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Plate tectonics is the movement and recycling of a planet's lithosphere as discrete plates over a deformable mantle. Mantle convection, the negative buoyancy of cool subducting slabs (slab pull), and gravitational sliding from elevated spreading ridges (ridge push) supply driving stresses; deformation and friction resist motion. The mantle mostly deforms by slow solid-state creep, rather than being a global liquid layer.

Its effects include subduction and recycling of crust, creation of new crust, mountain building, earthquakes and volcanism, transport of internal heat, and recycling of water and carbon. The carbonate-silicate cycle can couple volcanic CO2 supply to weathering and long-term climate.

Three major controls on a super-Earth's tectonic mode are:

A larger mass alone does not establish active plate tectonics. The competition between driving stress, yielding and sustained slab buoyancy must be evaluated for the planet's composition and thermal history.

Earthquake location. The hypocentre is rupture initiation; its surface projection is the epicentre. Record calibrated arrival times at stations of known coordinates, identify P wave and S wave phases, and predict their travel times through a stated velocity model. Earthquake location by arrival times fitsfor the three source coordinates and origin time $t_0$. Linearization supplies residual equations $\delta t_i=\delta t_0+\nabla T_i\cdot \delta \mathbf{x}$. A grid search or iterative weighted least squares inversion can use pick uncertainties, while station geometry controls whether those parameters are well constrained. Four independent arrival constraints are the minimum for four unknowns, not a guarantee of a reliable solution.

In a homogeneous medium, an arrival-time difference between an S wave and a P wave cancels origin time and estimates source-to-station distance,Several distances intersect to locate the event; real layered or three-dimensional Earth structure requires curved-ray travel times. Nearby stations and diverse takeoff angles help resolve depth. Clock errors, phase misidentification, poor azimuthal coverage and incorrect velocities introduce uncertainty or systematic bias. Closely spaced earthquakes can be relocated precisely relative to each other because common-path errors partly cancel, even when their absolute locations remain uncertain. Report a location uncertainty and model assumptions, not merely a best-fit point.

H. F. Reid's earthquake-cycle model. A fault can remain locked while long-term tectonic motion slowly deforms the surrounding rocks. Elastic strain energy and shear stress accumulate. When resistance is overcome, rapid fault slip releases part of that stored energy as seismic waves, frictional heat and other irreversible work. The adjoining rocks partly recover their elastic distortion while retaining a permanent displacement discontinuity across the fault: this is elastic rebound. Surface markers initially crossing the fault become bent during loading and offset after slip.^[ref]

A simple sketch is a slow rise of stress followed by a rapid stress drop, then renewed loading; the plate displacement continues throughout. Geodetic deformation, observed fault offsets and earthquake stress changes can test the picture. Actual cycles need not repeat with identical slips or times: creep, afterslip, stress transfer and heterogeneous friction complicate the idealization. The release need not remove all pre-existing stress. Elastic rebound explains storage and release; it is not a deterministic earthquake clock.

A dense array does not correct an incorrect velocity model. The faster southwest block permits shorter travel times than an assumed uniform medium, with refraction favouring paths through fast rock. First arrivals may include refracted or seismic head wave paths rather than the assumed direct straight paths. Fitting those arrivals with one constant speed can make an earthquake on the fault appear closer to southwest stations and farther from northeast stations.

The sign follows even from a two-station linearization. Put southwest and northeast stations at $x=-L,+L$, and the true event at $x=0$ with depth $h$. In a constant-speed model,A negative observed differential residual therefore produces $\delta x<0$, an apparent southwest displacement. A common origin-time adjustment cannot remove this directional residual. The stated kilometre-scale offset is a model bias, not proof that the fault dips towards the apparent epicentres. Its exact magnitude cannot be predicted without the actual velocities and station geometry; the question supplies that magnitude as an observation.

The relevant contrast is independently documented at Parkfield: higher velocities lie southwest of the fault, with lower velocities northeast.^[ref] Account for the lateral structure and correct phases, then relocate and test whether the bias remains.

Elastic rebound. Tectonic motion loads a fault whose shallow portion is locked. Rock on either side deforms and stores elastic strain energy while slip is inhibited. When failure permits rapid slip, part of the stored energy becomes seismic radiation and part is dissipated in friction and damage. The adjacent rock partly relaxes, while a permanent displacement remains across the fault. Geodetic strain accumulation and coseismic offsets support this loading–release picture.^[ref]

The model is useful for brittle crustal faulting but is not a prediction of precise recurrence, rupture size or frictional evolution. Aseismic creep can release deformation without a large sudden event. Viscoelastic flow, afterslip, fluid-pressure changes and interacting fault segments complicate a simple locked-fault cycle. Deep-focus earthquakes and non-shear source components require additional physics; not every earthquake source is adequately described by a shallow brittle double couple. Rebound also need not release all the pre-existing stress.

