Conclusions and Future Work

Non-stationary f-x domain interpolation appears to be a promising route to generate the vast quantities of data needed for surface-related multiple elimination. The process is embarrassingly parallel and leaves the data in a similar state as would be needed by subsequent processing algorithms. The process is also much faster than a t-x approach, and needs orders of magnitude less memory to run. However, the issue of non-stationarity in time is large, and impossible to ignore. This problem is more pronounced on the poorest-sampled axes, such as cross-line offset. Applying this non-stationary f-x methodology in time windows should hopefully address this problem.

One important thing to note is that while higher-dimensionality of the interpolation could improve the end result, this was only the case when the axis that was added was well-sampled, such as the in line source or inline offset axis. The addition of the 4 points on the cross-line offset axis did little to the end result.

In order to combine this approach with an extrapolator to quickly generate input data for a 3D surface-related multiple prediction, the next steps will be to apply this method in time-windows to address the time-non-stationarity issue as well as attempt to apply this method in the log-stretch frequency domain so that an efficient AMO operator could be applied.