Efficient viscoelastic wave propagation and attenuation-compensated reverse-time migration

Seismic attenuation, a fundamental physical property of the Earth, results in phase dispersion and amplitude loss during wave propagation. Attenuation-compensated reverse-time migration (Q-RTM) can effectively mitigate these effects and enhance the resolution of migrated images. Because the fractional viscoelastic wave equation contains decoupled dispersion and attenuation terms, it has been widely employed in Q-RTM. However, this equation involves several fractional Laplacian operators and typically requires computationally intensive spectral methods. To address this limitation, a generalized standard linear solid (GSLS) type approximation is introduced to develop a viscoelastic wave equation suitable for finite-difference implementation. Unlike the conventional GSLS method, the proposed equation explicitly incorporates the quality factor Q, thus enabling Q-based simulation and inversion. By introducing a compensation term, a compensated wave equation is further derived and applied to Q-RTM. Compared with conventional Q-RTM based on the fractional viscoelastic wave equation, the proposed approach significantly reduces computational costs associated with Fourier transforms used for viscoelastic wavefield extrapolation. In addition, a modified P- and S-wave decomposition algorithm is developed to reduce computational costs in viscoelastic RTM imaging. Numerical experiments on wavefield simulation and Q-RTM demonstrate that the proposed equation can yield results comparable to those from the fractional viscoelastic wave equation with significant reduction of computational costs. Furthermore, Q-RTM effectively counteracts the adverse effects of seismic attenuation, producing high-resolution migrated images comparable to reference solutions.