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Discussion of Heat

Anne Hofmeister, 30 June, 2014

We agree with most of the information supplied by Michele. The summary of proposals of mantle compositions is very useful. We would like to emphasize that our proposal is based on the recent recognition by the meteoritics community that calcium aluminum material originated near the center of the solar system. To his list we would like to add a fourth:

  1. True, whole mantle convection would require a deep heat source, an adiabatic profile, and chemical homogeneity that includes the upper and lower mantles. Analogous conditions are observed in Earth's convecting lower atmosphere.

In response to his remarks:

Convection is the sum of advection (material moving), radiation (heat diffused by photons), and conduction (heat diffused mainly by lattice vibrations). Convection generates circulating motions while normal advection, by itself, is not circular.

We agree that strong mantle convection should release more heat at the ridges than observed. The measured heat flux therefore indicates weak convection for which thermal gradients should be similar to conductive profiles.

The gradient in our paper of 1-10 K/km is not an adiabat, but is instead a conductive gradient.

The low core-mantle boundary temperatures of <4000 K by Nomura et al. (2014, Science, 31, 522-525) are based on melting of pyrolite and thus are connected with assuming a chondritic (silicate) mantle. If the mantle is refractory, then the melting temperatures are somewhat higher, 5000 K. A major point of our paper is that any such reasonable temperatures for Earth's core are inconsistent with large, deep power sources of any type.

Michele Lustrino, 30 June, 2014

I thank Anne for her detailed reply.
It seems that there are three main interpretations on the Earth's mantle composition:

  1. The lower mantle shows a CI-like composition (i.e., it is like the primitive Earth before plate tectonics and crustal differentiation). This volume is nearly completely isolated from the upper mantle. This is pursued by all plumologists.
  2. The lower mantle does not have a CI-like composition and is much more Ca-, Al- and Ti-rich compared with CI-estimates and typical upper mantle rocks. This is Anne’s view.
  3. The lower mantle is essentially an isolated portion of the Earth's mantle. It is not fertile (i.e., it does not have a CI-like composition), is rather depleted in terms of incompatible element content and is not necessarily characterized by higher temperatures compared with the shallow mantle. This is more or less the view of researchers opposed to the deep mantle plume theory.

Anne says that advection carries heat also vertically. What is the difference between this and convection?

I agree with Anne that magma crystallization near the place where magma forms cannot directly warm the region. It is, however also true that an upwelling, hotter-than-ambient-mantle magma, when stops, uses part of its heat to form crystal cumulates. This warms up the local mantle.

Anne also considers that plate motion is strictly related to mantle convection. I simply note (though I am not an expert in this field) that the crust is a very thin veneer compared with the bulk of the mantle. If active upwelling in convecting cells is truly located below oceanic ridges, I would expect much higher heat flux and major updoming.

Anne says that the adiabat classically assumed for the Earth's interior (0.6 K/km) is not much different from the adiabat she uses (1-10 K/km). Is this true? An adiabat of 10 K/km is much more like an air adiabat than a solid mantle adiabat. It is about twenty times higher.

As concerns the data on the Earth's core composition I can simply say that the differences among the different research groups are so large that every estimate is necessarily rough. Recently Nomura et al. (2014, Science, 31, 522-525) estimate the temperature of the Earth's core to be as low as 3570 +/- 200 K. This means the temperature range of the outer core varies from about 4300 to 3400 K. On these grounds only generic assumptions can be made, trying to avoid the most extreme values.

Anne Hofmeister, 27 June, 2014

Thanks to all for the thoughtful commentary on our paper.
Response to the comments by Don Anderson: We appreciate Don’s historical perspective on Earth’s heat.  However, the concern of our paper is the current, consensus view in geophysics that convection involves the whole mantle such that the Earth is emitting more heat than available models of radionuclide content indicate, that heat is deeply stored (e.g., as potassium in the core) and that leftover primordial heat is a large component of the current heat flux.

