Convection and lunar thermal history

The effect of solid convection on the thermal evolution of the Moon is explored for a variety of viscosities, radioactive differentiation efficiencies and initial temperature profiles. Convective heat flux in the models is calculated using an empirical relation derived from the results of laboratory experiments and numerical solutions of the Navier-Stokes equations. The method retains the spherically symmetric approximation and, therefore, greatly facilitates numerical calculations.Results show that even though solid convection may determine the thermal state of the lunar interior, it does not necessarily produce a quasi-steady thermal balance between heat sources and surface loss. An imbalance persists, due to the cooling and growth of the nonconvecting lithosphere. The state of the lithosphere is sensitive to the efficiency of heat source redistribution, while that of the convecting interior depends primarily on rheology. Convecting models have viscosities of 10²¹–10²² cm²s^?1 in their interiors; the central temperature must be above 1100°C. Convection occurring within the first billion years after formation could have led to mare flooding by magma produced in hot zones of convection cells. However, it cannot be shown from model calculations alone that solid convection must have dominated lunar thermal history.     

Uniform parameterized theory of convection in medium sized icy satellites of Saturn

We develop a parameterized theory of convection driven by radiogenic and tidal heating. The tidal heating depends on eccentricity e of a satellite’s orbit. Using parameterized theory we determine the intensity of convection as a function of e and satellite’s properties. The theory is used for 6 medium sized satellites of Saturn. We find that endogenic activity on Tethys and Dione is possible if e exceeds some critical values e _cr . For Enceladus, e was probably close to the present value for billions of years. We cannot find constrains for e of Mimas and Iapetus. The theory successfully predicts the possibility of present endogenic activity in Dione and rules out such activity in Tethys. Both these facts were recently confirmed by Cassini mission.     

On the thermal evolution of the earth

The two principal contributions to the surface heat flow of the earth are the cooling of the earth and the heat production of radioactive isotopes. As the rate of heat production decreases with time the temperature of the interior of the earth also decreases. The rate of decrease is determined by the ability of solid-state mantle convection to transport the heat to the surface. The dominant effect is the exponential temperature dependence of the mantle viscosity. The non-dimensional mantle temperature can be parameterised in terms of the Rayleigh number for mantle convection. It is found that the mantle is currently cooling at a rate of 36°K/10⁹ years and that three billion years ago the mean temperature was 150°K higher than it is today; 83% of the present surface heat flow is attributed to the decay of radioactive isotopes and 17% to the cooling of the earth. The corresponding mean concentration of uranium in the mantle is 32 ppb.     

Gravitational energy of core evolution: implications for thermal history and geodynamo power

Using density–pressure relationships for mantle silicate and core alloy closely matching PREM we have constructed six models of the Earth in different evolutionary states. Gravitational energies and elastic strain energies are calculated for models with homogeneous composition, separated mantle and liquid core, separated inner and outer cores with the inner core either liquid or solid and models with increased densities, representing cooling of either the mantle or core. In this way we have isolated the gravitational energy released by each of several evolutionary processes and subtracted the consequent increase in strain energy to obtain the net energy released as heat or geodynamo power. Radiogenic heat (∼7.8×10³⁰ J) is found to contribute only about 25% of the total heat budget, the balance originating as residual gravitational energy from the original accretion and from core separation (14×10³⁰ J). The total energy of compositional convection, driven by inner core formation, is 3.68×10²⁸ J and this is the most important (or even the only) energy source for the dynamo for the most recent 2 billion years. It appears unlikely that the inner core existed much before that time. The total net (gravitational minus strain) energy released in the core by the process of inner core formation, 11.92×10²⁸ J, is not much less than the thermal energy released in this process, 15.1×10²⁸ J. In the mantle the net (gravitational minus strain) energy released by thermal contraction is about 20% of the heat release. All of the numerical results are presented in a manner that allows simple rescaling to any revised density estimates.     

