A reversible transform for seismic data processing

William A. Burnett, Robert James Ferguson

We use the nonstationary equivalent of the Fourier shift theorem to derive a general one-dimensional integral transform for the application and removal of certain seismic data processing steps. This derivation comes from the observation that many seismic data processing steps can be viewed as nonstationary shifts themselves. The nonstationary frequency and time distortions inherent to many seismic data processes are predicted and quantified by this transform. Once the transform is developed, we demonstrate matrix-vector multiplication as a valuable tool for implementation.