Up in the Air, Down in the Ground! (Ancient Engineering Secrets) | Stonehenge Access All Areas Ep 5

Morphogenesis of Cup-Shaped Depressions in Sarsen Stones

 

The entrance to the Long Barrow at All Cannings, showing natural cup shaped voids in the sarsens.

Sarsen stones (Palaeogene silcretes) are intensely indurated, composed almost entirely of quartz sand grains bound by syntaxial quartz overgrowths. Despite their extreme hardness and chemical stability, their surfaces frequently exhibit circular or sub-circular, cup-shaped depressions. Distinguishing natural geological features from anthropogenic modification (e.g. Neolithic cup marks) requires analysis of a feature's micro-morphology, formational context, and weathering history.

Why the boundaries are sharp

A sarsen boulder typically goes from fully indurated rock to friable or loose sand with little sign of a graded 90%/70%/50%-cemented halo in between — true both at a boulder's outer surface and at internal boundaries against inclusions. This is a property of how silica cementation works, not a gap in the rock record, and it underpins several of the mechanisms described below.

1. Precipitation happens at interfaces, not through a volume. Silica tends to come out of solution where conditions change abruptly — at the water table, at permeability boundaries, where groundwaters of different chemistry mix, or across redox/pH fronts. Once supersaturation is crossed, cementation proceeds rapidly along that interface rather than diffusing evenly outward. This is documented directly in an analogous deposit: tightly cemented sandstone lenses in the Fontainebleau Sand (Oligocene, Paris Basin) sit immediately within otherwise loose, unconsolidated sand, with the sharp contrast attributed to silica precipitating along a specific hydrological interface (Thiry & Maréchal, 2001).
2. The cement grows in discrete pulses, not a steady film. Cathodoluminescence imaging of Stonehenge sarsen Stone 58 shows the quartz cement built up as an initial thin zone followed by around sixteen separate growth generations (Nash et al., 2021) — direct evidence that cementation proceeded episodically through time. That doesn't by itself prove the boundary is spatially sharp, but it rules out "slow, steady, uniform thickening" as the model, and is consistent with a threshold-driven process.
3. Cementation chokes off its own further spread. As a patch of sand cements, its porosity and permeability collapse, diverting silica-bearing groundwater around the cemented zone rather than through it. Ongoing precipitation concentrates at the still-open margin instead of thickening a broad halo evenly. This permeability feedback — cementation progressively sealing off the flow that feeds it — is a generic feature of reactive transport in porous media, and it sharpens fronts rather than blurring them.
4. Most UK sarsens are groundwater silcretes, not pedogenic ones, and that distinction matters: groundwater silcretes form along specific subsurface flow paths and interfaces, favouring sharp contacts, consistent with UK sarsen's simple, structureless fabric and lack of pedogenic features such as geopetal or colloform structures. Pedogenic silcretes, which form within a soil profile through repeated wetting, drying and translocation, are generally understood to show more gradational or nodular boundaries tied to soil horizons — though I haven't found a source making that comparison explicitly for sarsen, so treat it as a reasonable extension of the general pedogenic-vs-groundwater silcrete literature rather than a confirmed point.
5. Timing: the Palaeocene–Eocene Thermal Maximum (PETM). Several independent strands of work link UK Palaeogene silicification — sarsen and the related Hertfordshire Puddingstone — to the PETM (c. 56–55.5 Ma), when elevated temperatures and weathering rates would have raised silica mobility and favoured rapid, localised precipitation (Worsley, 2019). This is a separate question from why the boundaries are sharp, but it supports treating UK sarsen formation as a comparatively brief, climatically distinctive episode rather than slow uniform diagenesis over millions of years.

