7.2.1 Partial Melting in the Presence of CO₂ and H₂O: Incipient Melting

The fluxing effect of volatiles on silicate melting has been long recognized.Reference Wallace and Green^1, Reference Dasgupta^3, Reference Hammouda and Keshav^5, Reference Dasgupta^7, Reference Wyllie and Huang^12–Reference Stagno, Ojwang, McCammon and Frost¹⁴ In the case of mantle melting, the effects of H₂O and CO₂, whether separatelyReference Dasgupta^3, Reference Wyllie and Huang^12, Reference Stagno, Ojwang, McCammon and Frost^14, Reference Hirschmann, Tenner, Aubaud and Withers²⁸ or mixed,Reference Wallace and Green^1, Reference Dasgupta^3, Reference Dasgupta^7, Reference Taylor and Green^13, Reference Massuyeau, Gardés, Morizet and Gaillard^29, Reference Hirschmann³⁰ have been investigated. It is clear that peridotite systems equilibrated with H₂O–CO₂ mixtures have been poorly investigated in comparison to the (nominally) CO₂-only bearing system.Reference Hammouda and Keshav⁵

Figure 7.1 summarizes the main features for the case of melting at undersaturated CO₂–H₂O fluid conditions. In the temperature region below the fluid-free high-pressure solidus, the amount of melt is controlled by the low amount of available fluid. This melting regime is incipient melting. In the incipient melting regime, several cases must be highlighted.

Figure 7.1 Pressure–temperature plot showing the stability fields for different types of mantle melt as a function of the volatile contents. Different geotherms (10 My, 80 My, cratons) are superimposed. The CO₂-bearing hydrous peridotite solidus is calculated from the combination of solidus temperatures of Ref. 1 from 0 to ~4 GPa and Ref. 13 at higher pressures. We connected the melting curve of CO₂-bearing hydrous peridotite to that of the dehydration solidus of nominally anhydrous peridotiteReference Hirschmann, Tenner, Aubaud and Withers²⁸ (considering peridotite with 460 ppm H₂O) at low pressures.

For pressures less than 2 GPa (corresponding to depths of less than 60 km), the solidus is weakly depressed. In this pressure range, the solubility of CO₂ in silicate melts is low, most CO₂ is in the fluid, and the solidus is controlled by the availability of water.Reference Hirschmann, Tenner, Aubaud and Withers²⁸

At ~2 GPa, the CO₂ of the fluid reacts with the silicates, yielding carbonate mineral formation. This carbonation reaction has the effect of strongly depressing the solidus temperature, and the carbonate ledge (i.e. nearly isobaric melting curve) is developed in the phase diagram. Melts at the solidus are carbonatitic.Reference Wallace and Green^1, Reference Dasgupta^3, Reference Dasgupta^7, Reference Massuyeau, Gardés, Morizet and Gaillard²⁹ Away from the solidus, hydrated silicate melting takes places and the melt compositions shift from carbonatitic to carbo-hydrous silicates.Reference Dasgupta^3, Reference Dasgupta^7, Reference Massuyeau, Gardés, Morizet and Gaillard²⁹ As long as the temperature remains below that of the fluid-free solidus, the amount of produced melt is controlled by the fluid availability. Major melting only happens as the fluid-free solidus is crossed (temperature >1350°C at 2 GPa).

As pressure is further increased, the CO₂–H₂O fluid may be reduced by interaction with mantle silicates.Reference Dasgupta^3, Reference Hammouda and Keshav^5, Reference Taylor and Green^13, Reference Stagno, Ojwang, McCammon and Frost¹⁴ Along the mantle geotherm, carbonate reduction following this reaction would occur at about 120–250 km depth.Reference Hammouda and Keshav^5, Reference Stagno, Ojwang, McCammon and Frost¹⁴ In the presence of hydrogen, a mixed CH₄–H₂O fluid is formed.Reference Taylor and Green¹³ In this fluid, water activity is lowered, resulting in increasing solidus as depth (and therefore reduction) increases. The solidus evolution caused by fluid reduction at high pressure is indicated by the dashed line with arrows in Figure 7.1.

7.2.2 Carbonate to Silicate Melts in Various Geodynamic Settings

Following this broad picture of the process of incipient melting, we present here the range of melt compositions produced in various geodynamic settings. Two end-member cases are illustrated: adiabatic conditions showing regions where volcanism occurs at Earth’s surface versus intraplate conditions showing mantle melting without volcanism.