Anderson’s lead sentence “The accretion of Earth is not a slow grain-by-grain process spread out over billions of years…..” is not a view that we have espoused.  In a previous paper (Planetary and Space Science, 2012, p. 111), we argue the opposite: i.e., that the planets formed during fast, catastrophic collapse of a dusty nebula.

Response to comments by Michele Lustrino:  Our paper provides an alternative to the consensus view of Earth’s thermal state and gross chemical composition.  There may be other possibilities. We hope to have drawn attention to the problems associated with the prevalent view that the lower mantle is represented by C1 chondrites and is identical to the upper mantle.

Regarding heat flow, advection carries heat not only horizontally, but also vertically, because hot particles rise. Placement nearer to the surface provides a shorter path for heat to escape via conduction, thereby enhancing cooling.  The paper uses new laser flash analysis (LFA) measurements on thermal diffusivity (D) to construct reference conductive profiles.  LFA data exist for a fairly large number of minerals (about 100: see Hofmeister et al., Journal of Applied Physics, 2014) but not for all relevant chemical compositions. However, the variation in D amongst minerals is not terribly large, so that our representation of the lithosphere, should be reasonably accurate.  The temperature dependence is shown in Fig. 2 and the pressure dependence is given by Eq. 5.

Our LFA measurements are important because conduction dictates cooling over geologic time scales. This is true because the other microscopic mechanism, radiation, operates at a rate that is five orders of magnitude faster than conduction and thus governs transient events.

Observations suggest that magmas rise and disperse heat at or near the surface.  If a magma were to sink, because it was denser than its source rocks, this would lead to further melting of the surroundings, producing more evolved melts that would upwell.  Also, it is not correct to assume magma crystallization near the place the magmas form will warm the region. This is because formation of the magma uptakes the latent heat of crystallization and this same amount of heat is released when the magma crystallizes. The net warming is zero.

High ascent rates of kimberlite magmas were taken from literature references. 

Advection is not limited to horizontal motions.  The mechanism is active in the motions of convection.

Plate motion has been previously taken to indicate mantle convection. The influence of the moon on plate motions does not remove this basic connection.  The weakness of mantle convection is quantified by the Nusselt number, which we calculate as being near 1 for the upper mantle.  Nusselt numbers similar to unity indicates that the convective motions are little more efficient than conduction.

Regarding heat produced by core formation, the present paper discusses problems with the sinking mechanism and frictional heating in a temperature gradient.  The values we provide are from our conductive calculations.  Smaller values of dT/dZ for an adiabat as suggested by Michele Lustrino do not change our arguments.

We also discuss problems in producing positive heat from negative gravitational potential during core formation.  This topic is discussed further in a paper in press for Journal of Earth Science.  The topic of heating during accretion is discussed in detail in our 2012 paper in Planets and Space Science.  In a nutshell, the change in gravitational potential of the Earth during its formation is accounted for in the orbital rotational energy.  This finding points to heating of the Earth being due to radioactivity. 

Cratering is proposed in our PSS paper to be a late-stage event, following nearly complete formation of the planets.  Our view diverges from the popular planetesimal scenario, which conserves neither angular momentum nor energy.  The surfaces of the moons and planets reflect late stage events, not the main formation event which involved gravitational collapse of the dusty nebula.

Regarding core chemistry, seismic evidence discussed in many papers suggests 10% light elements.  The type of light element is debated.  We favor carbon as the dominant light element, on the basis of cosmic abundance and oxidation/reduction reactions.

Regarding the amount of heat producing elements, we use the global power of 30 TW in all of our cooling models.  The various models consider different placements of the heat producing elements in the interior.  We did not vary the absolute U-Th content as stated by Lustrino.

For the model with evenly distributed radioactive elements, conductive cooling produces very high temperatures of about 30000 K.  We agree this is impossible: that is our main point.  Any deeply situated radioactivity, or any other deep heat source (primordial remnants; core power, etc.)  produces unrealistically high temperatures in the deep interior.  Therefore, the drive in thermal and chemical evolution is to move the heat upwards. 