Relevance to what follows. This isn't a fifth mechanism alongside the four below — it's the underlying reason several of them produce sharp-edged features rather than blurred ones:

• The sharp rim of a selective-dissolution void (mechanism 3) isn't created by the dissolution itself. It's inherited from the moment of cementation: the inclusion never took part in the silica cementation reaction, so the boundary between it and the surrounding cemented sand was already sharp the day the sarsen finished forming. Dissolution, much later, just empties out a void whose edge was sharp from the start.
• Root holes and burrow traces (mechanism 1) are preserved sharply for the same reason: the cementation front "freezes" whatever was already in the sand — including an open or sediment-filled tube — at the moment it reaches that point, rather than blurring it as growth proceeds.
• A sarsen boulder's own outer edge, where it meets the sand body it grew within, is the largest-scale expression of the same principle: a sharp boundary between sand that got drawn into the self-reinforcing cementation process, and sand just outside it that never did.

A note on terminology

"Gnamma" and "tafoni" are both sub-aerial weathering-pit terms — gnamma conventionally for granite, tafoni for sandstone — and both depend on processes that only operate at an exposed surface: rainwater ponding, lichen colonisation and the organic acids it produces, and freeze-thaw cycling. None of these operate on a stone that is buried. Applying either term to a depression that formed while a sarsen sat below ground is a category error, however similar the resulting cup-shape looks.

For the burial-context mechanism, the more accurate and lithology-neutral term is selective dissolution (sometimes "differential dissolution"): a softer or more soluble inclusion is preferentially removed from a chemically resistant host, leaving a negative cast. This is the same process documented in "omar" pits, where carbonate concretions dissolve out of Hudson Bay greywacke erratics. Reserve "gnamma" / "tafoni" for genuinely sub-aerial features; use "selective dissolution void" (or "primary void") for the burial-context equivalent.

Cup-shaped depressions in sarsens generally originate from four distinct mechanisms. The first predates the rock's induration entirely; the next two are post-lithification natural processes (one needing surface exposure, one needing burial); the last is human.

1. Primary Biogenic Structures (Root Holes & Worm Burrows)

These form within the original loose Palaeogene sand, before or during silicification — the cavity, or the trace of it, was already part of the sediment body when it hardened. This sets them apart from every other mechanism below, all of which act on the sarsen after it had already become rock.

Root holes (rhizoliths). A plant root grows down through the loose sand; when it later decays, it leaves a tubular void that becomes fossilised in place as cementation proceeds around it.

• Typically irregular and often tapering along their length, following the natural shape of a root rather than a true cylinder.
• May show smaller rootlets branching from a main channel.
• Walls are often knobbly/irregular rather than smoothly bored — a plausible source of the bumpy "mammillated" texture seen on some sarsen surfaces.
• Broadly vertical relative to the original ground surface at the time of growth, though exhumation and movement since can scramble the apparent orientation on a loose boulder.

Worm/invertebrate burrows (bioturbation). Burrowing animals active in the sand before it lithified left tunnels that are now preserved as traces — referred to formally as ichnofossils, with named genera such as Skolithos (simple vertical lined tubes) or Ophiomorpha (burrows with a distinctive knobbly, pelleted lining). Burrow ichnofossils are independently documented from the Sparnacian (basal Eocene) deposits of south-east England — the same general depositional package implicated in sarsen genesis — so they're a plausible, if not yet specifically confirmed for any individual sarsen, source for this kind of hollow.

• More uniform in diameter along their length than a root hole — a true tube rather than a taper.
• Orientation can be horizontal, inclined, or vertical depending on the producing organism's behaviour — less consistently vertical than root holes.
• May show a meniscate (stacked crescent) backfill structure in longitudinal section, or a distinct lining texture (e.g. Ophiomorpha's knobbly wall) — neither of which a root hole produces.

Distinguishing this category from mechanism 3 (below): there is no "missing inclusion" to account for. The cavity, or its sediment fill, was already present in that exact form before the rock hardened around it — it isn't evidence that something solid was once there and later dissolved away. A useful field check, where a fresh break or core is available: root holes and burrows typically continue as a recognisable tube into the rock at a fairly constant diameter, whereas a selective-dissolution void (mechanism 3) is usually a single, roughly isometric cavity the size and shape of one clast, not an elongated tube.

A root hole that happens to lie at or near the exposed surface can also act as the nucleating "seed" for a sub-aerial weathering pit (mechanism 2) — the two categories aren't mutually exclusive; one can be the starting point for the other.

