High-Efficiency Viscoacoustic Least-Squares Reverse Time Migration With Q-Compensated Gradient Using Nearly Constant Q Model

The attenuation characteristics of subsurface media cause amplitude attenuation and phase dispersion in seismic waves. Ignoring these effects in conventional least-squares reverse time migration (LSRTM) may degrade imaging quality. To address this issue, we propose an efficient viscoacoustic LSRTM algorithm with Q-compensated gradient (Q-comp LSRTM) to enhance imaging quality in attenuating media. We begin by deriving a viscoacoustic wave equation with decoupled dissipation and dispersion terms, based on the nearly constant Q model, which can be solved using an efficient finite-difference method. We observed that the wavefield computation using the proposed viscoacoustic wave equation is nearly three times faster in calculation time compared to the traditional decoupled fractional Laplacian (DFL) viscoacoustic wave equations. Then, in the context of the proposed viscoacoustic wave equation, we derive the linearized viscoacoustic wave equation, the Q-compensated viscoacoustic wave equation, and the Q-compensated adjoint migration operator to implement the efficient Q-comp LSRTM algorithm. To mitigate the amplification of high-frequency noise during Q-compensated gradient computation, we introduce a stable regularization operator to ensure computational stability. Furthermore, we develop a bidirectional illumination compensation (Bi-comp) preconditioner to accelerate the convergence rate of the proposed Q-comp LSRTM algorithm. Finally, the two synthetic examples and one field dataset demonstrate that the proposed Q-comp LSRTM approach effectively compensates for amplitude attenuation and corrects phase dispersion, delivering high-quality images with fewer iterations.