4D binning & matching filters

§8.1 showed why dedicated 4D acquisition is the single biggest lever on repeatability. The next biggest lever is post-acquisition matching: identify the non-repeatability remaining in the data, estimate corrections from parts of the trace where baseline and monitor should agree, apply those corrections to bring the two surveys into alignment. This section covers two pillars of that matching: 4D binning (pairing traces by geometry) and matching filters (bringing paired traces into spectral/amplitude/phase agreement).

1. 4D binning — pairing traces by geometry

A streamer baseline and a streamer monitor will never have exactly repeated shot/receiver positions. 4D binning pairs each monitor trace with the nearest baseline trace in source-receiver position space. The distance in binning space between paired traces is called the bin diameter; typical values for dedicated 4D are 10–30 m. Larger bin diameter = larger residual non-repeatability.

• Near-source, near-receiver matching first; if not available, match far source or far receiver second.
• Source-receiver reciprocity allows pairing a source at A + receiver at B with a source at B + receiver at A. Doubles the bin population without doubling the acquisition cost.
• Cross-streamer matching is weaker than in-streamer matching because cross-streamer varies with feathering; track cable positions via GPS + compass data.
• Ocean-bottom nodes trivialise binning: nodes are stationary, so the receiver half of every bin is identical between surveys.

2. Matching filters — the principle

Given a binned baseline trace $B(t)$ and monitor trace $M(t)$, a matching filter is a linear operator $F$ such that

in the non-reservoir parts of the trace. The filter estimates and compensates for the non-repeatability between surveys. Three common forms of F:

• Scalar amplitude. F = $\alpha$, a single gain factor. Captures source-strength differences but nothing else.
• Time shift. F = delay by $\tau$. Captures tidal and geometry differences.
• Convolutional matching. F = convolution by a short filter $f(t)$ designed by Wiener to minimise $|M - f * B|^2$. Captures phase, spectral, and amplitude differences in one filter. The general case.

The critical design principle: estimate F using non-reservoir samples only. If you include the reservoir zone, F will partly match out the very 4D signal you are trying to preserve. Production flows define a "reservoir exclusion window" (typically ±100–200 ms around the target horizon) and compute $F$ on the remainder.

3. The widget — matching in stages

Set a 4D signal $\Delta R$, a non-repeat time shift, and a non-repeat amplitude scalar. The widget generates baseline and monitor, then applies matching in three stages:

• Raw: NRMS of raw difference.
• Amplitude match: estimate $\alpha = \text{RMS}(M_{non-res}) / \text{RMS}(B_{non-res})$, divide monitor by $\alpha$, recompute NRMS.
• Amp + time match: cross-correlate amp-matched monitor with baseline over non-reservoir samples, find the lag that maximises correlation, shift monitor by that amount, recompute NRMS.

At defaults (time shift = 3 ms, amplitude = ×1.08, 4D signal = 0.04), NRMS typically drops from ~50 % (raw) to ~15 % (amp) to < 5 % (amp+time). The reservoir residual stays at the 4D signal level because the non-reservoir estimator does not see it.

4. Why amplitude before time

Time-shift estimation uses cross-correlation $\sum B(i) \cdot M(i+\text{lag})$. If $M$ has a different amplitude from $B$, the correlation peak value is dominated by that amplitude difference, not by the lag. Matching amplitude first levels the two traces so the subsequent cross-correlation is in a well-posed regime. The difference in estimated lag between "amplitude-first" and "time-first" can be 30–50 % of a sample at typical 4D conditions.

5. Full convolutional matching (Wiener)

For surveys with spectral differences (different sources or Q differences), a scalar amplitude is insufficient. The Wiener filter $f$ minimises

giving a short FIR filter (typically 50–200 ms long) that captures the full frequency-domain mismatch between surveys. Production 4D processing routinely uses Wiener matching filters, often after an initial amplitude + time match to reduce the problem's dynamic range.

6. Window choice

• Too narrow a matching window → F is under-determined, overfits noise.
• Too wide → F absorbs 4D signal if the window wraps into the reservoir.
• Multiple disjoint windows (e.g., shallow + deep non-reservoir zones) usually give the best balance.
• Taper the window edges to avoid ringing in the filter design.

7. QC after matching

• Residual NRMS by time: plot NRMS as a function of TWT after matching. It should be approximately flat (lower NRMS above and below the reservoir, elevated only inside the reservoir window).
• Residual NRMS by offset: should be flat across the offset range; a rising trend indicates un-matched angle-dependent response.
• Spatial NRMS maps: plot NRMS per CDP location as a map. Localised high-NRMS zones often correspond to surface features (rivers, roads, weather fronts during acquisition).
• Reservoir isolation check: mask the reservoir zone from the difference and measure RMS. It should be below the expected 4D signal amplitude.

Where this goes next

§8.3 goes deep on the two main 4D QC metrics: NRMS and predictability. Where §8.1 introduced NRMS as a single number, §8.3 unpacks it as a spatially- and temporally-varying diagnostic, introduces the predictability metric (a cross-survey correlation), and catalogues the signatures of specific 4D failure modes.

References

• Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge UP.
• Claerbout, J. F. (1976). Fundamentals of Geophysical Data Processing. McGraw-Hill.