A simple two-dip example shows that both FX-decon and two-dimensional deconvolution retain the original signal. Figure 2 and Figure 3 compare the results of two-dimensional deconvolution and FX-decon in the noiseless case. The weak events seen in the difference sections are the result of the sampling used in creating the dipping events. Flat events may be completely removed using either of these techniques.
When noise is added, FX-decon and two-dimensional deconvolution show similar results, as seen in Figures 4 and 5. The noise is significantly attenuated, and the linear events are retained. Notice that the two-dimensional deconvolution removes more noise than FX-decon in the lowest window where no signal is present. Three windows in time and four windows in x with fifty percent overlap are used in Figures 4 and 5. The noise remaining at the top and bottom of the prediction section of Figure 4 is the original data, since the output is not predicted unless the filter covers a full set of data. This may be remedied by saving the filter after it is calculated and then applying it to a wider range of data. In this version of the two-dimensional deconvolution program, the calculation of the filter and the filtering is performed simultaneously.
Both processes applied to real data again show that the results are similar, as seen in Figures 6 and 7. In the shallow section, both filters have predicted the even-odd effect, where alternate traces have different amplitudes, since both filters can predict it. There were 16 overlapping windows in time and three windows in x in these examples.
The previous similarities between the processes are seen in the global image of a portion of a dataset created by Shearer1991 seen in Figures 8 and 9. Notice that there is some lineup of the noise with strong events in Figure 9. Otherwise, the FX-decon appears to do as well as two-dimensional deconvolution. A comparison using the full dataset is shown in Figure 10.
More significant differences are seen when 2-dimensional deconvolution and FX-decon are applied to random noise. The predictions shown by Figures 11 and 12 are seen to have lined up some of the random noise, but the FX-decon has left more noise than the two-dimensional deconvolution. This may be attributed to the greater degree of freedom FX-decon has in making predictions and to the extended length of the filter in the time domain.
FX-decon applies a prediction process to each frequency separately, while two-dimensional prediction-error filtering generates a single filter for each window. Figures 13 and 14 show the results of creating three dipping events with a high-cut frequency of 15 Hz. and another three dipping events with a low-cut of 35 Hz. and a high-cut of 60 Hz. While some differences may be expected when applied to events with different frequency ranges, the differences between the results are found to be small.
Events with amplitudes that vary spatially, even in what seems to be a predictable manner, tend not to be predicted well by either technique. Figures 15 and 16 show the comparisons. The weak events seen following the events in Figure 15 are caused by the finite width of the filter and the zeroed background. The main energy in Figure 15 is the same as Figure 16. Here, FX-decon may be considered to have a slightly better prediction, but no major differences are seen.