Interpolation with locally stationary PEFs

  In this chapter I show how to interpolate seismic data using time and space domain prediction error filters. I describe the scale invariant properties of PEFs and describe the first of two methods for dealing with nonstationarity in the data. The first method is patching, dividing the data into small regions where stationarity can be reasonably assumed. I use patching in a synthetic data example where data aliasing degrades the results of Radon demultiple. Interpolating the data dealiases it, and improves the demultiple results. The interpolation is successful in the sense that it improves the result, but the accuracy of the interpolation is less than perfect, especially in areas of complicated moveout, where the stationarity assumption does not hold. With that in mind, I broach the second method of dealing with nonstationarity, a new smoothing-based method, which is described in detail in the third chapter.