A thin negative-gradient velocity zone. In horizontal layering, use the seismic ray parameter $p=\sin i/v$, the conserved horizontal slowness. A ray turns when $pv=1$. Downward passage through decreasing speed makes $pv$ smaller, so a surface ray cannot turn in the negative-gradient interior. Rays either turn above the zone or penetrate it and turn below where speed has recovered sufficiently. This produces missing turning depths and a seismic shadow range from a low-velocity zone in the ideal ray model.

Retain all branches usingThe travel-time slope is $dT/dx=p$. Just below the critical value that permits passage beyond the upper speed maximum, the ray makes a finite extra excursion through the low-velocity region. Range can jump, and the deep branch can fold back before resuming its normal trend, giving multiple arrivals outside the shadow. A first-arrival curve alone hides some of these branches. Define the seismic intercept time byThe $x$–$p$ representation displays the gap and fold; the $\tau$–$p$ representation has separate shallow and deep branches and a branch jump at the critical ray parameter for the piecewise-linear cusp model. Do not join them by invented turning rays. Diffraction and finite-frequency energy soften a purely geometrical shadow.

The figures use an explicit illustrative profile, not measured Earth parameters: speed rises from 1 to 2 over depths 0 to 1, falls to 1.8 by depth 1.2, then rises with its original gradient. The asthenosphere beneath oceanic lithosphere is an important setting for a low-velocity zone. A major P-wave speed reduction also occurs at the boundary between the mantle and the outer core of the Earth; S waves do not propagate through the liquid outer core of the Earth.^[ref]

For a mode of positive frequency, differentiation of the causal convolution givesThe first boundary term vanishes because $\sin 0=0$; the second supplies $f(t)$ because $\cos 0=1$. Both initial values vanish. This verifies the forced-oscillator equation and its initial conditions, including a step source in the piecewise or distributional sense.

The spatial Dirac delta function reduces the excitation toFor an event at $t_s\ge 0$, put $\tau =t-t_s$. Integrating the oscillator kernel from $t_s$ to $t$ gives the normal-mode response to a step seismic moment:Non-unit mass normalization introduces the same factor $1/N_{\alpha }$ as above. Complex modes must be combined with their conjugate partners to produce a real displacement. The formal $\omega \to 0$ limit is $a=C{\tau }^{2}H(\tau )/2$; for rigid-body modes here, $C=0$ because their strain is zero.

The step produces a static component plus continuing oscillations in this lossless model. It does not predict physical damping. A point source is appropriate when rupture dimensions are small compared with the wavelengths being analysed and rupture duration is short compared with their periods. Long-period observations of a relatively small earthquake can meet these conditions; high-frequency finite-fault directivity generally cannot. A finite source-time function replaces the ideal instantaneous step when its duration matters.

First-motion source mechanisms. Locate an earthquake from arrival times and use a seismic velocity model to calculate each station's source takeoff direction. Measure the initial direct P wave polarity after checking instrument sign, component orientation, timing and phase identification. An upward trace at an instrument is not automatically a source compression without the propagation and component convention. Plot the inferred source radiation signs on a focal sphere, commonly using a lower-hemisphere equal-area projection, and seek nodal planes separating positive and negative observations.

For a shear dislocation with orthogonal unit slip and fault-normal vectors $\mathbf{s},\mathbf{n}$, the double-couple fault source has $M=M_0(\mathbf{s}{\mathbf{n}}^{\mathsf{T}}+\mathbf{n}{\mathbf{s}}^{\mathsf{T}})$. Its far-field P radiation sign is that ofThe two zeros are orthogonal nodal planes; the four quadrants alternate between outward and inward initial radiation. Their orientations and quadrant signs determine candidate strike, dip and rake. Normal, reverse and strike-slip mechanisms give different projected patterns. The earthquake pressure and tension axes are the negative and positive moment-tensor principal directions, respectively; they do not by themselves measure the complete regional stress tensor.

There is a fundamental fault-plane ambiguity: exchanging $\mathbf{s}$ and $\mathbf{n}$ leaves the radiation tensor unchanged. First motions therefore give a fault plane and an auxiliary plane without saying which actually slipped. Use mapped rupture, aftershock geometry or independent geodetic displacement to select the physical fault where possible. Polarity signs alone do not measure scalar seismic moment, source duration or rupture extent. A poorly sampled focal sphere or many near-nodal observations can admit several mechanisms rather than one defensible beachball.

