Geothermal Gradient

TECTONICS | Hydrothermal Activity

R.P. Lowell , P.A. Rona , in Encyclopedia of Geology, 2005

Geothermal gradient

Conductive heat flux, H , is related to the geothermal gradient by H  =   λ dT/dz, where λ is the thermal conductivity. For rocks, λ ranges from approximately 1.8 to 5   W (m   °C)−1, with most igneous and metamorphic rocks falling into a narrower range between 2.0 and 2.5 W (m   °C)−1. In older, stable continental cratons, the geothermal gradient may be as low as 10°C   km−1, whereas in active volcanic regions it may be more than 100°C   km−1. A typical geothermal gradient of ≈25°C   km−1 gives a conductive heat flux of ≈60   mW   m−2.

In terrestrial low-temperature hydrothermal activity, fluids driven by a topographic head circulate to a depth of ∼1–3   km in the crust where they are heated by the geothermal gradient. The fluids emerge through faults at the surface as warm or hot springs with temperatures ranging from a few tens of degrees above ambient to the local surface boiling temperature (Figure 3C). Such springs are found worldwide in areas of both normal and elevated heat flow.

Low-temperature hydrothermal circulation in oceanic crust occurs from ridge axes to a lithospheric age of ∼60   My. This circulation is partially controlled seafloor topography in combination with the geothermal gradient, with discharge occurring at highs and recharge occurring at topographic lows. Type and thickness of sediment cover also influences this circulation. More than 90% of all hydrothermal heat loss from the seafloor occurs at low temperature. This circulation impacts geochemical cycles as the equivalent of an ocean volume approximately evens 106 years.

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Mineral Physics

A.M. Hofmeister , ... M. Pertermann , in Treatise on Geophysics, 2007

2.19.1.1 The Importance of Thermal Conductivity to Geophysics

Fourier (c. 1820) recognized that the geothermal gradient could be used to estimate the Earth's age. His equation links thermal conductivity ( k) and temperature (T) to the flux:

[1] F = − k ∂ T / ∂ n

where the length-scale n is normal to the surface. To solve eqn [1], Kelvin (c. 1864) treated the Earth as a one-dimensional (1-D), semi-infinite solid; his age of 100   My for the Earth was accepted until the discovery of radioactivity in the early 1900s. Kelvin's solution is still used to model global power (flux times surface area) from measurements of oceanic heat flux (Pollack et al., 1993; discussed by Hofmeister and Criss 2005a, 2005b, 2006).

The surface flux is one clue to Earth's thermal state. Probing the workings of Earth's interior and its thermal evolution also requires detailed knowledge of k or of thermal diffusivity:

[2] D = k ρ C P

where ρ is density and C P is heat capacity. Temperature derivatives of D or k are crucial, which is revealed by examining the equation for heat conduction in an isotropic medium:

[3] ρ C P ∂ T ∂ t = k ∇ 2 T + H + ∂ k ∂ T ∂ T ∂ x 2 + ∂ T ∂ y 2 + ∂ T ∂ z 2

where t is time and H describes heat sources such as radioactivity (Carslaw and Jaeger, 1959). The specific forms and values of k(T), or D(T), strongly influence the temperature distribution obtained in conductive cooling models due to the nonlinear nature of eqn [3]. Examples include warming of subducting slabs, stability of olivine near the transition zone, occurrence of deep earthquakes (Hauck et al., 1999; Branlund et al., 2000), buckling of the lithosphere (Gerbault, 2000), the geotherm (Hofmeister, 1999), and lithospheric cooling (Honda and Yuen, 2001, 2004).