Paleointensity variations of Earth's magnetic field and their relationship with polarity reversals

Power-spectral analyses of the intensity of Earth's magnetic field inferred from ocean sediment cores and archeomagnetic data from time scales of 100 yr to 10 Myr have been carried out. The power spectrum is proportional to 1/f where f is the frequency. These analyses compliment previous work which has established a 1/f² spectrum for variations at time scales less than 100 yr. We test the hypothesis that reversals are the result of variations in field intensity with a 1/f spectrum which occasionally are large enough to cross the zero intensity value. Synthetic binormal time series with a 1/f power spectrum representing variations in Earth's dipole moment are constructed. Synthetic reversals from these time series exhibit statistics in good agreement with the reversal record, suggesting that polarity reversals may be the end result of autocyclic intensity variations with a 1/f power spectrum.     

On the tidal heating of Enceladus

Enceladus, one of Saturn's moons, shows significant volcanic activity identified by the Cassini spacecraft. The aim of the present study is to investigate – with the adaptation of mathematical tools used in geodynamics – the extent of tidal heating due to the mean motion resonance with Dione. For the purpose of calculations a two-layer model of Enceladus was used. The inner part of the model is a “rocky core” with a relative radius 0.55, while the outer part is composed of water ice. The results of model calculations show that the effective tidal heating is not uniformly distributed within Enceladus. It was found for the selected model of Enceladus, that the tidal heating is maximum within the depth interval (25–75) km. Due to the inhomogeneity within Enceladus, 85% of the tidal energy is generated in a volume that contains just 39% of its mass. In time intervals of 3.0 × 10⁸ and 5.3 × 10⁸ years the temperature increase in the relative depth range 0.70 ≤ r/a_E ≤ 0.90 is approximately 270 and 370 K, respectively.     

Thermal history and large scale differentiation of the Saturn’s satellite Rhea

Thermal history of Rhea from the beginning of accretion is investigated. We developed a numerical model of convection combined with the parameterized theory. Large scale melting of the satellite’s matter and gravitational differentiation of silicates from ices are included. The results are confronted with observational data from Cassini spacecraft that indicate minor differentiation of the satellite’s interior. We suggest that partial differentiation of the satellite’s interior is accompanied (or followed) by the process of light fraction uprising to the surface. The calculation indicates that the partial differentiation of the matter of the satellite’s interior is possible only for narrow range of parameters. In particular, we found that the time from the formation of CAI (calciumaluminum rich inclusions in chondrites) to the end of accretion of Rhea is in the range of 3–4 My.     

Two-dimensional mantle flow beneath a rigid accreting lithosphere

This study considers two-dimensional mantle flow beneath a rigid lithosphere. The lithosphere which forms the upper boundary of a convecting region moves with a prescribed uniform horizontal velocity, and thickens with distance from the accreting plate boundary as it cools. Beneath the lithosphere, the mantle deforms viscously by diffusion creep and is heated radiogenically from within. Solutions for thermal convection beneath the lithosphere are obtained by finite-difference methods. Two important conclusions have resulted from this study: (1) convective patterns of large aspect ratio are stable beneath a rigid moving lithosphere; (2) even for a lithosphere velocity as small as 3 cm/yr. and a Rayleigh number as large as 10⁶, mantle circulation with large aspect ratio is driven dominantly by the motion of the lithosphere rather than by temperature gradients within the flow. Gravity, topography and heat flow are determined and implications for convection in the upper mantle are discussed.     

Heat transport by variable viscosity convection and implications for the Earth's thermal evolution

The case is presented that the efficiency of variable viscosity convection in the Earth's mantle to remove heat may depend only very weakly on the internal viscosity or temperature. An extensive numerical study of the heat transport by 2-D steady state convection with free boundaries and temperature dependent viscosity was carried out. The range of Rayleigh numbers (Ra) is 10⁴?10⁷ and the viscosity contrast goes up to 250000. Although an absolute or relative maximum of the Nusselt number (Nu) is obtained at long wavelength in a certain parameter range, at sufficiently high Rayleigh number optimal heat transport is achieved by an aspect ratio close to or below one. The results for convection in a square box are presented in several ways. With the viscosity ratio fixed and the Rayleigh number defined with the viscosity at the mean of top and bottom temperature the increase of Nu with Ra is characterized by a logarithmic gradient β = ?ln(Nu)/? ln(Ra) in the range of 0.23–0.36, similar to constant viscosity convection. More appropriate for a cooling planetary body is a parameterization where the Rayleigh number is defined with the viscosity at the actual average temperature and the surface viscosity is fixed rather than the viscosity ratio. Now the logarithmic gradient β falls below 0.10 when the viscosity ratio exceeds 250, and the velocity of the surface layer becomes almost independent of Ra. In an end-member model for the Earth's thermal evolution it is assumed that the Nusselt number becomes virtually constant at high Rayleigh number. In the context of whole mantle convection this would imply that the present thermal state is still affected by the initial temperature, that only 25–50% of the present-day heat loss is balanced by radiogenic heat production, and the plate velocities were about the same during most of the Earth's history.     