Propagate uncertainty in event depth, velocity gradients and takeoff angles, allow for mispicked or reversed polarities, and report the range of mechanisms consistent with the observations. A primary method did this by testing alternative locations and velocity models and validated its uncertainty estimates using noisy synthetic data and clusters of events with similar waveforms.^[ref] Broadband waveforms and amplitude ratios add information, especially for non-double-couple sources, but they are additional measurements rather than a way to extract amplitude information from a sign-only data set.

Radial density structure. In an isotropic adiabatic material, the seismic parameter isFor a chemically homogeneous region whose background stratification is adiabatic, $d\rho /dP=\rho /K_S=1/\Phi$. Combine this with spherical hydrostatic balance and mass conservation to obtain the Adams-Williamson equationsThe inward density increase follows compressibility under the increasing pressure. A specified starting density and measured $\Phi (r)$ allow integration within a homogeneous adiabatic layer. Seismic velocities alone, however, do not determine that density normalization, since they contain ratios of moduli to density. Chemical boundaries, phase transitions, nonadiabatic thermal gradients and anisotropy require additional modeling; a composition jump is not obtained by blindly integrating the smooth relation across it.

Use travel times and surface waves to constrain elastic velocities, reflected/converted phases to locate interfaces, and normal-mode frequencies to constrain density as well as elastic structure through their sensitivity kernels. Impose independently known total mass and moment of inertia:Because these weight depth differently, they help distinguish admissible profiles, but two integrals alone do not specify an arbitrary radial function. Laboratory equations of state and mineral physics restrict composition, compressibility and density jumps. pressure and enclosed mass are matched across interfaces, while density may jump. In a liquid region $\beta =0$ and $\Phi ={\alpha }^2$, so the shear-wave absence constrains phase state without itself providing a direct density measurement.

The Preliminary Reference Earth Model is a concrete joint inversion of seismic travel times, normal modes, mass and inertia, including density and attenuation along with elastic structure. The original analysis combined these complementary data rather than deriving density uniquely from P wave speed.^[ref] A defensible radial density model combines hydrostatic/thermodynamic relations with seismic and global integral constraints, and states where homogeneity and adiabaticity fail.

The decisive change was from moving continents within a supposedly permanent ocean floor to moving coherent tectonic plates that include both continental and oceanic lithosphere. Several independent observations made that change testable.

Continental connections supplied the initial problem. In the early twentieth century, Alfred Wegener assembled matching continental margins, correlatable rock belts and mountain chains, shared fossil assemblages, and paleoclimate indicators into the case for continental drift. Reassembling Gondwana, for example, makes geographically separated glacial deposits and striation directions compatible with one ice-sheet system. Fits at the continental shelf edge are physically more meaningful than exact fits to modern coastlines, which have been modified by erosion and sea-level change. The evidence suggested relative movement, but did not justify the proposed forces: continents cannot readily plough independently through strong oceanic rock. A convincing mechanism and independent motion measurements were missing.

Oceanography changed the boundary conditions. Echo-sounding surveys revealed a connected spreading ridge system, axial valleys, subduction trenches and long fracture zones. Seismic refraction surveys established systematic differences between continental and oceanic crust. Thin oceanic sediment cover, high ridge heat flux and the lack of very old exposed oceanic basement made permanent, ancient ocean basins increasingly implausible. Harry Hammond Hess proposed creation of oceanic lithosphere at ridges and recycling at trenches: seafloor spreading without requiring an expanding Earth. Slow mantle convection supplied a physically plausible connection between surface transport and internal heat loss. The mechanism need not have been completely quantified before its kinematic predictions could be tested.^[ref]

Magnetic records supplied a clock and a speedometer. Dated continental lavas established a sequence of geomagnetic reversals. Marine magnetometers then found elongated, approximately paired marine magnetic stripes on either side of ridges. The 1963 interpretation by F. J. Vine and D. H. Matthews combined repeated reversals with seafloor spreading: cooling basalt locks in remanent magnetization, and continuous motion converts a time sequence into a spatial sequence. If a polarity interval lasts $\Delta t$ and occupies width $w$ on one ridge flank, its half-spreading rate is $w/\Delta t$. Matching several reversals tests the predicted sequence, rather than merely fitting a single stripe.^[ref] Different apparent polar wander paths for different continents also became mutually consistent after continental reconstruction, favoring relative continental motion over independent magnetic-pole histories.

Earthquakes identified creation, translation and consumption. Improved global seismology located shallow earthquakes along ridges and transforms, and dipping Wadati-Benioff zones beneath trenches. Their progressive focal depths identified cold, coherent slabs entering the mantle. Focal mechanisms showed extension at spreading boundaries, tangential slip at transforms and convergence at trenches. In 1965, John Tuzo Wilson's transform fault interpretation made a particularly discriminating prediction: active slip occurs between offset ridge segments, with a sense that can be opposite to that inferred by treating the entire lineament as an ordinary offset fault. The outer fracture zones are inherited traces, not continuing active plate boundaries. Agreement of focal mechanisms with the transform prediction linked magnetic and seismic evidence.

