Attenuation of seismic waves needs to be taken into account to improve the accuracy of seismic imaging. In viscoacoustic media, reverse time migration (RTM) can be performed with [Formula: see text]-compensation, which is also known as [Formula: see text]-RTM. Least-squares RTM (LSRTM) has also been shown to be able to compensate for attenuation through linearized inversion. However, seismic attenuation may significantly slow down the convergence rate of the least-squares iterative inversion process without proper preconditioning. We have found that incorporating attenuation compensation into LSRTM can improve the speed of convergence in attenuating media, obtaining high-quality images within the first few iterations. Based on the low-rank one-step seismic modeling operator in viscoacoustic media, we have derived its adjoint operator using nonstationary filtering theory. The proposed forward and adjoint operators can be efficiently applied to propagate viscoacoustic waves and to implement attenuation compensation. Recognizing that, in viscoacoustic media, the wave-equation Hessian may become ill-conditioned, we propose to precondition LSRTM with [Formula: see text]-compensated RTM. Numerical examples showed that the preconditioned [Formula: see text]-LSRTM method has a significantly faster convergence rate than LSRTM and thus is preferable for practical applications.
Rank $2r$ Iterative Least Squares: Efficient Recovery of Ill-Conditioned Low Rank Matrices from Few Entries
