T(^ EXPLORATION GEOPHYSICS 



2. The materials of the strata are such that the velocities in any 

 direction are the same, i.e., the velocities are constant throughout 

 each stratum. 



3. The strata are sufficiently thick. 



4. The boundaries between the strata are planes. 



If these conditions are satisfied, the travel-time curve will consist of 

 straight line segments having successively decreasing slopes. In practice, 

 these conditions are rarely, if ever, satisfied. Generally the velocity 

 increases with the depth through a single layer. Also, loose layers 

 frequently exist under dense layers, and the velocities in the loose layers 

 are less than the velocities in the dense layers. 



Mapping Subsurface Structure from Determinations of "Delay 

 Times." — The methods described in this section constitute a means 

 for mapping the surface of a marker horizon, which exhibits gentle relief 

 and a definite velocity increase over that of the overlying stratum.* 



Surfaccj o '.' a.,. ,■ 



~*" ~\^MarHer (ff^B — — -'^l- 



" " Horizon Vg 5 



Fig. 463. — Ray path of wave following marker horizon. (After Gardner, 

 Geophysics.') 



Referring to Figure 463, it is assumed that the actual ray path of the 

 refracted wave which traverses layer 5 is ^A'B'S, where the portion 

 of the ray path in layer 5 is here assumed to follow the interface. In 

 addition, to facilitate calculations, it is assumed that the actual ray path 

 OA'B'S may be replaced by a hypothetical path OABS defined as that 

 path which the waves would follow if all the beds in the neighborhood 

 of the paths OA' and B'S were horizontal. Calculations based on this 

 assumption will have only a small error if the dips are less than 10°. 

 Let 



am = OM = offset distance corresponding to 



a„ = NS = offset distance corresponding to 5" 



The travel-time T between and S is : 



T = Toab'b = Tqabs (approximately) 

 or 



T = Iqa "•" tAB + ^BS 



where Iqa, ^ab and Ibs denote the travel-times along the paths OA, AB and 

 BS respectively. 



* With the exception of some minor changes, this section follows L. W. Gardner, 

 "An Area! Plan of Mapping Subsurface Structure by Refraction Shooting," Geo- 

 physics, Vol. IV, No. 4, Oct., 1939, pp. 247-259. 



