I describe a method of estimating near-surface velocity structure from reflection seismic data by combining two inversion techniques in a two-step method. The first step is based on the qualitative observation that trace power calculated from seismic data and plotted in midpoint-offset coordinates results in distinctive trajectories which depend on the position and depth of near-surface velocity anomalies. By summing along these trajectories it is possible to create an image which positions the anomalies in terms of lateral position and depth. In the second step, this image is input to a wavefield extrapolation routine as a preliminary velocity model. The wavefield is then iteratively propagated through the near surface until a velocity model is converged upon. Once the velocity structure is estimated, the seismic data can be numerically propagated through it to remove distortions caused by focusing, kinematics, and amplitude effects. Because the iterative propagation step is based on wavefield redatuming, the method can be applied to land data with irregular acquisition topography as well as to marine data with near-surface velocity variations.