Abstract: Amplitude dissipation and phase dispersion occur when seismic waves propagate in attenuated anisotropic media, affecting the quality of migration imaging. To compensate and correct for these effects, the fractional Laplacian pure viscoacoustic wave equation capable of producing stable and noise-free wavefields has been proposed and implemented in the Q-compensated reverse time migration (RTM). In addition, the second-order Taylor series expansion is usually adopted in the hybrid finite-difference/pseudo-spectral (HFDPS) strategy to solve spatially variable fractional Laplacian. However, during forward modeling and Q-compensated RTM, this HFDPS strategy requires 11 and 17 Fast Fourier Transforms (FFTs) per time step, respectively, leading to computational inefficiency. To improve computational efficiency, we introduce two high-efficiency HFDPS numerical modeling strategies based on asymptotic approximation and algebraic methods. Through the two strategies, the number of FFTs decreased from 11 to 6 and 5 per time step during forward modeling, respectively. Numerical examples demonstrate that wavefields simulated using the new numerical modeling strategies are accurate and highly efficient. Finally, these strategies are employed for implementing high-efficiency and stable Q-compensated RTM techniques in tilted transversely isotropic media, reducing the number of FFTs from 17 to 9 and 8 per time step, respectively, significantly improving computational efficiency. Synthetic data examples illustrate the effectiveness of the proposed Q-compensated RTM scheme in compensating amplitude dissipation and correcting phase distortion.