Mantle plumes link magnetic superchrons to phanerozoic mass depletion events

The four most recent large mass extinction events in the Phanerozoic – the Cretaceous–Tertiary (KT), the Triassic–Jurassic (TJ), and the Permo-Triassic (PT) and Guadalupian–Tatarian (GT) doublet – are associated with a major flood basalt eruption, with the timing of peak volcanic activity corresponding within measurement uncertainties to the extinction event. Three magnetic superchrons precede the four largest Phanerozoic extinctions. The Cretaceous Long Normal Superchron (duration  35 Myr) precedes the KT and the Permian Kiaman Long Reversed Superchron ( 50 Myr) precedes the PT–GT doublet. In addition, the newly recognized Ordovician Moyero Long Reversed Superchron ( 30 Myr) precedes the end-Ordovician extinction event. There is a 10–20 Myr delay between the end of each superchron and the subsequent mass depletion event, both of which represent distant outliers from their respective populations. We propose that deep mantle plumes link these seemingly unrelated phenomena. Long-term ( 200 Myr) variations in mantle convection possibly associated with the Wilson cycle induce temporal and spatial variations in heat flow at the core–mantle boundary. Polarity reversals are frequent when core heat flow is high and infrequent when it is low. Thermal instabilities in the D”-layer of the mantle increase core heat flow, end the magnetic superchron, and generate deep mantle plumes. The plumes ascend through the mantle on a 20 Myr time scale, producing continental flood basalt (trap) eruptions, rapid climatic change, and massive faunal depletions.     

Regional Be production rate calibration for the past 12 ka deduced from the radiocarbon-dated Grøtlandsura and Russenes rock avalanches at 69° N, Norway

Two rock avalanches in Troms County – the Grøtlandsura and Russenes – were selected as CRONUS-EU natural cosmogenic ¹⁰Be production-rate calibration sites because they (a) preserve large boulders that have been continuously exposed to cosmic irradiation since their emplacement; (b) contain boulders with abundant quartz phenocrysts and veins with low concentrations of naturally-occurring ⁹Be (typically < 1.5 ppb); and (c) have reliable minimum radiocarbon ages of 11,424 ± 108 cal yr BP and 10,942 ± 77 cal yr BP (1σ), respectively. Quartz samples (n = 6) from these two sites contained between 4.28 × 10⁴ and 5.06 × 10⁴ at ¹⁰Be/g using the 1.387 Myr ¹⁰Be half-life. Determination of these concentrations accounts for topographic and self-shielding, and effects on nuclide production due to isostatic rebound are shown to be negligible. Persistent, constant snow and moss cover cannot be proven, but if taken into consideration they may have reduced ¹⁰Be concentrations by 10%. Using the ¹⁰Be half-life of 1.387 Myr and the Stone scaling scheme, and accounting for snow- and moss-cover, we calculate an error-weighted mean total ¹⁰Be production rate of 4.12 ± 0.19 at/g/yr (1σ). A corresponding error-weighted mean spallogenic ¹⁰Be production rate is 3.96 ± 0.16 at/g/yr (1σ), respectively. These are in agreement within uncertainty with other ¹⁰Be production rates in the literature, but are significantly, statistically lower than the global average ¹⁰Be production rate. This research indicates, like other recent studies, that the production of cosmogenic ¹⁰Be in quartz is lower than previously established by other production-rate calibration projects. Similarly, our findings indicate that regional cosmogenic production rates should be used for determining exposure ages of landforms in order to increase the accuracy of those ages. As such, using the total ¹⁰Be production rate from our study, we determine an error-weighted mean surface-exposure age of a third rock avalanche in Troms County (the Hølen avalanche) to be 7.5 ± 0.3 kyr (1σ). This age suggests that the rock avalanche occurred shortly after the 8.2 kyr cooling event, just as the radiocarbon ages of the Grøtlandsura and Russenes avalanches confirm field evidence that those rock-slope failures occurred shortly after deglaciation.     

