next up previous [pdf]

Next: Test 1: Elliptic Isochrons Up: Shragge: Generalized-coordinate ADCIGs Previous: Elliptic 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.


Subsections
next up previous [pdf]

Next: Test 1: Elliptic Isochrons Up: Shragge: Generalized-coordinate ADCIGs Previous: Elliptic coordinates

2009-04-13