The Gold Standard of Archaeology | Multiple Concurrent Sources, Rank Selection and Peak-Splitting Artefacts

1. Define what counts as a source for the analysis

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A physical source, a propagation mode and a coherent arrival are not interchangeable. One vehicle can generate several frequencies and modes; several distant sources can overlap in one slowness cell. State whether the target is source locations, arrival directions, modes or coherent components.

The answer determines the appropriate model order. Counting spectral peaks without defining the entity being counted invites category errors.

2. Understand how mixtures enter the array covariance

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Array methods summarise correlations among sensor traces. Concurrent sources contribute components whose strength and coherence depend on frequency, window, geometry and propagation. If sources are highly correlated, the covariance rank can be lower than the physical source count. Noise and finite samples can inflate apparent rank.

Rank is therefore an operational property of the observed mixture, not a guaranteed census of emitters.

3. Recognise merging, masking and peak splitting

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Close directions can merge into one broad beam; a powerful source can mask a weaker neighbour. Sidelobes and grating lobes can add false maxima. High-resolution methods may split one imperfectly modelled arrival into several peaks when the steering model, calibration or covariance estimate is wrong.

Plot the array response for the actual geometry and frequency. A second maximum aligned with a known sidelobe should not be promoted to a second archaeological source.

4. Choose rank with several diagnostics

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Inspect eigenvalue spectra, information criteria, permutation or noise-floor comparisons and stability across neighbouring windows. No single elbow or threshold is universal. Small sample counts, coloured noise and coherent sources can undermine textbook rules.

Treat plausible ranks as a sensitivity set. If the interpretation changes from one to two sources under equally reasonable choices, report that ambiguity.

5. Separate sources using assumptions you can defend

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Delay-and-sum beamforming makes few separation claims but has limited resolution. MUSIC separates a signal subspace from noise and needs a rank. Sparse or deconvolution methods assume a parsimonious source map; blind source-separation methods assume structure such as independence.

Choose the method because its assumptions fit the field setting, not because it creates the sharpest image. Validate with synthetic mixtures matched to station geometry and measured noise.

6. Worked example: two roads and one buried-wall survey

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A square array beside an archaeological mound records an 18 Hz band. Conventional beamforming shows one northeast peak. MUSIC with rank three shows three sharp maxima, two near roads and one crossing the mound; the third is initially described as a buried-wall response.

Forward simulation with the array geometry shows that a single strong road source plus calibration errors can split into the same three maxima at rank three. Rank two remains stable across windows and matches simultaneous traffic logs. After sensor timing correction, the mound-crossing peak disappears. The report retains two unresolved road-related components and no structural claim.

7. Use frequency and time continuity carefully

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A real source may trace a continuous path over time or a consistent dispersion branch over frequency. Artefacts can also move smoothly because array sidelobes scale systematically with wavelength. Track peaks alongside power, phase residuals and source logs.

Do not force one identity through crossings or gaps. Allow components to appear, merge and separate, and show uncertainty when assignments are not unique.

8. Changed-context transfer check: simultaneous active impacts

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Move from passive traffic to two weight drops fired too close together. Source positions are known, but overlapping wave trains can still create a mixed covariance and misleading dispersion picks. The transferable task is source-count and separation validation.

The changed remedy may be experimental: increase time separation, code sources differently or repeat one source at a time. Better acquisition can be more reliable than a sophisticated separation algorithm.

9. Distinguish multiple sources from multiple modes

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Rayleigh and Love waves, body waves and scattered phases can arrive from similar directions with different polarisations or velocities. A multi-peak slowness spectrum may represent modes from one event rather than several emitters.

Use three-component polarisation, expected dispersion, source timing and propagation modelling. Label the result as components or modes until evidence supports a physical source count.

10. Audit model order and array calibration together

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Retain covariance construction, window count, regularisation, rank rule, steering grid, station timing, response functions and excluded channels. Repeat the result over ranks, subarrays, frequencies and bootstrap windows.

Calibration errors can mimic extra rank. A source-count analysis should be rerun after timing and orientation checks rather than treating calibration as a separate housekeeping step.

11. Frequently asked questions

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Does every MUSIC peak represent a source? No; rank, sidelobes and mismatch can create peaks. Can eigenvalues reveal the exact source number? Only under assumptions that often fail in field noise. Is one broad beam always one source? No; unresolved sources can merge. Should the sharpest method be preferred? Only when its assumptions and validation support the sharper claim.

12. The gold standard makes source count an inference

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Concurrent wavefields require more than peak picking. Define the counted object, test plausible ranks, calculate the array response, compare separation models and challenge every source with calibration and synthetic mixtures.

The gold standard accepts that some windows contain unresolved components. That uncertainty is more informative than converting every maximum into a source and every split peak into buried structure.