Thermal transport properties play a crucial role in mantle convection, as this phenomenon results from competition between diffusion of heat (thermal conductivity), resistance to motion (viscosity), and buoyancy forces. Variable thermal conductivity has mostly been neglected in modern geodynamic studies, in view of the much stronger, exponential dependence of viscosity on temperature (e.g., Tackley, 1996), with a few exceptions (e.g., Yuen and Zhang, 1989). However, even regimes considered to be dominated by viscosity, as at high Rayleigh numbers, are impacted by variable k (Dubuffet et al., 2000). Numerical convection models of the Earth have shown that the functional form for k(T) strongly influences the character of the solutions through feedback in the temperature equation. Feedback occurs because k is a coefficient inside the differential operator of the temperature equation, which is nonlinear, much like eqn [3] for conduction. The effect of variable k on mantle convection is not overridden by simultaneously and strongly varying viscosity (van den Berg et al., 2004, 2005; Yanagawa et al., 2005). Small changes in k with T are important because (1) the time-dependence of an infinite Prandtl number fluid such as the mantle is primarily governed by the temperature equation, and (2) the temperature equation functions as a 'master' equation, whereas the momentum equation, which is governed by viscosity, responds instantaneously as the 'slave' equation (Haken, 1977; Hofmeister and Yuen (in press)). Consequently, accurate characterization of k (or D) at temperature is essential in modeling planetary heat flow on any scale (e.g., Starin et al., 2000; Yuen et al., 2000; Schott et al., 2001; Dubuffet et al., 2002).

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REGIONAL METAMORPHISM

A. Feenstra , G. Franz , in Encyclopedia of Geology, 2005

Facies of High Pressure

High-pressure rocks of the blueschist and/or eclogite facies were metamorphosed at a low geothermal gradient, i.e., small increase in temperature with depth ( Figure 1). They are typically formed during subduction of a cold oceanic plate underneath a continent. Mafic protoliths best document such high-pressure conditions by their diagnostic mineral assemblages in blueschist (sodic amphibole bearing; the term 'blueschist' derives from the blue sodic amphibole, glaucophane) and eclogite (dominated by garnet   +   omphacitic clinopyroxene). Metapelitic rock compositions may develop diagnostic minerals or assemblages such as carpholite, phengite, jadeite   + quartz, and talc   +   kyanite.

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ULTRA HIGH PRESSURE METAMORPHISM

H.-J. Massonne , in Encyclopedia of Geology, 2005

Mechanisms

The known UHP rocks at Earth's surface can be subdivided into two groups. One group suffered from metamorphism along geothermal gradients of about 7°C  km−1, reaching maximum pressures generally below 40   kbar (Figure 7). Frequently observed peak pressure and temperature conditions are 30   kbar at 650–700°C. Moderate cooling and uplift rates in the range of centimetre per year characterize the exhumation of this group of UHP rocks, commonly starting with the influx of hydrous fluids (for instance, into eclogites). The subduction of oceanic crust under continental crust, including the exhumation within a subduction channel, best explains the characteristics of these UHP rocks. However, formation of larger coherent UHP terranes consisting broadly of continental crust, as inferred from the WGR in Norway and the Triassic UHP belt in China, cannot be explained by this mechanism alone. If continental crust adherent to a slab of subducted oceanic crust is drawn into depth at the beginning of a continent–continent collision, as suggested by the slab-breakoff model (Figure 8), extended regions of continental crust can be affected by UHP metamorphism. Fast exhumation is caused by buoyancy forces exerted by continental material that is less dense than eclogites and garnet-bearing ultrabasic rocks, after the oceanic slab has been broken off to be subducted further down.

Figure 7. Range of peak pressure and temperature conditions of UHP rocks (patterned areas). The typical shapes of common pressure and temperature paths for UHP/ near-UHP (I) and UHP (II) are depicted.

Figure 8. The slab-breakoff model, evolution (from top to bottom). (A) Subduction; (B) slab weakening and narrow rifting; (C) slab breakoff, magmatism, and uplift of UHP sheets. Reproduced with permission from Hacker BR and Liou JG (1998) When Continents Collide: Geodynamics and Geochemistry of Ultrahigh-Pressure Rocks. Dordrecht, The Netherlands: Kluwer Academic Publishers.