Figure 7.2 illustrates melting along an adiabatic mantle (i.e. convective mantle) involving various H₂O- and CO₂-enrichmentsReference Le Voyer, Kelley, Cottrell and Hauri¹⁵ and a potential temperature of 1360°C. The calculated meltsReference Massuyeau, Gardés, Morizet and Gaillard²⁹ define an array of compositions ranging from low to high silica content in response to decompression melting: incipient melts evolving from carbonatite (i.e. <15 wt.% SiO₂), to carbonated basalts (15–50 wt.% SiO₂), to alkali basalts (SiO₂ >40 wt.%). Hereafter in the chapter, some of these compositions are used as reference compositions for which density, viscosity, and EC are defined (stars in Figure 7.2; see Section 7.3). Decreasing the bulk volatile contents decreases the absolute depth and the depth interval at which the equilibrium melt composition changes from carbonate to silicate melts: while the volatile-enriched mantle can produce silicate-bearing liquids down to 250 km, the volatile-depleted case shows an abrupt shift in composition at ~100 km depth within a ~10–20‑km interval. This indicates that dry systems must have a greater tendency for carbonate–silicate immiscibility. Notably, Figure 7.2 does not consider the possibility of redox melting at ~250 km depth.

Figure 7.2 Melt composition (left) and melt fraction (right) produced during adiabatic mantle melting (temperature = 1360°C or 1480°C when specified). Under most of the pressure–temperature–volatile content conditions shown here, incipient melting occurs. Incipient melting of depleted (100 ppm H₂O–100 ppm CO₂) to enriched (500 ppm) mantle sources is considered. The stars show compositions for which viscosities were determined by molecular dynamics (see Section 7.3).

Figure 7.3 illustrates the nature of equilibrium partial melts formed in an intraplate thermal regime considering both CO₂–H₂O depleted and enriched mantles. A young plate (10 Ma, red), an intermediate plate (80 Ma, green), and a craton (gray) are illustrated.Reference McKenzie, Jackson and Priestley³¹ These lithospheres of variable ages, and therefore variable thicknesses, can host melts with contrasting and strongly depth-dependent compositions. These lithospheres overlay a convective mantle having an age-independent pressure–temperature–melt composition pattern. The lithospheric and convective mantles are, by definition, separated by a thermal boundary layer, the LAB, separating the diffusive (lid) and the adiabatic (convective) mantles.Reference McKenzie, Jackson and Priestley³¹ To what extent discontinuities in ECsReference Naif, Key, Constable and Evans^22, Reference Kawakatsu and Utada²³ and seismic wave velocitiesReference Schmerr^25, Reference Burgos³² map the depth of this thermal LAB is a matter of a great debate. The depth range of the putative seismic G as broadly compiled from various studies and for various geodynamic environments is shown in Figure 7.3.Reference Naif, Key, Constable and Evans^22, Reference Kawakatsu and Utada²³ Notice that G values are reported at depths of ~60–80 km for oceanic lithospheres of variable ages (0–120 Ma),Reference Kawakatsu and Utada^23, Reference Schmerr²⁵ while the conventional LAB depths for similar lithospheric ages vary over a range of 0–110 km.Reference McKenzie, Jackson and Priestley³¹ We must also notice that the seismic signal of G may be manifold and feature variable depth–age relationships.Reference Burgos³²

Figure 7.3 Profiles of melt compositions in intraplate geodynamic settings of variable ages (cratons, 80 Ma, and 10 Ma from left to right) compared to the depth range of the Gutenberg discontinuity (G) and the LVZ. The curve labeled “LAB” corresponds to the thermal lithosphere–asthenosphere boundary. The LAB displays a depth that changes with the age of the plate.Reference McKenzie, Jackson and Priestley³¹ One sees that the degree of H₂O–CO₂ enrichment moderately affects the type of melt composition formed at lithospheric depth. It is essentially the temperature change with depth that controls the melt composition. This narrow range of lithospheric melt compositions is at odds with the large range of melt compositions that are formed in the convective mantle, which strongly depends on the degree of H₂O–CO₂ enrichment, as shown in Figure 7.2.

The broad correspondence between the stability field of incipient melting and the geophysical signals supposed to mark the LAB has long been known.Reference Dasgupta^3, Reference O‘Reilly and Griffin^4, Reference Dasgupta^7, Reference Eggler^20, Reference Hirschmann^30, Reference Sifré³³ These observations must be advanced by considering the physical properties of incipient melts and how they impact the mantle rock properties near to the LAB.

7.2.3 Structural Differences between Silicate and Carbonate Melts

From a structural viewpoint, silicate and carbonate melts are opposites. However, they are end members of a continuum going from network-forming iono-covalent silicate liquids (e.g. silica) to ionic carbonate liquids (e.g. molten salts). The former are characterized by their degree of polymerizationReference Mysen and Richet³⁴ (estimated from the NBO/T ratio, with “NBO” being the number of nonbridging oxygens and “T” the number of tetracoordinated cations, Si and Al), whereas the latter are fully depolymerized, with the liquid structure being controlled by the size ratio between anions and cations and by the ion valence state.Reference Jones, Genge and Carmody³⁵ The microscopic structure of silicate melts is also quantified using structural indicators such as the Q_n species (with n = 0–4, where “n” is the number of TO₄ tetrahedra sharing a common oxygen) and the coordination numbers associated with the network-forming and network-modifying cations (e.g. Nc ≈ 4 for Si and Al, and Nc ≈ 5 – 8 for Fe, Mg, Ca, and Na).

