Thermal History Of The Earth Research Articles

Thermal history of the Earth: Reply to “Less is not always more: A more inclusive data-filtering approach to secular mantle cooling” by Ross N. Mitchell and Jérôme Ganne

Thermal history of the Earth: Reply to “Less is not always more: A more inclusive data-filtering approach to secular mantle cooling” by Ross N. Mitchell and Jérôme Ganne

Thermal History of the Earth: On the Importance of Surface Processes and the Size of Tectonic Plates

AbstractGeochemical constraints on mantle temperature indicate a regular decrease by around 250 K since 3 Ga. However, models of Earth's cooling that rely on scaling laws for thermal convection without strong plates are facing a thermal runaway backwards in time, due to the power‐law dependence of heat loss on temperature. To explore the effect of surface dynamics on Earth's cooling rate, we build a two‐dimensional temperature‐dependent model of plate tectonics that relies on a force balance for each plate and on Earth‐like parameterized behaviors for the motion, creation, and disappearance of plate boundaries. While our model predicts the expected thermal runaway if plate boundaries are fixed, we obtain an average cooling rate consistent with geochemical estimates if the geometry of plate tectonics evolves through time. For a warmer mantle in the past, plates are faster but also larger (and less numerous) so that the average seafloor age and resulting heat flux always remain moderate. The predicted decrease in the number of plates backwards in time is in good agreement with recent plate reconstructions over the last 400 Myr. Our model also gives plate speed and subduction area flux consistent with these reconstructions. We finally compare the effect of parameters controlling mantle viscosity and individual plate speeds to the effect of localized surface processes, such as oceanization and subduction initiation. We infer that studies of Earth's thermal history should focus on surface processes as they appear to be key control parameters.

Peter Chadwick. 23 March 1931—12 August 2018

Peter Chadwick studied mathematics as an undergraduate at the University of Manchester, graduating with first-class honours in 1952, from where he moved to Cambridge and completed a PhD on the thermal history of the Earth in the Department of Geodesy and Geophysics under the supervision of Dr Robert Stoneley. His research then developed to focus primarily on the propagation of waves, and he made a major contribution to the mathematical theory of elastic wave propagation and became a world-leading authority in this area. He also made fundamental advances in the modelling of the thermo-elastic properties of rubberlike materials. At the University of East Anglia, where he was a professor for 26 years, he was the driving force behind the development of a research group in theoretical mechanics in the School of Mathematics and Physics, leading by example and supporting and encouraging fellow faculty members, especially the younger staff, academic visitors and students. He gave considerable service to the University of East Anglia in a number of capacities, including a period as Dean of the School, and to the scientific community, through substantial journal editorial activities and as a member of several national and international committees.

Plate bending, energetics of subduction and modeling of mantle convection: A boundary element approach

Several authors have suggested that mantle convection is primarily resisted by strong subduction zones, which if true implies small or even negative values of the exponent β in the Nusselt number/Rayleigh number relation Nu∼Raβ. To evaluate this hypothesis, we use the boundary element method (BEM) to study the energetics of subduction in a two-dimensional system comprising two purely viscous plates, a subducting plate (SP) and an overriding plate (OP), immersed in an infinitely deep ambient fluid beneath a free-slip surface. The negative buoyancy of the slab is the only driving force. The principal quantity of interest is the fraction R of the total viscous dissipation that occurs in the upper convective boundary layer comprising the SP, the OP and the subduction interface (SI) between them. Scaling analysis and BEM solutions of the instantaneous flow driven by an isolated SP yield R∼St/[St+F(θ)], where St is the flexural stiffness of the SP and F(θ) is a function of the dip θ of the plate's leading edge. More realistic time-dependent solutions for the SP+OP case show that R(t)≤0.4 for reasonable viscosity contrasts ηSP/ηambient∈[250,2500], indicating that the dissipation is dominated by the ambient mantle contribution. Finally, we formulate a parameterized model of mantle convection to evaluate the influence of subduction-zone dissipation on the effective value of β, motivated by the possibility that the use of the classical value β=1/3 in global parameterized convection models may be the cause of their failure to predict reasonable thermal histories. Using the correct length scale to describe bending (the ‘bending length’; Ribe (2010)), we find β∈[0.25,0.34], which is not much different than the classical result. We conclude that subduction zone dissipation is not large enough to change substantially the classical Nusselt number/Rayleigh number scaling law. It is therefore probably necessary to look elsewhere to reconcile geodynamical and geochemical arguments regarding the thermal history of the Earth.

