Simulation of wave propagation in an anisotropic viscoacoustic medium is an important problem, for instance within Q-compensated reverse-time migration. Processes of attenuation, dispersion, and anisotropic influence all aspects of seismic wave propagation, degrading resolution of migrated images. We present a new approach of the viscoacoustic wave equation in the time domain to explicitly separate amplitude attenuation with phase dispersion and develop a theory of viscoacoustic reverse time migration (Q-RTM) in tilted TI media. Because of this separation, we would be able to compensate the amplitude loss effect, the phase dispersion effect, or both effects. In the Q-RTM implementation, the attenuation-compensated operator was constructed by reversing the sign of amplitude attenuation. Using the TI approximation and ignoring all spatial derivatives of the anisotropic symmetry axis direction leads to instabilities in some area of the model with the rapid variations in the symmetry axis direction. A solution to this problem is proposed that involves using a selective anisotropic parameter equating in the model to reduce the difference of Thompson parameters in areas of rapid changes in the symmetry axes. The scheme is tested on a layer model and a modified acoustic Marmousi velocity model with a 2-4 staggered grid. We validate and examine the response of this approach by using it within a reverse time migration scheme adjusted to compensate for attenuation. The amplitude loss in the wavefield at the source and receivers due to attenuation can be recovered by applying compensation operators on the measured receiver wavefield. After correcting for the effects of anisotropy and viscosity, numerical test on synthetic data illustrates the higher resolution images with improved amplitude and the correct locations of reflectors, particularly beneath high-attenuation layers.
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