The Gold Standard of Archaeology | Cross-Frequency Peak Association, Peak Merging and Track Continuity

1. A peak is conditional on its frequency bin

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A narrowband peak says that one direction, slowness or location is supported under the wavelength, aperture, noise and propagation conditions of that bin. It does not automatically identify the same physical source as a nearby peak at another frequency. Resolution changes with wavelength; array aliasing changes; coherent arrivals can split; and attenuation can suppress one source while another remains. Preserve frequency-specific estimates, widths, heights and quality measures before building tracks. If the processing pipeline stores only the final wideband curve, there is no way to audit whether continuity came from evidence or from the association algorithm.

2. Generate candidates before choosing identities

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Detect candidate peaks with a prespecified rule that accounts for local background, minimum separation and the expected number of sources only where justified. Retain more than the winning peak when several candidates are plausible. A low threshold creates many sidelobe candidates; a high threshold turns weak-source intervals into dropout. Record the spectrum grid and interpolation method because off-grid peaks may shift between bins. Candidate uncertainty can be expressed as a peak interval, covariance estimate or bootstrap cloud rather than a single coordinate. Association works on these uncertain candidates. It should not pretend that every pixel maximum is a known source.

3. Gate matches using physical and resolution limits

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A gate defines which peaks in adjacent bins could plausibly belong to one track. Its width should reflect angular or slowness resolution, grid spacing, expected dispersion and estimation uncertainty. A fixed one-degree gate across the entire band may be too tight at low frequency and too permissive at high frequency. In dispersive media, a genuine arrival can move systematically with frequency; in a non-dispersive far-field model, large motion may signal error or a different source. State the physical model behind the gate. Sensitivity analysis should widen and narrow it to show when identities change.

4. Solve association as a global assignment problem

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Nearest-neighbour matching is easy but can swap identities when tracks approach or when one source briefly weakens. A global assignment can minimise a cost built from distance, peak strength, uncertainty, spectral coherence and continuity across several bins. Dynamic programming, network flow or other assignment methods may be suitable, but the cost function carries substantive assumptions. Penalising births, deaths and gaps too strongly produces unnaturally long tracks; penalising them too weakly fragments one source. Publish the cost terms, scaling and tie rules. Where two assignments are similarly supported, retain both or mark the interval ambiguous instead of choosing silently.

5. Distinguish merging from poor resolution

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Two sources can produce two peaks at one frequency and one broad peak at another because resolution changes or the responses overlap. That is not proof that the sources physically merged. Conversely, a single distorted source can split into two local maxima. Inspect peak width, valley depth, bootstrap stability and model order together. A merged interval may be represented as a many-to-one association with uncertain identity on exit. Do not force two hidden tracks through one unresolved peak unless the model and surrounding bins support that interpretation. The honest state may be “two before, unresolved here, two after.”

6. Worked example: two arrivals cross in slowness

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A 24-sensor field array is analysed in 20 frequency bins. Below 45 hertz, two stable peaks sit near 0.18 and 0.25 seconds per metre. Between 45 and 52 hertz, the peaks approach, form one broad maximum and separate with reversed strength. Nearest-neighbour matching swaps the source labels after the crossing. A global association using uncertainty-aware distance and a one-bin merged state preserves two plausible tracks but marks identity through the unresolved interval as ambiguous. Reprocessing alternate windows shows the crossing is stable while the exact label is not. The archaeological report therefore supports two dispersive arrivals, not a fully determined identity for each branch.

7. Let tracks contain principled dropout

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A source may disappear from some bins because of low signal-to-noise ratio, spectral notches, interference, sensor response or thresholding. Allow short gaps only under a stated rule, and charge a cost for bridging them. Interpolate for visualisation separately from the evidence record. A long smooth line drawn through five missing bins can create a source that was never observed. Check whether dropout coincides across sensors, windows or methods; shared dropout suggests acquisition or propagation effects, while method-specific dropout may expose the detector. Track continuity is stronger when independent windows recover compatible candidates on both sides of the gap.

8. Changed-context transfer check: a frequency-stepped geophysical survey

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Consider a frequency-stepped electromagnetic survey over a buried wall and a modern service trench. Reflections shift with frequency because penetration, attenuation and resolution change. The same association logic applies: generate candidates, gate by physical expectations, allow unresolved intervals and distinguish interpolation from observation. The context changes the mechanism—reflections are not acoustic far-field directions—and therefore the cost model must change. A spatially smooth ridge is not automatically one archaeological feature. Ground truth from trenching, survey geometry and independent geophysical methods should challenge, not merely decorate, the track assignment.

9. Know when continuity is the wrong prior

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Continuity fails when sources turn on and off, propagation modes appear at cut-off frequencies, aliasing creates discontinuous jumps or two physical processes occupy the same coordinate. It also fails when bins are too widely spaced for local matching. Do not use a smoothness penalty to erase a genuine bifurcation. Compare independent association models and inspect the unlinked spectra. If the final interpretation depends on one arbitrary bin order, one peak threshold or one continuity penalty, report that dependence. A collection of frequency-specific detections may be more defensible than a small set of elegant but model-driven tracks.

10. Audit candidates, assignments and alternatives

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Archive the sensor geometry, windows, frequency bins, spectra, candidate lists, peak uncertainty, quality measures, gate formula, association cost, birth and death penalties, gap rule and software version. Save the complete assignment graph, not only selected tracks. Rerun with plausible peak thresholds, grid resolutions, cost weights and bin subsets. Reverse the frequency order as a diagnostic: a strongly path-dependent method may return different identities. Compare tracks across bootstrap resamples, time windows and at least one alternative estimator. Report stable source count, uncertain intervals and label swaps separately.

11. Frequently asked questions

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Is the closest peak always the same source? No; crossings, dropout and changing resolution can make nearest-neighbour matching swap identities. Can a track bridge missing bins? Sometimes, under a prespecified short-gap rule, but interpolation must be marked. Does one broad peak mean one source? Not necessarily; two unresolved sources can merge spectrally. Should tracks always be smooth? Only when the propagation model makes smoothness plausible. Can an algorithm settle an ambiguous crossing? It can rank assignments, but if evidence is insufficient the correct result remains ambiguous.

12. The gold standard separates peaks from source histories

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Cross-frequency tracking is an inference layer between spectral estimation and archaeological meaning. The gold standard keeps every candidate visible, matches peaks with uncertainty-aware physical gates, permits births, deaths, gaps and unresolved merges, and preserves competing assignments when labels cannot be fixed. It then tests the result across thresholds, windows and estimators. A source track earns credibility because its continuity survives these challenges—not because a plotting routine drew a persuasive line through frequency.