2-D local-mono-plane wave annihilation

An early application of two-dimensional deconvolution was Claerbout's modification of Burg's two-dimensional filter to remove single plane waves from a dataset Claerbout (1992b). This modification constrained the filter to two columns so that only one linear event would be removed. After the plane waves were removed from a seismic section, events of interest such as faults, pinchouts, and migration artifacts would remain. This process was called LOMOPLAN for local mono plane annihilator.

The filter used in LOMOPLAN is shown below as Filter (8). The filter has only two columns that limit it to predicting and removing only one event in a window.  

$$\begin{array} {cc} a_{11} & a_{12} \\ a_{21} & a_{22} \\ 1 & a_{32} \\ \cdot & a_{42} \\ \cdot & a_{52} \end{array}$$ (8)

2-dimensional LOMOPLAN is used as a prediction-error filter, where the events of interest are those that are unpredictable. While the predicted events are just the difference between the input and the prediction-error output, the LOMOPLAN process stresses what cannot be predicted.