Solid Earth

The Solid Earth comprises a planet's solid inner core, liquid outer core, viscously deforming mantle, and mechanically stronger crust and lithosphere.

The interface between Earth's metallic core and silicate mantle, approximately 2890 km beneath the surface. It is a major material interface and a thermal boundary across which core heat enters the mantle. Its temperature is distinct from mantle potential temperature because pressure and the lower thermal boundary layer matter.

The Earth's outer core is liquid. P waves slow strongly across the mantle-to-outer-core transition, while ordinary shear waves do not propagate through the liquid. This produces major changes in seismic ray paths and shadow ranges.

A long-term carbon cycle coupling silicate weathering, carbonate formation and interior recycling with volcanic carbon dioxide supply. Its temperature- and water-dependent weathering can provide a climate feedback. Active plate tectonics can support recycling, but the effectiveness of the feedback also depends on rock exposure, water and reaction rates.

Transport and eruption or intrusion of molten rock and associated gases. Subduction, spreading and mantle upwellings can supply melt; volcanism does not require globally active plate tectonics. Outgassing couples interior evolution to atmospheric inventories.

A large region of unusually voluminous igneous emplacement within a comparatively limited geological interval.

A large volcanic and intrusive province associated in time with the end-Permian crisis. Gas release and interactions with surrounding sediments provide mechanisms for linked warming, ocean chemical change and physiological stress during mass extinction.

A mainly basaltic continental large igneous province in India, emplaced around the end of the Cretaceous. Its surface deposits provide a major example of volcanic loading. Deposited volume, loaded area and density must be distinguished when estimating isostatic adjustment.

An arcuate or elongated volcanic region associated with a subduction zone.

Magma generated and modified within a volcanic arc system; it may combine mantle-derived melt, slab-derived components and crustal contributions.

Accumulation and crystallization of magma beneath pre-existing crust.

Transfer of gases from magma to a surface or atmospheric reservoir.

A transient release of stored mechanical energy in the solid planet, often associated with fault motion. Plate tectonics is a major terrestrial driver, but earthquakes can also occur without an active global plate system.

A logarithmic measure of earthquake size based on seismic moment. A commonly used SI relation is $M_w=\frac{2}{3}[{\log }_{10}(M_0/(\mathrm{N}\mathrm{m}))-9.1]$. Because seismic moment integrates fault slip over the fault plane and includes the shear modulus, a peak slip value cannot replace the area integral.

An earthquake source with spatial extent and a history of fault slip, rather than a single instantaneous point. Local slip rise time, advance of the rupture front and radiation travel times jointly control observed pulse shapes.

The time history of a specified earthquake source quantity, commonly moment rate. It differs from recorded ground velocity, which also contains radiation, propagation, instrument response and rupture directivity. A measured pulse width requires those assumptions before it is called a rupture duration.

Azimuth-dependent compression or stretching of observed source radiation because later-rupturing patches have different source-to-receiver travel times. A unilateral rupture generally yields shorter apparent duration in its forward direction. Pulse width also contains local slip rise time, instrument response and path effects, so directivity requires controlled comparisons.

The speed at which the rupture front advances along a fault plane. It is distinct from the local particle slip velocity and the propagating seismic wave speeds. Length equals $V_{r}T$ only for the stated approximately constant-speed propagation geometry.

The change in stress during an earthquake, often inferred through a source model. It is not a direct measurement of the absolute pre-event stress.

A large earthquake involving slip on the shallow-dipping plate interface of a subduction zone.

Suppression of relative slip on part of a megathrust during an interval of plate convergence, producing a slip deficit and elastic deformation. GNSS, leveling and offshore geodesy constrain it through a fault-geometry and deformation model. A locking fraction is therefore an inferred kinematic quantity; it is not a direct measurement of friction or the magnitude of the next earthquake.

A proposed mechanism by which reactions releasing fluid promote brittle failure or instability at depth. A spatial association with dehydration alone does not demonstrate causation.

