3D shot-profile migration in ellipsoidal coordinates

Future Work

Our main motivation for exploring alternative 3D imaging geometries is to facilitate the propagation of overturning events in all directions. While this study suggests this goal is achievable, we recognize that imaging overturning events is likely to be of greater significance in situations where: i) the illumination from downgoing waves is minimal (i.e. salt body shadow zones); and ii) the seismic data acquisition enables the recording of these events (i.e. wide apertures and long recording times). Currently, SEP has neither a demonstrative wide-azimuth data set (with an isotropic velocity model) for testing purposes nor the computational power to do so. However, the ellipsoidal coordinate shot-profile algorithm will, hopefully, be tested on an appropriate data set using an industrial-sized cluster.

Another issue warranting mention is the additional computational overhead associated with ellipsoidal coordinate shot-profile migration. Below is a short list discussing 3D migration issues in ellipsoidal (ECC) and Cartesian (CCC) coordinate systems:

• Both the inline and crossline migration aperture could be reduced in an ECC because, unlike in a CCC, an ECC spreads out naturally and increases the effective aperture. (Sufficient volume sampling is still required to obtain a good image.)
• Imaging in non-Cartesian coordinate systems require two additional full-volume interpolations, one each between the corresponding velocity models and image spaces. While the former interpolation is easily parallelized, the later requires spraying each ECC image point to a neighborhood of CCC points. This remains difficult to parallelize efficiently, except by expanding the image volume by a factor equal to the number of threads used for interpolation.
• Migration costs can be lowered, perhaps by an order of magnitude, by imaging neighboring shot profiles in the same ECC system.
• Because the ECC and CCC originate on the same initial surficial plane, no wavefield injection is required. However, the sampling of the two initial surfaces is different and requires an initial interpolation.

3D shot-profile migration in ellipsoidal coordinates