Next: Interpolation in Stolt migration
Up: Popovici, Blondel, & Muir:
Previous: Popovici, Blondel, & Muir:
Downward continuation and imaging in the isotropic
case (Gazdag, 1978) can be written as
| |
(1) |
where
| |
(2) |
In equation (1), represents the
Fourier transform of the seismic field p(t,x) recorded at
the surface, following Claerbout's (1985) sign convention
and v represents half the velocity, as
used in the exploding reflectors model.
We can rewrite equation (1) as time migration replacing
the depth steps by equivalent time steps :
| |
(3) |
where we define
For a constant velocity medium, Stolt (1978) transforms the integral
in using a Fourier transform, which can be computed rapidly
via a Fast Fourier Transform (FFT) algorithm
| |
(4) |
where represents the Jacobian of the transformation
from to
and represents the initial data
as function of the new variable .
Next: Interpolation in Stolt migration
Up: Popovici, Blondel, & Muir:
Previous: Popovici, Blondel, & Muir:
Stanford Exploration Project
11/16/1997