Summary

Measurements and mapping have provided a foundation for scientific progress for centuries. This article seeks to relate available information on Earth’s internal layering, the properties of convection currents, Earth’s spherical geometry, and its rotation to the distribution of geological activity at its surface.

The analysis assumes that slow heat transport in Earth’s mantle may, under certain conditions of dynamic equilibrium, produce a regular system of convection rolls. By comparing the dimensions of Earth’s internal layers with the geometry of such rolls, a model is developed for their vertical and horizontal arrangement. Their horizontal positions are then described by mathematical curves that can be compared with volcanic belts, fissure swarms, and plate boundaries.

Iceland serves as the initial study area. A comparison of calculated convection-roll boundaries with the country’s geological structure provides a basis for investigating relationships among mantle convection, divergence, and the orientation of fracture systems.

The model is subsequently extended to a global comparison. Particular attention is given to whether the arrangement of convection rolls in the lower mantle could be associated with three principal zones of influence separated by 120° of longitude. The hypothesis is advanced that this arrangement may be related, among other factors, to the transfer of heat from the outer core across the core–mantle boundary. On this basis, three tectonic rings are defined: the Pacific Ring, associated with the so-called Ring of Fire; the Atlantic Ring; and the Indian Ocean Ring. Each is represented by a belt between two ellipses sharing a common center and principal orientation.

The objective of the article is to examine whether a common geometric and mechanical model can shed further light on relationships among upwelling, downwelling, divergence, subduction, and horizontal plate motions.

Abstract

Measurements and geographical mapping have provided a foundation for scientific progress over many centuries. This paper explores possible relationships between Earth’s internal layering, the geometry of mantle convection, planetary rotation, and the global distribution of tectonic activity. The proposed Convection Rolls Model assumes that slowly evolving mantle convection may develop a regular arrangement of elongated convection cells under particular conditions of dynamic balance. Their dimensions are compared with the internal structure of Earth, and their horizontal geometry is represented by mathematical curves that can be examined against volcanic zones, fracture systems, and plate boundaries.

Iceland provides the initial regional example. The calculated orientations of convection-roll boundaries are compared with the geometry of its divergent plate boundary and associated volcanic systems. The analysis is subsequently extended to the global scale. Three principal tectonic regions are proposed, separated by 120° in longitude and tentatively associated with large-scale thermal organization near the core–mantle boundary.

These regions are represented by three paired elliptical belts: the Pacific Ring, associated with the familiar Ring of Fire, the Atlantic Ring, and the Indian Ocean Ring. Their overlapping geometry is examined in relation to divergent, convergent, and transform plate boundaries.

The proposed framework seeks to connect the vertical transport of heat and matter within Earth with the horizontal organization of lithospheric deformation. Its geometric relationships provide hypotheses for testing against independent geophysical and geological observations.

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1. Introduction

Heat is continuously transferred from Earth’s interior to its surface and from there into space. This transfer of heat is one of the fundamental processes underlying the activity that shapes Earth’s surface. Heat may be transferred in three ways: conduction, radiation, and mass transport. In Earth’s mantle, much of the heat transfer occurs through convection, in which material moves in response to differences in density caused, among other things, by variations in temperature.

The mantle consists predominantly of solid rock, but under the high pressures, temperatures, and long timescales that prevail there, its material can deform and flow very slowly. These motions therefore differ from those in ordinary liquids, although several fundamental principles of fluid mechanics remain applicable. William Thomson, later Lord Kelvin, once calculated that Earth could not have been cooling for more than a few tens of millions of years. His calculation did not take account of heat production by radioactive elements, which was subsequently recognized as an important factor in explaining Earth’s thermal history.

Earth has several sources of heat. They include heat retained from its formation, heat generated through radioactive decay, and heat transferred from the core into the mantle. Earth’s cooling and the movement of heat within it affect the density, viscosity, and motion of mantle material. When mantle material is heated, its density generally decreases relative to cooler material at comparable pressure. It may therefore become buoyant and rise. Cooler material is correspondingly more likely to sink. Under these conditions, motions can develop that form circulatory patterns or convection rolls.

These movements operate over such long periods that it is reasonable to ask whether they may develop a regular organization. Equilibrium need not imply that the system is stationary. Rather, it may constitute a dynamic balance in which motion continues while some of its principal features remain relatively stable. This line of thought led to the development of a mathematical model referred to here as the Convection Rolls Model of Earth.

The initial objective was to investigate whether the positions and orientations of Iceland’s volcanic belts could be explained in terms of Earth’s internal structure. Subsequent analysis suggested that the approach might be extended to plate boundaries on a global scale. This development raises a new research question:

Could the same internal system of convection rolls influence both divergent and subduction zones, and could those influences be reflected in a regular global distribution of tectonic activity?

2. Assumptions Underlying the Convection Rolls Model

The calculation of possible positions and orientations of convection rolls in Earth’s mantle rests on three main considerations:

1. Earth’s internal layering and the measured boundaries between its principal layers.
2. The properties of convection currents and the geometric forms they can produce.
3. The geometry of horizontal movements on a spherical surface and the possible influence of Earth’s rotation on their organization.

