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From Antarctica to Iceland and Yellowstone: A Geometric Framework

May 22, 2026May 22, 2026 Steingrimur Thorbjarnarson

The influence of mantle convection upon the Earth’s surface can be examined through the tectonic patterns that develop above it. In this study, several recurring geometrical expressions are considered. First are the division lines between convection rolls. Second are the polygonal regions enclosed by those division lines, where geological structures frequently develop from one corner of a polygon to another, commonly in north–south or east–west directions. A third recurring expression is the appearance of elliptical forms under certain large-scale conditions.

These observations suggest that many aspects of geology may be investigated through geometric analysis. Once geometric consistency is identified, detailed geographic and geoscientific data can be used to further evaluate the resulting patterns and their possible physical significance.

The Pacific Ring of Fire provides an important example. Although the exact physical processes governing its overall geometry remain uncertain, the arrangement itself displays remarkable large-scale regularity. Antarctica presents a similar challenge. Its tectonic framework is difficult to explain in simple terms, yet its geometry also appears highly organized.

Antarctica is particularly difficult to examine because most world maps distort the continent, stretching it along the southern edge of the map projection. When viewed directly from above the South Pole, however, its remarkably circular form becomes evident. It is also well known that Antarctica can be divided into East and West Antarctica, with the western sector being considerably more tectonically and volcanically active.

The boundary between East and West Antarctica appears to coincide closely with the center of the minor axis of the system of mid-ocean ridges encircling the continent. Near this axis lies the famous volcano Mount Erebus, one of the most persistently active volcanoes on Earth. Because Erebus is located at approximately 77.5°S latitude, its distance from the inferred minor axis is only about 100 km.

Another important geometric relationship emerges offshore from Erebus. At this location, the minor axis of the Antarctic system appears to intersect the minor axis of the Pacific Ring of Fire. Thus, the most active volcano in Antarctica occupies a position where two large-scale tectonic geometries appear to converge: the minor axis of the Antarctic ring of mid-ocean ridges and the minor axis of the Ring of Fire.

This geometric axis can then be examined further in relation to external geological conditions. When the Antarctic minor axis is extrapolated northward, it intersects the inner margin of the Ring of Fire at the location of the Valley of Geysers on the Kamchatka Peninsula. A similar relationship appears when extending the major axis of Antarctica northward toward the East Pacific Rise, where the projected line crosses the region of Yellowstone National Park, also situated at the geometrical margin of the Ring of Fire.

These two regions, Kamchatka and Yellowstone, contain by far the greatest concentration of geysers on Earth. Beyond them, only a few additional major geyser regions exist worldwide, and these too may potentially be interpreted within a similar geometric framework, such as Iceland. New Zealand is another obvious example.

The implication is not necessarily that geometry alone explains tectonic activity, but rather that persistent mantle organization may leave detectable large-scale geometric expressions at the Earth’s surface. Such relationships may provide an additional tool for examining the long-term structure of mantle convection and its connection to volcanism, tectonics, and geothermal activity. The degree of accuracy is very high, only to be understood in context with the mathematics of the shape of the Earth.

For more details: https://pangea.stanford.edu/ERE/db/GeoConf/papers/SGW/2024/Thorbjarnarson.pdf

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A Degree of Regularity Around Antarctica

May 20, 2026June 1, 2026 Steingrimur Thorbjarnarson

Everyone notices that Antarctica is centered around the South Pole. It has not always occupied this position, and over geological time it will eventually drift toward other latitudes. So why should its present location matter? Many people may consider it coincidental, yet the degree of regularity surrounding Antarctica is nevertheless worth examining.

The mainland of Antarctica is not perfectly circular, but a circle drawn around the coastline of East Antarctica, centered on the South Pole, also broadly encompasses the Antarctic Peninsula. This gives the continent as a whole a remarkably regular appearance https://www.sciencedirect.com/science/article/pii/S1674984722000775.