2. Sub-Aerial Weathering Pits (Gnammas / Tafoni)

When sarsens are exposed on the surface, horizontal or gently sloping planes can develop weathering pits.

• Initiation: a structural "seed" — a localised pocket of incomplete silica cementation, a soft clay gall, or a root hole (see mechanism 1) — is generally required to start the pit.
• Mechanism: once a small depression is exposed, it acts as a micro-catchment for rainwater. Standing water, combined with humic/oxalic acids from endolithic lichens and freeze-thaw wedging, attacks the syntaxial quartz cement.
• Morphology: granular disintegration expands the pit into a bowl shape with a flared rim. The interior retains a rough, sandpaper-like texture, since dissolution removes the cement but leaves individual, un-sheared quartz grains palpable.

3. Sub-Surface Selective Dissolution (Primary Voids)

Sarsens that remained buried — in clay-with-flints, coombe rock, or other superficial deposits — are shielded from sub-aerial weathering but subject to constant sub-surface moisture.

• Mechanism: during Palaeogene silicification, migrating silica fluids frequently bypassed or encased non-siliceous inclusions — chalk clasts, clay galls, ironstone nodules, dense organic material. Over millennia, percolating groundwater dissolves or flushes out these softer inclusions.
• Morphology: because the surrounding silica matrix resists dissolution far more strongly than the inclusion did, the void does not expand into a bowl. It instead remains a comparatively faithful negative cast of the evacuated inclusion, with rim and interior geometry reflecting the original clast shape rather than the smooth, gravity-expanded geometry of mechanism 2.

4. Anthropogenic Modification (Cup Marks)

Human-made depressions, whether symbolic (rock art) or functional (grinding, polissoirs), can overlap in scale with natural pits — typically from a few centimetres up to around 20 cm in diameter.

• Mechanism: created through direct mechanical force — pecking, pounding, or grinding with another stone.
• Morphology: mechanical action fractures and shears quartz grains rather than dissolving the cement around them, producing a smoother, sometimes glazed or "bruised" interior with truncated grains — distinct from the loose, palpable grains of a dissolution feature.

Comparative summary

	Root hole / worm burrow (primary biogenic)	Gnamma / tafoni (sub-aerial)	Selective dissolution void (sub-surface)	Cup mark (anthropogenic)
Formed	Before/during lithification	After lithification, exposed	After lithification, buried	After lithification, human
Context	Within original sand body	Exposed surface	Buried	Usually exposed / portable stone
Shape	Tapering tube (root) or uniform tube (burrow)	Bowl, flared rim	Negative cast of inclusion	Hemispherical, regular
Interior texture	Knobbly (root) or lined/meniscate (burrow)	Rough, loose grains	Follows original inclusion surface	Smooth, glazed/bruised, sheared grains
Diagnostic check	Tube continues at constant width into the rock; no "missing clast" to explain	Lichen/weathering nearby	Burial history; matching inclusions elsewhere in matrix	Use-wear polish; fracture signatures under microscopy

Macroscopic description can suggest a category; confirming it generally needs field microscopy or thin-section work.

Are Stonehenge's Sarsens Really From West Woods?

A reanalysis of the sarsen fragments from Stonehenge argues that they point to many more sources than expected, some perhaps as far off as Sussex and Kent. The obvious question follows: does that unsettle the idea that the great standing stones came from West Woods?

When sarsen sourcing makes the news it is usually about the monoliths — the conclusion, from Nash and colleagues in 2020, that fifty of the fifty-two surviving standing sarsens share the chemistry of West Woods, on the Marlborough Downs about 25 km away. Less attention goes to the smaller stone fragments dug up across the site. When Ciborowski and colleagues analysed 54 of these in 2024 they called them debitage — a knapping term for the waste struck off while working stone — and found them more varied than the monoliths, drawn from at least three regions beyond West Woods.

A new paper in Archaeological and Anthropological Sciences — Michelaki, Barham, Gorton, Mahaney, Aufreiter and Hancock (2026) — reworks that same fragment dataset using raw element concentrations rather than the zirconium-normalised ratios of the original, and argues the picture is more varied still. I can’t judge the geochemistry, so what follows is what the paper claims.

