Computation of ADCIGs

In 2-D, ADCIGs are computed for each midpoint by applying a slant-stack decomposition to the prestack image along the subsurface-offset axis. The kinematics of the angle-domain transformation are defined by the following change of variable:

$$\begin{eqnarray} \widehat{\gamma} &=& \arctan \left. \frac{\partial z_\xi}{\part... ...i}, \\ z_{\widehat{\gamma}} &=& z_\xi-h_\xi \tan \widehat{\gamma},\end{eqnarray}$$ (1) (2)

where $z_{\widehat{\gamma}}$ is the transformed image-point depth. Assuming flat reflectors and VTI media, Biondi (2005a) demonstrates that the angle $\widehat{\gamma}$ is equal to the phase aperture angle $\widetilde{\gamma}$, thereby simplifying equations 1 and 2:

$$\begin{eqnarray} \widetilde{\gamma} &=& \arctan \left. \frac{\partial z_\xi}{\pa... ...\\ z_{\widetilde{\gamma}} &=& z_\xi-h_\xi \tan \widetilde{\gamma}.\end{eqnarray}$$ (3) (4)