The theoretical background includes studies of convection and the formation of elongated convection rolls, as discussed by Manneville (2010), and studies of inertial trajectories on a rotating sphere by Paldor and Killworth (1988). Walzer (1971) has also discussed relationships between mantle convection and large-scale features of Earth’s topography. Convection experiments can produce regular, elongated rolls. Under certain conditions their cross sections approach equal height and width. That geometry is used here as a reference in constructing the model. The model assumes that, over long periods, mantle motions may tend toward a relatively efficient configuration in which buoyancy, gravity, viscosity, and other forms of resistance interact.

It is important, however, to distinguish this assumption from a demonstration that actual convection rolls within Earth possess precisely this geometry. Mantle properties are complex and depend, among other things, on temperature, pressure, composition, and strain rate. Similarly, a geometric comparison with inertial trajectories on a rotating sphere must be distinguished from a direct mechanical description of mantle convection. In conventional models of slow mantle flow, Coriolis forces are considered very small in comparison with gravitational and viscous forces. Applying such trajectories to mantle convection is therefore a specific research assumption of the present model and requires further physical justification.

With this qualification, a geometric framework can nevertheless be formulated and tested for measurable correspondence with Earth’s geological structure.

3. Earth’s Internal Layering and the Dimensions of Convection Rolls

Earth’s internal structure is known to a considerable extent from seismological measurements. These reveal, among other boundaries, those between the crust, mantle, outer core, and inner core. In 1936, Inge Lehmann demonstrated the existence of Earth’s inner core. Its radius is approximately 1,221 km, giving it a diameter of about 2,442 km. The outer core extends from a depth of approximately 2,900 km down to the inner core. The mantle lies between the crust and the outer core. Within the mantle, seismic observations reveal important changes in wave velocity at depths of approximately 410 and 660 km. These discontinuities are primarily associated with pressure-induced changes in mineral crystal structure.

The Convection Rolls Model places particular emphasis on comparing the thicknesses of these layers with possible dimensions of circulating flow units.

Figure 1. Cross section of Earth showing the inner core, outer core, lower mantle, upper mantle, and lithosphere. The inner core has a radius of approximately 1,221 km.

3.1. The Larger Convection Rolls

If a regular circulating flow is assumed within the lower mantle, it is possible to investigate whether the dimensions of the convection rolls could be related to the thickness of the layer they occupy. The model assumes that two layers of convection rolls may be stacked between depths of approximately 670 and 2,900 km. On this basis, 24 major units are proposed around Earth, each spanning 15° of longitude on the model’s coordinate grid. Two neighboring units then form a combined circulation spanning 30°.

Thus:

24 × 15° = 360°

Alternatively, there are 12 combined pairs, each spanning 30°. This division becomes important when considering how upwelling and downwelling may alternate within the system.

Figure 2. Cross section of Earth showing two layers of large convection rolls in the lower mantle. Upwelling and downwelling are shown on opposite sides of the combined units.

3.2. The Smaller Convection Rolls

Much smaller units are considered in the upper mantle.

In the Convection Rolls Model, the interval from approximately 120 to 410 km depth is divided into two layers. Likewise, the interval from approximately 410 to 670 km depth is divided into two layers, although the lower boundary of the mantle transition zone is generally measured at approximately 660 km.

The model thus assumes a total of four layers of smaller convection rolls. If each unit spans 1.5° of longitude on the coordinate grid, there are 240 units in each layer:

240 × 1.5° = 360°

A notable consequence is that ten smaller units correspond to the width of one larger unit:

10 × 1.5° = 15°

This establishes a regular geometric correspondence between the proposed convection-roll systems of the upper and lower mantle. This arrangement is one of the model’s central assumptions. It does not, however, follow directly from seismic measurements. Further investigation is required to determine whether actual variations in viscosity, density, and flow conditions could produce such regular units.

Figure 3. Arrangement of convection rolls in the upper mantle. Two layers are shown between 120 and 410 km depth, and two between 410 and 670 km, together with their mathematical relationship to the larger units of the lower mantle.

4. Horizontal Geometry of the Convection Rolls

The vertical arrangement of convection rolls does not by itself establish their positions at Earth’s surface. Their horizontal orientation must also be described. The Convection Rolls Model assumes that horizontal flow may follow regular curved paths that change direction with increasing distance from the equator. A particular mathematical construction represents these trajectories as circles in a coordinate system of longitude and latitude. The calculations are based on a combined 30° unit at the equator and a reference condition relating the size of a horizontal circular path to Earth’s radius.

Under the model’s assumptions, the center of each circular trajectory lies at approximately 32° north or south latitude. The radius of the circle in the coordinate system is:

r = √(32² + 15²) = 35.34°

The equation for a circular trajectory in the Northern Hemisphere is therefore:

(λ − Cₙ)² + (φ − 32°)² = (35.34°)²

where:

• λ denotes longitude;
• φ denotes latitude;
• Cₙ is the longitudinal coordinate of the center of the relevant trajectory.

The centers are spaced at intervals of 1.5° when the smaller convection rolls are plotted, and at 15° intervals when only the principal lower-mantle arrangement is shown. The corresponding trajectory in the Southern Hemisphere has its center at 32°S:

(λ − Cₙ)² + (φ + 32°)² = (35.34°)²

Together, these trajectories form a regular network over much of the planet.

