INTRODUCTION

Data interpolation can be cast as in inverse problem, where the known data remains constant, and the empty bins are regularized to constrain the null space. A two-stage linear approach was developed () where a prediction-error filter (PEF) is estimated on known data, and is then used to constrain the unknown data by minimizing the output of the model after convolution with the PEF. When the data is not stationary, a non-stationary filter has been used to fill the unknown data (). This gives better results than a patching approach, where the data is broken up into separate patches that are assumed to be stationary, largely because most data is smoothly non-stationary. In the case of sparsely (but regularly) sampled data, the non-stationary filter can be stretched over various scales to fit the data. Most recently, a PEF was estimated on irregularly sampled data by scaling the data to various grid sizes and simultaneously estimating a single filter on the various scales of data in a multi-scale approach ().

Here, I take the multi-scale approach for irregular data, and extend it to estimate a non-stationary PEF. I examine how to choose the parameters needed for this non-stationary PEF estimation, namely micro-patch size, scale choice, regularization, and filter size, and how they are related when using this estimation method. I use this approach to interpolate a poorly sampled 2D test case, where existing methods would fail, with promising results. I then interpolate a suitable 3D test case with very promising results, with the eventual goal of seismic data interpolation.