Chap. 9] 



SEISMIC METHODS 



557 



tance between the shot point S and any receptor R at the surface, d be the 

 depth, and Vi the velocity in the section above the reflecting bed. Then 

 the reflection travel time is 



Vi 



If X is small compared with d (vertical shooting), 



2d 



Vif ^~ 



Vi 



(9-69a) 



(9-696) 



The travel-time curve represented by eq. (9-69o) is shown in Fig. 9-816, 

 together with the corresponding travel-time curve for the refracted wave. 

 The reflection-time curve is a hyperbola and is almost horizontal for steep 

 angles of incidence (vertical shooting). For larger distances it rises rapidly 



Fig. 9-81a. Reflection path. 



Fig. 9-816. Relation of refraction and 

 reflection travel-time curves. 



until it approaches asymptotically a straight line representing the over- 

 burden velocity. If the second part of the refraction travel-time curve is 

 extended toward the shot point, it will be tangent to the reflection travel- 

 time curve at a point corresponding to the critical ray (that is, for which 

 the path in the lower medium is zero). The reflection- time gradient de- 

 pends on distance as shown by differentiation of eq. (9-69a) : 



dtr _ X 



dx Vi Va;2 -f 4^2 



-f (see Fig. 9-82). 



(9-70) 



It is often convenient to calculate travel times for vertical incidence 

 and to apply a correction expressed by the ratio of depth and shot distance, 

 R = d/x, so that 



''=^4A+W "' "--W'^i^l ^'-'"' 



