# 3-D migration velocity analysis

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

Earlier in this section we learned that a workflow based on 3-D DMO correction combined with 3-D common-offset migration can include a step for estimating a 3-D rms velocity field from the migrated prestack data. Now, we shall develop an alternative workflow for 3-D migration velocity analysis based on a 3-D extension of the velocity-independent imaging technique by Fowler  described in migration velocity analysis.

1. Start with 3-D prestack data P(x, y, h, t) in coordinates of inline x, offset 2h, crossline y, and event time t in the unmigrated position, and apply NMO correction, 3-D DMO correction followed by inverse NMO correction.
2. Create a constant-velocity stack (CVS) volume P(x, y, t0; vDMO) using a constant velocity vDMO, where t0 is the zero-offset event time after 3-D DMO correction. Shown in Figure 7.4-35 is a CVS volume created by using a velocity of 2400 m/s. The prestack data are from the same survey as that of the data shown in Figure 7.4-33.
3. Migrate the constant-velocity stack (CVS) volume P(x, y, t0; vDMO) to create a constant-velocity migration (CVM) volume P(x, y, τ; vmig), where τ is the event time after migration, using the constant velocity associated with the CVS volume itself and a 3-D constant-velocity Stolt algorithm (Section G.4). Shown in Figure 7.4-36 is the CVM volume associated with the CVS volume of Figure 7.4-35 with a velocity of 2400 m/s.
4. Repeat steps (b) and (c) for a range of constant velocities. In the present example, a total of 50 CVS volumes and corresponding 50 CVM volumes were created using a velocity range of 1200-3650 m/s with an increment of 50 m/s.
5. Extract the time slices from the CVM volumes for a specified time τj and combine them to form a velocity cube P(x, y, vmig; τj). Figure 7.4-37a shows such a velocity cube for a time of 2000 ms. Repeat for a set of N times τj, j = 1, 2, …, N. In the present example, a total of 26 velocity cubes were created for times from 600 to 3100 ms with an increment of 100 ms.
6. For 3-D visualization and interpretation, form a super volume that is a composite of the 26 velocity cubes from step (e) placed one on top of the other (Figure 7.4-38).
7. Based on the maximum-event-amplitude picking strategy described in migration velocity analysis, interpret each of the velocity cubes and create velocity strands associated with the constant times τj, j = 1, 2, …, N, along selected crossline (or inline) traverses (Figure 7.4-37b).
8. Combine the velocity strands for a specific time τj and create an rms velocity map associated with that time. Repeat for all times τj, j = 1, 2, …, N, and obtain a set of rms velocity maps (Figure 7.4-39).
9. Create a 3-D rms velocity field using the rms velocity maps from step (h). Figures 7.4-40 and 7.4-41 show selected inline and crossline sections from the rms velocity volume. Compare with the corresponding image sections from time migration shown in Figure 7.4-34, and note that the 3-D rms velocity field honors the structural characteristics of the subsurface. Specifically, the inline sections in Figure 7.4-40 manifest the basin boundary indicated by the change in color from green (the basin interior) to orange-red. The crossline sections in Figure 7.4-41 manifest the presence of young sediments with low velocities (the shallow purple zone) and older sediments with relatively higher velocities (the green) disrupted by an erosional channel between 1-2 s (the dark green).

The 3-D rms velocity field derived from the workflow outlined above is associated with events in their migrated positions. Compared to the 3-D DMO velocity field associated with events in their yet unmigrated positions, it is the preferred velocity field with which you would want to migrate your data using a desired 3-D post- or prestack time migration algorithm (Appendix G). If you wish to extend your analysis from time to depth domain, the 3-D rms velocity field associated with time-migrated data also is the preferred velocity field to derive a 3-D interval velocity field that can then be used to obtain an image in depth (3-D structural inversion applied to seismic data from the Northeast China).