The late-1960s synthesis made these observations one quantitative theory. Relative motion of rigid tectonic plates on a sphere can be described by an Euler angular velocity vector, with $\mathbf{v}=\mathbf{\omega }\times \mathbf{r}$. Spreading rates, transform azimuths and slip directions must fit the same rotation, and relative angular velocities must close around plate circuits. The resulting framework accounted for global boundary geometry and earthquake mechanisms without moving continents separately from the seafloor. Deep-ocean drilling beginning in 1968 subsequently confirmed that basement and overlying sediments generally become older away from ridges; this was a powerful confirmation of an already emerging synthesis, not a prerequisite discovered decades earlier.^[ref]

Thus plate tectonics succeeded through agreement between geological reconstruction, magnetic chronology, ocean-floor structure, seismology and rigid-plate kinematics. Modern satellite geodesy verifies motions directly, but belongs to the later confirmation of the theory, not its original 1960s evidence.

Choose an ocean–continent convergent margin. The essential relationship is recycling of oceanic lithosphere by subduction, together with production and modification of crust in a volcanic arc.

The incoming tectonic plate consists of thin oceanic crust, chiefly basalt and gabbro, above colder lithospheric mantle. As that oceanic lithosphere approaches the subduction zone, bending produces the subduction trench. Its cold interior can become denser than the surrounding mantle; the resulting slab pull helps sustain subduction. The descending slab carries both oceanic crust and lithospheric mantle into the interior. Thus the recycled unit is an entire portion of lithosphere, rather than just its crust.

At the subduction trench, some incoming sediment is scraped off and stacked by thrust faults into an accretionary prism. Material can also be added beneath the overriding plate by tectonic underplating. A forearc basin collects sediment between the accretionary prism and the volcanic arc. This is an accreting example: other convergent margins lose upper-plate material through tectonic erosion, so an accretionary prism is not universal.

The cold slab undergoes increasing pressure and metamorphism. Conversion of basaltic rocks and gabbro towards eclogite increases their density, while slab dehydration releases water from hydrated minerals. The rising fluid lowers the solidus of hot peridotite in the mantle wedge, causing flux melting. The usual source of arc magma is therefore the fluid-modified mantle wedge; extensive slab melting is not required. Thermal-petrological calculations show that the depth and amount of slab dehydration depend on the incoming slab's thermal structure.^[ref]

Buoyant magma rises through the overriding plate, freezes in igneous intrusions or erupts in the volcanic arc. Fractional crystallization, interaction with existing continental crust and repeated intrusion can produce more evolved arc magmas and add new crust. Some material merely reworks old crust, and simultaneous tectonic erosion can remove it: volcanism alone does not measure net continental growth. Tectonic shortening, folding and thrust faults can thicken and raise the upper plate.

The Wadati-Benioff zone marks earthquakes along and within the cold descending slab. Shallow interface earthquakes reflect unstable slip where the plates are coupled; deeper earthquakes require mechanisms such as dehydration embrittlement and are not simply dry shallow friction operating at every depth. In contrast, the hot mantle wedge deforms mainly by material creep. Together, the subduction trench, accretionary prism, forearc basin, volcanic arc and inclined seismicity connect surface features to the processes recycling and creating crust.

Cascadia subducts a young, warm plate and lacks the enormous plateau and crustal root of the central Andes; the central Andean Nazca Plate system also supports much deeper intraslab earthquakes. These are regional comparisons: neither western margin is uniform along its length.

First, the Juan de Fuca Plate entering Cascadia is young, typically of order 10 million years old, because its spreading ridge lies close to the margin. Its lithosphere is comparatively thin and warm. Much of the Nazca Plate entering the central Andes is older and colder. A cold plate carries low temperatures farther into the mantle, sustaining deep intraslab seismicity; the warm Cascadia slab loses its brittle seismogenic character much shallower. This concerns earthquakes within the slab, not the size of megathrust earthquakes: both margins can generate very large plate-interface events. The official warm-slab synthesis treats Cascadia as an endmember.^[ref]

Second, the central Andes have undergone major sustained crustal shortening and tectonic thickening, building a high plateau and locally roughly 60–70 km thick continental crust. Cascadia has an active volcanic arc and mountains but no equivalent continuous central-Andean plateau and crustal root. The difference reflects the accumulated history of convergence, upper-plate deformation, slab dip, trench motion and mechanical coupling, not just the instantaneous existence of subduction. The Andes include flat-slab segments with gaps in arc volcanism as well as normally dipping segments.^[ref][ref]

A young warm incoming plate and a faster, colder incoming plate can therefore generate different thermal structures, dehydration patterns and deformation histories. Plate age alone is insufficient to predict the thickness of the overriding continental crust.

