Introduction

Focusing-effect AVO (FEAVO) is the focusing of seismic wavefield amplitudes through velocity lenses too small to generate fully developed triplications. The amplitude effects are large enough to thwart proper AVO analysis in the affected area Kjartansson (1979). The effects can be eliminated by migrating with a velocity model containing the respective lenses Bevc (1994). However, the traveltime effects are too small to allow classical velocity analysis approaches such as Dix inversion or traveltime tomography to succeed. New approaches are needed to deal with such small velocity anomalies.

Biondi and Sava (1999) introduced Wave-Equation Migration Velocity Analysis (WEMVA), which finds the unknown part of the true velocity field by optimizing image quality in the angle domain after prestack depth migration. Vlad et al. (2003) have shown on a synthetic dataset that WEMVA resolves the FEAVO-causing velocity anomalies. The solution was verified by showing that the amplitude anomalies disappear after migration with the updated velocity model.

Error can be introduced in WEMVA by two classes of factors. The first one consists of the approximations undertaken by the mathematical and numerical procedures. The second one encompasses the limitations of the ability to transform a given image into an optimal one. In a synthetic dataset, in which the optimal image is known, this second source of error is completely eliminated. This allowed Vlad et al. (2003) to evaluate solely the effect of the first class of error-generating factors (Born approximation, linearized wavefield continuation, etc.), and they found that it is too small to impede WEMVA from resolving the small FEAVO-causing velocity lenses. This paper, on the other hand, deals with eliminating the second class of error-generating factors by obtaining the optimal image in a way that is as error-free as possible.