An elastic rebound model describes slow loading of a locked fault, storage of elastic strain energy, and sudden slip with stress reduction when the fault fails. The surrounding rock partly relaxes while retaining a permanent displacement across the fault. It does not by itself predict the failure time, rupture extent or frictional dynamics, and continuous creep need not follow this ideal cycle.

An earthquake centroid is an effective average location of seismic moment release. It differs from the hypocenter, where rupture starts, and can depend on the source representation and observations. An associated centroid time similarly averages release rather than marking its first instant.

The hypocenter is the point where an earthquake rupture starts, rather than necessarily the centroid of its eventual slip distribution.

Distance from an earthquake hypocenter to a receiver. In a uniform velocity model it is the straight ray-path length; in layered material an interphase delay instead constrains a model-dependent path.

The epicenter is the projection of an earthquake's hypocenter onto the surface directly above it.

Surface distance from an earthquake epicenter to a receiver. It differs from hypocentral distance when the source has nonzero depth.

A fault plane is an idealized planar surface across which rock has slipped. A curved fault can be described by local fault planes. Its orientation is specified by fault strike and fault dip, and the slip direction within it by fault rake.

The fault rake specifies the slip direction within a fault plane. With an along-strike unit vector $\mathbf{s}$ and a down-dip unit vector $\mathbf{d}$, one explicit convention is $\mathbf{b}/b=\cos \lambda \mathbf{s}-\sin \lambda \mathbf{d}$. Positive $90^{\circ }$ then denotes up-dip slip. A convention must accompany a signed fault rake.

The fault dip is the angle between a fault plane and a horizontal plane, measured perpendicular to fault strike towards the descending side. It lies between $0$ and $90^{\circ }$.

The fault strike is the azimuth of the intersection of a fault plane with a horizontal plane. A right-hand convention chooses the along-strike direction for which the fault dips to the observer's right.

The relative displacement across a fault surface. Its vector and the fault normal determine an ideal double-couple seismic moment; a finite rupture can have spatially and temporally variable slip.

The observed separation of an originally correlated marker across a fault. Its value depends on marker geometry and measurement direction; apparent map separation is not automatically the full fault slip vector. Matching channel reaches, beds or dated surfaces supplies candidate piercing constraints.

Displacement across a fault per unit time, with the component and averaging interval specified. A long-term geological average and a short-term geodetic rate need not coincide.

A marker that starts with zero offset and accumulates displacement at a constant fault slip rate $v$ has age $t=d/v$. More generally $d={\int }_0^{t}v(s)ds$. The inferred age belongs to the establishment, abandonment or last resetting of that particular marker. A channel incised into an alluvial fan can be younger than the sediment it cuts. Uncertain channel correlation, erosion, distributed slip and time-variable rates require corresponding age uncertainty; a numerical ratio alone does not date a fan’s deposition.

The horizontal dip-direction component of displacement across a fault. The displayed expression assumes pure dip slip, with magnitude $D$ and fault dip $\delta$.

The vertical component of displacement between correlated markers across a fault. For pure dip slip of magnitude $D$ at fault dip $\delta$, the displayed formula applies. Erosion and ground slope can make surface fault scarp height different from throw.

An earthquake occurring in the region affected by an earlier event during its subsequent relaxation and stress redistribution. A spatial aftershock pattern can help identify a fault, but not every aftershock must lie on the main rupture plane.

The mechanically strong outer shell of a rocky planet, including crust and the colder upper mantle. It can form mobile plates in plate tectonics or a relatively stagnant lid. Its temperature, water content and damage affect its ability to yield.

Thermal or chemical modification that changes an older lithosphere's properties, potentially reducing its strength or effective thickness. Magma transport, mantle plumes and other mantle flow can contribute. A younger thermal signature does not automatically imply complete replacement of the old crust or lithospheric mantle.

A seismically inferred transition associated with the base of the lithosphere, often identified by a decrease in shear-wave velocity. Its depth and sharpness constrain combinations of temperature, composition, hydration, melt fraction and seismic anisotropy. A sharp discontinuity inside a craton can instead lie within its thick lithospheric mantle.^[ref]

The transition between strong lithosphere and weak asthenosphere. A thermal definition uses the temperature structure; a mechanical definition uses long-term strength or viscosity; a seismic definition uses wave properties. These depths need not coincide. Neither the Moho nor every sharp upper-mantle reflector is necessarily a lithosphere-asthenosphere boundary.