In carbonate melts, experimental and simulation studiesReference Jones, Genge and Carmody^35–Reference Vuilleumier, Seitsonen, Sator and Guillot³⁸ have shown that the number of carbonate ions (playing the role of O^2– in silicate melts) around Mg and Ca is about five to six, with one oxygen of each carbonate ion pointing preferentially toward the cation (with d_Mg–O = 2.0 Å and d_Ca–O = 2.35 Å, distances similar to those found in silicate melts), whereas the number of carbonate ions around each carbonate is about 12, a value similar to the oxygen coordination number in depolymerized silicate melts.Reference Dufils, Sator and Guillot³⁹ The self-diffusion coefficients (D) of Mg²⁺, Ca²⁺, and CO₃^2– are of the same order of magnitude, contrary to silicate melts in which the D values of network-forming ions (e.g. Si and O) are much smaller than those of network-modifying ions (e.g. Mg and Ca).Reference Guillot and Sator⁴⁰ In carbonate melts, cations and anions exchange with each other at the same rate, preventing network formation, which is at odds with silicate melts where network formation occurs.

As a silicate component is added to a carbonate melt, recent spectroscopic studies and molecular dynamics (MD) simulationsReference Vuilleumier, Seitsonen, Sator and Guillot^38, Reference Moussallam^41, Reference Morizet, Florian, Paris and Gaillard⁴² indicate that the carbonate ions are preferentially linked to alkaline earth cations,Reference Moussallam⁴¹ as in carbonate melts (Figure 7.4). The silicate-forming network therefore mixes poorly with the carbonate units. This atomic configuration reveals a two-subnetwork structure in carbonated basalts, reflecting a tendency to immiscibility, though this has been observed in samples quenched into clear glassy structures that do not show immiscibility.Reference Moussallam^41, Reference Morizet, Florian, Paris and Gaillard⁴² The link between a two-subnetwork atomic structure and macroscopic separation in a two-liquid system remains unclear despite its major geochemical importance.Reference Brooker and Kjarsgaard^43, Reference Novella⁴⁴ Finally, the transport properties of such a melt are difficult to predict a priori, as the silicate component implies high viscosity while the carbonate component implies low viscosity.Reference Morizet⁴⁵

Figure 7.4 MD-generated snapshots of a carbo-silicate melt (17 wt.% SiO₂ and 28 wt.% CO₂) at 8 GPa and 1727 K. In the left panel, all atoms are depicted (SiO₄ in yellow and red, CO₃ in cyan and red, Mg in green, Ca in cyan, Na in blue, K in pink, and Fe in purple, with Al and Ti not being represented for clarity reasons). In the middle panel, the carbonate ions are not depicted in order to show the silicate network, whereas in the right panel, the SiO₄ units are not depicted in order to better visualize the arrangement of the carbonated component of the melt. It is clear that the SiO₄ and CO₃ ions do not mix well and form two subnetworks. A movie of the MD simulation may be found in the supplementary online material.

7.3.1 Evolution of the Melt Density with Composition, CO₂, and H₂O Contents

It is well documented that the incorporation of both CO₂ and H₂O decreases the density of silicate melt. Establishing quantitative models describing this decrease as a function of the volatile content, melt composition, and pressure–temperature remains challenging, however. For illustration, we have evaluated by MD simulation the density evolution of the CO₂-bearing melt (H₂O free for technical reason, since melts containing both CO₂ and H₂O cannot be run) along the adiabatic geotherm used in Figure 7.2. The melt composition and its CO₂ content change along this adiabatic path (from a CO₂-rich kimberlitic composition at 8 GPa to a CO₂-poor basaltic composition at 2 GPa). The resulting density–pressure path is shown in Figure 7.5 (“melt + CO₂”). For the sake of comparison, the density evolutions of two CO₂-free compositions – a basalt and a kimberlite – are also reported in Figure 7.5. It is clear that, at 2 GPa, the addition of 4 wt.% CO₂ (to the basaltic composition) has a small effect on the melt density, whereas at 8 GPa, addition of 28 wt.% CO₂ causes a large density drop (notice the huge density contrast between the CO₂-free and CO₂-bearing kimberlitic melts at 8 GPa). However, it is noteworthy that along the chosen thermodynamic path, the melt also contains a significant amount of H₂O (from 8–9 wt.% H₂O at 8 GPa to 2–3 wt.% at 2 GPa). We have reported in Figure 7.5 the density curve of a basaltic melt with 2.5 wt.% H₂O and of a (CO₂-free) kimberlitic melt incorporating 8 wt.% H₂O. Briefly, along the chosen geotherm, the melts must be increasingly less dense with increasing pressure in comparison to conventional basaltic liquids. This yields an apparent lesser compressibility due to CO₂ incorporation.

