An Efficient Least-squares Reverse-time Migration Using True-amplitude Imaging Condition as an Optimal Preconditioner

A preconditioned least-squares reverse-time migration algorithm is formulated for common shot prestack depth migration to speed up the convergence of the standard least-squares reverse-time migration. The preconditioner is based on a true amplitude imaging condition. Its construction is borrowed from the past effort to design true amplitude Kirchhoff/Born depth migration in the frame of asymptotic theory and has been adapted to the case of reverse-time migration imaging method. A 2D numerical experiment on the synthetic Marmousi II model first shows the speed up of the convergence compared to standard least-squares reverse-time migration. Moreover, the resulting images after only 5 iterations show a significant improvement compared to standard reverse-time migration images, in terms of quantitative recovery of the slowness perturbation, reduction of the migration artefacts and spectral resolution. To sum up, to recover the full bandwidth of the data in the migrated image and provide a faithful reflectivity section, the preconditioned least-squares reverse-time migration only require a few iterations which makes this algorithm affordable.