Sensitivity to Velocity Error

To test how the proposed method performs in the presence of migration velocity errors, the migration velocity model in Figure (b) is scaled by 0.95 to introduce a 5% velocity error, and the above 31 plane-wave gathers are migrated with the wrong velocity. If the inversion is computed by conventional LSM, the convergence stalls at high data residual (dashed line with stars in Figure ), but inverting prestack images separately (see equation ) provides a robust convergence (solid line with circles in Figure ). Figure  shows (a) the RTM image, (b) the conventional plane-wave LSRTM image after 30 iterations, and (c) the plane-wave prestack LSRTM image (30 iterations also). It is obvious that the plane-wave LSRTM image contains many fewer artifacts present in the RTM image. The result obtained with the new method (Figure (c)) contains fewer high frequency artifacts and shows better continuity for many reflectors compared to the result obtained by conventional method.

Figure  shows the CIGs extracted from the RTM image, where all the events are curved upwards indicating that migration velocity is too low. The CIGs extracted from the plane-wave LSRTM image (Figure ) are more continuous and show better S/N. There are no CIGs available from conventional least-squares migration.

Figure 3.9: The convergence curves for LSRTM with the stacked image and the prestack image. It is clear that the convergence of LSRTM is improved when more unknowns are incorporated into the inversion and the migration velocity contains 5% error.

Figure 3.10: (a) The plane-wave RTM image of the Marmousi2 model, (b) image obtained by plane-wave LSRTM with the stacked image after 30 iterations, and (c) image obtained by plane-wave LSRTM with the prestack image after 30 iterations. All the 31 plane-wave gathers are migrated with 5% velocity error.

Figure 3.11: The common image gathers extracted from the plane-wave RTM image obtained with 5% velocity error.

Figure 3.12: The common image gathers extracted from the plane-wave LSRTM image after 30 iterations when the migration velocity contains 5% error.