The development of global plate tectonics in relation to Robert J. Stern’s research and the Mantle Convection Rolls Model

Two Perspectives on the Same Tectonic System

When considering the Earth’s tectonic activity, an important distinction must be made between the present operation of the system and its long-term geological evolution.

On a human timescale, tectonic processes appear relatively stable. Earthquakes and volcanic eruptions take place, tectonic plates move a few centimetres each year, and deformation accumulates along plate boundaries. Nevertheless, the general geographical arrangement of the major tectonic systems changes very little during the period of human observation.

On the timescale of millions or billions of years, however, the situation is entirely different. Oceans open and close, continents assemble and separate, and subduction zones develop, migrate, and eventually disappear.

These are not two different systems. They are two perspectives on the same evolving physical processes.

The distinction is particularly important when examining the Pacific Ring of Fire. The Ring of Fire represents a major component of the Earth’s present tectonic activity. It is not, however, a geographical structure that has remained unchanged throughout geological history.

Understanding its present configuration therefore requires two complementary approaches: investigating the historical development of subduction tectonics and analysing the physical processes responsible for the present distribution of tectonic boundaries.

Robert J. Stern and the Geological History of Subduction

Robert J. Stern, a geologist at the University of Texas at Dallas, has devoted considerable attention to the origin and evolution of subduction zones.

In a paper published in Geology in 2005, Stern argued that the present episode of modern-style subduction tectonics may have begun during the Neoproterozoic Era, within approximately the last billion years.

His interpretation was based on three important types of geological evidence:

1. Ophiolites, representing fragments of oceanic lithosphere preserved within continental geological formations.
2. Blueschists, metamorphic rocks formed under high-pressure and relatively low-temperature conditions, typically associated with subduction.
3. Ultrahigh-pressure metamorphic rocks, indicating that crustal material has descended to considerable depths before returning to the surface.

These geological indicators are particularly useful because they preserve evidence of tectonic processes that can no longer be observed directly.

One remarkable feature of the geological record is that ophiolites are predominantly young when compared with the age of the Earth.

This observation raises a fundamental question: did subduction develop relatively late in Earth’s history, or have most traces of earlier subduction simply disappeared?

The distinction is important because oceanic lithosphere is continuously recycled into the mantle. The geological record of ancient ocean basins is therefore much less complete than that of continental crust.

The Age Distribution of Ophiolites

A particularly useful quantitative investigation was published by Kent C. Condie and Robert J. Stern in 2023.

Their paper, Ophiolites: Identification and tectonic significance in space and time, examined 257 occurrences identified as ophiolites and evaluated their geological ages, tectonic environments, and reliability of identification.

The following table summarizes their findings.

Table 1. Distribution of ophiolites through geological time

Geological interval	Number	Forearc settings	Occurrences per 100 million years
Phanerozoic (539 Ma–present)	175	94%	32
Neoproterozoic (1,000–539 Ma)	49	92%	11
Mesoproterozoic (1,600–1,000 Ma)	16	87%	2.6
Paleoproterozoic (2,500–1,600 Ma)	10	50%	1.1
Neoarchean (2,800–2,500 Ma)	7	100%	2.3
Total	257

Source: Condie and Stern (2023), Table 1. The numbers describe preserved and identified occurrences, not the total number of subduction zones that existed during each interval. Geological boundaries are rounded.

The age distribution is striking.

Of the 257 identified occurrences, 224 belong to the Neoproterozoic and Phanerozoic, representing approximately 87% of the total.

Furthermore, the number of recorded occurrences per 100 million years increases considerably toward the present.

This does not necessarily imply that subduction was absent during earlier geological periods.

Indeed, Condie and Stern identify much older examples. The Zunhua ophiolite in northern China dates to approximately 2,550 million years ago, while the Jormua and Purtuniq ophiolites date to approximately 1,950–2,000 million years ago.

The oldest preserved ophiolites therefore indicate that processes resembling modern oceanic spreading and subduction were operating long before the Neoproterozoic.

Nevertheless, the marked increase in younger ophiolites suggests that something important changed during the later stages of Earth’s geological history.

Condie and Stern consider three possible explanations: more extensive investigation of young geological formations, better preservation of younger ophiolites, and an actual increase in the geographical extent of interconnected plate tectonics.

These explanations are not mutually exclusive.

From Local Subduction to Global Plate Tectonics

An important aspect of Stern’s interpretation is the distinction between the occurrence of individual subduction zones and the existence of a globally integrated plate-tectonic system.

It is possible for localized subduction to occur without the entire lithosphere being divided into the interconnected system of moving plates observed today.

This suggests three general levels of tectonic development.

Stage 1 — Mantle convection and crustal deformation

Heat transfer from the Earth’s interior produces mantle circulation, magmatism, and deformation of the overlying lithosphere. These processes do not necessarily require a global network of moving tectonic plates.

Stage 2 — Localized or intermittent subduction

Under suitable mechanical conditions, parts of the oceanic lithosphere may descend into the mantle. Such processes can occur regionally and need not immediately establish a global plate-tectonic system.

Stage 3 — Globally interconnected plate tectonics

Oceanic spreading ridges, subduction zones, transform faults, and moving lithospheric plates become components of an integrated global system.

The present Ring of Fire belongs to this third category.

These stages are best understood as different levels of tectonic organization rather than a simple sequence that occurred only once.

Stern’s More Recent Interpretation

Stern has subsequently developed the idea that the Earth may have experienced alternating episodes of global plate tectonics and single-lid tectonics.

In a paper published online in 2024 and appearing in the 2025 volume of the Geological Society of America Bulletin, he proposed four successive tectonic episodes during the last 2.5 billion years.

Two were dominated by plate tectonics and two by single-lid regimes.

In a single-lid regime, the lithosphere forms a relatively coherent outer shell, although substantial internal deformation and volcanic activity can still occur.

Stern identified an earlier episode of plate tectonics during the Paleoproterozoic, followed by a long Mesoproterozoic interval dominated by single-lid behavior.

According to his interpretation, the present episode of global plate tectonics began approximately 800 million years ago.

This is an important development of his earlier theory.

Rather than asking exclusively when plate tectonics first began, Stern now emphasizes the possibility that Earth has experienced different tectonic regimes at different times.

It is therefore possible that subduction existed very early in geological history, temporarily became widespread, declined, and subsequently developed into the global system operating today.

This interpretation remains debated. Other researchers place the emergence of widespread plate tectonics much earlier, and ancient rock assemblages can be interpreted in different ways.

Nevertheless, Stern’s framework provides an interesting evolutionary perspective on the tectonic system.

The Initiation of Individual Subduction Zones

An additional distinction concerns the initiation of individual subduction zones within an already established global tectonic system.

Stern and Scott A. Whattam examined the connection between subduction initiation and ophiolite formation in their 2011 paper describing the subduction initiation rule.

Their work showed that many ophiolites preserve a characteristic sequence of magmatic rocks formed during the early stages of subduction.

The Izu–Bonin–Mariana system provides a particularly important modern example.

Subduction began there approximately 52 million years ago. During the early development of the system, seafloor spreading and extensive magmatism produced new crust within the forearc.

The resulting geological formations resemble the sequences preserved in many ancient ophiolites.

This relationship allows present-day subduction systems to be used in interpreting geological formations hundreds of millions of years old.

It also emphasizes an important chronological distinction.

The global tectonic regime may have existed for hundreds of millions of years, while individual subduction systems within it may be much younger.

Consequently, the geological age of an individual trench or volcanic arc cannot be used as the age of the global tectonic system itself.

The Ring of Fire in Its Present Configuration

The Pacific Ring of Fire comprises a broad geographical arrangement of active subduction zones, volcanic arcs, major faults, and associated tectonic structures surrounding much of the Pacific Ocean.

It extends along the western margins of the Americas, through Alaska and the Aleutian Islands, and southward through the western Pacific toward New Zealand.

Although this structure is often represented as a continuous ring, its individual components have different geological histories and mechanical characteristics.

Some of the principal subduction systems are separated by major transform faults or other tectonic boundaries. Their initiation and development occurred at different times.