The portion of a planetary outer shell capable of supporting loads elastically on a specified timescale. Its effective elastic thickness need not equal the full thermal thickness.

The mantle portion of the mechanically defined lithosphere, distinct from the overlying crust and underlying weak asthenosphere.

The mechanically strong oceanic plate, including oceanic crust and underlying lithospheric mantle.

An oceanic plate cooling model solves the heat equation in a layer of fixed thickness $a$, with fixed cold surface and hot basal temperatures. A hot initial interior cools towards a linear steady profile. Unlike a half-space cooling model, it has a finite limiting thermal thickness and a nonzero old-age surface heat flux. Its transient sine coefficients must reproduce the chosen initial profile as well as the boundary values.

For a hot initial plate cooled from above, Fourier's law gives the displayed upward heat flux. At old ages only the steady value $k\Delta T/a$ remains. At young ages the sum approaches a Gaussian integral, giving $q_s\sim k\Delta T/\sqrt{\pi \kappa t}$. This divergence is an idealized sudden surface cooling, not an infinite observed ridge heat flux.

The half-space cooling model solves the one-dimensional heat equation for initially hot material cooled at a fixed-temperature surface. For constant thermal diffusivity $\kappa$, a fixed interior-temperature isotherm deepens proportional to $\sqrt{\tau }$. Applied to an oceanic lithosphere, it explains the leading age dependence of cooling; finite plate thickness and basal heat supply limit its extrapolation to old ages.

Cooling oceanic lithosphere contracts and increases its column mass, causing isostatic deepening. Integrating a half-space cooling profile gives an excess mass proportional to $\sqrt{t}$. Converting this to seafloor depth includes the density contrast between mantle and seawater. Finite-plate cooling and basal heat supply limit indefinite square-root subsidence at old ages.

Lithospheric flexure is bending of a mechanically strong outer shell under loads. A flat elastic plate approximation balances bending, buoyancy and applied loading. In the Fourier domain, bending contributes a term proportional to the flexural rigidity times the fourth power of horizontal wavenumber; it therefore suppresses short-wavelength deflection particularly strongly.

A region of upward deflection beyond the main downward flexure caused by loading an elastic lithosphere. Its position and amplitude depend on flexural rigidity, load geometry and boundary conditions. It is regional bending of the plate, rather than a separate buoyant load.

In the linear flat-elastic plate model, let downward deflection be $w$, applied downward pressure be $q$, flexural rigidity be $D$, and the restoring geophysical density contrast be $\Delta \rho >0$. The static balance isFor a sinusoidal Fourier mode of horizontal wavenumber magnitude $k$, applying the fourth spatial derivative multiplies its amplitude by $k^4$. HenceThe displayed dimensionless ratio compares bending resistance with buoyant restoration. Large $\chi$ means substantial elastic support and suppressed deflection. Small $\chi$ gives nearly local isostasy. The associated length $L_f=(D/\Delta \rho g{)}^{1/4}$ makes the load-width dependence explicit; some conventions define a flexural parameter with an additional factor $4^{1/4}$. At zero wavenumber, bending contributes nothing: total support remains buoyant even when the spatial distribution of subsidence changes.

The effective elastic thickness is the thickness of a homogeneous elastic plate with the same effective bending stiffness as the loaded lithosphere. In an isotropic thin-plate model, $D=E{T}_e^3/[12(1-{\nu }^2)]$, with Young's modulus $E$ and Poisson's ratio $\nu$. It depends on thermal state, material creep, loading history and yielding, and is not generally the crust's thickness or the full thermal thickness.

Magma is molten or partially molten rock within a planet. Its dynamic viscosity, cooling and interaction with the surrounding elasticity influence transport and storage.

A melt composition in equilibrium with its source before substantial post-segregation fractional crystallization, mixing or crustal contamination. Reconstructing it from an erupted basalt commonly requires restoring lost crystals and checking mineral–melt equilibrium. A crystal-rich erupted rock is not automatically a high-temperature primary liquid merely because its bulk Mg content is high.

