Liu, Y.H. and Tsvankin, I., 2021. Methodology of time-lapse elastic full-waveform inversion for VTI media. Journal of Seismic Explorarion, 30: 257-270. Time-lapse seismic processing can provide important information about the variations of reservoir properties during hydrocarbon production and CO, injection. High-resolution results for time-lapse seismic can potentially be obtained from full- waveform inversion (FWI), but most existing time-lapse FWI methods are limited to isotropic and, often, acoustic media. Extension of these techniques to more realistic anisotropic elastic models is hampered by the trade-offs between the medium parameters and significantly increased computational cost. Here, we develop a time-lapse FWI algorithm for VTI (transversely isotropic with a vertical symmetry axis) media and evaluate several strategies of applying it to multicomponent and pressure data. The adjoint-state method and a nonlinear conjugate-gradient technique are employed to derive the gradient of the objective function and update the model parameters. We test the algorithm on a relatively simple VTI graben model using the parallel-difference, sequential-difference and double-difference time-lapse methods. The results confirm the ability of the proposed technique to reconstruct localized time-lapse parameter variations in anisotropic media with sufficient spatial resolution. The double-difference approach proves to be more accurate than the other methods in reconstructing the time-lapse variations from noise-free multicomponent data. When FWI operates with clean pressure data, the parallel-difference method is generally more accurate than the other techniques, especially in estimating the shear-wave vertical velocity Vso. For multicomponent and pressure data contaminated with realistic noise, the double-difference method produces large errors in the temporal variations of the VTI parameters. The parallel-difference technique outperforms its sequential-difference counterpart in reconstructing the time- lapse variations inside the target zone from the noisy data while the latter approach performs better in suppressing the false artifacts outside the “reservoir”. The tests also demonstrate that including more information in time-lapse FWI does not always improve the inversion results, likely due to the increased multimodality of the objective function.