7.2 Ridge Push & Slab Pull
The Force Balance on Tectonic Plates
Tectonic plates move across Earth's surface because the forces driving them exceed the forces resisting their motion. Since plates move at constant velocities (no measurable acceleration on geological timescales), the net force on each plate must be zero โ the system is in quasi-static equilibrium. The central question of plate dynamics is: which forces drive plates, and what is their relative importance?
The landmark analysis by Forsyth and Uyeda (1975) established that plates attached to long subducting slabs move systematically faster than those without subduction zones, pointing to slab pull as the dominant driving force. This section examines each force acting on a plate, derives order-of-magnitude estimates, and discusses the torque balance framework that constrains the relative magnitudes.
The Plate Force Balance
The total force per unit length acting on a plate can be written as the sum of driving and resisting terms. For a plate in quasi-static equilibrium:
\(F_{\text{sp}} + F_{\text{rp}} + F_{\text{drag}} + F_{\text{collision}} + F_{\text{suction}} = 0\)
where Fsp is slab pull, Frp is ridge push, Fdrag is basal drag (which can be driving or resisting), Fcollision is collision resistance, and Fsuctionis trench suction. Since plates are extended objects on a sphere, the proper formulation uses torques rather than forces: the net torque about Earth's center must vanish for each plate.
Because forces are distributed along plate boundaries and across the plate base, each force is integrated over the relevant area or length and then resolved into a torque about Earth's center. The constraint that the total torque equals zero for all plates simultaneously provides a system of equations that can be solved for the unknown coupling parameters (e.g., asthenospheric viscosity).
Slab Pull: The Dominant Force
As oceanic lithosphere ages, it cools and becomes denser than the underlying asthenosphere. When this lithosphere subducts, the negative buoyancy of the cold, dense slab generates a downward gravitational pull that is transmitted to the surface plate through the mechanical continuity of the lithosphere. This force per unit length of trench is estimated as:
\(F_{\text{sp}} \approx \Delta\rho \cdot g \cdot L \cdot h\)
where ฮฯ is the density contrast between the slab and surrounding mantle (~80 kg/mยณ), g is gravitational acceleration (~10 m/sยฒ), L is the length of the slab in the mantle (~600โ700 km for typical slabs reaching the transition zone), and h is the slab thickness (~80โ100 km). This yields:
Fsp โ 80 ร 10 ร 700,000 ร 100,000 โ 3.3 ร 1013 N/m
This is by far the largest force in the plate tectonic system, accounting for roughly 90% of the driving force for plates with attached subducting slabs. The slab pull force explains the first-order observation of Forsyth and Uyeda (1975): plates with long subduction zones (Pacific, Nazca, Cocos, Philippine Sea, Indian) move at 5โ10 cm/yr, while plates without subduction (African, Eurasian, Antarctic, North American) move at only 1โ3 cm/yr.
| Plate | Speed (cm/yr) | Subduction Zone? | % Boundary Subducting |
|---|---|---|---|
| Pacific | 6โ10 | Yes | ~45% |
| Nazca | 5โ7 | Yes | ~40% |
| Cocos | 5โ8 | Yes | ~55% |
| Eurasian | 1โ2 | Minimal | ~5% |
| African | 2โ3 | Minimal | ~10% |
Ridge Push
Ridge push is the gravitational force arising from the elevated topography and lower density of young, hot oceanic lithosphere at mid-ocean ridges relative to the cold, dense lithosphere far from the ridge. It is not a lateral โpushโ from the upwelling mantle but rather a body force distributed throughout the plate, arising from the lateral pressure gradient due to the difference in gravitational potential energy (GPE) between the ridge and the abyssal plain.