Deep mantle roots and continental emergence: implications for whole-Earth elemental cycling, long-term climate, and the Cambrian explosion

ABSTRACTElevations on Earth are dominantly controlled by crustal buoyancy, primarily through variations in crustal thickness: continents ride higher than ocean basins because they are underlain by thicker crust. Mountain building, where crust is magmatically or tectonically thickened, is thus key to making continents. However, most of the continents have long passed their mountain building origins, having since subsided back to near sea level. The elevations of the old, stable continents are lower than that expected for their crustal thicknesses, requiring a subcrustal component of negative buoyancy that develops after mountain building. While initial subsidence is driven by crustal erosion, thermal relaxation through growth of a cold thermal boundary layer provides the negative buoyancy that causes continents to subside further. The maximum thickness of this thermal boundary layer is controlled by the thickness of a chemically and rheologically distinct continental mantle root, formed during large-scale mantle melting billions of years ago. The final resting elevation of a stabilized continent is controlled by the thickness of this thermal boundary layer and the temperature of the Earth’s mantle, such that continents ride higher in a cooler mantle and lower in a hot mantle. Constrained by the thermal history of the Earth, continents are predicted to have been mostly below sea level for most of Earth’s history, with areas of land being confined to narrow strips of active mountain building. Large-scale emergence of stable continents occurred late in Earth’s history (Neoproterozoic) over a 100–300 million year transition, irreversibly altering the surface of the Earth in terms of weathering, climate, biogeochemical cycling and the evolution of life. Climate during the transition would be expected to be unstable, swinging back and forth between icehouse and greenhouse states as higher order fluctuations in mantle dynamics would cause the Earth to fluctuate rapidly between water and terrestrial worlds.

A Finite Difference Model for the Thermal History of the Earth

The present study is an investigation of the thermal history of the earth using heat transfer modeling. Assuming that the earth was a hot ball at a homogeneous temperature upon its formation, the model makes the following two predictions about conditions 4.5 Ga later (the earth's approximate present age): (i) there will be a geothermal gradient within a range of 1.5-5.0 C per 100 meters in the first km of the earth crust; and (ii) the earth's crust will be about 45 km thick, which is in agreement with average continental crust thickness. The fact that oceanic crust is much thinner (around 5-10 km thick) is explained by convective heat transfer and plate tectonics. The strong agreement between the predicted thicknesses of earth's crust with the average actual continental crust thickness helps confirm the accuracy of the current inner core model of the earth indicating a solid inner core made of iron based on seismological studies.

The role of Poiseuille flow in creating depth-variation of asthenospheric shear

SUMMARY Asthenospheric flow accommodates differential shear between plate and mantle motions (Couette flow) and hosts additional flow driven by horizontal pressure gradients (Poiseuille flow) that may be associated with mantle upwelling and subduction. Large uncertainties in the upper mantle flow field and its rheological structure have thus far hindered our ability to constrain the relative importance of Couette and Poiseuille flows in the asthenosphere. However, quantifying the relative contributions of asthenospheric Couette and Poiseuille flows and determining the pattern of their distribution around the globe could help discriminate among competing theories of asthenospheric origin and shed light on thermal history of the Earth. We propose a new method to quantify asthenospheric Poiseuille flow using observations of the depth-dependence of azimuthal seismic anisotropy, which can be obtained from frequency-dependent surface wave tomography models. In particular, we employ a simple 1-D Couette-Poiseuille flow model and analytically solve for depth-profiles of the strain axis orientations, which approximates the orientations of azimuthal seismic anisotropy. We show that Couette-Poiseuille flow induces rotation of azimuthal seismic anisotropy with depth provided that the horizontal pressure gradient has a component transverse to plate motion. We then construct an algorithm that uses depth rotations of azimuthal anisotropy to invert for horizontal pressure gradients everywhere in the asthenosphere and test it on a global numerical mantle flow model. A comparison of pressure gradients predicted using our method with those computed directly from the numerical model shows that our algorithm is stable and accurate, unless the pressure gradient is nearly parallel to plate motion. Applying this method to seismic data will require additional constraints on asthenospheric geometry and viscosity structure. In the numerical model, we establish that Poiseuille flow drives ∼40 per cent of the total flow velocity amplitude in the asthenosphere, which indicates that pressure gradients from mantle convection may be an important component of asthenospheric dynamics that can, in principle, be constrained seismically.

