Low-, intermediate-, and high-wavenumber components of P- and S-wave velocities jointly influence the elastic wave propagation and scattering in an isotropic medium. By taking advantage of all information in the data, elastic full-waveform inversion (E-FWI) has the potential to recover these model components. However, if the transmitted wave data are insufficient to illuminate the deeper part of the subsurface, we should rely on the solutions using reflection data. To reduce the nonlinearity of waveform inversion, we choose to decouple the effects of the model background and perturbation on the reflected waves within a linearized inversion framework. This resorts to three stages aiming to gradually fit the traveltimes and waveforms of the reflected PP and PS waves based on data or gradient preconditioning through P/S mode decomposition. For the first two stages, once the multicomponent seismograms have been separated into PP and PS reflection recordings, reflection traveltime inversion using an acoustic wave propagator (A-RTI) can successively recover the low-wavenumber components of P- and S-wave velocities. In the last stage, starting from the models having reliable low-wavenumber components, elastic reflection waveform inversion (E-RWI) can easily get out of the local minima and continue to retrieve the increasing wavenumber features sensitive to the waveform and amplitude variations. This is supported by gradient preconditioning through P/S mode decomposition of the extrapolated normal and adjoint wavefields, and alternately updating model background and high-wavenumber components in terms of linearized least-squares inversion. Numerical examples have demonstrated the performance of our E-RWI approach and the validity of the three-stage inversion workflow.