Time-variant filtering
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| Series | Investigations in Geophysics |
|---|---|
| Author | Öz Yilmaz |
| DOI | http://dx.doi.org/10.1190/1.9781560801580 |
| ISBN | ISBN 978-1-56080-094-1 |
| Store | SEG Online Store |
The seismic spectrum, especially the high-frequency end, is subject to absorption along the propagation path because of the intrinsic attenuation of the earth (gain applications). Consider the portion of a stacked section and its narrow band-pass filtered panels in Figure 1.1-31. A signal is present from top to bottom within the 10-to-20-, 20-to-30-, 30-to-40-, and 40-to-50-Hz bands. Not much signal is noted below 3.5 s in the 50-to-60-Hz band. Nevertheless, the signal content appears to be retained down to 3.5 s with the 60-to-70-Hz band. Finally, the 70-to-80-Hz band shows signal down to 2.5 s. Higher frequency bands of useful signal are confined to the shallow part of the section. Thus, temporal resolution is reduced greatly in the deeper portion of the section.
From a practical standpoint, the time-variant character of the signal bandwidth requires an application of frequency filters in a time-varying manner. By so doing, the ambient noise, which begins to dominate the signal at late times, is excluded and a section with a higher signal-to-noise ratio is obtained. Table 1-11 lists the time-variant filter (TVF) parameters selected from the panels in Figure 1.1-31. The filtered section is shown on the far right panel of the same figure. In practice, the filters are blended across adjacent time windows to establish a smooth transition of the passband regions.
A second band-pass series of filter scans, which is shown in Figure 1.1-32, allows an assessment of the right choice of the bandwidth for a given time gate. Here, we start with a narrow band-pass filter at the low-frequency end of the spectrum and gradually broaden the passband by including higher frequencies.
For some data, the bandwidth may be kept quite large from top to bottom. The stacked section in Figure 1.1-32 can tolerate wide-band filtering from early to late times. The filter panels for the stacked section in Figure 1.1-33, however, indicate that the signal band rapidly becomes confined to lower frequencies at late times. A signal is present from top to bottom within the frequency bands up to 40 Hz. Noise is noted below 2.5 s in the 40-to-50-Hz band. This noise quickly builds up to shallower times at a higher frequency band.
| Time, ms | Filter Band, Hz |
| 0 | 5, 10-70, 80 |
| 2500 | 5, 10-60, 70 |
| 3500 | 5, 10-50, 60 |
| 5000 | 5, 10-40, 50 |
Figure 1.1-31 The far left panel is a portion of a CMP stack without filtering. The following panels show the same data with different narrow band-pass filters. The frequency bands specified correspond to the corner frequencies B and C in Figure 1.1-26. Appropriate slopes were assigned to both low- and high-frequency ends of each passband. The far right panel is the same section as that in the far left panel after the application of the time-variant filter specified in Table 1-11.
Figure 1.1-32 The far left panel is a portion of a CMP stack without filtering. The remaining panels show the same data with different band-pass filters which have increasingly wider passbands. The frequency bands specified correspond to the corner frequencies B and C in Figure 1.1-26. Appropriate slopes were assigned to both low- and high-frequency ends of each passband.
Figure 1.1-33 The upper far left panel is a portion of a CMP stack without filtering. The remaining panels show the same data with different narrow band-pass filters.
Time-variant filters typically are applied on stacked data. A uniform bandwidth must be established when filtering two sets of data that may have different vintages, source types, or noise levels. This is especially significant when trying to tie two lines and follow a reflector across them. The interpreter uses the frequency character of a marker horizon as a reference in the tracking procedure. Therefore, two intersecting lines should be filtered so that the reflection character is consistent from one to the other, thus simplifying the interpretation.
See also
- Analog versus digital signal
- Frequency aliasing
- Phase considerations
- Time-domain operations
- Convolution
- Crosscorrelation and autocorrelation
- Vibroseis correlation
- Frequency filtering
- Practical aspects of frequency filtering
- Bandwidth and vertical resolution
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