560 



SEISMIC METHODS 



[Chap. 9 



Fig. 9-83 shows two charts for the calculation of this correction. For 

 any velocity between 6000 and 15,000 feet (ordinate) and any mean re- 

 flection time between 0.3 and 1.4 seconds (abscissa), the first chart gives 

 the denominator of the above equation, or the factor a = 2v^M0~*. 

 This factor is the ordinate in the second chart on the right. By intersec- 

 tion with the spread distance x (from shot point to center detector), the 

 time correction A^ is located on the abscissa. Thus, this chart carries 

 out the operation a; • 10~ /a. 



In summary, the following expressions are available for depth calcula- 

 tion from reflection, assuming straight paths: 



(general formula) 



d = hVylt^ - x" 



(in terms of vertical time) d = ^^lU A/ 1 — { — ) 



(vertical shooting) 



d = hfiU 



(9-72) 



*-a'' 



h 



Fig. 9-84. Relative reflection travel time, in a 

 medium of continuous linear velocity increase 

 (after Slotnick). 



In eqs. (9-72) the speed 

 of the overburden is as- 

 sumed to be constant; in 

 practice, an average veloc- 

 ity Vo is substituted for Vi . 

 For reflections from differ- 

 ent depths, different aver- 

 age velocities are generally 

 used. Eqs. (9-72) may be 

 modified for curved ray 

 paths, that is. when there 

 is a variation of the aver- 

 age velocity with depth. 

 Slotnick*^ has calculated the 

 travel-time curves for (1) 

 a linear, and (2) an expon- 

 ential velocity increase. 

 For a linear increase given 

 by the relation v^ = Vo + 

 kA {h = depth), the travel 



time at the distance x is 



-H^^\/m-^] 



t = ,- 



" hoc. cit. 



