Mantle convection

Mantle convection is buoyancy-driven motion in a rocky planetary mantle. Heating and cooling create density differences; chemical and mineral-phase differences can also affect buoyancy. Although the mantle is mostly solid, deformation by material creep permits slow flow over geological time.

A simple model balances viscous resistance with buoyancy and transports heat by both flow and thermal conduction. Its Rayleigh number compares those effects. Temperature-dependent mantle viscosity and the strength of the lithosphere help determine whether the surface moves as plates or remains a stagnant lid. Seismic structure, surface deformation and heat flux constrain different parts of this model.

The buoyancy of the mantle beneath a descending slab. Thermal, compositional or melt-related density anomalies can modify pressure and traction on the slab, potentially changing its contact with the overriding plate. It differs from the slab's own slab buoyancy. Inferring it from low seismic velocities requires independent constraints because temperature, fluids, melt and composition can produce overlapping signatures.

An energy balance for heat stored in the mantle. Here $C_m$ is its effective heat capacity, $H_m$ internally generated radioactive power, $Q_{\mathrm{cmb}}$ power entering across the core-mantle boundary and $Q_m$ power leaving the mantle. The sign of the right-hand side determines warming or secular cooling in this reduced model. Different reservoirs and latent heat may require additional terms. Surface heat loss includes crustal contributions and should not be substituted for $Q_m$ without specifying the partition.

The ratio of radiogenic heating to heat loss for a stated planetary reservoir, named for Harold Urey. A convective mantle Urey ratio uses mantle radioactive production and heat leaving the mantle; a bulk-silicate or surface ratio uses a different reservoir and heat budget. It must be labeled accordingly. A ratio below one is consistent with drawing on stored heat, but core heat or other inputs must also be included before inferring the sign of the mantle's temperature change.

Deformation and transport of mantle material on geological timescales; plate motions can drive flow as well as respond to it.

The component of three-dimensional mantle flow that circulates around a sinking slab's lateral edges.

A mantle plume is a localized buoyant upwelling in a planetary mantle. Hot material can rise because thermal expansion lowers its density relative to its surroundings; compositional differences may strengthen or oppose that buoyancy. As it rises and decompresses, it can cross a rock's solidus and produce melt without requiring heat to be added during ascent.

A volcanic chain, a broad topographic swell or a seismic anomaly can motivate a plume interpretation, but they measure different consequences. Plate motion, background mantle flow, melt transport and crustal structure influence the surface expression. A plume hypothesis is tested by combining those observations rather than reading a unique source depth from a hotspot's position.

The Yellowstone hotspot is the region of anomalous volcanism and subsurface thermal structure associated with Yellowstone and the younger end of the eastern Snake River Plain. The observed volcanic progression constrains a relative history of the surface plate and the source of heat; it does not by itself prove an immobile vertical conduit.

Laboratory experiments have tested how subduction-driven mantle flow can distort a buoyant mantle plume and produce contrasting surface thermal progressions. This provides a physical mechanism to compare with the Snake River Plain and High Lava Plains patterns, while remaining conditional on the model geometry and flow properties.^[ref]

A regime in which surface lithosphere participates substantially in overturn and horizontal motion. Additional organization into long-lived plates and narrow boundaries is needed for a close analogue of plate tectonics.

A strong surface thermal boundary layer largely immobile relative to convecting material beneath it. Local volcanism and occasional foundering can still occur.

Two separately mixed layers with an interfacial thermal bottleneck require separate energy budgets. For lower input $F$, interlayer transfer $J$, surface loss $E$, and per-area heat capacities $H_l,H_u$, these are $H_l{\dot{T}}_l=F-J$ and $H_u{\dot{T}}_u=J-E$. At equilibrium all three fluxes agree, but a finite interface resistance retains a temperature difference. Thus layer count alone does not specify the cooling rate.

For heat capacity per area $H=kd/\kappa$, imposed basal flux $F$, fixed top temperature, and marginal-stability thermal boundary-layer scaling, the well-mixed interior has $H\dot{\theta }=F-C{\theta }^{4/3}$. Its steady excess temperature is ${\theta }_{\ast }=(F/C{)}^{3/4}$. The near-equilibrium relaxation time is $\tau =3H{\theta }_{\ast }/(4F)=3d{\delta }_{\ast }/(4\kappa )$, with ${\delta }_{\ast }=k{\theta }_{\ast }/F$. A full large-amplitude cooling history is nonlinear rather than a single exponential.