Regarding the geotherm: we did not assume this temperature profile, but have calculated the temperatures expected for a conductively cooled earth.  We refer to these as “reference conductive geotherms.”  The temperatures are high because (1) our model is only a two-layer model and (2) convection would redistribute temperatures in the upper mantle and transition zone.

The constant temperature for the basalt melting is provided for reference only.

Regarding melts and chemistry, one of our main points is that the lower mantle composition is unlike that of the upper mantle and transition zone.  We suggest refractories on the basis of density stratification and meteoritic reservoirs. Therefore, details such as melt density are equivocal. 

The surface temperature of the Earth is indeed held constant by the Sun’s flux. This is a boundary condition for determining  the geotherm, and therefore pertains to interior temperatures.

Re composition of the lower mantle:  Our meteoritic model calls on three reservoirs because the measured K/U ratio for the upper mantle is vastly different from the K/U ratio of chondritic meteorites. This difference is emphasized in our Figure 8, which combines geophysics and geochemistry. A refractory reservoir is proposed based on meteoritic studies, which deduced that calcium-aluminate material originated near the center of the solar system. The densities of minerals in CAIs are compatible with density stratification of the early earth into a refractory lower mantle and a silicate upper mantle. 

Regarding the moon:  Clearly Al exists, whatever the mode of formation of anorthosites.  The composition of the moon is important for understanding the Earth: we call for better constraints.  Because we have no samples from below 670 km for the Earth, constraining its composition will be very difficult.  Our paper provides a 1st order estimate, not a refined model.

Regarding Anderson’s 29 March comment, our point is that the core is not warming  the mantle, but that the core is cooling at the same rate that the mantle is cooling.  This statement is based on the flow of heat down the temperature gradient, required by themodynamic  law.

Warren Hamilton’s post summarizes and expands upon some crucial points.  One crucial point is the problems associated with the popular value of global power as 45 TW.  Another is the problems with justifying 15 TW of heat lost from the core.

Don Anderson, 12 June, 2014

The accretion of Earth is not a slow grain-by-grain process spread out over billions of years and resulting in a cold primordial planet. This was Urey's idea and is the basis of all geochemical models (Urey, Wasserberg, DePaolo, Craig etc.....see below). The late core formation, continuous growth of crust, undegassed mantle ideas etc are all children of this idea. A long time ago, Hanks and I showed that accretion had to be hot. Early determinations of isotope ages were interpreted as evidence for slow drawn out accretion. This problem was resolved by recognizing that accretion may have been spread out but it was due to occasional huge impacts and not small grains. Geochemistry has now caught up with the physics (e.g., Carlson) and early differentiation and core formation, and recycling, are now accepted.

Most geodynamic models assume uniform radioactivity and geochemical models assume deep high radioactivity zones but most likely radioactivity and other LIL elements are swept toward the surface during radial zone refining. Mass balance (crust, delaminated crust, kimberlites, Q etc.) also suggest little radioactivity in the deep mantle (see TOE).

The italicised phrase below are Googlets. Copy and paste into Google.

One can trace the divergence of opinion about the interior of the Earth to three monumental publications in 1952; Harold Urey’s The Planets, Sir Harold Jeffreys The Earth (3d Edition) and Francis Birch’s The Internal Constitution of the Earth. These were joined in 1959 by Beno Gutenberg’s Physics of the Earth’s Interior. These were the bibles of students of the Earth in the 1960s and 1970s. These present different views of our planet but the common element in the last three is fundamental physics and the view that Earth is radially zoned, differentiated and dynamic. Earth is not a left over undegassed undifferentiated primordial object.

The Planets is based on meteorites, observations of lunar and planetary surfaces, a belief that planets accreted slowly (adiabatically) and maintained an adiabatic geotherm, and that primordial objects survive in the solar system. The canonical model of geochemistry [godfather, Urey, Wasserburg, DePaolo, Armstrong] evolved (slightly) from the Chicago school. Ironically, theoretical considerations combined with further study of rocky planet formation, summarized by Bernard Wood in Physics Today, gives results that are the precise opposite of the slow cold accretion model. Jeffreys’ Earth is based on mathematics and theoretical seismology, Birch 1952 is based on classical solid-state physics and thermodynamics [Birch 1952]; Gutenberg, a meteorologist and seismologist, integrated geology, geophysics and fluid dynamics [Gutenberg physics Earth interior].

