4D noise discrimination (NRMS, predictability)

NRMS is the universal 4D repeatability metric, $\\mathrm{NRMS} = 200\\,\\mathrm{rms}(M-B)\\,/\\,(\\mathrm{rms}\\,B + \\mathrm{rms}\\,M)$ in percent, measured in a window with no production. It runs from 0 % (identical traces) through 141 % (uncorrelated traces of equal energy) to 200 % (polarity reversal), and it aggregates every kind of non-repeatability into one number. An NRMS of 50 % could come from a monitor about 1.67 times too loud (fixable with a scalar), from a static of about 3 ms or a phase rotation of about 29^\\circ (fixable with a matching filter), or from random noise (not removable by matching). Production 4D QC adds a second metric, predictability, that separates the differences a filter can fix from the one it cannot.

1. Definition of predictability

Kragh and Christie (2002) define predictability over a window of lags $\\tau$: $\\phi\_{bb}$ and $\\phi\_{mm}$ are the autocorrelations of baseline and monitor and $\\phi\_{bm}$ their cross-correlation. PRED measures how well the monitor can be predicted from the baseline by a linear filter. A scalar ($M = \\alpha B$) scales the numerator and the denominator alike; a static slides $\\phi\_{bm}$ sideways without changing its shape, and the lag sum still collects it; a phase rotation or a change of bandwidth is also a filter. All of them leave PRED near 1. Only a difference that no filter can produce, above all random noise, pulls it down. Summed over every lag PRED would be exactly 1, so the lag window is kept a little wider than the largest expected shift. The zero-lag correlation $r = \\langle BM \\rangle / \\sqrt{\\langle B^2 \\rangle \\langle M^2 \\rangle}$ is a different quantity: it falls for a static or a phase rotation as well as for noise, so it cannot tell them apart.

2. The NRMS and predictability plane

Figure 8.3 opens on a monitor 0.85 times as strong as the baseline and 3 ms late, with noise at 25 dB S/N in both surveys. NRMS in the overburden is 52 %, yet PRED is 0.99, and matching, scored on overburden samples its filter never saw, brings NRMS to 10 %: the difference was large and nearly all of it was fixable. The plane in (d) has three useful regions:

• Repeatable (NRMS below about 15 %, PRED near 1): dedicated 4D acquisition and careful processing. What remains in the overburden is residual non-repeatability, and the 4D signal is judged against it in the reservoir window.
• Matchable (high NRMS, high PRED): the surveys differ by something a filter can undo, such as a scalar, a static, a phase rotation or a bandwidth change from a different source. A Wiener matching filter designed in the overburden brings NRMS down.
• Noise-limited (high NRMS, low PRED): the difference is unpredictable, from swell, rig noise, or a changed acquisition footprint. Matching cannot fix it; noise attenuation or rejection of the traces can.

Low NRMS with low PRED does not occur: noise raises NRMS as it lowers PRED, so the pair slides right and down together, along the dotted pure-noise curve in (d). The exercises under the figure isolate each cause:

• Amplitude only: at a scalar of 0.70, NRMS rises to about 35 % while PRED stays at 1.00; switch on the matching filter and the point after matching lands in the top-left corner of (d), NRMS about 2 % with PRED 1.00.
• Static only: at 4 ms, NRMS jumps to about 68 % and the zero-lag correlation $r$ falls to 0.77, but PRED stays at 1.00; the static is fully matchable.
• Phase only: a 30^\\circ rotation gives an NRMS of about 53 %, close to 200 \\sin 15^\\circ = 52 %, with PRED still 1.00.
• Noise only: at 10 dB S/N the point moves right and down to NRMS 45 % and PRED 0.84, and matching, scored on samples its filter never saw, does not lower NRMS (50 %). This is the one failure PRED flags, though mild noise, at 15 to 20 dB, lowers PRED only to about 0.95 to 0.98: judge it by what matching removes.
• Production: with the reservoir top changed by +0.05 and 4 ms of pull-down, the reservoir window reads NRMS 48 % while the overburden still reads 2 %. Measured there, the 4D signal would be mistaken for non-repeatability, and a filter matched there would absorb it.

3. Thresholds in practice

Production acceptance bands for the two metrics (the hairlines in (d)):

• NRMS: < 15 % target for OBN or dedicated 4D streamer; < 25 % for best-effort streamer; 25-40 % for legacy-to-modern comparisons; > 40 % flags major issues.
• Predictability: > 0.95 ideal; 0.85-0.95 good; 0.75-0.85 marginal; < 0.75 poor.

Both should be measured per CDP (spatial map) and per time window (depth), not just as global averages. Spatial maps reveal localised issues (rivers crossing the survey, weather events during acquisition); time-varying maps reveal overburden changes that hurt repeatability at some depths more than others.

4. Spatial NRMS maps

Plot NRMS per CDP bin across the survey area. In good 4D:

• Mapped in the overburden window, NRMS is spatially uniform and low.
• Mapped in the reservoir window, the production footprint stands out above that background, localised to the changed region.
• Non-reservoir areas all show comparable NRMS regardless of position.

Common spatial pathologies:

• Coherent bands of elevated NRMS = weather or sea-state artefacts during one acquisition.
• Radial pattern centred on a shot line = source problem on that line.
• Pipe/platform shadows = infrastructure installed between surveys.
• Sparse high-NRMS dots = outlier traces (bad shots, tangled streamers).

5. Time-varying NRMS

NRMS vs TWT is also diagnostic:

• Rising NRMS with time = falling S/N with depth, or an attenuation (Q) mismatch between surveys; if PRED stays high as NRMS rises, suspect Q and run Q compensation (Section 7.3) or match Q explicitly.
• Spike at one time = localised reflector change, possibly 4D signal.
• Flat except at reservoir = ideal 4D data.

6. The matching-strategy decision tree

1. Compute NRMS and PRED in the overburden on the raw data.
2. If NRMS is low and PRED is near 1 → ship the difference as the 4D result.
3. If NRMS is high and PRED is high → apply a Wiener matching filter designed in the overburden (it absorbs scalar, static, phase and bandwidth differences) and re-measure.
4. If PRED is low → flag for noise attenuation or trace rejection; matching filters will not help until the noise is reduced.
5. Repeat until NRMS and PRED both pass thresholds.

Where this goes next

Section 8.4 closes Part 8 with the modern joint-processing approach: rather than process baseline and monitor independently and match the outputs, process them together with shared parameters and data-driven regularisation that enforces repeatability at every stage. The result is a lower NRMS at lower cost than post-acquisition matching.

References

• Kragh, E., Christie, P. (2002). Seismic repeatability, normalized rms, and predictability. The Leading Edge, 21(7), 640-647.
• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Claerbout, J. F. (1976). Fundamentals of Geophysical Data Processing. McGraw-Hill.
• Oppenheim, A. V., Schafer, R. W. (2009). Discrete-Time Signal Processing (3rd ed.). Prentice Hall.