Dynamic topography is surface or internal-boundary relief supported by stresses from interior flow. Inferring it requires separating effects of the thickness of the crust, thermal subsidence and other loads, and depends on the assumed interior viscosity and density structure.

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.

Repeated assembly, reorganization and dispersal of supercontinents. It is not necessarily periodic or synchronous across all continents. A Wilson cycle concerns the opening and closure of an individual ocean basin, whereas a supercontinent cycle describes global-scale changes in continental configuration.

A continental assembly containing most of the Earth's continental area or major cratons. Its reconstruction requires age-compatible geological connections and paleomagnetism; similarity of modern continental outlines alone is insufficient.

Separation and sinking of a relatively dense lower lithospheric layer from material above. It can recycle material without requiring a sustained global system of tectonic plates.

A Wilson cycle describes the opening and eventual closure of an ocean basin. Continental rifting thins and separates continental lithosphere; subsequent seafloor spreading can create an ocean between the fragments. Later subduction consumes oceanic lithosphere, and convergence can end in continental collision.

The sequence helps connect present structures with former environments. A suture zone, remnants of oceanic material and dated deformation can support closure of an earlier basin. The cycle concerns one basin's history, whereas the supercontinent cycle describes global continental assembly and dispersal; neither name requires an exact periodic clock.

A continental-oceanic transition that is not an active plate boundary during the interval being considered.

Convergence involving continental regions after consumption or closure of an intervening basin.

A boundary marking the joining of previously separated tectonic regions, often associated with remnants of an intervening oceanic system.

Localized extension that separates or thins a region of lithosphere.

Extension and thinning of continental lithosphere, potentially preceding ocean-basin formation.

Emplacement of a portion of oceanic lithosphere over another plate, commonly a continental margin.

Movement of a tectonic plate relative to another body or a specified reference frame.

Traction transmitted between the base of a tectonic plate and the mantle. Its component parallel to the plate can drive or resist plate motion, depending on the relative motion and surrounding mantle flow. Its direction should not be inferred from the word “drag” alone.

A region separating tectonic plates, accommodating divergent, convergent or relative lateral motion.

A boundary region where adjacent plates approach one another, potentially involving subduction or continental collision.

A geological fault is a fracture or fracture zone across which rock has undergone relative displacement. Its local geometry is described by a fault plane, fault strike, fault dip and fault rake. A locked fault can store elastic strain while surrounding rock deforms; some faults also accommodate displacement by slow creep.

A lateral separation between adjacent or overlapping fault strands. Displacement transfer can be accommodated by distributed deformation, a tilted relay ramp, or a connecting fault. Its releasing or restraining effect depends on both the stepping direction and the sense of fault slip.

A polished or striated surface on a fault, produced or modified by sliding. Striation direction constrains the orientation of fault slip; determining the sense of motion can require additional asymmetric indicators.

A finite-width region containing the main slip surface, subsidiary fractures and mechanically or chemically modified rock associated with a fault. It can include a comminuted core and a surrounding damaged region. Porous permeability can be enhanced along connected fractures while fine fault gouge reduces cross-fault flow.

One of a pair of fault orientations that can form under a common principal stress field with opposite senses of resolved shear stress. For newly formed, optimally oriented faults obeying the same Mohr-Coulomb failure criterion, their acute intersection angle is $90^{\circ }-\varphi$, where $\varphi$ is the friction angle. The maximum compressive principal stress bisects that acute angle. This permits an estimate $\mu =\tan \varphi$ only under the common-formation and optimal-orientation assumptions, rather than for arbitrary inherited faults.

A local principal stress model associated with Ernest Masson Anderson in which one principal stress is vertical, as suggested by negligible shear stress on a flat free surface. With compression positive and ${\sigma }_1\ge {\sigma }_2\ge {\sigma }_3$, vertical ${\sigma }_1$ gives normal faulting, vertical ${\sigma }_2$ gives strike-slip faulting, and vertical ${\sigma }_3$ gives reverse faulting. The other two principal stresses are horizontal. Topography, mechanical layering and local fault geometry can violate the idealization.

For a cohesionless, optimally oriented normal fault with vertical maximum compression and horizontal minimum compression,where $\delta$ is fault dip and $\phi$ the internal friction angle. This is a geometric inference under the model, not a measurement of friction from dip alone.

