SEISMIC METHODS 



673 



The distance OB equals O'B so that OBS equals O'^.S". O'BS is the 

 hypotenuse of the right triangle O'^O'^" ; hence 



(O'^^-)- = (O'O")^ + (O^'OSy = 4^2 + .v2 + 4^^, sin 6 

 Thus the length of the reflected ray path is 



OBS = O'BS = V4&^ + x^ + Axb sin d 



Let Vi denote the velocity in the upper bed, then the travel-time T to a 

 seismometer located down-dip from the shot-point is : 



T- 



\/Ab^ + x^ + Axh sin 6 



(13) 



If the seismometer is located up-dip from the shot-point, the angle 

 6 entering into Equation 13 is replaced by — 6. Hence, the travel-time 

 T' to a seismometer located up-dip from the shot-point is : 



T = 



V Ab^ + A'2 - Axb sin 6 



Vi 



(13a) 



Since three unknowns (Fi, b, and 6 appear in Equations 13 and 13a, 

 a set of three reflection times from three seismometers located at different 

 distances from the shot-point would suffice to determine the dip, depth, 

 and velocity for a reflecting bed.* In the general practical procedure, 

 however, it is not customary to evaluate the velocity with each dip-depth 

 determination. Instead, the velocity is investigated separately, as dis- 

 cussed in a later section. 



The difference in the reflection times to the two seismometers 

 located on either side of is : 



AT 



^y4b^ + x^ 



L/i I Axbsind ^l . 4xbsme] 



A tabulation of the AT values corresponding to a fixed value of the 

 dip 6 and various values of the depth h is given in Table 21. 



TABLE 21 

 VALUES OF AT COMPUTED FROM EQUATION 14 



Legend: 



dip = ^= 10° 

 h =. b cos 6 



* This is true because the spread was assumed in the direction of maximum dip. 

 Otherwise four reflection times would be required. 



