MVA can be done with infinite-frequency (ray-based) operators Clapp (2001) or with finite band (wave-equation) operators Biondi and Sava (1999). The advantages of the latter over the former are detailed in the WEMVA chapter of Biondi (2001). In particular, ray theory breaks down if its high frequency assumption does not hold Woodward (1990), as is the case with velocity anomalies of the size of those that generate the FEAVO effect. Multipathing is another instance when the wave equation methods are more appropriate. They also treat more correctly the amplitudes.
WEMVA proceeds as follows: the wavefield at a certain depth is downward continued a depth step through the known velocity model with an accurate (nonlinear) operator. The result is transformed to angle domain and an improved image is created by eliminating either the curvature of the events in angle-domain common image gathers Prucha et al. (1999), or the FEAVO anomalies. An image perturbation (Image) is obtained by subtracting the two images, and is backprojected through an invertible operator in order to obtain a velocity update. The velocity model is updated and the cycle proceeds again until Image becomes negligible. Figure 1 illustrates this process.
WEMVA is at the forefront of research. As the comparison in the next section will show, it avoids all the shortcomings of the previous attempts.