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The coefficients of a 2-D monoplane annihilator filter
are defined to be the same as those of a 2-D PEF
of spatial order unity; in other words,
those defined by either (1) or (2).
The filter can be lengthened in time but not in space.
The choice of exactly two columns is a choice
to have an analytic form that can exactly destroy
a single plane, but cannot destroy two.
Applied to two signals that are statistically independent,
the filter (2)
reduces to the well-known prediction-error filter
in the left column and zeros in the right column.
If the filter coefficients were extended
in both directions on *t* and to the right on *x*,
the two-dimensional spectrum of the input would be flattened.

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Stanford Exploration Project

4/27/2004