SUMMARY
We describe best-fitting angular velocities and MORVEL, a new closure-enforced set of angular velocities for the geologically current motions of 25 tectonic plates that collectively occupy 97 per cent of Earth's surface. Seafloor spreading rates and fault azimuths are used to determine the motions of 19 plates bordered by mid-ocean ridges, including all the major plates. Six smaller plates with little or no connection to the mid-ocean ridges are linked to MORVEL with GPS station velocities and azimuthal data. By design, almost no kinematic information is exchanged between the geologically determined and geodetically constrained subsets of the global circuit—MORVEL thus averages motion over geological intervals for all the major plates. Plate geometry changes relative to NUVEL-1A include the incorporation of Nubia, Lwandle and Somalia plates for the former Africa plate, Capricorn, Australia and Macquarie plates for the former Australia plate, and Sur and South America plates for the former South America plate. MORVEL also includes Amur, Philippine Sea, Sundaland and Yangtze plates, making it more useful than NUVEL-1A for studies of deformation in Asia and the western Pacific. Seafloor spreading rates are estimated over the past 0.78 Myr for intermediate and fast spreading centres and since 3.16 Ma for slow and ultraslow spreading centres. Rates are adjusted downward by 0.6–2.6 mm yr−1 to compensate for the several kilometre width of magnetic reversal zones. Nearly all the NUVEL-1A angular velocities differ significantly from the MORVEL angular velocities. The many new data, revised plate geometries, and correction for outward displacement thus significantly modify our knowledge of geologically current plate motions. MORVEL indicates significantly slower 0.78-Myr-average motion across the Nazca–Antarctic and Nazca–Pacific boundaries than does NUVEL-1A, consistent with a progressive slowdown in the eastward component of Nazca plate motion since 3.16 Ma. It also indicates that motions across the Caribbean–North America and Caribbean–South America plate boundaries are twice as fast as given by NUVEL-1A. Summed, least-squares differences between angular velocities estimated from GPS and those for MORVEL, NUVEL-1 and NUVEL-1A are, respectively, 260 per cent larger for NUVEL-1 and 50 per cent larger for NUVEL-1A than for MORVEL, suggesting that MORVEL more accurately describes historically current plate motions. Significant differences between geological and GPS estimates of Nazca plate motion and Arabia–Eurasia and India–Eurasia motion are reduced but not eliminated when using MORVEL instead of NUVEL-1A, possibly indicating that changes have occurred in those plate motions since 3.16 Ma. The MORVEL and GPS estimates of Pacific–North America plate motion in western North America differ by only 2.6 ± 1.7 mm yr−1, ≈25 per cent smaller than for NUVEL-1A. The remaining difference for this plate pair, assuming there are no unrecognized systematic errors and no measurable change in Pacific–North America motion over the past 1–3 Myr, indicates deformation of one or more plates in the global circuit. Tests for closure of six three-plate circuits indicate that two, Pacific–Cocos–Nazca and Sur–Nubia–Antarctic, fail closure, with respective linear velocities of non-closure of 14 ± 5 and 3 ± 1 mm yr−1 (95 per cent confidence limits) at their triple junctions. We conclude that the rigid plate approximation continues to be tremendously useful, but—absent any unrecognized systematic errors—the plates deform measurably, possibly by thermal contraction and wide plate boundaries with deformation rates near or beneath the level of noise in plate kinematic data.

Geologically current plate motions

Tropical peatlands are one of the largest near-surface reserves of terrestrial organic carbon, and hence their stability has important implications for climate change1,2,3. In their natural state, lowland tropical peatlands support a luxuriant growth of peat swamp forest overlying peat deposits up to 20 metres thick4,5. Persistent environmental change—in particular, drainage and forest clearing—threatens their stability2, and makes them susceptible to fire6. This was demonstrated by the occurrence of widespread fires throughout the forested peatlands of Indonesia7,8,9,10 during the 1997 El Nino event. Here, using satellite images of a 2.5 million hectare study area in Central Kalimantan, Borneo, from before and after the 1997 fires, we calculate that 32% (0.79 Mha) of the area had burned, of which peatland accounted for 91.5% (0.73 Mha). Using ground measurements of the burn depth of peat, we estimate that 0.19–0.23 gigatonnes (Gt) of carbon were released to the atmosphere through peat combustion, with a further 0.05 Gt released from burning of the overlying vegetation. Extrapolating these estimates to Indonesia as a whole, we estimate that between 0.81 and 2.57 Gt of carbon were released to the atmosphere in 1997 as a result of burning peat and vegetation in Indonesia. This is equivalent to 13–40% of the mean annual global carbon emissions from fossil fuels, and contributed greatly to the largest annual increase in atmospheric CO2 concentration detected since records began in 1957 (ref. 1).

