Core-mantle Coupling Research Articles

Paul Harry Roberts. 13 September 1929—17 November 2022

Paul Roberts was a physicist and applied mathematician. He made important and often pioneering contributions in diverse research areas, but mainly with a fluid dynamic theme, which include rotating fluids, geophysical and astrophysical flows and superfluids. The cornerstone was magnetohydrodynamics with particular application to the geodynamo. His most notable achievement was the first three-dimensional self-consistent numerical geodynamo model, which built on the equations he had derived previously governing the Earth's core dynamics. His considerations included the role of thermal and compositional convection, and the inner core boundary layer (a mixed phase region). In addition to his remarkable illustration of magnetic field reversals, he applied his model to core–mantle coupling and variations in the length of the day. Paul investigated superfluid liquid helium on two fronts. He had a lifelong interest in Bose–Einstein condensates on the microscale governed by the nonlinear Schrodinger equation. His early work on the robust derivation of the mean-field Hall–Vinen–Bekharevic–Khalatnikov equations was far ahead of its time. Their importance and relevance was not appreciated until much later.

Secular changes in length of day: Effect of the mass redistribution

In this paper the secular change in the length of day due to mass redistribution effects is revisited using the Hamiltonian formalism of the Earth rotation theories. The framework is a two-layer deformable Earth model including dissipative effects at the core–mantle boundary, which are described through a coupling torque formulated by means of generalized forces. The theoretical development leads to the introduction of an effective time-averaged polar inertia moment, which allows us to quantify the level of core–mantle coupling throughout the secular evolution of the Earth. Taking advantage of the canonical procedure, we obtain a closed analytical formula for the secular deceleration of the rotation rate, numerical evaluation of which is performed using frequency-dependent Love numbers corresponding to solid and oceanic tides. With this Earth modeling, under the widespread assumption of totally coupled core and mantle layers in the long term response, a secular angular acceleration of − 1328.6′′ cy−2 is obtained, which is equivalent to an increase of 2.418 ms cy−1 in the length of day. The ocean tides and the semidiurnal band of the mass-redistribution-perturbing potential, mostly induced by the Moon, constitute the main part of this deceleration. This estimate is shown to be in very good agreement with recent observational values, and with other theoretical predictions including comparable modeling features.

Research on the scatter features of the PKiKP/PcP amplitude ratio and the inner core boundary density contrasts beneath Northeast Asia

Quantifying the density contrasts of the Earth’s inner core boundary (ICB) is crucial to understand core-mantle coupling and the generation of the geodynamo. The PKiKP/PcP amplitude ratio is commonly used to obtain the density contrast at the ICB, but its applications are limited by scattered observed data. In this study, we selected the PKiKP and PcP phases reflected at the same region of inner-core and core-mantle boundaries beneath Northeast Asia from different earthquakes for the first time, and the observations suggested that the PKiKP/PcP amplitude ratio is widely scattered. We also compared the PKiKP and PcP amplitudes, which demonstrated that the scatter cannot be attributed only to ICB anomalies but might also arise from raypath differences and heterogeneities throughout the crust and mantle. By fitting the observed PKiKP/PcP amplitude ratio, we obtained a density contrast of approximately 0.65 g cm−3 and a compressional velocity contrast of approximately 0.87 km s−1 at the ICB beneath Northeast Asia. The larger contrast values indicate the possible occurrence of local crystallization occurring at the inner core surface.

Analysis of Ocean Bottom Pressure Anomalies and Seismic Activities in the MedRidge Zone

The Mediterranean Ridge accretionary complex (MAC) is a product of the convergence of Africa–Europe–Aegean plates. As a result, the region exhibits a continuous mass change (horizontal/vertical movements) that generates earthquakes. Over the last 50 years, approximately 430 earthquakes with M ≥ 5, including 36 M ≥ 6 earthquakes, have been recorded in the region. This study aims to link the ocean bottom deformations manifested through ocean bottom pressure variations with the earthquakes’ time series. To this end, we investigated the time series of the ocean bottom pressure (OBP) anomalies derived from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On (GRACE-FO) satellite missions. The OBP time series comprises a decreasing trend in addition to 1.02, 1.52, 4.27, and 10.66-year periodic components, which can be explained by atmosphere, oceans, and hydrosphere (AOH) processes, the Earth’s pole movement, solar activity, and core–mantle coupling. It can be inferred from the results that the OBP anomalies time series/mass change is linked to a rising trend and periods in the earthquakes’ energy time series. Based on this preliminary work, ocean-bottom pressure variation appears to be a promising lead for further research.