Figure 7.5 Effects of H₂O and CO₂ on the melt density curve as a function of pressure. (a) Calculations of melt density are performed for the melts produced along the adiabatic path of Figure 7.2. The black dots correspond to the chemical compositions marked by stars in Figure 7.2. Open symbols are H₂O free and full symbols contain both CO₂ and H₂O. Values along the line “melt + CO₂” indicate the CO₂ content in wt.%, and those along the line “melt + CO₂ + H₂O” indicate the CO₂ content (first number) in wt.% and the H₂O content (second number) in wt.%. The effects of H₂O content on the compressibility curve of a basaltic melt (red) and a CO₂-free kimberlitic melt (blue) are given for comparison. (b) The evolution of the partial molar volumes of CO₂ and H₂O as a function of pressure at 2000 K as given by the Vinet equation of state for CO₂Reference Sakamaki⁵¹ and for H₂O.Reference Sakamaki⁴⁹ Notice that these partial molar volumes are independent of the melt composition. The temperature dependence of VCO₂ is negligible in the range 1673–2000 K.

To generalize these density curves, we will assume ideal mixing between CO₂, H₂O, and the silicate melt:

where V(T,P) is the molar volume of the volatile bearing melt, V_H2O(T, P)$V_{H_{2}O}\left(T,P\right)$ is the partial molar volume of H₂O in the melt, V_CO2(T, P)$V_{{\mathrm{CO}}_2}\left(T,P\right)$ is the partial molar volume of CO₂ in the melt, and V_sm(T, P)$V_{\mathrm{sm}}\left(T,P\right)$ is the molar volume of the volatile-free silicate melt. It has been shownReference Guillot and Sator^40, Reference Liu and Lange^46, Reference Bouhifd, Whittington and Richet⁴⁷ that the assumption of ideal mixing is very accurate when only one volatile species is considered, and we will assume that this assumption still holds in the presence of both H₂O and CO₂.

V_sm(T, P)$V_{\mathrm{sm}}\left(T,P\right)$ is given with a very good accuracy (±1%) by a third-order Birch–Murnaghan equation of state parametrized either from density measurementsReference Jing and Karato⁴⁸ or using MD calculations.Reference Dufils, Sator and Guillot³⁹ For V_H2O(T, P)$V_{H_{2}O}\left(T,P\right)$, we adopt the Vinet equation of state,Reference Sakamaki⁴⁹ which is based on the partial molar volume data of water in various melts (78 wt.% SiO₂ to 35 wt.% SiO₂, 1473–2573 K, and 1–20 GPa). Astonishingly, experimental and simulation studiesReference Dufils, Sator and Guillot^39, Reference Bouhifd, Whittington and Richet⁴⁷ show that V_H2O(T, P)$V_{H_{2}O}\left(T,P\right)$ is independent of water concentration and depends very little on the melt composition. For this reason, we can describe for any melt composition the evolution of V_H2O(T, P)$V_{H_{2}O}\left(T,P\right)$ with pressure and temperature (see Figure 7.5b). Similarly, empirical measurements and MD simulation studiesReference Vuilleumier, Seitsonen, Sator and Guillot^38, Reference Guillot and Sator^40, Reference Ghosh^50–Reference Ghosh, Bajgain, Mookherjee and Karki⁵³ show that the value for V_CO2(T, P)$V_{{\mathrm{CO}}_2}\left(T,P\right)$ depends very little on the melt composition, while in all these studies CO₂ is found to be much less compressible than H₂O in silicate melts. Changes in V_CO2(T, P)$V_{{\mathrm{CO}}_2}\left(T,P\right)$ along the geotherm were calculated using the Vinet equation of state.Reference Sakamaki⁵¹

The density curve of the H₂O–CO₂-bearing melts is shown in Figure 7.5 (see the curve entitled “melt + CO₂ + H₂O”). As expected, the influence of H₂O content on the density curve of the carbonated silicate melt is significant (compare the two curves with and without H₂O). We also note that the volatile-bearing melt becomes more buoyant as pressure increases.

