David E. Loper

The core‐mantle boundary region

The 75 year history of the American Geophysical Union has accompanied great advances in our understanding of the physics and chemistry of the transition zone between the Earths core and mantle. The core-mantle boundary (CMB) is the most significant internal boundary within our planet, buried at remote depths and probably forever hidden from direct observation; yet this region is very important to our understanding of the dynamic Earth system. The thermal and chemical processes operating near the CMB have intimate relationships to fundamental events in Earth history, such as core formation, and continue to play a major role in the planets evolution, influencing the magnetic field behavior, chemical cycling in the mantle, irregularities in the rotation and gravitation of the planet, and the mode of thermal convection of the Earth. The D″ region, comprising the lowermost 300 km of the mantle, is known to be highly heterogeneous in material properties on large and small scales, presumably due to thermal and chemical variations, while the outermost core is much more uniform. The substantial knowledge that we now have about this remote region is testimony to the remarkable progress made in geophysical remote sensing, prompted by prodigious increases in data, computational power, and experimental methodologies used to investigate deep earth structure and processes. In the past decade in particular there have been unprecedented multidisciplinary advances in understanding the CMB region, and there are excellent prospects for developing a comprehensive understanding of this region in the next few decades. Fundamental issues yet to be resolved include the causes of layering extensively observed in D″, whether or not downwelling slabs accumulate at the base of the mantle, whether plumes arise from the CMB region to feed hotspots at Earths surface, the extent of core-mantle chemical reactions, the relative importance of topographic versus electromagnetic coupling across the CMB, and the degree to which mantle structure influences the geomagnetic field and its reversals. This overview highlights the progress and future directions in geophysical investigations of the CMB region.

The thermal boundary-layer interpretation of D″ and its role as a plume source

The “anomalous” layer in the lowermost mantle, identified as D″ in the notation of K.E. Bullen, appears in the PREM Earth model as a 150 km-thick zone in which the gradient of incompressibility with pressure, dKdP, is almost 1.6, instead of 3.2 as in the overlying mantle. Since PREM shows no accompanying change in density or density gradient, we identify D″ as a thermal boundary layer and not as a chemically distinct zone. The anomaly in dKdP is related to the temperature gradient by the temperature dependence of Ks, for which we present a thermodynamic identity in terms of accessible quantities. This gives the numerical result (∂Ks/∂T)P=−1.6×107 Pa K−1 for D″ material. The corresponding temperature increment over the D″ range is 840 K. Such a layer cannot be a static feature, but must be maintained by a downward motion of the lower mantle toward the core-mantle boundary with a strong horizontal flow near the base of D″. Assuming a core heat flux of 1.6 × 1012 W, the downward speed is 0.07 mm y−1 and the temperature profile in D″, scaled to match PREM data, is approximately exponential with a scale height of 73 km. The inferred thermal conductivity is 1.2 W m−1 K−1. Using these values we develop a new analytical model of D″ which is dynamically and thermally consistent. In this model, the lower-mantle material is heated and softened as it moves down into D″ where the strong temperature dependence of viscosity concentrates the horizontal flow in a layer ∼ 12 km thick and similarly ensures its removal via narrow plumes.

The dynamical and thermal structure of deep mantle plumes

Abstract If the interpretation of the D″ layer at the base of the mantle as a thermal boundary layer, with a temperature increment in the order of 800 K, is correct, then the formation of deep-mantle plumes to vent material from it appears inevitable. We demonstrate quantitatively that the strong temperature dependence of viscosity guides the upward flow into long-lived chimneys that are ∼ 20 km in diameter near the base of the mantle and decrease in width with progressive upward softening and partial melting of plume material. The speed of flow up the axis of the plume is correspondingly fast; 1.6 m y −1 at the base and 4.8 m y −1 at 670 km depth. Thermal diffusive spreading of a heated plume is compensated by a slow horizontal convergence of mantle material toward the chimney in response to the lower pressure there. This convergence, which contributes only a small increment to the flux of material up the plume, also serves to throttle the flow in the chimney. The global plume mass flux necessary to transport 1.6 × 10 12 W of core heat upward through the mantle is 1.8 × 10 6 kg s −1 . At its base, plume material is probably still significantly below its solidus or eutectic temperature, but substantial partial melting is very likely as it rises. We speculate that a small fraction of this fluid component eventually emerges at the surface in “hot spots”, with the fate of the remainder being unknown. The behaviour and properties of D″ and of plumes are closely coupled. Not only are plumes a necessary consequence of a thermal boundary layer, but their existence is impossible without that layer.

A study of conditions at the inner core boundary of the earth

Abstract A study is made of the thermal and compositional conditions which the liquid outer core must satisfy at the inner core boundary, assuming the inner core to be growing by continual solidification of the heavy component of the liquid alloy in the outer core. It is found that the outer core is strongly destabilized by the compositional gradients driven by the separation process associated with the freezing. Further, it is argued that all the freezing necessary for the growth of the solid inner core cannot occur on a flat interface; most of it must occur above the solid boundary in a region labeled the slurry layer.

