Bevc (1993) generates a synthetic dataset exhibiting FEAVO anomalies and proposes a data-space tomography approach using downward continuation as the operator in tomography. This line of work is continued by Bevc (1994b), who shows using the synthetic that the FEAVO anomalies can indeed be eliminated by finding the velocity model, and then by downward continuing through it until under the FEAVO-causing velocity anomalies (redatuming). He also theoretically discusses inversion schemes. In the follow-up, Bevc (1994a) picks times from sags in the FEAVO-affected quasi-hyperbolic arrivals in CMP gathers and does traveltime tomography to find the velocity model. He operates under the assumption that the velocity anomalies are in the near surface. The tomography works in the following way: 1) apply NMO; 2) find the departures from the flatness of the events in CMP gathers (time lags) by crosscorrelating a pilot trace with the data; and 3) the lags are backprojected onto the velocity model that will be used for the NMO at the first step. The inversion in the last tomographic step uses a styling goal with PEFs. The method is shown to work on a simple synthetic dataset, but the conclusions contain a warning that it may not work on real data.
With a different approach (inverting picked maximum amplitudes and using ray-based operators), Harlan (1994) does not produce a velocity model, but a transmission anomaly section that is used to eliminate the FEAVO effect for a 2D dataset.