524 



SEISMIC METHODS 



[Chap. 9 



minus infinite in this range and negative after dip angles pass the critical 

 range. The lower layer is not detectable ii i -\- <p exceeds 90°; the ray 

 emerging from it does not return to the surface. 



The depths of an inclined layer under either shot point may be deter- 

 mined from the overburden velocity, the up- and down-dip velocity, and 

 the distances of the intercepts from the shot points. For the two direc- 

 tions of shooting, two intercepts are observed, Xu and Xd . As at the inter- 

 cept, ti = t2u = t2d^nd h = x/vi , we have, from eq. (9-51), 



„ 1 — sin (i — (p) , , 1 — sin (i -\- (p) .„ __ >. 



Hu = Xu • —^ ^^ r- and hd = xa- —^ r- , (9-55o) 



2 cos cp cos i 



2 cos <p cos i 



where Hu is the depth vertically under the shot point when shooting up dip, 



^<^»w ~* sr rr f«' «* 



^r->V 



m for ^ '4 





Fig. 9-62. Apparent velocities for up- and down-dip angles from 0° to 40° (after 



Meisser). 



and hd is the depth under the shot point when shooting down dip. By 

 substitution of (9-52), 



and 



i7„ = 



hd = 



2 cos 



<p cos i \ VzuJ 



_^ — (i - ^Y 



2 cos <p cos I \ Vm/ 



> (9-556) 



Calculation of depth proceeds, therefore, in the following order: (1) plot 

 travel-time curves; (2) determine V2d and V2u ; (3) determine x„ and Xd ; 



