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Equation (1) in (y,h)space is
 
(5) 
A basic insight into equation (1) is to notice
that at constantoffset h and constant travel time t
the locus of possible reflectors is
an ellipse in the (y ,z)plane centered at y_{0}.
The reason it is an ellipse
follows from the geometric definition of an ellipse.
To draw an ellipse,
place a nail or tack into s on Figure 1
and another into g.
Connect the tacks by a string
that is exactly long enough to go through (y_{0} ,z).
An ellipse going through (y_{0} ,z) may be constructed
by sliding a pencil along the string,
keeping the string tight.
The string keeps the total distance tv constant as is shown in
Figure 3
ellipse1
Figure 3
Prestack migration ellipse, the locus of all scatterers with
constant traveltime for source S and receiver G.

 
Replacing depth z in equation (5)
by the vertical traveltime depth
we get
 
(6) 
Next: Constant offset migration
Up: PRESTACK MIGRATION
Previous: Cheops' pyramid
Stanford Exploration Project
12/26/2000