P- and S-wavefield separation is necessary to extract PP and PS images from prestack elastic reverse time migrations. Unlike traditional separation methods that use curl and divergence operators, which do not preserve the wavefield vector component information, we did P and S vector decomposition, which preserves the same vector components that exist in the input elastic wavefield. The amplitude and phase information was automatically preserved, so no amplitude or phase corrections were required. We considered two methods to realize P and S vector decomposition: selective attenuation and decoupled propagation. Selective attenuation uses viscoelastic extrapolation, in which the Q-values are used as processing parameters, to remove either the P-waves or the S-waves. Decoupled propagation rewrites the stress and particle velocity formulation of the elastic equations into separate P- and S-wave components. In both methods, the decomposition is realized during the extrapolation of an elastic wavefield. These algorithms could also perform P and S decomposition in gather data by extrapolating the data downward from the receivers, during which the decomposition is performed, and then back upward to record the decomposed P- and S-waves at the receivers. Comparisons of the two methods in terms of efficiency, accuracy, and memory showed that both could separate P- and S-waves in the vector domain. The decoupled propagation is preferable in terms of speed and memory cost, but was applicable only to elastic propagation.