A large, potentially global region of extensive silicate melting in a young or strongly heated rocky body. Its crystallization involves latent heat, crystal settling or flotation, and chemical fractionation. An early magma ocean is distinct from the later, mostly solid mantle convection of a planet. The Moon's proposed example is the lunar magma ocean.

A body formed by emplacement and solidification of magma within pre-existing rock. Dikes and deeper intrusive bodies add material and heat to crust without requiring surface eruption.

The production, movement, storage, emplacement and eruption of magma. It includes both igneous intrusions and surface volcanism, so the volume of erupted material does not measure the whole magmatic addition to crust.

The liquid phase produced by melting of rock, distinct from the entire crystal-bearing mixture called magma.

Physical and chemical interaction of two or more magmas; the resulting rock can retain evidence of incomplete mixing.

A geological dike is a sheet-like body or conduit formed when magma enters a fracture cutting across the surrounding rock. A vertical narrow dike can be modeled as a two-dimensional channel for coupled flow, heat transfer and wall melting.

A spatially related group of dikes, commonly formed during an episode of extension and magmatism. Matching ages, compositions and restored geometries of now-separated dike swarms can test a continental reconstruction; similar orientations without age control are much weaker evidence.

With equal solid and liquid densities, magma entering a dike at constant flux $Q_0$ has $bw=Q_0$: melt added by the walls exactly supplies the increasing cross-sectional storage. If wall heat flux is ${\alpha }_T\rho c_{p}w(T-T_m)$, both walls give $b_t=2{\alpha }_T{c}_{p}w(T-T_m)/L$. Combining this with sensible-heat conservation admits $b=B(t)f(\eta )$, $\eta =2{\alpha }_{T}z/B$, $B^2=4{\alpha }_T{Q}_{0}t/S$. The shape equations are $f(f-\eta f^{\prime })=\vartheta$ and $(S-\eta f){\vartheta }^{\prime }=-(S+\vartheta )\vartheta /f$.

New wall melt enters at the wall melting temperature $T_m$. Besides supplying its latent heat, the flowing magma must warm this added melt. Relative to $T_m$, conservative heat storage is $b(T-T_m)$, so differentiating it retains $(T-T_m)b_t$ and gives the displayed dilution term. Omitting that term requires an additional approximation, such as a small sensible-to-latent heat ratio; it does not follow from equal densities alone.

A lava lake is a persistent exposed body of molten or partly molten magma. Surface radiative cooling, thermal convection, latent heat, and internal radiogenic heating can jointly control formation and melting of its crust.

For a well-mixed lava lake of depth $H$ and a thin conductive crust of thickness $a$, put $\Delta T=T_m-T_s$, and use the convective flux $K(\overline{T}-T_m)$ with constant heat transfer coefficient $K>0$. The Stefan condition and liquid heat balance give, to leading order in $a/H$,Here latent heat $L_f$ is per unit mass and $k=\rho c_p\kappa$. Crust heating and changes of liquid depth are neglected. The linear conductive profile uses a quasi-steady approximation; thinness alone does not justify neglecting crust thermal storage. During initial growth, a small Stefan number supplies a sufficient rapid-adjustment regime. Define $h=a/H$, $\theta =(\overline{T}-T_m)/\Delta T$, and $\tau =\kappa t/H^2$. Scaling by the thermal diffusion time $H^2/\kappa$ and $\Delta T$ gives $h^{\prime }=S(1/h-B\theta )$ and ${\theta }^{\prime }=R-B\theta$, where $B=KH/k$, $R=Q{H}^2/(c_p\kappa \Delta T)$, and $S=c_p\Delta T/L_f$ is the Stefan number. Thus $\theta =R/B+({\theta }_0-R/B)e^{-B\tau }$ exactly. The reduction applies while $a/H\ll 1$, the conductive profile is approximately linear, and the thermal convection closure remains valid; it does not model complete freezing of a deep lake.

