The northerly flowing rivers of northern Iceland provide an intriguing window into the deeper tectonic and geological structure of the region. North of Iceland lies the Kolbeinsey Ridge, a spreading ridge that exerts a significant influence on the country’s geology. Unlike the Reykjanes Ridge, the Kolbeinsey Ridge does not visibly intersect or “reach” the Icelandic mainland. Nevertheless, its structural imprint is evident.

The ridge exhibits a pronounced north–south (N–S) orientation, and this same directional trend can be observed across much of northern Iceland. One of the most compelling expressions of this alignment is seen in the river systems. Major rivers such as Hrútafjarðará, Héraðsvötn, Eyjafjarðará, Skjálfandafljót, Jökulsá á Fjöllum, Hofsá, and Lagarfljót largely follow northerly courses, reflecting a structural control that is unlikely to be coincidental.

In addition to their general N–S alignment, these rivers display occasional deviations that appear to coincide with subtle structural boundaries or division lines in the crust. These interruptions in flow direction may mark transitions between different tectonic domains or the influence of underlying mantle dynamics.

The estuaries of these rivers further reinforce this pattern. Their distribution shows a striking regularity that aligns with the proposed grid of convection rolls beneath Iceland. Each estuary can be interpreted as forming a “hub” within this grid, suggesting that surface hydrology may be responding to deeper, organized mantle processes. This spatial consistency lends support to the idea that convection rolls patterns influence not only volcanic and tectonic features, but also the development of drainage systems.

A careful comparison of topographic and geological maps with the river network makes these relationships more apparent. The rivers are not randomly distributed; rather, they appear to trace out an underlying structural framework. In this sense, northern Iceland’s river systems may serve as surface indicators of deeper geodynamic organization (the grid formed by mantle convection rolls), reflecting the combined influence of the Kolbeinsey Ridge and broader mantle convection patterns.

The Reykjanes Ridge is the dominant structural feature in the geology of Iceland. Its importance lies not only in its scale, but also in the way it appears to express a broader tectonic principle that influences much of the country’s geological architecture.

On the map, a red line traces the continuous (holistic) segment of the Reykjanes Ridge, extending for roughly 900 km. What is particularly notable is that this line can be described by a simple geometric relationship (of relevant degrees of latitude x and logitude y. In this case Cn = -7.66):$$(x – C_n)^2 + (y – 32)^2 = 35.34^2$$This is not merely a mathematical curiosity. In the southern half of Iceland, several major rivers and geomorphological features align closely with this same trend. Among the most prominent examples are Norðurá, Hvítá, and Þjórsá, as well as the lake Langisjór. Many additional rivers, lakes, and volcanic features follow these orientations across southern Iceland.

This alignment is not a new observation. It is widely recognized that Iceland’s rivers and tectonic features often follow consistent directional trends, and this has long been apparent to geologists and observers alike. However, what is less commonly emphasized is that this pattern can be captured, and better understood, through a specific mathematical form such as the equation above.

Seen in this light, the alignment is not just descriptive but diagnostic. It points toward an underlying organizing mechanism. The interpretation proposed here is that convection rolls beneath the lithosphere are arranged in a geometry that gives rise to this pattern at the surface.

If the Earth’s interior consisted of only a single layer of convection rolls, the resulting surface pattern would likely be much simpler and more direct. In reality, multiple layers and interacting systems of mantle flow are involved, which complicates the expression of these structures at the surface. A full treatment of these layered interactions is beyond the scope of this discussion. Nevertheless, the essential idea can be understood by focusing on one layer, which includes the pair of convection rolls shaping this section of the Reykjanes Ridge.

A useful way to visualize this is to imagine convection rolls arranged side by side, like parallel cylinders. In this framework, the Reykjanes Ridge occupies precisely a boundary between two of those rolls, and its path follows the equation given above with notable accuracy. At Iceland’s latitudes, tectonic activity becomes more diffuse. Instead of being confined to a narrow ridge, divergence is distributed across broader volcanic zones. This produces a wider ara of deformation, magmatism, and surface restructuring. As a result, the structural signal of the underlying convection is expressed not only with a single line, but across a much wider region.