7.3.2 Transport Properties: Viscosity–Diffusion

That carbonatite melts have unconventional transport properties in comparison to mantle silicate melts has long been clear to the research community, but acquiring robust quantitative data at the relevant pressure and temperature conditions has been challenging.Reference Jones, Genge and Carmody³⁵ The first hints were indirectly found using analyses of molten salts,Reference Jones, Genge and Carmody³⁵ which are well studied at atmospheric pressures by material scientists. MD have then provided insights on viscosity and diffusion propertiesReference Genge, Price and Jones⁵⁴ at various pressures and temperatures, and Dobson et al.Reference Dobson⁵⁵ provided the first in situ viscosity measurements at various pressures and temperatures. A significant step in our understanding of the transport properties of molten carbonates was realized by MD calculations,Reference Vuilleumier, Seitsonen, Sator and Guillot³⁷ which, together with high-precision viscosity measurements,Reference Kono⁵⁶ recently provided an internally consistent model. All of this indicates that carbonate melts have viscosity values of ~0.01 Pa/s with small to negligible temperature and melt chemical composition dependences. As these are ionic liquids in which all ionic groups move at similar rates, viscosity and ionic diffusion properties are closely linked.Reference Vuilleumier, Seitsonen, Sator and Guillot³⁷ This has been made clear experimentally,Reference Sifré, Hashim and Gaillard⁵⁷ with a remarkably simple relationship existing between the viscosity and EC of carbonate melts in the system Na–K–Ca–Mg–CO₃: log η = –log σ. As EC corresponds to the charge transfers due to the transport of all ionic groups, this essentially means that the ionic groups constituting carbonate melts have diffusion coefficients of ~10^–9 m²/s. Notably, this also matches diffusion-limited processes such as those from melt infiltration experiments in olivine aggregates.Reference Hammouda and Laporte⁵⁸ This relatively well-established model of the transport properties of molten carbonate contrasts with our poor understanding of the physical properties of mixed carbonated basalts (e.g. kimberlites).

These findings have motivated a series of MD simulations determining the viscosity of hydrated carbonated silicate melts (Figure 7.6). The investigated compositions are those shown in Figure 7.2, and they globally correspond to a temperature range 1360–1440°C (pressure = 2–8 GPa; Figure 7.6). From carbonate to basalt melts, the viscosity increases by 2.5 log units, and it follows a logarithmic relationship with the melt SiO₂ content. Such variations due to changes in melt composition clearly overwhelm the expected changes due to pressure and temperature (ΔT of 150°C implies a change in basalt viscosity of ~0.5 log units). We noticed that the calculated viscosity change from carbonate to basalt melts exceeds that which has been experimentally determined.Reference Kono⁵⁶ This is not surprising since Kono et al.Reference Kono⁵⁶ considered CaSiO₃ melts as silicate melt end members instead of basalts (i.e. Al-bearing systems) in our case. Interestingly, we notice that the logarithmic relationship still holds, but the slope differs. The effect of water has been addressed for three different CO₂-free compositions (basalt, peridotite, and kimberlite) and it also shows a logarithmic relationship. The magnitude of the viscosity change due to water incorporation in the melt is much less than that described upon changing from carbonate to basalt, but an important point is that the effect of water is independent of the melt chemical composition: addition of 1 wt.% H₂O decreases the melt viscosities by ~0.1 log units for all melt compositions. This implies that the following relationship can describe the viscosity changes of hydrated melts having a composition between carbonate (0 wt.% SiO₂) and basalts (45 wt.% SiO₂):

Figure 7.6 Viscosity changes as a function of melt silica content in dry carbonated melts (left) and as a function of H₂O content in CO₂-free melts (right). The conditions of calculation are 1400–1450°C and 2–8 GPa. Left: the melt compositions change from carbonatite (0 wt.% SiO₂) to basalt (45 wt.% SiO₂); both MD calculations (this work) and experimental measurementsReference Kono⁵⁶ are shown. Right: the effect of water on the viscosity of silicate melts; basaltic, peridotitic, and kimberlitic melts are similarly affected by water. MORB = mid-ocean ridge basalt.

In this relationship, notice that the effects of pressure and temperature are neglected. These effects were determined in basalts,Reference Sakamaki⁵⁹ but the above equation quantifies an effect of melt chemical compositions being much greater than the expected pressure–temperature effects (see arrows in Figure 7.6).

7.3.3 Electrical Conductivity

The EC of mantle melts is an important geophysical property as it may guide the interpretation of magnetotelluric data. Conductivities in specific regions of Earth’s mantle reaching or exceeding 0.1 S m^–1 have long been considered as anomalously high. Several interpretations are possible, including water in olivineReference Karato⁶⁰ (which is, however, a controversial issueReference Gardés, Gaillard and Tarits⁶¹), hydrated basalts,Reference Ni, Keppler and Behrens⁶² and carbonatite.Reference Gaillard²¹ Carbonatite melts and hydrated basalts are not singular geological objects, but they constitute end-member products of incipient melting.Reference Hirschmann³⁰ Carbonated basalts, constituting intermediate compositions between carbonatites and hydrated basalts, form the dominant melt compositions featuring incipient melting. Incipient melting could therefore be mapped from mantle EC, offering the exciting prospect of a direct visualization of the deep carbon and water cycles using geophysical data. This has motivated several recent experimental and theoretical surveys.Reference Sifré^33, Reference Desmaele^36, Reference Vuilleumier, Seitsonen, Sator and Guillot^37, Reference Sifré, Hashim and Gaillard^57, Reference Ni, Keppler and Behrens^62–Reference Yoshino, Gruber and Reinier⁶⁵ A summary of these surveys is shown in Figure 7.7, delineating the conductivity–temperature domains for dry and hydrated basalts, kimberlites, and carbonatites. Carbonatites at mantle pressure and temperature have conductivities exceeding 200 S m^–1, while carbonated basalts (e.g. kimberlites) are in the range 30–200 S m^–1. Sifré et al.Reference Sifré³³ proposed a model describing the changes in conductivity as the melt chemical composition evolves from carbonate to basalt melts:

${\sigma }_{\text{model}}=\left({\sigma }_0^{\mathrm{basalt}}\times exp\left(\frac{-E_a^{\mathrm{basalt}}}{\mathrm{RT}}\right)\right)+\left({\sigma }_0^{{\mathrm{CO}}_2}\times exp\left(\frac{-E_a^{{\mathrm{CO}}_2}}{\mathrm{RT}}\right)\right).$(7.3)

Figure 7.7 The EC of incipient melts either pure (left) or embedded into a olivine matrix (right). (Left) Basalts, kimberlites, and carbonatites are shown. The basalts are labeled in terms of water contents.Reference Ni, Keppler and Behrens⁶² The kimberlite are labeled in terms of CO₂.Reference Sifré^33, Reference Yoshino, Laumonier, McIsaac and Katsura^63, Reference Yoshino⁶⁴ Carbonatite melts are compiled from Refs. Reference Sifré33, Reference Sifré, Hashim and Gaillard57, Reference Yoshino, Gruber and Reinier65. (Right) The conductivity of the mantle during incipient melting. The four cases from Figure 7.2 are converted here into EC versus depth signals. The solid mantle is approximated by hydrated olivine using the model of hydrated olivine.Reference Gardés, Gaillard and Tarits⁸⁵ The melt conductivity is calculated from Ref. Reference Sifré33. Values of 0.1 S m^–1 are identified by the magnetotelluric community as anomalies.

Figure 7.7 shows the effect of incipient melting on the conductivity of mantle rocks along the adiabatic path of Figure 7.2. It shows that the depleted mantle produces moderately high ECs (<0.1 S m^–1), while the enriched mantle produces conductivities that match or exceed most geophysical assessments (>0.1 S m^–1). Given that the mantle source of mid-ocean ridge basalts (MORBs) varies in CO₂ content from 20 to 1200 ppm, this implies that mantle ECs may vary by greater than an order of magnitude.

7.5.1 Melt Mobility as a Function of Melt Composition

Knowledge of melt compositions and their viscosities (Sections 7.2 and 7.3) and evidence for their interconnection at very small melt fractions (Section 7.4) allow us to estimate the mobility of small fractions of CO₂-rich melts in the upper mantle. The mobility of a fluid embedded in a solid matrix is commonly addressed using the well-known Darcy’s law. According to Darcy’s law, the melt mobility is due to buoyancy (δρg$\mathrm{\delta \rho g}$) and is favored by low viscosity of the fluid (η_f${\eta }_f$) and high permeability (k(Φ)$k\left(\Phi \right)$):

$V=\frac{k\left(\Phi \right)}{{\eta }_f}\mathrm{\delta \rho g}.$(7.6)

In the case of mantle incipient melting and metasomatism, permeability goes down to very small values. Viscosity of the liquids increases by more than two orders of magnitude as the melt changes from carbonatite to basalt (Figure 7.7), while density variations are moderate (at 2 GPa, density changes from 2.4 to 2.8 g cm^–3 from carbonatiteReference Desmaele³⁶ to basaltReference Mysen and Richet^34,47,49,Reference Sakamaki⁵⁹).

Permeability is related to the degree of melting (porosity) as:

$k\left(\Phi \right)=\frac{d^2}{C}{\Phi }^n,$(7.7)

where d is the grain size, Φ$\Phi$ is the melt fraction (variable), and the parameters C and n are empirical values.

Here, we address the mobility of three types of incipient melts: carbonatites, carbonated basalts, and hydrated basalts. We assume a mantle grain size of 1 mm and we use an experimental permeability lawReference Miller, Montési and Zhu⁷³ that is based on observations of samples with basaltic melt contents in the range of 1.5–18.0 vol.% (C = 58 and n = 2.6). We therefore operate an extrapolation toward much smaller melt fractions, which is justified in Section 7.4.