Antarctica is also almost completely encircled by mid-ocean ridges. The Antarctic Plate can therefore be regarded as a growing tectonic plate, since mid-ocean ridges expand outward on both sides according to the standard plate-tectonic model accepted by most geologists.

When the oceanic part of the Antarctic Plate is examined, it roughly fits an elliptical form centered on the South Pole, with one side extending from East Antarctica and the other from West Antarctica, along the geometrical major axis. Tracing the East Pacific Rise, and the Mid-Indian Ridge, they connect closely with the endpoints of the ellipse’s major axis.

Looking at the minor axis, the Mid-Atlantic Ridge approaches one endpoint rather closely, while the Puysegur Trench subduction zone, extending from New Zealand, connects near the opposite endpoint. Another major subduction system, along the western margin of South America where the Nazca Plate meets the South American Plate, touches the elliptical form at a position approximately equidistant from the Pacific and Atlantic ridge systems.

This degree of regularity can be observed directly on a simple world map. In addition, it fits well with the convection-roll framework examined here, since mid-ocean ridges outside this elliptical form around Antarctica, mainly tend to follow north–south alignments inherent in the mantle convection rolls model.

Within this interpretation, Antarctica is confined within the polar portion of the convection-roll system, bordering the transition zone of the model between 60.7°S and 67.3°S. From this perspective, the present position of Antarctica becomes relevant not only because of the regularity visible on the world map itself, but also because of the way these large-scale features appear to correspond with the mantle convection-roll model being explored here.

In addition, comparing with the Icelandic elliptical form, the minor axis is found along the same longitude.

Location of Hekla (red circle) and the Elliptical Outline of the Continental Shelf of Iceland.

Those two elliptical forms of the Antarctic and Icelandic continental shelfs, which can be identified with reasonable accuracy, both have a minor axis along 19°40′W. The Mid-Atlantic Ridge is obviously north-south oriented, but this consistency between Iceland and Antarctica clearly adds to that concept.

Major and minor axes of the Antarctic continental shelf, centered around the South Pole and reflecting the large-scale elliptical geometry of the Antarctic Plate margin.

The Icelandic continental shelf is indicated on the map. This interpretation is based on the mantle convection rolls model and the related large-scale structural pattern. The minor axis coincides with the transition zone between polar- and equatorial-related convection rolls, while the major axis extends toward the central part of the equatorial convection rolls. Map base: https://oceanobservatories.org/2022/11/nature-review-paper-reveals-new-understandings-of-mid-ocean-ridge-systems/

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The Geometry of the Pacific Ocean

May 19, 2026May 22, 2026 Steingrimur Thorbjarnarson

Comparing large-scale convection rolls with the shape of the Pacific Ocean reveals several intriguing geometrical structures. The first step is to consider the equator itself. It forms a simple reference line, but one with important physical implications, because the effects of Earth’s rotation differ there from those at other latitudes. At the equator, the clockwise deflection characteristic of the Northern Hemisphere, and the tendency of horizontally moving particles to turn anticlockwise, do not apply in the same way.

The presence of major subduction zones on either side of the Pacific, Indonesia in the west and South America in the east, approximately 150° apart, provides two stable reference points.

As the Ring of Fire is a well-established concept, the volcanic regions can be outlined in a relatively simple way, beginning from these two equatorial reference points. The San Andreas Fault provides particularly strong support for this geometry, as it forms the sliding boundary between the Pacific Plate and the North American Plate. https://www.youtube.com/watch?v=YQtMBmS49Ew It thereby marks the approximate position of the minor axis of the elliptical form that appears when the Ring of Fire is sketched onto a map. This essay contains a lot of details:

Stanford 2024 Download

Several principal lower-mantle division lines from the mantle convection rolls model are also drawn on the map. It should perhaps have been mentioned earlier that the major intersections between the main lower-mantle convection rolls coincide with the subduction regions on both the Indonesian and South American sides of the Pacific (shown with red dots). This observation alone deserves attention when comparing the model with the map.