Michele Lustrino, 26 April, 2014

I thank Warren for having brought to my attention the article by Hofmeister & Criss (2013) [hereafter H&C]. I found the paper provocative and authoratative, but also difficult for most Earth scientists to follow. I am also troubled by what seems to be lack of consideration of alternatives.

PROBLEMS WITH HEAT TRANSPORT

Paragraph 2. The physics of head flow and cooling of large bodies (p. 491).

H&C write that convection is not a mechanism for heat transport. Is this true? Yes, I agree with them when they write that magma upwelling is much more important in transporting heat because of the rate of transport and the amount of heat transported as latent heat, but they also write that heat can be transported by advection. Is also this true? Does advection assume only horizontal movement (in contrast with convection, which needs also vertical movements and the closure of a circle)? Is this a process according which it is possible to cool a body?

At page 492 H&C define the lithosphere as “mafic”, but it is essentially ultramafic, i.e., there are almost no feldspars nor quartz.

On the same page H&C show in their Fig. 2 the thermal conductivity of Earth material as function of temperature. H&C use augite instead diopside as mantle clinopyroxene, and this may have some influence, I guess. H&C also assume that the continental crust is made up of 40% Ca-rich plagioclase, 25% augite, 20% sanidine and 15% quartz. Na-rich plagioclase and carbonate material forms about 65-70% of the crust is covered by sediments, more or less rich in a carbonate fraction, and, even if it is very thin, it cannot be ignored. In any case, the thermal conductivity calculated for the Earth’s lithosphere is shown at different temperatures (from nearly zero to 2500 K) but at 1 atm. Can this parameter change with depth?

Later on, p. 496, H&C write that the effects of increasing P can neutralize the effects of T increase, resulting in a constant thermal conductivity of the Earth = 6 W/(m.K). If so, what is the meaning of their Fig. 2?

On p. 493, left column, H&C write: “conduction dictates cooling over geological time scales”. It is correct to infer this?

On p. 493 (paragraph 2.2.1 Advection: motion without chemical change) H&C assume that advection of lithospheric plates is rather slow. This may be correct, but what happens at sub-lithospheric depths, i.e., in the LLAMA volume of the mantle (Anderson, 2010)? They also write that “internal motions within the solid plates are not important to planetary heat transfer”.

On the same page (paragraph 2.2.2. Motions accompanied by physio-chemical changes) H&C emphasize the role of magmatism and outgassing in cooling the planet. This is a very important statement, because the heat capacity of magma is much higher than that of solid rocks, and magma moves towards the surface. H&C assume that the magma is mobile because it is buoyant. Buoyancy is essential in magma mobility, but also important is the influence of viscosity or the chemical reactions between magma and the peridotite matrix that can strongly reduce magma mobility. Magmas produced at very high depths (i.e., around 410 km) may be denser than the ambient mantle. Their sinking can, as a consequence, heat up the lower mantle (not cool it!). Moreover, crystallization of silica-rich magma at magma depths can heat up the mantle, not simply cool it (and this can happen at various depths). All we should remember that only 10-20% of the magma produced reaches the surface. Most of it crystallizes at mantle depths and, consequentially, warms the mantle.

In the same paragraph H&C describe very high ascent rates of kimberlitic magma, which are able to travel from ~200 km depths to the surface in only ~8 hours. Is this possible? The presence of CO2 as magma propellant can be hypothesized only at very small depths (<2 GPa), while at greater depths carbon is stored in carbonate minerals or carbonatite and carbonate-silicatic melts.

On the same page (paragraph 2.3 Convection) H&C describe convection as “the sum of conduction and advection”. Is this definition correct? Does advection assume only horizontal movements? How can coupling of advection and conduction produce convection?

