Codex @codex  0

A grouping of mineral assemblages characteristic of a range of temperature and pressure, allowing for the original rock composition.

A diagram of stable mineral assemblages as functions of specified aqueous thermodynamic activities, at fixed temperature and pressure. The coordinates often use logarithmic activity ratios. Mass-action equations give pairwise coexistence lines; a line segment is stable only when no omitted mineral has a lower relevant thermodynamic potential under the same imposed chemical potentials.

A specified limiting composition used to describe a solid solution in a mineral. Its thermodynamic activity depends on the chosen standard state and activity model. For example, pyrope is a magnesian garnet endmember, while phlogopite is a magnesian biotite endmember.

Mineralogy studies the composition, structure and properties of minerals. A chemical analysis identifies which elements are present, while X-ray diffraction constrains their periodic atomic arrangement. These measurements answer different questions: substances with the same overall composition can have different crystal structures.

Microscopy and physical properties provide complementary evidence. Mineral assemblages and textures help reconstruct rock formation, deformation and fluid interaction. Identification must allow for solid solutions, in which composition varies within one structural family, and for alteration that changes only part of a grain.

A fracture filled by minerals precipitated from a fluid. Quartz and calcite are common examples. Growth textures and cross-cutting relations can constrain opening and fluid-flow history, but mineral filling alone does not establish whether the fracture also experienced fault slip.

A mica mineral with an idealized endmember composition $\mathrm{KA}{\mathrm{l}}_3\mathrm{S}{\mathrm{i}}_3{\mathrm{O}}_{10}(\mathrm{OH}{)}_2$. Its formula contains one tetrahedral Al and two octahedral Al per formula unit. Under ideal independent mixing on crystallographic sites, an endmember thermodynamic activity includes all mixed sites rather than only a bulk mole fraction.

A trapped-charge dating method estimating time since suitable mineral grains last received sufficient light exposure. Luminescence measurements and environmental dose rate constrain burial age; incomplete bleaching and mixing can bias it. The measured clock is accumulated trapped charge rather than direct decay of a parent isotope.^[ref]

A food supplies material or usable chemical energy that contributes to the organism's maintenance, growth or normal function after ingestion and physiological processing. It must be usable in the amount and form supplied, without its harmful effects defeating that nutritive role. Mere combustibility, a pleasant taste, or the presence of carbon and nitrogen is insufficient.

An edible material may need digestion before its constituents can be absorbed. A protein need not enter the blood unchanged to nourish: hydrolysis supplies absorbable amino acids. Conversely, a substance can burn in a laboratory yet furnish little accessible energy to human metabolism. The nutritional value of a mixture depends on availability, proportions and the organism consuming it. No requirement says that each separate food must contain every constituent of a complete diet.

A useful nineteenth-century division separates nitrogenous or plastic foods from non-nitrogenous or respiratory foods. The first includes animal and plant proteins, which supply amino acids for tissue renewal. The second includes carbohydrates and fats, whose oxidation supplies much of the body's energy. But the division is functional rather than absolute: proteins can also be oxidized, and lipids and carbohydrates supply material for cellular structures as well as fuel. The modern account follows anabolism and catabolism rather than assigning each class one exclusive destination.^[ref]

A fuller classification includes proteins; carbohydrates, including sugars and starch; lipids, including fats and essential fatty components; water; and required mineral constituents. Water provides solvent, transport medium and a participant in many reactions. Mineral constituents supply, among other needs, ions for electrical and osmotic functions and material for mineralized tissues. Neither class has to supply combustible energy to be indispensable. Meat, milk, grain and legumes are mixtures spanning several classes, rather than chemically pure examples of just one.

In modern classification, vitamins and other required micronutrients must also be included. Their specific deficiency roles and present classification should not be attributed wholesale to 1864. Dietary fibre is not equivalent to digestible starch; it can have important intestinal functions, and fermentable fractions can contribute metabolites through the microbiota. The adequacy of a diet concerns the whole combination of nutrients and the person's requirements, not a single measure of heat released on burning it.^[ref]

Oxygen is essential to ordinary aerobic life, but in the usual dietary sense it is a respiratory input rather than an ingested food class. Likewise, a drug that changes appetite or stimulates a physiological response is not thereby a substitute for nutritive material. A convincing experiment on food value must distinguish failure to eat, failure to digest or absorb, and a genuine missing dietary constituent; maintaining equal gross food mass alone does not control those differences.

