Figure 4.1-1a shows a velocity-depth model that contains a dipping reflector segment CD buried in a homogeneous medium. Zero-offset modeling using normal-incidence rays yields the time section in Figure 4.1-1b. Although not shown in the figure, the time section also should include diffractions off the edges of the reflecting segment.
Migration moves event C′D′ on the time section to its true subsurface position CD, which is overlaid on the time section for comparison. The horizontal extent of the zone of interest is OA. If the line length were confined to OA during recording, then the time section would be blank. On the other hand, if the recording were confined to line segment AB, then event C′D′ would be absent from the migrated section. Although the target is confined to line segment OA, the time section must be recorded over a longer segment OB. The line length also must be long enough to include a significant part of the diffractions that may be present in the data. Additionally, the recording time must be long enough to include diffraction tails and all of the dipping events of interest. The spatial (in the horizontal direction) and the temporal (in the vertical direction) displacement of a point on a dipping event resulting from migration depends on medium velocity, depth, and dip of the event (Table 4-2). Thus, line length and line position on the surface must be chosen carefully based on the migration aperture needed to adequately image the target zone of interest.
|t (s)||v (m/s)||dx (m)||dt (s)||Δt/Δx (ms/trace)||Δτ/Δx (ms/trace)|
These considerations apply just as well to 3-D surveys. Figure 7.1-1 is a depth contour map of a fictitious structural high. The subsurface extent of the objective portion of the structure is indicated by the smaller rectangle. Using the principles discussed above and in migration principles (based on Figure 4.1-14), the actual survey size needed to define the objective area is outlined by the larger rectangle.
Note that the survey area does not have to be extended equally in all directions. The northern flank of the structure is the steepest part. Therefore, the survey area must be extended most in that direction. Extensions in other directions are determined accordingly. Another consideration in extending the survey area is the required additional length in profile to achieve full-fold coverage over the already extended survey area. A typical subsurface anomaly with a lateral extent of, say, 4 × 4 km may require a 3-D survey over an area as large as 10 × 10 km.
3-D prestack depth migration
Because of cost considerations in 3-D prestack depth migration, it is compelling to make a careful choice of aperture width in the inline and crossline directions. While an excessively large aperture unnecessarily increases run time, a small aperture can produce a poor image from 3-D prestack depth migration. Migration aperture in the Kirchhoff summation was discussed already in kirchhoff migration in practice. Recall that a small aperture causes destruction of steeply dipping events. Excessively small aperture width also organizes random noise, especially in the deeper part of the section, as horizontally dominant spurious events.
Figure 8.5-11 shows aperture tests for 3-D prestack depth migration. A small aperture in both inline and crossline directions causes poor imaging of the steeply dipping fault planes and the steep reflector that defines the base of the sedimentary basin. Note also the organizing effect of small aperture on random noise.
- Chun and Jacewitz, 1981, Chun, J.H. and Jacewitz, C., 1981, Fundamentals of frequency-domain migration: Geophysics, 46, 717–732.
- Spatial sampling
- Other considerations
- Marine acquisition geometry
- Cable feathering
- 3-D binning
- Crossline smearing
- Strike versus dip shooting
- Land acquisition geometry
- 3-D prestack depth migration
- Kirchhoff summation
- Calculation of traveltimes
- The eikonal equation
- Fermat’s principle
- Summation strategies
- Operator antialiasing
- 3-D common-offset depth migration