The Ring of Fire must therefore be understood as a present-day arrangement of active tectonic systems rather than the remains of one ancient, continuous geological structure.

However, this raises another question.

Why does the present arrangement of tectonic boundaries form such an extensive and apparently systematic geographical pattern?

The conventional plate-tectonic explanation describes the movement and interaction of individual lithospheric plates. It also provides the mechanical framework for understanding subduction, spreading, and transform motion.

The Mantle Convection Rolls Model investigates an additional possibility: whether the geometry of mantle circulation contributes to the spatial organization of these boundaries.

The Ring of Fire and the Mantle Convection Rolls Model

The Mantle Convection Rolls Model is based on the proposed development of organized convection rolls within the Earth’s mantle.

The model distinguishes between larger convection structures in the lower mantle and smaller convection rolls in the upper mantle and asthenosphere.

The geometry of the upper-mantle roll system has been developed using approximately 1.5° intervals, while larger-scale mantle divisions are proposed to influence the organization of major tectonic structures.

Within this interpretation, the surface expression of mantle circulation may involve several different types of interaction between mantle flow and the lithosphere.

These interactions include divergent boundaries, convergent boundaries, and deformation zones in which the relative orientation of the proposed convection structures changes.

The Ring of Fire is particularly important because it contains some of the world’s most extensive convergent boundaries.

The model proposes that their present spatial arrangement may reflect a larger geometrical organization of mantle circulation.

Three Global Tectonic Rings

Recent geometrical investigations presented on MagicMagma have extended the analysis beyond the Pacific.

The working hypothesis identifies three adjacent large-scale tectonic ring systems associated with the Pacific, Atlantic, and Indian Oceans.

Their reference centers are separated by 120° of longitude:

Tectonic ring	Reference center
Pacific	149.3°W, 6°S
Atlantic	29.3°W, 6°S
Indian Ocean	90.7°E, 6°S

The proposed ring boundaries are represented by families of inclined ellipses, with their major axes oriented at approximately −45° in longitude–latitude coordinates.

In the basic geometrical construction, the inner ellipse has a major-to-minor axis ratio of 3:2.

These angular relationships are part of the proposed model. Their application to the spherical Earth requires consideration of the changing physical distance represented by degrees of longitude at different latitudes.

The essential idea is that the Ring of Fire may represent one component of a larger geometrical system rather than an isolated tectonic feature.

The relationship between the Pacific ring and the Atlantic and Indian Ocean systems consequently becomes important.

This approach is particularly interesting because it attempts to examine divergent and convergent tectonic boundaries within the same geometrical framework.

For example, the Gulf of California and the Red Sea represent different extensional environments, but their geographical positions may be compared with the proposed inner and outer ring boundaries.

Likewise, the relationships between the Mariana Trench, Japan, New Zealand, the Andes, and the Aleutian Islands can be examined relative to the predicted convection-roll divisions.

Such comparisons provide possible geometrical evidence, but geographical correspondence alone cannot establish the underlying mechanical cause. The model must also be evaluated against plate velocities, mantle-flow constraints, and the geological history of the boundaries.

Geological Evolution and the Persistence of Mantle Convection

Here the distinction between geological history and present-day activity becomes especially important.

Mantle convection is a fundamental mechanism of heat transfer within the Earth. It must have operated under a wide range of thermal and mechanical conditions during the planet’s history.

The organization and interaction of mantle convection and the lithosphere, however, need not have remained constant.

The early Earth was considerably hotter than the present Earth. Oceanic lithosphere was probably different in thickness, density, and mechanical strength.

These factors would have influenced the conditions under which subduction could begin and continue.

In Stern’s interpretation, the cooling and mechanical evolution of the lithosphere eventually allowed long-lived subduction to become a dominant component of global tectonic activity.

The Convection Rolls Model approaches the same development from the perspective of mantle circulation.

One possibility worth investigating is that mantle convection provided a persistent source of deformation and stress while the response of the overlying lithosphere changed through geological time.

Under this interpretation, the difference between early tectonic regimes and the present system would not necessarily require the appearance of mantle convection as an entirely new process.

Instead, it could reflect changes in the mechanical coupling between the mantle and the lithosphere.

This possibility does not imply that the detailed geometry of the present convection-roll model has existed unchanged since the early Earth.

Changes in mantle temperature, viscosity, lithospheric strength, and plate configuration could all influence the geometry and dynamics of convection.

The question is whether the present system exhibits an underlying geometrical organization that can be explained by the proposed convection-roll mechanism.

Tectonic Evolution and the Development of Life

The geological development of plate tectonics may also have had important consequences for the evolution of life.

In 2024, Stern and Taras V. Gerya published a paper investigating the importance of continents, oceans, and plate tectonics for the development of complex life.

Their interpretation connects the transition toward modern plate tectonics with major environmental and biological changes during the Neoproterozoic.

Life had existed on Earth for billions of years before this transition.

However, the later development of large and complex multicellular organisms took place during a period of significant changes in the atmosphere, oceans, climate, and tectonic environment.

Several possible connections can be considered.

First, increased tectonic activity can promote mountain building, continental weathering, and the transport of nutrients into the oceans.

Second, changing continental configurations influence ocean circulation, marine habitats, and the distribution of shallow seas.

Third, tectonic activity affects the long-term carbon cycle and can contribute to changes in atmospheric carbon dioxide and global climate.

Finally, changes in biological productivity, organic carbon burial, and nutrient cycling may influence the oxygenation of the oceans and atmosphere.

These relationships are particularly relevant to the interval between approximately 800 and 500 million years ago.

The great Neoproterozoic glaciations occurred between approximately 717 and 635 million years ago. The Ediacaran Period, from about 635 to 539 million years ago, witnessed the appearance and diversification of many large, complex organisms.

The subsequent Cambrian Period saw a major expansion in the diversity of animals preserved in the fossil record.

Stern and Gerya suggest that changes in the Earth’s tectonic regime may have contributed to the environmental conditions supporting this biological development.

This interpretation is not established as a direct causal relationship. Evolutionary innovations, ecological interactions, and changes in oxygen availability all require separate consideration.

Nevertheless, the chronological relationship is significant.

It suggests that the evolution of the Earth’s interior and the evolution of surface environments cannot always be treated as entirely separate subjects.

Two Timescales, One Physical System

The main distinction can now be summarized.

Over geological time, the Earth has experienced major changes in the thermal state of its interior, the mechanical properties of the lithosphere, and the organization of its tectonic boundaries.

Stern’s work investigates this long-term development using evidence preserved in ancient rocks.

The present Ring of Fire, however, represents only the contemporary configuration of part of that evolving system.

The Convection Rolls Model investigates the geometry of this present configuration and proposes that organized mantle circulation may contribute to the position and orientation of the major tectonic boundaries.

These approaches address different aspects of the same general problem.

The historical record constrains when different tectonic processes were operating. The geometry of the present system provides information about how the Earth’s tectonic activity is organized today.

An important next step is to determine whether the proposed mantle-convection geometry is mechanically consistent with the observed motion of tectonic plates and whether it can account for the changes in plate-boundary configuration revealed by geological reconstructions.

In particular, the Ring of Fire provides opportunities to compare major subduction systems with the predicted positions of mantle-flow divisions.

The tests should include the geographical distribution of trenches, the inclination and geometry of descending slabs, plate-motion vectors, and the timing of subduction initiation.

A successful explanation should account not only for the position of tectonic boundaries but also for the forces responsible for their development.

Conclusion

The age distribution of ophiolites and other geological indicators suggests that the organization of Earth’s tectonic system has changed significantly throughout geological history.

Robert J. Stern’s investigations provide an evolutionary framework in which localized subduction, globally integrated plate tectonics, and alternative tectonic regimes may have occurred during different periods.

The present Ring of Fire forms part of the current globally integrated plate-tectonic system.

Its individual components have different geological ages, but together they define an extensive geographical arrangement of active convergent boundaries.

The Mantle Convection Rolls Model approaches this arrangement from the perspective of an organized mantle-flow system and proposes that the geometry of the Ring of Fire may be related to a wider set of tectonic rings distributed around the Earth.

