# Stacking velocity inversion

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

The procedure for estimating layer velocities from stacking velocity inversion requires the horizon times picked from unmigrated stacked data (Figure 9.2-2) and stacking velocities at time horizons that correspond to layer boundaries in the model (Figure 9.2-4). Horizon-consistent stacking velocities are estimated by computing semblance for a range of constant velocities continuously along the time horizon picked from the stacked data (Figure 9.2-2). The velocity spectrum for each time horizon (Figure 9.2-4) then is picked to derive a stacking velocity curve along the midpoint axis. As for coherency inversion, the velocity estimate from stacking velocity inversion is local, independent of data away from the analysis location.

A procedure for velocity-depth model estimation that includes stacking velocity estimation is conducted layer-by-layer starting from the surface. Assume that the velocity-depth model for the first n − 1 layers already has been estimated. For the nth layer, follow the steps below for stacking velocity inversion:

1. For a trial constant velocity assigned to the nth layer, perform normal-incidence traveltime inversion to convert the time horizon corresponding to the base-layer boundary to a trial depth horizon.
2. Given the geometry of the CMP gather at the analysis location (not the CMP gather itself, but only the source-receiver geometry associated with it), compute the CMP traveltimes. The modeled CMP traveltime trajectory that corresponds to the base of the layer under consideration is in general nonhyperbolic, because the ray tracing used to compute the CMP traveltimes accounts for ray bending at layer boundaries and incorporates vertical velocity gradients within layers above.
3. Compute the best-fit hyperbolic traveltime trajectory, and thus determine the modeled stacking velocity for the trial interval velocity.
4. Measure the discrepancy between the modeled and the actual stacking velocities by way of semblance.
5. Repeat all the steps above for a range of constant velocities.
6. Pick the constant trial velocity as the layer velocity for which the difference between the modeled and the actual stacking velocities is minimum or the semblance is maximum.

Following the steps described above, perform stacking velocity inversion to obtain the layer-velocity semblance spectra shown in Figure 9.2-5. Note that velocity estimates down to Horizon 3 are fairly accurate. The estimates for Horizons 4 and 5 show some departure from the true velocity but are largely acceptable. Note the variations in the estimate for Horizon 6 — the method is attempting to distinguish the units within the deltaic sequence with different velocities. The velocity estimate for Horizon 7a has significant departures from the true velocity of 3500 m/s. Finally, the method has failed to estimate the internal velocity variations within the deep sequence, correctly.