Theory of ADCIGs in anisotropic media from a ``plane-wave'' viewpoint

From the ``plane-wave'' viewpoint of the theory of ADCIGs in anisotropic media, the expression for the generalized impulse response of prestack anisotriopic migration leads to the following expressions for the offset and midpoint dips:

$$\begin{eqnarray} \left. \frac{\partial z_\xi}{\partial h_\xi} \right\vert _{m_\... ...tilde{\gamma}\tan \widetilde{\alpha}_x } =\tan \widehat{\alpha_x},\end{eqnarray}$$ (5) (6)

where $\widetilde{\alpha_x}$ is the group dip angle, $\widetilde{\gamma}$ is the group average aperture angle, $\widehat{\alpha_x}$ and $\widehat{\gamma}$ are two angles we introduce and that are related to the midpoint and offset dips. $\widetilde{S}_s$ and $\widetilde{S}_r$ are the phase slownesses for the source and receiver wavefields, respectively.

The phase aperture and group dip angles can then be related to the offset and midpoint image dips:

$$\begin{eqnarray} \tan \widetilde{\gamma} &=& \frac { \tan \widehat{\gamma} - \D... ...ta_{\tilde{S}} \tan \widetilde{\gamma} \tan \widehat{\alpha_x} },\end{eqnarray}$$ (7) (8)

where $\Delta_{\tilde{S}}$ is the ``normalized slowness difference'' $(\widetilde{S}_r-\widetilde{S}_s)/(\widetilde{S}_r+\widetilde{S}_s)$.