This broader influence is clearly reflected in the landscape. The rivers of southern Iceland do not flow randomly; their courses frequently align with the same geometric trend as the Reykjanes Ridge. When viewed from this perspective, their paths are not merely shaped by local topography, but are part of a larger, coherent tectonic pattern. Recognizing this connection is important. Everyone knows this trend, but general trend is not the same as accurate mathematical equation. This is how over a century of accurate measurements and mapping can be used to take an additional step towards understanding tectonics of the surface, and of course the inner structure of the Earth.

Working with numerical models is ultimately grounded in measurements and physical principles. The observational basis for Earth’s internal structure has been accumulating for more than a century, and the discovery of the inner core 90 years ago illustrates that our knowledge of the deep Earth is not new. However, it remains significantly more challenging to resolve the structure of the mantle itself, primarily because seismic observations are affected by multiple factors, including:

• limited resolution of seismic tomography,
• dependence on inversion methods and starting models,
• heterogeneity in temperature and composition,
• anisotropy and attenuation effects,
• uneven global distribution of seismic data.

Modelling therefore plays an essential role in filling the gaps between observations. We have relatively robust constraints on the layering of the Earth, and the physical behaviour of mantle materials under pressure and temperature. This makes it possible to explore simplified but physically consistent flow structures within these layers. One such approach is to introduce convection rolls into the mantle, layer by layer, guided by physical constraints.

Under an adiabatic temperature gradient, and with mantle material close to the melting point (and solidus as well) of peridotite, conditions favour Rayleigh–Bénard-type convection, which naturally produces convection rolls with approximately equal height and width. Based on this principle, a geometrically consistent model can be constructed and subsequently tested against observations.

However, this approach raises an important question: What if our current understanding of mantle layering is itself incomplete?

There are several indications that the lower mantle may not be as homogeneous as the commonly assumed continuity between ~670 km and ~2700 km suggests. For example:

• Subducting slabs often change direction or flatten at depth rather than descending vertically.
• Seismic waves may show reflections or scattering, suggesting internal structure.
• The upper mantle is already organized into paired layers:
  • the asthenosphere (~120–410 km), and
  • the transition zone (~410–670 km).

One possible interpretation of these paired layers is that they facilitate horizontal circulation within the mantle. If large-scale convection rolls exist below 670 km, it would seem inconsistent if that part of the mantle lacked a comparable capacity for lateral circulation. This motivates the exploration of a model in which the lower mantle is also divided into two layers, enabling similar circulation behaviour at greater depths.

Importantly, introducing such a subdivision does not significantly alter the aspects of the model that most strongly affect surface observations. The dominant surface expressions remain controlled by the ~1.5°-wide convection rolls in the asthenosphere and transition zone. Furthermore, processes below 670 km remain difficult to observe directly, and many key constraints are still derived from shallower structures such as slabs and convergent boundaries.

One intriguing aspect, however, is the possibility that there are more large-scale division lines than the 12 ones predicted by simpler whole-mantle convection models. For instance, the relatively stationary distribution of continental masses on the equator, geologically found to be 30° wide and spaced 60° apart, can be more readily interpreted if two large-scale convection rolls exist beneath them, circulating in opposite directions. This interpretation would also imply that the three major north–south trending oceanic ridges near the equator are associated with large-scale upwelling systems, with convection rolls diverging beneath them.

Based on this reasoning, an alternative geometric model can be constructed. This model:

• uses circular convection cells with equal height and width,
• connects each cell to its neighbours at a single point,
• allows global horizontal circulation, in addition to the more emphasized vertical convection.

Within this framework, geometric constraints suggest that an additional transition layer in the lower mantle should exist. Specifically:

• a discontinuity zone is predicted at approximately 1850–2030 km depth,
• with a central depth near ~1940 km,
• and a thickness of roughly ~180 km.

This construction follows the same mathematical logic used for the upper mantle, where the key divisions occur near 410 km and 670 km. Similarly, at the base of the mantle, the core–mantle boundary region (2700–2900 km) reflects comparable geometric considerations.