Multidisciplinary Constraints on the Thermal-Chemical Boundary Between Earth's Core and Mantle

Abstract: Heat flux from the core to the mantle provides driving energy for mantle convection thus powering plate tectonics, and contributes a significant fraction of the geothermal heat budget. Indirect estimates of core‐mantle boundary heat flow are typically based on petrological evidence of mantle temperature, interpretations of temperatures indicated by seismic travel times, experimental measurements of mineral melting points, physical mantle convection models, or physical core convection models. However, previous estimates have not consistently integrated these lines of evidence. In this work, an interdisciplinary analysis is applied to co‐constrain core‐mantle boundary heat flow and test the thermal boundary layer (TBL) theory. The concurrence of TBL models, energy balance to support geomagnetism, seismology, and review of petrologic evidence for historic mantle temperatures supports QCMB ∼15 TW, with all except geomagnetism supporting as high as ∼20 TW. These values provide a tighter constraint on core heat flux relative to previous work. Our work describes the seismic properties consistent with a TBL, and supports a long‐lived basal mantle molten layer through much of Earth's history

Thermal and electrical conductivity of iron at Earth's core conditions

The Earth acts as a gigantic heat engine driven by decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes, and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing to grow the solid inner core, and on chemical convection due to light elements expelled from the liquid on freezing. The power supplied to the geodynamo, measured by the heat-flux across the core-mantle boundary (CMB), places constraints on Earth's evolution. Estimates of CMB heat-flux depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent difficulties in experimentation and theory. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles- the first directly computed values that do not rely on estimates based on extrapolations. The mixtures of Fe, O, S, and Si are taken from earlier work and fit the seismologically-determined core density and inner-core boundary density jump. We find both conductivities to be 2-3 times higher than estimates in current use. The changes are so large that core thermal histories and power requirements must be reassessed. New estimates of adiabatic heat-flux give 15-16 TW at the CMB, higher than present estimates of CMB heat-flux based on mantle convection; the top of the core must be thermally stratified and any convection in the upper core driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted and future models of mantle evolution must incorporate a high CMB heat-flux and explain recent formation of the inner core.Comment: 11 pages including supplementary information, two figures. Scheduled to appear in Nature, April 201

Elasticity of iron at the temperature of the Earth's inner core

Seismological body-wave(1) and free-oscillation(2) studies of the Earth's solid inner core have revealed that compressional waves traverse the inner core faster along near-polar paths than in the equatorial plane. Studies have also documented local deviations from this first-order pattern of anisotropy on length scales ranging from 1 to 1,000 km (refs 3, 4). These observations, together with reports of the differential rotation(5) of the inner core, have generated considerable interest in the physical state and dynamics of the inner core, and in the structure and elasticity of its main constituent, iron, at appropriate conditions of pressure and temperature. Here we report first-principles calculations of the structure and elasticity of dense hexagonal close-packed (h.c.p.) iron at high temperatures. We find that the axial ratio c/a of h.c.p. iron increases substantially with increasing temperature, reaching a value of nearly 1.7 at a temperature of 5,700 K, where aggregate bulk and shear moduli match those of the inner core. As a consequence of the increasing c/a ratio, we have found that the single-crystal longitudinal anisotropy of h.c.p. iron at high temperature has the opposite sense from that at low temperature(6,7). By combining our results with a simple model of polycrystalline texture in the inner core, in which basal planes are partially aligned with the rotation axis, we can account for seismological observations of inner-core anisotropy.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62959/1/413057a0.pd

