3-D poststack depth migration

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

Earth imaging in depth

The fundamentals of 3-D migration are discussed in 3-D poststack migration and its mathematical aspects are provided in Appendix G. By now, we should be familiar with one-pass and two-pass, implicit and explicit 3-D time migration algorithms. In this section, we shall examine aspects of 3-D poststack migration within the context of imaging beneath complex structures: (a) 3-D poststack time versus depth migration, (b) one-pass versus two-pass 3-D poststack depth migration, and (c) implicit versus explicit 3-D poststack depth migration. In the next section, we shall extend the analysis to 3-D depth migration of prestack data.

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

By using the gridded velocity field, we perform 3-D poststack depth migration down to a depth just below the current layer under consideration (Figure 10.6-8). The algorithm used in the present case for 3-D poststack depth migration is based on a frequency-space explicit scheme and the McClellan transform for designing a 3-D extrapolation operator (3-D poststack migration). It can handle arbitrary vertical and lateral velocity variations and is accurate for dips up to 80 degrees. A 2-D stable explicit operator is converted into a 3-D operator by applying the McClellan transform coefficients. For each frequency component and a given velocity ratio, the explicit operator is stored in a table and fetched as needed at each step of downward continuation. The McClellan transform coefficients are optimized to attain a near-perfect circular symmetry for the impulse response of the 3-D operator. This means that the algorithm, unlike the conventional one-pass 3-D poststack migration algorithms (3-D poststack migration) based on the splitting of the 3-D operator into inline and crossline components, does not cause azimuthal positioning errors.

The image volume derived from 3-D poststack depth migration is used in an interpretation session to incorporate the layer under consideration into the earth model.

  1. We interpret the base of the layer under consideration — the Cretaceous chalk, to delineate the reflector geometry in depth (Figure 10.6-8). Interpretation of the depth horizon is done on crosslines from the 3-D volume of poststack depth-migrated data at every tenth line.
  2. By using the interpretation results from the crosslines, horizon strands are created (Figure 10.6-9a). These strands then are spatially interpolated to create the surface that represents the reflector geometry associated with the base of the layer (Figure 10.6-9b). A way to represent the surface in the computer is by a set of triangles, the size and shape of which vary depending on the complexity of the reflector geometry (Figure 10.6-9c). The reflector geometry is taken into account during ray tracing used in coherency inversion to honor ray bending at layer boundaries, and in 3-D poststack depth migration to account for lateral velocity variations.
  3. Finally, the base Cretaceous chalk surface is added to the model (Figure 10.6-10), and the procedure that includes 3-D coherency inversion and 3-D poststack depth migration is repeated for the next layer within the overburden.

Figure 10.6-11 shows a cross-section of the 3-D velocity field in the crossline direction at each iteration of the procedure described above. Starting from the top, note how the velocity field is updated as the velocity estimate for the next layer is included in the model. The horizons indicated in Figure 10.6-11 correspond to base Tertiary (TH2), Cretaceous chalk (TH3), and Upper Triassic (TH4).

Figure 10.6-12 shows selected crosslines from 3-D poststack depth migrated volumes of data after each iteration. The reflector geometries associated with the layer boundaries included in the overburden model are delineated from such cross-sections — base Lower Tertiary (TH2) from Figure 10.6-12a, base Cretaceous chalk (TH3) from Figure 10.6-12b, base Upper Triassic (TH4) from Figure 10.6-12c, and base Lower Triassic (TH5) from Figure 10.6-12d.

Figure 10.6-13 shows the results of earth modeling using the procedure described above. The left column shows the map view of the layer velocities and the right column shows the perspective view of the base-layer boundaries. Starting from the top, we see layer velocities and reflector geometries for Lower Tertiary, Cretaceous chalk, Upper and Lower Triassic. Note the collapsed zone (A) on the base-Tertiary surface and the auxiliary structural feature (B) that is oblique to the axis of the collapsed zone. The latter becomes more prominent on the surface associated with the base-Cretaceous chalk (C). The ridge of the salt diapiric structure (D) and the collapsed zone (E) to the left of the salt diapir are evident on the surface associated with the base-Upper Triassic. Finally, note that the base-Lower Triassic (equivalent to the top Zechstein) is represented by a multisegmented surface. This is because the Lower Triassic section is missing in the collapsed zone (E) to the left of the salt diapir.

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