FUTURE WORK AND CONCLUSIONS

Preliminary results are encouraging. The data focuses at the predicted $\gamma$ when given an inaccurate velocity model. In addition, for the case of a DC error in global travel-times, $\gamma$ can be found iteratively, reducing the need for costly back projections. A theory relating how to actually to map $\gamma$ perturbations to changes in the focusing operator needs to be developed. Building a linear operator relating travel-time pertubations to change in $\gamma$reponse seems to be the next step. Changing the focusing operator is at best a first order approximation. At some stage we must back project the focusing operator to the the velocity field, recalculate travel-times and repeat the focusing analysis. An open question is what is the best method for back projection, is the central ray approach of Audebert1996 sufficient? Another potential area of research is to see if we can avoid going back to the data when scanning over $\gamma$.Is it possible to apply a small convolution operator, similar to residual migration, on the image space that simulates changes in $\gamma$?