720 EXPLORATION GEOPHYSICS 



velocity layer and the ^th seismometer. The first arrival-time to the ^th 

 seismometer is derived in the same manner as was Equation 12. That is, 



. _ O^'fc — Uk tan Ok _,_ Ujc 



tk — t;- t" 



Vc Vu,k cos Ok 



where 05"^ is the horizontal distance from the shot-point to the ^th seis- 

 mometer. But from the critical angle relation, 



^,= Vl- (i^)'and tan^. = -%f-- 

 \ K c / l/c cos Ok 



COS 



h=- 



Referring to the approximately vertical direction assumed by those 

 rays in the low velocity layer which are of importance, it is desired to 

 determine the vertical travel-time tu,k through the low velocity layer, 

 where 



f„,,^-^ (74) 



y u,Tt 



On solving Equation 73 for Uu, one obtains 



Hence 





, ^'~ Vc 



^"'^= / /r/ "=^2 (75) 



v>-(^) 



Because, in general, the effect of Vu,k in this equation is only about 5% 

 or less in the practical case, it is sufficient to assume that Vu,k may be 

 replaced by the F„ found from up-hole shooting at the shot-point. 



It is seldom felt justified to expend the effort in up-hole shooting 

 at every shot-point in a prospect for low velocity layer data alone. In- 

 stead, a seismometer is left at the shot-point in routine set-ups and is used 

 to record the shot-hole time. (See fifth trace of Figure 441.) This 

 shot-point seismometer acts as a rough gauge of the change in F„ from 

 point to point and is used in conjunction with the low velocity layer re- 

 fraction diagram. 



The correction for variation in velocity or thickness of low velocity 

 zone is particularly important when the difiference in reflection times due 

 to dip of reflecting strata is to be determined. This time difference AT 

 is itself a comparatively small quantity ; hence, it frequently is of the 



