One of these current methods of seismic data interpolation is a two-stage linear least-squares scheme Claerbout (1999), where a prediction-error filter (PEF) is estimated on some known data, and then the newly-estimated PEF is used to regularize the missing data. This method can use non-stationary PEFs, and can also work on coarsely-sampled data Crawley (2000). Most recently, methods for PEF estimation on sparse data have been developed for both stationary Curry and Brown (2001) and non-stationary Curry (2002) PEFs.
Since these methods are based on least-squares inversion, certain assumptions are made about the statistics of the noise, i.e. that the noise has a Gaussian distribution and zero mean. As such, least-squares methods are less successful when dealing with erratic, bursty noise. Erratic data can be dealt with by the use of an -norm Claerbout and Muir (1973), or by removing the data by preprocessing Abma (1995); Claerbout (1999). Existing -norm-based methods can be adapted to use a variable norm by the use of iteratively re-weighted least-squares (IRLS) algorithms Fomel and Claerbout (1995); Guitton (2000).
I improve the interpolation of bursty data by using an IRLS-based approach to estimate non-stationary PEFs on both regularly-sampled and sparse data. I then use this PEF to interpolate the data, again using an IRLS-based approach to fill in the missing data. I show how both changes can improve the interpolated result in the presence of erratic noise. I will first show this on a synthetic case with a simple noise model, and then on a 2D land data set.