Make the inference visible before trusting it
Ambient vibrations can be correlated into useful inter-station responses, but a virtual source is an inference from the noise field, not a controlled pulse with uniform coverage.
Ambient-noise tomography uses continuous ground vibration rather than deliberately fired seismic sources. Cross-correlation between receivers can recover waveforms that approximate parts of the response between them, allowing dispersion or travel-time measurements and a velocity inversion. For archaeological targets, the attraction is quiet, repeatable acquisition. The central risk is that traffic, machinery, wind and other sources illuminate the array unevenly and change through time.
Frame the claimROUTE 02 · CHAPTERS 4–6
Work the evidenceROUTE 03 · CHAPTERS 7–9
Test transferROUTE 04 · CHAPTERS 10–12
Audit and continue
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Chapter contents
01 · Frame the claim
02 · Work the evidence
03 · Test transfer
State the target size, depth and physical reason for a velocity contrast. Disturbed fill, masonry, voided ground and moisture change can affect surface-wave dispersion, but several materials can produce similar values. Compare the expected wavelength range with the target dimensions before deploying sensors. Ambient noise is not a universal substitute for an active survey; it is useful only when the available frequencies and geometry can resolve the question.
Cross-correlating simultaneous records at two receivers can retrieve a response resembling waves travelling between them under suitable assumptions about the noise field and recording duration. One receiver is described as a virtual source, but it did not emit a known pulse. The recovered function depends on the distribution, direction, spectrum and stability of real noise sources. Treat the virtual-source language as a processing interpretation, not proof of complete Green’s-function recovery.
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Roads, generators, visitors and construction can dominate one azimuth or time window. A one-sided correlation, asymmetric causal and acausal arrivals, or strong day–night change can reveal unequal illumination. Plot beam direction, spectrograms and correlation asymmetry by time. Long recording can improve convergence but cannot guarantee an isotropic field when one persistent source controls the band of interest.
| Noise pattern | Diagnostic | Interpretive risk |
|---|---|---|
| Balanced arrivals | Similar causal and acausal energy | Still frequency-limited |
| One-sided arrivals | Persistent source direction | Biased virtual response |
| Time-variable band | Day–night spectral shift | Unstable dispersion |
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4. Extract dispersion only where the signal supports it
Surface waves of different periods sample different depths. Measure phase or group velocity across frequency with explicit signal-to-noise and uncertainty criteria. Avoid tracing a smooth dispersion curve through gaps simply because the software permits it. High-frequency near-surface work is vulnerable to short-lived local sources, sensor coupling and aliasing. Show representative correlation functions and rejected measurements, not only the final colourful section.
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5. Map illumination, path density and inversion smoothing
Each accepted station pair contributes information along a sensitivity region, not an infinitely thin straight ray. Dense station spacing can produce many pairs while leaving some directions or boundary cells weakly constrained. Display path and azimuth coverage, point-spread or checkerboard tests, regularisation and posterior or bootstrap uncertainty. Grid size is a display choice; it is not evidence that every grid cell is independently resolved.
| Coverage element | Show | Failure signal |
|---|---|---|
| Station pairs | Path and azimuth density | Many parallel paths only |
| Frequency | Usable period range | Depth inferred beyond wavelength |
| Resolution | Recovery or point spread | Cell size treated as resolution |
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6. Worked example: a buried foundation beside a service road
A courtyard array records two nights of vibration. The first velocity map shows a narrow high-velocity band aligned with a suspected buried wall. Inspection reveals that most usable correlations are parallel to the adjacent service road, and a checkerboard test smears compact anomalies along the same direction. Adding weekend data and a second line of sensors improves cross-azimuth coverage; the band persists but is broader than the trench plan. The defensible result is a resolved stiff zone consistent with masonry, not an exact wall outline.
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Repeat the workflow across day, night and independent recording blocks. Vary temporal normalisation, spectral whitening, frequency bands and station exclusions within defensible limits. A genuine structural feature should be reasonably stable, while source artefacts often track traffic schedules or one sensor. Processing choices can suppress transients and amplitude information; document them so stability is evidence rather than an unreported tuning result.
| Sensitivity check | Question | Warning |
|---|---|---|
| Independent stacks | Does the feature repeat? | Only one time block works |
| Processing variants | Is it parameter-stable? | Anomaly follows whitening choice |
| Station deletion | Does one sensor dominate? | Feature disappears |
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8. Changed-context transfer check: imaging a possible chamber
Move from shallow masonry to a possible subsurface chamber. The transferable method checks wavelength, noise direction, correlation recovery, coverage and resolution. The changed target may be deeper and smaller relative to wavelength, and a void can produce complex scattering rather than a simple low-velocity body. Combine passive results with radar, resistivity, gravity or active seismic evidence before calling a closed anomaly a chamber.
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Cross-correlation does not create information absent from the recorded wavefield. More hours do not repair the wrong frequency band, poor coupling or a permanently one-sided source distribution. A virtual source is not equivalent to a calibrated hammer. Smooth inversion can connect separate anomalies, and boundary structure is usually less constrained. Cultural noise can be useful signal, but its changing operation must be measured rather than assumed away.
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10. Audit the passive chain from vibration to interpretation
Archive continuous raw data, clock checks, sensor orientation and coupling, source-environment logs, preprocessing, correlation windows, stacking rules, rejected pairs, dispersion picks, sensitivity kernels, regularisation and recovery tests. Publish maps of azimuth and temporal stability. Refit after removing dominant source periods and compare with an independent method. The archaeological label should be attached only after the velocity inference survives these checks.
| Audit layer | Retain | Failure signal |
|---|---|---|
| Acquisition | Raw streams and clocks | Only stacks survive |
| Correlation | Windows and convergence | Virtual source assumed exact |
| Inversion | Coverage and regularisation | Map without resolution tests |
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Does ambient noise mean random noise? Not necessarily; it can include persistent and directional sources. Is a virtual source a real source? No, it is a response inferred from correlations. Does a dense array guarantee resolution? No; wavelength and illumination still control it. Can traffic help? Yes, if its directionality and frequency content are characterised. How long should recording last? Long enough for stable measurements in the relevant band, demonstrated by convergence rather than a universal duration.
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12. The gold standard makes missing illumination visible
A credible ambient-noise study defines a physical target, demonstrates recoverable frequencies, measures source directionality and shows where the array has sensitivity. It treats correlation, dispersion and inversion as separate inferential steps. Passive acquisition becomes powerful when quiet fieldwork is matched by loud methodological transparency: the strongest map is one that shows both the anomaly and the places the wavefield could not reliably see.
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Continue through verified routes
Core route
- Archaeology: subject root and specialist index
- The Gold Standard of Education: learning transfers into life
- The Gold Standard: eduKate Singapore
- How X Works: systems and first-principles hub
Specialist route
- Seismic attenuation tomography, amplitude decay and coupling bias
- Full-waveform inversion, cycle skipping and starting-model dependence
- Crosshole seismic tomography, ray coverage and inversion smearing
- Seismic reflection, velocity pull-up and migration artefacts
- Seismic refraction, velocity inversion and layer ambiguity
