4D processing concepts & repeatability

4D seismic, more formally "time-lapse" seismic, is the practice of repeatedly imaging the same subsurface volume at different calendar times and comparing the images to track changes. The principal application is reservoir monitoring: fluid fronts migrating under injection, gas coming out of solution as reservoir pressure drops, compaction as a field depletes. A 4D dataset is two or more 3D surveys of the same target plus a processing chain designed to preserve the differences that reflect actual reservoir change while suppressing everything else.

1. What makes 4D hard

A reservoir pressure or saturation change typically perturbs the reflection coefficient at the reservoir horizon by 5-15 % of its baseline value. This is the 4D signal. Non-repeatability between baseline and monitor surveys, different shot positions, different tides, different source signatures, different noise, produces differences of the same order of magnitude or larger at every reflector in the volume. The signal is local to the reservoir; the noise is everywhere, including at the reservoir. If you subtract the two surveys directly, the reservoir change is typically invisible underneath the repeatability noise.

A successful 4D acquisition and processing flow drives the non-repeatability noise down to below the signal level, ideally at every reflector including the ones above and flanking the reservoir. That is what "repeatability" means in 4D.

2. Measure repeatability where nothing changed

In Figure 8.1 you record the same section twice, a baseline and a monitor, and subtract them. The monitor carries a real change, the reflections of a sand lens brightening by $\\Delta R/R$, and whatever non-repeatability you add: a static time shift, a gain mismatch, a shift that varies along the line and random noise. Your job is to find out how much non-repeatability the lens can survive, and how much of it cross-equalization can remove.

The figure opens on a realistic pair: a 1.5 ms static shift, a 5 % gain mismatch and 5 % random noise give an overburden NRMS of 34 %, and the lens, whose reflections brightened by 10 %, is buried; the reservoir window reads 31 %, 0.9 times the overburden. Set every non-repeatability control to zero and the overburden reads 0 % while the reservoir window reads 9.4 %: NRMS measures repeatability, and the 4D change shows only where it happened. Now add 2 ms of static shift at 30 Hz. The overburden jumps to 44 %, a little above the single-frequency law $200\\,|\\sin(\\pi f \\Delta t)| = 37\\,\\%$ because a Ricker wavelet carries frequencies above its peak, and every reflector reappears in (c). At 60 Hz the same 2 ms costs 79 %. A gain mismatch $g$ is cheaper, $200\\,|1-g|/(1+g)$, or 9.5 % for $g = 1.1$, about as large as the 9.4 % the lens change is worth, but it does not bury the change: it scales the lens too, whose reflections now change by $1.1 \\times 1.1 - 1 = 21\\,\\%$, so the reservoir window reads 19 %, 2.0 times the overburden, and the lens stands out partly because of the mismatch. A monitor 10 % weaker does the opposite: the lens changes by $0.9 \\times 1.1 - 1 = -1.0\\,\\%$ and the reservoir window reads 1.7 %, less than the change alone is worth. A gain error can fake or cancel a 4D signal, which is why the gain is matched in the overburden before anything is read.

The readout table measures NRMS in two windows: the overburden, from 0.30 to 1.20 s, where nothing changed between the surveys, and a window within 40 ms of the lens. Their ratio is the test: at 2 or more the change stands out, from 1.3 to 2 it is marginal, and below 1.3 it is buried. Cross-equalization finds one time shift and one gain in the overburden and removes them from the monitor. On the legacy pair of the last exercise it takes the overburden from 76 % to 44 %; the shift that varies along the line and the random noise remain, because no single shift and gain can remove them.

3. NRMS, the standard metric

The factor is 200 rather than 100 because the denominator is the sum of the two RMS values, so NRMS is the difference RMS as a percentage of the average RMS. It runs from 0 % for identical traces, through about 141 % for uncorrelated traces of equal energy, to 200 % for traces of opposite polarity (Kragh and Christie, 2002). It must be measured where nothing changed, usually the overburden, or the 4D signal itself counts as non-repeatability. Interpretation bands, the same as in Figure 8.1:

• NRMS below 10 %: excellent. Ocean-bottom nodes and permanent arrays reach it; small 4D changes are visible.
• NRMS 10-20 %: good. Dedicated streamer 4D surveys reach it; medium changes are visible, small ones marginal.
• NRMS 20-40 %: usable for large changes only, such as gas coming out of solution.
• NRMS above 40 %: poor. Only gross changes survive; usually a geometry mismatch or a legacy baseline.