Thermal histories of the core and mantle

Recognition that the cooling of the core is accomplished by conduction of heat into a thermal boundary layer (D″) at the base of the mantle, partly decouples calculations of the thermal histories of the core and mantle. Both are controlled by the temperature-dependent rheology of the mantle, but in different ways. Thermal parameters of the Earth are more tightly constrained than hitherto by demanding that they satisfy both core and mantle histories. We require evolution from an early state, in which the temperatures of the top of the core and the base of the mantle were both very close to the mantle solidus, to the present state in which a temperature increment, estimated to be ∼ 800 K, has developed across D″. The thermal history is not very dependent upon the assumption of Newtonian or non-Newtonian mantle rheology. The thermal boundary layer at the base of the mantle (i.e., D″) developed within the first few hundred million years and the temperature increment across it is still increasing slowly. In our preferred model the present temperature at the top of the core is 3800 K and the mantle temperature, extrapolated to the core boundary without the thermal boundary layer, is 3000 K. The mantle solidus is 3860 K. These temperatures could be varied within quite wide limits without seriously affecting our conclusions. Core gravitational energy release is found to have been remarkably constant at ∼ 3 × 1011 W. nearly 20% of the core heat flux, for the past 3 × 109 y, although the total terrestrial heat flux has decreased by a factor of 2 or 3 in that time. This gravitational energy can power the “chemical” dynamo in spite of a core heat flux that is less than that required by conduction down an adiabatic gradient in the outer core; part of the gravitational energy is used to redistribute the excess heat back into the core, leaving 1.8 × 1011 W to drive the dynamo. At no time was the dynamo thermally driven and the present radioactive heating in the core is negligibly small. The dynamo can persist indefinitely into the future; available power 1010 y from now is estimated to be 0.3 × 1011 W if linear mantle rheology is assumed or more if mantle rheology is non-linear. The assumption that the gravitational constant decreases with time imposes an implausible rate of decrease in dynamo energy. With conventional thermodynamics it also requires radiogenic heating of the mantle considerably in excess of the likely content of radioactive elements.

On the motion of an iron-alloy core containing a slurry: I. general theory

Abstract Braginsky (1963) has suggested that the geodynamo is gravitationally powered through the settling downwards of the heavy iron-rich component in the fluid outer core to form a growing solid inner core. Supposing for simplicity that the core is a binary alloy, we examine implications of Braginskys idea and, in particular, discuss the importance of slurry layers in the fluid core. A thermodynamically acceptable theory for the motion of a slurry is developed, and approximations that make it tractable are discussed. The structure of a well-mixed slurry layer is elucidated. The theory is used to show how seismic waves traversing a slurry are damped and dispersed as a result of melting and re-freezing of the solid phase caused by the passage of the wave.

On the diffusive instability of some simple steady magnetohydrodynamic flows

The stability characteristics of some simple steady magnetohydrodynamic flows within an axisymmetric container of arbitrary electrical conductivity are investigated. Attention is focused upon rapidly rotating fluids in which the unperturbed velocity and magnetic field are axially symmetric and purely zonal. Detailed solutions are obtained for the particularly simple basic state representing a rigidly rotating homogeneous fluid with a uniform axial current. The theory of dynamic (dissipationless) instabilities is reviewed and its shortcomings are elucidated. A stability criterion is derived for an inviscid fluid of small electrical conductivity within a perfectly conducting axisymmetric container and it is shown that a certain class of inertial modes is unstable for any non-zero magnetic field strength. When the effects of container conductivity are included it is found that a class of slow modes with westward phase speed may be unstable. These modes are shown to be unstable within a cylinder but appear to be stable within a sphere. The influence of density gradients within a spherical container is investigated and it is found that for a certain class of exceptional slow modes with westward phase speed, a bottom-heavy density gradient is destabilizing. This surprising behaviour is explained in terms of a new branch of the stability curve developed by Eltayeb & Kumar (1977).

Structure of the inner core boundary

Abstract A model of the inner-core boundary (ICB) is constructed which is consistent with current ideas of the dynamic and thermodynamic state of the core and which is capable of reflecting seismic waves with period of one second. This requires the mass fraction of solid below the ICB to grow to an appreciable fraction in roughly one kilometer. This rapid growth of solid with depth is a result of downward fluid flow from the outer core which is a part of the convective motions which sustain the geodynamo. The solid which crystallizes from this descending fluid after it crosses the ICB continually coats the dendrites which occur there. The gradual cooling of the outer core causes the ICB to advance by growth of dendrites at their tips. The balance of these two effects gives an equilibrium profile for the mass fraction of solid with depth below the ICB which is capable of yielding sharp reflection of seismic waves.

On the stability of the D” layer

Abstract The steady solution for the flow in the D” layer given by Stacey and Loper (1983) is generalized and placed on a firmer mathematical foundation. The stability of this flow is then analyzed and a stability criterion is developed. It is found that the stability of the flow is consistent with a lower-mantle viscosity of 0.5–1.0 1023 Pas and a temperature jump of 700–800K across the layer, but if the viscosity is only 3–5 1021 Pas, stability of the flow requires a much lower temperature jump. If the higher value of viscosity is correct and the flow is believed to be close to marginally stable, this argues against a second thermal boundary layer occurring elsewhere in the mantle.

A Model of Correlated Episodicity in Magnetic-Field Reversals, Climate, and Mass Extinctions

Correlated periodicities of mass extinctions, climate, magnetic-field reversals, and other geological phenomena may best be explained by cycles of activity within the mantle and core. We propose that these cycles are due to variations in the thickness of the thermal boundary layer at the base of the mantle as the layer alternates between two phases of activity. In the quiescent phase little flow occurs and the layer thickens with time by thermal diffusion. The active phase begins when the thickening layer becomes dynamically unstable. Hot material erupts from the layer, causing it to become thinner. As the layer thins, the rate of energy supply to the geodynamo, and hence its reversal frequency, increases. The hot material rises to the surface, where it causes widespread basaltic volcanic eruptions. These eruptions release large amounts of