The force per unit length of ridge can be computed by integrating the horizontal pressure difference between a column at the ridge and a column in old oceanic lithosphere:
\(F_{\text{rp}} = g \int_0^{\infty} \left[ \rho_{\text{column}}(z) - \rho_{\text{ridge}}(z) \right] z \, dz \approx 2\text{--}3 \times 10^{12} \; \text{N/m}\)
This is about an order of magnitude smaller than slab pull (~3 ร 1012 vs ~3 ร 1013 N/m). However, ridge push acts on all plates that contain mid-ocean ridges, including those without subduction zones. For the African and Antarctic plates, ridge push is the primary driving force, supplemented by basal drag from the underlying mantle flow.
Ridge push increases with lithospheric age because the density contrast and topographic difference both increase as the plate cools and subsides following the half-space cooling model. The force is proportional to the age of the lithosphere at the far end of the plate, making it a distributed body force rather than a boundary force.
Basal Drag, Slab Suction & GPE
The base of the lithosphere is coupled to the underlying asthenosphere through viscous shear stresses. The basal drag force per unit area is estimated as:
\(\tau_{\text{drag}} = \eta \frac{v}{d_{\text{asth}}}\)
where ฮท is the asthenospheric viscosity (~1019โ1020 Paยทs), v is the plate velocity, and dasth is the thickness of the asthenospheric channel (~200 km). For v = 5 cm/yr and ฮท = 1020 Paยทs, the shear stress is ~104โ105 Pa. Whether this force drives or resists plate motion depends on the relative velocity between the plate and the underlying mantle flow.
Mantle Drag as Driving Force
When the underlying mantle flow is faster than the plate (or in the same direction), drag becomes a driving force. This may apply to plates overlying vigorous mantle upwellings or return flows. For slow-moving continental plates like Africa, mantle drag from the underlying large-scale flow may be the primary driving mechanism.
Mantle Drag as Resisting Force
For fast-moving plates driven primarily by slab pull (Pacific, Nazca), the plate moves faster than the underlying mantle, and basal drag acts to resist the motion. This viscous resistance ultimately limits the speed of the plate, establishing a terminal velocity where slab pull and ridge push balance drag and collision resistance.
Slab Suction
As a slab sinks into the mantle, it induces a large-scale return flow in the ambient mantle. This flow creates a suction force that draws the overriding plate toward the trench (trench retreat) and can also entrain distant plates. Slab suction is distinct from slab pull because it acts through the mantle viscous coupling rather than through the mechanical continuity of the slab itself. It may explain why some plates move toward trenches even when they have no attached slab.
Gravitational Potential Energy (GPE)
Elevated regions (mid-ocean ridges, continental plateaus, orogenic belts) have higher gravitational potential energy than low-lying regions. The lateral gradient in GPE generates a horizontal force that pushes material from high to low GPE. The Tibetan Plateau, for instance, exerts a radial compressive stress of ~50 MPa on the surrounding lowlands, contributing to the deformation of Southeast Asia. Ridge push is really a special case of GPE contrast.
Collision Resistance
When continental lithosphere arrives at a subduction zone, its buoyancy prevents it from subducting. The resulting collision generates enormous compressive stresses that resist plate motion. The India-Eurasia collision has slowed the Indian plate from ~18 cm/yr (prior to 50 Ma) to ~4โ5 cm/yr today. Continental collisions consume gravitational potential energy through crustal thickening and mountain building rather than through subduction.
Torque Balance & Relative Force Magnitudes
Because forces on a plate are distributed along different boundaries and across the base, and because plates are curved objects on a sphere, the proper constraint is that the net torque (moment) about Earth's center vanishes for each plate:
\(\sum_i \int \mathbf{r} \times \mathbf{F}_i \, dA = 0 \quad \text{for each plate}\)
Forsyth and Uyeda (1975) solved this system for all major plates simultaneously, using the observed plate geometries and velocities as constraints. Their key finding was that slab pull provides ~90% of the net driving torque for plates with subduction, and that the asthenospheric drag coefficient must be relatively low to allow fast plate motions.
~90%
Driving force from slab pull (oceanic plates)
~10%
Contribution from ridge push
1013 N/m
Order of magnitude of slab pull