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INTRODUCTION

Data interpolation is a long standing problem in exploration geophysics, especially in the case of 3-D land data. Many different interpolation methods exist, such as kinematic methods Chemingui (1999); Fomel (2001); Vlad and Biondi (2001), where the missing data is predicted with operators such as NMO or AMO, Fourier-based methods Schonewille (2000) that can now interpolate non-uniformly-sampled data, and prediction-error filter based methods, both in the f-x Spitz (1991) and t-x Claerbout (1992, 1999) domains.

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 $\ell^1$-norm Claerbout and Muir (1973), or by removing the data by preprocessing Abma (1995); Claerbout (1999). Existing $\ell^2$-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.


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Next: BACKGROUND Up: Curry: Iteratively re-weighted least-squares Previous: Curry: Iteratively re-weighted least-squares
Stanford Exploration Project
7/8/2003