The amount of carbon released from peat and forest fires in Indonesia during 1997

SUMMARY We study numerically an extensive set of dynamo models in rotating spherical shells, varying all relevant control parameters by at least two orders of magnitude. Convection is driven by a fixed temperature contrast between rigid boundaries. There are two distinct classes of solutions with strong and weak dipole contributions to the magnetic field, respectively. Non-dipolar dynamos are found when inertia plays a significant role in the force balance. In the dipolar regime the critical magnetic Reynolds number for self-sustained dynamos is of order 50, independent of the magnetic Prandtl number Pm. However, dynamos at low Pm exist only at sufficiently low Ekman number E. For dynamos in the dipolar regime we attempt to establish scaling laws that fit our numerical results. Assuming that diffusive effects do not play a primary role, we introduce non-dimensional parameters that are independent of any diffusivity. These are a modified Rayleigh number based on heat (or buoyancy) flux Ra ∗ , the Rossby number Ro measuring the flow velocity, the Lorentz number Lo measuring magnetic field strength, and a modified Nusselt number Nu ∗ for the advected heat flow. To first approximation, all our dynamo results can be collapsed into simple power-law dependencies on the modified Rayleigh number, with approximate exponents of 2/5, 1/2 and 1/3 for the Rossby number, modified Nusselt number and Lorentz number, respectively. Residual dependencies on the parameters related to diffusion (E, Pm, Prandtl number Pr) are weak. Our scaling laws are in agreement with the assumption that the magnetic field strength is controlled by the available power and not necessarily by a force balance. The Elsasser number � , which is the conventional measure for the ratio of Lorentz force to Coriolis force, is found to vary widely. We try to assess the relative importance of the various forces by studying sources and sinks of enstrophy (squared vorticity). In general Coriolis and buoyancy forces are of the same order, inertia and viscous forces make smaller and variable contributions, and the Lorentz force is highly variable. Ignoring a possible weak dependence on the Prandtl numbers or the Ekman number, a surprising prediction is that the magnetic field strength is independent both of conductivity and of rotation rate and is basically controlled by the buoyancy flux. Estimating the buoyancy flux in the Earth’s core using our Rossby number scaling and a typical velocity inferred from geomagnetic secular variations, we predict a small growth rate and old age of the inner core and obtain a reasonable magnetic field strength of order 1 mT inside the core. From the observed heat flow in Jupiter, we predict an internal field of 8 mT, in agreement with Jupiter’s external field being 10 times stronger than that of the Earth.

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Scaling properties of convection-driven dynamos in rotating spherical shells and application to planetary magnetic fields

The current state of understanding of the lunar interior is the sum of nearly four decades of work and a range of exploration programs spanning that same time period. Missions of the 1960s including the Rangers, Surveyors, and Lunar Orbiters, as well as Earth-based telescopic studies, laid the groundwork for the Apollo program and provided a basic understanding of the surface, its stratigraphy, and chronology. Through a combination of remote sensing, surface exploration, and sample return, the Apollo missions provided a general picture of the lunar interior and spawned the concept of the lunar magma ocean. In particular, the discovery of anorthite clasts in the returned samples led to the view that a large portion of the Moon was initially molten, and that crystallization of this magma ocean gave rise to mafic cumulates that make up the mantle, and plagioclase flotation cumulates that make up the crust (Smith et al. 1970; Wood et al. 1970). This model is now generally accepted and is the framework that unifies our knowledge of the structure and composition of the Moon. The intention of this chapter is to review the major advances that have been made over the past decade regarding the constitution of the Moon’s interior. Much of this new knowledge is a direct result of data acquired from the successful Clementine and Lunar Prospector missions, as well as the analysis of new lunar meteorites. As will be seen, results from these studies have led to many fundamental amendments to the magma ocean model.

