Attenuation Compensation and Anisotropy Correction in Reverse Time Migration for Attenuating Tilted Transversely Isotropic Media

The propagation of seismic waves in attenuating and anisotropic earth media is accompanied by amplitude attenuation and phase distortion. If these adverse effects are not addressed in seismic imaging, we may end up with inaccurate reflector positions, dimming amplitudes, and reduced spatial resolution in the imaging results. We use a pure pseudo-viscoacoustic TTI wave equation as a forward engine to implement Q-compensated TTI reverse time migration (RTM) because the wavefields simulated by the conventional coupled pseudo-viscoacoustic tilted transversely isotropic (TTI) wave equation contain shear wave artifacts and are unstable when the anisotropic parameters ε < δ. The high-frequency noise in the wavefield will be amplified exponentially during amplitude-compensated extrapolation, resulting in numerical instability when using Q-compensated TTI RTM. To eliminate the destabilizing effect of boosted high-frequency noise, we introduce a complex velocity that can be used to describe amplitude compensation over the limited frequency band. Then, based on this complex velocity, we derive a stable amplitude-compensated operator and apply it to the Q-compensated TTI RTM. The numerical simulation results show that, in comparison with the coupled pseudo-viscoacoustic TTI wave equation, the pure pseudo-viscoacoustic TTI wave equation is free from shear wave artifacts and is not restricted by anisotropic parameters. In addition, the pure pseudo-viscoacoustic TTI wave equation has high accuracy in describing velocity anisotropy and attenuation isotropy. Synthetic and field data examples demonstrate the effectiveness of our Q-compensated TTI RTM in compensating amplitude dissipation and correcting phase distortion.