# Interval velocity maps

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

The Dix equation (1), which relates rms velocities to interval velocities, is used to derive interval velocity maps. RMS velocities, in principle, are most appropriately estimated from prestack time-migrated data (3-D prestack time migration). Recall from normal moveout that the type of velocity that can be most reliably estimated from CMP data is the velocity used to apply normal-moveout correction. To stack the data we also substitute NMO velocities for stacking velocities. The use of NMO velocities as stacking velocities is based on the small-spread hyperbola assumption. To further substitute stacking velocities for rms velocities is only allowed if the CMP data are associated with horizontally layered earth. To justify the use of stacking velocities as rms velocities, we first need to correct for the dip effect on stacking velocities by way of dip-moveout (DMO) correction (principles of dip-moveout correction). In the case of a 3-D survey, we also need to correct for the source-receiver azimuthal effects on stacking velocities by way of 3-D DMO correction (processing of 3-D seismic data). This means that it is the stacking velocity field derived from 3-D DMO-corrected data that should be considered as a plausable substitute for the rms velocity field. But then the DMO velocities are associated with CMP gathers in their unmigrated positions. Strictly, we need the moveout velocities not only corrected for dip and azimuth effects but also estimated from gathers in their migrated positions. This is because the rms velocities used in Dix equation (1) are defined for a horizontally layered earth model (Section J.4). Thus the desired strategy is that velocities derived from 3-D prestack time migration should be substituted for rms velocities.

 ${\displaystyle v_{n}={\sqrt {\frac {V_{n}^{2}\tau _{n}-V_{n-1}^{2}\tau _{n-1}}{\tau _{n}-\tau _{n-1}}}},}$ (1)

Although prestack time migration velocities are most desired to substitute for rms velocities, the interpreter may be compelled to use whatever velocity functions that may be available. These may have been derived from velocity analysis applied to DMO-corrected data or even, although hardly desirable, to CMP data without DMO correction. Under those circumstances, the velocity functions picked at analysis locations need to be edited for any dip effect by either eliminating the suspect functions altogether or by smoothing.

Whatever the source of information, the interpreter starts with a set of velocity functions, each made up of a set of time-velocity pairs and associated with analysis locations over the survey area. The analysis grid typically varies from 500 × 500 m to 2 × 2 km; hence, there may be as many as 400 velocity functions per 100 km-squared of the survey area. The gridded time horizons are intersected with the velocity functions and, for each horizon, velocity nodes are extracted from the velocity functions coincident with the horizon times at the locations of the velocity functions themselves. These velocity nodes are then used as control points input to a gridding algorithm to create horizon-consistent rms velocity maps (Figure 9.4-6). There may be a need for further editing and smoothing of the rms velocity grids.

Finally, the horizon-consistent rms velocity values and the horizon times at each grid point are used in Dix equation (1) to compute the interval velocity values, which are then used to create the horizon-consistent interval velocity maps (Figure 9.4-7). Once again, there may be further need for editing and smoothing of the interval velocity maps to remove any geologically implausible velocity variations.