Even small shifts (less than a sample interval in magnitude) may cause enough misalignment that false events appear in the difference sections. Without access to the full pre-stack data, there are a limited number of ways such differences can be corrected.
Residual post-stack migration Rothman et al. (1985), or velocity continuation Claerbout (1986); Fomel (1997), provide operators that map between different migration velocities. However, without detailed knowledge of the velocity fields used for NMO and/or migration, and in cases where the migration algorithms differ significantly between surveys, it will be difficult to determine the correct residual migration operator to apply a priori. Instead the operator may have to be estimated from the data.
As an alternative to standard residual migration, we use a `warping' operator Wolberg (1990) to correct for kinematic differences between surveys. A 3-D shift vector, or `warp-function' that maps one survey onto another can be estimated at every point in the data volume, and applied directly.
At node points throughout the seismic data-volume, we calculate local 3-D cross-correlation functions between surveys. Picking the maxima of these functions produces a sparse cube of 3-D shift vectors that map one survey onto the other. Before applying the warp, we median-filter, then smooth, then interpolate the warp-function to fill the volume. To apply the warp, we look back down the shift vector, interpolating a value at every point in the output space.
Grubb and Tura (1997) used a similar algorithm to estimate uncertainty in AVO migration/inversion results. They migrated the same dataset many times with slightly different velocity fields. They then co-located reflectors with a warping algorithm, which allowed them to separate the kinematic and amplitude effects of the different migration velocities.