As is shown in Figure 7.9, carbonatites are very mobile, reaching velocities in the order of centimeters per year, even at melt fractions as low as 0.1 vol.% (typical of mantle metasomatismReference Aulbach, Massuyeau and Gaillard^2, Reference O‘Reilly and Griffin^4, Reference Tappe^6–Reference Coltorti⁸). Hydrated basalts can move as fast as carbonatites when they have at ten times greater melt fractions (i.e. 1 vol.% hydrated basalt moves as fast as 0.1 vol.% carbonatites). A velocity of 1 cm yr^–1 (0.1% of carbonatite melt) is high, but this only corresponds to 10 km of ascent within 1 Myrs. Nevertheless, ten times greater velocities are reached at 0.2–0.3% carbonatite. Furthermore, compaction processes, which are not considered here, must enhance the melt velocities.Reference Keller and Katz¹⁹ This simple analysis implies that carbonatites can be efficient metasomatic agents operating over long distances at geological timescales, as has been suggested many times.Reference Aulbach, Massuyeau and Gaillard^2, Reference O‘Reilly and Griffin^4, Reference Tappe^6, Reference Dasgupta^7, Reference Pilet, Baker and Stolper^9, Reference Hammouda and Laporte⁵⁸ Hydrated basalts can have similar metasomatic roles if present at melt fractions exceeding 2–3%.

Figure 7.9 The melt vertical velocity at mantle depth versus melt fractions during incipient melting. Carbonatites, carbonated basalts, and hydrated basalts are shown. Carbonatites (containing 40 wt.% CO₂) are labeled in equivalent ppm CO₂ contents in the bulk rock. This concentration range covers depleted to enriched MORB sources.Reference Le Voyer, Kelley, Cottrell and Hauri¹⁵ The basalt contains 2 wt.% H₂O and 0.2 wt.% CO₂, while the carbonated basalt contains 2 wt.% H₂O and 15 wt.% CO₂.

In the most depleted mantle sources containing <100 ppm CO₂, incipient melts are not mobile due to too small melt fractions (i.e. <0.02 vol.% carbonatite). In contrast, carbonatite melts formed in the most enriched mantle are very mobile (>10 cm yr^–1). Such a high mobility implies that these melts would rapidly migrate and would hardly be preserved if in physical contact with their source. This also implies unavoidable mixing processes in the column of melting where deep incipient melts rise fast and mix with upper-mantle regions (Figures 7.2 and 7.3), where melts produced at 200 km depth would rise fast and mix with the melts produced at shallower levels. The radioactive disequilibria found in MORBs have already been interpreted considering these mixing processes,Reference Faul⁷⁴ but how they impact the highly variable CO₂/Nb ratios of MORBsReference Le Voyer, Kelley, Cottrell and Hauri¹⁵ remains unaddressed.

7.5.2 EC versus Mobility of Incipient Melts

The identification of the exact nature of the melts responsible for high EC anomalies in the mantle is critical. It would allow us to decipher whether these electrical anomalies reflect lithospheric processes, being cold and involving carbonatites, or asthenospheric processes, being warm and involving (hydrated) basalts. If the electrical anomalies result from carbonated basalt (low-SiO₂) melts, they may indicate both asthenospheric and lithospheric processes, since these melts can be stable in both domains (see Figure 7.3).

We calculate that incipient melting of a peridotite can produce an electrical anomaly (~0.1 S m^–1)Reference Naif, Key, Constable and Evans^22, Reference Kawakatsu and Utada^23, Reference Sarafian^27, Reference Tada⁷⁵ if it contains 0.1 ± 0.04% of carbonatite melts, 0.3 ± 0.15% of carbonated basalts, or 1–6% of hydrated basalts at 1350°C and 3 GPa (Figure 7.10). Note that the calculation is only weakly dependent on temperature given the low temperature dependence of the EC of incipient melts (Figure 7.7).

Figure 7.10 Incipient melting conditions producing high EC and the corresponding melt mobility. (Top) The range of melt fraction–melt compositions producing high ECs; three curves corresponding to three values of conductivity are shown. (Bottom) The mobility of incipient melt at the melt content required to produce high EC. A minimum in melt mobility appears in the case of carbonate basalts, while carbonatites and hydrated basalts are very mobile.

The comparison of Figures 7.3 and 7.10 indicates that electrical anomalies in a young plate (<10 Ma) at ~80 km depthReference Kawakatsu and Utada²³ can reasonably be matched with hydrated basalts,Reference Ni, Keppler and Behrens⁶² while deeper anomalies observed beneath older plates (i.e. >50 Ma)Reference Kawakatsu and Utada^23, Reference Tada⁷⁵ may match any kind of CO₂-rich melt.Reference Sifré³³

The mobility of melts produced during incipient melting conditions matching a conductivity of 0.1 S m^–1 are reported in Figure 7.10. Both carbonatite and the hydrated basalt cases yield the highest velocities, favoring melt extraction, while carbonated basalts (low-SiO₂ melts) yield minimum velocities, favoring melt stability. Whether melts can be stabilized and detected by geophysical means therefore depends on the convection velocity of the mantle sourcing the melts. Highly mobile melts such as >0.1 vol.% carbonatite or 3 vol.% basalts can be detected in settings with mantle velocities of ~10 cm yr^–1 or more (e.g. the center of mantle plumes feeding volcanic hotspots such as HawaiReference Ballmer, Ito, van Hunen and Tackley⁷⁶ or the East Pacific RiseReference Kawakatsu and Utada^23, Reference Evans⁷⁷).

