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To realize the four-pass method, we first apply the diffraction term
along the *x* axis for all *y* and along the *y* axis for all *x*,
just as in the two-pass method, except that we use *dz* / 2
to get the differencing star. We then sort the data along the *x*' axis and
apply the diffraction term along *x*' for all *y*'.
Next we sort the data along the
*y*' axis and apply the diffraction term for all *x*'. Finally, the thin lens
term is applied, followed by imaging for each depth.
We use Dave Hale's coding method of the boundary condition
(Claerbout, 1985, Page 106)
since the zero-slope boundary treatment resulted from taking

*d*(1)=0. ; *d*(*nx*)=0.

*endl*=-*a* ; *endr*=-*c*

causes the instability after the wave field is downward
continued to a certain depth.

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Stanford Exploration Project

11/16/1997