List of Figures

1. Division of energy from an incident P-wave. The transmitted arrivals are extant in the receiver well, no reflections can be recorded.
2. Comparison of (a) PP reflection migration isochrons and (b) PS converted-wave isochrons in seconds. The PP isochrons form ellipses with the source and receiver as foci, while the PS converted-wave isochrons form oblate ellipsoid (egg shaped) isochrons. The tangents to the dashed portions of the isochrons denote the interfaces that can give rise to transmitted PS arrivals; solid lines indicate those for reflected waves. A transmission ray is shown in green and reflections in red.
3. (a) Homogeneous velocity model with source-receiver spacing of 1000 m and a depth of 200 m. The depth of reflectors (1) and (2) is 759 m and 1066 m, respectively. (b) Isochrons are governed by $\tau _{sr}^{P} + \tau _{rg}^{P}$. The direct wave (D) migrates to the line connecting the source and receiver. (c) Migration isochrons for (a) by the traces have been shifted by 0.2 s prior to migration. (d) Same as for (c) but reduced-time migration was used.
4. Comparison of the effect of velocity errors on conventional migration and reduced-time migration. (a) Identical to Figure 2.3a. (b) Migration isochrons for the true velocity model. (c) Conventional PP migration isochrons for the 110% velocity model. (d) Reduced-time PP migration isochrons for the 110% velocity model. Note, migration velocity errors introduce isochron distortions that are similar to those due to static shifts in the previous figure.
5. Vertical boundary model used to generate synthetic crosswell and RVSP data. Density is constant for the entire 100 m$^2$ model and a 1500 Hz Z-component source was used. Sources for both crosswell and RVSP simulations are on the left at one meter intervals (101 total). Receivers (101) at one meter intervals are distributed along the right for the crosswell simulation, and across the top for the RVSP simulation.
6. Synthetic RVSP seismogram for a source at 100 m depth. The source frequency is 1500 Hz, receiver spacing is 1 m, and the total record length is 0.06 seconds.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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.
12. 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.
13. Migration images for reflected PP events in the RVSP experiment.
14. 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.
15. (a) Salt diapir model used to generate synthetic seismograms. Figures (b), (c), and (d) show wavefield snapshots at 0.4 s, 0.7 s, and 0.8 s, respectively. (e) The unprocessed CSG is migrated with PS transmission migration. (f) Only transmitted PS events from the right salt flank are migrated.
16. Synthetic seismograms generated from the salt diapir model in the previous figure.
17. Kidd Creek P-wave velocity model assuming a 3.5 ms time delay. The inversion data residual is 0.086 ms. The source- (right) and receiver-well (left) locations are indicated by the solid black lines. The dashed lines represent the boundaries of the ore body as inferred from well information.
18. Common receiver gather for a receiver at a depth of 20 m. The gather has been bandpass filtered between 1000 and 6000 Hz.
19. The gather in the previous figure has been flattened to the direct P-wave traveltime and median filtered, and the direct S-wave and later events have been muted.
20. (a) Result from migrating the SP transmission events from the bottom of the ore body. Eight CRG's were migrated and stacked to produce this image; each CRG contained 140 traces. (a) Conventional SP transmission migration image. (b) The same data for (a) were migrated with reduced-time migration. (c) Result from migrating the PP reflection events from the top of the ore body with a convention migration algorithm. Seven CRG's were migrated and stacked to produce this image. (d) The same data for (c) were migrated with the reduced-time migration equation for PP reflections.
21. Offshore VSP acquisition geometry. The top image shows a plan view of the relative location of the sources to the well head, denoted by $\otimes$. Since the source was on a ship there is some scatter in each offset's source location. The bottom two figures show the relative location of the receiver array to the source position for the different offsets.
22. Shot gather for a source at 152 m with the Z-component at the top and the X-component at the bottom. The Y-component is not shown.
23. Top shows P-wave migration velocity model (left) and a velocity profile (right), bottom shows similar figures for the S-wave migration velocity model. The solid lines of the velocity profiles indicate the actual velocity distribution with depth and the dashed lines represent the smoothed velocity function used for migration.
24. A comparison of before and after reorientation of the seismograms in the XY-plane. The 3-component geophones were rotated until the energy in a small window surrounding the direct P-wave was maximized.
25. The rotation angle used to reorient the X- and Y-components (top). An X- and Z- rotation was also performed (bottom). After rotation the continuity of events was improved and transverse waves were largely removed from the Z-component.
26. Compare with Figure 4.6. Desired events were picked, flattened, median filtered, unflattened, and bandpass filtered to produce these gathers. FK filtering could not be used because single events have a large range of velocities some of the S-wave are aliased.
27. Migration of the gather shown at the top of Figure 4.10, the reflected P-waves. A synthetic zero-offset reflection section calculated solely from borehole velocities is shown on the left. There is good correlation with the base of salt and the strong event in the migrated gather.
28. Migration of the reflected PS transmitted wave gather shown at the bottom of Figure 4.10. There are strong events at both the base and top of the salt sheet.
29. Migration of transmitted PS arrivals (right). The traces of the synthetic depth section have been rotated 180 degrees from the previous two figures to emphasize the top of the salt boundary. Notice the excellent correlation between the top of salt in the synthetic and migrated traces. The dip of the lower events may be due to anisotropy because corresponding events in Figure 4.12 (right) are flat.
30. Migration of reflected P-waves from a source position of 610 m. The active receivers range from depths of 3049 to 4482 m.
31. Migration image of reflected PS waves for a source at 610 m offset.
32. Migration of transmitted PS waves. Notice that there are migrated events above to uppermost receiver (3049 m). The dipping events in this gather may be due to shear-wave anisotropy within the salt.
33. Comparison of wavepath and Kirchhoff migration for transmitted PS arrivals. The wavepath image contains much less noise and is richer in high wavenumber energy.