The subsampled BP synthetic data were used as input to a two-stage, PEF-based interpolation algorithm. The first stage calculated a PEF using equation pefest, the second stage calculated missing data using equation interp. Both steps were solved with conjugate gradients. To deal with nonstationarity, the data were divided into 3-D rectangular patches, chosen to overlap so that every data sample (barring those along the edges of the input data cube) was in several patches. Along a single axis, a data point is typically in 1.5 to 2 patches, which translates to 3 to 8 3-D patches.
The results, shown in the next few sections in the prestack, stack, and radon domains, are mostly very good. After interpolation, Radon transforms and stacks of the data are basically indistinguishable from the same results using the full original data, and significantly better than the same results using the subsampled data.