The long-term evolution of tectonic regimes and the present geometry of tectonic boundaries should therefore be considered as related but distinct problems.

The geological history tells us how the tectonic system developed. Its present geometry may help reveal how the system is organized and operates today.

---

References

1. Stern, R. J. (2005). Evidence from ophiolites, blueschists, and ultrahigh-pressure metamorphic terranes that the modern episode of subduction tectonics began in Neoproterozoic time. Geology, 33(7), 557–560.
   https://doi.org/10.1130/G21365.1
2. Whattam, S. A., & Stern, R. J. (2011). The ‘subduction initiation rule’: A key for linking ophiolites, intra-oceanic forearcs, and subduction initiation. Contributions to Mineralogy and Petrology, 162, 1031–1045.
   https://doi.org/10.1007/s00410-011-0638-z
3. Stern, R. J., & Gerya, T. (2018). Subduction initiation in nature and models: A review. Tectonophysics, 746, 173–198.
   https://doi.org/10.1016/j.tecto.2017.10.014
4. Stern, R. J. (2020). The Mesoproterozoic Single-Lid Tectonic Episode: Prelude to Modern Plate Tectonics. GSA Today, 30(12).
   https://www.geosociety.org/gsa-today/december-2020/the-mesoproterozoic-singlelid-tectonic-episode-prelude-to-modern-plate-tectonics
5. Condie, K. C., & Stern, R. J. (2023). Ophiolites: Identification and tectonic significance in space and time. Geoscience Frontiers, 14(6), 101680.
   https://doi.org/10.1016/j.gsf.2023.101680
6. Stern, R. J., & Gerya, T. V. (2024). The importance of continents, oceans and plate tectonics for the evolution of complex life: Implications for finding extraterrestrial civilizations. Scientific Reports, 14, 8552.
   https://doi.org/10.1038/s41598-024-54700-x
7. Stern, R. J. (2025). A reinterpretation of the past 2.5 billion years of Earth’s tectonic history: Two episodes each of plate and single-lid tectonics. Geological Society of America Bulletin, 137(5–6), 2079–2100. Published online December 2024.
   https://doi.org/10.1130/B37966.1

Related articles on MagicMagma

• The Red Sea, the Mediterranean, and the Great Rift Valley in a Global Tectonic Context
• Geometric Comparison of the San Andreas and Alpine Faults

The accompanying illustration compares the proposed system of lower-mantle convection rolls with the three global tectonic rings. According to the Convection Rolls Model, the lower-mantle rolls occupy two superimposed layers extending from approximately 670 km to 2,900 km depth, with their projected patterns partly overlapping. The general concept of mantle convection is familiar from introductory geology textbooks, which commonly illustrate the circulation of mantle material by means of paired convection cells. Similarly, the concept of a tectonic ring is familiar through the widely recognized Pacific Ring of Fire. A comparison of these two features suggests that they may represent related expressions of recurring geometrical patterns within the Earth.

At first glance, the mirrored arrangement of the green lines may appear confusing. This is because the illustration represents a three-dimensional convection system in two dimensions, with the patterns of two vertically superimposed layers projected onto a single geographical plane. Each lower-mantle convection roll extends approximately 15° from east to west, and the rolls are arranged side by side within their respective layers. The smaller convection rolls of the upper mantle, extending between approximately 120 and 670 km depth, are considerably more numerous. They are represented in the model by four layers of rolls, each approximately 1.5° wide. These smaller rolls are not included in the present illustration.

The Mid-Atlantic Ridge can be traced through the central region of the Atlantic tectonic ring, while the mid-ocean ridge system of the Indian Ocean occupies a corresponding position within the Indian Ocean ring. The Pacific Ocean requires particular consideration because of its extensive convergent plate boundaries along both its eastern and western margins, together with the divergent boundary represented by the East Pacific Rise.

The two-sided nature of the Pacific tectonic system is particularly relevant when considering the geometrical relationships of Antarctica. The Antarctic elliptical structure has two principal axes, each with two endpoints. These four directions appear to correspond to four major branches of the proposed global tectonic framework. One endpoint of the minor axis extends towards New Zealand, while the opposite endpoint points towards the Mid-Atlantic Ridge. Similarly, one endpoint of the major axis is associated with the East Pacific Rise, whereas the other corresponds to the region of the Indian Ocean ridge system and its triple junction.

In the proposed model, the three tectonic rings are represented by elliptical structures. The inner ellipse spans approximately 120° of longitude along the equator and has a major-to-minor axis ratio of 3:2. Its major axis is oriented NW–SE, at an angle of 45° to the north–south and east–west directions. On an equirectangular map, where each degree of longitude and latitude is represented by an equal unit of length, this orientation corresponds to a slope of −1.

The model proposes that the stresses generated by mantle convection provide the mechanical conditions necessary for the formation of these regularly arranged elliptical tectonic structures. Their dimensions are related to the 15° spacing of the lower-mantle convection rolls, which influence the smaller convection systems within the transition zone and asthenosphere. The width of the tectonically active zones may exceed the 15° width of an individual lower-mantle roll because of the additional effects of the smaller convection rolls in the overlying mantle.

The present distribution of geological activity and the dynamics of plate motion can be compared with this geometrical framework. Several relevant relationships have already been identified in connection with Antarctica. The Gulf of California and the Red Sea, for example, provide an interesting comparison because both occur at similar latitudes and are associated, in this interpretation, with the margins of elliptical tectonic structures.

Other examples can be identified throughout the world. New Zealand, Japan and Kamchatka are associated with the western Pacific tectonic system. The East African Rift, the volcanically active parts of the Mediterranean region and Iceland can be examined in relation to different sections of the Atlantic tectonic ring. Similarly, the western margin of South America follows a major convergent boundary associated with the Pacific tectonic ring.

Many of these locations have already been examined in previous articles. Comparing their geological characteristics with the proposed geometrical framework may help explain relationships between divergent boundaries, convergent boundaries, volcanic activity and the underlying mantle convection system.

It is important, however, to distinguish between the geometrical relationships demonstrated by the model and the dynamic processes that may produce them. The geometrical arrangement provides a framework within which present-day geological structures can be compared, while plate motions continuously modify the position and character of tectonically active zones. The proposed system is therefore not intended to represent a static Earth, but rather a recurring geometrical organization within an evolving tectonic environment.

The most immediately recognizable feature of the illustration is the large-scale division of the Earth’s tectonic framework into three principal systems associated with the Atlantic, Pacific and Indian Oceans. These are represented by the three global tectonic rings, whose geometrical relationships can be examined alongside the proposed system of mantle convection rolls.

Convection and tectonic rings relationship:

The Three Global Tectonic Rings: Geometrical Relationships with Mantle Convection Rolls and Major Plate Boundaries

Abstract

The proposed model of three global tectonic rings provides a geometrical framework for comparing the distribution of divergent, convergent and transform plate boundaries with the underlying system of mantle convection rolls. The rings are represented by elliptical structures associated with the Atlantic, Pacific and Indian Oceans. Their centers are separated by 120° of longitude, and their major axes are oriented NW–SE on an equirectangular geographical grid.

A particularly interesting geometrical relationship is found along the minor axis of the inner Pacific tectonic ring. Its northeastern endpoint lies near the Gulf of California, while its southwestern endpoint is situated near New Zealand. At both locations, the inner Pacific ellipse intersects the outer ellipse of an adjacent tectonic ring. The northern intersection, involving the Atlantic ring, occurs at approximately 31.017°N, 113.063°W. The southern intersection, involving the Indian Ocean ring, occurs at 43.017°S, 174.463°E.

Both intersections are remarkably close to the corresponding endpoints of the minor axis. These relationships, together with the orientation of major fault systems and the proposed convection-roll geometry, provide a basis for investigating whether the elliptical structures represent a recurring organization of tectonic deformation.

1. The geometrical framework of the tectonic rings

The general distribution of active plate boundaries reveals three large oceanic systems associated with the Atlantic, Pacific and Indian Oceans. These systems are interconnected, but their tectonic characteristics differ considerably.