The new paper makes a deliberate point of not calling this material debitage. It prefers the neutral “fragments,” on the grounds that “debitage” presumes human workmanship — waste from dressing stone — whereas some of these pieces may be natural detritus, weathered off bedrock and never worked by anyone. The distinction is not pedantry: as we shall see, it bears directly on what the fragments can and cannot tell us about the standing stones.

Fragments from all over

On the paper’s sorting, 33 of the 54 fragments can be tentatively tied to known sarsen sources, while the remaining 21 cannot be placed at all and appear to represent at least seven chemistries not documented anywhere yet. Some fragments are tentatively matched to sources well to the south-east — Hampshire, and possibly Sussex and Kent — though the authors are careful to say there are inadequate data to make any of these assignments firm.

They draw one striking implication from that. If some fragments really do derive from south-east England, which the last ice sheet never reached, then ice cannot have carried them, and intentional human transport over long distances is the only explanation left — a reading that fits the wider argument, made by Parker Pearson and colleagues, that Stonehenge deliberately gathered stone from across Britain. For once a critique from the Hancock group cuts against the glacial-transport idea rather than for it.

But the fragments are not the standing stones

Here is the distinction that matters, and that a quick headline will tend to blur. The fragments and the monoliths are not the same population of stone. They need not all come from dressing the great sarsens at all: some may be packing stones, hammerstones or pieces of broken-up earlier features, and — on the very point the paper’s terminology is at pains to keep open — some may be natural detritus that was never part of any worked stone. A varied bag of fragments is therefore perfectly compatible with a uniform set of standing stones. Indeed the original 2024 study already found the fragments more diverse than the monoliths; this paper widens that gap, but it does not invent it.

So finding more sources in the rubble does not, on its own, move the monoliths. The West Woods case for the standing stones rests on a different body of evidence — the analyses of the stones themselves, the Stone 58 core, the proximity of a large, dense silcrete field at the right distance, and the recent extension of the same chemistry to the outlying Cuckoo and Tor Stones. None of that is reanalysed here.

Where it does reach the monoliths

Two threads do connect back to the big stones, and they pull in the cautious direction.

The first is the method itself. If, as the paper argues, normalising every element to zirconium can mask real differences and manufacture apparent agreements — a hazard it says is acute when raw concentrations range over more than a factor of ten, as these do — then that charge applies wherever the technique was used, the monoliths included. The standing stones were placed at West Woods with the same normalised approach. The data behind that conclusion aren’t revisited here, but the tool used to reach it is exactly what the paper is questioning.

The second is more concrete, and I have checked it against the original data. Nash et al. published the full chemistry behind their conclusion, and only one Stonehenge monolith appears in it with the high-precision analyses that source-matching requires: the Phillips’ Core drilled from Stone 58 in the 1950s. The other fifty-odd standing stones were measured only by the coarser portable XRF, and were never individually tested against the sources this way — their West Woods attribution rests on resembling Stone 58, not on being matched to a source themselves. So “re-sourcing the monoliths” really comes down to re-sourcing Stone 58.

Running its core against all twenty source areas, the answer depends entirely on the method — and the dependence runs one way. The more the calculation leans on normalising to zirconium, the better West Woods looks; strip that step out and rank the sources on raw concentrations, as the critics prefer, and West Woods slides down the table.

Approach used on Stone 58’s core	Nearest source(s)	West Woods rank
Geometric mean of element/Zr ratios (Nash & Ciborowski’s own method)	West Woods	1st of 20
Element/Zr ratios, nearest-neighbour distance	Bramdean, Castle Rising	3rd
Raw concentrations, nearest-neighbour distance	Castle Rising, Piggledene	6th
Raw concentrations, ±50% agreement count	Castle Rising, Piggledene	8th

Under Nash and Ciborowski’s own geometric-mean method West Woods comes top, with a real margin — that is how they reached their result, and it is not a marginal call on their own terms. Without the normalising step, West Woods falls to sixth or eighth and the nearest neighbours become Castle Rising and Piggledene. So the assignment is real under one method and gone under another, and the thing doing the work is the zirconium step that both critique papers are arguing about.