P. 494 (first line, left column). H&C write: “Plate motion is clear evidence of circulation” meaning that plate movements are related to convection. Is this correct? Is the dynamics of the sublithospheric mantle governing plate movement? This is a bottom-up model. What about the possible forces exerted by the gravitational field of the Moon (as modelled in several papers by Carlo Doglioni and others)? H&C conclude this paragraph writing that “observational evidence indicates a weakly convecting state with activity concentrated in the outermost layer”. Is there a quantification of such a “weak” convection system in the upper mantle?

ORIGIN OF EARTH’S INTERNAL HEAT (NO ROLE FOR CORE FORMATION AND ACCRETION)

On the same page (paragraph 3.1 Limits on core heating via friction during core formation imposed by the 2nd law”) H&C aim to demonstrate how the chemical differentiation of the Earth was a cooling, not a heating process. In particular, H&C exclude any Earth’s heating by core formation, as commonly assumed by classical models. Regarding this, H&C feel that this classical approach is against the second law. H&C assume that temperature changes in the Earth are gradual, 1-10 K/km. Is this correct? The correct adiabatic gradient of the solid Earth around 0.4-0.6 K/km.

H&C assume that frictional heating of solid metal particles, coupled with a temperature increase with depth could have inhibited strong sinking, therefore limiting the release of potential energy. In other words, H&C say that the separation of the core from the mantle is not due to sinking of the metal phase, but, rather to upwelling of the silicate material, transporting to shallow depth the most radioactive elements. Is there no possibility of invoking the presence of heat in the Earth associated with potential energy release? Is the only heat source in the Earth radioactivity? On these grounds the core is cooling the Earth from inside.

On p. 495 (paragraph 3.2.2 Can impacts provide internal heat?) H&C exclude also the accretion of the Earth as a potential source of heat of our planet. Classical models assume that most of the heat of the Earth is associated with the transfer of kinetic energy from colliding asteroids and meteorites with the planetesimal body. H&C assume that accretion of the Earth was associated not with impact of large bodies, but, rather, with constant addiction of cosmic dust. Under these circumstances, “most impacts were small and shallow so their heat was radiated to space in a short time interval”.

Is this correct? All the terrestrial planets are craterized. How is it possible that there were no large impacts on Earth and on other planets or satellites such as the Moon?

A required element of any model is to explain why nearly all the meteorites from the Moon and the Apollo lunar rocks have an age of 3.8 Ga. This means that something catastrophic (such as the collision of the Moon with a second Moon) happened not much later the Moon formation.

On the same page, right column (paragraph 3.31 Evidence in chemistry) H&C assume that the core contains ~10 wt% C. Is this amount possible? It is accepted that the Earth’s core is not made up of Fe-Ni alloys only, but the presence of 10% C seems to me too much.

On the same page, a few lines below (paragraph 3.3.2 Physical effects of outgassing) H&C propose that mantle outgassing cools the mantle and reduces its volume, favouring the particle motion needed for core formation. In other words, the core would have formed also as a consequence of the primitive Earth outgassing.

ORIGIN OF EARTH’S INTERNAL HEAT (ONLY RELATED TO RADIOACTIVITY)

On p. 496 (paragraph 4.1 Calculated steady-state conductive profiles for the present-day Earth) H&C calculate possible temperatures assuming various volumes of mantle free of U-Th (Fig. 6). Of course, in the model where the inner sphere lacking radioisotopes is very large, the amount of radiogenic heat is low. If the inner sphere lacking radioisotopes is small (i.e., limited to the inner core) the amount of radiogenic heat is high. What I do not understand is the amount of U-Th H&C put in their model. It is not stated what amount they have chosen, and they have assumed constant U-Th ppm multiplied by the amount of mantle where these elements could be found. In other words it is obvious that, assuming a large volume of the mantle with a given abundance of U-Th (e.g., tens of ppm), a large amount of radiogenic heat is produced. On the other hand, I would have left immobile the absolute amounts of U-Th (i.e. their mass), varying their concentration if the radiogenic mantle was very large or very low. I am uncomfortable with the approach H&C have chosen, which is to vary the absolute U-Th content with the volume of the radiogenic Earth.