Modern dedicated 4D surveys routinely achieve NRMS of 8-15 % over the non-reservoir section. A legacy-to-modern comparison (baseline from 1998, monitor from 2020) typically sits at 40-70 % no matter what you do.

4. Sources of non-repeatability

• Acquisition geometry. Shot and receiver positions not exactly repeated between surveys. For streamer data, the tow direction, cable feathering, and streamer depth all vary.
• Tides and currents (marine). Water column thickness changes; so does its velocity. A 20 cm tidal difference alone shifts two-way times by only about 0.3 ms, but a water-velocity change of a few m/s over a deep water column can shift them by a millisecond or more, enough to raise NRMS noticeably.
• Weather and sea state. Wind and swell modulate the hydrophone depth; surface noise differs.
• Source signature. Air-gun bubble period depends on source pressure, water temperature, and array geometry. A 5 % pressure difference modulates bubble amplitude at a specific frequency.
• Near-surface changes (land and shallow-water). Groundwater table, freeze-thaw, vegetation growth. These change the shallow velocity and statics between surveys.
• Processing differences. If baseline and monitor are processed with different flows (different filter settings, different demultiple parameters), the differences show up as 4D "signal".
• Overburden strain. A depleting reservoir compacts and the overburden above it stretches, lowering its velocity, so time shifts build up above the target; part of the 4D difference is therefore overburden response, not reservoir change.

5. Strategies to drive NRMS down

1. Dedicated 4D acquisition. Plan both surveys with identical shot-receiver grids, streamer layouts, and source arrays. Pre-plan and maintain positions to within meters.
2. Ocean-bottom nodes. Nodes sit on the seafloor permanently, exact repeatability by construction. The gold standard for 4D. Expensive but transformative.
3. Joint processing (Section 8.4). Baseline and monitor go through the same processing chain with shared parameters, eliminating processing-induced differences.
4. 4D binning and matching filters (Section 8.2). Post-acquisition, match traces from baseline and monitor by nearest-neighbour binning and apply a spectral / phase / amplitude matching filter.
5. 4D noise attenuation. Coherent shot/swell noise that appears in one survey but not the other can be attenuated by specific filters designed in the difference domain.
6. NRMS-aware QC (Section 8.3). Monitor NRMS through the processing chain; each processing step should either lower NRMS or leave it unchanged. A step that raises overburden NRMS is adding non-repeatability; a step that also shrinks the difference inside the reservoir window may be removing real 4D signal along with the noise.

6. What 4D can measure

• Fluid front tracking. Oil-to-water contacts move as injection proceeds. 4D shows the water sweep.
• Gas out of solution. As reservoir pressure drops below the bubble point, dissolved gas comes out and reflectivity brightens dramatically.
• Pressure depletion. Depletion lowers pore pressure and raises effective stress, which stiffens the rock frame and raises reservoir velocity; injection that raises pore pressure does the opposite and slows the reservoir down.
• Compartment identification. A reservoir with internal barriers shows 4D changes only in the compartments being produced; no-change zones mark the barriers.
• Compaction. The reservoir compacts as pore pressure drops and the overburden above it stretches; the stretched overburden slows down, producing time delays that grow with depth to the top of the reservoir, the well-known overburden time-shift signal in 4D.

7. What 4D cannot (easily) do

• Quantify absolute saturation. 4D tells you that saturation changed; converting to absolute water saturation requires rock physics and is imprecise.
• Very small reservoirs. Below thin-bed tuning, 4D signal is ambiguous.
• Very deep reservoirs. Accumulated non-repeatability noise scales with travel time; deep reservoirs have less favourable SNR.
• Image what never reflected. If the reservoir did not produce a seismic reflection in the first place (sub-tuning thickness, low impedance contrast), 4D changes are invisible too.

Where this goes next

Section 8.2 goes into the post-acquisition tools that reduce NRMS: 4D binning (match traces by nearest source-receiver geometry), matching filters (align spectra, amplitudes, phases), and 4D-specific denoise. These are the workhorses that take a 40 % NRMS raw dataset down to 10-15 %.

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.
• Kragh, E., Christie, P. (2002). Seismic repeatability, normalized rms, and predictability. The Leading Edge, 21(7), 640-647.