The Atlantic Ocean is dominated by divergent boundaries along the Mid-Atlantic Ridge, whereas the Pacific Ocean is characterized by extensive subduction zones, transform faults and the divergent East Pacific Rise. The Indian Ocean contains an extensive network of spreading ridges and plate-boundary intersections.

The proposed tectonic-ring model attempts to place these different structures within a common geometrical framework.

Each ring consists of an inner and an outer elliptical boundary. Their dimensions, expressed in degrees on an equirectangular map, are:

Parameter	Inner ellipse	Outer ellipse
Semi-major axis	77.7°	96.5°
Semi-minor axis	51.8°	71.0°
Major/minor axis ratio	1.500	1.359
Major-axis orientation	−45°	−45°

The elliptical structures share a common central latitude of 6°S.

Their central longitudes are:

• Atlantic tectonic ring: 29.3°W.
• Indian Ocean tectonic ring: 90.7°E.
• Pacific tectonic ring: 149.3°W.

The centers are separated by 120°, corresponding to one-third of the Earth’s circumference along the equator.

The general equation of an ellipse rotated through an angle (\theta) is:

[
\frac{x’^2}{a^2}+\frac{y’^2}{b^2}=1
]

where

[
x’=(x-x_0)\cos\theta+(y-y_0)\sin\theta
]

[
y’=-(x-x_0)\sin\theta+(y-y_0)\cos\theta
]

and (\theta=-45^\circ).

The major axis therefore follows a line with a slope of −1, while the minor axis is perpendicular to it, with a slope of +1.

All calculations use equal numerical scales for longitude and latitude. Consequently, the elliptical structures are exact within the chosen rectangular coordinate system, although their corresponding dimensions and orientations on the spherical Earth require geographical corrections.

2. The equator and the dimensions of the tectonic rings

The equator provides a fundamental reference for the geometrical arrangement of the tectonic rings.

The three centers are positioned at 120° intervals in longitude, while the entire system is displaced 6° southward.

The dimensions of the inner ellipses provide an equatorial span of approximately 120°, equivalent to one-third of the Earth’s circumference in longitude.

The relationship between the inner and outer elliptical boundaries is particularly interesting.

At the western intersection with the equator, the separation between the boundaries is calculated to be approximately:

[
\Delta x=19.451^\circ
]

This is remarkably close to 19.5°, which can be expressed in terms of the dimensions of the proposed convection-roll system:

[
19.5^\circ=15^\circ+3(1.5^\circ)
]

In the model, the lower-mantle convection rolls are arranged at 15° intervals, whereas smaller rolls in the upper-mantle system occur at 1.5° intervals.

One possible interpretation is that the width of the tectonically active region reflects the combined influence of one major lower-mantle unit and three smaller upper-mantle units.

However, this correspondence is geometrical. A mechanical calculation is required to determine whether the stresses transmitted between the different convection systems could actually produce the proposed width.

The 6° southward displacement introduces another important feature. The tectonic rings are not symmetrical about the equator, although their internal geometrical arrangement remains symmetrical about their common central latitude.

This displacement may be significant when considering the interaction between the northern and southern parts of the mantle convection system.

3. The northeastern endpoint of the Pacific minor axis: California

The inner Pacific tectonic ellipse has its center at:

[
(x_0,y_0)=(-149.3^\circ,-6^\circ)
]

Its semi-minor axis measures 51.8°.

Because the minor axis is inclined at 45° to the coordinate axes, its northeastern endpoint can be calculated directly:

[
x=x_0+\frac{51.8^\circ}{\sqrt2}
]

[
y=y_0+\frac{51.8^\circ}{\sqrt2}
]

The resulting coordinates are:

[
\boxed{30.628^\circ N,\ 112.672^\circ W}
]

This location is near the northern Gulf of California.

The geographical relationship is particularly interesting because the Gulf of California and the San Andreas Fault System represent connected sections of the Pacific–North American plate boundary.

The Gulf of California is characterized by oblique divergence and transform motion, whereas the San Andreas Fault is predominantly a right-lateral transform boundary.

The inner Pacific ellipse follows a NW–SE orientation near California, broadly corresponding to the orientation of the Gulf of California and major sections of the San Andreas Fault System.

At the northeastern endpoint of the minor axis, the tangent to the ellipse is parallel to its major axis. This provides a direct geometrical explanation for the NW–SE orientation of the elliptical boundary in this region.

A comparison with the San Andreas Fault also reveals an interesting relationship between the distance of the fault system from the inner ellipse at its northern and southern extremities.

Using representative locations near the Salton Sea and Cape Mendocino, the calculated distances to the ellipse are approximately 32 km and 44 km, respectively.

Although the intermediate parts of the fault system do not follow a constant distance from the ellipse, the similarity of these two endpoint distances deserves closer examination.

The orientation of the relative motion between the Pacific and North American plates also corresponds broadly to the tangent of the ellipse in southern California. The agreement becomes less precise farther north.

Thus, the geometrical relationship concerns not only the location of the fault system but also its orientation and the direction of relative plate motion.

4. The intersection of the Pacific and Atlantic tectonic rings

Another important geometrical relationship occurs near the northeastern endpoint of the Pacific minor axis.

The inner Pacific ellipse intersects the outer Atlantic ellipse at:

[
\boxed{31.017^\circ N,\ 113.063^\circ W}
]

This intersection is located close to the northern Gulf of California, approximately 57 km from the calculated endpoint of the Pacific minor axis.

The two ellipses intersect slightly south of 32°N.

This latitude is important within the proposed convection-roll system because the centers of the northern hemispheric convection arcs are positioned along the 32nd parallel.

The corresponding equation is:

[
(x-C_n)^2+(y-32)^2=35.341^2
]

At 32°N, the tangents to these circular convection boundaries are oriented north–south on the rectangular geographical grid.

Therefore, the northern Gulf of California occupies an interesting position in the model: it is situated near the intersection of two tectonic rings, near the endpoint of a principal elliptical axis and close to the latitude at which the convection-roll boundaries have a north–south orientation.

This combination suggests a possible location where different components of the proposed mantle-driven stress system might interact.

Whether such an interaction has mechanical significance remains to be established through calculations of mantle flow, transmitted traction and lithospheric deformation.

5. The southwestern endpoint of the Pacific minor axis: New Zealand

The opposite endpoint of the same minor axis is found by subtracting the horizontal and vertical components from the center of the Pacific ellipse.

The calculated coordinates are:

[
\boxed{42.628^\circ S,\ 174.072^\circ E}
]

This point lies near the northeastern part of New Zealand’s South Island, in the broader Kaikōura tectonic region.

The geological setting differs considerably from California.

New Zealand is situated along the boundary between the Pacific and Australian plates. The Alpine Fault is a major oblique-slip plate-boundary fault extending along the western side of the South Island. Farther northeast, the Marlborough Fault System connects the Alpine Fault to the Hikurangi Subduction Zone.

The endpoint of the Pacific minor axis is not located directly on the principal trace of the Alpine Fault. Nevertheless, it is situated within the broader region where the geometry and character of the Pacific–Australian plate boundary change significantly.

The most important geometrical relationship involves the intersection between the inner Pacific ellipse and the outer Indian Ocean ellipse.

Their southern intersection occurs at:

[
\boxed{43.017^\circ S,\ 174.463^\circ E}
]

The intersection is approximately 54 km from the southwestern endpoint of the Pacific minor axis.

This result closely resembles the corresponding relationship in California, where the Atlantic and Pacific ellipses intersect approximately 57 km from the northeastern endpoint.

Consequently, the two ends of the Pacific minor axis display a similar geometrical arrangement involving the boundary of an adjacent tectonic ring.

6. The symmetrical relationship between California and New Zealand

The results can be summarized as follows:

Geometrical feature	California	New Zealand
Pacific minor-axis endpoint	30.628°N, 112.672°W	42.628°S, 174.072°E
Adjacent tectonic ring	Atlantic	Indian Ocean
Intersection with Pacific inner ellipse	31.017°N, 113.063°W	43.017°S, 174.463°E
Distance from minor-axis endpoint	~57 km	~54 km
Principal tectonic setting	Transform and oblique divergence	Oblique collision, transform faulting and subduction

The similarity is particularly striking because the two intersection points lie on opposite sides of the Pacific Ocean.