Away from these extreme geodynamic settings, many types of convections can occur in the mantle at rates in the range 0.1–1.0 cm yr^–1.Reference Morency, Doin and Dumoulin^16, Reference Ballmer, van Hunen, Ito, Tackley and Bianco^17, Reference Keller and Katz¹⁹ There, the most likely type of incipient melts producing high conductivity are carbonated basalts. These melts contain 30–40 wt.% SiO₂, implying that their viscosity is close to that of basalt but with enhanced EC, as their CO₂ contents are ~10–20 wt.%. About 0.3 ± 0.15% of such melts are required to produce high EC. This corresponds to 180–440 ppm CO₂ in the mantle. Notably, these melts resemble petit-spot volcanism.Reference Hirano^11, Reference Okumura and Hirano⁷⁸ These CO₂-rich melts are believed to remain in the mantle beneath plates and to be extracted when particular stress regimes just ahead of subduction zones trigger diking at a lithospheric scale.Reference Hirano¹¹

7.6.1 LAB versus Geophysical Discontinuities

The LAB is a concept assuming that Earth’s upper mantle is composed of two layers: the lower one, the asthenosphere, being adiabatic (convection controls heat transport); and the upper one, the lithosphere, being diffusive (diffusion dissipates heat). The electrical and seismic discontinuities mapped worldwide supposedly mark these boundaries, but the magmatic processes at the LAB and their geophysical visibility remain debated. The analysis provided in this chapter shows that several types of incipient melting can produce high mantle ECs. These melting processes can be lithospheric or asthenospheric, and therefore geophysical discontinuities may not image the LAB, but rather illuminate the dynamics of melting and melt transfers in the region of the LAB. Furthermore, geochemical observations have long defined the LAB as a movable boundary; that is to say, melt productions, melt infiltrations, and mantle metasomatism can cause major modifications of lithospheric roots.

Anomalous EC and regions with low seismic velocities have been mapped in many mantle region.Reference Naif, Key, Constable and Evans^22, Reference Kawakatsu and Utada^23, Reference Evans^77, Reference Tada, Tarits, Baba, Utada, Kasaya and Suetsugu^79, Reference Baba, Utada, Goto, Kasaya, Shimizu and Tada⁸⁰ A broadly distributed LVZ beneath oceanic domains is deduced from large-scale surveys,Reference Kawakatsu and Utada^23, Reference Schmerr²⁵ but the magnitudes of the velocity decreases locally vary. Beneath cratons, no such LVZ is observed.Reference Eaton²⁶ After the Mantle ELectromagnetic and Tomography (MELT) experiment that imaged the mantle beneath the ultrafast East Pacific Rise,Reference Evans⁷⁷ several surveys have investigated quieter geodynamic settings hoping for more conventional geophysical signals, but high conductivities and low seismic velocities have often been observed.Reference Kawakatsu and Utada²³ The recently investigated NoMelt areaReference Sarafian²⁷ (70 My old oceanic plates) provides the first geophysical survey identifying no anomalous conductivity and a weak LVZ. If mantle melting is one of the ingredients causing geophysical anomalies, why does such an area exist?

7.6.2 Manifold Types of Mantle Convection Fuel Incipient Melting

The driving force of melt production is mantle convection, which produces decompression melting. There are sound geodynamic reasons to argue that decompression melting does not only occur where hot spot volcanoes pierce the surface: the inward mass transfers associated with slab sinking must be compensated by an upward flow being broadly distributed and probably more pronounced beneath oceanic basins.Reference Morency, Doin and Dumoulin¹⁶ The rate at which this upward mantle flow occurs should not exceed the melt velocities described in Figure 7.10 (i.e. ≤1 cm yr^–1), except in large plumes such as Hawaii.Reference Ballmer, Ito, van Hunen and Tackley⁷⁶ Clearly, convections, decompressions, incipient melting, and melt extractions must occur in many regions of Earth’s mantle. Convection-related decompression melting must fuel the LAB where upwelling occurs. Where mantle upwelling does not occur, a source of incipient melts simply does not exist. It is not completely clear whether this vision can explain the distribution of mantle geophysical anomalies.Reference Kawakatsu and Utada²³ Furthermore, if high EC can be explained by incipient melts, it remains unclear whether the same process could explain the low S-wave velocities in the asthenosphere.