Seismic image volumes are non-stationary. To estimate reasonable PE filters, I break the input image into small local volumes that are approximately stationary. After computing a coherency image using the method described above, I merge the local volumes to a single coherency image. Claerbout Claerbout (1994) implemented a method to split and merge a data volume into small local image volumes (patches).
To process an image volume, I split it into small local volumes, subvolumes. I then filter each subvolume individually and merge the resulting subvolumes back into a single output image volume. The split into individual subvolumes ensures that the local signal is approximately stationary and the filter step is optimal.
Figure 1 illustrates the data flow. The input data at the upper left hand is split into individual subvolumes (shaded rectangle). Next we find an optimal 1-D filter for each subvolume (symbolized by the elliptic symbol). The filtered subvolume is merged to the intermediate pre-whitened image volume at the top center of the flow chart.
Next we split the pre-whitened image into subvolumes (not necessarily of the same size as in the first filter step). We find the set of three 2-D filters as described in the companion paper Schwab (1997). The filter step yields three output images, which I discard.
The three PE filters are used to filter a corresponding subvolume of the original data, indicated by the elliptical operation symbol in the lower right corner of the diagram. This final filter step yields a single image output volume (shown at the bottom right) since it comprises a forward and adjoint filtering step.