Random Traces

The top left-side of Figure  shows a dataset composed of randomly generated seismic traces. The top right-hand-side shows the result of filtering this dataset with constant filters applied in three time windows corresponding to the top third, the middle third and the bottom third of the traces. The applied filters were: in the top window (4-12-90-125) Hz, in the middle window (4-12-60-90) Hz and in the bottom window (4-12-30-50) Hz. The bottom left-hand-side shows the same dataset filtered a different way: the top third and the bottom third were filtered as before, but the middle third was filtered with a linearly changing spectrum that matched the filters above and below at the window limits. The bottom right-hand side shows the difference between the two filtered datasets. As expected, there is no difference in either the top or bottom third of the datasets. In the middle dataset, however, there is a difference which is greatest at the limits between the three zones where the difference in the filters is greatest.

Figure  shows a time-frequency analysis of the original data on the left and the filtered data with the linear spectra on the right. Since the data are random traces, they have all the frequencies from 0 to Nyquist (250 Hz in this case). After the filtering the spectrum is shaped by the applied filters. The bold line represents approximately the high pass frequency of the filters applied at each sample. There is no evidence of distortion in the spectrum even though the spectrum was made to change sample-by-sample in the middle third of the dataset.

 

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Figure 5 Time-frequency analysis for random data. On the left, the time-frequency display of the input data and on the right the result of the filter with the linear spectrum. The white areas represent large amplitudes. The thick solid line represents approximately the high cut frequency of the filters in every window