3-D coherency inversion
Perform 3-D coherency inversion to estimate velocity nodes for the layer under consideration. Accompanying the velocity-depth model (Figure 10.6-4), use the time horizon (Figure 10.6-3) associated with the layer boundary picked from the 3-D unmigrated CMP-stacked data volume (Figure 10.6-2) and CMP gathers at analysis locations (Figure 10.6-5). Three-dimensional coherency inversion involves the same steps as for 2-D coherency inversion (models with horizontal layers), except for 3-D ray tracing. For a range of trial constant velocities for the half-space defined by the unknown part of the velocity-depth model, follow the steps below:
- Perform 3-D normal-incidence traveltime inversion of the time horizon associated with the layer boundary (Figure 10.6-3) under consideration using the trial constant velocity assigned to the layer above.
- Compute 3-D CMP traveltimes using the known overburden 3-D velocity-depth model.
- Measure the discrepancy between the modeled and actual CMP traveltimes by way of semblance.
- Assign the trial constant velocity that yields the maximum semblance as the velocity of the layer above.
For each layer, velocity estimation using 3-D coherency inversion is done at grid locations 1 km apart in the inline and crossline directions. The panels in Figure 10.6-5 show the CMP gathers at six analysis locations and the semblance curves derived from coherency inversion. The modeled traveltime trajectories associated with the selected velocities that correspond to semblance maxima are plotted on the CMP gathers. For a given CMP location, note from Figure 10.6-6 that the center data window exhibits a flat event coincident with the velocity selection made in Figure 10.6-5.
Vertical velocity gradients, which were available from sonic logs, were accounted for in the ray tracing to model the CMP traveltimes that are required in coherency inversion (models with horizontal layers). Additionally, we want to use available sonic logs to guide coherency inversion and choose an optimum range of constant velocities in computing semblances. As a reminder, coherency inversion also honors ray bending at layer boundaries (models with horizontal layers). Nevertheless, application of coherency inversion should be confined to parts of a subsurface velocity-depth model where no severe raypath distortions may occur (model building).
We circumvent picking of prestack reflection travel-times in coherency inversion by measuring the discrepancy between modeled and actual traveltimes based on semblance. Although picking of time horizons is done from the 3-D DMO-stacked volume of data, note that the common-cell gathers used in the analysis are not processed for dip-moveout (DMO) correction. This is because we model 3-D prestack traveltimes from source locations at the surface to the actual reflection points along each layer boundary and back to receiver locations at the surface associated with traces in a CMP gather.
Figure 10.6-5 Coherency inversion at six analysis locations. Top and bottom frames in each panel show the semblance curves and the CMP gathers, respectively. See text for details.
Figure 10.6-6 Data windows along the modeled traveltime trajectories used in coherency inversion. The semblance curves are shown in Figure 10.6-5. See text for details.
Figure 10.6-7 Velocity field created from the velocity nodes denoted by the green squares which were derived from coherency inversion applied to a layer within the overburden.
Results of coherency inversion are used to pick velocities at analysis locations. In a 3-D structural inversion project, quality control of the velocity nodes at analysis locations is imperative for deriving a spatially consistent layer velocity field. We select the layer velocity at a given location based on a combination of the following factors to make sure that the estimated velocities are geologically plausable:
- The maximum of the semblance curve derived from coherency inversion as a function of trial constant velocity (Figure 10.6-5),
- the flatness of the event in the data windows along the modeled traveltime trajectories (Figure 10.6-6),
- the fit of the modeled traveltime trajectory over-layed on top of the actual event on the common-cell gather (Figure 10.6-5),
- the lack of anomolous behavior in the raypath associated with the modeled traveltime trajectory, and
- the magnitude of the velocity node with respect to the neighboring velocity nodes.
We create the velocity field for the half-space by spatial interpolation between the nodes (Figure 10.6-7). This is followed by the application of some smoothing to the velocity field.
We then create a gridded velocity-depth model that includes the known and unknown part of the model. Gridded velocity fields are desirable for doing 3-D poststack depth migration based on finite-difference schemes. Gridding recognizes layer boundaries and vertical velocity gradients.
- 3-D structural inversion applied to seismic data from the Southern North Sea
- Estimation of the overburden model
- Model representation by tessellation
- 3-D poststack depth migration
- Estimation of the substratum model