Viscoacoustic least-squares reverse time migration, also denoted as Q-LSRTM, linearly inverts for the subsurface reflectivity model from lossy data. Compared with conventional migration methods, it can compensate for the amplitude loss in the migrated images due to strong subsurface attenuation and can produce reflectors that are accurately positioned in depth. However, the adjoint Q propagators used for backward propagating the residual data are also attenuative. Thus, the inverted images from Q-LSRTM with a small number of iterations are often observed to have lower resolution when compared with the benchmark acoustic LSRTM images from acoustic data. To increase the resolution and accelerate the convergence of Q-LSRTM, we used viscoacoustic deblurring filters as a preconditioner for Q-LSRTM. These filters can be estimated by matching a simulated migration image to its reference reflectivity model. Numerical tests on synthetic and field data demonstrate that Q-LSRTM combined with viscoacoustic deblurring filters can produce images with higher resolution and more balanced amplitudes than images from acoustic RTM, acoustic LSRTM, and Q-LSRTM when there is strong attenuation in the background medium. Our preconditioning method is also shown to improve the convergence rate of Q-LSRTM by more than 30% in some cases and significantly compensate for the lossy artifacts in RTM images.

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