Additional features emerge when examining the northeastern section of the Ring of Fire. When the outer limits of the Ring of Fire are outlined, the resulting elliptical form crosses Yellowstone National Park, a volcanic region unlike any other. Within the model, the pattern created by the division lines between convection rolls of different mantle layers produces a north–south axis between the predominantly north–south-trending rolls. Yellowstone is located directly on such a north–south axis.

With this in mind, the position of Hawaii also becomes significant. Hawaii is located not only on the north–south axis emerging from the convection-roll division pattern, but also on the central north–south axis of the Ring of Fire as represented on this map.

Looking at the western side of the Pacific, one of the first indications of a broader geometrical structure is the position of New Zealand along the minor axis of the elliptical form, opposite the San Andreas region and Yellowstone on the same axis. The Taupō Volcanic Zone is located where this minor axis intersects a principal lower-mantle division line. On the map, that mantle division line is drawn somewhat exaggerated in order to emphasize its significance.

The western Pacific is subject to intense geophysical and tectonic stress, and this particular division line — extending from Japan to New Zealand — appears to accommodate much of that stress. Comparing the Northern and Southern Hemispheres, New Zealand and Japan, together with the subduction systems extending southward and northward from them respectively, display a mirrored relationship. Because stress is concentrated along this division line, and because rotational effects differ symmetrically between the hemispheres, New Zealand appears within the inner elliptical form of the Ring of Fire.

Further similarities emerge when examining the convection-roll division lines. Not only do Japan and New Zealand occupy corresponding positions within the model, but major volcanic centres such as Mount Fuji and Taupō are also found in analogous hemispherical settings on opposite sides of the globe. Likewise, the Kermadec Trench and the Izu–Bonin Trench display mirrored alignments.

The circular — or more precisely elliptical — geometry of the Pacific can therefore be compared with many details of the mantle convection rolls model. At the same time, the dimensions and shape of the Pacific have continually changed through tectonic drift. Over geological time, plate motion gradually alters the geometry of the basin itself.

The geological development of the region is equally revealing. Research has shown that much of the crustal material now forming southern Alaska originated at far more southern latitudes and has since been transported more than a thousand kilometres toward the northwest. The Denali Fault and Tintina Fault systems appear to have played a major role in this transport after island arcs had been sutured onto the North American continent. This partly illustrates how the Ring of Fire functions and why it extends across a geometrically well-defined region composed primarily of two concentric elliptical forms and the area enclosed within them.

This perspective also suggests that subduction zones may remain relatively fixed once established within the mantle convection rolls system. As the geometry evolves through tectonic drift, slabs descending into the mantle may become detached from their original surface plates, while new subduction zones eventually develop elsewhere.

It should be added here, tht there is a possible explanation for the formation of north–south axes within the framework of convection rolls. This becomes apparent when examining the detailed geometry of the division lines and polygonal regions formed between them. These polygons often tend toward a diamond-shaped geometry, with corners aligned approximately east–west and north–south.

Pressure exerted along the sides of such polygons may then create preferential lines of weakness or activity extending from one corner to the opposite corner. When this process is repeated across many adjacent small polygons, the resulting alignment can be extrapolated into the large-scale north–south patterns observed across the Pacific and elsewhere.

A particularly clear example of this type of geometry can be examined in Iceland. There, the North Volcanic Zone forms a pronounced north–south volcanic alignment, while the South Iceland Seismic Zone follows an east–west-oriented structural trend. Together, these systems illustrate how polygonal stress geometry within the mantle convection rolls framework may influence both volcanic and seismic alignments on the surface.

