Past exam of the mathematics course of the University of Cambridge 2015 iii Paper 59 4 h Solution Created 2026-10-03 Updated 2026-10-06
Plate tectonics is the movement and recycling of a planet's lithosphere as discrete plates over a deformable mantle. Mantle convection, the negative buoyancy of cool subducting slabs (slab pull), and gravitational sliding from elevated spreading ridges (ridge push) supply driving stresses; deformation and friction resist motion. The mantle mostly deforms by slow solid-state creep, rather than being a global liquid layer.
Its effects include subduction and recycling of crust, creation of new crust, mountain building, earthquakes and volcanism, transport of internal heat, and recycling of water and carbon. The carbonate-silicate cycle can couple volcanic CO2 supply to weathering and long-term climate.
- Mass and pressure-dependent material behavior: gravity and mantle depth affect buoyancy and convective stresses, but high-pressure changes in viscosity and density also affect whether slabs sink.
- Thermal state and heat budget: age, radiogenic heating, residual formation heat and surface temperature set convective vigor, plate thickness and the strength of the lid.
- Water and lithospheric weakening: hydration, rock rheology, fault damage and yield strength determine whether driving stresses can break and recycle the lithosphere rather than leave a stagnant lid.
Ridge push is a horizontal pressure force integrated with depth, equivalently a difference in gravitational potential energy per horizontal area. It is not the weight of a slab multiplied by the surface slope at one chosen point.
For an explicit compensated-column derivation, let measure depth below the ridge seafloor; the old seafloor is at . Set . The hot column has greater pressure. Its pressure excess over the old column isThe second line follows by integrating upwards from the compensation level. The two expressions agree at because . Integrating this positive pressure excess gives the ridge-push force in a plate model, directed away from the ridge:Consistently retaining only first order in thermal expansion givesIf the topographic term is retained within the same linear-density column model, it adds , giving . This is a useful small correction, not a claim that all other second-order material effects have been included. Both values use the intended hot initial plate, not the inconsistent printed zero-age profile.
Hot-ridge and old-plate columns, and their compensated pressure difference in the intended cooling model
. Details. The depth-averaged added horizontal compressive stress is . Resolving its traction on a plane dipping at angle gives the fault shear stress from a plate-integrated force,Keeping the previous topographic correction gives about . This is the mean additional shear from ridge push, assuming the force is transmitted through thickness and resolving the nonisotropic stress increment. An isotropic lithostatic pressure adds normal traction but no shear. The force integral alone does not specify the local stress at each point on the fault or establish failure.
Past exam of the plate tectonics course of the University of Oxford 2023 Question 1 b Solution 2026-10-25
Slab pull is generally the largest direct driving contribution for plates attached to substantial cold descending slabs. Cooling makes oceanic lithosphere negatively buoyant; sinking slabs transmit a pulling force to the rest of the tectonic plate. The comparison is a force balance, so the following driving and resisting processes both matter.
- Ridge push is gravitational sliding away from an elevated spreading ridge. Cooling, contraction and deepening of oceanic lithosphere establish the lateral difference in integrated pressure; ridge push is not simply magma squirting sideways into a plate.
- Basal traction on a tectonic plate transfers shear stress between the lithosphere and circulating mantle. It can help or oppose plate motion, depending on their relative velocities. Slab suction is the contribution of slab-induced mantle flow and its associated pressure and traction to nearby plate motion.
- Frictional sliding along faults, shearing along the plate interface, bending of the incoming slab and viscous dissipation in the surrounding mantle resist plate motion. Continental collision introduces additional resistance through buoyancy and deformation of thick continental crust.
- Mantle plumes and continental rifting can locally promote uplift, weakening and separation, but do not provide a universal explanation for all plate motion.
The first two gravitational contributions ultimately belong to the same coupled mantle convection system: the plates are its cold upper thermal boundary layer. They are not passive rafts on a prescribed conveyor belt. A plate with little attached descending slab need not have slab pull as its largest local driver, and a large gross slab pull can be partly consumed by bending and interface resistance. Geological observations and force comparisons nonetheless support the general dominance of slab pull for rapidly moving subducting plates.[ref]
What causes earthquakes? by British Geological Survey. Section explaining mantle circulation, ridge push and slab pull, including the association between subducting plate edges and faster motion.
Plate tectonics Created 2026-10-06 Updated 2026-10-20
A mobile-lid mode of planetary evolution in which coherent pieces of the lithosphere move, form at spreading regions and can recycle through subduction. Slab pull, ridge push and mantle flow compete with deformation resistance. It affects heat transport, volcanism, earthquakes and the carbonate-silicate cycle. It is not guaranteed solely by an exoplanet's mass.
Institutional explanation by the British Geological Survey. Its plate-driving discussion distinguishes mantle convection, ridge push and slab pull and explains the association between subducting edges and plate speed.