Cosmogenic isotopes and their role in present-day solar paleoastrophysics

Present-day data on ¹⁴C and ¹⁰Be concentration in natural archives have been statistically analyzed. It has been established that it is difficult to extract information about solar activity variations on long (several Myr and longer) and, especially, short (to 30 years) time scales using radiocarbon data. It has been indicated that beryllium series bear reliable information about short-term, secular, and, probably, 1000-year variations in solar activity. Moreover, ¹⁰Be concentration in polar ice can also be used to study the internal dynamics of solar activity. It has been concluded that beryllium data are more promising than radiocarbon ones from the viewpoint of solar paleoastrophysics.     

Formation,history and energetics of cores in the terrestrial planets

The cores of the terrestrial planets Earth, Moon, Mercury, Venus and Mars differ substantially in size and in history. Though no planet other than the Earth has a conclusively demonstrated core, the probable cores in Mercury and Mars and Earth's core show a decrease in relative core size with solar distance. The Moon does not fit this sequence and Venus may not. Core formation must have been early (prior to ～4 · 10⁹ yr. ago) in the Earth, by virtue of the existence of ancient rock units and ancient paleomagnetism and from UPb partitioning arguments, and in Mercury, because the consequences of core infall would have included extensional tectonic features which are not observed even on Mercury's oldest terrain. If a small core exists in the Moon, still an open question, completion of core formation may be placed several hundred million years after the end of heavy bombardment on tectonic and thermal grounds. Core formation time on Mars is loosely constrained, but may have been substantially later than for the other terrestrial planets. The magnitude and extent of early heating to drive global differentiation appear to have decreased with distance from the sun for at least the smaller bodies Mercury, Moon and Mars.Energy sources to maintain a molten state and to fuel convection and magnetic dynamos in the cores of the terrestrial planets include principally gravitational energy, heat of fusion, and long-lived radioactivity. The gravitational energy of core infall is quantifiable and substantial for all bodies but the Moon, but was likely spent too early in the history of most planets to prove a significant residual heat source to drive a present dynamo. The energy from inner core freezing in the Earth and in Mercury is at best marginally able to match even the conductive heat loss along an outer core adiabat. Radioactive decay in the core offers an attractive but unproven energy source to maintain core convection.     

Finite-Amplitude thermal convection within a self-gravitating fluid sphere

Abstract

Finite-difference calculations have been carried out to determine the structure of finite-amplitude thermal convection within a self-gravitating fluid sphere with uniform heat release. For a fixed-surface boundary condition single-cell convection breaks up into double-cell convection at a Rayleigh number of 3 × 10⁴, at a Rayleigh number of 5 × 10⁵ four-cell convection is observed. With a free-surface boundary condition only single cell convection is obtained up to a Rayleigh number of 5 × 10⁶.     

The geomagnetic dynamo-elementary energetics and thermodynamics

This paper is a non-mathematical review, summarising the work in this field.Estimates are made of the power needed to maintain the electric currents which give the main geomagnetic field. The observed surface field needs at least 2×10⁸ W, but unobservable fields may need much more; a toroidal field of peak value 10 or 50nT would need 10¹⁰ or 2.5×10¹¹ W.Ways of obtaining this power from the Earth's rotation, particularly through precession, are considered and rejected.Thermal power sources have the disadvantages that there is inherent thermodynamic inefficiency in driving the dynamo, and that a significant fraction of the heat input will be carried away by conduction rather than convection. Radioactivity will only be important if there is a substantial amount of potassium in the core. If this is not the case the core might be cooling; cooling at 20K per 10⁹ yr would release specific heat at a rate of 10¹² W. If the cooling causes the inner core to grow by freezing from the liquid core, then an additional 10¹² W would be released from the latent heat of freezing. These heat fluxes might support a dynamo having a small toroidal field.If, as seems likely, the solid inner core is significantly denser than the liquid, such cooling would also release 0.6×10¹² W of gravitational energy, giving compositional convection which would drive the dynamo very efficiently and give a large toroidal field.     