In the radiogenically heated lava-lake crust model, the thickness derivative vanishes at $h_e=1/(B\theta )$ when the liquid superheat $\theta$ is positive. This moving curve balances thermal conduction and convective heat flux; it is not itself the evolving crust. Cooling raises the curve and keeps an initially absent crust below it. Warming lowers the curve, allowing lava-crust overshoot under warming. At zero superheat the stationary thickness is infinite, so its finite formula applies only after positive superheat develops.

In the radiogenically heated lava-lake crust model, initially cool liquid warms exponentially and its instantaneous stationary lava-crust thickness $1/(B\theta )$ decreases. The actual crust can cross this moving value, reach a maximum, and melt back to $h_{\ast }=1/R$. Overshoot is not automatic. Linearizing about equilibrium givesIf $B<S{R}^2$ and ${\theta }_0<R/B$, the slowly decaying forced response has positive sign, so the crust eventually approaches equilibrium from above; an initially absent crust must then have overshot. In contrast, initially hot liquid cools, its instantaneous stationary thickness increases, and an initially absent crust cannot cross it from below: at a proposed first crossing its own derivative is zero but the stationary thickness has positive derivative. The hot-start crust therefore grows monotonically. These comparisons assume nonnegative liquid superheat.

In the radiogenically heated lava-lake crust model, temperature stays constant precisely when ${\theta }_0=R/B$. Then $h^{\prime }=S(1/h-R)$, and an initially absent crust satisfies the displayed law for $0\le h<1/R$. It follows by integrating $h/(1-Rh)$ from zero to $h$. The crust starts as $\sqrt{2S\tau }$ and tends to $1/R$ only at infinite time. The equilibrium remains thin only if $R\gg 1$.

A magma intrusion is the emplacement of magma into surrounding rock. A shallow, approximately axisymmetric intrusion can lift an elastic plate roof, with spreading determined by viscous peeling of an elastic plate or fracture toughness.

A body of igneous rock crystallized from magma emplaced beneath the surface. Granite is a common plutonic composition. A pluton's gravity anomaly depends on its geophysical density contrast and geometry, rather than on the rock name alone.

With the axisymmetric clamped-plate deflection and fixed front curvature ${\kappa }_f>0$, a magma intrusion hasThese relations describe the advancing fracture branch, with roof bending rather than hydrostatic pressure controlling the interior load.

Let $V_T$ be total magma volume shared between a reservoir and an advancing toughness-controlled magma intrusion, $p_r=E(V_T-V)$, and conduit conductance $\beta >0$. With $A=\sqrt{8\pi /3}B{\kappa }_f^{3/2}$,Equilibria satisfy $\sqrt{V}(V_T-V)=A/E$. Two positive equilibria exist when $A/E<2V_T^{3/2}/(3\sqrt{3})$; the smaller is unstable and the larger is stable under this volume equation. An advancing solution between them approaches the larger. The singular pressure as $V\to 0$ prevents this late-time model from nucleating an intrusion by itself.

If a positive vapour-tip pressure magnitude $p_T$ sets $h_f\sim p_T{l}_p^4/B$, matching $h_f/l_p^2$ to the interior curvature ${\kappa }_i$ gives $l_p\sim (B{\kappa }_i/p_T{)}^{1/2}$. The viscous peeling of an elastic plate law then yields $\dot{R}\sim B^{3/2}{\kappa }_i^{7/2}/(\mu p_T^{1/2})$. For constant injected volume flux $Q$, $V=Qt$ and ${\kappa }_i\sim V/R^4$, henceOrder-one coefficients require solving the local peeling profile. The scaling assumes a front region much shorter than the intrusion radius.

Mantle convection is the slow buoyancy-driven motion of a rocky planetary mantle. On geological timescales the solid mantle behaves as a highly viscous Newtonian fluid to first approximation.

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 localized buoyant upwelling in the mantle. Its origin and relation to surface volcanism require independent constraints.

The mantle thermal anomaly associated with Yellowstone volcanism and the age-progressive eastern Snake River Plain.

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.

Opening and closure of ocean basins through continental rifting, oceanic spreading, convergence and continental collision.

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.