For a compression-positive Mohr circle, put $C=({\sigma }_1^{\prime }+{\sigma }_3^{\prime })/2$ and $R=({\sigma }_1^{\prime }-{\sigma }_3^{\prime })/2$. Tangency to the cohesionless Mohr-Coulomb failure criterion $\tau ={\mu }_f{\sigma }_n^{\prime }$ gives $R/C=\sin \phi$. The contact point is $({\sigma }_n^{\prime },\tau )=(C{\cos }^2\phi ,C\sin \phi \cos \phi )$. The physical plane-normal angle to ${\sigma }_1^{\prime }$ is half the corresponding central angle, giving the stated dip. Equivalently the plane itself makes $45^{\circ }-\phi /2$ with ${\sigma }_1^{\prime }$.

The associated stress ratio is ${\sigma }_1^{\prime }/{\sigma }_3^{\prime }=(1+\sin \phi )/(1-\sin \phi )$. A reactivated nonoptimal plane, nonzero cohesion or unknown principal stress directions defeats the simple dip-only inversion.

An opening crack formed by local extension. Near a normal fault it may accompany primary shear, but shaking, slope instability or compaction can also produce fissures.

Rock whose structure and composition record deformation within a fault zone.

A cohesive fault rock produced predominantly by mechanical grain fragmentation and granular rearrangement. It differs from a loose fault breccia or fault gouge in cohesion, while sharing a brittle crushing mechanism rather than requiring bulk melting.

Coarse angular rock fragments produced by crushing during fault slip, commonly in a finer matrix. Fine-grained, poorly cohesive comminuted material is fault gouge; cohesive material formed by similar grain-size reduction can be called cataclasite.

Deformation involving slip on geological faults.

A major continental strike-slip fault system in California; its strength has been studied with boreholes, heat flux and seismic observations.

Fine-grained fault rock produced by comminution and alteration; its mineralogy and fluid state can strongly affect friction.

A crustal fault system beneath the Seattle region capable of producing damaging earthquakes and local tsunamis.

The block below an inclined fault plane. It is paired geometrically with the hanging wall.

The block above an inclined fault plane. In reverse faulting it moves upward relative to the footwall.

A topographic step associated with displacement across a surface-reaching fault. Erosion and distributed deformation can modify its height and shape.

An exposed fault plane revealed as fault slip, differential motion and removal of cover bring it to the surface. On a normal fault, lowering the hanging wall can expose a planar footwall face. Continued exposure may preserve a bedrock scarp while weathering, erosion and collapse progressively modify its older portions. A hillslope following the plane therefore need not be an independent erosional surface that accidentally has the same orientation.

A simple model of hillslope smoothing in which sediment flux is proportional to negative slope. For constant transport coefficient $\kappa$, an ideal initial step broadens on scale $\sqrt{\kappa t}$. Real free-face collapse, nonlinear transport, changing climate and deposition can invalidate the linear diffusion equation approximation.

The relationship between characteristic accumulated fault slip and fault-system length. Approximately $D\propto L$ follows in self-similar elastic models at comparable driving stress, but natural faults can accumulate displacement at nearly constant length over part of their history.

A fault with displacement predominantly parallel to its strike.

Dip-slip faulting is relative motion on a geological fault predominantly along the steepest direction within the fault plane. That direction is perpendicular to the fault strike and follows the fault dip. It differs from strike-slip faulting, whose motion is mainly along strike.

For an inclined plane, normal faulting lowers the hanging wall relative to the footwall; reverse faulting raises it. The surface step is only a projection of the full fault slip, so vertical offset alone is not the total displacement unless the geometry is known. Mixed motion belongs to oblique-slip faulting, and an observed focal mechanism must be interpreted with independent evidence for the actual fault plane.

Shortening accommodated by a hanging wall moving up relative to the footwall. The centre of its dip-slip focal mechanism is compressional under the usual lower-hemisphere convention. Low-angle reverse faulting is commonly called thrust faulting.

A fault on which the hanging wall moves up relative to the footwall, accommodating shortening. A low-angle reverse fault is a thrust fault. The fault dip is a geometric property and should be distinguished from the direction of fault slip.

A low-angle reverse fault. Near-surface splays may accompany either a surface-breaking or a blind main rupture.

A mechanically weak detachment along which an overlying package can move relative to its substrate. A décollement can follow weak bedding and connect to steeper thrust ramps, so its orientation need not equal the optimum dip for a new fracture in homogeneous rock.

