Suppose the data set is a collection of seismograms uniformly sampled in space. In other words, the data is numbers in a -plane. For example, the following filter destroys any wavefront aligned along the direction of a line containing both the ``+1'' and the `` ''.
A two-dimensional filter that can be a dip-rejection filter like (22) or (23) is
Fitting the filter to two neighboring traces that are identical but for a time shift, we see that the filter coefficients should turn out to be something like or , depending on the dip (stepout) of the data. But if the two channels are not fully coherent, we expect to see something like or . To find filters such as (24), we adjust coefficients to minimize the power out of filter shapes, as in
With 1-dimensional filters, we think mainly of power spectra, and with 2-dimensional filters we can think of temporal spectra and spatial spectra. What is new, however, is that in two dimensions we can think of dip spectra (which is when a 2-dimensional spectrum has a particularly common form, namely when energy organizes on radial lines in the -plane). As a short (three-term) 1-dimensional filter can devour a sinusoid, we have seen that simple 2-dimensional filters can devour a small number of dips.