Angle-domain common-image gathers in generalized coordinates

Discussion

Extending the above theory of generalized coordinate ADCIGs to 3D coordinate systems is fairly straightforward, though more difficult to implement numerically. () presents a theory for 3D Cartesian coordinates that specifies the differential travel-time expressions required to express the reflection opening angle, $\gamma$, in 3D Cartesian ADCIGs [see equation 16 in ()]. Applying Jacobian change-of-variable transformations to these equations should yield a 3D expression for reflection angle. Similar to 3D Cartesian coordinates, though, this quantity will depend on geologic dips and need to be computed by one of the two algorithms suggested by ().

Given that a 3D expression can be formulated, there are a number of coordinate systems well-suited to imaging steep geologic dips where 3D ADCIG volumes could be a good diagnostic tool for velocity analysis. () discusses how a judicious choice of 3D coordinate system depends greatly on the acquisition geometry and the desired migration geometry. For example, the migration geometries employed in shot-profile migration of wide-azimuth data sets are well-matched with 3D ellipsoidal meshes that enable high-angle and turning-wave propagation in all directions. Evaluating ADCIG image focussing in such a 3D coordinate geometry would then provide information on velocity model accuracy for steeply dipping reflectors - such as salt flanks. These somewhat speculative extensions, though, are beyond the scope of this paper and remain an active area of research.

Angle-domain common-image gathers in generalized coordinates