Migration Results

Prior to migration PS transmission events were isolated by muting all other arrivals. Using no restriction on incidence angles, Kirchhoff and wavepath PS migrations were applied to the PS events for both the true velocity (Figures 3.3a and 3.3c) and for a 90% velocity model (Figures 3.3b and 3.3d). The PS events are migrated to their actual position for the true velocity model and to an incorrect position for the 90% velocity model. Reduced-time migration was also applied to the transmission PS arrivals. Results for reduced-time PS migration are shown in Figure 3.4 where the location of the transmitting boundary for the 90% velocity model is much closer to the true boundary position. It is also evident that, as shown by Sun and Schuster (1999a; 1999b; 2000), wavepath migration reduces artifacts by migrating energy only to the Fresnel zone of the specular reflection point.

The results for synthetic RVSP data are similar to those for crosswell data. Figures 3.5 and 3.6 show the results for conventional and reduced-time migration of transmitted PS-waves. Figures 3.7 and 3.8 show the results for transmitted SP waves. In addition to transmitted events, reflected PP-waves were migrated by both Kirchhoff and wavepath techniques (Figure 3.9) and reduced time migration was used (Figure 3.10) to mitigate the incorrect migration velocity errors.

Note, much more of the boundary is imaged by migrating the SP waves than by migrating the PS-waves. This is because the velocity contrast for SP waves is greater than that for PS-waves, hence, the SP waves are refracted more to give a wider target illumination. Also note that the vertical boundary in the wavepath migration images, Figures 3.7d and 3.8d, lack continuity. The wavepath algorithm calculated an erroneous incidence angle from the incorrect migration velocity. Therefore the calculated Fresnel zone does not coincide with the actual focusing point. This was not a problem for the crosswell or RVSP PS migrations since the events were being migrated to a location much closer to the receivers, which rendered incidence angle errors less important.

Figure 3.3: Migration images for the crosswell experiment. The sources were on the left and the receivers on the right. The PS transmitted waves were isolated by muting. Images (a) and (c) use the true velocity model while (b) and (d) use a velocity 10% slower than the actual velocity model.

Figure 3.4: Similar to Figure 3.3 but reduced-time migration was used. Images (a) and (c) are identical to those in Figure 3.3. Notice how the migrated position of the boundary is much closer to the true positions in images (b) and (d) than for the standard migration images in Figure 3.3, validating the effectiveness of reduced-time migration.

Figure 3.5: Migration images for the RVSP experiment. The sources were on the left and the receivers were along the top, both emplaced at one meter intervals. Note that in (a) and (c) only a small portion of the vertical boundary is imaged due to the restricted RVSP geometry and refraction effects; Also wavepath migration has fewer artifacts than Kirchhoff migration.

Figure 3.6: Reduced-time migration images of PS-waves for the RVSP experiment. Notice that the transmitting boundaries in (b) and (d) for reduced-time migration are imaged much closer to their true positions than for (b) and (d) in Figure 3.5.

Figure 3.7: SP migration for the RVSP experiment. Note that much more of the transmitting boundary is imaged than with PS transmitted waves (Figure 3.5). Wavepath image (d) has poor quality since the 90% velocity model led to the erroneous calculation of incidence angles.

Figure 3.8: Similar to Figure 3.7 but reduced-time migration was used. The location of the boundary image is less sensitive to migration velocity errors in (b) than for (Figure 3.7). The wavepath image still suffers from the incorrect calculation of incidence angles.

Figure 3.9: Migration images for reflected PP events in the RVSP experiment.

Figure 3.10: Similar to Figure 3.9 but reduced-time migration was used. The incorrect velocity model has less of an effect on the boundary location in (b) than for Figure 3.9.