most areas of low to moderate dip. Migration of reflecting points to their spacial 

 position using straight wave paths and the dip angle expression, sin <f> = 

 VAT\$Ax, usually leads to a reasonable structural picture. 



In areas of significant dip, more complicated velocity distributions have 

 been postulated (for a summary, see Kaufman, 1953) , two of which predominate. 

 All presume an increase of velocity with depth within a medium of parallel iso- 

 velocity surfaces and imply curved travel paths whose emergent angles are defined 

 by the expression sin oc = V JT<f>/Jx. (fig. 26-9). 



The most widely used of these velocity functions is one requiring a linear 

 increase of the intantaneous velocity, V, with depth, z, or V — V + kz, wherein 

 V is the initial or datum velocity and k is the velocity gradient. Expressed in 

 verticle time, r, instead of depth, this function becomes V = V e kT and is hence 



coincident ray 



= dip of 

 horizon 



smoc = 



V = datum velocity 



oc = emergent angle 



AT^ = dip stepout time 



z = depth to coincident pt. 

 x = offset or migration 

 distance 



coincident 



RAY- PATH DIAGRAM OF DIPPING REFLECTING 

 HORIZON (CURVED -RAY ASSUMPTION) 



Figure 26-9. Curved-ray ray-path diagram of a dipping reflecting horizon. If the seismo- 

 meters are deployed on a line normal to the strike of the reflecting horizon and if the 

 emergent wave front is taken to be plane, then the emergent angle ( oc ) can be obtained 

 from the equation sin cc = V AT<p/Ax. Note that with curved-ray paths the angle of 

 emergence and angle of dip of the horizon are not the same. Knowledge of the velocity 

 distribution must be gained before the coincident point can be located and before 

 the relationship of to oc can be ascertained. 



574 