It is important to emphasize that these are circles in a flat longitude–latitude coordinate grid. They are not necessarily circles defined by equal surface distances on Earth, because the distance represented by one degree of longitude decreases toward the poles.

Accurate comparisons with geological orientations and distances must therefore account for this spherical-geometric variation.

Figure 4. Horizontal trajectory of convection rolls in a longitude–latitude coordinate system. The center at 32°N, the radius of the trajectory, and its relationship to a 30° unit at the equator are shown.

4.1. Boundaries at 64° Latitude

The model assumes that a different arrangement of convection rolls takes over closer to the poles.

In the Northern Hemisphere, the centers of these trajectories lie at 96°N in an extended coordinate system:

(λ − Cₙ)² + (φ − 96°)² = (35.34°)²

The corresponding Southern Hemisphere trajectories have their centers at 96°S:

(λ − Cₙ)² + (φ + 96°)² = (35.34°)²

These trajectories connect with those at lower latitudes in the vicinity of 64°N and 64°S.

According to the model, four principal belts of horizontal trajectories are thereby distinguished:

• From the equator to 64°N, where westward trajectories dominate the principal representation.
• From 64°N to the North Pole, where eastward trajectories take over.
• From the equator to 64°S, where eastward trajectories dominate.
• From 64°S to the South Pole, where westward trajectories take over.

This division forms part of the model’s geometric representation. It is not an independent measurement of actual mantle-flow directions. The boundary at 64° latitude has particular importance for the analysis of Iceland, as discussed below.

5. The Convection Rolls System and the Geology of Iceland

Iceland occupies a distinctive position among Earth’s volcanic regions. The country lies on the divergent boundary between the North American and Eurasian plates, where the Mid-Atlantic Ridge rises above sea level. Both vertical and horizontal motions occur there. Mantle material rises, magma is generated through decompression melting, new crust is added, and the tectonic plates move apart. The volcanic belts, however, do not follow a single straight line. On the Reykjanes Peninsula and in the Western Volcanic Zone, fissure swarms have orientations that differ from those across much of the Eastern Volcanic Zone. The Northern Volcanic Zone also has a distinctive structure, particularly north of the central highlands. The Convection Rolls Model seeks to compare these orientations with calculated boundaries between convection rolls.

5.1. Volcanic Belts South of 64–65°N

In southern Iceland, the calculated boundaries of the convection rolls form large, relatively regular diamond-shaped patterns. In the model, these patterns are associated with the interaction of two directional influences: the calculated organization of the convection rolls and the horizontal divergence of the tectonic plates. The Eastern Volcanic Zone, extending in part from Hekla and the Laki fissures northward toward Vatnajökull and Kverkfjöll, is of particular interest in this comparison. Important portions of this volcanic zone have orientations similar to certain lines in the convection-roll system. The model proposes that correspondence between these orientations might influence the distribution of divergence among individual fissure swarms. This does not imply that every fracture or volcano directly follows a single convection-roll line. On the contrary, interactions among several kinds of motion may produce complex structures.

5.2. Changes at 64–65°N

The calculated arrangement of convection rolls changes substantially toward 64–65°N. Here, trajectories associated with lower latitudes approach those of the polar system. Changes in the arrangement of Iceland’s volcanic belts are also observed in nature. Large diamond-shaped patterns and oblique fracture systems are common in the south, whereas north–south orientations become more prominent farther north, including in the Northern Volcanic Zone from Kverkfjöll and Askja toward Öxarfjörður.

According to the Convection Rolls Model, this transition could be associated with a change in the geometric organization of mantle convection at similar latitudes. This is one of the hypotheses that can be tested by detailed comparison with mapped fractures and measured plate motions.

5.3. The South Iceland Seismic Zone

The South Iceland Seismic Zone is another important study area. It contains strike-slip movements and fracture systems that cannot be explained by simple divergence alone. In the Convection Rolls Model, the calculated roll boundaries form diamond-shaped patterns that can be compared with the orientations of different fracture sets. Such comparisons may be useful when examining relationships among plate motions, the stress field, and the distribution of individual fracture systems. The measured properties of the seismic zone must nevertheless be distinguished from the forms generated by the mathematical model. In particular, the model must be compared with measured strike-slip orientations and interconnected fracture systems.

5.4. Iceland as Part of a Larger System

The analysis of Iceland was originally the primary focus of the Convection Rolls Model. It sought to show how calculated trajectories of internal Earth motions might correspond to the positions and orientations of geological features in a relatively small area. If the model has general validity, however, studying Iceland alone is insufficient. The same principles must be examined in relation to other divergent zones, subduction zones, transform faults, and volcanic systems. This question leads from the geology of Iceland to global plate tectonics.

Figure 5. Calculated convection-roll boundaries across Iceland. The change in pattern at 64–65°N is shown alongside the volcanic belts and major fracture systems.

6. From Local Divergence to a Global Plate System

Plate tectonics describes the motions of lithospheric plates and their positions relative to one another. At divergent boundaries, plates move apart and new oceanic crust may form. At convergent boundaries, plates collide and oceanic lithosphere may descend back into the mantle. At transform boundaries, plates move laterally past one another.