Two caveats keep this honest, and both cut against over-reading it. The distant front-runner, Castle Rising in Norfolk, almost certainly owes its place to an accident of scale: Stone 58 is very low in zirconium, Castle Rising lower still, and a raw-concentration comparison simply rewards stones that are uniformly low — the very dilution effect that normalising to zirconium was meant to cancel. And the other near neighbour, Piggledene, lies about two kilometres from West Woods on the same stretch of the Marlborough Downs; on the geology they are all but the same place. So the non-normalised re-sort does not move Stone 58 off the Downs at all. It simply cannot separate West Woods from the source next door, while coughing up one spurious long-distance match. What it shows is not a different source, but that the headline precision — this stone, that hillside — is more fragile than it looks.

So what happens to West Woods?

On the strength of this paper, West Woods is not overturned as the source of the standing sarsens, and the authors do not claim it is. What erodes a little is the confidence attached to the headline figure. “Fifty of fifty-two from West Woods” is a tidy number; the picture from the fragments — many sources, much undocumented variability, signatures that overlap and won’t cleanly separate — and the behaviour of Stone 58 above, which can’t be told from its neighbouring valley once you change the sum, both point the same way: the silcrete chemistry of southern Britain may be too smeared-together for any single method to pin a stone to one hillside with great precision. That is a caution about resolution, not a new provenance.

It is also now the second such caution in a matter of weeks, after Pearce, Bevins, Ixer and Pirrie’s comment on the related arithmetic-similarity method. The two come from opposite ends of the field and agree on little else, but they converge on one unglamorous point: don’t let a processed number stand in for the raw data, and check every match against the plots and the petrography. The most likely upshot is not that West Woods is wrong, but that the next round of sourcing will have to lean less on a single clever statistic and more on the unglamorous business of looking hard at the rock.

Under Nash and Ciborowski’s own geometric-mean method, West Woods is the closest of all twenty sources, with a real margin — that is how they reached their result, and it is not a marginal call on their own terms. Read the same data without normalising, scoring each source by how many elements fall within ±50% of Stone 58, and West Woods drops into the bottom half. The table below shows every source on that non-normalised basis, closest first.

Source area (mean of 3)	Zr	Ba	Sr	TiO2	Hf	Nb	Y	Pass
Castle Rising	25	6.47	1.63	0.04	0.63	0.9	1.33	7/7
Piggledene	62	10.37	1.7	0.05	1.57	0.87	1.33	5/7
Lewes Road	56.67	64.7	11.23	0.05	1.17	1.03	1.17	4/7
Bramdean	60.67	30.83	5.17	0.05	1.27	1.33	1.13	4/7
Stoney Wish	77.67	35.83	4.5	0.06	1.8	1.27	1.2	3/7
Clatford Bottom	98	10.23	1.77	0.11	2.47	2.07	2.63	2/7
Standean	83.33	56.63	11.17	0.05	1.8	1.33	1.83	2/7
Sudbury	49.67	23.3	22.2	0.09	1.3	1.6	3.57	2/7
West Woods	96.33	32.43	1.83	0.12	2.27	2.4	2.2	1/7
Lockeridge Dene	133.33	17.67	2.47	0.13	3.33	2.3	2.53	1/7
Monkton Down	225	33.9	5.6	0.21	5.17	4.53	4	0/7
Totterdown Wood	188	19.6	4.13	0.09	4.67	2	2.13	0/7
Blue Bell Hill	201.67	91.83	10.43	0.15	4.67	3.8	1.83	0/7
Gestingthorpe 1	106.33	48.43	11.97	0.11	2.53	1.83	2.2	0/7
Mutter's Moor 1	415.67	140.83	13.3	1.75	10.2	32.8	7.17	0/7
Mutter's Moor 2	471.33	245	14.27	1.42	11.33	25.97	6.77	0/7
Valley of the Stones 1	436.67	88.8	8.2	0.56	10.47	10.67	5	0/7
Valley of the Stones 2	415.33	83.6	6.9	0.47	9.63	8.97	4.53	0/7
Lenham Quarry	433.33	58.73	10.73	0.28	9.73	6.17	3.13	0/7
Gestingthorpe 2	115.33	83.07	163.83	0.11	2.8	2.23	9.77	0/7
Stone 58 (reference)	37.67	12.1	1.27	0.06	1	1	1.13	–

within ±50% of the Stone 58 mean    outside ±50% (below 0.5× or above 1.5×). ICP-MS/AES data, Nash et al. (2020); ppm except TiO₂ (%).

