Stable Q-compensated reverse time migration in TTI media based on a modified fractional Laplacian pure-viscoacoustic wave equation

The anisotropy and attenuation properties of real earth media can lead to amplitude reduction and phase dispersion as seismic waves propagate through it. Ignoring these effects will degrade the resolution of seismic imaging profiles, thereby affecting the accuracy of geological interpretation. To characterize the impacts of viscosity and anisotropy, we formulate a modified pure-viscoacoustic (PU-V) wave equation including the decoupled fractional Laplacian (DFL) for tilted transversely isotropic (TTI) media, which enables the generation of stable wavefields that are resilient to noise interference. Numerical tests show that the newly derived PU-V wave equation is capable of accurately simulating the viscoacoustic wavefields in anisotropic media with strong attenuation. Building on our TTI PU-V wave equation, we implement stable reverse time migration technique with attenuation compensation (Q-TTI RTM), effectively migrating the impacts of anisotropy and compensates for attenuation. In the Q-TTI RTM workflow, to remove the unstable high-frequency components in attenuation compensated wavefields, we construct a stable attenuation compensated wavefield modeling (ACWM) operator. The proposed stable ACWM operator consists of velocity anisotropic and attenuation anisotropic parameters, effectively suppressing the high-frequency artifacts in the attenuation compensated wavefield. Synthetic examples demonstrate that our stable Q-TTI RTM technique can simultaneously and accurately correct for the influences of anisotropy and attenuation, resulting in the high-quality imaging results.