These three principal types of plate boundary are closely related. New crust is continuously produced along the Mid-Atlantic Ridge and other oceanic ridges. Over long periods, this production must be considered alongside subduction and crustal recycling elsewhere. Many of today’s most important subduction zones are situated around the Pacific Ocean. They form a large part of the region commonly known as the Ring of Fire.

The discussion therefore turns to two major aspects of the same global process: the creation of new crust at divergent boundaries and the return of oceanic crust to the mantle through subduction. Such an analysis must include both vertical and horizontal movements. At divergent boundaries, mantle material rises and also spreads laterally. At subduction zones, cooler and denser oceanic lithosphere descends into the mantle, potentially modifying the flow of surrounding mantle material. At transform boundaries, lateral displacement occurs without necessarily producing or destroying significant amounts of crust at the boundary itself.

The question is whether these different phenomena might be described as local expressions of a larger system of motion. This does not disregard recognized forces such as slab pull, gravity-driven motions associated with oceanic ridges, or forces connected with mantle flow. Rather, the objective is to investigate whether a common internal geometry can help explain how these forces are distributed.

7. A Threefold Organization of the Lower Mantle and Its Relationship to the Outer Core

When the calculated boundaries of lower-mantle convection rolls are plotted on a world map, a regular pattern appears at intervals of 15°. If only selected major units are displayed, a simple pattern extending around the globe becomes apparent. Within this arrangement, three principal longitudinal regions can be identified and associated with active areas in or near Iceland, Hawaii, and western Indonesia. These three regions invite consideration of whether the global organization of heat transport may have a threefold character.

7.1. The Role of the Outer Core

Earth’s outer core consists predominantly of liquid, iron-rich material. Movements occur there because of thermal and compositional differences. These motions are fundamental to the process that maintains Earth’s magnetic field. The mantle lies above the outer core, separated from it by the core–mantle boundary (CMB) at a depth of approximately 2,900 km. Substantial heat can be transferred across this boundary from the core to the mantle.

Heat flow across the boundary need not be uniform. Uneven distribution of heat can affect temperature, density, and upwelling in the lowermost mantle. This raises the possibility of a connection between motion in the outer core and the convection-roll system in the mantle.

7.2. Three Principal Upwelling Pathways

As an extension of the Convection Rolls Model, the hypothesis is proposed that, at a large scale, the outer core may be conceptualized as containing three principal upwelling pathways and three principal downwelling pathways. Such an arrangement would consist of six interacting sectors of a circulating flow system. At the core–mantle boundary, this organization might influence the distribution of heat entering the lower mantle. The model does not assume that outer-core material flows directly upward through the mantle. The proposed connection concerns primarily heat transfer and its possible influence on motions within the solid mantle.

The mantle is very thick, and influences originating at the CMB may spread, change, and interact with other flow systems before being expressed closer to the surface. Nevertheless, the research hypothesis advanced here is that such a threefold arrangement may be reflected in three major regions of influence at the global scale.

In the model, these are associated with areas near Iceland, Hawaii, and Indonesia. They are not defined as three precise points at which upwelling from the core has been measured. Instead, they are reference regions for further comparison of the geographical and geometric organization of tectonic activity.

Figure 6. World map showing lower-mantle convection-roll boundaries at 15° intervals. Three principal regions of influence are highlighted, together with their proposed relationships to the central meridians of the tectonic rings.

8. Three Tectonic Rings

One of the main new elements of the analysis is the proposal that the global distribution of active plate boundaries may be compared with three extensive elliptical regions.

These are designated as:

1. The Pacific Ring, or Ring of Fire.
2. The Atlantic Ring.
3. The Indian Ocean Ring.

The three rings are defined by the same fundamental geometric dimensions, but their centers are separated by 120° of longitude. Dividing the 360° circumference of Earth into three equal parts gives:

360° / 3 = 120°

Moreover, 120° is an integer multiple of the 15° subdivision of the larger lower-mantle convection rolls:

120° = 8 × 15°

The threefold global arrangement can therefore be related geometrically to the same fundamental division used in the Convection Rolls Model. This numerical correspondence does not, in itself, demonstrate that the rings are generated by the convection rolls. Establishing that connection requires a mechanical explanation and comparison with geological observations.

8.1. Mathematical Geometry of the Rings

In the model, each tectonic ring is defined by two ellipses. The inner ellipse has the following semi-axes:

• Semi-major axis: 77.7° (units).
• Semi-minor axis: 51.8° (units).

Their mathematical ratio is:

77.7 / 51.8 = 1.5

Thus, the ratio of the major to minor axes of the inner ellipse is exactly 3:2.

The outer ellipse has the following semi-axes:

• Semi-major axis: 96.5° (units).
• Semi-minor axis: 71° (units).

Their ratio is approximately 1.36.

The principal axes of both ellipses are tilted by 45° on the longitude–latitude coordinate grid. The major axis extends from northwest to southeast, while the minor axis runs perpendicular to it, from southwest to northeast.

The centers of all three rings are situated at 6°S.

Their central longitudes are:

• Atlantic Ring: 30.5°W.
• Indian Ocean Ring: 89.5°E.
• Pacific Ring: 150.5°W.