According to their results, if we assume that U-Th are distributed throughout the entire Earth, the temperature of the innermost Earth would be around 31,520 K. This is impossible. Assuming a distribution of U-Th in the lithospheric mantle only, the temperature of the innermost Earth would be about 900 K. Assuming a distribution of U-Th in the upper mantle only, the temperature of the innermost Earth would be about 4000 K.

On the same page (paragraph 4.2 Implications for Earth’s current thermal state) H&C write that “Significant power production in the core, or primordial heat retention, are clearly impossible for reasonable input parameters”. I am not convinced. This conclusion is correct only assuming their model and their own input parameters. I agree, obviously, that the core is essentially U-Th-K-free, but I do not believe that the only source of heat of the Earth is radiogenic. H&C also assume “insignificant concentrations of radioactive elements in the lower mantle”. Yes, U-Th-K are lithophile elements and cannot be concentrated in the core, but why should these elements be concentrated in the upper mantle only? Because the lower mantle is restitic in nature? Ok, this may be an option, but certainly it is not a fact. On these grounds H&C conclude writing that “lower mantle thermal transport properties are irrelevant”. Assuming a core and lower mantle essentially U-Th-K-free, it is obvious that they conclude emphasizing the role of the upper mantle and lithosphere.

EARTH’S GEOTHERM

An important feature is shown in Fig. 7, p. 496. H&C assume a conductive geotherm for the entire upper mantle. Is this correct? Moreover, the lower mantle is considered isothermal. Can this be right? Moreover, the calculated temperature for a geotherm built assuming 30 TW heat flux and variable k, would be more than 5200 K at the base of the TZ–a very high temperature. Is seismology compatible with such an estimate? Also assuming a constant thermal conductivity [k = 6 W(m*K)], the calculated temperature at the base of the TZ is about 3800 K, again a very high value. Under these circumstances, some (most of the) upper mantle would be above its solidus temperature, also assuming completely volatile-free sources. Obviously, adding C and/or H the solidus of the mantle would be dramatically reduced, producing huge amounts of melts in the shallow mantle. I am skeptical that seismology is compatible with this.

In the same Fig. 7 H&C assume a constant melting temperature to produce basaltic magma = 1600 K, independent of the depth of the solidus. How is it possible to assume this?

EFFECTS OF PARTIAL MELTING

On p. 497 (paragraph 4.4 Melting controls the mantle geotherm and limits secular cooling) H&C assume that melts are always buoyant, perhaps ignoring the possibility of the density crossover between melts and restitic matrix around 12 GPa, as experimentally demonstrated (e.g., Ohtani et al., 2009, Chem. Geol., 265, 179-288). H&C write that production of partial melts leaves “refractiories such as MgO and aluminates at depth”. It is not correct to say this. While Fe abandons the peridotitic matrix preferentially with respect to Mg, it is also true that Al is easily extracted from peridotitic mantle minerals (spinel and garnet) compared with other trivalent cations (e.g., Cr). Above all, spinels and garnets are typical solidus minerals (together with cpx) during upper mantle anatexis. It is wrong that a refractory residuum is Al-rich.

In the same paragraph H&C write that “Peridotite melting curves characterize lower density, less refractory upper mantle material that was filtered out of the lower mantle by melting”. The upper mantle is Fe-richer than the lower mantle. Why do they assume the opposite? H&C confirm that the uppermost lower mantle reaches temperatures as high as >5000 K. Can seismology give constraints for these very high values?

A few lines lower down, H&C emphasize that the lower mantle is isothermal and the secular cooling of the Earth is balanced by freezing of the outer core. In other words, the crystallizing core is releasing heat (i.e. = core is warming the mantle) but this heat simply balances the heat lost by conduction along the upper mantle conductive geotherm. Assuming an isothermal mantle means assuming decrease in Tp in the lower mantle, correct?

