List of Figures

1. Schematic plot of the quadratic line search method.
2. The HESS VTI model: (a) the P-velocity model, (b) the delta-parameter, and (c) the epsilon-parameter models.
3. The smoothed HESS P-velocity model (a) and (b) the corresponding slowness perturbation distribution relative to the original slowness model.
4. The migration images obtained with (a) conventional RTM, (b) LSRTM with one supergather and 30 iterations, (c) LSRTM with four supergathers and 30 iterations, and (d) LSRTM with eight supergather and 30 iterations.
5. The convergence curves for (a) LSRTM with 300 shots conventional source data; and (b) LSRTM with a supergather of 300 shots. The data residuals are normalized by the initial value.
6. The first iteration results of (a) conventional RTM, (b) LSRTM with one supergather. The images in Figures (a) and (b) have been high-pass filtered. Figure (c) shows the difference between (a) and (b) before filtering.
7. The measured SNR (solid line with squares) as a function of the number of iterations compared to the prediction (dashed line).
8. The LSRTM image obtained with the quasi-linear inversion scheme using one supergather (30 iterations).
9. The convergence curves for quasi-linear and linear inversions. The Red line with stars indicates the convergence for the quasi-linear approach and the blue line (squares) for the linear approach.
10. A smoothed P-velocity model generated by triangle smoothing (a) and (b) the corresponding slowness perturbation relative to the original slowness model.
11. The images obtained with the smooth velocity model in Figure 6 with (a) the conventional RTM, (b) LSRTM with one supergather and 30 iterations, (c) LSRTM with four supergathers and 30 iterations, and (d) LSRTM with eight supergather and 30 iterations.
12. The 3D SEG/EAGE salt model for (a) a vertical slice along x=6.8 km and (b) a horizontal slice at 0.8 km depth.
13. The smoothed 3D SEG/EAGE salt model for (a) a vertical slice along x=6.8 km and (b) a horizontal slice at 0.8 km depth.
14. The conventional RTM images for 400 evenly distributed shots : (a) a vertical slice along x=6.8 km and (b) a horizontal slice at 0.8 km depth.
15. The multisource LSRTM images for 16 supergathers with 25 shots each after 10 quasi-linear iterations: (a) a vertical slice along x=6.8 km and (b) a horizontal slice at 0.8 km depth.
16. The conventional RTM images for 100 evenly distributed shots : (a) a vertical slice along x=6.8 km and (b) a horizontal slice at 0.8 km depth. Note the streaks along X direction in the horizontal slices.
17. The multisource LSRTM images for 10 supergathers with 10 shots each after 10 quasi-linear iterations: (a) a vertical slice along x=6.8 km and (b) a horizontal slice at 0.8 km depth. Note the streaks in the conventional RTM image is removed.
18. The Marmousi2 model: (a) the modified Marmousi2 velocity model and (b) the smooth migration velocity.
19. A 20 Hz Ricker wavelet (a) and its associated frequency spectrum.
20. Harmonic simulation for a 25-Hz source at $x=4km$ and recorded at $x=6km$ (a). Panel (b) plots the frequency spectrums of the first 8 secs (black) and second 8 secs (red) and panel (c) shows the zoom view of the part between 20-30 Hz.
21. Comparison of recorded traces with different simulation method. The black line indicates the recorded trace from time-domain simulation with a broadband wavelet; the red line is the stack of 400 harmonic traces (0-8 secs) and blue line (8-16 secs).
22. Ray diagrams for the reflections for the ocean bottom and the deepest reflector. The difference in arrival times of these two phases is used to estimate the necessary frequency sampling rate.
23. The true reflectivity of the Marmousi2 Model.
24. A common shot gather with shot location at 3 km offset.
25. Migration images obtained by (a) the conventional shot-domain RTM method and (b) the iterative stacking method.
26. The frequency-selection LSRTM image after (a) 1 iteration, (b) 20 iterations, and (c) 80 iterations.
27. Zoom view comparison of (a) shot-domain RTM image and (b) frequency-selection LSRTM image for the shallow part.
28. Zoom view comparison of (a) shot-domain RTM image and (b) frequency-selection LSRTM image for the deep part.
29. The migration velocity model for the field data.
30. A common shot gather with shot location at 11.3 km offset after preprocessing.
31. The migration images obtained with (a) the conventional RTM method and (b) the frequency-selection LSRTM method. Red and blue boxes indicate the area for zoom views.
32. Zoom view of the red box for (a) the conventional RTM image and (b) the frequency-selection LSRTM image.
33. Zoom view of the blue box for (a) the conventional RTM image and (b) the frequency-selection LSRTM image.
34. The steps for creating super-virtual diffraction arrivals. (a) Correlation of the recorded trace at with that at for a source at to give the correlated trace with the virtual diffraction having traveltime denoted by $\tau _{A'B}-\tau _{A'A}$ . This arrival time will be the same for all source positions $x$ , so stacking will enhance the SNR of the virtual diffraction by $\sqrt {N}$ . (b) Similar to that in (a) except the virtual diffraction traces are convolved with the actual diffraction traces and stacked for different geophone positions $x'$ to give the (c) super-virtual trace with an enhanced SNR. Here, $N$ denotes the number of coincident source and receiver positions.
35. (a) Geometry for computing virtual Green's functions $G({\bf B}\vert{\bf A})$ from the recorded data $G({\bf A}\vert{\bf x})$ and $G({\bf B}\vert{\bf x})$ using the reciprocity theorem of correlation type in an arbitrary acoustic medium of constant density. (b) Geometry for computing super-virtual Green's functions $G({\bf B}\vert{\bf A})^{super}$ from the recorded data $G({\bf A}\vert{\bf x'})$ and the virtual data $G({\bf B}\vert{\bf x'})^{virt.}$ using the reciprocity theorem of convolution type.
36. Part of the BP2004 velocity model with three diffractors below the salt body.
37. Synthetic data results for part of the BP2004 model. (a) A common shot gather with a source at offset 6 km. Red lines indicate the time window and the moveout of the diffraction event. (b) The diffraction event within a small time window. (c) The result after median filtering and (d) after processing the median filtered data to get the super-virtual diffraction.
38. Velocity model with a fault and two diffractors.
39. Synthetic data results for the fault model. (a) A common shot gather with a source at offset 36 m. Red lines indicate the time window of the diffraction event. (b) The diffraction event within a small time window. (c) The result after median filtering and (d) after processing the raw data to get the super-virtual diffraction.
40. The super-virtual diffraction. In this figure, the red line indicates the predicted diffraction arrival times and the blue line indicates the picked arrival times.
41. Friendswood cross-well data example. (a) A common shot gather with a source at depth of 36.6 m. Red lines indicate the time window and the moveout of the diffraction event. (b) The diffraction event within a small time window. (c) The result after median filtering and (d) the super-virtual diffraction.