Subducting slabs provide the main driving force for plate motion and flow in the Earth's mantle, and geodynamic, seismic and geochemical studies offer insight into slab dynamics and subduction-induced flow. Most previous geodynamic studies treat subduction zones as either infinite in trench-parallel extent (that is, two-dimensional) or finite in width but fixed in space. Subduction zones and their associated slabs are, however, limited in lateral extent (250-7,400 km) and their three-dimensional geometry evolves over time. Here we show that slab width controls two first-order features of plate tectonics-the curvature of subduction zones and their tendency to retreat backwards with time. Using three-dimensional numerical simulations of free subduction, we show that trench migration rate is inversely related to slab width and depends on proximity to a lateral slab edge. These results are consistent with retreat velocities observed globally, with maximum velocities (6-16 cm yr(-1)) only observed close to slab edges (<1,200 km), whereas far from edges (>2,000 km) retreat velocities are always slow (<2.0 cm yr(-1)). Models with narrow slabs (< or =1,500 km) retreat fast and develop a curved geometry, concave towards the mantle wedge side. Models with slabs intermediate in width ( approximately 2,000-3,000 km) are sublinear and retreat more slowly. Models with wide slabs (> or =4,000 km) are nearly stationary in the centre and develop a convex geometry, whereas trench retreat increases towards concave-shaped edges. Additionally, we identify periods (5-10 Myr) of slow trench advance at the centre of wide slabs. Such wide-slab behaviour may explain mountain building in the central Andes, as being a consequence of its tectonic setting, far from slab edges.

[1] Subduction of tectonic plates limited in lateral extent and with a free-trailing tail, i.e., ''free subduction,'' is modeled in a three-dimensional (3-D) geometry. The models use a nonlinear viscoplastic rheology for the subducting plate and exhibit a wide range of behaviors depending on such plate characteristics as strength, width, and thickness. We investigate the time evolution of this progressive rollback subduction, measure the accompanying return flow in the upper mantle, and quantify the plate kinematics. Due to the 3-D geometry, flow is allowed to accompany slab rollback around the lateral edges of the slab (the toroidal component), as opposed to 2-D geometry, where material is forced to flow underneath the slab tip (the poloidal component). A simple force balance is provided which relates the speed of backward trench migration to the resistive forces of generating flow and weakening the plate. Our results indicate most of the gravitational energy of the system (i.e., the negative buoyancy of the subducting slab) is converted into a toroidal flow ($69%), a much smaller amount goes into weakening the plate ($18%), and the remaining amount goes into driving flow parallel to displacement of the slab ($13%). For the trench widths (W) we investigate ( 1500 km), a maximum trench retreat rate occurs for trenches 600 km wide, which is attributed to the interaction between a plate of finite width and the induced flow (which has a lengthscale in the horizontal direction). These numerical results quantitatively agree with comparable 3-D laboratory experiments using analogue models with a purely viscous plate material (Schellart, 2004a(Schellart, , 2004b, including correlations between increasing retreat rate with increasing plate thickness, trench width for maximum retreat rate (500 km), and estimated amount of slab buoyancy used to drive rollback-induced flow ($70%). Several implications for plate tectonics on Earth result from these models such as rollback subduction providing a physical mechanism for ephemeral slab graveyards situated above the more viscous lower mantle (and endothermic phase transition) prior to a flushing event into the lower mantle (mantle avalanche).

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Mantle plumes are thought to play an important part in the Earth's tectonics, yet it has been difficult to isolate the effect that plumes have on plate motions. Here we analyse the plate motions involved in two apparently disparate events--the unusually rapid motion of India between 67 and 52 million years ago and a contemporaneous, transitory slowing of Africa's motion--and show that the events are coupled, with the common element being the position of the Indian and African plates relative to the location of the Réunion plume head. The synchroneity of these events suggests that they were both driven by the force of the Réunion plume head. The recognition of this plume force has substantial tectonic implications: the speed-up and slowdown of India, the possible cessation of convergence between Africa and Eurasia in the Palaeocene epoch and the enigmatic bends of the fracture zones on the Southwest Indian Ridge can all be attributed to the Réunion plume.

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Although the Moon currently has no internally generated magnetic field, palaeomagnetic data, combined with radiometric ages of Apollo samples, provide evidence for such a magnetic field from approximately 3.9 to 3.6 billion years (Gyr) ago, possibly owing to an ancient lunar dynamo. But the presence of a lunar dynamo during this time period is difficult to explain, because thermal evolution models for the Moon yield insufficient core heat flux to power a dynamo after approximately 4.2 Gyr ago. Here we show that a transient increase in core heat flux after an overturn of an initially stratified lunar mantle might explain the existence and timing of an early lunar dynamo. Using a three-dimensional spherical convection model, we show that a dense layer, enriched in radioactive elements (a 'thermal blanket'), at the base of the lunar mantle can initially prevent core cooling, thereby inhibiting core convection and magnetic field generation. Subsequent radioactive heating progressively increases the buoyancy of the thermal blanket, ultimately causing it to rise back into the mantle. The removal of the thermal blanket, proposed to explain the eruption of thorium- and titanium-rich lunar mare basalts, plausibly results in a core heat flux sufficient to power a short-lived lunar dynamo.

The building of the Andes results from the subduction of the oceanic Nazca plate underneath the South American continent. However, how and why the Andes and their curvature, the Bolivian orocline, formed in the Cenozoic era (65.5 million years (Myr) ago to present), despite subduction continuing since the Mesozoic era (251.0-65.5 Myr ago), is still unknown. Three-dimensional numerical subduction models demonstrate that variations in slab thickness, arising from the Nazca plate's age at the trench, produce a cordilleran morphology consistent with that observed. The age-dependent sinking of the slab in the mantle drives traction towards the trench at the base of the upper plate, causing it to thicken. Thus, subducting older Nazca plate below the Central Andes can explain the locally thickened crust and higher elevations. Here we demonstrate that resultant thickening of the South American plate modifies both shear force gradients and migration rates along the trench to produce a concave margin that matches the Bolivian orocline. Additionally, the varying forcing along the margin allows stress belts to form in the upper-plate interior, explaining the widening of the Central Andes and the different tectonic styles found on their margins, the Eastern and Western Cordilleras. The rise of the Central Andes and orocline formation are directly related to the local increase of Nazca plate age and an age distribution along the margin similar to that found today; the onset of these conditions only occurred in the Eocene epoch. This may explain the enigmatic delay of the Andean orogeny, that is, the formation of the modern Andes.