Improved iterative least-squares migration using curvelet-domain Hessian filters

Least-squares migration (LSM) can potentially provide better amplitude fidelity, higher image resolution, and fewer migration artifacts than standard migration. Conventional LSM is often solved iteratively through linearized inversion, and therefore is often referred to as iterative LSM. In recent years, various single-iteration LSM approaches have been proposed as a cost-effective approximation of iterative LSM and have produced promising results. To exploit the full potential of LSM, we propose to employ the curvelet-domain Hessian filter (CHF), useful in single-iteration LSM, as a preconditioner for conventional iterative LSM. We call this approach CHF-preconditioned LSM (CPLSM). We first validate our CPLSM approach using SEAM I synthetic data and show that it produces better amplitude fidelity over the single-iteration CHF approach and converges faster than conventional iterative LSM. Furthermore, we demonstrate with an application to field data that CPLSM produces fewer migration artifacts and less noise than conventional iterative LSM. This addresses a known problem of iterative LSM that is caused by the use of inaccurate modeling algorithms followed by overfitting the modeled synthetic data to the recorded data.