The centers are therefore separated by exactly 120° when measured around Earth.

On a flat coordinate grid, the ellipses may be described by the following transformation:

u = (Δλ − (φ + 6°)) / √2

v = (Δλ + (φ + 6°)) / √2

where Δλ is the longitudinal difference from the center of the relevant ring.

The equation of the ellipse is then:

u²/a² + v²/b² = 1

where a is the semi-major axis and b is the semi-minor axis.

This formulation makes it possible to calculate ring boundaries on the map grid and compare them with the locations of geological features.

Because degrees of longitude and latitude do not represent equal distances everywhere, the shape on a coordinate map must be distinguished from the shape on the spherical surface. Particular care is needed when interpreting ellipses near the poles or across the 180° meridian.

8.2. Inner and Outer Boundaries

The inner ellipse defines one principal reference boundary of the region of influence, and the outer ellipse defines the other. The region between them is referred to here as the tectonic ring. This does not imply that all parts of the ring are equally active or that geological boundaries exactly follow the ellipses. Some regions may be characterized by divergence, others by subduction, and still others by transform motion. The width of the ring also varies. Because the inner and outer ellipses do not have precisely the same axis ratios, the belt between them is not of uniform width.

In this coordinate representation, the inner ellipse spans approximately 120° along the equator. The outer ellipse extends over a much greater range of longitude and therefore overlaps more extensively with neighboring rings. The result is a system of three adjacent and partly overlapping regions of influence.

Figure 7. Mathematical map of the three tectonic rings. Inner and outer ellipses are shown on a longitude–latitude coordinate grid without a basemap. Their centers lie at 6°S and are spaced 120° apart.

9. The Pacific Ring and the Ring of Fire

The Ring of Fire around the Pacific Ocean is one of the best-known features of Earth’s geology.

It consists of extensive zones of earthquakes, volcanism, and subduction, extending along the western coast of South America, through Central America and western North America, Alaska, the Aleutian Islands, Kamchatka, Japan, Indonesia, and southward to New Zealand.

It is not a continuous ring in the conventional geometric sense, but a belt composed of numerous distinct yet connected plate boundaries.

Large portions of the region contain subduction zones where oceanic plates descend beneath other plates. Elsewhere, transform movements and other plate-boundary types occur. The Convection Rolls Model places the Ring of Fire in a broader context. The Pacific Ring is defined as an elliptical region of influence centered at 149.3°W and 6°S.

Within that region, it is possible to investigate whether the distribution of plate boundaries is related to the inner boundary, the outer boundary, the axes, or other properties of the ellipse.

9.1. California and the San Andreas Fault

The San Andreas Fault is one of the world’s best-known transform faults. It forms part of the boundary between the Pacific and North American plates. In the elliptical model, attention is directed, among other places, to the central sectio of the San Andreas Fault near 36.4°N, 121°W. There, the orientation of the fault can be compared with the inner boundary of the Pacific Ring.

The Gulf of California and the Salton Sea region also provide important reference areas for examining the northern part of the ring. The comparison concerns not only the proximity of individual points to the ellipse, but also whether the orientation of the plate boundary corresponds to the tangent of the calculated curve. This approach provides more testable quantities than a simple comparison of locations.

9.2. New Zealand and Overlapping Rings

New Zealand occupies a distinctive position where extensive plate-boundary systems meet in the southwestern Pacific. The Alpine Fault on the South Island is one of the region’s most important strike-slip faults. The model investigates whether its location is related to the minor axis of the Pacific Ring, as well as to areas where the proposed rings overlap. The relevant comparisons concern both the geometric position of plate boundaries and whether calculated convection-roll trajectories have corresponding orientations.

This location is of particular interest because of its relationship to other active plate boundaries near New Zealand, including the Tonga–Kermadec subduction zone.

9.3. Hawaii and the Central Meridian of the Ring

Hawaii differs from these examples. Its volcanoes lie within the Pacific Plate, far from its major plate boundaries. In the model, Hawaii is not primarily associated with the boundary of the ellipse, but with the principal north–south meridian running through the center of the Pacific Ring.

On one hand, a region of influence is associated with the center of the system and possible mantle upwelling. On the other, the elliptical boundaries are compared with the distribution of lateral stress and deformation zones. Volcanoes within plates and tectonic activity along plate boundaries may therefore occupy different geometric categories within the same research model.

10. The Atlantic Ring

The Atlantic Ring constitutes the second major component of the threefold system. Its center is at 29.3°W and 6°S. Unlike much of the Pacific Ring, the Atlantic Ocean is characterized primarily by divergence. The Mid-Atlantic Ridge extends from the northern oceans southward through the Atlantic, forming boundaries between major tectonic plates. New oceanic crust is continuously formed along it. Iceland is one of the clearest examples of this activity, since the ridge emerges above sea level there.

10.1. Iceland in a Global Context

When the Atlantic Ring is superimposed on a world map, its mathematical geometry can be compared with the position of the Mid-Atlantic Ridge and other active regions. This places the earlier analysis of Iceland’s volcanic belts in a new context. The convection rolls previously compared with fracture orientations in Iceland are now considered as part of a much larger system. Iceland consequently becomes not only a regional example of divergence but also a reference area for investigating the global distribution of heat and stress. Particular attention may be given to Iceland’s position relative to other principal regions of influence, including Hawaii. Their longitudes differ by approximately 90°, suggesting a further comparison with the regular organization of the convection-roll system.

