IMPLEMENTATION OF THE FOUR-PASS METHOD

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.