Efficient <i>Q</i> -compensated reverse time migration using a new decoupled viscoacoustic wave equation based on the generalized standard linear solid

ABSTRACT Seismic attenuation is an intrinsic property of subsurface media, and neglecting this effect during seismic migration will degrade imaging quality. To achieve seismic migration with attenuation compensation, a viscoacoustic wave equation that decouples amplitude dissipation and phase dispersion is essential. However, the traditional decoupled fractional Laplacian (DFL) viscoacoustic wave equation requires computationally expensive fast Fourier transforms for numerical simulation, posing challenges for large-scale industrial applications. In contrast, the generalized standard linear solid (GSLS) viscoacoustic wave equation with multiple relaxation mechanisms can be efficiently solved using the finite-difference (FD) method. Nevertheless, it includes coupled dissipation and dispersion terms, making it inappropriate for implementing Q-compensated reverse time migration (RTM). Therefore, we derive an equivalent GSLS viscoacoustic wave equation that decouples amplitude dissipation and phase dispersion effects, which can be solved using the FD method. To ensure numerical stability during attenuation compensation, we introduce a regularization operator into the attenuation-compensated viscoacoustic wave equation and implement Q-compensated RTM in attenuating media. Numerical analysis indicates that our wave equation, using three relaxation mechanisms, achieves simulation accuracy comparable to the DFL viscoacoustic wave equation while offering higher computational efficiency. Synthetic and field data examples suggest that our Q-compensated RTM approach effectively corrects phase dispersion and compensates for amplitude loss, outperforming the DFL-based Q-compensated RTM in computational efficiency.