Appendix B

We develop here the calculation of the second derivative of the phase from its expression in narrow-azimuth migration:

$$\begin{eqnarray} \phi & = & DSR(\omega,\bold k_m,\bold k_h,z) dz + k_{hy} h_y \n... ..._{sy}^2 \right) \right)^{\frac{3}{2}}} \right\} \leq 0 \nonumber\end{eqnarray}$$

We derive our conclusions concerning the validity of the stationary-phase approximation from this final formula. It also highlights intrinsic limitations of the algorithm with steep dips and evanescent waves.