Estimation of the substratum model

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Seismic Data Analysis
Series Investigations in Geophysics
Author Öz Yilmaz
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store

Subsalt imaging in the North Sea

We now want to estimate a velocity field for the substratum region — Zechstein and the underlying strata. Again, consider the velocity-depth model in two parts — the overburden, the known part, and the substratum, the unknown part, which is defined as a half-space.

  1. Shown in Figure 10.1-4 are four different velocity-depth models with the same overburden but different constant velocities assigned to the substratum. These constant velocities span the range that correspond to the velocity variations within Zechstein. The anhydrite-dolomite rafts (5900 m/s) floating within the halite formation (4400 m/s) have little thickness (less than 100 m), but can influence the velocity of the Zechstein unit as a whole depending on the spatial distribution of the rafts.
  2. Perform prestack depth migration using the four earth models in Figure 10.1-4, and generate a set of image gathers along the line (Figures 10.1-5 and 10.1-6). Examine the image gathers from the four velocity panels at the same location and note that they all represent the same image associated with the overburden down to a depth that corresponds the the top-salt boundary. Nevertheless, the event associated with the base Zechstein exhibits different moveout characteristics depending on the half-space velocity. For instance, at midpoint location 321, flatness for the base-Zechstein event at a depth of 3500 m is achieved with the 4700-m/s substratum velocity (event A in Figure 10.1-5). Similarly, at midpoint location 1681, flatness for the base-Zechstein event at a depth of 3950 m is achieved, again, with the 4700-m/s substratum velocity (event B in Figure 10.1-6). In principle, one may be able to determine velocity nodes from these image gathers based on the flatness of the event that corresponds to the base-Zechstein boundary. It is not just flatness, but event strength and continuity across the offset axis of the image gather, that we take into consideration when picking velocity nodes. If the event is weak, it could mean that the velocity assigned to the layer above is erroneously too low or too high, causing migration errors. To gain confidence in the velocity determination, the image gathers are used in combination with the image-gather stacks as in the next step.
  3. Stack the image gathers as from step (b) to generate the depth images (Figures 10.1-7 and 10.1-8) associated with the earth models in Figure 10.1-4. The stack power associated with the base-Zechstein event can be used as an additional criterion in combination with the flatness criterion for image gathers (Figures 10.1-5 and 10.1-6) to derive the velocity profile for the Zechstein formation.
  4. Assign the velocity field for the substratum derived from step (c) to the half-space below the overburden. Then, combine this velocity field for the half-space with the overburden model to construct a new velocity-depth model.
  5. Next, perform prestack depth migration using the new velocity-depth model from step (d).
  6. Interpret the depth image from step (e) to delineate the base-Zechstein horizon. Subsequently incorporate this horizon into the velocity depth-model, and assign a velocity of 5400 m/s to the subsalt region based on well data to construct a final velocity-depth model (Figure 10.1-9).
  7. Perform prestack depth migration once more using the final velocity-depth model from step (f) to obtain the image gathers and their stacks which represent the final image in depth.
  8. Convert the depth-migrated sections from depth to time using the final velocity-depth model from step (f) to apply poststack spiking deconvolution, band-pass filtering and AGC scaling. Finally, convert the sections back to depth. It usually helps improve the vertical resolution of depth-migrated data to apply poststack deconvolution. This also is needed for a fair comparison of images from prestack depth migration and poststack depth migration, since the latter normally would be performed using stack with poststack processing applied.

Selected image gathers and the depth images using the final velocity-depth model (Figure 10.1-9) from the two segments of the line are shown in Figures 10.1-10 and 10.1-11. Compare the depth image obtained from prestack depth migration with the images obtained from poststack depth and time migrations (Figures 10.1-12 and 10.1-13). We should not expect significant differences between the three images within the overburden region where time migration often yields acceptable results. Note, however, the differences in the substratum region. Specifically, the base-Zechstein horizon (event A in Figure 10.1-10b and events E and F in Figure 10.1-11b) cannot be delineated from poststack depth migration, nor can it be delineated accurately from poststack time migration (events G and H in Figure 10.1-12b, and event K in Figure 10.1-13). The anhydrite-dolomite rafts (such as event D in Figure 10.1-11b) and the 3-D behavior of the diapiric structure limit the accuracy of the final image obtained from prestack depth migration. Specifically, note the poor image of the base Zechstein represented by events B and C in Figure 10.1-10b.

