Synthetic examples

The accuracy of the RMO function predicted from equations 5 to 7 is demonstrated in Biondi (2005a,b), for a large range of velocity perturbations. Figure  presents the ADCIGs obtained when a flat reflector is migrated with inaccurate migration velocity models. The data were modeled using the anisotropic parameters of the Taylor Sand Tsvankin (2001): $\epsilon=0.110$ and $\delta=-0.035$. It was then migrated using: a) a velocity uniformly perturbed by $\rho_V=0.99$, b) a velocity uniformly perturbed by $\rho_V=0.9$, and c) an isotropic velocity with the correct vertical velocity. The predicted residual moveouts derived from equations 5 to 7 are superimposed. The solid line was computed when $\tan \gamma$ was derived from $\tan \widetilde{\gamma}$ by applying equation 11, whereas the dashed line was computed using the approximation $\tan \gamma \approx \tan \widetilde{\gamma}$.

The predicted RMO functions accurately track the actual RMO functions when the perturbations are sufficiently small to be within the linearization accuracy range (Figure -a). Even when the perturbations are large (Figures -b and -c) and cause a substantial RMO, the predicted RMO functions are excellent approximations of the true RMO functions. In contrast, the approximation of the group angles with the phase angles (dashed lines in the figures) seriously lowers the accuracy of the predicted RMO functions.

 

Aniso-rmo
Figure 2 ADCIG obtained when data modeled using constant anisotropic parameters (Taylor Sand) have been migrated using: a) a velocity uniformly perturbed by $\rho_V=0.99$, b) a velocity uniformly perturbed by $\rho_V=0.9$, and c) an isotropic velocity with the correct vertical velocity. Superimposed onto the images are the RMO functions computed using equations 5 to 7. The solid line was computed when $\tan \gamma$ was derived from $\tan \widetilde{\gamma}$ by applying equation 11, whereas the dashed line was computed with the approximation $\tan \gamma \approx \tan \widetilde{\gamma}$.