Again in the same paragraph, H&C write that “the surface temperature is held constant by the Suns’ influx”. Is this true? The power we receive from the Sun (about 28000 TW) is much higher than the internal power (30 to 44 TW), but is this heat contribution relevant to the Earth? It is obviously essential for life, but for the solid Earth?

H&C conclude paragraph 4.4 by writing that “the reference conductive geotherm (Fig. 7) [...] will remain so until the outer core freezes completely”.

Again, p. 497 (paragraph 5.1 Neutrino studies do not constrain Earth’s power) H&C criticize the power of geoneutrino studies, because the uncertainty of the estimates (20 GW ± 20 GW). This is interesting.

COMPOSITION OF THE LOWER MANTLE

Again, on p. 497 (paragraph 5.2 A new type of meteorite model for Earth’s chemical composition) H&C make many assumptions to constrain the Earth’s composition divided into three main reservoirs. One is a metallic reservoir (U-Th-K-free core), the second is a silicatic reservoir (upper mantle) and the third is a refractory reservoir (lower mantle). The first reservoir has no U-Th-K, the second reservoir has a lot of K, U and Th, the third reservoir has no K but much more U and Th. I did not understand the rationale in calculating the third refractory reservoir. Essentially they calculated them “assuming” a given K/U ratio and a 30 TW heat flux (i.e., it is a derivative value obtained from other assumptions).

On p. 498 (paragraph 5.4 Lower mantle composition, formation and comparative planetology) H&C infer the composition of the lower mantle. In their Table 1 they indicate the condensation temperature of early forming-minerals that should constitute the lower mantle. They write that Al (very abundant in the lower mantle) should be present in the form of corundum and that Ca should be present in three main minerals, Hibonite (CaAl12O19), Perovskite (CaTiO3) and Gehlenite (a type of melilite, a mineral resembling a diopside with more CaO and with two Al in place of Mg-Si; Ca2Al2SiO7, wrongly reported as Ca2AlSiO3). I do not know the meaning of these four minerals, because none of them has ever been hypothesized in the lower mantle. Yes, these have been occasionally found in silicatic meteorites, but can their existence be exported to the Earth’s lower mantle too?

As concerns perovskite, this is a likely a lower mantle phase, but not the Ca-Ti type proposed by H&C, but rather the Mg-Si type (MgSiO3), with some Fe. H&C also write that Mg in the lower mantle is stored in forsterite. Is it possible to write this?

At the end of the right column on p. 498, H&C write that the presence of anorthosites on the Moon’s surface is evidence for the existence of Al cations in our satellite. This may be obvious (if we have plagioclase-rich rocks, the source must be Al-bearing), but the origin of lunar anorthosites is quite different (at least this is what I know), i.e., they are considered a fraction of the original lunar magma ocean after the crystallization of Fe-Mg-rich phases like cpx and olivines, leaving a relatively less dense Si-Al-rich residual magma that would have evolved into anorthosites after cooling.

ORIGIN OF SEISMIC CHANGES IN UPPER AND LOWER MANTLE

On p. 499 (paragraph 6.1 Crustal control on upper mantle circulation) H&C make some inferences on the differences in seismic velocities at upper and lower mantle depths. Upper mantle differences are vaguely attributed to temperature only, whereas “changes in the lower mantle are mostly compositional, requiring reinterpretation of tomographic images”. Of course they say this because their model assumes an isothermal and chemically refractory and homogeneous lower mantle.

In the same paragraph H&C underline the importance of recycling of heat-producing elements (in the form of subducted slabs) to maintain high TZ temperature and upper mantle convection. This assumes that nearly all the U-Th-K budget, originally present in the slab entering the trench, survives the metamorphic dehydration subduction filtering.

On the same page (paragraph 6.2 The lower mantle and core) H&C assume a similar isothermal core characterized by ~5500 K, due to its dearth of radioactive elements. H&C calculate an average cooling rate of <107 K/y, i.e., assume a core temperature about 500 K higher just after its formation (~6000 K).

