For the most part, the results in the BP synthetic example later in this chapter are good. However, they could improve. Near offsets and wherever the data has strong curvature tend to be poorly interpolated. The assumption that we can divide the data into rectangular regions where it is composed of linear events with constant dip seems like a bad assumption. Events are strongly curved, their dips change over short ranges of offset, but they don't change abruptly. The dips change continuously and smoothly. In order to have a set of assumptions which better fit this observed quality of the data, I extend the notion of time-variable deconvolution Claerbout (1997) to time- and space-variable interpolation. As an alternative to dividing the data into independent regions, we can estimate a PEF for every data sample, and use a smoothness criterion to calculate smoothly-varying filters to fit the smoothly-varying dips in the input data. This is the subject of the next chapter.