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Dislocation creep is time-dependent crystal deformation through motion and interactions of dislocations. A common constitutive model is $\dot{ϵ}=A{\sigma }^n\exp [-(E^{\ast }+P{V}^{\ast })/(RT)]$ with $n>1$, giving stress-dependent effective viscosity. Unlike diffusion creep, it often has weak grain-size dependence over the regime being modelled.

Homologous temperature and deformation. Homologous temperature is $\Theta =T/T_m$, with both temperatures in kelvin and $T_m$ the appropriate pressure- and composition-dependent melting temperature. It measures proximity to melting more meaningfully than an absolute temperature alone. Pressure, composition and water can alter both $T_m$ and the flow law, so equal $\Theta$ does not imply identical rheology.

A useful thermally activated material creep law iswith stress $\sigma$, grain size $d$, activation energy $E^{\ast }$ and activation volume $V^{\ast }$. Water activity can add another factor. Increasing temperature raises the rate at fixed stress when the activation enthalpy is positive, greatly lowering effective viscosity. Solid material can therefore flow on geological timescales well below melting.

Diffusion creep is approximately linear in stress: bulk-diffusion Nabarro-Herring creep has grain-size scaling $d^{-2}$, while grain-boundary Coble creep has $d^{-3}$ in their ideal regimes. Dislocation creep usually has a stress exponent greater than one and weaker grain-size dependence. Its effective viscosity scales as ${\eta }_{\mathrm{eff}}\propto {\sigma }^{1-n}$ at fixed temperature, so stronger forcing changes the apparent viscosity. At lower homologous temperature, brittle/frictional deformation or high-stress dislocation mechanisms can become important. The dominant process also depends on pressure and confinement; low temperature is not by itself a guarantee of brittle failure deep in a planet.

A deformation mechanism map compares the competing rates or strengths as functions of stress and homologous temperature at specified grain size, pressure and composition. Fine grains favour diffusion creep; larger stress favours nonlinear dislocation creep. There is no universal temperature dividing all these regimes. This sensitivity helps explain a strong outer lithosphere above a slowly flowing solid mantle and why modest thermal or water variations can reorganize deformation.

Determining the actual planform of mantle convection. The task is to infer the geometry of upwellings, downwellings and connecting flow in the present Earth, rather than to draw a preferred laboratory convection cell. Plate velocities and the distribution of subduction zones directly constrain surface motion and likely cold downwellings. Ridges, volcanism and hotspots provide further clues, but a ridge need not mark the centre of a deep plume, nor is every hotspot uniquely explained by one plume geometry.

Seismic tomography supplies three-dimensional velocity structure from body-wave travel times, waveforms and surface-wave dispersion. Fast slab-like structures can often be traced beneath subduction zones into the lower mantle. The 1997 global P-wave study reported long narrow lower-mantle structures connected with convergence and interpreted some slab segments as reaching the deepest mantle; that is evidence for deep circulation, not proof that every slab follows one route.^[ref] Temperature affects seismic speed, but composition, phase changes, water and anisotropy also matter, so velocity is not itself a flow map.

Gravity and the geoid constrain the spatially integrated density field and its induced boundary deformation. Dynamic topography supplies information about vertical stresses, after separating crustal structure, isostatic loads and thermal subsidence. Seismic anisotropy can constrain deformation and fabric orientations, subject to a mineral-physics relation between fabric and flow. Discontinuity topography and the mantle's heat budget provide further tests. Each observation has a different sensitivity to density, temperature and viscosity, making their combination more useful than any one image.

Compare these observations with three-dimensional geodynamic models that solve creeping-flow force balance, mass conservation and thermal transport, including buoyancy from temperature and composition, realistic plate motions, viscosity structure and phase boundaries. Predict seismic observables, gravity, geoid and dynamic topography from the same model, and assess data coverage and resolution before interpreting a feature. Whole-mantle exchange, impeded or deflected slabs near transition zones, and broad deep anomalies can coexist; the evidence does not require identical stacked or single-layer cells everywhere. The actual planform is constrained by joint seismic, gravitational, surface-kinematic and thermal evidence, with substantial nonuniqueness in its detailed flow and history.

Use a rock strength envelope: at each depth plot the smaller differential stress needed for frictional failure and for sustained ductile material creep at a specified strain rate. Shallow rock generally strengthens with depth because effective confining pressure increases; sufficiently deep hot rock weakens because thermally activated material creep becomes efficient.

