Non-hyperbolic correction of seismic data

A method for improving seismic images by correction of distortions in the underlying seismic data caused by a near-surface anomaly that produces a non-hyperbolic move-out component of the seismic reflection below the anomaly includes the steps of: a. redatuming the input seismic data to go from the surface to a target horizon using true one-way traveltime operators to provide a first new redatuming dataset; b. redatuming the input seismic data using hyperbolic one-way travel time operators to provide a second new redatuming dataset; and c. redatuming the combination of a first causal part of the first new redatuming dataset and an anti-causal second part of the second redatuming dataset to go from the target horizon back to the surface using hyperbolic one-way traveltime operators to provide a dataset that is referenced to the surface without an imprint of the anomaly.