Much of the energy removed in a typical standard seismic data preprocessing sequence corresponds to approximately horizontal propagation in very near-surface structure. Such energy includes direct (first-break) compressional waves, direct shear waves, and ground roll; these may be effectively separated from deeper reflections by downward continuation of the recorded common-source wavefield, by reverse-time extrapolation, to a depth beneath which these waves propagate. The subhorizontally traveling waves get left behind in the shallow part of the model. Subsequent upward continuation of the wavefield reconstructs the original surface-recorded wavefield with the subhorizontally traveling waves removed. Only a very simple (even constant) velocity distribution is required for the wavefield extrapolation; no net distortion is produced since both downward and upward continuations are performed using the same velocity model.