Performance benchmarks for a next generation numerical dynamo model

Numerical simulations of the geodynamo have successfully represented many observable characteristics of the geomagnetic field, yielding insight into the fundamental processes that generate magnetic fields in the Earth's core. Because of limited spatial resolution, however, the diffusivities in numerical dynamo models are much larger than those in the Earth's core, and consequently, questions remain about how realistic these models are. The typical strategy used to address this issue has been to continue to increase the resolution of these quasi-laminar models with increasing computational resources, thus pushing them toward more realistic parameter regimes. We assess which methods are most promising for the next generation of supercomputers, which will offer access to O(106) processor cores for large problems. Here we report performance and accuracy benchmarks from 15 dynamo codes that employ a range of numerical and parallelization methods. Computational performance is assessed on the basis of weak and strong scaling behavior up to 16,384 processor cores. Extrapolations of our weak-scaling results indicate that dynamo codes that employ two-dimensional or three-dimensional domain decompositions can perform efficiently on up to ∼106 processor cores, paving the way for more realistic simulations in the next model generation

Probabilistic structure of the geodynamo

One of the most intriguing features of Earth's axial magnetic dipole field, well known from the geological record, is its occasional and unpredictable reversal of polarity. Understanding the phenomenon is rendered very difficult by the highly nonlinear nature of the underlying magnetohydrodynamic problem. Numerical simulations of the liquid outer core, where regeneration occurs, are only able to model conditions that are far from Earth-like. On the analytical front, the situation is not much better; basic calculations, such as relating the average rate of reversals to various core parameters, have apparently been intractable. Here, we present a framework for solving such problems. Starting with the magnetic induction equation, we show that by considering its sources to be stochastic processes with fairly general properties, we can derive a differential equation for the joint probability distribution of the dominant toroidal and poloidal modes. This can be simplified to a Fokker-Planck equation and, with the help of an adiabatic approximation, reduced even further to an equation for the dipole amplitude alone. From these equations various quantities related to the magnetic field, including the average reversal rate, field strength, and time to complete a reversal, can be computed as functions of a small number of numerical parameters. These parameters in turn can be computed from physical considerations or constrained by paleomagnetic, numerical, and experimental data

Probabilistic structure of the geodynamo

One of the most intriguing features of Earth's axial magnetic dipole field, well known from the geological record, is its occasional and unpredictable reversal of polarity. Understanding the phenomenon is rendered very difficult by the highly nonlinear nature of the underlying magnetohydrodynamic problem. Numerical simulations of the liquid outer core, where regeneration occurs, are only able to model conditions that are far from Earth-like. On the analytical front, the situation is not much better; basic calculations, such as relating the average rate of reversals to various core parameters, have apparently been intractable. Here, we present a framework for solving such problems. Starting with the magnetic induction equation, we show that by considering its sources to be stochastic processes with fairly general properties, we can derive a differential equation for the joint probability distribution of the dominant toroidal and poloidal modes. This can be simplified to a Fokker-Planck equation and, with the help of an adiabatic approximation, reduced even further to an equation for the dipole amplitude alone. From these equations various quantities related to the magnetic field, including the average reversal rate, field strength, and time to complete a reversal, can be computed as functions of a small number of numerical parameters. These parameters in turn can be computed from physical considerations or constrained by paleomagnetic, numerical, and experimental data

A physical interpretation of stochastic models for fluctuations in the Earth's dipole field

Several recent studies have used palaeomagnetic estimates of the virtual axial dipole moment to construct a quantitative stochastic model for fluctuations and reversals in the Earth's dipole field. We investigate the physical significance of the terms in a standard stochastic (Langevin) model using output from a numerical geodynamo model. The first term, known as the drift term, characterizes the slow adjustment of the dipole field toward a time-averaged state. We find that the timescale for this slow adjustment is set by the magnetic decay time of dipole fluctuations. These fluctuations are typically be represented by the first few decay modes. The second term is often called the noise term because it characterizes the influence of short-period convective fluctuations in the core. We establish a connection between the noise term and the rms variation in magnetic induction. Applying these results to the palaeomagnetic field suggests that the rms variation in dipole generation exceeds the mean rate of generation. Such large fluctuations may be necessary to permit magnetic reversals. Palaeomagnetic estimates of the drift term favour a high electrical conductivity in the core. A lower bound on electrical conductivity is 0.6 × 106 S m-1. Similarly, we establish an upper bound on turbulent magnetic diffusivity (0.8 m2 s-1), although realistic estimates may be much less. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society