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DAS-VSP utilizes optical fiber deployed in wellbore to measure seismic signals, which significantly reduces the acquisition cost and enables continuous monitoring of the subsurface. However, DAS-VSP only records single-component axial strain or strain rate, leading to incomplete observation of the elastic wavefield. This limitation, coupled with the angle-dependent sensitivity of DAS measurements, presents challenges for accurate P/S wavefield separation, velocity model building and seismic imaging. To fully exploit the elastic information in DAS-VSP data, we introduce a workflow for building high-quality P- and S-wave velocity models to facilitate subsequent elastic seismic imaging and full-waveform inversion (FWI). First, we employ a deep learning method to reliably obtain up- and down-going P/S-wave data. Then, FWI with down-going P-wave data and reflection traveltime inversion (RTI) with up-going P-wave data are cascaded to invert the P-wave velocity model. Eventually, the traveltimes of down- and up-going S-waves are inverted with wave-equation-based methods to build the S-wave velocity model. Synthetic DAS-VSP data examples demonstrate that the proposed approach can provide accurate P- and S-wave velocities for seismic imaging.