On the fuller 12-element mean comparison West Woods passes 4 of 12, Castle Rising 11 of 12 and Piggledene 9–10 of 12 — but Piggledene fails on zirconium itself, the primary sorting element. The table shows where Stone 58 is not (West Woods) more reliably than where it is: the green for Castle Rising and Piggledene arises largely because all three are uniformly low in every trace element, so a ±50% test is easily met — the dilution effect that normalising to zirconium is meant to cancel. Piggledene also lies ~2 km from West Woods on the same downs. The table therefore shows non-resolution, not a Norfolk or Piggledene source for Stone 58.

References

Michelaki, K., Barham, D., Gorton, M. P., Mahaney, W. C., Aufreiter, S., and Hancock, R. G. V. 2026. “Geochemical Data Treatment and Interpretive Uncertainty: A Reanalysis of Stonehenge Stone Fragments (‘Debitage’).” Archaeological and Anthropological Sciences 18: 162. doi:10.1007/s12520-026-02518-1.

Ciborowski, T. J. R., Nash, D. J., Darvill, T., Chan, B., Parker Pearson, M., Pullen, R., Richards, C., and Anderson-Whymark, H. 2024. “Local and Exotic Sources of Sarsen Debitage at Stonehenge Revealed by Geochemical Provenancing.” Journal of Archaeological Science: Reports 53: 104406. doi:10.1016/j.jasrep.2024.104406.

Harding, P., Nash, D. J., Ciborowski, T. J. R., Maniatis, G., and Colman, K. 2024. “Earliest Movement of Sarsen Into the Stonehenge Landscape: New Insights from Geochemical and Visibility Analysis of the Cuckoo Stone and Tor Stone.” Proceedings of the Prehistoric Society 90: 229–251 (published online January 2025). doi:10.1017/ppr.2024.13.

Nash, D. J., Ciborowski, T. J. R., Ullyott, J. S., Parker Pearson, M., Darvill, T., Greaney, S., Maniatis, G., and Whitaker, K. A. 2020. “Origins of the Sarsen Megaliths at Stonehenge.” Science Advances 6(31): eabc0133. doi:10.1126/sciadv.abc0133.

Parker Pearson, M., Bevins, R., Bradley, R., Ixer, R., Pearce, N., and Richards, C. 2024. “Stonehenge and Its Altar Stone: The Significance of Distant Stone Sources.” Archaeology International 27(1): 113–137. doi:10.14324/AI.27.1.13.

Pearce, N. J. G., Bevins, R. E., Ixer, R. A., and Pirrie, D. 2026. “Arithmetic Approaches Alone Are Inadequate in Defining Similarity.” Journal of Archaeological Science: Reports: 105874. doi:10.1016/j.jasrep.2026.105874.

The Numbers Ain’t Enough

Reporting the arguments in a new comment paper on geochemical similarity methods

A comment paper has now been published in the Journal of Archaeological Science: Reports examining an arithmetic method for assessing geochemical similarity between artefacts and potential sources.

Pearce, N. J. G., Bevins, R. E., Ixer, R. A., and Pirrie, D. 2026. “Arithmetic Approaches Alone Are Inadequate in Defining Similarity: A Comment on Ciborowski and Nash 2026 ‘Defining Similarity: An Arithmetic Method for Archaeological Source Provenance Targeting Using Geochemical Data’.” Journal of Archaeological Science: Reports: 105874. 10.1016/j.jasrep.2026.105874 (ScienceDirect)

The method under discussion

Ciborowski and Nash (2026) proposed an arithmetic method that uses ratios of selected elements to zirconium, converts differences into percentages, and calculates the geometric mean of those percentages. They presented it as a straightforward way to compare artefacts with potential sources.