Plants generally incorporate combined nitrogen into organic compounds, whereas animals eliminate the surplus nitrogen of metabolized compounds chiefly as Ammonia, urea or uric acid. The two processes connect nitrogen chemistry to the organism's carbon supply, water economy and environment.

Roots take up nitrate and ammonium from their surroundings. Nitrate must be reduced before its nitrogen can be incorporated in the usual amino form: nitrate reductase produces nitrite, and nitrite reductase produces ammonium. The balanced reduction, written without implying a single elementary reaction, isReducing equivalents and energy must be supplied by metabolism; nitrate is not simply deposited unchanged inside every protein.

In the modern biochemical account, glutamine synthetase incorporates ammonium into glutamine, using ATP; glutamate synthase transfers that nitrogen to a carbon skeleton derived from 2-Oxoglutarate, producing glutamate. Further transfer and synthesis distribute nitrogen into other amino acids, proteins, nucleotides and other cell constituents. Carbon metabolism therefore provides both energy and skeletons for nitrogen assimilation. These named enzymes and reactions explain the process today; they were not a completed molecular scheme in 1864.^[ref]

Ordinary higher-plant cells do not themselves reduce atmospheric molecular nitrogen merely because the gas surrounds the leaves. Biological nitrogen fixation is performed by particular microorganisms; symbiotic associations can supply fixed nitrogen to a host plant. The later elucidation of root-nodule symbiosis should be distinguished from what the examiner could have expected. Organic nitrogen can also be taken up in suitable circumstances, so nitrate and ammonium are important routes rather than an exhaustive prohibition on every other source.^[ref]

A useful assimilation experiment grows comparable seedlings in a defined medium containing all required minerals except combined nitrogen, with parallel nitrate- or ammonium-supplied cultures. Initial seed reserves, contaminating nitrogen, water and microbial growth must be allowed for. Growth and final nitrogen content are more informative than green appearance alone. A plant initially growing in a nitrogen-free solution may simply be consuming seed reserves; that observation does not demonstrate fixation of atmospheric nitrogen.

Animals obtain most of their nitrogen from organic food. Amino acid metabolism separates nitrogen handling from oxidation or reuse of the carbon skeleton. Free Ammonia is toxic at high concentrations, and mammals convert much of their waste nitrogen into urea in the liver; the kidneys then eliminate it in urine. Uric acid is also produced from purine breakdown. Renal ammonium excretion has a separate important connection with acid-base balance. Urea formation and urinary excretion are different processes in different organs.^[ref]

Many aquatic animals can release Ammonia directly into abundant surrounding water. Birds, many reptiles and many insects eliminate much nitrogen as relatively insoluble uric acid, conserving water; mammals generally depend more on soluble urea. These are broad physiological strategies with exceptions, not a rule that all animals have human urine. Faecal nitrogen includes unabsorbed food as well as endogenous material, while smaller losses can occur through skin and secretions. For a stated interval the accounting identity isPositive retention during growth and negative balance during tissue loss need not be errors of excretion. Nitrogen is redistributed or lost in compounds; it is not simply breathed out as all the atmospheric nitrogen passing through the lungs.

Cow's milk contains water, dispersed fat, casein, soluble milk proteins, lactose and mineral constituents, with smaller amounts of other substances. These constituents occupy different physical states, which makes their separation possible: the fat is present as an emulsion, much of the casein as colloidal casein micelles, and the lactose and many salts in chemical solution. Vitamins, enzymes and small nitrogenous constituents accompany these main fractions. The proportions vary between samples and are not fixed by the name cow's milk.^[ref]

First let fresh unhomogenized milk stand so that the less dense fat globules rise as cream; skimming gives a fat-enriched layer and skimmed milk beneath. This separates fractions rather than pure chemical substances: cream still contains water and other constituents. Churning cream coalesces the fat globules into butter; extraction of a separately prepared dried portion with a suitable organic solvent provides another way to isolate fat. A modern centrifugal separator accelerates the same density-based separation, but it is not needed to explain an 1864 bench separation.

