$Q$-compensated viscoelastic reverse-time migration ($Q$-ERTM) counteracts subsurface quality-factor ($Q$) filtering effect for attenuated multicomponent seismic data to produce high-quality migrated images. Compared with $Q$-compensated viscoacoustic reverse-time migration ($Q$-ARTM), $Q$-ERTM provides more informative geological and structural characterization of the subsurface, but poses greater challenges on viscoelastic wavefield decomposition and stabilization. On the basis of our previously proposed stabilization operator for $Q$-ARTM, we have developed a mode-dependent adaptive stabilization scheme for $Q$-ERTM, which has the ability to handle numerical instability issue arising from viscoelastic compensation. The stabilization scheme exhibits superior properties of time-variance and $Q$-dependence over commonly used low-pass filtering method. In the context of viscoelastic wave equation with decoupled fractional Laplacians (DFLs), we have thoroughly investigated the staggered-grid pseudo-spectral (SGPS) approach for viscoelastic simulation, vector-based wavefield decomposition for imaging, and mode-dependent adaptive stabilization for compensation. These indispensable modules eventually form the whole framework for stable and accurate $Q$-ERTM. The $Q$-ERTM results including PP and PS images from both synthetic and field data set are provided to verify the feasibility and superiority of the proposed approach in terms of fidelity and stability..