A very large plate-interface thrust fault at a subduction zone.

A reverse fault dipping oppositely to the dominant thrust system and accommodating part of its shortening.

A fault with reverse slip whose upper tip remains beneath the ground surface. It can deform the overburden through folding, localized fold scarps, and secondary faults.

Extension accommodated by a hanging wall moving down relative to the footwall. Its focal mechanism has an extensional dip-slip pattern, with the centre unshaded under the convention that shaded quadrants denote compression.

A tilted region transferring displacement between overlapping normal fault segments. Opposing gradients of fault throw can produce an unbroken ramp. Continued extension can breach the ramp with a connecting fault, generating a linked segmented trace.

A relatively down-dropped block bounded by opposing normal faults. A small secondary graben can form within the distributed surface rupture zone of one earthquake.

A fault on which the hanging wall moves downward relative to the footwall. Local bending or collapse can create small normal faults even during a regional reverse-faulting event.

A long-lived low-angle normal fault that can exhume deep crust or mantle. Its mapped scarp need not be a plate-motion arrow.

Fault slip with both dip-slip and strike-slip components. The focal mechanism can have an off-centre nodal intersection, with the central polarity indicating its dip-slip sense under a specified shading convention. A reverse component with horizontal shear is compatible with transpression.

Transpression combines horizontal shearing with shortening across a deforming region. On individual geological faults, that combination can appear as oblique-slip faulting with a reverse component. At larger scales, different structures can partition the motion: some accommodate strike-slip faulting, while others accommodate reverse faulting or folding.

A restraining bend in an otherwise laterally moving fault system illustrates the mechanism: the geometry makes neighbouring blocks converge as well as slide past one another, promoting uplift and distributed deformation. A vertical surface displacement consequently does not mean that every part of the regional motion is vertical. The relevant comparison is between measured displacements, the fault strike and the full regional deformation pattern.

Predominantly horizontal relative motion along a fault. A pure strike-slip double couple has two vertical nodal planes; a focal mechanism gives both possible planes, and independent evidence selects the actual one.

Strike-slip faulting in which the opposite side moves to an observer's right when looking across the fault.

Strike-slip faulting in which the opposite side moves to an observer's left when looking across the fault. The sense is the same from either side.

A point where three plate boundaries meet. Kinematic stability means that one instantaneous junction velocity is compatible with all three moving boundaries, so a connected junction can persist. It is not a guarantee of dynamical stability for arbitrary future plate motion.

A junction whose persistence depends on the two overriding-plate trench constraints and the transform velocity line meeting at one point. Specifying only the boundary-type letters does not specify the compatibility geometry or trench polarities.

For pure normal symmetric spreading, the two ridge constraints are perpendicular bisectors of two edges of the plate velocity triangle. The transform constraint lies along the third edge. For a nondegenerate triangle their common intersection exists only when the angle opposite that third edge is a right angle; the junction velocity is then the midpoint of the transform edge.

For a boundary with in-plane normal $n$, an admissible junction velocity $U$ obeys $(U-v_{\mathrm{boundary}})\cdot n=0$. A ridge uses the mean of adjacent plate velocities in the symmetric model, a trench uses the overriding plate velocity, and a transform uses either adjoining plate velocity. Compatibility requires a common intersection of the three velocity-space lines.

The three plate velocities plotted in a common reference frame form a triangle whose directed edges are the pairwise relative velocities. Adding the same reference velocity translates the triangle without changing its edges.

An accreting divergent plate boundary. In the symmetric normal-spreading model, its normal velocity equals the mean normal velocity of the adjoining plates; motion parallel to the ridge does not change that normal compatibility condition.

Seafloor spreading creates oceanic crust at a spreading ridge and carries it away with the adjoining plates. With symmetric steady spreading, an age interval maps to distance by the half-spreading rate, not the full relative opening speed. A time sequence of field polarities can therefore become paired marine magnetic stripes.

The speed of one side of newly formed crust relative to the ridge axis in a symmetric spreading model. It is half the full relative opening speed; the width formed during a polarity interval is this speed times the interval duration.

A plate boundary at which relative motion is tangential to the boundary. It neither creates nor consumes lithosphere in the ideal kinematic model. The admissible junction velocities form a line parallel to the fault through either adjacent plate velocity in velocity space.

