Discussion and Conclusion

To improve the quality of RTM images and increase the computational efficiency, a least-squares reverse time migration algorithm combined with a blended source phase-encoding technique is proposed. The numerical examples show that both the quasi-linear and linear approaches of multisource LSRTM method can improve the image quality compared to the conventional RTM image.

For the 2D examples, the quality of the LSRTM images depends the accuracy of the migration velocity model and the number of sub-supergathers in the input file. The best image for the 2D HESS VTI model is obtained by migrating eight supergathers with 30 iterations, which shows balanced amplitudes, is almost free of migration artifacts and crosstalk noise, and demonstrates a speedup of 3.75 compared to conventional RTM. The computational speedup depends on the number shots encoded in one supergather, the number of encoded sub-supergathers, and the number of iterations needed for an image of acceptable quality. The numerical tests on the 2D HESS VTI model show a range of computational speedups from 3.75 to 30. For some data sets, it might be feasible to quickly compute a background migration image with a small number of iterations and use many more iterations to delineate a smaller target zone (Dong et al., 2009).

The 3D examples illustrate the advantages of least-squares migration: balancing the reflector amplitudes, improving the spatial resolution, and reducing migration artifacts. The empirical examples show that the multisource LSRTM can produce images of better quality with similar computation cost.

Similar to conventional reverse time migration, the proposed LSRTM is sensitive to the error in the migration velocity model. The numerical tests show that when the velocity model is not accurate enough, the convergence rate of the linearized inversion is slowed down and crosstalk reduction is lessened. The phase encoding scheme presented here is effective only for a fixed-spread geometry, and requires modification for a marine acquisition geometry, as demonstrated in another chapter. Future work will explore the use of preconditioning and regularization methods to accelerate the reduction of crosstalk noise to test the method on field data, and incorporate the updating of the migration velocity with iterations.

Figure 2.1: Schematic plot of the quadratic line search method.

Figure 2.2: The HESS VTI model: (a) the P-velocity model, (b) the delta-parameter, and (c) the epsilon-parameter models.

Figure 2.3: The smoothed HESS P-velocity model (a) and (b) the corresponding slowness perturbation distribution relative to the original slowness model.

Figure 2.4: 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.

Figure 2.5: 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.

Figure 2.6: 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.

Figure 2.7: The measured SNR (solid line with squares) as a function of the number of iterations compared to the prediction (dashed line).

Figure 2.8: The LSRTM image obtained with the quasi-linear inversion scheme using one supergather (30 iterations).

Figure 2.9: 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.

Figure 2.10: A smoothed P-velocity model generated by triangle smoothing (a) and (b) the corresponding slowness perturbation relative to the original slowness model.

Figure 2.11: 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.

Figure 2.12: 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.

Figure 2.13: 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.

Figure 2.14: 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.

Figure 2.15: 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.

Figure 2.16: 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.

Figure 2.17: 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.