Apollo 16 neutron stratigraphy

The Apollo 16 soils have the largest low energy neutron fluences (up to 10¹⁷ n/cm², E < 0.18eV) yet observed in lunar samples. Variations in the isotopic ratios ¹⁵⁸Gd/¹⁵⁷Gd and ¹⁵⁰Sm/¹⁴⁹Sm (up to 1.9% and 2.0% respectively) indicate that the low energy neutron fluence in the Apollo 16 drill stem increases with depth throughout the section sampled. Such a variation implies that accretion has been the dominant regolith “gardening” process at this location. The data may be fit by a model of continuous accretion of pre-irradiated material at a rate of ～70 g/(cm² · 10⁸yr) or by models involving as few as two slabs of material in which the first slab could have been deposited as long as 10⁹ yr ago.The ratio of the number of neutrons captured per atom by Sm to the number captured per atom by Gd is lower than in previously measured lunar samples, which implies a lower energy neutron spectrum at this site. The variation of this ratio with chemical composition is qualitatively similar to that predicted by Lingenfelter, Canfield and Hampel.Variations are observed in the ratio ¹⁵²Gd/¹⁶⁰Gd which are fluence correlated and probably result from neutron capture by¹⁵¹Eu.     

Numerical model of convection in sills

The numerical model of convection in magma sills is developed. The model is based on a full system of equations of fluid dynamics and includes heat transfer, buoyancy effects and diffusion of some minor component (marker). Solidification is treated as a phase transition. The results indicate that there are some qualitative differences between very thin sills with Rayleigh number Ra = 10⁵ and thin sills with Ra = 10⁶. For a basaltic magma the first case corresponds to the thickness of the sills of approximately 30 cm and the second case corresponds to the thickness of 60 cm. In the first case mixing is inefficient and conduction is the dominant form of heat transfer. In the second case mixing is efficient and convection is the dominant form of heat transfer. Some of the results can be scaled for the more viscous magmas in thicker sills.     

Cooling and inferred exhumation history of the Ryoke metamorphic belt in the Yanai district, south-west Japan: Constraints from Rb–Sr and fission-track ages of gneissose granitoid and numerical modeling

Abstract The Ryoke metamorphic belt in south-west Japan consists mainly of I-type granitoids and associated low-pressure/high-temperature metamorphic rocks. In the Yanai district, it has been divided into three structural units: northern, central and southern units. In this study, we measured the Rb–Sr whole-rock–mineral isochron ages and fission-track ages of the gneissose granodiorite in the central structural unit. Four Rb–Sr ages fall in a range of ca 89–87 Ma. The fission-track ages of zircon and apatite are 68.9 ± 2.6 Ma and 57.4 ± 2.5 Ma (1σ error), respectively. Combining the newly obtained ages with previously reported (Th–)U–Pb ages from the same unit, thermochronologic study revealed two distinctive cooling stages; 1) a rapid cooling (> 40°C/Myr) for a period (~7 Myr) soon after the peak metamorphism (~ 95 Ma) and 2) the subsequent slow cooling stage (~ 5°C/Myr) after ca 88 Ma. The first rapid cooling stage corresponds to thermal relaxation of the intruded granodiorite magma and its associated metamorphic rocks, and to the uplift by a displacement along low-angle faults which initiated soon after the intrusion of the magma. Uplift by the later stage deformation having formed large-scale upright folds resulted in progress of the exhumation during the first stage. The average exhumation velocity of the stage is ≥ 2 mm/yr. During the second stage, the rocks were not accompanied by ductile deformation and were exhumed with the rate of 0.1–0.2 mm/yr. The difference in the exhumation velocity between the first and second cooling stages resulted from the difference in the thickness of the crust and in the activity of ductile deformation between the early and later stages of the orogenesis.     

