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It is often convenient to arrange the calculation of a wave
to remove the effect of overall translation,
thereby making the wave appear to ``stand still.''
This subject, wave retardation,
will be examined more thoroughly in chapter .
Meanwhile, it is easy enough to introduce
the time shift t_{0} of a vertically propagating wave
in a hypothetical medium of velocity , namely,
 
(14) 
A time delay t_{0} in
the time domain corresponds to multiplication
by in the domain.
Thus, the wave pressure P is related
to the timeshifted mathematical variable Q by
 
(15) 
which is a generalization of equation (3)
to depthvariable velocity.
(Equations (15) and (17) apply in both x and
k_{x}space).
Differentiating with respect to z gives
 
(16) 
 (17) 
Next, substitute (15) and (17)
into Table .3
to obtain the retarded equations in Table .4.
Table 4:
Retarded form of phaseshift equations.




zero 

























general 
diffraction 
+ thin lens 



Next: Lateral velocity variation
Up: WAVEEXTRAPOLATION EQUATIONS
Previous: Depthvariable velocity
Stanford Exploration Project
10/31/1997