Abstract

The large-scale rift systems that broke apart the Laurasian and Gondwanan supercontinents conform to the precise dimensions of a truncated-icosahedral tessellation of the Earth's surface, with triple junctions separated by 23° along great-circle arcs, and rift segments intersecting at 120° and 108°. The rift tessellations provide a minimum edge-length and therefore a least-work configuration for the fracturing of a spherical shell. Anorogenic magmatic provinces, including flood basalts, anorthosite, and granite-rhyolite and some hotspots evolved along the rift edges, especially at triple junctions. The brittle fracture pattern favors a top-down tectonic origin for some large igneous outbreaks.

Introduction

Laurasia and Gondwana broke along the geometrically regular patterns of a truncated icosahedron, an energy-minimizing configuration. The icosahedron, one of the five platonic solids, has 20 similar equilateral-triangle faces that meet in groups of five at each of 12 vertices (Figure 1). Truncation of the icosahedron reduces each vertex to a pentagonal facet and each triangular face to a regular hexagon. All edge-lengths of the truncated icosahedron are equal. Each vertex of the truncated icosahedron touches an encapsulating sphere. Projection of the truncated icosahedron onto the surface of this sphere traces the familiar soccer-ball pattern in which each seam forms a 23.28° great-circle arc, and each triple junction joins two hexagons and one pentagon. The tessellation of polygons is mathematically precise and intolerant, fixed by projection of a single pentagon. The truncated icosahedron provides a least-work rift configuration because it embraces the largest hexagonal plates permissible on a spherical tessellation and thereby minimizes the total length of fractures needed to tessellate a spherical shell. It would accommodate uniform layer-parallel extension of the strongest breakable lithosphere; it thus establishes the upper limit for a fracture system on a globe.

For both Laurasia and Gondwana, truncated icosahedral rifting coincided with drift stagnation, and may have been driven by lithospheric extension above an insulated and thermally-expanded mantle (Ed: see also McHone et al., 2005). Decompression melting of asthenosphere beneath opening fractures along the precise lines of the truncated icosahedral tessellation may have augmented anorogenic magmatism. The tessellation self-organizes within the brittle lithosphere, and so favors a top-down origin for these continental rift systems and associated anorogenic magmatic provinces (see Anderson, 2001, 2002).   Figure 1: The icosahedron. Truncation produces a semi-regular space figure with 20 hexagonal and 12 pentagonal faces. Each edge has central angle of 23.28°. Projection of the figure onto a sphere yields the familiar soccer-ball pattern of alternating hexagons and pentagons. Laurentian and Gondwanan rift systems precisely match this tessellation, which minimizes the length and energy needed to propagate fractures to relieve layer-parallel tension in a stagnant spherical shell.

Laurasia

The break-out of Laurentia from Laurasia followed rift zones that match a truncated-icosahedral hexagon and part of a neighboring pentagon (Figure 2). In order for a rift system to achieve this congruence, each rift zone must follow a great circle having an arc-length of 23° (2600 km on the Earth's surface) and must intersect neighboring rifts at 120° for hexagons, or 108° for pentagons. The Greenland, Arctic, western Canadian, and Montana-Tennessee sides of the Laurentian hexagon indeed have arc-lengths of 23° and turn at 120°, closely congruent with a truncated-icosahedral hexagon. The Alabama, Montana, Yukon, Greenland, and Scottish promontories of Laurentia are closely congruent with five vertices of the hexagon. Figure 2 suggests that the late Mesoproterozoic Grenville continental collision collapsed the sixth hexagonal vertex. Broad zones of Proterozoic anorogenic magmatism follow these edges. The anorogenic suites are characteristically bimodal, A-type magmatic rocks having within-plate trace-element signatures (Van Schmus & Bickford, 1993). The rifts evolved into early Paleozoic passive margins.

Figure 2: Truncated-icosahedral-fracture tessellation of Laurentia, after Sears (2001). Each side of a hexagon subtends ~ 23° of arc. Mesoproterozoic and Neoproterozoic anorogenic provinces occur along edges. Restored for Cenozoic continental drift. This map is a central projection onto two faces of a truncated icosahedron.

Gondwana

Figure 3 restores Gondwana into its 200-Ma configuration and illustrates the close congruence of Gondwanan rift zones and anorogenic magmatic provinces to 15 edges of a singular tessellation. The truncated-icosahedral tessellation is rigorous; Antarctica defines a pentagon, the other polygons are dependent. More than 20,000 km of rifts followed tessellation edges during breakup of the supercontinent.

Figure 3: A. Gondwana configuration at 200 Ma, after Lawver et al. (2002), showing congruence of Gondwanan rifts with truncated icosahedral tessellation. Circles at truncated-icosahedral vertices (triple junctions) are separated by ~ 23° of arc. B. Simplified map of Gondwana on the same base as A, except Earth coordinates rotated slightly from Lawver to demonstrate the congruence of active hotspots associated with Gondwanan large igneous provinces and tessellation triple-junctions. Stars: Active hotspots, names italicised. Yellow: Large igneous provinces and dikes. Blue: Gondwanan rifts. Red: Ideal truncated-icosahedral tessellation. P, Pentagon; H, Hexagon. Ages of rifts from Sengor & Natalin (2001): Pe, Permian; Tr, Triassic; J, Jurassic, K, Cretaceous. Click here for enlarged figure .

Large anorogenic igneous provinces broke out near vertices of the Gondwanan tessellation. Several volcanic hotspots are thought to represent continuing anorogenic magmatism at the original sites of the initial outbreaks. The following hotspot-igneous province links are possible: Cape Verde (or Fernando?) hotspot – CAMP, St Helena hotspot – Maranhão, Tristan hotspot – Parana-Etendeka, Bouvet hotspot – Karoo, Marion hotspot Gallodai-Trivandrum, and Heard hotspot – Naturaliste. With the exception of Cape Verde (or Fernando?), these hotspots conform rather closely to the vertices of a single truncated-icosahedral tessellation. As shown in Figure 3, the hotspot and rift tessellations are approximately congruent when Gondwana is restored onto the hotspot framework.

The fracture tessellation apparently propagated across Gondwana before Late Jurassic sea-floor spreading began to separate its parts. Fracture propagation may have begun in the Permian or Triassic. The fractures relieved tensile strain within the lithosphere, but may not have erupted magma until the resulting tiles separated sufficiently to drive decompression melting. Organization of the fractures may have been a passive, within-Gondwana response to tension, but separation of the tiles and magmatic outbreaks may have depended on global plate-dynamics.

If the hotspots were indeed generated top-down, drifting of Gondwana during propagation of the fractures should have left behind a distorted framework of asthenospheric hotspots. Initial opening of the Central Atlantic may have moved Gondwana and its fracture tessellation off the outbreak point of CAMP, displacing the younger parts of the hotspot tessellation with respect to the Cape Verde (or Fernando) hotspot. The overall congruence of the hotspots to the tessellation implies, however, that Gondwana was largely stagnant during Late Jurassic-Early Cretaceous magmatic outbreaks, consistent with a loop in the Gondwanan apparent polar wander path (DeWitt et al., 1988).

Because sea-floor spreading and truncated icosahedral symmetries conflict, Gondwanan plate boundaries evolved new ridge-transform configurations as the continental fragments dispersed. The incongruent southeast coast of Africa is one such transform boundary.

This webpage summarizes the paper Sears, J.W., St. George, G.M. and Winne, J.C., 2005, Continental rift systems and anorogenic magmatism: LITHOS, v. 80, in press.

References