The northern intersection occurs at approximately 31°N, while the southern intersection occurs at approximately 43°S.

Their latitudes are symmetrical around 6°S:

[
\frac{31.017^\circ+(-43.017^\circ)}{2}
=-6^\circ
]

This relationship follows directly from the common latitude of the ellipse centers and the symmetrical mathematical construction.

It is therefore an exact prediction of the chosen geometry rather than an independent geological confirmation.

Nevertheless, its geological relevance can be tested by comparing the locations and orientations of active faults, plate movements and deformation zones with the predicted elliptical boundaries.

The California and New Zealand regions provide two important opportunities for doing so.

7. Mantle convection rolls and the origin of elliptical stress fields

The proposed relationship between the tectonic rings and mantle convection involves both vertical and horizontal mechanical effects.

Vertical movements within the mantle convection system may influence the distribution of buoyancy forces, pressure and lithospheric stresses.

At the same time, horizontal mantle flow can transmit shear traction to the overlying lithosphere.

These forces interact with plate motion, including spreading at divergent boundaries, convergence at subduction zones and lateral displacement along transform faults.

In the proposed model, the lower mantle contains large convection rolls arranged at characteristic intervals of 15°. Their geometrical organization may influence smaller convection systems in the overlying mantle.

The mathematical approximation of the convection-roll boundaries employs circular arcs with a radius of:

[
R=35.341^\circ
]

and centers along the latitudes:

[
y=\pm32^\circ,\qquad y=\pm96^\circ
]

An important question is whether the stresses generated by these systems could organize lithospheric deformation into large elliptical structures.

The orientation of the tectonic rings provides one possible constraint.

A shear-dominated horizontal stress field can have principal directions inclined at 45° to the geographical coordinate axes, provided the horizontal normal stress components are equal.

This offers a possible mechanical route towards explaining the orientation of the ellipses.

However, an additional explanation is required for their axis ratios, geographical positions and 6° southward displacement.

The geometry of the Earth must also be included. Longitude intervals become progressively shorter towards the poles, changing the relationship between geographical coordinates, distances and local flow directions.

The curvature of the Earth therefore enters the mathematical description of mantle flow and deformation, although it does not, by itself, establish the proposed circular convection trajectories or elliptical tectonic boundaries.

The physical origin of the complete system remains an important subject for further investigation.

8. The role of Antarctica in the global framework

Antarctica provides another important reference for the proposed global organization.

The Antarctic Plate is surrounded by extensive divergent plate boundaries connecting the southern Atlantic, Indian and Pacific oceanic ridge systems.

The geometry of these spreading systems can be compared with the major and minor axes of the proposed Antarctic elliptical structure.

The two principal axes define four directions. These can be examined in relation to New Zealand, the Mid-Atlantic Ridge, the East Pacific Rise and the Indian Ocean ridge system.

The development of oceanic lithosphere around Antarctica represents a major component of the horizontal plate-motion system.

Accordingly, the tectonic-ring model proposes that the observed distribution of active plate boundaries reflects the combined effects of horizontal plate movement and stresses associated with the underlying mantle.

A quantitative examination of this relationship would require reconstruction of plate motions through geological time, rather than comparison with present-day geography alone.

9. Geological implications and further investigation

The geometrical relationships identified in California and New Zealand are sufficiently specific to permit quantitative testing.

The locations of ellipse intersections and minor-axis endpoints can be calculated without reference to the positions of individual faults.

Their relationship to observed tectonic structures can then be evaluated independently.

A particularly important test concerns the orientations of the ellipse tangents, convection-roll boundaries and measured plate-motion vectors.

The San Andreas Fault System provides one opportunity for such an analysis. The Alpine Fault, Marlborough Fault System and Hikurangi plate boundary provide another.

Further investigation should examine whether the observed relationships are more systematic than would be expected from alternative elliptical geometries or other possible arrangements of the global tectonic system.

The mechanical interpretation also requires an explicit model of the stresses transmitted from mantle convection into the lithosphere.

This should include the effects of mantle viscosity, velocity gradients, vertical circulation, lithospheric resistance and existing plate-boundary forces.

The ultimate question is whether a mechanically self-consistent convection model can generate the proposed elliptical boundaries without prescribing their shapes in advance.

10. Conclusions

The proposed three-ring model provides a common geometrical framework for examining the relationship between major oceanic tectonic systems and mantle convection.

The most significant results presented here concern the minor axis of the inner Pacific tectonic ellipse.

Its northeastern endpoint lies near the Gulf of California, while its southwestern endpoint lies near New Zealand.

At both ends, the inner Pacific ellipse intersects the outer ellipse of an adjacent tectonic ring at a distance of approximately 54–57 km from the corresponding minor-axis endpoint.

In California, the relevant intersection is between the Pacific and Atlantic rings. In New Zealand, it is between the Pacific and Indian Ocean rings.

These relationships follow from the proposed mathematical geometry and provide two geographically distinct locations for testing its geological significance.

The correspondence between the elliptical boundaries, plate-boundary orientations and regional tectonic structures is particularly interesting in the context of the San Andreas Fault System and the complex Pacific–Australian boundary in New Zealand.

The equator, the 6° southward displacement of the ellipse centers, the 15° spacing of the proposed lower-mantle convection rolls and the 45° orientation of the ellipse axes provide additional geometrical constraints.

Together, these properties form a coherent mathematical description of the proposed global tectonic-ring system.

Their physical significance, however, depends on establishing a mechanical relationship between mantle convection, lithospheric stress and plate motion.

The present analysis should therefore be regarded as a geometrical hypothesis supported by specific, testable correspondences, rather than a completed dynamical explanation of the Earth’s plate-boundary system.

The central objective of further research is to determine whether the large-scale organization represented by the three tectonic rings can emerge from the interaction between mantle convection and the moving lithospheric plates.

According to the tectonic-ring model associated with the mantle convection-roll system, the Red Sea and the Gulf of California occupy remarkably similar geometrical positions.

Both form elongated zones of crustal extension situated along the margins of large tectonic rings, although they occur on opposite sides of the global system.

The Red Sea

In the model, the Red Sea is situated along the outer periphery of the Atlantic tectonic ring, which is theoretically derived as the counterpart of the Pacific Ring of Fire. Its elongated form follows the curvature of the corresponding elliptical boundary.

On the map, 32°N latitude is shown as a reference line and marks the northern limit of the section highlighted in red. From there, the tectonically active zone extends southward toward the Afar region, where the Red Sea system connects with the Gulf of Aden and the East African Rift.

The Gulf of California

The Gulf of California occupies a comparable position along the inner periphery of the Pacific tectonic ring, or Ring of Fire. As in the Red Sea, the elongated tectonic zone approximately follows the geometry of the relevant elliptical boundary.

Again, 32°N latitude is shown as a reference, allowing the geographical positions of the two systems to be compared directly. The Gulf of California extends southward from approximately this latitude and forms part of the active boundary between the Pacific and North American plates.

A striking geometrical comparison

Comparison of the two regions reveals several noteworthy similarities:

• Both form long, narrow tectonic basins produced by crustal extension.
• Both are associated with active plate separation and magmatism.
• Both occupy marginal positions within the proposed tectonic-ring geometry. The Red Sea follows the outer boundary of the Atlantic ring, whereas the Gulf of California follows the inner boundary of the Pacific ring.
• The highlighted sections occupy broadly comparable latitude ranges and can therefore be compared directly using the 32°N reference line.
• Both systems developed mainly during the Cenozoic and underwent major tectonic reorganization during the Miocene and later.
• In both cases, extension is not expressed as a single simple fracture. Instead, deformation is distributed through rift basins, faults, volcanic zones, and, in more developed sections, spreading centres.

The similarity is particularly interesting because the two systems belong to different conventional plate-tectonic settings. The Red Sea records the separation of Arabia from Africa, whereas the Gulf of California forms part of the Pacific–North America plate boundary. Nevertheless, when viewed within the tectonic-ring framework, both occupy equivalent geometrical positions along major elliptical boundaries. The precondition of this comparison is of course at first to analyse the form of the Ring of Fire, and the to transfer that analysis to the Atlantic Ocean.

