Conclusions

We present a stable definition of R=ik_z that includes the causality and viscosity concepts in phase-shift migration; moreover, this expression is valid for any value of $\omega$ and k_x.

We implemented the damping factor $\epsilon$ in the R definition, equation (12), such that there is no loss of high frequency information. This redefinition also presents the possibility of having different damping factors in order to improve even more the quality of the final image.

The fact that we use Muir recursion to develop a stable R definition lets us have control over the migration angle just as wavefield migration does.