Translations:Phase-shift migration/6/en

1. Start with the stacked section — an approximation to the zero-offset section P(x, z = 0, t), and perform 2-D Fourier transform to get P(k_x, z = 0, ω).
2. By using equation (22), for each frequency ω, extrapolate the transformed wavefield P(k_x, z, ω) at depth z with a phase-shift operator exp(−ik_zΔz) to get the wavefield P(k_x, z + Δz, ω) at depth z + Δz. At each z step, a new extrapolation operator with the velocity defined for that z value is computed.
3. As for any other migration, invoke the imaging principle t = 0 at each extrapolation step to obtain the migrated section P(k_x, z, t = 0) in the transform domain. The imaging condition t = 0 is met by summing over all frequency components of the extrapolated wavefield at each depth step. This is easily shown from the integral representing the inverse Fourier transform of the extrapolated wavefield (equation D-84).
4. Repeat steps (b) and (c) for downward continuation and imaging, respectively, for all depth steps to get the migrated section in the transform domain P(k_x, z, t = 0).
5. Final step involves inverse transforming in the x direction to get the migrated section P(x, z, t = 0).