4D noise discrimination (NRMS, predictability)

NRMS is the universal 4D repeatability metric, but it is a single scalar aggregating every type of non-repeatability into one number. An NRMS of 50 % could be 50 % amplitude mismatch (fixable with a scalar), or 50 % phase mismatch (needs a Wiener filter), or 50 % noise (impossible to remove). Production 4D QC uses a second metric — predictability — that responds differently to these different failure modes, turning the scalar NRMS into a two-dimensional diagnostic.

1. Definition of predictability

the maximum normalised cross-correlation between baseline and monitor, searched across a small lag window. By construction $P \in [-1, +1]$, typically close to +1 for good surveys. The normalisation by $\sqrt{\langle B^2\rangle \cdot \langle M^2\rangle}$ is the key feature: if monitor is a scaled copy of baseline ($M = \alpha B$), then $P = 1$ regardless of $\alpha$. Predictability is blind to scalar amplitude scaling. NRMS is not. Their joint response diagnoses the nature of the non-repeatability.

2. The four-quadrant diagnostic plane

The widget plots the (NRMS, P) point on a 2D plane split into four quadrants at NRMS = 30 % and P = 0.85:

• Excellent (low NRMS, high P): dedicated 4D acquisition + good processing. Small remaining NRMS is the 4D signal itself.
• Amplitude mismatch (high NRMS, high P): shape is correct, only overall level differs. A scalar or short Wiener filter recovers repeatability.
• Phase/shape mismatch (high NRMS, low P): different wavelet between surveys (different source, Q differences, time shift). Needs Wiener matching or Q compensation.
• Noise-dominated (low NRMS despite low P): correlation-killing noise. Either the signal is buried in noise or the two surveys are recording different things (e.g., different ambient seismicity). Unmatchable without noise attenuation.

Drag the four sliders to place the point in each quadrant and read the diagnostic. Note:

• Amplitude non-rep only (slider 2): moves right (higher NRMS), P stays near 1 → amp-mismatch quadrant.
• Time non-rep only (slider 3): moves right AND down → phase/shape quadrant.
• Random noise only (slider 4): moves right AND down, similar to phase mismatch, but the residual is incoherent rather than a systematic shape change.

3. Thresholds in practice

Production acceptance bands for the two metrics:

• 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 (wavelet differences); < 0.75 problematic.

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:

• NRMS is spatially uniform — low everywhere except inside the reservoir footprint.
• Reservoir footprint shows elevated NRMS 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 = attenuation / Q mismatch between surveys. Run Q compensation (§7.3) more aggressively or match Q between surveys explicitly.
• Spike at one time = localised reflector change, possibly 4D signal.
• Flat except at reservoir = ideal 4D data.

6. The matching-strategy decision tree

• Compute NRMS and P on the raw data.
• If in Excellent quadrant → ship the difference as the 4D result.
• If in Amplitude-mismatch quadrant → apply scalar amplitude balancing, re-measure NRMS.
• If in Phase/shape quadrant → apply Wiener matching filter designed on non-reservoir samples, re-measure.
• If in Noise-dominated quadrant → flag for noise attenuation workflow; matching filters will not help until noise is reduced.
• Repeat until NRMS + P both pass thresholds.

Where this goes next

§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

• 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.