A stable Q-compensated reverse-time migration method using a modified fractional viscoacoustic wave equation

Seismic wave propagation inside the earth is usually accompanied by amplitude dissipation and velocity dispersion. It is essential to accurately characterize these effects and make the corresponding compensations in seismic reverse-time migration (RTM) and the following interpretation. Due to the approximation of omega approximate to kv0 in the derivation, the conventional fractional viscoacoustic wave equation in strongly attenuative media is unsatisfactory. This paper develops a modified viscoacoustic wave equation by combining the relationship between angular frequency and complex wavenumber. The numerical simulation demonstrates its advantage of high accuracy in describing constant-Q effects, especially in strongly attenuative media with small Q values. A truncated Taylor-series expansion algorithm and a pseudospectral method are developed to solve this equation during wave propagation. To address the issue of numerical instability in Q-compensated RTM (Q-RTM), a stabilized technology with regularization is further developed. Unlike the conventional filtering method implemented in the wavenumber domain, our approach only adds an explicit regularization term, which can be directly computed in the space domain. Furthermore, this regularization depends on velocities and quality factors, significantly improving its applicability in complicated structures. Noise-free data tests demonstrate that our Q-RTM method can effectively correct phase distortion, compensate for amplitude attenuation, and produce high-resolution migrated images without any cutoff-frequency artifacts caused by filtering. Noisy data experiments further verify the antinoise performance and robustness of our method.