When there are dipping interfaces, the upcoming-wave profile needs to be migrated; that is, the energy must be mapped to the actual subsurface reflection points. This is true even for zero-offset VSP data. A ray-tracing procedure for reflector mapping is illustrated in Figure 11.4-4. Note that reflection points D, E, and F have different lateral displacements OA, OB, and OC, respectively, from borehole Oz (Figure 11.4-4a). However, upcoming wave energy from all three reflection points is recorded on the same VSP trace at the receiver location R. The reflection times RG, RH, and RK (Figure 11.4-4b) are associated with raypaths SDR, SER, and SFR, respectively. Mapping this energy to reflection points involves a coordinate transformation  . In this transformation, the amplitudes on a single VSP trace are mapped onto several traces on the x − t plane, where x is the lateral distance of reflection points from the borehole (Figure 11.4-4b). The event times RG, RH, and RK are mapped onto two-way vertical times AL, BM, and CN, respectively. These vertical times are associated with raypaths AD, BE, and CF in Figure 11.4-4a. The resulting (x, t) section consists of traces similar to the traces of a migrated zero-offset section. Hence, the described ray-tracing procedure often is called VSP-CDP transformation.
Figure 11.4-4 (a) Source-receiver geometry for offset VSP; (b) VSP-CDP transformation: Traveltimes RG, RH, and RK, associated with raypaths SDR, SER, and SFR are mapped to traveltimes AL, BM, and CN, associated with the two-way vertical raypaths 2AD, 2BE, and 2CF. Also note that the amplitudes on the VSP trace are positioned on traces after transformation with x-coordinate values the same as those of the reflection points OA, OB, and OC.
The VSP-CDP transform of the data in Figure 11.4-3d is shown in Figure 11.4-3e . Comparison with the migrated surface seismic section at the well location indicates a good correlation of events. The difference in frequency content is partly attributed to differences in processing these two sections and is partly attributed to less high-frequency attenuation effects because of the shorter traveltimes associated with VSP recording.
The VSP-CDP transformation requires knowledge of the velocity-depth model around the borehole, since we must determine the location of the reflection points in the subsurface to perform mapping. The velocity-depth model can be derived using an iterative approach . Starting with an initial velocity-depth model and the recording geometry for the VSP data, traveltimes for upcoming waves are computed. When these estimated traveltimes are compared with the observed traveltimes, discrepancies are noted and the velocity-depth model is modified accordingly. The process is repeated until a good match is attained between the estimated and observed traveltimes.
Finally, note that the VSP-CDP transform is not exactly a migration process. It handles neither diffractions nor curved interfaces. To handle these features, VSP data must be migrated . The VSP geometry is like the geometry of a common-shot gather, except the shot axis is perpendicular to the receiver axis. Migration of VSP data can be viewed as mapping amplitudes along semielliptical trajectories with their focal points being the source and receiver locations. Superposition of all these trajectories yields the migrated section. The aperture width for VSP data often is inadequate to obtain a migrated section without much smearing.
- Wyatt and Wyatt, 1981, Wyatt, K. and Wyatt, S.B., 1981, Determination of subsurface structural information using the vertical seismic profile: Presented at the 51st Ann. Internat. Mtg., Soc. Expl. Geophys.
- Cassell et al., 1984, Cassell, B., Alam, A., and Millahn, K., 1984, Model-based interactive VSP-CDP transformation: Presented at the 54th Ann. Internat. Soc. Expl. Geophys.
- Alam and Millahn, 1986, Alam, A. and Millahn, K., 1986, Interactive model-based VSP-CDP transform: Presented at the Symp. on Practical Aspects of Modeling in Exploration and Development, Kristiansand, Norway.
- Dillon and Thomson, 1983, Dillon, P. B. and Thomson, R. C., 1983, Image reconstruction for offset source VSP surveys: Presented at the 45th Ann. Eur. Assoc. Expl. Geophys. Mtg.