Bandwidth & spectral QC

Every step in this part either repairs traces or separates signal from noise, and every one of them can quietly damage the data while looking like it helped. The discipline that keeps you honest is bandwidth QC: before you touch anything, measure the frequency content the field actually recorded; after every step, measure it again. The job of processing is to recover geologically meaningful reflectivity from the recorded wavefield, and the recorded bandwidth is the budget you work within. You cannot create signal that was never recorded; you can only fail to lose it.

1. Investigate your bandwidth up front

Acquisition was designed around bandwidth: the source was tuned or selected for its frequency output, and the receivers and sample rate were chosen to capture a usable recorded band. So the first thing post-acquisition preprocessing should do is look at what you actually got. Run filter panels, narrow band-pass slices of a representative gather (for example 5 to 10, 10 to 20, 20 to 40, and 40 to 80 Hz), and inspect the amplitude spectrum. The panels that show coherent reflections mark your usable band; the panels that show only noise mark its edges. Record the low cut and the high cut. This baseline is the reference that every later step is judged against.

That baseline also feeds parameter choices elsewhere. At the residual-statics step (section 2.4), for instance, make the maximum static you allow larger than half the dominant period you just measured, $T_d/2 = 1/(2 f_d)$, so that reversed-polarity traces, which correlate best at a half-period shift, stand out. Bandwidth analysis is not a side activity; it informs the rest of the flow.

Figure 2.9 does this on a synthetic recording: measure its usable band from the data, run it through spiking decon, a low-pass and a matched final filter, and measure the band again after each step.

The figure opens on a low-pass at 35 Hz. Choose Raw first: in (a) the signal beats the noise from 5.5 to 56 Hz, 3.3 octaves, and in (b) the panels up to 80 Hz hold continuous reflections while the 80 to 120 Hz panel holds only noise. Spiking decon flattens the spectrum and thins the tuning thickness in (d) from 25.5 to 19.5 m, yet the usable band stays at 5.5 to 56 Hz while the noise outside it rises by 16.0 dB: you gained flatness, not new signal. The low-pass is the cautionary one: the display looks cleaner, yet the usable high cut drops from 56 to 45 Hz and that signal is gone. The matched filter, with its high cut on the recorded 56 Hz edge, keeps the band and removes 13.1 dB of noise outside it. It gains no bandwidth, because a linear filter scales signal and noise alike at every frequency.

2. Check before and after every step

Make a spectral plot a standing output of the flow, not a one-off. Compare the amplitude spectrum, and ideally a time-variant version since the earth absorbs the high frequencies with depth, before and after every operation: trace editing, statics, noise attenuation, each decon pass, radon demultiple, and the stack. The question at each step is the same: did the usable band survive, or did you trade signal for a cleaner-looking display? A step that narrows the band has cost you resolution, and you want to know that before you move on, not after the interpreter notices.

3. Match the final filter to the recorded band

The filter applied to the migrated data should fit the bandwidth of the recorded signal for any given time window. Hit that target and you have done nothing to hurt the data. The acceptable cut depends on the objective. A structural play, where you need to map a horizon or a fault, tolerates a lower high cut, because the structure is resolved at lower frequency. A stratigraphic play, where thin-bed thickness and pinch-outs are the prize, needs the full band preserved, low end and high end, with the filter optimized across the whole section because bandwidth varies areally and temporally. Use the Target control in Figure 2.9 to see the requirement change: a 30 Hz low-pass leaves a usable band to 40 Hz, which meets a structural target (a working rule of about 30 Hz for mapping horizons and faults; tuning, set by the dominant frequency rather than the top of the band, thickens only from 25.5 to 30 m) and fails a stratigraphic one.

References

• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Sheriff, R. E., & Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.