Possible significance

The comparison therefore raises an important question: can the similar geometry of the Red Sea and the Gulf of California be explained solely by their individual plate-tectonic histories, or does their position within a larger global geometrical system also play a role?

Within the convection-roll model, the resemblance is not regarded as accidental. The two regions can be interpreted as corresponding expressions of extension along the boundaries of two different tectonic rings: one on the outer side of the Atlantic ring and the other on the inner side of the Pacific ring.

Their similar elongated forms, broadly comparable latitudinal positions, young geological development, and relationship to active extension make the Red Sea–Gulf of California comparison a useful test case for examining the proposed connection between mantle convection rolls and the large-scale geometry of plate boundaries.

A particularly striking feature of the proposed mantle-convection framework is a regular sequence of principal lower-mantle divisions along the equator. Taking 21.16°W as the theoretical reference longitude beneath the central Atlantic, equivalent divisions occur at intervals of exactly 30°. Moving eastward around the Earth, the relevant sequence considered here is:

1. 111.16°W — East Pacific Rise
2. 81.16°W — western margin of South America
3. 51.16°W — Amazon mouth and northeastern South America
4. 21.16°W — central Atlantic / Mid-Atlantic Ridge
5. 8.84°E — western coast of equatorial Africa
6. 38.84°E — East African Rift region
7. 68.84°E — Central Indian Ridge
8. 98.84°E — western margin of Indonesia
9. 128.84°E — eastern Indonesia
10. 158.84°E — possible additional boundary east of Papua New Guinea

These are theoretical longitudes. The model does not require the principal surface expression to occur precisely on each lower-mantle division. Upper-mantle upwelling lines occur approximately 1.5° to either side, while the effects of the adjacent convection roll may be expressed as much as 3° from the principal division. The appropriate comparison is therefore with a narrow longitudinal belt rather than with a geometrically infinitesimal line.

1. 111.16°W — East Pacific Rise

The first point lies in the eastern Pacific and corresponds closely to the East Pacific Rise, one of the Earth’s major oceanic spreading systems. Around the equatorial and southeastern Pacific, the East Pacific Rise occupies approximately the 110°W region, although its longitude varies with latitude. The theoretical longitude of 111.16°W therefore falls within about one degree of the broad ridge system. Studies of the eastern tropical Pacific commonly place the Rise near 110°W, while the EPR can be followed continuously southward from the equatorial region.

This is an important starting point because here the expected mantle division is expressed by an unmistakable oceanic spreading system. In the convection-roll interpretation, the surface ridge need not coincide exactly with the lower-mantle division; displacement toward an adjacent upper-mantle upwelling line would be expected.

2. 81.16°W — the western margin of South America

Thirty degrees farther east gives 81.16°W. At the equator this lies immediately west of the coast of Ecuador. Ecuador itself straddles the equator and its western boundary is the Pacific continental margin.

This is a fundamentally different tectonic environment from the East Pacific Rise. Instead of oceanic spreading, the eastern Pacific basin terminates against the South American margin, where the Nazca Plate converges with South America. Thus, within one 30° interval, the system passes from a major zone of crustal production to the continental margin toward which that oceanic plate moves.

The correspondence should not be interpreted as a claim that 81.16°W itself is the trench axis. Rather, it marks the equatorial longitude of the broader western South American tectonic boundary zone.

3. 51.16°W — the mouth of the Amazon

The next theoretical division, 51.16°W, reaches the opposite side of South America near the great outlet of the Amazon River.

This point is different from most of the others because the dominant surface expression is not an active plate boundary. Nevertheless, the Amazon mouth marks one of the major geological and physiographic transitions on Earth: the enormous Amazon drainage system reaches the Atlantic margin here. NASA describes the Amazon as carrying the largest freshwater discharge of any river, delivering roughly one fifth of global river discharge to the oceans.

Within the proposed framework, the significance would therefore not necessarily be present-day faulting. The question is whether the continental-scale drainage architecture, sedimentary basin and Atlantic continental margin preserve a longer-term structural influence associated with the same regular mantle division.

This point consequently needs to be treated more cautiously than the active ridges and rifts.

4. 21.16°W — the central Atlantic

Another 30° east brings the sequence to its reference point, 21.16°W.

This correspondence is particularly close. The Mid-Atlantic Ridge crosses the equatorial Atlantic in the vicinity of 21–22°W. For example, a large 2022 earthquake classified by the USGS as occurring on the central Mid-Atlantic Ridge was located at 0.934°S, 21.716°W. The theoretical value of 21.16°W is therefore within roughly half a degree of this active ridge position.

In the model, this longitude represents a principal lower-mantle division, while the actual surface spreading system may occupy the adjacent 1.5° roll positions. This distinction is important: the geometric reference is defined at depth, while the observable ridge records the response of the upper mantle and lithosphere.

5. 8.84°E — western equatorial Africa

The next 30° step gives 8.84°E, which reaches the Atlantic coast of equatorial Africa near Gabon. Independent geographical data place the equatorial portion of Gabon between approximately 9°E and 14°E, making 8.84°E essentially a coastal or immediately offshore position. Thus the 30° sequence produces another striking basin-scale relationship:

South American Atlantic margin → Mid-Atlantic Ridge → African Atlantic margin, at intervals of approximately 30°.

This does not mean that the Atlantic basin is geometrically symmetrical in conventional plate-tectonic terms. Rather, it suggests that the theoretical mantle sequence intersects three very different parts of the Atlantic system: one continental margin, the spreading axis, and the opposite continental margin.

6. 38.84°E — the East African Rift region

The next theoretical lower-mantle division is 38.84°E. Here the distinction between the lower-mantle division and the surface response becomes particularly important. The main Kenya Rift at the equator does not lie at 38.84°E. Its axial region is farther west. Lake Bogoria, for example, lies at approximately 36.05–36.12°E immediately north of the equator, within the central Kenya Rift. However, the model predicts:

38.84°E — principal lower-mantle division
37.34°E — upper-mantle upwelling line
35.84°E — outer influence/downwelling side of the adjacent 1.5° roll

The last value, 35.84°E, falls remarkably close to the active Kenya Rift. The central Kenya Rift itself is a roughly 100-km-wide asymmetric extensional structure in this region.

Seismic and gravity studies along the equator have additionally suggested that the elevated East African plateau requires a regional mantle contribution and is compatible with dynamic support by mantle convection. This makes the African point particularly useful for distinguishing the deep theoretical division from its displaced lithospheric expression.

7. 68.84°E — the Central Indian Ridge

Thirty degrees farther east lies 68.84°E, almost directly on the active ridge system of the central Indian Ocean. The Central Indian Ridge extends northward from the Rodrigues Triple Junction toward the Carlsberg Ridge. Near the equatorial region it lies broadly between 67°E and 69°E. Published ridge-axis locations include approximately 1.19°S, 67.52°E, and farther south several segments occur between about 68.1° and 68.6°E.

The theoretical 68.84°E position therefore falls comfortably within the ±1.5° influence interval and extremely close to the actual spreading system.

Together with the Mid-Atlantic Ridge and East Pacific Rise, this gives the sequence three major oceanic spreading systems separated by intervening continental and tectonic domains.

8. 98.84°E — western Indonesia

At 98.84°E, the sequence reaches the western Indonesian region, close to Sumatra and the Sunda convergent margin.

This is no longer a spreading environment. Southwest of Sumatra, the Indo-Australian plate converges with the Sunda plate along the Sunda–Java trench system. The USGS describes this as part of an immense collision zone extending from the Indonesian region toward the Himalaya and notes the intense seismicity and volcanism produced by the Sumatra–Andaman subduction system.

The theoretical longitude therefore lies near one of the Earth’s major transitions from Indian Ocean lithosphere into the Indonesian convergent system.

9. 128.84°E — eastern Indonesia

Another 30° east gives 128.84°E, in the exceptionally complex tectonic region of eastern Indonesia, close to the Molucca Sea–Halmahera system.