Relationship between free core nutation and geomagnetic jerks

Recent studies have indicated a correlation between Earth’s free core nutation (FCN) and geomagnetic jerks (GMJs). However, some uncertainties still need to be resolved before their relationship can be confirmed. The variations in the amplitude and phase of the FCN result from the comprehensive influence of the surface fluid layer and core–mantle couplings, which makes its correlation with GMJs difficult to verify. The FCN period mainly depends on the inertia coupling and the dissipative couplings (such as viscous, electromagnetic and topographic couplings) at the core–mantle boundary according to the theory of Earth rotation. Whatever the GMJ mechanism, it is most likely to affect the FCN by changing the core–mantle couplings. This study was conducted to effectively determine variations in the FCN period by considering atmospheric and oceanic effects, investigate any correlation between the two phenomena, and analyze how the FCN relates to GMJs. Using the normal time–frequency transform, we extracted signals in the nutation band from the atmospheric and oceanic angular momentum functions. We used the broadband Liouville equations to estimate the atmospheric and oceanic effects on nutation terms. Using a sliding window of 2 years, we fitted five nutation terms most affected by FCN resonance from the celestial pole offsets with FCN model removed. The FCN period variation was estimated by using weighted least square method. The results indicated a correlation between the FCN and GMJ. Further, we analyzed the relationship between the geomagnetic fluctuations and FCN based on both the core–mantle couplings and the possible GMJ mechanism.

Reassessment of electromagnetic core-mantle coupling and its implications to the Earth's decadal polar motion

The observed Earth's polar motion on decadal time scales has long been conjectured to be excited by the exchange of equatorial angular momentum between the solid mantle and the fluid outer core, via the mechanism of electromagnetic (EM) core-mantle coupling. However, past estimations of the EM coupling torque from surface geomagnetic observations is too weak to account for the observed decadal polar motion. Our recent estimations from numerical geodynamo simulations have shown the opposite. In this paper, we re-examine in detail the EM coupling mechanism and the properties of the magnetic field in the electrically conducting lower mantle (characterized by a thin D″-layer at the base of the mantle). Our simulations find that the toroidal field in the D″-layer from the induction and convection of the toroidal field in the outer core could be potentially much stronger than that from the advection of the poloidal field in the outer core. The former, however, cannot be inferred from geomagnetic observations at the Earth's surface, and is missing in previous EM torque estimated from geomagnetic observations. Our deduction suggests further that this field could make the actual EM coupling torque sufficiently strong, at approximately 5 × 1019 Nm, to excite, and hence explain, the decadal polar motion to magnitude of approximately 10 mas.

Mantle-induced temperature anomalies do not reach the inner core boundary

SUMMARY Temperature anomalies in Earth’s liquid core reflect the vigour of convection and the nature and extent of thermal core–mantle coupling. Numerical simulations suggest that longitudinal temperature anomalies forced by lateral heat flow variations at the core–mantle boundary (CMB) can greatly exceed the anomalies that arise in homogeneous convection (i.e. with no boundary forcing) and may even penetrate all the way to the inner core boundary. However, it is not clear whether these simulations access the relevant regime for convection in Earth’s core, which is characterized by rapid rotation (low Ekman number E) and strong driving (high Rayleigh number Ra). We access this regime using numerical simulations of non-magnetic rotating convection with imposed heat flow variations at the outer boundary (OB) and investigate the amplitude and spatial pattern of thermal anomalies, focusing on the inner and outer boundaries. The 108 simulations cover the parameter range 10−4 ≤ E ≤ 10−6 and Ra = 1−800 times the critical value. At each Ra and E we consider two heat flow patterns—one derived from seismic tomography and the hemispheric $Y_1^1$ spherical harmonic pattern—with amplitudes measured by the parameter q⋆ = 2.3, 5 as well as the case of homogeneous convection. At the OB the forcing produces strong longitudinal temperature variations that peak in the equatorial region. Scaling relations suggest that the longitudinal variations are weakly dependent on E and Ra and are much stronger than in homogeneous convection, reaching O(1) K at core conditions if q⋆ ≈ 35. At the inner boundary, latitudinal and longitudinal temperature variations depend weakly on Ra and q⋆ and decrease strongly with E, becoming practically indistinguishable between homogeneous and heterogeneous cases at E = 10−6. Interpreted at core conditions our results suggest that heat flow variations on the CMB are unlikely to explain the large-scale variations observed by seismology at the top of the inner core.

Enhanced Core-Mantle Coupling Due to Stratification at the Top of the Core

Fluctuations in the length of day (LOD) over periods of several decades are commonly attributed to exchanges of angular momentum between the mantle and the core. However, the forces that enable this exchange are less certain. Suggestions include the influence of pressure on boundary topography, electromagnetic forces associated with conducting material in the boundary region and gravitational forces due to mass anomalies in the mantle and the core. Each of these suggestions has strengths and weaknesses. Here we propose a new coupling mechanism that relies on the presence of stable stratification at the top of the core. Steady flow of the core over boundary topography promotes radial motion, but buoyancy forces due to stratification oppose this motion. Steep vertical gradients develop in the resulting fluid velocity, causing horizontal electromagnetic forces in the presence of a radial magnetic field. The associated pressure field exerts a net horizontal force on the boundary. We quantify this hybrid mechanism using a local Cartesian approximation of the core-mantle boundary and show that the resulting stresses are sufficient to account for the observed changes in LOD. A representative solution has \SI{52}{\meter} of topography with a wavelength of \SI{100}{\kilo\meter}. We specify the fluid stratification using a buoyancy frequency that is comparable to the rotation rate and adopt a radial magnetic field based on geodetic constraints. The average tangential stress is \SI{0.027}{\newton\per\meter\squared} for a background flow of $\bar{V}=\SI{0.5}{\milli\meter\per\second}$. Weak variations in the stress with velocity (i.e. $\bar V^{1/2})$ introduce nonlinearities into the angular momentum balance, which may generate diagnostic features in LOD observations.

