Attenuation compensation for time-reversal imaging in VTI media

The time symmetry of the wave equation enables application of time-reversal modeling in acoustic and elastic media. Time reversal represents a key component not just in reverse-time migration (RTM), but also in source localization using passive seismic (e.g., microseismic) data. This symmetry in time, however, is no longer valid in attenuative media, and attenuation is often anisotropic. Here, we employ a viscoelastic anisotropic wave equation that decouples the influence of energy dissipation from that of dispersion. That equation helps compensate for anisotropic attenuation and restore the time symmetry by changing the signs of the dissipation-dominated terms in time-reversed propagation, while keeping the terms responsible for dispersion unchanged. The Q-compensated time-reversal imaging algorithm is tested on synthetic microseismic data from 2D transversely isotropic media with a vertical symmetry axis (VTI). After back-propagating multicomponent data acquired in a vertical borehole, we image microseismic sources using wavefield focusing. Accounting for attenuation anisotropy in time-reversal imaging produces superior source images compared to those obtained without attenuation compensation or with a purely isotropic Q-factor.