Time-variant spectral whitening
Frequency attenuation and a way to compensate for it are illustrated in Figure 2.6-8. Let us assume that we have an input seismogram with amplitudes decaying in time, as depicted. Now apply a series of narrow bandpass filters to this trace. Examine the field record in Figure 2.6-1 and associate the filter panels with the traces sketched in Figure 2.6-8. Note that the low-frequency component of trace FL has a lower decay rate than the moderate-frequency component FM. Likewise, the moderate-frequency component FM has a lower decay rate than the high-frequency component of the signal FH. A series of gain functions, such as G1, G2, G3, can be computed to describe the decay rates for each frequency band. This is done by computing the envelope of the band-pass filtered traces (Figure 2.6-8). The inverses of these gain functions then are applied to each frequency band and the results are summed. The amplitude spectrum of the resulting trace has thus been whitened in a time-variant manner. This time-variant spectral whitening process is outlined in Figure 2.6-9. The number of the filter bands, the width of each band, and the overall bandwidth of application of time-variant spectral whitening are parameters that can be prescribed for a particular application.
Figures 2.6-10 and 2.6-11 show some field records before and after spiking deconvolution, respectively. Note that this process not only has compressed the wavelet, but also has tried to suppress any reverberations in the data. Refer to Figure 2.6-12 and note that time-variant spectral whitening mainly has compressed the wavelet without changing much of the ringy character of the data. Also note that little was done explicitly to the phase. Therefore, the action of time-variant spectral whitening may be close to a zero-phase deconvolution, although there is no rigorous theoretical proof of this.
In practice, one of the main differences between time-variant spectral whitening and conventional deconvolution is that the former seems to be able to do a better job of flattening the amplitude spectrum. This difference can be significant for broad-band data with large dynamic range.
Time-variant spectral whitening sometimes helps attenuate ground roll on land records by way of its spectral balancing effect. Note that, in Figure 2.6-13, spiking deconvolution with different operator lengths has failed to flatten the spectrum, sufficiently. On the other hand, following spiking deconvolution, application of time-variant spectral whitening has balanced the spectrum and thus attenuated the ground-roll energy.
The ability of time-variant spectral whitening in flattening the spectrum within the passband of stacked data is observed in Figure 2.6-14. Note that spiking deconvolution is fairly effective, but not sufficient, for attaining a flat spectrum (Figure 2.6-14b). Following time-variant spectral whitening, the spectrum is flattened within the passband of the data as seen in Figure 2.6-14c.
It is a requirement to prepare stacked data input to amplitude inversion with the broadest possible bandwidth and flattest possible spectrum. Hence, a processing sequence tailored for amplitude inversion almost always includes poststack deconvolution and time-variant spectral flattening steps.
Figure 2.6-8 A schematic illustration of the rate of decay of the frequencies in a seismic trace .
Figure 2.6-13 (a) A land record with its average amplitude spectrum (top) and autocorrelogram (bottom); (b) t2-scaling, (c) AGC scaling of amplitudes. Spiking deconvolution with operator length of (d) 160 ms, (e) 240 ms, and (f) 320 ms. (g) Spiking deconvolution using an operator length of 240 ms followed by time-variant spectral whitening.
- Time-variant deconvolution
- Frequency-domain deconvolution
- Inverse Q filtering
- Deconvolution strategies
- The problem of nonstationarity
- Gibson and Larner, 1982, Gibson, B. and Larner, K. L., 1982, Comparison of spectral flattening techniques: unpublished technical document, Western Geophysical Company.