Fast least-squares migration with a deblurring filter

Least-squares migration (LSM) is a linearized waveform inversion for estimating a subsurface reflectivity model that, relative to conventional migration, improves spatial resolution of migration images. The cost, however, is high because LSM typically requires 10 or more iterations, which is at least 20 times more than the CPU cost of conventional migration. To alleviate this expense, we offer a deblurring filter that can be used in a regularization scheme or a preconditioning scheme to give acceptable LSM images with less than one-third the cost of the standard LSM method. Our results in applying deblurred LSM to synthetic data and field data support this claim. In particular, a Marmousi2 model test shows that the data residual for preconditioned deblurred LSM decreases rapidly in the first iteration, which is equivalent to 10 or more iterations of LSM. Empirical results suggest that regularized deblurred LSM after three iterations is equivalent to about 10 iterations of LSM. Applying deblurred LSM to 2D marine data gives a higher-resolution image compared to those from migration or LSM with three iterations. These results suggest that LSM combined with a deblurring filter allows LSM to be a fast, practical tool for improved imaging of complicated structures.