10.2. The Red Sea and East Africa

According to the elliptical model, the Atlantic Ring extends beyond the Atlantic Ocean itself. Areas considered in this context include the Red Sea and the East African Rift System. The Red Sea is a divergent zone where the Arabian Plate is moving away from Africa. In the model, its position may be compared with the outer boundary of the Atlantic Ring. It is particularly interesting to examine whether the geometry there has any relationship to comparable features in the Gulf of California, where divergence and transform motion are also associated with long, relatively narrow marine basins.

This comparison does not imply that the two regions formed in the same way or are at the same stage of development. The objective is to examine whether larger-scale geometric factors may affect their orientations.

10.3. The Galápagos Islands and Overlap with the Pacific

The Galápagos Islands provide another interesting study area. They lie near plate boundaries in the eastern Pacific, where both divergence and the movements of oceanic plates are involved. In the elliptical model, this region may be compared with the margins of the Atlantic and Pacific rings. Such overlap becomes particularly interesting if it can be linked to the orientation and activity of measured plate boundaries.

11. The Indian Ocean Ring

The third ring is the Indian Ocean Ring, centered at 90.7°E and 6°S. The Indian Ocean contains an extensive system of oceanic ridges forming interconnected divergent boundaries. These involve the motions of several major plates and the formation of new oceanic crust. The Indian Ocean Ring, however, is not limited to the divergent boundaries within the Indian Ocean. According to the elliptical model, its region of influence also extends into parts of Asia, Indonesia, and the southwestern Pacific.

11.1. Indonesia and Subduction Zones

Indonesia is one of Earth’s most active volcanic regions. Several tectonic plates and extensive subduction zones converge there. Krakatau, or the Krakatau volcanic system, is among the features that can be used for geographical comparisons within the Convection Rolls Model. In the threefold hypothesis, western Indonesia is associated with one of the principal regions of influence in the proposed heat-transfer system.

The region also lies partly within the area where the Pacific and Indian Ocean rings meet.

This overlap provides an opportunity to investigate whether more than one large-scale directional or stress influence is present.

11.2. Tonga–Kermadec and the Southwestern Pacific

The Tonga–Kermadec belt is one of Earth’s most active subduction zones. There, the Pacific Plate descends beneath an adjacent plate system, and subduction is associated with extension in back-arc regions. This is an important study area for the Convection Rolls Model because three factors can be compared:

• The downward movement of the subducting oceanic plate.
• Lateral movements and extension behind the subduction zone.
• The calculated geometry of the convection rolls and tectonic rings.

This offers an opportunity to test whether interactions between subduction and mantle flow are more complex than the simple relative movement of two rigid plates. Conventional explanations consider, among other factors, slab pull, migration of the subduction boundary, and flow of mantle material around the slab.

The Convection Rolls Model proposes an additional perspective, investigating whether the positions and orientations of calculated convection rolls can influence this development.

12. Overlapping Rings and the Mechanics of Plate Boundaries

Although the three rings are defined using the same mathematical assumptions, geological activity within them varies considerably. Some regions are characterized by divergence, others by subduction, and still others by transform motion. This diversity does not necessarily preclude a connection with a common internal system of motion.

On the contrary, one of the principal aims of the analysis is to investigate whether different forms of local activity can arise from differing conditions within a larger system.

12.1. Interaction Between Vertical and Horizontal Motions

Convection is fundamentally a three-dimensional motion. Material rises in one region, moves laterally in another, and descends in a third. Near Earth’s surface, this motion is affected by rigid lithospheric plates, local stress conditions, and the variable physical properties of rock. Consequently, the same internal system of heat transport may have different effects under different conditions. At a divergent boundary, space is available for new material to rise and form new crust. At a subduction zone, a cold oceanic plate may descend through a region in which mantle material is also flowing laterally. If a subducting slab passes through a system of convection rolls, it may alter their circulation. Some rolls may lose part of their regular circulation, whereas others may influence the orientation or deformation of the region.

This is one of the ideas that the Convection Rolls Model proposes for further study.

12.2. The Importance of Horizontal Forces

Research on subduction has placed considerable emphasis on the downward pull of cold oceanic lithosphere. This force is important in conventional mechanical explanations of plate motions. Here, however, it is proposed that the influence of horizontal components of mantle flow on the subduction process should also be examined. If convection rolls have particular orientations relative to a subducting slab, they may affect the movement of material toward and away from the subduction zone.

This provides an opportunity to investigate whether the positions and orientations of particular subduction zones are partly related to the larger-scale organization of mantle convection. The hypothesis calls for mechanical calculations that account for viscosity, density contrasts, pressure, flow velocity, and the actual properties of mantle material.

12.3. Why Ellipses?

The elliptical form of the rings is not an arbitrary assumption in this investigation, but is based on comparisons with the locations and orientations of particular plate boundaries.

In particular, relationships involving the San Andreas Fault, New Zealand, and other regions have been used to define the inner ellipse of the Pacific Ring. The outer ellipse is then defined to encompass a larger region of influence. The tilt of approximately 45° is especially noteworthy. Within the Convection Rolls Model, the calculated trajectories are compared with such an oblique organization of stress and deformation.

