Lithosphere

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.