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## Prestack migration ellipse

Equation (1) in (y,h)-space is
 (5)
A basic insight into equation (1) is to notice that at constant-offset h and constant travel time t the locus of possible reflectors is an ellipse in the (y ,z)-plane centered at y0. 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 (y0 ,z). An ellipse going through (y0 ,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