Pearce et al. (2026) assessed the application of this method to examples included in the Ciborowski and Nash paper.

Examples examined in the comment

The comment analyses two published datasets.

In the case of Neolithic and Bronze Age obsidian artefacts from Ustica, Pearce et al. report that the arithmetic method produced different source assignments from those reached through bivariate plots of elements such as Rb, Ba, Zr, Nd and U.

In the case of Stonehenge Stone 62 (a non-spotted dolerite), the comment notes that the arithmetic method identified Carn Goedog as a relatively close match. Pearce et al. point out that Carn Goedog is a spotted dolerite and that Stone 62 belongs to a different petrographic group, with differences also visible in compatible elements such as Ni and Cr.

Issues raised by the comment

Pearce et al. raise several points about the arithmetic approach:

• The results can change with small variations in input data, including those caused by rounding or normal analytical precision.
• The use of many rare earth elements can influence the outcome because these elements tend to behave similarly.
• The method as applied in the examples focuses on incompatible elements and does not incorporate compatible elements that may show variation between sources.
• Every element contributes equally to the final geometric mean, without adjustment for differences in analytical precision.
• Petrographic information is not included in the calculation.

The authors of the comment argue that these factors limit the reliability of the method when used on its own.

Alternative approach described

Pearce et al. advocate what they term a “total” approach, combining petrographic examination, mineralogical data, geochemical analysis and geological context.

Summary of the debate

Year	Paper	Main development reported
2020	Nash et al., Science Advances	West Woods suggested as source for most sarsens using pXRF and statistical analysis.
2024–2025	Hancock et al., Archaeometry	Re-examination of data for Stone 58 and discussion of methodological choices.
2025	Harding et al.	Additional stones linked to West Woods area.
Early 2026	Ciborowski & Nash	Arithmetic similarity method proposed.
June 2026	Pearce et al.	Comment examining the arithmetic method and its application to published examples.

Note on the paper

The comment by Pearce et al. (2026) focuses on the application and limitations of one specific arithmetic method. It does not claim to resolve the broader question of sarsen sources at Stonehenge.

References

• Ciborowski, T. J. R., and Nash, D. J. 2026. “Defining Similarity: An Arithmetic Method for Archaeological Source Provenance Targeting Using Geochemical Data.” Journal of Archaeological Science: Reports 69: 105513. 10.1016/j.jasrep.2025.105513
• Hancock, R. G. V., et al. 2024. “Stonehenge Revisited: A Geochemical Approach to Interpreting the Geographical Source of Sarsen Stone #58.” Archaeometry 67(1): 1–19. 10.1111/arcm.12999
• Harding, P., et al. 2024. “Earliest Movement of Sarsen Into the Stonehenge Landscape: New Insights from Geochemical and Visibility Analysis of the Cuckoo Stone and Tor Stone.” Proceedings of the Prehistoric Society 90: 229–251 (published online January 2025). 10.1017/ppr.2024.13
• Nash, D. J., and Ciborowski, T. J. R. 2025. “Comment on: Stonehenge Revisited.” Archaeometry 67: 1423–1436. 10.1111/arcm.13105
• Nash, D. J., et al. 2020. “Origins of the Sarsen Megaliths at Stonehenge.” Science Advances 6(31): eabc0133. 10.1126/sciadv.abc0133
• Pearce, N. J. G., Bevins, R. E., Ixer, R. A., and Pirrie, D. 2026. “Arithmetic Approaches Alone Are Inadequate in Defining Similarity: A Comment on Ciborowski and Nash 2026 ‘Defining Similarity: An Arithmetic Method for Archaeological Source Provenance Targeting Using Geochemical Data’.” Journal of Archaeological Science: Reports: 105874. 10.1016/j.jasrep.2026.105874
• Pearce, N. J. G., Bevins, R. E., and Ixer, R. A. 2022. “Portable XRF Investigation of Stonehenge Bluestone 62 and Potential Source Outcrops in the Mynydd Preseli.” Journal of Archaeological Science: Reports 44: 103525.