Without considering intrinsic attenuation, reverse time migration (RTM) of data from lossy media produces smeared migration images because of the Q effects (amplitude loss and velocity dispersion). To mitigate the Q effects during RTM, amplitudes need to be compensated and the propagation velocity of the compensated wavefield needs to be the same as in the attenuating wavefield. We have compared the decoupled constant Q (DCQ) viscoacoustic equation with the viscoacoustic equation based on the generalized standard linear solids (GSLS), for modeling and for Q compensation. The DCQ propagator separates amplitude loss and velocity dispersion operators; for the GSLS propagator, memory variables are used to introduce the Q effects. Amplitude loss and velocity dispersion are decoupled in the DCQ equation, whereas they are coupled in the GSLS equation. Viscoacoustic modeling by the two viscoacoustic propagators produces visually identical seismograms. To compensate for the Q effects, for the DCQ equation, we reverse the sign of the amplitude loss operator and keep the sign of the velocity dispersion operator unchanged. For the GSLS equation, the sign of the memory variables is reversed. Both approaches can compensate for the amplitude loss. Propagation velocities in the attenuating and Q-compensated wavefields are the same for the DCQ equation and are different for the GSLS equation. The Q-compensated wavefield propagates faster than the attenuating wavefield for the GSLS equation. Viscoacoustic RTM is implemented with the source normalized crosscorrelation imaging condition; the source wavefield is attenuated, and Q compensation is applied during receiver wavefield extrapolation. Results of Q-compensated migration on a three-layer model, a salt model, and the BP 2004 model using the DCQ equation are more consistent with the acoustic (nonviscous) RTM results, but they have a wider wavelet and a different Q-dependent amplitude behavior; there is a phase shift in the migration results when using the GSLS equation.

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