Fast least squares migration with a deblurring filter

Summary: Least squares migration (LSM) is equivalent to linearized waveform inversion for the subsurface reflectivity distribution. The benefit is a reduction in migration artifacts and an increase in spatial resolution, but the cost, however, is that LSM typically requires 10 or more iterations, which is about 20 times or more the CPU cost of conventional migration. To alleviate this expense, we present a deblurring filter that can be employed in either a regularization scheme or a preconditioning scheme to give acceptable LSM images with less than 1/3 the cost of the standard LSM method. Our results in applying deblurred LSM (DLSM) to synthetic data and field data support this claim. In particular, a Marmousi2 model test showed that the data residual for preconditioned DLSM decreases rapidly in the first iteration, which is equivalent to 10 or more iterations of LSM. Empirical results suggest that regularized DLSM after 3 iterations is equivalent to about 10 iterations of LSM. Applying DLSM to 2-D marine data gives a higher resolution image compared to those from migration. These results suggest that LSM combined with a deblurring filter allows LSM to be a fast and practical tool for improved imaging of complicated structures.