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The Central Role of Hekla Volcano

May 17, 2026June 2, 2026 Steingrimur Thorbjarnarson

Hekla is known to occupy a uniquely important geological position within Iceland. It lies at the eastern end of the South Iceland Seismic Zone (SISZ) and simultaneously forms the southwestern gateway into the East Volcanic Zone (EVZ). In many ways, Hekla stands at the transition between two fundamentally different tectonic expressions: the transform-style seismic deformation of South Iceland and the broad volcanic rifting of the eastern volcanic systems.

The rifting process commonly described in Icelandic geology, where one side of Iceland drifts roughly 1 cm westward each year while the other moves about 1 cm eastward, can be visualized as being organized around a central tectonic division line that reaches the latitude and structural position of Hekla. This gives Hekla a particularly important geometric and tectonic role within the overall framework of Iceland.

The East Volcanic Zone is more difficult to represent with a single line than the oceanic ridges north and south of Iceland, because the EVZ is not a narrow ridge crest but rather a broad tectono-volcanic corridor 1.5° wide from east to west. In this interpretation, special emphasis is placed on the eastern boundary of the EVZ, which appears to function as a major division between tectonic domains associated with the North American and Eurasian plates. Rather than viewing the EVZ simply as a diffuse volcanic belt, it can therefore be examined as a structured rift system occupying a broad zone between deeper mantle flow divisions.

When zooming out to examine the large-scale geometry of Iceland itself, including the mid-ocean ridges and the surrounding continental shelf, an even more remarkable arrangement becomes visible, with Hekla occupying a central position within the overall symmetry.

The continental shelf surrounding Iceland has a surprisingly regular form. The southeastern quarter of the shelf, in particular, remains relatively undisturbed and displays a sharp elliptical geometry that can be detected mathematically. The ellipse possesses clearly identifiable major and minor axes aligned directly east–west and north–south respectively. Significantly, Hekla is located on the north–south minor axis of this elliptical structure.

If the major and minor axes of the Icelandic shelf ellipse are drawn, and the oceanic segments of the Reykjanes Ridge and Kolbeinsey Ridge are extended toward Iceland from the south and north, the two ridge extensions converge precisely in the central point of the ellipse itself (extrapolation shown with dotted lines). This creates a striking geometric relationship between:

the elliptical form of the Icelandic continental shelf,
the mid-ocean ridge system north and south of Iceland,
the tectonic division between the North American and Eurasian plates,
and the position of Hekla within the overall structure.

https://images.openai.com/static-rsc-4/f0-26YLRxhCiJe-Z8uX1Q2B7ceulF2OD7H-1f2yVrPH5odNHbqA4tI9Z60AV0DdbyQbG7U0xvQZqy8F5o3SFFts3s8l2aDaW7zROriGXKW_8bQwV4MMAjj4BZzGOvQavqSl9XDhOBwfYs9x2TPJwF0-AMJY-NMqUhZ_rI9iOXk9R2U2qgLRgWCi-sHkWsqZT?purpose=fullsize

The tectonic division line through Iceland also appears remarkably symmetrical when compared with both the elliptical outline of the shelf and the extended ridge axes. North and south of Iceland alike, the plate division lines merge naturally into the mid-ocean ridges exactly where those ridges intersect the elliptical margins of the shelf.

Within this broader framework, the detailed geometry of mantle convection-roll polygons and their division lines becomes increasingly important. The interaction between different mantle layers, tectonic boundaries, volcanic zones, and continental-shelf geometry may together help explain why Hekla occupies such an exceptional position within Icelandic geology.

Hekla has been regarded as Iceland’s most famous volcano for centuries, and perhaps not only because of its frequent eruptions and dramatic appearance. Its location suggests that it occupies one of the most structurally significant positions in the entire geological framework of Iceland.

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The Three Corners of Vatnajökull

May 15, 2026 Steingrimur Thorbjarnarson

The largest glacier in Iceland, Vatnajökull, covers several major volcanic systems. Direct geological research beneath the glacier is difficult because of the extreme environmental conditions, thick ice cover, and active geothermal areas. Nevertheless, a remarkable amount is known about the volcanic framework beneath the ice.

