Interpolating missing data : convergence and accuracy , t and f

Prediction error filters (PEFs) can be used to interpolate seismic data, in the time domain (Claerbout, 1992) or in the frequency domain (Spitz, 1991). The theory for PEFs assumes stationarity, so typically the data are considered a little bit at a time in patches, and assumed to be locally stationary within a patch. An alternative is to use nonstationary filters, which effectively sets the patch size to one sample (or slightly larger). With small patches, filter calculation is an underdetermined problem, and some method for controlling the null space is required to get a good result. In this paper, I compare some different strategies for controlling the null space on a test data set. A more basic (and presumably prior) choice is which domain to do the interpolation in. Interpolation in ( f , x) is well known. The frequency domain is fast, and both domains give good results on fairly noise-free data. Abma (1995) argues that (t , x) should resist noise better. Later in this paper, I test both domains with some sample noisy data, and my results confirm Abma’s conclusions.