Core–mantle boundary heat flow

Emerging evidence for threefold higher heat flow across the core–mantle boundary prompts a re-evaluation of the role of thermal plumes in geodynamics and the thermal history of the Earth's core and lower mantle.

Revised Decay Energies of Potassium, Thorium and Uranium, and the Thermal History of the Earth

Revised Decay Energies of Potassium, Thorium and Uranium, and the Thermal History of the Earth

Instabilities from phase transitions and the timescales of mantle thermal evolution

We have investigated the effects of mantle phase‐transitions on the Earth's thermal evolution by numerical modelling. Our results show that the tendency of layering grows with increasing vigor of convection. A self‐consistent model which couples the convective dynamics of the mantle to the secular cooling of the core is constructed. For a temperature‐dependent effective viscosity, we found that the thermal history of the Earth is characterized by two timescales, one is associated with layered convection in the early period, which is followed by a transition period with dramatic overturns. As the Rayleigh number decreases sufficiently low, whole mantle convection prevails and a faster cooling timescale ensues.

Evolution of terrestrial proto-CO 2 atmosphere coupled with thermal history of the earth

The effect of volatile exchange between surface reservoirs and the mantle on the evolution of proto-CO 2 atmosphere on the Earth is investigated using a global carbon cycle model coupled with thermal evolution of the mantle. Carbon is assumed to circulate among five reservoirs (atmosphere, ocean, continents, seafloor and mantle) and the carbon flux of each reservoir is calculated under varying conditions, such as an increase in solar luminosity, continental growth, and a decrease in tectonic activity with time. We consider processes such as continental weathering, carbonate precipitation in the ocean, carbonate accretion to the continents, metamorphism of carbonates followed by CO 2 degassing through arc volcanism, carbon regassing into the mantle, and CO 2 degassing from the mantle. The degassing rate of volatiles from the mantle is assumed to be proportional to the volatile concentration in the mantle multiplied by the mantle degassing volume. The mantle degassing volume is determined by the seafloor spreading rate and the melt generation depth in the mantle. We use a parameterized convection model to calculate the thermal evolution of the mantle, from which we estimate the seafloor spreading rate and the melt generation depth in the mantle. Numerical simulations suggest that the amount of surface carbon at the present time would be in a steady state. This is because the response time of the carbon cycle system against the perturbation for surface carbon is short, being estimated at about 900 million years under the present conditions. Thus the present amount of surface carbon would not be affected by the initial amount of surface carbon. The seafloor spreading rate would have been almost constant throughout the Earth's history to explain apparent constancy of the carbon isotope ratio in the mantle after about 3.5 billion years ago. The surface carbon might probably have been circulated between surface reservoirs and the mantle once or twice after the Archean period. In any event, CO 2 in the proto-atmosphere on the Earth is suggested to have decreased with the growth of continents, resulting in stabilization of the terrestrial environment against the increase in solar luminosity.

