Conclusions

In this paper, we demonstrated the feasibility of migration velocity analysis using wave-equation methods. The results we obtained on 2-D synthetic models are very encouraging. Cost remains a major limitation, although as our method progressively matures, we have more and more computer power at our disposal.

The main point we would like to make is that unlike other velocity inversion techniques, our method updates the velocity model by improving the quality of the migrated image, and not by fitting the recorded data. It therefore takes full advantage of the intertwined nature of migration and velocity analysis,

Wave-equation migration techniques are known for their potential to handle complex wavefields. Since our velocity analysis method is also based on processing with the wave-equation, it inherits stability and constrains the derived velocity to be smoother than what a traveltime-based method would allow. Furthermore, we can control the shape of our derived velocity anomalies by imposing external constraints, either model-independent, like Laplacian smoothing, or model-dependent steering filters.

The Born approximation on which we base our method limits the amount of improvement we can allow on the starting image. For lack of a better procedure, we now chose to continue with a technique in which we scale-down the image perturbation and later scale-up the slowness perturbation. Handling the limitations imposed by the Born approximation is one of the most useful and exciting areas of future research.

In addition to improvements in scaling and rescaling the image and slowness perturbations, other potential directions of future research include semblance and differential semblance analysis for more reliable image enhancements and an analysis of the implications of the complex nature of the wavefields, specifically the benefits of implicitly using all the arrivals in the wavefield for velocity analysis rather than merely a single one.