Spatial variability of hydraulic conductivity and bulk density along a blanket peatland hillslope

This article presents the results of a field investigation of saturated hydraulic conductivity K_sat and bulk density (ρ_bd) in an Atlantic blanket bog in the southwest of Ireland. Starting at a peatland stream and moving along an uphill transect toward the peatland interior, ρ_bd and K_sat were examined at regular intervals. Saturated horizontal hydraulic conductivity (Kh_sat) and vertical (Kv_sat) was estimated at two depths: 10–20 and 30–40 cm below the peat surface, whereas ρ_bd was estimated for the full profile. We consider two separate zones, one a riparian zone extending 10 m from the stream and a second zone in the bog interior. We found that the K_sat was higher (~10^–5 m s^–1) in the bog interior than that in the riparian zone (~10^–6 m s^–1), whereas the converse applied to bulk density, with lowest density (~0.055 g cm^–3) at the interior and highest (~0.11 g cm^–3) at the riparian zone. In general, we found Kh_sat to be approximately twice the Kv_sat. These results support the idea that the lower K_sat at the margins control the hydrology of blanket peatlands. It is therefore important that the spatial variation of these two key properties be accommodated in hydrological models if the correct rainfall runoff characteristics are to be correctly modelled. Stream flow analysis over 3 years at the peatland catchment outlet showed that the stream runoff was composed of 8% base flow and 92% flood flow, suggesting that this blanket peatland is a source rather than a sink for floodwaters. Copyright © 2011 John Wiley & Sons, Ltd.     

Flexural uplift of a lithospheric slab near the Vema transform (Central Atlantic): Timing and mechanisms

The Vema Transverse Ridge (VTR) is a prominent, long and narrow topographic anomaly that runs for over 300 km along a sea floor spreading flow line south of the Vema transform at 11° N in the Atlantic. It rises abruptly about 140 km from the axis of the Mid-Atlantic Ridge (MAR) in 10 Myr old crust and runs continuously up to 25 Myr old crust. It reaches over 3 km above the predicted lithospheric thermal contraction level. It is absent in crust younger than 10 Myr; thus, the uplift of the VTR must have ended roughly 10 Ma. The VTR is interpreted as the exposed edge of a flexured and uplifted slab of oceanic lithosphere that was generated at an 80 km long MAR segment. Based on satellite gravimetry imagery this MAR segment was born roughly 50 Ma and increased its length at an average rate of 1.6 mm/yr. Multibeam data show that the MAR-parallel sea floor fabric south of the VTR shifts its orientation by 5° to 10° clockwise in 11–12 Myr old crust, indicating a change at that time of the orientation of the MAR axis and of the position of the Euler rotation pole. This change caused extension normal to the transform, followed between 12 and 10 Ma by flexure of the edge of the lithospheric slab, uplift of the VTR at a rate of 2 to 4 mm/yr, and exposure of a lithospheric section (Vema Lithospheric Section or VLS) at the northern edge of the slab, parallel to the Vema transform. Ages of pelagic carbonates encrusting ultramafic rocks sampled at the base of the VLS at different distances from the MAR axis suggest that the entire VTR rose vertically as a single block within the active transform offset. A 50 km long portion of the crest of the VTR rose above sea level, subsided, was truncated at sea level and covered by a carbonate platform. Subaerial and submarine erosion has gradually removed material from the top of the VTR and has modified its slopes. Spreading half rate of the crust south of the transform decreased from 17.2 mm/yr between 26 and 19 Ma to 16.9 mm/yr between 19 and 10 Ma, to 13.6 mm/yr from 10 Ma to present. The slowing down of spreading occurred close in time to the change in ridge/transform geometry, suggesting that the two events are related. A numerical model relates lithospheric flexure to extension normal to the transform, suggesting that the extent of the uplift depends on the thickness of the brittle layer, consistent with the observed greater uplift of the older lithosphere along the VTR.