FINAL COMMENT

In conclusion it has been very useful to me to read this article, but it also raises many questions and doubts in my mind. I hope that some discussion can bring further clarification of the points I raise.

Don L. Anderson, 29 March, 2014

The core must be cooling and this is important for the dynamo and mantle convection. The mantle is allowing the core to cool; the core is not "heating the mantle".

Question; why do tornadoes and dust devils only happen in the spring and in the early afternoon? The ground is still hot in the evening and in the summer.

Warren Hamilton, 29 March, 2014

The "Collisional erosion" and "Depleted Mantle" models of Sramek et al. (*) involve endless chains of dubious assumptions and should be discarded. The first one chains assumptions from the starting one of a collision with Earth by a Mars-like body, both with assumed starting K-U-Th contents and going a long way on from there. (No collisioner has explained why Earth's orbit is almost a perfect circle; compare Mercury, which obviously did take a big hit.) The DM speculations assume all links in the De Paolo chain of assumptions to be valid, despite the lack of evidence for any of them.

Van Schmus' tabulation, which I used, was for present K = 200 ppm, U = 20 ppb, Th = 74 ppb. Those are bang on for the "terrestrial rocks and CI chondrite" tabulations by Sramek et al. (*). Van Schmus' specific 200 ppm K is based not on rocks & chondrites but = 70% of the K which would have produced the 40Ar now in Earth's atmosphere, which you cannot conceivably reconcile with Sramek's numbers for collision, enstatite chondrite, or DM. Yes, you can come down below 30 TW for radiogenic heat, but not down to the numbers you suggest or that plume-advocates want.

The present radiogenic heat must be multiplied by approx. 5 to get the heat 4.55 b.y. ago. That hopelessly invalidates all models of an unfractionated Earth (or of a molten Earth that maintained uniformity by mixing), which so far as I know no plume-advocate has ever factored into his models.

If you check the literature, you will find that, as Gillian showed in her book and I illustrated with Hasterok's recent compilation of the 4000? measurements now available, anyone claiming a heat loss of ~45 TW is assuming, out of the clear blue sky, that s/he can double all measurements from seafloor <60 m.y. old. Anyone who says it is a measured value is, to put it charitably, mistaken. The number is pulled out of a hat because the fluid-dynamic modelers have agreed that this amount, as spread around wherever desired, enables plume models. (The earliest proponents of 45 TW were not specifically looking to support plumes, but wanted whole-mantle convection to drive tectonic plates.)

Core heat? The standard model assumes that downward-moving metal drops took most of the heat out of proto-silicate-Earth and concentrated it in a superheated core, which has been shedding whatever heat is desired for plumes ever since. Beyond the problem of the 2nd Law of Thermodynamics, none of the proponents of this scheme have ever calculated heat losses through time from this superheated core so far as I am aware. The heat is just there, eternal, to provide its present 15 TW or whatever else is wanted.

Yes, the outer core must be partly molten, and thus must be lowing latent heat. But how much, and what is its source? Latent heat can only be released to the extent that it is carried away. How long would a hypothetical starting core have stayed partly molten? Plume-advocates ignore this. Not only do they assume the heat is infinite, but (again, the 2nd Law of Thermodynamics does not apply) heat can be concentrated where desired to drive plumes. I continue to wonder if tidal heating will not prove to be what keeps the core partly molten.

Back to radioactivity: its current heat production must be a large fraction of Earth's heat loss, which means that internal temperatures are dominated by the radial distribution of RA. Gone are adiabats and much more. I urge that your read Hofmeister & Criss (2013).

References

Anderson, D.L., Hawaii, boundary layers and ambient mantle–geophysical constraints, J. Petrology, published online December 2, 2010, doi: 10.1093/petrology/egq068, available on-line at Journal of Petrology, Advanced Access

Hofmeister, A.M. & Criss, R.E., How irreversible heat transport processes drive Earth's interdependent thermal, structural, and chemical evolution, Gondwana Research, 24, 490–500, 2013.

 

last updated 11th June, 2014

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