Introduction

Data interpolation has been performed with the use of multidimensional prediction-error filters (PEFs) Claerbout (1999); Spitz (1991). However, methods to generate a prediction-error filter require regularly-sampled data. When the data are not regularly sampled, the data is first transformed to a regular grid (or multiple grids), and then the PEF is estimated on those copies of the data.

In the case of interlaced data (where traces are sampled at regular intervals) the PEF is stretched Claerbout (1999); Crawley (2000) such that the coefficients fall on the interlaced traces during convolution. This method can be used to estimate a PEF only in those circumstances, and relies on the assumption of scale invariance, where a stretched filter and an unstretched filter behave in a similar fashion.

In the case of a line of irregularly-sampled traces, a small PEF can be determined by dynamically stretching the filter so that it fits each trace pair. This method does not require the distance between traces to be cleanly divisible by the shortest distance, nor does it even require the data to be gridded in all dimensions. It also does away with many of the parameter choices needed by other PEF estimation methods for irregular data. The method is first tested on a simple plane-wave model, with promising results.