A second group of UHP rocks experienced significantly higher temperatures, or at least higher pressures (Figure 7). Often both groups of UHP rocks occur together in one crystalline complex. Moreover, both crustal material and mantle material were metamorphosed at peak pressure conditions, between 60 and 80   kbar, as has been proved at least for the UHP regions of the Kokchetav Massif and the Bohemian Massif. The slab-breakoff model may explain this situation as well, because it is believed that continental crust can be dragged to depths of about 200   km by the adherent oceanic slab, despite the buoyancy forces of the continental material. An alternative explanation, however, is delamination of continental lithosphere after continent–continent collision and significant thickening of continental crust, a process that is currently observable in the range of the Himalaya and in the Tibetan Plateau. Modelling experiments suggest that material from the continental crust can be involved in the delamination process and deeply submerged into Earth's mantle. There, anatectic processes in the continental material are caused by the hot environment before fast uplift starts. Because there is limited coherency among the hot-temperature UHP rocks of the Bohemian Massif or the Kokchetav Massif, the debate continues as to whether the slab-breakoff model, lithospheric delamination, or any other process can sufficiently explain the UHP rocks there.

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MINING GEOLOGY | Hydrothermal Ores

M.A. McKibben , in Encyclopedia of Geology, 2005

Hydrothermal Fluids Not Directly Affiliated with Magmatic Processes

Hydrothermal fluids and ores can be formed via heating mechanisms that have no direct association with magmatic processes. Basin subsidence through the normal geothermal gradient can heat sediment pore fluids and induce free convection, enhancing their ability to carry and redistribute metals. Such processes may be responsible for unconformity-related basinal uranium deposits such as those found in Saskatchewan (Canada) and Northern Territory (Australia). Rapid subsidence may also induce compaction and overpressuring of basin sediments, promoting the flow of warm pore fluids.

Pore fluids in deforming sedimentary basins adjacent to uplifting forelands can be forced to flow laterally in response to gravity, a scenario that is best developed during continental plate collisions. A widely accepted theory for the origin of many carbonate-hosted Mississippi Valley-type (MVT) Pb–Zn deposits in central and eastern North America is westward gravity-driven flow of warm basinal brines, caused by Late Palaeozoic collisions between the ancient North American and European continents (Figure 6). Compositional and colour banding ('sphalerite stratigraphy'), fluid inclusions, and other geochemical features of the ores are remarkably consistent over long distances between the Pb–Zn deposits, supporting the occurrence of regional fluid-flow events. Gravity-driven lateral flow of basinal brines has emerged as the most effective mechanism that can account for the thermal and mass balances in many MVT systems.

Figure 6. Schematic model for formation of carbonate-hosted Mississisppi Valley type Pb–Zn ores, via lateral gravity-driven flow of basinal brines from an upland region. (Reproduced with permission from Evans AJ (1993) Ore Geology and Industrial Minerals: An Introduction, 3rd edn. Oxford: Blackwell.)

Overthrusting and consequent sediment compression in fold-mountain belts may also drive the flow of deeper, warmer fluids into shallower or more peripheral environments. Shale-hosted stratiform copper deposits such as the Kupferschiefer (Europe) and White Pine (North America) may have formed via this type of mechanism.

Dehydration reactions associated with regional metamorphism can also provide sources of hot fluids, although they are initially low in salinity and high in CO2. Such fluids may have been responsible for hydrothermal gold deposits associated with CO2 metasomatism, found in shear zones and faults in Archaean and younger greenstone belts. Earthquake-induced seismic pumping could provide a mechanism of fluid flow along fault zones.

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Carbon Dioxide Utilization for Global Sustainability

M.M. Toribio , ... S. Shimada , in Studies in Surface Science and Catalysis, 2004

3.2 Effects of Pressure on the Adsorption Capacity

Previous researchers have assumed that the pressure distribution in a sedimentary basin is hydrostatic and increases linearly with depth at a rate of 1   MPa per 100 m. And with the average geothermal gradients of 25  °C/km, it has been said that the conditions for supercritical CO2 can be roughly met at depths greater than 800   m [7,8]. Thus an analysis extending beyond the critical point was then conducted.

It can be seen from Figure 2 -b that there was negative sorption at the vicinity of the critical point (i.e. 7.3   MPa), which was then followed by an abrupt increase in the sorption capacity. This suggests that injecting CO2 at high-pressure condition is highly preferable due to increased sorption capacity of coal. Such a trend was true for both the Akabira and Taiheiyo samples clearly suggesting that the trend is likely due to the increased density of CO2 at supercritical conditions.