Three earthquake sources matter: the offshore Cascadia megathrust, deep events inside the Juan de Fuca Plate, and shallow upper-plate faults, including the Seattle Fault. Shaking can damage buildings, bridges, ports and utility networks, interrupting transport, electricity and water supply. Soft basin sediments can amplify or prolong shaking; saturated loose fill can undergo soil liquefaction and lateral spreading. Steep slopes can fail as landslides. The same regional event can therefore have very different consequences on bedrock and on artificial fill.^[ref]

Large Cascadia tsunamis chiefly threaten the outer Pacific coast. Seattle's inland waterways also have local tsunami hazards from crustal faults and underwater landslides; one should not equate a Seattle waterfront site with an open-ocean coastal site. Cascade eruptions can affect the region through volcanic ash and transport disruption. Lahars are strongly channelled by river valleys, so their exposure is location dependent rather than uniform across Seattle. These geological differences influence infrastructure design, land-use decisions and emergency planning.^[ref][ref]

Support for the left curve comes from high laboratory friction and substantial in situ differential stress; support for the right curve comes from low inferred fault traction, weak fault materials or high pore pressure. No single observation directly measures the whole plotted envelope.

For the left, stronger shallow-crust model:

For the right, weak shallow-layer model:

To discriminate, measure the strength-controlling quantities through depth and across both faults and their surroundings. Obtain borehole stress, pore pressure and temperature profiles where feasible; use borehole breakouts and hydraulic tests to constrain effective stress. Recover fault and host rocks and test their friction and material creep at relevant fluid conditions. The right curve specifically predicts an end to the shallow weakening near its sharp rise: investigate changes in permeability of a porous medium, alteration and fault gouge with depth, rather than testing only a surface sample.

Combine those measurements with heat flux transects, magnetotelluric sounding for conductive fluids, accurate earthquake depths and focal mechanisms, and GNSS or InSAR observations of deformation. The latter can help constrain the depth distribution of locking and postseismic relaxation, but neither locking nor seismicity alone gives absolute strength. Earthquake stress drop is a change in stress, not the pre-event stress. Low heat flux can also reflect heat transport or transient weakening; high electrical conductivity can have causes other than free water. A joint explanation of all these data is needed to choose between the models locally.

At a convergent margin, the incoming oceanic lithosphere is a chemically and mechanically layered package: sediments, oceanic crust and lithospheric mantle. Subduction does not deliver this whole package unchanged to one destination. Solids can be accreted, underplated, exhumed or recycled deeply, while released fluids and melts carry selected components to the overriding plate. The outcome depends on incoming composition and hydration, slab age, convergence rate, thermal structure, interface coupling and subsequent tectonic history.

The incoming material already contains a history. Sediments include terrigenous debris, biogenic carbonates, siliceous deposits, clay minerals, pore water and organic matter. Oceanic crust consists mainly of basalt, sheeted dikes and gabbro; hydrothermal alteration can add water, carbonates and mobile elements before subduction. Beneath it, residual peridotite forms the lithospheric mantle. Faulting at a spreading environment, a transform boundary or an outer-rise bending region can let seawater enter and cause serpentinization. The lithospheric mantle is not uniformly hydrated to its full thickness. Consequently, sediment thickness alone does not measure the incoming volatile inventory.

Sediments: separation starts near the trench. Compaction and increasing effective pressure expel pore fluids, which can escape through the forearc, transport dissolved constituents and influence pore pressure on the plate interface. Some sediments are scraped off into an accretionary prism, shortened by thrusts and retained in the upper plate. Others pass beneath the leading edge, then detach and undergo tectonic underplating beneath the forearc. Deeper underplated material may return to the surface during tectonic exhumation, preserving a record of burial and deformation. At a sediment-starved erosive margin, little prism may form, and tectonic erosion can entrain material from the overriding plate as well. Thus net continental gain and net continental loss are both possible; they can even alternate at one margin.

