed as a means of indicating 

 the methods of solution for others. For example, following this discussion 

 of end-shots, the problem of cross-spreads which are not at right angles 

 will be treated. 



The computation of end shots may be carried out by the construction 

 of a set of charts based on a specific length of spread, shot-point to detector 

 distance, and on the condition that V = Vi + aZ. The labor of such an 

 undertaking would be greater than that involved in the construction of 

 the charts for split spreads and would be limited to a specific set-up. A 

 simpler method of procedure is found in reducing the observed value of 

 the reflection and move-out times of an end shot to the effective values 

 which would have been observed in a split spread set-up. 



This may be accomplished by use of a so-called "normal move-out" 

 function which gives the value of the move-outs observed from horizontal 

 reflecting interfaces as a function of spread length, distance from the shot- 

 point and time of the reflection. Any given reflection obtained from an end 

 shot may be corrected by subtracting from the observed move-out the 

 normal move-out increment of time computed for that particular set-up. 

 This correction is rigorous only for horizontal reflecting beds, but the error 

 is small for dips up to 15 or 20 degrees, beyond which the correction is 

 seldom used. 



In cases where a certain type of end-shot must be used frequently, the 

 corrections may be plotted for ready reference in the form of a normal 

 move-out curve. The basic equation used for this computation gives the 

 reflection time for a horizontal bed of depth Z as a function of distance x 

 from the shot-point to the center of the spread. 



From this equation it can be shown by differentiation that the observed 

 move-out time for an end shot of spread length 6" (center of spread a dis- 

 tance X from the shot-point) is 



\ -1 



Sax ^z^{ . , aT 



^ 2 7 



^^ = ^7' ' ) ''''^-Tl (61) 



1 



The time T used in this equation represents the reflection time to the shot- 

 point. Since the shot point is usually not far from the nearest seismometer, 

 the error involved in using this seismometer to obtain T for computing 

 purposes is usually negligible. However, if the spread is a long distance 

 from the shot-point, the normal move-out correction cannot utilize the 

 reflection time to the shot-point, and a more complicated expression using 

 the reflection time to the center of the spread is necessary. 