Indeed, at conditions near the critical point, a small pressure difference could result in large density increases. To date, testing this close to the critical point (i.e. at 35   °C) has never been reported before in any published literature, and thus the data presented here are unique.

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The Crust

A.I.S. Kemp , C.J. Hawkesworth , in Treatise on Geochemistry, 2003

3.11.3.1.2 Secular evolution in TTG composition

If fusion of subducted oceanic crust is the correct origin for many Archean TTG, we might anticipate some secular variation in TTG compositions as the Earth cooled. This is because the attendant decrease in the geothermal gradient along the Benioff plane should lead to an increasing depth of slab melting, and thus TTG generation. The angle of subduction is also likely to increase, since the envisaged decrease in the rate of seafloor spreading from the earliest Archean ( Bickle, 1978) leads to an increase in plate dimensions and thus the average age of oceanic crust, and older, colder lithospheric slabs are less buoyant (Christensen, 1997). A direct implication is that the thickness of the overlying mantle wedge that slab-derived magmas must traverse, and potentially interact with, will increase with time, and this is consistent with observed changes in TTG compositions. In a compilation of TTG data, Martin and Moyen (2002) demonstrate that between 4.0   Ga and 2.5   Ga the least differentiated TTG evolve to progressively higher Mg# and Ni contents, consistent with greater assimilation of olivine during passage through the mantle for the younger TTG. In the same period strontium contents also increase appreciably, which is interpreted as evidence for a declining role for residual plagioclase, and thus an increase in the depth of TTG formation from the Early to Late Archean (Martin and Moyen, 2002). It appears that systematic changes in TTG compositions with time in the Archean can be related to likely changes in the conditions of melt generation, if the subducted slab model is adopted. Such secular chemical trends seem less easy to accommodate by models where TTG are formed by remelting basaltic rocks in the lower crust, given that the Mg# and Ni contents of mantle-derived magmas (and thus the potential TTG source rocks) has decreased appreciably with time.

Modern adakites extend to higher strontium and Mg# values than Archean TTG of similar silica contents (Smithies, 2000; Martin and Moyen, 2002). Higher strontium implies lower degrees of partial melting, compatible with a progressively cooling Earth, whereas the elevated Mg# suggests greater interaction with mantle peridotite (Martin and Moyen, 2002). The implication of the latter is that modern adakitic melts are generated even deeper than the TTG, near the threshold between slab melting and slab dehydration. Thermal conditions do not favor slab melting in most modern day subduction zones, except under the exceptional circumstances of anomalously elevated heat flow associated with ridge subduction (Stern and Kilian, 1996), or the consumption of hot, newly created oceanic crust (Martin, 1986; Drummond and Defant, 1990; Peacock et al., 1994) (but see Chapter 3.18 for an alternative view). Hence, the volume of TTG-like rocks emplaced into the continental crust has waned dramatically since the Archean, and in some cases such compositions have been attributed to melt generation at depth within thickened continental arcs (see above). Nevertheless, the continental crust shares the low (subchondritic) Nb/Ta, high Zr/Sm signature relative to the primitive mantle that characterises the TTG (Foley et al., 2002), suggesting that this style of magmatism has made an important imprint on the bulk crustal composition.

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Seismology and the Structure of the Earth

A. Souriau , in Treatise on Geophysics, 2007

1.19.2.1 Indirect Evidences for the Existence of a Core, and Historical Controversies

The fascination for the bowels of the Earth is present in the literature since the Antiquities (see historical aspects in Brush (1980), Bolt (1982), Poirier (1996) ). The high geothermal gradient experienced in the mines (∼30  °C   km−1) led to propose, at the beginning of the seventeenth century, that a fire is present at the center of the Earth. This theory was however refuted by the argument that not enough oxygen is present at the Earth's center to maintain this fire. The high geothermal gradient has also driven the idea that the Earth could be of solar origin, but controversial arguments have concerned its possible differentiation.