At shallow depth, Byerlee's law or a Mohr-Coulomb failure criterion gives a relation of the formwhere $C$ is cohesion, $\mu$ a coefficient of friction, ${\sigma }_n$ the compressive normal stress and $P_f$ the pore pressure. Increasing overburden generally increases effective stress, hence the frictional strength. Conversion from fault shear stress to differential stress depends on the stress regime and fault orientation; a sketch should not label a universal numerical slope. High pore pressure or weak fault gouge can lower the frictional strength substantially.

A simplified dislocation creep relation isHere $Q$ is activation energy, $V^{\ast }$ activation volume, $R$ the molar gas constant and $T$ absolute temperature; $A$ and $n$ depend on composition and deformation mechanism. At fixed strain rate, increasing temperature usually decreases the required stress strongly. The competing effects of pressure, water weakening of rocks, grain size and composition also matter. The intersection with frictional failure gives a brittle-ductile transition, not a change from solid to liquid.

For the Indian continental interior, a useful first sketch has an upper-crustal strength peak, a weaker lower continental crust, and renewed strength in lithospheric mantle beneath the Moho. Quartz-bearing rocks can undergo ductile material creep at conditions where colder, drier olivine-rich mantle retains appreciable strength. This creates a possible two-peak, or “jelly sandwich”, rock strength envelope. With further depth the mantle also weakens. A cold craton can retain strong lithospheric mantle to much greater depths than a tectonically heated continental region.

For the central Pacific, show thin mafic oceanic crust above a relatively thick layer of strong lithospheric mantle. There need not be a conspicuous weak lower-crustal layer. Much of the integrated strength can reside below the Moho, with a broad strength peak followed by ductile weakening towards the asthenosphere. Cooling and age control the thickness: young hot oceanic lithosphere would give a much shallower and weaker profile than an old central-Pacific plate.

The plotted Moho depths of about 38 km and 7 km, and all plotted stresses, are illustrative assumptions. “India” alone does not specify a unique geothermal gradient, water content or strain rate, and the Pacific includes plates of different ages. The robust comparison is the possible crust–mantle layering in a continent versus the thin oceanic crust and mantle-dominated strength of an old oceanic plate. The Moho is a compositional boundary; neither it nor the deepest small plotted strength is automatically the seismic lithosphere-asthenosphere boundary.

Left: ordinary frictional strengthening with depth followed by thermally activated material creep. Right: a very weak shallow faulted layer above a narrow strong region near 10 km, followed by essentially the same weakening material creep branch. These are the shapes actually plotted in Figure 2. The right curve is not a strong upper crust over a uniformly weak lower crust; neither diagram displays a second mantle-strength peak.

For the left curve, increasing overburden increases the effective normal load on faults. A schematic Coulomb friction law iswhere $C$ is cohesion, $\mu$ the coefficient of friction, ${\sigma }_n$ the compressive normal stress and $P_f$ the pore pressure. With ordinary rock friction and approximately hydrostatic pressure, ${\sigma }_n-P_f$ increases roughly linearly with depth. The stress needed for frictional sliding therefore increases, as in the straight shallow branch. Byerlee's law summarizes the relatively high friction found in many laboratory rocks.^[ref]

At higher temperature, dislocation creep or another ductile mechanism accommodates the imposed deformation at lower stress. For example,Here $\dot{ϵ}$ is strain rate, $Q$ an activation energy, $R$ the molar gas constant and $T$ absolute temperature. At fixed strain rate, increasing $T$ lowers the required stress. The operative envelope is approximately $\min ({\sigma }_f,{\sigma }_d)$, expressed in a consistent stress convention; the peak marks the brittle-ductile transition. This accounts for the left curve's peak near 100 MPa and its decline toward small strength by about 20 km.

For the right curve, normal high-friction sliding with depth-independent fluid-pressure ratio cannot explain the nearly vertical weak shallow branch. Plausible weakening includes high pore pressure tracking the overburden, low-friction fault gouge, or a connected network of pre-existing weak faults. Roughly constant small ${\sigma }_n-P_f$ yields roughly constant small frictional strength. The abrupt increase near the base of this layer requires a change of conditions: for example, the weak fluid-rich fault network terminates or becomes discontinuous, leaving stronger intact or less altered rock below. A change in mineralogy or deformation localization can also give a contrast. Simply saying “there are fluids” does not explain the return to high strength. Below the strong region, thermal material creep again lowers the strength.

The figure alone does not identify the weakening mechanism or a particular lithological boundary. In particular, a 10 km strength maximum is not evidence for a 10 km deep Mohorovičić discontinuity. The strong-fault/weak-fault evidence and the distinction between fault strength and surrounding crustal strength are discussed in Stress orientations at intermediate angles to the San Andreas Fault, California by Jeanne L. Hardebeck and Andrew J. Michael.