It is nevertheless important to distinguish the appearance of this orientation in a geometric comparison from its derivation from the fundamental equations of mechanics. It therefore remains a specific research task to determine whether the combined influence of the convection rolls can provide a mechanical explanation for the elliptical shape and its 45° tilt.

13. Antarctica and the Relationships Among the Rings

The southern part of Earth is of particular importance for the global geometry of the tectonic rings. Here, the oceanic ridge systems of the Atlantic, Indian, and Pacific oceans converge with extensive plate boundaries surrounding Antarctica.

The investigation has also considered a particular elliptical representation of the tectonic structure of the Antarctic region. This distinguishes between the major and minor axes, which are related to different portions of the Antarctic Plate boundaries.

Particular attention has been given to points near 64°S, including approximately 64°S, 160°22.5′E and 64°S, 19°37.5′W. These locations serve as geometric reference points for comparison with the calculated axes and principal trajectories of the system. One reason why 64°S is of particular interest is that the Convection Rolls Model also predicts a change in the arrangement of horizontal trajectories at that latitude.

It may therefore be possible to relate three features:

• The calculated transition in the convection-roll system at 64°S.
• The mathematical axes of the tectonic rings.
• The positions and orientations of active plate boundaries around Antarctica.

Demonstrating an actual relationship, however, requires calculation of the positions and intersections of these trajectories on Earth’s surface, followed by comparison with measured plate boundaries.

This part of the investigation is particularly important because it may link the three tectonic rings to a common global geometry.

14. Geological Evolution and the Present-Day Ring of Fire

Interpretations of global plate tectonics must distinguish between geological evolution and present-day activity. The Ring of Fire is recognized from its present geological structure and activity. This does not mean that all existing subduction zones have occupied the same positions or maintained the same forms throughout Earth’s history.

On the contrary, plates have formed, moved, fragmented, and joined during different geological periods. In this context, the relationship between Earth’s internal motions and its surface may be considered to have evolved through several major stages. In the earliest stages of Earth’s history, local upwelling and downwelling regions may have existed without the fully developed global plate system familiar today. Distinct or temporary subduction zones may subsequently have formed where conditions allowed.

At later stages, a global plate system emerged with extensive and long-lived divergent and subduction boundaries. Under this interpretation, the present Ring of Fire need not be regarded as an original or immutable form of Earth’s internal motion system. Rather, it may be one manifestation of that system during a particular period of geological history.

The same consideration applies to the Atlantic and Indian Ocean rings. If the rings are related to long-lived influences of internal heat transport, it is possible that they have affected the development of plate boundaries over very long periods, even as individual boundaries change or disappear. A distinction is therefore necessary between two aspects: the present geometry and activity of plate boundaries, and the possible long-term evolution of the internal organization affecting their motions.

15. Comparison with Geological Data

A mathematical model has explanatory value if it produces results that can be compared with independent observations. The Convection Rolls Model is subject to the same requirement. Numerous locations have already been examined where calculated trajectories appear to lie close to recognized geological features.

Examples include Iceland, Yellowstone, Hawaii, the San Andreas Fault, New Zealand, Kamchatka, Indonesia, the Galápagos Islands, the Red Sea, and the Tonga–Kermadec belt. Such comparisons may provide indications of possible relationships. It is nevertheless essential to determine whether the correspondences are statistically significant and better than those that might occur by chance when large numbers of locations and trajectories are compared. Further tests should therefore address several questions.

First, precise distances should be calculated between observed geological features and the trajectories defined by the model. Second, the orientations of faults, fissure swarms, oceanic ridges, and subduction zones should be compared with calculated tangents. Third, the mathematical boundaries of the proposed stress fields should be compared with measured deformation directions and present-day plate motions. Fourth, it should be established whether the correspondence persists when all relevant locations within a study area are considered, rather than only those that appear to fit the model well.

Finally, the model should be examined in relation to seismological observations and tomographic imaging of Earth’s interior.

This is especially important for the hypothesis that three principal regions of influence at Earth’s surface could be connected with the organization of heat flow at the CMB.

Measurable and reproducible results from such comparisons would strengthen the model. A lack of correspondence, or disagreement with observed mechanics, would instead require revision of its assumptions.

16. Discussion

The Convection Rolls Model is founded on the idea that Earth’s internal system of motion may be approached using relatively simple geometric assumptions. Its starting point was Earth’s internal layering and the fact that convection currents can form regular units under certain conditions. By comparing the sizes of such units with the thicknesses of Earth’s internal layers, a division into larger and smaller convection rolls was proposed. Their horizontal trajectories were then calculated and compared with the geological structure of Iceland. The analysis has subsequently been extended to the global distribution of plate boundaries.

The proposal of three tectonic rings forms part of that development. It does not assume that the Ring of Fire is the only major region related to internal processes within Earth. Instead, it proposes that three comparable regions of influence may form a common global arrangement. The differences among the rings therefore lie not primarily in their basic geometry, but in the geological activity expressed at particular locations.

