PEF-based methods can now deal with irregularly-sampled data Curry and Brown (2001); Curry (2002), where multiple rescaled copies of the data are used to estimate a non-stationary PEF. This multi-scale methodology has been shown to work on sparse synthetic data.
I use the multi-scale method on a prestack 2D land dataset from Colombia. The data suffers from many missing shots but the receiver coverage is relatively uniform, meaning that in source-receiver coordinates only one axis is poorly-sampled. In cmp-offset coordinates the coverage is not uniform in either the cmp or the offset axes. The multi-scale PEF estimation should be robust to this problem, however.
I test the interpolation with non-stationary, multi-scale PEFs in both source-receiver as well as cmp-absolute offset coordinates. In source-receiver coordinates, additional traces predicted by reciprocity are added, so that the known data looks like a grid of crossing tracks. The crossing tracks are quite reminiscent of the Madagascar interpolation problem Curry (2004); Ecker and Berlioux (1995); Lomask (1998, 2002, 2004). I also propose a method using two orthogonal 2D non-stationary single-scale PEFs, based largely on a proposed method for the Madagascar problem Curry (2004).