The Gold Standard of Archaeology | Full-Waveform Inversion, Cycle Skipping and Starting-Model Dependence

1. Start with the archaeological target and wave physics

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Define the target as a physical contrast before choosing an inversion. A void, wall, ditch fill, weathered layer or buried foundation must alter velocity, density, attenuation or another modelled property at scales supported by frequency and geometry. State target depth, thickness, orientation and competing explanations. FWI is not a generic image enhancer; it estimates parameters inside a specified wave equation. If the selected physics ignores strong attenuation, anisotropy, three-dimensional propagation or source coupling, the inversion may force those effects into the velocity model.

2. Understand the forward problem first

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For each source, the forward model predicts the wavefield at receiver locations using the current subsurface parameters, source signature, boundary conditions and acquisition geometry. The inversion only makes sense if these ingredients are sufficiently accurate. Check timing, sensor coordinates, topography, source repeatability, coupling and waveform bandwidth. Preserve raw records and model preprocessing explicitly. A residual caused by a trigger delay is not geological information, yet gradient-based optimisation may turn it into a broad velocity change. Forward modelling tests should precede confidence in any recovered detail.

3. Treat the starting model as evidence, not housekeeping

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FWI normally uses local optimisation. It begins from a model and follows a descent direction, so the result can depend strongly on the initial large-scale velocity structure. Construct the starting model from independently defensible information such as refraction tomography, travel-time inversion, boreholes or smooth geological expectations. Show it alongside the final model. Compare several plausible starts rather than selecting only the run that resembles the expected archaeology. If different starts fit the data similarly but produce different features, the data have not uniquely resolved those features.

4. See why waveform matching is non-convex

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A conventional objective may sum squared differences between predicted and observed traces. Shifting one oscillatory waveform relative to another creates many local minima: different peaks and troughs can be paired. The objective landscape also changes with source wavelet, noise, missing physics and parameter trade-offs. Gradient descent can therefore reduce misfit while moving away from the correct model. Examine trace alignments and objective behaviour, not only a final global misfit number. A small residual is necessary but not sufficient when preprocessing or model flexibility allows the wrong wavefield to fit.

5. Diagnose cycle skipping before trusting detail

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Cycle skipping occurs when corresponding waveforms differ by enough phase that optimisation aligns the wrong cycle. A common rule of thumb links risk to a time shift near half a dominant period, but real multi-arrival data require trace-level diagnosis. Plot observed and modelled records, estimate time shifts by offset and frequency, and inspect where phase residuals jump. Low frequencies and long wavelengths enlarge the basin of attraction. If the acquisition lacks them, acknowledge the missing information rather than implying that more iterations will solve the problem.

6. Worked example: a buried wall from two starting models

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A seismic line crosses a suspected masonry foundation. Starting model A is a smooth velocity gradient derived from first arrivals; starting model B contains a shallow fast layer based on an uncertain historical map. Both inversions reduce waveform misfit by 70 percent. Model A yields one broad fast body beneath the trench, while model B retains two narrow fast bands. Synthetic recovery shows that the available low-frequency cutoff cannot distinguish the bands and that model B’s pattern persists even when no walls are simulated. The defensible result is a resolved fast zone, not two mapped walls. Targeted excavation or denser acquisition must decide the geometry.

7. Use multiscale and alternative objectives deliberately

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A common strategy begins with low frequencies, early arrivals or strongly smoothed models, then introduces shorter wavelengths and more complex wave modes. This can reduce but not abolish cycle skipping. Travel-time, envelope, optimal-transport, source-extension and wavefield-reconstruction objectives each change sensitivity and assumptions. Do not present a robust objective as universally immune. Document frequency bands, windows, stage transitions and stopping rules. Test whether recovered archaeological features appear before high-frequency refinement and remain stable under reasonable workflow choices.

8. Changed-context transfer check: a suspected chamber

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Move from a wall to a possible chamber beneath a monument. Air, loose fill and moist sediment can all lower effective velocity or alter attenuation. A starting model built from straight-ray travel times may smear a low-velocity zone upward, while FWI with inadequate three-dimensional geometry can sharpen the smear into a chamber-like outline. The transferable method compares starts, inspects phase alignment, tests synthetic alternatives and uses independent methods. The changed context adds access and conservation constraints, so the appropriate conclusion may be a bounded anomaly for further non-invasive study rather than a named chamber.

9. Know the limits and common misconceptions

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FWI is not automatically higher truth because it uses the full waveform. It may use only selected windows or an imperfect acoustic approximation. Smaller grid cells do not create resolution beyond wavelength, aperture and signal-to-noise. A lower objective value does not establish archaeological identity. Density and velocity can trade off, source errors can map into structure and two-dimensional models can misplace off-line objects. Regularisation, bounds and starting models add prior information. Report those choices as part of the result, not as neutral software settings.

10. Audit acquisition, optimisation and interpretation

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Archive raw waveforms, geometry, timing tests, preprocessing, source estimation, model parameterisation, bounds, objective definitions, regularisation, starting models, frequency stages and convergence histories. Publish representative observed-versus-predicted traces. Run synthetic recovery tests shaped like the proposed target and deliberately wrong alternatives. Repeat from multiple plausible starts and perturb calibration choices. Map where models agree, where only the data fit agrees and where gradients are weak. Archaeological interpretation should be cross-checked with excavation, boreholes or another geophysical method when feasible.

11. Frequently asked questions

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Does FWI use every part of a seismic trace? Not necessarily; windows and physics define what is used. Is cycle skipping just a poor final fit? No; the optimisation can achieve a lower fit while matching the wrong cycles. Can low frequencies fix everything? They improve convergence but do not remove geometry or model error. Why show the starting model? Because local optimisation can inherit its large-scale structure. Does a sharp anomaly identify a wall? No; material identity requires context and independent evidence.

12. The gold standard separates resolution from convergence

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A credible FWI study shows that the forward model is adequate, the start is defensible, corresponding waveforms are aligned and the target survives alternative workflows. It distinguishes a model that fits from a feature that is resolved and a feature that is archaeologically identified. The most useful result may be a broad, stable anomaly with explicit uncertainty. That result can guide the next survey without turning algorithmic sharpness into invented masonry.