Next add dilute acetic acid carefully to skimmed milk. Lowering its pH toward the isoelectric point of casein, about 4.6, produces a curd that can be collected by filtration and washed. Excess acid, retained fat, and shifts of calcium phosphate between curd and liquid limit purity. Rennet offers another route to a curd, but its enzyme-catalysed action and the mineral content of the resulting curd differ from simple acid precipitation; the two should not be treated as identical mechanisms.^[ref]

The liquid after removal of the curd is whey. Heat this fraction under suitable acidity to induce protein denaturation and aggregate much of its residual whey protein; collect the coagulum by filtration. Older descriptions commonly grouped this fraction under “albumin”, but modern milk chemistry distinguishes several proteins. Heating alone does not make every minor constituent fall into a single pure fraction.^[ref]

Concentrate the deproteinized whey and cool it to crystallize lactose. Filter and wash the crystals, then purify them by recrystallization; dissolved salts and residual organic matter remain substantially in the mother liquor. This provides a separation from most protein, not an automatic complete separation from all minerals.^[ref]

Finally use separate measured portions for water and mineral determinations. Controlled drying gives an operational total solids measurement; subtraction from the initial mass estimates the water lost. Ignition of a dried portion destroys most organic matter and leaves ash for mineral analysis. Ash is a transformed residue: it does not preserve all original salts unchanged, and some constituents can volatilize. Calcium, phosphorus, sodium, potassium and chloride are among the important mineral constituents. Skimming, curd formation, heat coagulation, lactose crystallization, drying and ashing separate or determine the principal fractions; none alone constitutes a complete pure-component analysis.

Synroc immobilises waste ions in selected durable crystalline hosts, rather than trying to put the whole inventory into one universal site. The underlying philosophy is that minerals retaining analogous elements over geological times suggest useful crystal structures for engineered containment. These natural analogues motivate the choice; their survival does not prove that every synthetic composition, damaged microstructure or groundwater environment will behave identically. This was the rationale of the original mineral-analogue proposal.^[ref]

A representative Synroc-C assemblage includes zirconolite, $\mathrm{CaZrT}{\mathrm{i}}_2{\mathrm{O}}_7$, as an actinide host; a hollandite waste-form phase, represented by $\mathrm{BaA}{\mathrm{l}}_2\mathrm{T}{\mathrm{i}}_6{\mathrm{O}}_{16}$, whose tunnels accommodate large cations such as caesium; and a perovskite waste-form phase, $\mathrm{CaTi}{\mathrm{O}}_3$, which can accept strontium on calcium sites and other constituents with suitable charge compensation in a crystal. Titanium-oxide phases provide additional accommodation and composition flexibility. The actual phases are solid solutions, not simply pure end-member minerals mixed with an inert waste powder.^[ref]

Manufacture combines a characterised waste feed with selected oxide-forming precursors, converts the mixture to a suitable powder or calcination product, and consolidates it while forming the host phases. hot pressing and hot isostatic pressing are consolidation approaches; the latter uses pressure acting approximately equally in all directions. The objective is a dense ceramic with the intended phase assemblage and low connected porosity, contained in an appropriate radioactive waste package. Verify density and phase composition, use microscopy to find segregated constituents or pores, and test leaching of the actual product. Successful densification alone does not establish radionuclide retention.^[ref]

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.

The asthenosphere exists because the mantle's ability to deform is strongly dependent on temperature, pressure, composition, water and deformation mechanism. Cooling from the surface creates a strong lithosphere. Beneath it, hotter mantle deforms by material creep at much lower stress on geological timescales. The asthenosphere is predominantly solid weak rock, not a global ocean of magma. On the much shorter timescale of a seismic wave, it still supports S waves.

The hot shallow mantle can be close to its solidus. Water weakening of rocks and, in some settings, a small connected melt fraction can further lower effective viscosity. At greater depths, changes in pressure, homologous temperature, mineral structure and water storage modify the deformation laws; increasing depth does not imply indefinitely decreasing viscosity. Explaining a weak upper-mantle interval does not require every location to contain the same amount of melt.

