Q-compensated wavefield depth extrapolation-based migration using a viscoacoustic wave equation

In a viscoacoustic medium, intrinsic attenuation causes seismic wavefields to attenuate in amplitude and become dispersed in phase, leading to distorted structural imaging and inaccurate migrated amplitudes. To address this problem, viscoacoustic reverse time migration corrects for dispersion and amplitude attenuation effects in wavefield propagation in forward and backward directions. To provide a parallel alternative approach, the time fractional derivative viscoacoustic wave equation in the depth domain is solved and a Q -compensated wavefield depth extrapolation scheme is established to compensate for viscoacoustic effects during recursive wavefield depth extrapolation. This approach decouples the amplitude attenuation and phase dispersion effects from the viscoacoustic vertical wavenumber. To suppress high wavenumber components and address the problem of exponential amplitude growth during wavefield depth extrapolation, we limit the imaginary part of the vertical wavenumber in the frequency wavenumber domain and use an adaptive stabilization solution. Numerical experiments of impulse responses in a viscoacoustic isotropic medium demonstrate that our proposed scheme can observe calculated wavefields exhibiting amplitude attenuation and phase dispersion effects in comparison to wavefields of the acoustic medium, indicating good agreement with theoretical expectations. We also demonstrate the capability of our proposed scheme to recover imaging amplitudes through a variety of numerical experiments, such as imaging of three -layer, Marmousi, and BP gas reservoir models. The results indicate that our proposed scheme can recover amplitude attenuation and phase dispersion effects more accurately than acoustic migration. We also use marine seismic data featuring natural gas hydrates to indicate that our proposed Q -compensated scheme can generate an enhanced imaging result, especially for the bottom simulating reflectors, compared with the conventional imaging algorithm without Q -compensation.