Vatnajökull with Öræfajökull, Grímsvötn and Kverkfjöll.

Three prominent volcanic regions are especially important in this context because they appear to fit clearly into the proposed pattern of mantle convection roll division lines.

The first is Öræfajökull, the tallest volcano in Iceland, situated close to the 64th parallel. The second is Grímsvötn, a vast but more obscure volcanic and geothermal complex beneath central Vatnajökull. The third is Kverkfjöll, which occupies a relatively small polygon directly north of Öræfajökull.

Kverkfjöll is particularly significant because it marks the southern starting point of the North Volcanic Zone. From there, a remarkably direct volcanic axis can be traced northward all the way to Öxarfjörður, where the North Volcanic Zone meets the Tjörnes Fracture Zone. This fracture zone, in turn, connects the volcanic systems of Iceland with the offshore Kolbeinsey Ridge.

The geometrical relationship between these three volcanic centers is striking. The polygon formed by Öræfajökull, Grímsvötn, and Kverkfjöll appears exceptionally clear within the proposed convection-roll framework. In addition, Grímsvötn and Kverkfjöll are known to be petrologically related, suggesting a deeper structural connection beneath Vatnajökull.

Grímsvötn was also the source region of the magma and dyke propagation that eventually produced the catastrophic Laki eruption in 1783. Within this framework, the magma migration becomes especially interesting because the dyke propagated from one calculated division line toward another before the eruption began. Laki itself lies on one division line, whereas Grímsvötn occupies another.

The line extending from Kverkfjöll through Grímsvötn to Laki closely coincides with the eastern boundary of the East Volcanic Zone. The width of this volcanic zone can be measured directly on the surface, and it corresponds closely to the calculated width of the relevant convection roll in the model.

On the opposite side of the Grímsvötn–Kverkfjöll line lies Öræfajökull, which also marks the beginning of another volcanic alignment: the Öræfajökull Flank Zone. This zone trends northeast–southwest and extends toward Snæfell northeast of Vatnajökull. In total, the flank zone spans approximately the equivalent of two polygons within the proposed geometrical framework.

The repeated appearance of the same fundamental geometrical unit — polygons with an approximate east–west width of 1.5° — is one of the main reasons the model may provide a valuable tool for examining geological structures. According to this interpretation, the same geometrical relationships are not confined to Iceland alone, but may also appear in tectonic and volcanic systems throughout the world.

Geothermal areas of Iceland with superimposed mantle convection roll division lines and the tectonic boundary between the North American and Eurasian plates.

Within Iceland, however, Vatnajökull provides one of the clearest large-scale examples. Beneath the ice cap, some of the country’s most powerful volcanic systems appear organized in a pattern that mirrors the calculated geometry of the mantle convection roll model. Each polygon therefore becomes something like a chapter in a book, with each one containing its own distinct geological characteristics, tectonic structures, volcanic systems, geothermal activity, and landscape evolution.

Viewed in this way, Iceland can be examined as a sequence of interconnected geological “chapters,” where every polygon reveals a slightly different expression of the same underlying mantle convection roll system. One polygon may be dominated by rifting and fissure swarms, another by central volcanoes and geothermal fields, while a third may display transform faulting, glacial volcanoes, or complex magma interactions beneath ice caps.

This approach is valuable because it provides a structured way to examine geology step by step. Instead of viewing Icelandic geology as a collection of isolated volcanic systems, each region can be interpreted as part of a larger geometrical framework extending through the crust and into the mantle below.

The same method can also be applied to other parts of Iceland. The Reykjanes Peninsula, the South Iceland Seismic Zone, the Hengill area, the central highlands, and the northern volcanic systems all become individual “chapters” whose geological behaviour can be compared within the same overall framework.

In that sense, the polygon system is not only a geometrical model. It also becomes an organizational tool for understanding geology across many different scales — from magma migration beneath a glacier to the overall tectonic structure of Iceland itself.