562 



SEISMIC METHODS 



[Chap. 9 



(6) Dipping bed. Since in Fig. 9-86 

 the path I'R from the image of the 

 shot point may be substituted for the 

 path to and from the reflection point 

 C on a horizontal bed, it follows that 

 the down-dip travel time for a dipping 

 bed may be written 



\U = IR. (9-74) 



If td is varied and x is varied, vtd = 

 IRi , vt'd = IR2 , yt'd" = IRs , and so 

 on. These relations may be solved 

 graphically for the point / by drawing 

 circles with radii vtn about the re- 

 ceiving points which intersect in /. 

 Increased accuracy is obtained by using 

 two sets of receiving points on either side of the shot point. Analytic- 

 ally, the following relations follow from Fig. 9-86: 



(Down Dip) 

 Ir^ = 1)1^ + DR^; DR = x cos ip; 

 IR = vtd; DS = x sin cp; DI = 2z + DS; 

 hence, 



vhl = ^z^ + ^zx sin <p -\- x\ (9-75a) 



{Up Dip) (for the same distance x): 



Fig. 9-86. Reflection wave path for 

 dipping bed. 



V r„ = 42' - 42a; sin (p + x\ (9-756) 



Subtracting the up-dip from the down-dip time (for the same shot 

 distances), 



V {Jtd - tu) 



%ZX 



= Sin (f, 



and adding. 



Atl + tl) - 2x' 

 8 



= z 



(9-75c) 



(9-75d) 



Hence, up- and down-dip times furnish both depth (normal to the bed) 

 and dip, so that the depth d vertically below the shot point becomes 



d 



cos <p 



(9-75e) 