The Pacific Ring is characterized to a considerable extent by subduction, the Atlantic Ring by divergence, and the Indian Ocean Ring by interactions among divergence, subduction, and complex plate boundaries. This division is not absolute, however. More than one type of plate boundary occurs within each ring. This emphasizes that the tectonic rings are not defined as three different types of plate boundary, but as three potential regions of influence in Earth’s global geometry.

The exact 120° separation of their centers and the 3:2 axis ratio of their inner ellipses are particularly noteworthy. Their tilt of approximately 45° is another important feature. Together, these dimensions invite further investigation of whether the elliptical geometry can be derived from the magnitudes and directions of interacting motions.

Geometric correspondence should not, however, be treated as a sufficient mechanical explanation. An independent analysis is required to establish how heat transport, buoyancy, viscosity, and stress distribution could create such regions. The Convection Rolls Model as a geometric hypothesis must therefore be distinguished from a fully developed physical model satisfying the conservation laws of mass, energy, and momentum. This distinction is essential if the hypothesis is to be tested through theoretical and numerical methods.

17. Conclusions and Closing Remarks

This article has sought to connect Earth’s internal structure, the properties of convection currents, and the global distribution of tectonic activity through a common research framework. It began by showing how a regular system of larger and smaller convection rolls might be proposed in relation to the mantle’s internal layering.

The horizontal geometry of these rolls was then defined using calculated trajectories that can be compared with the geology of Iceland. This analysis emphasized relationships among divergence, the orientation of volcanic belts, and the arrangement of fracture systems. Attention was subsequently directed toward the global distribution of plate boundaries.

The hypothesis was advanced that three principal regions of influence could be associated with the organization of lower-mantle convection rolls and, potentially, an uneven distribution of heat from the outer core.

On this basis, three tectonic rings are defined: the Pacific Ring, the Atlantic Ring, and the Indian Ocean Ring. These rings share a common geometric structure, with centers at 6°S separated by 120° of longitude. Their inner boundaries have a major-to-minor axis ratio of 3:2, while their outer boundaries delimit a wider region of influence.

The central idea is that these three rings are not independent systems of motion, but three large regions of influence potentially connected with Earth’s common internal heat transport and motions. In this interpretation, the Ring of Fire is one manifestation of a larger arrangement in which different kinds of plate boundary emerge under different conditions. This suggests an opportunity to investigate divergence, subduction, and transform motion within a shared geometric and mechanical framework.

The findings are presented primarily as research hypotheses. Confirming them will require further comparison with geological and geophysical observations, together with mechanical analyses of the forces capable of producing such an arrangement.

The Convection Rolls Model may thereby develop from a geometric description of possible internal Earth motions into a testable model linking mantle convection, plate motions, and the global structure of Earth’s crust.

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References

Allen, C. W. (1983). Astrophysical Quantities. The Athlone Press.

Davies, G. F., and Richards, M. A. (1992). Mantle Convection. The Journal of Geology, 100(2).

Foulger, G. R. (2010). Plates vs Plumes: A Geological Controversy. Wiley-Blackwell.

Francis, P. (2000). Volcanoes: A Planetary Perspective. Clarendon Press.

Frost, D. A., et al. (2022). Multidisciplinary Constraints on the Thermal-Chemical Boundary Between Earth’s Core and Mantle. Geochemistry, Geophysics, Geosystems. https://doi.org/10.1029/2021GC009764

Guðmundur Þór Valsson (2007). ISNET 2004 – Results from the Remeasurement of Iceland’s Fundamental Geodetic Network [Icelandic title: ISNET 2004 – Niðurstöður úr endurmælingum Grunnstöðvanets Íslands]. National Land Survey of Iceland.

Korenaga, J. (2016). Can Mantle Convection Be Self-Regulated? Science Advances, 2(8). https://doi.org/10.1126/sciadv.1601168

Lay, T., Hernlund, J., and Buffett, B. A. (2008). Core–Mantle Boundary Heat Flow. Nature Geoscience, 1, 25–32.

Manneville, P. (2010). Instabilities, Chaos and Turbulence. Imperial College Press.

Paldor, N., and Killworth, P. D. (1988). Inertial Trajectories on a Rotating Earth. Journal of the Atmospheric Sciences, 45(24), 4013–4019.

Shen, Y., Solomon, S. C., Bjarnason, I. Þ., and Purdy, G. M. (1996). Hot Mantle Transition Zone Beneath Iceland and the Adjacent Mid-Atlantic Ridge Inferred from P-to-S Conversions at the 410- and 660-km Discontinuities. Geophysical Research Letters, 23(24), 3527–3530.

Smithsonian Institution, Global Volcanism Program (2026). What Volcanoes and Volcanic Regions Form the Pacific Ring of Fire? https://volcano.si.edu/faq/Pacific_Ring_of_Fire.cfm

Walzer, U. (1971). Convection Currents in the Earth’s Mantle and the Spherical Harmonic Development of the Topography of the Earth.

Þorbjarnarson, S. (2000). Hnettirnir. Steindórsprent–Gutenberg.

Þorbjarnarson, S. The Convection Rolls System of Earth. Unpublished research manuscript.

Further research material and discussion of the Convection Rolls Model of Earth can be found at MagicMagma.

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.

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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

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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.