Geochemical Constraints on the Early Thermal History of the Earth

Abstract Theories of the formation of the Earth strongly suggest that the Earth should have been substantially molten during and immediately after accretion. Estimates of the composition of the upper mantle indicate that many elements are present in chondritic ratios. Experimental measurements of element partition coefficients show that segregation of perovskite, majorite garnet, or olivine would fractionate the ratios of these elements away from chondritic values. The implication of these geochemical observations is that the Earth did not undergo extensive fractionation during and immediately following accretion. One possibility is that the Earth did not become substantially molten. Alternatively, if the Earth was indeed substantially molten, then it is possible that minerals were entrained in magma and were unable to segregate. In the former case, the accretional process must have delivered gravitational potential energy more slowly than current theory predicts, and an origin of the Moon in a giant impact would be unlikely. In the latter case, the high Mg/Si ratio in the upper mantle of the Earth relative to most classes of chondrites would be intrinsic to the silicate portion of the Earth. Unless significant amounts of Si exist in the core, the high Mg/Si ratio is a bulk planetary property, implying that the accretional process did not mix material between 1 AU and 2-4 AU.

Thermal history of the Earth: a corollary concerning non-linear mantle rheology

Abstract Mantle rheology and the convective cooling process exert a close mutual control on one another, so that the cooling rate can be calculated with only a rudimentary idea of the material properties of the mantle. However, the distinction between linear, i.e. Newtonian, viscous behaviour and non-linear or power-law rheology, in which the creep rate ϵ depends upon stress σ as σ n with n > 1, it isportant. We find that the present rate of loss of residual heat is almost twice as great with n = 3 as it si tn the linear case ( n = 1). Since this net heat loss is simply the difference between the observed total mantle heat flux and the radiogenic heat input, the radioactive content of the mantle is predicted to be substantially less in the non-linear case. An examination of the plausible ranges of the U, Th and K contents of the mantle shows that the requirement for radiogenic heat by the linear model us unreasonably high. This observation strengthens an earlier very tentative conclusion, based on temperatures of komatiite lavas, that convective mantle rheology is non-linear. The alternative conclusion would be that the Earth contains ≈ 30 ppb of U compared with carbonaceous chondrites (20 ppb) or ordinary chondrites (15 ppb).

Onset of mantle plumes in the presence of preexisting convection

The onset of plumes where broad‐scale convection already exists is investigated along with the thermal history of the earth. Geological evidence relating to the onset time of mantle plumes is not definitive: no well‐defined hotspot tracks older than Mesozoic have been identified, but it is difficult to tell whether this absence is a reliable indication of a late onset of mantle plumes, since only continental crust of this age exists. Using the hotspot track distribution for the Pacific, the absence of Pre‐Mesozoic hotspot tracks on the Canadian Shield cannot easily be attributed to chance. However, young continental hotspot tracks are controversial, and it is not clear whether tracks such as the Monteregian Hills/White Mountain Magma Series would be recognized as such without considering the contributing evidence of the adjacent oceanic crust and its well‐defined seamount chains. Our simple models yield potentially testable predictions: the instability of plume formation in a system where broad‐scale convection already exists depends on horizontal conduit flow in the basal boundary layer toward the plume source. Geographically, plumes are most likely to form where the boundary layer is thickest and where broad‐scale ascending flow already exists. Parameterized convection indicates that the heat transport by conduit flow in the boundary layer toward plumes depends linearly on the ratio of effective viscosity for broad‐scale convection to effective boundary layer viscosity. In terms of material properties, this ratio is the ratio of viscosity across the boundary layer to about the 0.45 power for the case where the broad‐scale convection is heated from below. The viscosity contrast across the boundary layer depends on the temperature contrast across the layer. A late onset of mantle plumes is implied if the temperature contrast at the base of the mantle has increased with time, that is, if the core has cooled more slowly than the interior of the mantel. In one scenario, before about 3 b.y. B.P., the mantle temperature varied slowly because surface heat flow was nearly balanced by internal radioactivity. During this time the mantle was hotter than present, and its internal viscosity lower. Hie temperature contrast at the base of the mantel was thus small. After 3 b.y., internal radioactivity no longer balanced surface heat flow, and the mantle cooled about a few hundred degrees Celsius, as indicated by petrological observations. The core cooled slower than the mantle, and the temperature contrast across the bottom boundary layer increased with time, leading to a late onset of plumes. Phenomenological inferences are obtained, as Venus may have cooled more rapidly than the Earth. Its mantle may be too cool for rapid plate tectonics, and the gravity field and the convective pattern are dominated by hot upwelling regions.