During the nineteenth century, there is a general agreement that the Earth has been fluid at its origin. This idea resulted mostly from the observation of the Earth flattening, an equilibrium figure supposed to be acquired during fluid stage, and from the identification of plutonic rocks. The question was raised of whether the Earth is still fluid in its interior, or solid as a result of its complete cooling, or partly solid. The geothermal gradient predicts a fusion of the Earth silicates at ∼80–100   km depth, an idea reinforced by the fluid lavas rejected by volcanoes. An argument against this model is given by Ampère (1775–1836), who noted the impossibility, for such a model, to resist the high stresses induced by the lunar tides on the thin solid envelope. On the other hand, Poisson (1781–1840) noted that the melting temperature of rocks increases with pressure, opening the possibility of a completely solid Earth.

Two discoveries have allowed to reconcile a solid Earth model with the high geothermal gradient: (1) the idea that the internal heat is eliminated not only by conduction, but also (and mostly) by convection and (2) the discovery of radioactivity as a source of internal heat, in addition to the initial heat. These two discoveries explain the impossibility to extrapolate the upper crust geothermal gradient downward. On the other hand, the comparison of the precession and nutations of the Earth observed from astronomy with those computed for different structures led Hopkins (1793–1866) to propose a solid envelope of at least 1000   km thickness, the fluid center being thus much too deep for being the feeding region of the volcanoes. More refined computations by Kelvin (1824–1907) gave a 2000–2500   km thickness for the solid envelope.

The mean density of the Earth, 5.52   ×   103  kg   m−3, is much higher than that of the rocks (∼2.6   ×   103  kg   m−3 for granite), even at the temperature and pressure conditions present at 2500   km depth. Its moment of inertia, I  =   0.33Ma 2, where M is the mass of the Earth and a its radius, is smaller than that of a homogeneous sphere (I  =   0.40Ma 2), implying higher densities at depth, and hence probably a differentiation. Geochemical arguments, in particular, cosmic abundances and the existence of both silicate and iron meteorites, led to propose an iron core. The discovery of stony-iron meteorites such as pallasites, which may represent the CMB, gives some additional arguments in favor of a differentiated Earth with an iron core. At the end of the nineteenth century, a model with a silicate mantle above an iron core was widely accepted (e.g., Wiechert, 1896).

The effective discovery of the core is however due to seismology. In 1889, the first record of a remote earthquake (from Japan) was obtained at Potsdam by Von Reuber Pachwitz on a low-frequency instrument devoted to tide recording. This opened the new field of global Earth structure analysis from teleseismic data, thanks to the deployment of worldwide observatories, and to the international organization of seismology.

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A Summary of Field Test Methods in Fractured Rocks

P. Jouanna , ... P. Valla , in Flow and Contaminant Transport in Fractured Rock, 1993

Principle

This method is derived from the classical measure of conductivity used in the laboratory (Van der Held and van Drunen, 1949). For a steady flow Q of water in a vertical hole, a uniform geothermal gradient g = ∂ T i / ∂ z is equivalent to a heat source, existing at a large distance from the well; this heat source provides, to the flow Q of water, a constant radial heat flux q 0 = ρ w c w Q g per depth meter of the rock formation, with:

T i (z) = temperature in the formation at depth z, far away from the well.

ρ w = mass density of water.

c w = specific heat of water.

At depth z in the well, water temperature varies versus time t. Starting from an initial thermal equilibrium established at temperature T i without any flow in the well, the water temperature variations, after establishing a constant quantity of flow Q at t = 0, lead to an estimation of the rock thermal conductivity λ f and the rock diffusivity α f = λ f / ( ρ f c f ) , ρ f being the mass density of the rock formation.

