Approaches for GSLS based nearly constant- Q viscoacoustic wave equations and its application in reverse time migration calculated by finite-difference method

Abstract Seismic waves are attenuated and distorted during the propagation. The amplitude attenuation can decrease the energy of the wavefields, and dispersion effect distort the phase of seismic waves, thereby degrading the imaging resolution. In nearly constant-Q reverse time migration (Q-RTM), it is essential to decouple the dispersion and dissipation components of the viscoacoustic wave equation (WE) to facilitate attenuation compensation and phase correction. Conventional decoupled viscoacoustic WEs are typically formulated with fractional Laplacian operators, requiring the computationally expensive pseudo-spectral method (PSM). Although viscoacoustic WEs derived from the generalized standard linear solid (GSLS) model has widely applied due to high computational efficiency, their viscous terms are usually coupled, rendering them unsuitable for Q-RTM. To address this limitation, a new GSLS-based viscoacoustic decoupled WE is derived for the Q-RTM framework. The proposed WE offers three main advantages: Firstly, when the number of SLS is greater than one, the dispersion and dissipation terms are explicitly decoupled under various reference frequencies, making it well-suited for Q-RTM. Secondly, the proposed WEs can be efficiently solved using finite-difference method (FDM), thereby avoiding the high computational cost. Thirdly, by using a regularization method to suppress high-frequency components in the seismic wavefield, the proposed WE enables stable and effective Q-RTM. The modified Marmousi and BP gas models demonstrates superior computational efficiency and imaging accuracy. Furthermore, application to field seismic data shows that the new method enhances the imaging resolution, particularly in deeper sections, thereby confirming its potential for practical exploration scenarios.