Much of what we know from sample analyses has been previously summarized elsewhere, and only their most important aspects will be discussed in this chapter. The reader is referred to the relevant chapters in the books Basaltic Volcanism on the Terrestrial Planets (Basaltic Volcanism Study Project 1981), The …

The Constitution and Structure of the Lunar Interior

The Swarm mission was selected as the 5th mission in ESA’s Earth Explorer Programme in 2004. The mission will provide the best ever survey of the geomagnetic field and its temporal evolution that will lead to new insights into the Earth system by improving our understanding of the Earth’s interior and its effect on Geospace, the vast region around the Earth where electrodynamic processes are influenced by the Earth’s magnetic field. Scheduled for launch in 2010, the mission will comprise a constellation of three satellites, with two spacecraft flying sideby- side at lower altitude (450 km initial altitude), thereby measuring the East-West gradient of the magnetic field, and the third one flying at higher altitude (530 km). High-precision and high-resolution measurements of the strength, direction and variation of the magnetic field, complemented by precise navigation, accelerometer and electric field measurements, will provide the necessary observations that are required to separate and model the various sources of the geomagnetic field. This results in a unique “view” inside the Earth from space to study the composition and processes of its interior. It also allows analysing the Sun’s influence within the Earth system. In addition practical applications in many different areas, such as space weather, radiation hazards, navigation and resource management, will benefit from the Swarm concept.

/pdf/swarm-a-constellation-to-study-the-earth-s-magnetic-field-3iaqkjgwd2.pdf

Swarm: A constellation to study the Earth’s magnetic field

Although the Moon currently has no internally generated magnetic field, palaeomagnetic data, combined with radiometric ages of Apollo samples, provide evidence for such a magnetic field from ∼3.9 to 3.6 billion years (Gyr) ago1, possibly owing to an ancient lunar dynamo1,2. But the presence of a lunar dynamo during this time period is difficult to explain1,2,3,4, because thermal evolution models for the Moon5 yield insufficient core heat flux to power a dynamo after ∼4.2 Gyr ago. Here we show that a transient increase in core heat flux after an overturn of an initially stratified lunar mantle might explain the existence and timing of an early lunar dynamo. Using a three-dimensional spherical convection model6, we show that a dense layer, enriched in radioactive elements (a ‘thermal blanket’), at the base of the lunar mantle can initially prevent core cooling, thereby inhibiting core convection and magnetic field generation. Subsequent radioactive heating progressively increases the buoyancy of the thermal blanket, ultimately causing it to rise back into the mantle. The removal of the thermal blanket, proposed to explain the eruption of thorium- and titanium-rich lunar mare basalts7, plausibly results in a core heat flux sufficient to power a short-lived lunar dynamo.

https://www.eoas.ubc.ca/~mjelline/Papers%20PDFs/Stegman_2003.pdf

An early lunar core dynamo driven by thermochemical mantle convection

Geomagnetic jerks, which in the second half of the twentieth century occurred in 1969 (refs 1, 2), 1978 (refs 3, 4), 1991 (ref. 5) and 1999 (ref. 6), are abrupt changes in the second time-derivative (secular acceleration) of the Earth's magnetic field. Jerks separate periods of almost steady secular acceleration, so that the first time-derivative (secular variation) appears as a series of straight-line segments separated by geomagnetic jerks. The fact that they represent a reorganization of the secular variation implies that they are of internal origin (as has been established through spherical harmonic analysis7), and their short timescale implies that they are due to a change in the fluid flow at the surface of the Earth's core (as has also been established through mapping the time-varying flow at the core surface8). However, little is understood of their physical origin. Here we show that geomagnetic jerks can be explained by the combination of a steady flow and a simple time-varying, axisymmetric, equatorially symmetric, toroidal zonal flow. Such a flow is consistent with torsional oscillations in the Earth's core, which are simple oscillatory flows in the core that are expected on theoretical grounds9, and observed in both core flow models10 and numerical dynamo models11.

