Wang, W. and McMechan, G.A., 2019. P- and S-wave separation and decomposition of two- and three-component elastic seismograms. Journal of Seismic Exploration, 28: 425-447. Multi-component seismic data are valuable in estimating subsurface elastic parameters. The coexistence of P- and S-waves in multi-component surface seismic data poses an obstacle in extracting the elastic properties. Thus, it is crucial to separate the P- and S-waves in elastic seismograms, or during wavefield extrapolations. We analyze an algorithm that can perform both P- and S-wave separation and vector decomposition of multi-component elastic seismograms that are collected from various media, including isotropie, heterogeneous and transversely isotropie, and we extend it to 3D. This algorithm is based on the dispersion relations of P- and S-waves in isotropic and anisotropic wavefields; the near-surface velocity zone can be separated into several segments horizontally to handle heterogeneity. The algorithm is efficient, and no elastic wavefield extrapolations are needed to perform the separation or decomposition, so no subsurface information is needed, apart from the near-surface model parameters (i.e., P- and S-wave velocities, anisotropic parameters) along the receiver arrays. Tests with synthetic data from various 2D and 3D models show high accuracy by comparing the separation and decomposition results from benchmarks that can only be obtained during elastic wavefield forward modeling.