The seafloor continuation beyond the actively slipping ridge-to-ridge transform fault. Its two sides can differ in age without continuing relative plate-boundary slip.

The direction of the instantaneous angular-velocity vector describing relative rigid-plate motion on a sphere. At position $\mathbf{r}$, the relative velocity is $\mathbf{\omega }\times \mathbf{r}$. The antipodal pole represents the same physical rotation if the angular-velocity sign is reversed.

Relative angular velocities add as vectors: ${\mathbf{\omega }}_{B/C}={\mathbf{\omega }}_{B/A}+{\mathbf{\omega }}_{A/C}$. Geographic pole latitudes and longitudes must first be converted into Cartesian vector directions.

A region of lithosphere approximated as rigid on the spatial and temporal scale of a plate-kinematic model. Its instantaneous motion on a sphere is a rotation; deformation within boundary zones limits the rigid-plate approximation.

The tectonic plate containing most of North America and adjacent parts of the ocean floor.

A young oceanic tectonic plate entering the Cascadia subduction zone.

The oceanic tectonic plate subducting beneath much of western South America.

A prominent oceanic ridge on the Nazca Plate entering the Peruvian subduction zone. Its association with variations in slab dip motivates tests using seismic geometry, plate reconstructions and the thermal and compositional contributions to slab buoyancy.

A volcanic ridge system entering the South American subduction zone near central Chile, associated with the southern transition of the Pampean flat-slab region. Its crustal structure, hydration and past geometry constrain explanations of the slab dip; present-day bathymetry alone does not give the buoyancy of its already subducted continuation.

Gravitational sliding of lithospheric material away from elevated spreading regions. It supplies a driving contribution to plate tectonics together with slab pull and mantle stresses.

The ridge-push force in a plate model is the depth integral of the horizontal pressure difference between hot and cold compensated columns. To leading order, the old plate's linear excess density gives $F=g{\int }_0^{a}s\delta \rho (s)ds={\rho }_{m}g\alpha \Delta T{a}^2/6$. Here $s$ is depth below the old seafloor. Retaining the geometrical contribution from its lowered surface adds $g({\rho }_m-{\rho }_w)h^2/2$ within the linear-density model. Force per ridge length has units $\mathrm{N}{\mathrm{m}}^{-1}$, distinct from stress.

Downward recycling of a lithospheric plate into the mantle. A sufficiently cold, dense slab can provide slab pull, while bending and friction resist motion. The resulting material and volatile recycling connects plate tectonics with volcanism and long-term climate.

Release of water-rich fluid by reactions that destabilize hydrated minerals in a descending slab. It can promote flux melting of the mantle wedge and contribute to dehydration embrittlement. The released water is not evidence that the whole slab has melted.

The effect of slab-induced mantle flow, pressure and traction on the motion of neighbouring plates and their boundary. It is part of the coupled response to a sinking slab, rather than an unrelated energy source that can always be added independently to slab pull.

Migration of a subduction trench relative to the surrounding mantle as a slab retreats; the associated mantle flow can advect thermal anomalies.

Partial melting of material within a descending slab, distinct from flux melting of the mantle wedge by fluids released from the slab.

A proposed buoyant ascent of mixed sedimentary, crustal and hydrated mantle material from an interface region into the mantle wedge.

Removal of material from the overriding plate into a subduction zone.

Mechanical addition of solid slices beneath the overriding plate. Distinct from crystallization of new magma by magmatic underplating.

Establishment of sustained downward plate motion, distinct from its later continuation under existing plate forces.

The region containing a descending plate, its interface and the associated upper-plate and mantle wedge system.

A coupled phenomenon in which transient slow fault slip occurs with low-frequency seismic tremor, often near the downdip transition from locked to steadily creeping parts of a megathrust. Geodetic displacement and seismic signals provide complementary observations. Along-strike differences in recurrence, migration and cumulative slip help characterize subduction zone segmentation; tremor counts alone do not uniquely give fault slip or coupling.

Along-strike changes in the structure, deformation, coupling or thermal state of a subduction zone. Segments inferred from megathrust locking, episodic tremor and slip, past earthquake ruptures, slab dip and seismic tomography need not have identical boundaries. A common spatial pattern can motivate a physical hypothesis, but does not alone prove a persistent rupture barrier or identify a unique cause.

The subduction zone beneath the Pacific Northwest of North America, where the Juan de Fuca Plate and adjacent oceanic plates descend beneath the North American Plate.