Random noise and frequency-wavenumber filtering
Treatment of random noise uncorrelated from trace to trace by f − k filtering is an important aspect of the process. Figure 6.2-2 shows a synthetic CMP gather which contains only band-limited random noise. Note that the f − k spectrum exhibits the random character of the data — there is energy at all wavenumbers up to the Nyquist and at all frequencies within the passband.
After the application of a narrow-fan f − k dip filter, note that the CMP gather contains coherent events with dips that correspond to the pass-fan in the f − k domain. By widening the pass-fan of the f − k dip filter, dip range of the coherent events in the gather is broadened as demonstrated in Figure 6.2-3. As the pass-fan is widened, the coherence of events in the gather becomes increasingly less apparent, while the randomness character becomes more predominant and eventually similar to that of the input gather.
Figure 6.2-4a shows a stack of several CMP gathers as in Figure 6.2-2a with band-limited random noise. Note that stacking of CMP gathers which contain just random noise yields a stack which contains, again, random noise. The f − k spectrum exhibits the random character of the stacked data — there is energy at all wavenumbers up to the Nyquist and at all frequencies within the passband. Figure 6.2-4b shows a stack of f − k filtered CMP gathers as in Figure 6.2-2b. Note that stacking of f − k filtered CMP gathers with random noise yields, once again, a section which largely contains just random noise, despite the nonrandom character of the input gathers (Figure 6.2-2b).
Figure 6.2-2 (a) A synthetic CMP gather with band-limited random noise uncorrelated from trace to trace; the same gather after f − k filtering with different pass-fans with dip bands: (b) (+2,-2) ms/trace, and (c) (+4,-4) ms/trace. The f − k spectra are shown at the bottom of each panel. Note that random noise in t − x domain maps onto a rectangular zone in the f − k domain, with its top and base corresponding to the low- and high-frequency end of the passband.
Figure 6.2-3 A synthetic CMP gather as in Figure 6.2-2 with band-limited random noise uncorrelated from trace to trace after f − k filtering with different pass-fans with dip bands: (a) (+6,-6) ms/trace, (b) (+8,-8) ms/trace, and (c) (+10,-10) ms/trace. The f − k spectra are shown at the bottom of each panel.
The stacked section in Figure 6.2-4a was displayed at a very high gain to differentiate the noise levels at shallow and late times. The reason why the noise level is stronger at the shallow portion is because the muting after NMO correction has caused lower fold in stacking, and hence less attenuation of the random noise during stacking. The stack of the CMP gathers with f − k dip filtering (Figure 6.2-4b) does not exhibit the organized character seen in the CMP gathers themselves (Figure 6.2-2b), because the stacked amplitudes are uncorrelated from one gather to another. The relatively higher amplitudes at late times in Figure 6.2-4b result from less attenuation of the organized noise on CMP gathers at late times during stacking — less attenuation, because the stepout of the organized noise at late times happens to be very similar to the moveout implied by the velocity function used in NMO correction.
- Statics corrections and frequency-wavenumber filtering
- Dip filtering of coherent linear noise
- Frequency-wavenumber multiple attenuation