Geometrical acoustic and wave theory lead to a second‐order partial differential equation that links seismic sections with different offsets. In this equation a time‐shift term appears that corresponds to normal moveout; a second term, dependent on offset and time only, corrects the moveout of dipping events. The zero‐offset stacked section can thus be obtained by continuing the section with maximum offset towards zero, and stacking along the way the other common‐offset sections. Without the correction for dip moveout, the spatial resolution of the section is noticeably impaired, thus limiting the advantages that could be obtained with expensive migration procedures. Trade‐offs exist between multiplicity of coverage, spatial resolution, and signal‐to‐noise; in some cases the spatial resolution on the surface can be doubled and the aliasing noise averaged out. Velocity analyses carried out on data continued to zero offset show a better resolution and improved discrimination against multiples. For instance, sea‐floor multiples always appear at water velocity, so that their removal is simplified. This offset continuation can be carried out either in the time‐space domain or in the time‐wave number domain. The methods are applied both to synthetic and real data.

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LOINGER, E. 1983, A Linear Model for Velocity Anomalies, Geophysical Prospecting 31, Variations of seismic interval velocities within the cable length cause anomalies in the stacking velocity analyses. Utilizing the approximation of rectilinear ray propagation, i.e. supposing that the velocity changes cause time delays only, it is shown that the stacking velocity anomalies are linearly related to the interval velocity variations. In particular, the stacking velocity anomaly is calculated when the interval velocity of an intermediate layer undergoes a stepwise variation. The amplitude of the anomaly increases with the ratio between horizon depth and cable length. From the forward model, a program for the inversion is derived in order to identify lateral changes of interval velocities from unsmoothed stacking velocity analyses.Some examples of the application of this technique to synthetic and real data are presented.98-118.

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