Sediments that remain attached to the slab undergo metamorphism, dehydration, and potentially decarbonation or carbonate dissolution. The released fluids can transport boron, barium, strontium, lead and other soluble constituents. Carbon can leave as dissolved species, remain in carbonate, or occur as reduced carbon depending on redox conditions and reaction history. Along sufficiently hot paths, sediment-derived melts or mixtures of sediment and altered rock can transfer material into the mantle wedge; buoyant mixed material may rise as a mélange diapir. Cold paths can instead retain more solid material and some volatile-bearing phases to greater depths. These are alternative reaction and transport pathways, not a single compulsory sequence. A carbon-budget study explicitly includes fluid dissolution, sediment diapirism and storage in the upper plate, showing why volcanic carbon dioxide alone cannot close the whole subduction carbon budget.^[ref]

Oceanic crust: metamorphic transformation and chemical filtration. Altered basalt and gabbro are progressively buried. Depending on their pressure-temperature paths and reaction kinetics, they can pass through blueschist facies or warmer assemblages and eventually form eclogite, dominated by garnet and omphacite. Eclogitization increases density and can strengthen negative slab buoyancy, but a kinetic delay can leave metastable rock. It is incorrect to assign every slab the same sequence or the same fixed depths for these changes.

During burial, breakdown of hydrous phases releases water-rich fluids; different mineral assemblages retain different quantities of water. The fluids migrate through or along the interface and into the mantle wedge, where they cause metasomatism and lower the solidus of peridotite. Flux melting of the mantle wedge generates much of the primary magma feeding a volcanic arc. This is different from saying that the entire descending oceanic crust melts beneath the arc. Most of its refractory mass can remain solid. Partial melting of oceanic crust is more plausible for unusually hot or young slabs, or other favorable thermal conditions, and produces a distinct crustal contribution.

The depth of dehydration is controlled by thermal structure and composition. Global thermal-petrological calculations, for example, predict more efficient deep water transport in old, fast, cold slabs than in hot ones, with substantial differences between volcanic crust, gabbro and hydrated peridotite. Such a calculation supports conditional deep retention; its modeled proportions should not be imposed on every margin.^[ref]

Mechanical detachment adds more branches. Upper-crustal slices, seamounts or oceanic plateaus may be accreted or underplated instead of continuing down the slab. A complete or partial ophiolite can be emplaced onto another plate by obduction in suitable convergence histories. Most intact oceanic crust is not saved this way. High-pressure fragments may be entrained in an interface channel or mélange and exhumed; their small preserved volume should not be mistaken for the dominant global mass flux. Magma generated after slab-derived transfer may also pond and crystallize beneath the upper crust by magmatic underplating, which is a different process from mechanical tectonic underplating of solid slices.

Lithospheric mantle: residual rock and a variable water carrier. Most incoming lithospheric mantle is depleted peridotite left after extraction of ridge melts. Its cold, dense, mechanically coherent portion contributes to slab pull and generally sinks with the plate. Hydrated portions contain serpentine and possibly other hydrous minerals. Breakdown of these phases releases water at conditions that depend on the thermal path, feeding further metasomatism of the mantle wedge and sometimes dehydration embrittlement. The latter is a proposed contributor to intermediate-depth earthquakes, not an exclusive explanation for all such events. Very cold paths may transfer some water onward in high-pressure hydrous phases or as hydrogen incorporated in nominally anhydrous minerals.

Do not confuse the incoming hydrated lithospheric mantle with newly serpentinized forearc mantle in the overriding plate. The latter receives slab-derived fluids and can temporarily store their water. Hydrated, relatively buoyant interface material can facilitate return flow and tectonic exhumation, while the colder deeper bulk of the lithospheric mantle continues down. Some peridotite may also be accreted or obducted with an ophiolite. These exchanges mean that even an exposed serpentinite requires structural and chemical context before it can be assigned to its original plate.

Deep recycling and eventual return. The residual eclogite, remaining sediments and lithospheric mantle can enter the deeper mantle. A slab can temporarily stagnate around the mantle transition zone or penetrate into the lower mantle, depending on buoyancy, phase transformations, geometry and mantle viscosity. Crustal material can remain as compositionally distinct domains, mix, or react with surrounding peridotite; it need not retain the near-surface eclogite assemblage indefinitely as pressure rises. Subsequent mantle convection can return recycled components toward spreading regions or mantle plumes, where partial melting incorporates them into new basalt. A primary study of Hawaiian basalt illustrates a specific model in which melts derived from recycled crust react with peridotite to form a pyroxenite source. It is an interpretation of combined chemical evidence, not a unique label attached to every enriched basalt.^[ref]

How the pathways can be observed. Seismic reflection profiles, drilling, wedge geometry and balanced structural sections constrain accretion, fluid escape and tectonic erosion. High-pressure metamorphism, mineral zoning, radiometric dating and pressure-temperature-time paths in exhumed rocks reveal burial, reaction and return. Their reconstructable histories are especially useful when deformation and fluid inclusions are linked to the dated mineral growth. Earthquake distributions, seismic tomography, seismic attenuation and electrical conductivity constrain the geometry and physical state of the slab and mantle wedge, although fluids, melts and temperature can produce nonunique signals.