This is one of the most unusual convergent environments on Earth. The Molucca Sea plate has been consumed by oppositely directed subduction beneath the Sangihe and Halmahera arcs, producing an active arc–arc collision. Modern studies describe the Molucca Sea as one of Southeast Asia’s most complicated tectonic regions and document the interaction of the Philippine Sea, Eurasian/Sunda and Australian plate systems.

A USGS regional tectonic map of the central Molucca Islands uses 128°E as its central meridian and shows subduction zones, strike-slip faults, thrusts and volcanic arcs concentrated through this longitude range. Thus the 128.84°E point corresponds not merely to the eastern edge of Indonesia geographically, but to a major zone of tectonic reorganisation.

10. 158.84°E — a possible additional point east of Papua New Guinea

The next step, 158.84°E, is particularly interesting because it lies east of Papua New Guinea in the Woodlark–Solomon region. This point has not yet been incorporated into the principal sequence in the same way as the preceding nine because the geological relationships are much more complicated. Nevertheless, there is clearly major tectonic and magmatic activity within the predicted belt.

The USGS places the Woodlark Basin between approximately 157° and 159.5°E, directly encompassing the theoretical longitude of 158.84°E. The basin contains the boundary between the Solomon Sea and Australian/Woodlark plates and is an active extensional system. Immediately farther east, the Guadalcanal segment of the Solomon plate boundary occupies approximately 159–161°E.

The broader Solomon system combines active seafloor spreading, subduction of young Woodlark lithosphere, microplate motion, intense seismicity and interaction with the Ontong Java Plateau. The USGS tectonic synthesis shows spreading across the Woodlark Ridge and subduction along the Solomon system, while the Solomon arc has experienced very high levels of large-earthquake activity.

The importance of this tenth point is therefore not that a single simple plate boundary lies precisely at 158.84°E. Rather, the predicted 158.84°E ±3° belt coincides with an exceptionally active zone in which spreading, subduction, arc volcanism and microplate deformation interact. For this reason, 158.84°E should probably be retained as a candidate tenth equatorial node, even if its precise geological expression remains unresolved.

The larger pattern

The sequence is noteworthy because the theoretical coordinates are generated independently of the geological features:

111.16°W → 81.16°W → 51.16°W → 21.16°W → 8.84°E → 38.84°E → 68.84°E → 98.84°E → 128.84°E → 158.84°E.

Across these ten consecutive 30° positions one encounters, in order: East Pacific spreading → South American continental margin → Amazon/Atlantic continental margin → Mid-Atlantic spreading → African continental margin → East African rifting → Indian Ocean spreading → Sunda subduction → Molucca arc collision → Woodlark–Solomon spreading/subduction.

The geological processes are therefore not of one type. Some points correspond to spreading ridges, others to continental margins, rifts, subduction systems or complex collision zones. What they potentially have in common is their position relative to a regular deep-mantle framework.

This distinction is central to testing the model. The proposed lower-mantle divisions should not be expected to produce identical structures everywhere. The lithosphere above them differs greatly in age, thickness, composition and pre-existing tectonic architecture. The test is instead whether major changes in tectonic organization occur repeatedly within the predicted ±1.5° to ±3° belts around an independently defined 30° sequence.

The correspondence at 21.16°W, 68.84°E and approximately 111.16°W is particularly interesting because all three are associated with major oceanic spreading systems. The 38.84°E case provides a different and potentially important test: the lower-mantle division itself lies east of the Kenya Rift, while the predicted western influence line at 35.84°E approaches the actual rift axis closely. Eastern Indonesia at 128.84°E and the candidate point at 158.84°E show yet another manifestation, where the regular sequence enters some of the most structurally complicated convergent regions on Earth.

The Papua–Solomon point therefore deserves further investigation rather than premature classification. If 158.84°E ultimately proves to occupy a systematic position within the Woodlark–Solomon tectonic and magmatic system, it would extend an already remarkable 30° equatorial sequence by one further major tectonic node.

The 30° Equatorial Sequence and the ±3° Mantle-Roll Belts

Taking 21.16°W as a principal lower-mantle division, twelve equivalent divisions occur at exact 30° intervals around the equator. In the proposed convection-roll model, the surface expression does not necessarily coincide with the principal lower-mantle longitude. Upper-mantle upwelling occurs approximately 1.5° to either side, while geological effects of the adjacent roll may occur as far as 3° from the principal division.

The 30° Equatorial Sequence (yellow dots on the map)

No.	Principal division / belt	Main geological correspondence	Interpretation
1	111.16°W ±3°	East Pacific Rise	Major oceanic spreading system; ridge axis lies within the predicted mantle-roll belt.
2	81.16°W ±3°	Western margin of South America	Nazca–South America convergence and subduction along the Ecuador–Colombia margin.
3	51.16°W ±3°	Amazon mouth / NE South America	Major continental and sedimentary transition at the Atlantic margin; less directly tectonic than most other points.
4	21.16°W ±3°	Equatorial Mid-Atlantic Ridge	Major spreading system. The ridge/transform system approaches the eastern side of the predicted belt, near 18.16°W.
5	8.84°E ±3°	West coast of equatorial Africa	Atlantic continental margin and inherited structural zone of the Gabon Basin.
6	38.84°E ±3°	East African Rift	Kenya Rift lies toward the western side of the belt, close to the predicted 35.84°E outer influence line.
7	68.84°E ±3°	Central Indian Ridge	Major Indian Ocean spreading system; the ridge axis falls within the predicted belt.
8	98.84°E ±3°	Western Indonesia / Sunda margin	Major subduction system west of Sumatra, with strong seismic and volcanic activity.
9	128.84°E ±3°	Eastern Indonesia / Molucca–Halmahera	Exceptionally complex arc–arc collision, opposing subduction systems and intense magmatism.
10	158.84°E ±3°	Woodlark–Solomon region	Broad magmatic and tectonic zone involving spreading, subduction, microplates and the Solomon arc.
11	171.16°W ±3°	Phoenix / Nova–Canton region	Major old Pacific fracture-zone system; Nova–Canton Trough lies remarkably close to the 168.16°W outer line.
12	141.16°W ±3°	Central Pacific	Weakest equatorial case; no major active plate boundary directly at the principal longitude, although important fracture-zone and volcanic structures occur within the wider region.

What stands out

The most striking feature is that the sequence does not repeatedly select the same type of structure. Instead it encounters very different manifestations of lithospheric deformation:

spreading ridge → subduction margin → passive continental margin → spreading ridge → passive margin → continental rift → spreading ridge → subduction → arc collision → spreading/subduction complex → fracture zone → intraplate volcanic/fracture-zone province.

That heterogeneity may actually be important for the model. If the 30° divisions represent a deep mantle framework, one should not necessarily expect identical surface structures. Oceanic and continental lithosphere respond differently, and the existing plate geometry determines whether a mantle-related influence is expressed as spreading, faulting, rifting, volcanism or enhanced deformation at a pre-existing boundary.

Three cases are particularly clean geometrically:

21.16°W: the Romanche/Mid-Atlantic ridge region approaches the predicted +3° position at 18.16°W.

38.84°E: the Kenya Rift near 36.1°E approaches the predicted −3° position at 35.84°E.

171.16°W: Nova–Canton Trough near 168.01°W approaches the predicted +3° position at 168.16°W.

There is also an important distinction at 148°E, which is not one of the 30° lower-mantle divisions. As we discussed, that longitude belongs instead to the strong tectonic line produced by the overlapping tectonic-ring geometry. Independent studies find major tectonic changes around 147–149°E: east of ~148°E the Papuan plate boundary becomes increasingly extensional, while around 147–148°E earthquake slip-vector orientations and microplate relationships change markedly.

So we now have two different geometrical systems that should not be mixed:

The 30° sequence describes the proposed regular lower-mantle/convection-roll framework.

The ~29°E → ~91°W → ~148°E set arises from the geometry of the tectonic rings and appears to identify unusually strong zones of tectonic reorganisation.

One of the most striking features of the convection-roll model is the degree of spatial correspondence between the predicted roll boundaries and the observed volcanic zones of Iceland. This correspondence is not restricted to a single volcanic zone or to a few isolated localities. It is repeated in the positions of volcanic-zone margins, changes in direction, intersections, volcanic centres, and the polygonal areas enclosed by the modelled boundaries.

