Conclusions

We have introduced a novel way of preconditioning least-squares RTM to achieve a faster convergence rate in viscoacoustic media. The data-space preconditioner is implicitly defined by the $Q$-compensated RTM operator, with the goal of recovering amplitude loss due to attenuation and removing low frequency artifacts in the gradient. Since the square matrix to be inverted becomes numerically non-Hermitian, we adopt the GMRES algorithm to perform iterative inversion. Our synthetic examples show that the proposed $Q$-LSRTM is capable of producing an accurate $Q$-compensated image within significantly fewer iterations than LSRTM, and thus is preferable in application to accurate seismic imaging in attenuating media.