Arc magmas carry complementary chemical evidence: relatively mobile barium, boron, lead or strontium can trace fluid-mediated transfer, whereas sediment-sensitive thorium and isotope ratios can help identify other contributions. Element mobility changes with fluid composition and pressure-temperature conditions, so no one element is an infallible tracer. Boron isotope ratios, radiogenic strontium isotope ratios and lead isotope ratios should be interpreted with measured incoming sediments and altered oceanic crust. Arc gases and forearc fluid discharge constrain volatile return; ocean-island basalts, mantle xenoliths and diamond inclusions provide possible evidence of deeper recycling. Each observation samples only part of the system.

For any element $X$, a useful control-volume statement isHere permanent accretion is counted outside the chosen reactive control volume, return includes fluid, melt and exhumed-solid exports, and transient underplating or reservoir growth contributes to storage until exported. For a different boundary choice, the terms must be regrouped consistently. The three incoming layers can have very different transfer efficiencies for bulk rock, water, carbon and a particular trace element. A small mass of escaping fluid can dominate an element's return while most of the solid slab continues into the deep mantle.

For a heterogeneous fault slip distribution, seismic moment iswhere $G=30\times 10^9\mathrm{Pa}$ is the shear modulus, $A$ the fault plane area, and $\overline{D}$ the area-averaged fault slip. The peak colour cannot be used as $\overline{D}$: most of the illustrated fault plane has much smaller fault slip.

One reproducible graphical estimate divides the approximately $190\mathrm{km}$ long and $40\mathrm{km}$ down-dip panel into seven $25\mathrm{km}$ strips and a final $15\mathrm{km}$ strip. Reading area averages from the colour scale, from southwest to northeast, gives roughly $1.7,2.7,3.1,1.8,1.9,1.7,1.0,0.3\mathrm{m}$. This includes the pale, nearly unslipped lower part of each strip. Henceand $M_0\simeq 4.2\times 10^{20}\mathrm{N}\mathrm{m}$. A reasonable graphical range is approximately $3$–$6\times 10^{20}\mathrm{N}\mathrm{m}$, dominated by colour averaging and the down-dip extent of small fault slip. The corresponding moment magnitude is about $M_w=7.7$, using $M_w=\frac{2}{3}({\log }_{10}(M_0/\mathrm{N}\mathrm{m})-9.1)$. This is an estimate from the supplied distribution, rather than a substitution of a catalogued earthquake magnitude.

Effective stress and frictional strength generally increase with depth through the shallow crust undergoing brittle fracture. At $1\mathrm{km}$, small overburden and often weak, fractured near-surface materials limit the shear stress and elastic energy that can accumulate. Some shallow materials also undergo stable sliding rather than unstable earthquake nucleation. Near $15\mathrm{km}$, a locked fault prone to brittle fracture can sustain a much larger differential stress before frictional instability releases stored elastic energy.

This depth is plausibly near the lower, strong part of the seismogenic layer: below it, increasing temperature eventually promotes material creep across the brittle-ductile transition. Once nucleated at depth, a dynamic finite-source rupture can propagate into shallow regions that could not independently nucleate the same event. Depth alone does not determine the nucleation point: local pore pressure, frictional stability and stress heterogeneity also matter.

Use repeat-pass interferometric synthetic-aperture radar. An orbiting radar transmits coherent microwave pulses and records the amplitude and phase of the returning field. Form an interferogram from registered complex images acquired before and after the earthquake, remove the orbital contribution and the topographic phase predicted by a digital elevation model, and correct atmospheric and other long-wavelength phase delays. Where interferometric coherence is adequate, unwrap the residual phase to estimate line-of-sight displacement:with sign set by the instrument's displacement convention. Each $2\pi$ phase cycle represents $\lambda /2$ of range change.

This maps a distributed earthquake displacement field day or night and through cloud, including areas inaccessible on foot. Roughly $10$–$30\mathrm{m}$ ground sampling and a scene spanning many kilometres on both sides of the fault can resolve regional deformation; a narrow surface break benefits from finer pixels or complementary sub-metre optical surveys. Sensitivity to displacement can be millimetres to centimetres in coherent areas, but that does not equal spatial resolution. A single viewing direction measures one component; ascending and descending tracks and GNSS constrain more components. At the rupture itself, large gradients and changed ground cover can destroy interferometric coherence; radar pixel-offset tracking or before/after optical correlation can then recover metre-scale fault offsets.

The $31.7^{\circ }$ result predicts initial failure in a uniform material under the assumed principal-stress orientations. The actual Figure 3 is a present-day NW–SE cross section through a thick, heterogeneous Alpine stack, extending to about 50 km depth. It contains near-horizontal basal stretches, curved ramps, tightly bent contacts, and steep structures in the internal zones around Viso and the Dora Maira complex. It does not show a single undeformed conjugate pair newly formed in horizontal uniform rock.

