EXAMPLES

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.

 

dips
Figure 2 Two-D prediction-error filtering

 

dipsfx
Figure 3 FX-decon filtering

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.

 

noise
Figure 4 Two-D prediction-error filtering. Notice how weak the noise is on the lower part of the output compared to Figure 5. The original data are output at the top and bottom because the filters have not been applied past the edges there.

 

noisefx
Figure 5 FX-decon filtering. Notice how strong the noise is on the lower part of the output compared to Figure 4.

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.

 

WGstack
Figure 6 Two-D prediction-error filtering applied to a Gulf of Mexico line.

 

WGstackfx
Figure 7 FX-decon filtering applied to a Gulf of Mexico line.

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.

 

transverse
Figure 8 Two-D deconvolution filtering of the horizontal component of Shearer's global image dataset. There is less ringing here than in Figure 9.

 

transversefx
Figure 9 FX-decon filtering of the horizontal component of Shearer's global image dataset. There is more ringing here than in Figure 8.

 

s2Dfx
Figure 10 Two-D deconvolution and FX-decon of the horizontal component of Shearer's global image dataset. Two-D deconvolution has passed less noise and produced fewer artificial lineups.

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.

 

rnoise
Figure 11 Random noise with two-D prediction filtering. There is less noise on output than seen in the comparable FX-decon output seen in Figure 12.

 

rnoisefx
Figure 12 Random noise with FX-decon filtering. There is more noise on output than seen in the comparable two-D prediction filter output seen in Figure 11.

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.

 

fdips
Figure 13 Dips of different frequency content with two-D prediction-error filtering

 

fdipsfx
Figure 14 Dips of different frequency content with FX-decon filtering

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.

 

conflict
Figure 15 Two-D prediction-error filtering applied to conflicting events with changing amplitudes.

 

conflictfx
Figure 16 FX-decon filtering applied to conflicting events with changing amplitudes.