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In migration by downward continuation, the wavefield at depth
() is obtained by phase-shift from the wavefield at
depth z ()
| |
(1) |
where the depth wavenumber depends linearly
through a Taylor series expansion
on its value in the reference medium () and
the slowness in the depth interval from z to ,
and :
| |
(2) |
where, by definition, .
If we denote the wavefield downward continued through the
reference velocity as
| |
(3) |
we obtain
| |
(4) |
The Born approximation linearizes the phase-shift exponential
, such that we can write
| |
(5) |
Therefore, at any particular depth level,
the wavefield perturbation is
| |
(6) |
which we can also write as
| |
(7) |
The image perturbation is simply obtained from the wavefield
perturbation by summation over frequencies:
| |
(8) |
Next: Image perturbation by residual
Up: Sava and Biondi: Image
Previous: Introduction
Stanford Exploration Project
9/18/2001