Assumptions and limitations

The weakness of the method presented in this thesis is what it tries to overcome, the non-linearity of tomography. When we are far from the correct solution and/or we have an inaccurate model covariance estimate, the method is susceptible to non-convergence, or convergence to an unreasonable model.

The ray-based tomography used in this thesis is limited by the ray tracing high-frequency approximation. The high frequency approximation requires that the model varies smoothly over a wavelength. For the datasets presented in this thesis that assumption is valid except at the salt edge. In more complex environments, much more expensive wave equation tomography methods (, ) have the potential to do better under these adverse conditions.

For the steering filters of Chapter  to be effective, they must adequately describe the model covariance. Often velocity does not follow dip, and the velocity gradient for the region would need to be used instead of the early migrated reflector position. In addition, a steering filter might not describe a complex media's covariance. For the frequencies used in reflection seismology, practice shows that velocity can be approximated as a smoothly varying function, so steering filters are a valid representation of the model's covariance.

This thesis assumes that no anisotropy exists in the data. In theory, it is not hard to incorporate anisotropy into the velocity estimation process presented in this thesis, in fact, the method presented has great potential for anisotropic estimation. The reflector stability of the tau domain method would lead to much better ability to constrain the $\eta$ () or equivalent anisotropic parameter. In addition, steering filters, with their ability to spread information along layers, are ideal for defining and determining anisotropic layers.