The principal volcanic zones used for comparison are the Western Volcanic Zone (WVZ), Eastern Volcanic Zone (EVZ), Northern Volcanic Zone (NVZ), the Reykjanes volcanic zone, and the volcanic belt crossing Central Iceland. These are well-established components of the Icelandic volcanic and plate-boundary system, although different terminology has been used for the Central Iceland connection between the main rift zones.

Specific examples of correspondence

A number of locations are particularly useful for illustrating the geometrical precision of the correspondence shown on the map:

1. The Reykjanes volcanic zone south of Hveragerði.
   Here, one of the modelled boundaries coincides closely with the transition towards the South Iceland Seismic Zone (SISZ). The relationship is particularly informative because the SISZ forms the tectonic connection between the western and eastern rift systems of South Iceland.
2. The Western Volcanic Zone and Langjökull.
   A modelled roll boundary closely follows the margin of the volcanic zone in the Langjökull area. The spatial relationship is sufficiently sharp to make this an important reference point when the model is compared with mapped volcanic systems.
3. The Eastern Volcanic Zone north of Mýrdalsjökull.
   Another model boundary corresponds to the margin of the EVZ immediately north of the Mýrdalsjökull–Katla region.
4. The Vatnajökull boundary and Grímsvötn.
   Within the Vatnajökull region, a major boundary in the convection-roll pattern passes through the area of Grímsvötn, one of the principal volcanic centres of the EVZ.
5. The boundary extending northeastwards from Kverkfjöll.
   From the Kverkfjöll region, the mapped volcanic structures and the modelled roll boundary follow the same general northeastward direction.
6. The outer boundary of the Kverkfjöll volcanic system.
   The extent of the Kverkfjöll system provides another example in which the margin of a volcanic system corresponds to a boundary in the convection-roll pattern.
7. Internal boundaries within the Northern Volcanic Zone.
   The correspondence is not restricted to the outer margins of the NVZ. Several internal divisions within the volcanic zone also coincide with modelled roll boundaries.
8. The northwestward bend of the Central Iceland volcanic belt.
   The Central Iceland Volcanic Zone, as defined here, bends towards the northwest in a manner that follows the geometry of the convection-roll pattern.
9. A comparable bend in the Western Volcanic Zone.
   The WVZ displays a related change in orientation, extending towards another boundary in the modelled system.

10–11. The polygon occupied by the Northern Volcanic Zone.
A particularly clear geometrical relationship occurs in North Iceland, where the volcanic systems of the NVZ occupy a polygonal sector approximately 1.5° in longitudinal width. Both sides of this sector are defined by boundaries in the convection-roll system.

12. The northern intersection point.
    The northernmost point highlighted on the map coincides with an intersection of two boundaries in the convection-roll framework. This is significant because intersections represent geometrically more restrictive predictions than correspondence with a single line.

The Eastern Volcanic Zone

The most continuous correspondence on the map occurs along the Eastern Volcanic Zone (EVZ).

Four large polygonal sectors of the convection-roll framework are occupied by the volcanic systems shown in yellow on the map. Rather than simply following a single line, the volcanic zone repeatedly fills the areas enclosed by successive boundaries.

The relationship also places several major volcanic centres and systems—including Hekla, Tindfjöll, Eyjafjallajökull, Katla beneath Mýrdalsjökull, and the Vestmannaeyjar volcanic system—within the same geometrical arrangement.

This is important because the comparison therefore involves several different geometrical properties simultaneously: boundaries, intersections, enclosed areas, changes in orientation, and the positions of individual volcanic centres.

The Western Volcanic Zone

Immediately west of the EVZ, the eastern margin of the Western Volcanic Zone (WVZ) is particularly distinct.

In the convection-roll framework, this boundary occurs approximately 3° west of the corresponding eastern boundary of the EVZ. Thus the two volcanic zones are not treated as unrelated features. They occupy neighbouring parts of the same regularly spaced geometrical system.

The WVZ also changes orientation towards its northern end, and this curvature can be compared with the orientation of the modelled roll boundaries.

Central Iceland

The Central Iceland volcanic belt shows a somewhat different type of correspondence.

Here the most prominent geometrical control is not simply a volcanic zone centred on a modelled line. Instead, one of the sharpest boundaries of the volcanic area corresponds to a downwelling boundary extending northeastwards from the region.

This distinction may be important. If upwelling and downwelling boundaries have different mechanical effects on the lithosphere, volcanic zones should not necessarily occupy identical positions relative to each type of boundary.

The Northern Volcanic Zone

The Northern Volcanic Zone (NVZ) provides another particularly clear example.

Its principal volcanic systems are arranged along a predominantly north–south to NNE–SSW axis, while their outer limits correspond to polygonal boundaries in the convection-roll framework. Independent geological studies also show that the NVZ consists of several overlapping volcanic systems and fissure swarms, including Kverkfjöll, Askja, Fremrinámur, Krafla and Þeistareykir.

In the present model, both upwelling and downwelling lines appear to contribute to the geometry of the volcanic zone. The correspondence therefore concerns not merely the central axis of volcanism but also its width and internal subdivision.

Features not fully visible on the map

The map does not show all the relationships that can potentially be tested.

Among the additional examples are the position of Öræfajökull, the geometrical relationship between Snæfellsjökull and Snæfell, and the former Skagafjörður volcanic zone.

The Skagafjörður system is particularly interesting in this context because its position is approximately 3° west of the Northern Volcanic Zone in the geometrical framework used here. Older rift structures in the Skagi region are independently recognised in geological studies of Iceland.

The offshore continuation provides further constraints. The orientations and positions of both the Reykjanes Ridge and the Kolbeinsey Ridge can be compared with the same convection-roll geometry. The Icelandic volcanic zones therefore form only the subaerial part of a considerably larger geometrical pattern.

Plate motion and the orientation of the roll boundaries

The two-dimensional geometrical correspondence is only part of the problem. The system must ultimately be interpreted in three dimensions because the lines on the map represent boundaries associated with several superimposed levels of convection rolls.

Plate motion must also be incorporated.

In the interpretation proposed here, the motion of the North American Plate away from the spreading system produces a major westward to northwestward extensional component across Iceland. This regional movement interacts with the directions of rotation of the underlying convection rolls.

This provides a possible explanation for an important feature of the map: the eastern margins of several volcanic zones are commonly associated with the blue boundaries of the model.

In the convection-roll interpretation, the roll adjacent to such a boundary rotates in a direction opposite to the motion imposed from the North American side. The opposing motions would increase differential movement across the boundary and could therefore favour extension of the overlying lithosphere.

A comparable relationship can be seen along the eastern side of the Northern Volcanic Zone, where several of the principal extensional structures are again bounded on their eastern side by blue lines.

This proposed relationship between plate motion, roll rotation and surface extension is important because it introduces a dynamic component into what would otherwise be only a geometrical comparison.

From geometrical correspondence to a testable model

The significance of the pattern lies in its repetition.

No single coincidence between a volcanic centre and a modelled boundary would provide strong evidence for a relationship. The more relevant observation is that similar relationships recur independently at the margins of several volcanic zones, at changes in their direction, at volcanic centres, at intersections, and within polygonal sectors of the model.

The Eastern Volcanic Zone is especially informative because the correspondence is repeated through several consecutive polygons rather than occurring at only one locality.

The Icelandic pattern can therefore be tested at several levels:

• the distance between mapped volcanic-zone margins and predicted roll boundaries;
• the angular agreement between volcanic structures and the modelled lines;
• the positions of volcanic centres relative to predicted intersections;
• the width of volcanic zones relative to the predicted polygonal cells;
• the relationship between active and extinct volcanic zones and successive boundaries in the model;
• and the relationship between the direction of plate motion and the inferred rotation of individual convection rolls.

Such tests would allow the apparent correspondence to be expressed quantitatively rather than only visually.

The important point is therefore not simply that volcanic activity occurs near individual lines. It is that the geometry of the Icelandic volcanic zones repeatedly reproduces several different elements of the proposed convection-roll framework—lines, margins, bends, intersections and enclosed polygons—at a range of locations across Iceland.