Time-Fractional Viscoacoustic Wave Equation-Based Frequency-Domain Stable Q-RTM

The anelastic properties of geophysical media lead to amplitude loss and phase distortion of the seismic waves propagating through the subsurface strata, which significantly affects accurate seismic migration and reasonable interpretation of seismic data. To accurately restore the true information of subsurface media, it is now a consensus among geophysicists to no longer consider subsurface media as acoustic cases, but to incorporate the viscosity of subsurface media. To obtain precise imaging results using the time-fractional viscoacoustic wave equation based on the constant Q model, we derived frequency-domain decoupling of amplitude loss and phase dispersion in the forward simulation and developed two Q-compensated reverse time migration (Q-RTM) methods in the frequency domain by using two imaging conditions involving cross correlation imaging condition (CCIC) and deconvolution imaging condition (DIC), considering the attenuation effect of viscosity media. Numerical experiments on a simple three-layer model and a gas chimney model demonstrate the feasibility and effectiveness of the developed strategies. Compared with conventional acoustic RTM schemes, Q-RTM can enhance the resolution of imaging results and compensate for attenuated seismic waves. The superiority of the suggested approach is further confirmed by applying real seismic data. In summary, the proposed method, after fully considering the realistic information of the viscoacoustic medium, achieves imaging results with a wider frequency spectrum compared to conventional RTM in nonattenuating media, filling the gap in frequency-domain RTM with constant Q model.