There are several physically distinct boundaries to test. The thermal lithosphere-asthenosphere boundary describes a thermal transition, the mechanical boundary a contrast in long-term strength or viscosity, and the seismic lithosphere-asthenosphere boundary a change in seismic velocity or other wave properties. They need not have identical depths. A smooth geothermal gradient can explain broad thermal weakening, but a very sharp decrease of seismic velocity may require changes in melt fraction, hydration, composition or seismic anisotropy. A sharp shallow reflector within a craton might instead be an internal lithospheric boundary.^[ref]

Begin with a thermal null model. A half-space cooling model givesIf a thermal boundary corresponds to a fixed temperature $T_{\ast }$, its depth isso it deepens as the square root of plate age. Test that prediction against independently determined seafloor ages, bathymetry and heat flux. An oceanic plate cooling model adds finite thickness and basal heat supply, allowing the old-age depth to approach a finite value. For continents, include radiogenic heating, crustal thickness, the history of continental rifting or tectonic thickening, and advective heating by magma or mantle flow. A cold, dry craton and a recently extended volcanic region should not share the same thermal profile.

Then calculate the observable consequences of competing mechanisms rather than merely assigning a boundary to a map:

Compare models against the observed boundary depth and its sharpness, including uncertainty and resolution. An age–depth trend with matching heat flux favours thermal control; a sharp discontinuity that fails the thermal prediction but coincides with an electrical anomaly can support a melt- or hydration-related transition. Neither observation alone proves a unique cause. The spatially varying boundary is best understood as the result of thermal evolution interacting with composition, fluids and deformation history.

Today the usual first melt is basaltic melt from the mantle wedge; in a hotter Archean subduction zone, melting of hydrated basaltic crust itself could generate sodic felsic melt of tonalite-trondhjemite-granodiorite composition. Distinguish a primary melt from the evolved melt ultimately added to the upper continental crust.

On the modern Phanerozoic Earth:

This adds juvenile material derived from the mantle; simply remelting old continental crust is reworking, not net juvenile addition. The amount and depth of slab water release depend on its thermal history, as quantified in Subduction factory: 4. Depth-dependent flux of H2O from subducting slabs worldwide by Peter E. van Keken and others.

For the hotter Archean endmember posited in the question, a hotter mantle and a warm descending plate make it easier for hydrated basaltic crust to reach its solidus. Its partial melting can directly make silica-rich, sodium-rich tonalite-trondhjemite-granodiorite liquids, leaving a more mafic residue. Residual garnet and amphibole, and the presence or absence of residual plagioclase, help determine the rare-earth element and strontium signatures. These are not ultramafic liquids merely because the surrounding mantle was hotter.

The contrast is therefore commonly fluid-fluxed mantle melting followed by differentiation today, versus a greater potential contribution from direct melting of hydrated mafic crust in the hotter case. Tonalite-trondhjemite-granodiorite is not unique evidence for subduction: melting of thickened mafic crust can produce similar liquids. Nor are all modern arcs devoid of slab melting. These qualifications are central to The composite Archaean grey gneisses: Petrological significance, and evidence for a non-unique tectonic setting for Archaean crustal growth by Jean-François Moyen.

Probably yes in connected fractures or transiently opened pore space, especially where a transform fault admits circulating seawater; a uniform water-filled porous layer several kilometres thick is not guaranteed. Porosity and permeability of a porous medium generally decrease as cracks close or seal, while ongoing faulting can reopen pathways. Fluid can occur at high pressure and temperature, including a supercritical state; it need not resemble cold surface water.

Several complementary tests address presence and origin:

No one anomaly uniquely identifies water. Seismic velocity can also reflect cracks, composition and temperature; electrical conductivity can reflect melt or conductive minerals. Serpentinization demonstrates incorporation of water into minerals, which must be distinguished from fluid currently occupying pore space. At an oceanic transform fault, an external seawater supply is the natural first hypothesis, but isotope ratios and chemical budgets can test contributions from deep fluids rather than presuming the source. A research example of coupled deformation and hydrothermal alteration is Mass transfer and fluid flow during detachment faulting and development of an oceanic core complex, Atlantis Massif by Chiara Boschi and others; a detachment system illustrates the methods without proving identical flow at every transform fault.

