The viscoacoustic wave equation with decoupled amplitude attenuation and phase dispersion terms is convenient for implementing reverse time migration (RTM) in attenuating media. However, the traditional viscoacoustic wave equations are expressed by the fractional Laplacian, which requires computationally expensive fast Fourier transforms to perform numerical solutions. This is not conducive for commercial applications with seismic data in terabyte, particularly in three dimensions. Based on the memory-variable-represented viscoacoustic wave equation, the new dispersion- and dissipation-dominated wavefield extrapolation operators that can be solved using the economical finite-difference method (FDM) are developed. In numerical simulation, the staggered-grid FDM is used to solve the temporal and spatial derivatives. The computational efficiency analysis indicates that, compared to the traditional viscoacoustic wave equation, the new viscoacoustic wave equation has an efficiency improvement of approximately more than two times. The accuracy of simulations of amplitude attenuation and phase dispersion is evaluated in viscoacoustic media with varying Q values. The proposed viscoacoustic wave equation is also extended to Q-compensated RTM. Two synthetic tests and one field data test indicate that the Q-compensated RTM can produce high-resolution images by correcting phase dispersion and compensating amplitude loss.

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