Image rays associated with the base-Zechstein boundary (Figure 10.1-14), however, clearly indicate the need for prestack depth migration for accurate imaging of the substratum region. Note the significant lateral shifts on the image rays, especially beneath the salt diapirs — demonstrative evidence of the presence of strong lateral velocity variations associated with a complex overburden.

3-D structural inversion applied to seismic data from the Southern North Sea

After the completion of model estimation for the overburden and before moving down to the substratum region, the overburden model must be verified. Model verification usually is done by examining selected image gathers from prestack depth migration along selected crosslines. If the overburden model is correct, events from the overburden on image gathers should exhibit a flat character with negligible moveout. If the residual moveout is significant, then it must be corrected for by residual moveout analysis (model updating), and the overburden model must be updated prior to estimating the substratum model.

To estimate the substratum model, we perform a series of 3-D prestack depth migrations using velocity-depth models that have the same overburden but different constant velocities assigned to the half-space that includes Zechstein and the underlying strata. We examine the image gathers (Figure 10.6-14) to derive velocity nodes for the substratum. As shown in the close-up display in Figure 10.6-15, image gathers associated with different half-space velocities differ only at and below the base Zechstein (shown by the arrow) since they all have been derived using the same overburden velocity-depth model. The event associated with the base Zechstein exhibits a different moveout character from one half-space velocity to another. Based on the flatness criterion (Figure 10.6-15) and the behavior of the geometry of base-Zechstein that can be traced from the image-gather stacks (Figure 10.6-16), we determine velocity nodes at selected locations for the Zechstein formation.

We expect some spatial variation in Zechstein velocities because of the effect of the high-velocity anhydrite-dolomite rafts within the halite unit. By spatial interpolation between the nodes, we create a velocity field for the half-space defined by the substratum region of the model (Figure 10.6-17). We then combine the overburden and the substratum regions of the velocity-depth model. Figure 10.6-18 shows cross-sections of the complete 3-D velocity-depth model along selected crosslines. Finally, we perform 3-D prestack depth migration using this velocity-depth model to obtain crosssections of the depth image along selected crosslines (Figure 10.6-19).

The algorithm for prestack depth migration used in the present case study is based on the Kirchhoff summation (3-D prestack depth migration). Output can be a subsurface image in depth along an arbitrary traverse, inlines and crosslines, or within a specified volume. Also, the output can be image gathers at specified locations for updating layer velocities. The algorithm involves computing traveltimes and summation of amplitudes as implied by the Kirchhoff integral. Traveltimes for all shot and receiver locations at the surface and reflection points in the subsurface are computed by efficient ray tracing. Ray bending at layer boundaries with velocity contrast is honored in computing traveltimes. Migrated data are obtained by summation along maximum-amplitude traveltime trajectories. Prior to summation, data are treated for operator antialiasing (3-D prestack depth migration).

Figure 10.6-20 shows selected image gathers along the crosslines shown in Figure 10.6-19. Except for some events on a few of the image gathers, events exhibit a flat character, which indicates that the earth model (Figure 10.6-18) and the earth image (Figure 10.6-19) are fairly accurate. The base-Zechstein event (denoted by the arrow in Figure 10.6-19) exhibits an improved continuity below the complex zone associated with the salt diapir in the center as compared to the image from 3-D poststack depth migration (Figure 10.6-21).

Note that the structural interpretation of the overburden from the images obtained by 3-D post- and prestack depth migrations should not be different. It is the substratum region where 3-D prestack depth migration would yield an improved image. The differences in amplitude characteristics and the bandwidth between the images from 3-D post- and prestack depth migrations are due to the use of different algorithms. The algorithm for 3-D poststack depth migration is based on an explicit finite-difference scheme, whereas the algorithm for 3-D prestack depth migration is based on the Kirchhoff summation. Although not done in the present case, results of prestack depth migration should be treated with a signal processing sequence commonly applied to stacked data in the time domain, such as poststack deconvolution and frequency filtering.

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Estimation of the substratum model
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