Angle-domain common-image gathers in generalized coordinates

Conclusions

I extend the Cartesian ADCIG theory to 2D generalized coordinate systems. The generalized ADCIG expressions related the reflection opening angle to differential traveltime operators and spatially varying weights derived from the non-Cartesian geometry. I show that these geometric expressions cancel out for coordinate systems satisfying the Cauchy-Riemann differentiability criteria, which include tilted Cartesian and elliptic meshes. The procedure for calculating ADCIGs in elliptic coordinates is very similar to that in Cartesian coordinates. I validate the approach by comparing analytically and numerically generated ADCIG volumes, and with tests on the BP synthetic data set. ADCIGs calculations are more robust where computed in elliptic coordinates than in Cartesian coordinate. I assert that this result is due to improved large-angle propagation and enhanced sensitivity to steep structural dips afforded by the coordinate transforms. Finally, the imaging advantages afforded by elliptic coordinates should improve the procedure of any migration velocity analysis approach that uses residual ADCIG curvature on steeply dipping reflectors to compute velocity model updates.

Angle-domain common-image gathers in generalized coordinates