The origin of geomagnetic jerks

An estimate of the magnitude and geometry of the magnetic field within the Earth's core would be valuable for understanding the dynamics of the liquid outer core and for constraining numerical models of the geodynamo. The magnetic field down to the core–mantle boundary can be estimated from surface observations by assuming that the mantle is an insulator1, but such estimates cannot be further extrapolated into the conducting core itself. The magnetic field within the core has therefore remained largely unconstrained. Here we construct a simple picture of part of the magnetic field within the core by first showing that the fluid flow at the surface of the core is consistent with the presence of two large waves—‘torsional oscillations’ of the type that have been proposed to explain the temporal variation of the magnetic field at the core–mantle boundary. We then use the structure of these waves to calculate a one-dimensional map of the part of the magnetic field that points away from the rotation axis. These results may help distinguish between the different dynamic states proposed for outer-core flow2,3,4,5 and provide a test for recent numerical models of the geodynamo6,7,8,9.

Torsional oscillations and the magnetic field within the Earth's core

Summary

Some plates deform across zones that are many hundreds to thousands of kilometres wide, much broader than traditional boundaries such as mid-ocean ridges, deep-sea trenches and oceanic transform faults, across which most deformation is concentrated in a zone just a few kilometres wide. These wide zones of deformation, commonly referred to as diffuse plate boundaries, occur in both continental and oceanic lithosphere. Composite plates are composed of two or more rigid, or nearly rigid, component plates separated by one or more diffuse plate boundaries (Royer & Gordon 1997); such ‘complete’ diffuse boundaries are terminated at both ends by triple junctions (although there are other diffuse boundaries that transform into narrow boundaries). Here we consider the dynamics of complete diffuse oceanic plate boundaries by constructing simple analytical models on a flat earth and on a spherical earth assuming that the viscous force resisting deformation is described by either a linear Newtonian law or a high-exponent power law.



We investigate the observed tendency for the pole of relative motion between component plates separated by a diffuse plate boundary to lie within the diffuse boundary itself. We show that this tendency is due to geometrical effects that make it unlikely that the total torque acting between plates at a diffuse boundary could be oriented such that relative rotation occurs between the plates about a pole lying outside the boundary. This is demonstrated for both flat and spherical earth cases, assuming that resistance to strain along the diffuse boundary increases linearly with stress (Newtonian rheology). We further show that the pole of rotation is even more likely to lie in the diffuse plate boundary if the viscous force resisting deformation is described by a high-exponent power law rather than a Newtonian law.

/pdf/analytic-models-for-the-dynamics-of-diffuse-oceanic-plate-2n6d8z532l.pdf

Analytic models for the dynamics of diffuse oceanic plate boundaries

SUMMARY Recent work has shown that the zonal, equatorially symmetric, time-varying part of a model of the £ow at the surface of the Earth’s core can be well explained by only two standing waves, and that by making certain assumptions these waves may be inverted for rms Bs (the component of ¢eld pointing away from the rotation axis) and a quantity parametrizing friction or excitation (F) of the waves. Here, we discuss the two-wave ¢t, and describe the implications of models of rms Bs and friction/excitation for the dynamic state of the core, for the torque balance on axial cylinders, and for recent numerical simulations of the geodynamo.We ¢nd several possible explanations for why only two standing waves are needed to ¢t the data, including the possibility that it is due to the resolution of the core £ow model rather than conditions within the core itself.We ¢nd that the ¢ts of rms Bs and F suggest that the role of inertia should not be discounted in the core, and that care should be taken in constructing geodynamo simulations so that the eiective friction at the core^mantle boundarydoes not swamp the inertial term. A ratio of the magnitude of the two appears to be O(1) in the Earth’s core: we believe that, ideally, a numerical model of the Earth’s core should reproduce this result.

/pdf/on-the-dynamical-implications-of-models-of-bs-in-the-earth-s-25is7j3q2w.pdf

Stephen Zatman

Papers

An early lunar core dynamo driven by thermochemical mantle convection

The origin of geomagnetic jerks

Torsional oscillations and the magnetic field within the Earth's core

Analytic models for the dynamics of diffuse oceanic plate boundaries

On the dynamical implications of models of Bs in the Earth’s core