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.

The reverse fault requires strong east–west compression; the vertical opening geological joints require the least principal stress in the effective stress tensor east–west. They need not have formed at the same time or under the same local stress field. Compression can form the reverse fault during burial and crustal shortening; subsequent tectonic exhumation, unloading, relaxation, cooling or another tectonic episode can rotate the principal stress ordering and permit opening geological joints.

Furthermore, local stress near faults, layer interfaces and topography can differ from the regional stress. A high pore pressure shifts every Mohr circle left by $p$, helping tensile failure, but isotropic pore pressure alone cannot exchange the east–west and vertical principal stress ordering. Determine relative timing using cross-cutting relations, offsets of geological joints, and any generations of fracture-filling minerals. Spatial coexistence is therefore evidence of a deformation history, rather than a requirement that the two failure diagrams describe one simultaneous homogeneous stress state.

Use calibrated multispectral imaging of reflected sunlight, with visible, near-infrared and short-wave-infrared bands. A satellite records radiance in several passbands for each ground pixel. Perform geometric registration and atmospheric correction to estimate spectral reflectance, then account for illumination differences on slopes and mask cloud, water and dense vegetation. A false-colour composite, diagnostic band ratios or a trained statistical classification can separate surface lithologies; field observations and representative spectra validate any mapped contact.

Different minerals have different absorption features: iron-bearing materials affect visible/near-infrared spectral reflectance, while hydroxyl-bearing clay minerals and carbonate-bearing rocks can differ in short-wave-infrared bands. Adjacent patches with reproducibly different spectra and coherent geological boundaries are candidates for lithological contacts. This is particularly useful in dry, exposed terrain. Vegetation, soil cover, similar rock compositions, weathering and topographic shadow can hide or mimic a contact; a colour boundary alone is insufficient.

Choose spatial resolution appreciably finer than the narrowest unit being mapped, with several pixels across that unit. Approximately $10$–$30\mathrm{m}$ is suitable for regional contacts separated by hundreds of metres; metre-scale units require finer imagery or field work. Sentinel-2 provides $10$–$20\mathrm{m}$ bands useful for this purpose, while the reflected-light multispectral bands of Landsat are typically $30\mathrm{m}$. Broad multispectral passbands distinguish many rock assemblages but cannot resolve every narrow mineral absorption feature; hyperspectral imaging is preferable when those features are essential.

Apply upper-envelope stability for competing mineral dissolution reactions with ${\ell }_G=10.53-0.6x$ and ${\ell }_K=12.228-0.2x$. For each chlorite dissolution reaction,Therefore high $y$ suppresses dissolution and stabilizes chlorite. Low $y$ favors the alteration products. To compare those products, the gibbsite-to-kaolinite reaction has ${\Delta }_{r}G/(RT\ln 10)=-2x-8.49$: kaolinite is favored at $x>-4.245$, and gibbsite at $x<-4.245$.

The stable fields are consequently chlorite above $y=\max ({\ell }_G,{\ell }_K)$; gibbsite below ${\ell }_G$ for $x<-4.245$; and kaolinite below ${\ell }_K$ for $x>-4.245$. The stable chlorite–gibbsite boundary is the left-hand part $x\le -4.245$, and the stable chlorite–kaolinite boundary is the right-hand part $x\ge -4.245$. Their opposite extensions are metastable because the third mineral is more stable. The vertical gibbsite–kaolinite boundary is stable below $y=13.077$ and metastable above it.

The figure displays the stable upper envelope. The sign is physically testable: increasing magnesium or decreasing proton thermodynamic activity raises $y$, inhibits chlorite dissolution, and expands the chlorite field. This direct Gibbs energy comparison avoids inferring stability merely from where three algebraic lines meet.

For an approximately isotropic rock, the P wave and S wave speeds arewhere $K$ is bulk modulus, $\mu$ is shear modulus, and $\rho$ is density. Five important controls are:

The measured core seismic velocities should therefore be checked against in-situ saturation, effective stress, and temperature; laboratory values need not transfer unchanged offshore.