Angle-domain common-image gathers in generalized coordinates

Numerical Examples

This section presents numerical tests of the generalized theory by comparing the ADCIG volumes for elliptic and Cartesian coordinate systems. I generated the results using a shot-profile migration algorithm altered to account for elliptic geometry by replacing the Cartesian extrapolator, $E_{x_3}[\cdot]$, with an elliptic coordinate operator, $E_{\xi_3}[\cdot]$. In both coordinate systems, the implemented extrapolation operators were accurate to roughly $80^\circ$ (Lee and Suh, 1985) with respect to the extrapolation axis. The reader is referred to () for further implementation details on shot-profile migration in elliptic coordinates.

I calculated ADCIG image volumes for each shot-profile by following a three-step procedure: 1) generate image volume $I(\xi_1,\xi_3,h_{\xi_1})$ by computing the image for 64 subsurface shifts in $h_{\xi _1}$ at each point in every extrapolation step; 2) calculate ADCIG volume $I(\xi_1,\xi_3,\gamma)$ using the procedure described in (); and 3) output the image $I(x_1,x_3,\gamma)$ by sinc-based interpolation of single-shot ADCIGs to the global volume. Steps 1-3 were repeated for all shot-profile sections contributing to the final image.

Angle-domain common-image gathers in generalized coordinates