The interpolation of a 3-D data set by a pair of 2-D filters

Seismic 3-D field data is often recorded as a set of relatively sparse and often irregular 2-D lines. Under the assumption that the data consists of the superposition of local plane waves, such data can be interpolated by prediction-error techniques using a set of two 2-D filters instead of the conventional single 3-D filter. The two 2-D prediction-error filters are found by two independent linear minimization problems along sets of parallel linearly-independent lines. A third linear minimization yields the missing data. Fortunately, such an approach avoids the nonlinear minimization that is required when trying to find simultaneously the missing data and the 3-D filter on a sparse 3-D data set.