Core cooling by subsolidus mantle convection

Although vigorous mantle convection early in the thermal history of the Earth is shown to be capable of removing several times the latent heat content of the core, we are able to construct a thermal evolution model of the Earth in which the core does not solidify. The large amount of energy removed from the model Earth's core by mantle convection is supplied by the internal energy of the core which is assumed to cool from an initial high temperature given by the silicate melting temperature at the core-mantle boundary. For the smaller terrestrial planets, the iron and silicate melting temperatures at the core-mantle boundaries are more comparable than for the Earth, and the cores of these planets may not possess enough internal energy to prevent core solidification by mantle convection. Our models incorporate temperature-dependent mantle viscosity and radiogenic heat sources in the mantle. The Earth models are constrained by the present surface heat flux and mantle viscosity. Internal heat sources produce only about 55% of the Earth model's present surface heat flow.

The Flow of Heat from the Earth's Interior

The discussion is presented under the following section headings: measuring heat flow; heat flow and plate tectonics; global heat flow; the thickness of the lithosphere; and thermal history of the earth. A global heat-flow map was drawn on the basis of thousands of individual field measurements on continents and ocean floors. The heat-flow pattern is interpreted in terms of plate tectonics. JGB)

Excess of atmospheric neon in pumice from the Islands of Lipari

LORD RAYLEIGH1 reported an excess of neon (over argon) in pumice from the Lipari Islands. Dymond and Hogan2 have reported excesses of neon in mid-oceanic tholeitic basalts and have suggested that they indicate primordial neon. As the search for primordial gases in terrestrial rocks has an important bearing on our understanding of the formation and thermal history of the Earth, we decided to look at the isotopic composition of the neon in pumice from the Lipari Islands. We collected fresh specimens from the largest quarry on the islands and extracted the included gases by crushing in a vacuum line and by stepwise heating. The five noble gases were measured in a mass spectrometer.

Convection at the melting point: A thermal history of the earth's core

Abstract Higgins and Kennedy (1971) concluded that the Earth's fluid core has a stable stratification if it is at its melting point. Busse (1972) and Elsasser suggested as an alternative that a hydrostatic-isentropic distribution of particulate solid can produce neutral stability in a partially molten core. Here this suggestion is quantified and a determination is made of the efficiency of the production of fluid motion from the heat flux. This is used to establish that macroscopic convection can exist only if the particulate solid is of sufficiently small size. A thermal history of the core compatible with upper mantle heat flux is advanced in which it is suggested that the inner core is a fairly recent feature. The implication of these results for convection-driven and precession-driven dynamos is that both can function for a small enough suspended particulate, that the convection-dynamo will fail for particles greater than one micron in diameter, and that the precession-driven dynamo probably cannot su...

Thermal History of the Earth with Consideration of the Formation of Its Core

Various possible ways of core formation are tested from the thermal history of the Earth. Calculation shows that the conversion of gravitational to thermal energy from a uniform to the present differentiated Earth is 1.68×1038 ergs. It is concluded that the release of the gravitational energy on core formation dominates the thermal state of the Earth.Earth models in which the core has been growing slowly since 4500 My ago or 3000 My ago fail to meet the requirement of a solid mantle. In these models the present surface heat flows are in excess of the observed heat flow.Earth models in which the core was substantially complete at 4500 My ago or 3000 My ago within a short period less than 100 My give the observed heat flow.The gravitational energies released in reconstruction of the terrestrial planets are also calculated. Calculation gives the gravitational energies of 1.02×1038 ergs, 1.10×1036 ergs, and 1.34×1036 ergs for Venus, Mars, and Mercury respectively. The results show that the energies released by the formation of iron cores of the Earth and Venus play an important role for the internal heating of these planets.

Factors determining the temperature evolution of thermally convecting earth models

The thermal history of the Earth is posed as a problem in convection theory. The concept of stabilisation temperature is introduced and its significance for the cooling process is assessed. The rapidity of heat transport at higher temperatures combined with the fact that stabilisation temperatures are only half the melting temperature, cf. the classical literature of cooling from a “hot origin”, makes present temperatures relatively insensitive to initial conditions.