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ATMOSPHERE EVOLUTION

S.J. Mojzsis , in Encyclopedia of Geology, 2005

Origin of the Secondary Atmosphere

Following the loss of the primary planetary atmosphere as a result of the energetic solar wind, bombardments, and the Moon-forming event, the secondary atmosphere began to accumulate. The large masses of the Earth (5.97   ×   1024  g) and Venus (4.87   ×   1024g) and their planetary inventories of heat-producing elements allow the long-term persistence of high geothermal gradients and associated volcanism. In the case of the Earth, plate tectonics is possible in part because of a steep geothermal gradient that allows for the ultimate recycling of sediments and volatiles. On smaller bodies, such as the asteroids, the Moon, Mercury, and the icy moons of the outer planets, geothermal gradients are shallow; these bodies cooled quickly and early in Solar System history and are effectively cold dead worlds. Mars is an intermediate case between the warmer Earth and Venus and 'dead' worlds such as Mercury and the Moon. Comparisons of terrestrial volcanic-gas compositions with the atmospheres of the neighbouring planets show broad similarities ( Tables 1 and 2). Water appears to have been lost on Venus due to thermal escape and was trapped in the crust of Mars by weathering and cold temperatures.

Table 2. Terrestrial volcanic-gas compositions

St Helens Etna Kilauea
H2O * 91.58 53.69 78.7
H2 0.269 0.57 1.065
CO2 0.913 20.00 3.17
CO 0.0013 0.42 0.0584
SO2 0.073 24.85 11.5
H2S 0.137 0.22 3.21
OCS 2   ×   10−5 nd 0.0054
S2 0.0003 0.21 1.89
SO nd 0.03 nd
HCl 0.089 nd 0.167
HF nd nd 0.20
*
Values are given in volume % (=mol %); nd, not detected.

There is a growing consensus that the early (secondary) atmosphere of Earth was dominated by carbon dioxide, nitrogen, and water vapour, with minor components of noble gases, hydrogen, methane, and sulphurous compounds. To explain the early presence of liquid water when solar output was considerably less than today (Figure 1), it is necessary to assume that a dense carbon dioxide greenhouse atmosphere (possibly including methane) increased insolation on the early Earth. Such an atmosphere must have had a partial pressure of carbon dioxide (pCO2) of at least 1 bar (and probably more) to keep the planet from freezing over (see SOLAR SYSTEM | Asteroids, Comets and Space Dust SOLAR SYSTEM | Meteorites SOLAR SYSTEM | Mercury SOLAR SYSTEM | Venus SOLAR SYSTEM | Mars SOLAR SYSTEM | Jupiter, Saturn and Their Moons SOLAR SYSTEM | Neptune, Pluto and Uranus).

Weathering and hydrothermal reactions of crustal materials immediately commenced once the atmosphere and hydrosphere were established. Hydrothermal vents would have been ubiquitous on the early Earth, and it is estimated that the total volume of Earth's oceans could have cycled through the crust in less than 1   Ma. Carbon dioxide and water (as carbonic acid) react with silicate minerals to add carbonate and silica to the oceans, as represented in the Urey equation:

C O 2 + H 2 O + CaSi O 2 = H 2 C O 3 + Si O 2 + C a 2 +

This reaction was the major control on the amount of carbon dioxide in the atmosphere before the onset of photosynthesis, respiration, and organic-matter sequestration. During subduction, carbonate minerals carried in the descending oceanic crust are heated, releasing carbon dioxide and water as volatile components in arc magmas, completing the cycle back to the atmosphere. In hydrothermal vents within basaltic crust, water oxidizes Fe2+ in olivine, yielding hydrogen, magnetite, and serpentine. In gas-phase high-temperature reactions, hydrogen can reduce carbon dioxide to methane, but it is not likely that much hydrogen was maintained in the atmosphere, owing to its high rate of escape from the top of the atmosphere. The currently held view is that the early secondary atmosphere was, at most, weakly reducing, with the major components – carbon dioxide, nitrogen, water vapour, and carbon monoxide – supplemented by minor mixing fractions of hydrogen and methane. Estimates have been made of the rate of decline of carbon dioxide over geological time that provided the major greenhouse forcing to the atmosphere, while tracking secular changes in solar luminosity. Initially high partial pressures of carbon dioxide, possibly supplemented by biogenic methane, would have kept surface temperatures warm enough to avoid freezing of the planet until the crisis conditions of the snowball Earth in the Late Proterozoic. Since the era of severe Proterozoic glaciations, there has been a generally gentle decline in levels of carbon dioxide, maintaining the stability of the biosphere in the face of rising solar luminosity (of the order of about 6% per billion years).

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