Several processes explain the departures:

Finally, a section shows apparent dip unless it is perpendicular to fault strike. For an ideal plane, $\tan {\delta }_{\mathrm{app}}=\tan {\delta }_{\mathrm{true}}\sin \alpha$, where $\alpha$ is the angle between the section direction and fault strike. Obliquity can make a plane look shallower, but cannot on its own explain an apparent dip steeper than its true dip. Do not infer that each black curve is a currently active brittle earthquake fault.

Fault slip must taper toward zero at the tips of an isolated finite fault, because its two sides are still joined beyond the tips. Accumulating more central displacement at a fixed short length steepens the displacement gradient and loads the surrounding rock, especially near the tips. In a simple elastic scaling, a fault of length $L$ and characteristic displacement $D$ requires a characteristic driving shear stress of orderwhere $\mu$ is the shear modulus and the omitted coefficient depends on fault geometry. The host's finite strength prevents this gradient increasing indefinitely. Tip damage, new cracking and linkage with neighboring segments allow the fault system to lengthen and accommodate more displacement without unbounded tip loading. Self-similar growth at roughly comparable driving stress consequently gives the approximate fault displacement-length scaling $D\propto L$; displacement also commonly increases toward the interior of a fault segment.^[ref]

The word “must” describes this mechanical limitation over sustained growth. It is not a rule that every earthquake or every increment of accumulated fault slip lengthens the mapped trace: strong barriers, interactions and early establishment of fault length can permit substantial later displacement at nearly constant length.

Interferometric synthetic-aperture radar compares the phase of coherent radar returns acquired before and after the earthquake from closely repeated viewing geometry. After image registration and removal of orbital and topographic phase, the residual interferometric phase constrains relative ground displacement along the radar line of sight. Defining $u_{\mathrm{LOS}}$ positive toward the satellite and choosing the interferogram's phase order accordingly,One complete colour cycle therefore represents $\lambda /2$ of relative line-of-sight displacement. Reversing the image order reverses the displayed phase sign. This observes a projection of both horizontal and vertical motion, not uplift alone.^[ref]

If the main reverse rupture reaches the surface, coherent areas on opposite sides can show a displacement step: fringes become offset, truncated or abruptly juxtaposed along a trace. A narrow belt can lose interferometric coherence where cracking, intense gradients or changed scatterers prevent reliable phase comparison. If the rupture remains blind, a simple elastic model instead predicts a continuous surface displacement field, often a broad asymmetric lobe with continuous curved or closed fringes and a smooth displacement gradient across the projected tip.

These are diagnostic tendencies, not a unique test. An ordinary wrapped-phase boundary is just a $2\pi$ colour reset and is not itself a rupture. A step of an integer number of cycles can be hidden in wrapped phase; loss of interferometric coherence can hide either kind of near-field deformation. Vegetation, atmosphere and viewing direction also affect the pattern, and a displacement perpendicular to the radar line of sight is poorly sensed. Inspect coherence and unwrapped displacement, compare ascending and descending views where possible, and test a fault model against field observations. A sharp fold scarp above a blind rupture or a secondary shallow fault can also create localized gradients, so smooth fringes do not prove a buried tip and broken fringes alone do not prove a surface-breaking main rupture.

For a surface-breaking reverse earthquake, expect a fault scarp or disrupted belt with the hanging wall displaced upward and commonly over the footwall. Small thrust faults, splays and backthrusts may repeat or override shallow deposits. Shortened soil, roads or other markers may buckle, while soft sediment can form pressure ridges and compression folds. Near the scarp, gravitational collapse and local bending can also produce tensile fissures and small normal faults; a reverse event need not create compression everywhere at the surface.

For a blind reverse rupture, expect coherent uplift and warping, newly tilted surfaces, or a fold scarp without a throughgoing primary fault offset. Small flexural-slip surfaces along bedding, secondary thrust faults or backthrusts, and opening cracks or small normal faults over the bent outer arc of the anticline can accompany the folding. Deformation may be distributed or localized at fold hinges. Thus a blind main fault does not imply an entirely unbroken ground surface, and secondary cracking must be distinguished from the principal rupture by its geometry and displacement pattern. Shaking-triggered landslides or soil liquefaction can accompany either case and should not automatically be mapped as primary tectonic rupture.^[ref]

Geophysicist and author of primary studies of earthquake ground motion and rupture directivity. His authorship and USGS affiliation are documented on the 2004 report: pubs.usgs.gov/of/2004/1268/ .