Proposed approach

We intend to eliminate the FEAVO anomalies by finding an accurate velocity model, then by downward continuing the data through it until under the FEAVO-causing velocity anomalies. The velocity will be found by migration velocity analysis (MVA), an iterative inversion process whose optimization goal is not fitting the recorded data, but providing the best focused migrated image Biondi and Sava (1999). The chapter pertaining to velocity analysis in Biondi (2001a) shows (with examples) why dipping reflectors in laterally varying velocity media require the velocity analysis to be performed in the migrated domain (image domain) instead of the unmigrated domain (data domain). A wave-equation MVA (WEMVA) Sava (2000) will be used instead of a ray-based MVA Clapp (2001). The advantages of the former over the latter are detailed in the WEMVA chapter of Biondi (2001a). One particular advantage is the better treatment of amplitudes by wave-equation methods.

The usual WEMVA criterium describing the quality of the image is flatness in angle gathers. This is directly related to traveltime anomalies. As it is visible in Figure 1a, the traveltime changes associated with the FEAVO effect are very small and they do not produce curvatures in angle gathers. Biondi and Sava (1999) show on a synthetic, and this paper will show on a real dataset, that FEAVO anomalies keep their ``V'' shapes through prestack migration and conversion from offset to angle gathers. Therefore, the fitting goal of the inversion must be related to the distribution of amplitudes in the midpoint-angle space. The desired image will not exhibit these characteristic ``V'' patterns.

The inversion will proceed as follows: the wavefield at a certain depth is downward continued a depth step down through the known velocity model with an accurate (nonlinear) operator. The result is transformed to angle domain and a ``perfect'' image is created by eliminating the FEAVO anomalies. A image perturbation ($\Delta W$) is obtained by substracting the two images, and is backprojected through an invertible operator in order to obtain a velocity update ($\Delta s$). The velocity model is updated and the cycle proceeds again, until $\Delta W$ becomes negligible. The construction of the operator that links $\Delta s$ and $\Delta W$ is very important. The number of iterations and the accuracy of the result depends on its accurate invertibility. In order to make it invertible, Born Sava and Biondi (2001b) or other Sava and Fomel (2002) types of linearization are employed.