Earth\u2019s Subdecadal Angular Momentum Balance from Deformation and Rotation Data

Length-of-Day (LOD) measurements represent variations in the angular momentum of the solid Earth (crust and mantle). There is a known ~6-year LOD signal suspected to be due to core-mantle coupling. If it is, then the core flow associated with the 6-year LOD signal may also deform the mantle, causing a 6-year signal in the deformation of the Earth’s surface. Stacking of Global Positioning System (GPS) data is found to contain a ~6-year radial deformation signal. We inverted the deformation signal for the outer core’s flow and equivalent angular momentum changes, finding good agreement with the LOD signal in some cases. These results support the idea of subdecadal core-mantle coupling, but are not robust. Interpretation of the results must also take into account methodological limitations. Gravitational field changes resulting from solid Earth deformation were also computed and found to be smaller than the errors in the currently available data.

Eclipses and the Earth’s Rotation

AbstractAnalysis of historical records of eclipses of the Sun and Moon between 720 BC and AD 1600 gives a measure of the time difference, TT − UT = ΔT. The first derivative in time along a smooth curve fitted to the values of Δ T measures the changes in the length of the day (lod). The average rate of change of the lod is found to be significantly less than that expected on the basis of tidal friction. Fluctuations on a time-scale of centuries to millennia are mainly attributed to the effects of post-glacial uplift and core-mantle coupling.

Mechanism of the interannual oscillation in length of day and its constraint on the electromagnetic coupling at the core–mantle boundary

A significant 6 yr oscillation exists in the length of day (LOD) on the interannual scales. There are mainly two models currently to explain this oscillation, i.e., mantle–inner core gravitational (MICG) coupling mode and the fast torsional waves within the fluid outer core. The former has been doubted, while the source of the excitation of the latter is not yet understood. Therefore, the mechanism of the 6 yr oscillation is still not clear. Here, by considering the mantle and inner core angular momentum, we investigate the MICG coupling mode and its natural period (T0). Given that the strength of gravitational core–mantle coupling (Γ¯) within a recently constrained range is quite weaker than that estimated previously, the mechanism of the 6 yr oscillation still can be attributed to MICG coupling mode (i.e., T0 equals to 6 yrs), but, we require the inertia moment of fluid within the tangent cylinder involved in the 6 yr oscillation to be smaller than 1.23×1035 kgm2. This interpretation can be used to constrain the electromagnetic (EM) coupling at the inner core boundary (ICB). In order to study quantitatively the constraints on the EM coupling at the core–mantle boundary (CMB) from the observed 6 yr oscillation with a quality factor Q (∼51.6), we further develop the mathematical expression between the Q value based on the observations and EM coupling at the CMB. According to the Γ¯ value from recent estimates and assuming that the 6 yr oscillation is in a free decay, we can obtain the radial magnetic field at the CMB is 0.52 mT∼0.62 mT when conductance at the CMB is 108 S.

Phase equilibria of a low S and C lunar core: Implications for an early lunar dynamo and physical state of the current core

Multiple lines of geochemical and geophysical evidence suggest the Moon has a small metallic core, yet the composition of the core is poorly constrained. The physical state of the core (now or in the past) depends on detailed knowledge of its composition, and unfortunately, there is little available data on relevant multicomponent systems (i.e., Fe–Ni–S–C) at lunar interior conditions. In particular, there is a dearth of phase equilibrium data to elucidate whether a specific core composition could help to explain an early lunar geodynamo and magnetic field intensities, or current solid inner core/liquid outer core states. We utilize geochemical information to estimate the Ni, S and C contents of the lunar core, and then carry out phase equilibria experiments on several possible core compositions at the pressure and temperature conditions relevant to the lunar interior. The first composition is 0.5 wt% S and 0.375 wt% C, based on S and C contents of Apollo glasses. A second composition contains 1 wt% each of S and C, and assumes that the lunar mantle experienced degassing of up to 50% of its S and C. Finally a third composition contains C as the dominant light element. Phase equilibrium experiments were completed at 1, 3 and 5 GPa, using piston cylinder and multi-anvil techniques. The first composition has a liquidus near 1550 °C and solidus near 1250 °C. The second composition has a narrower liquidus and solidus temperatures of 1400 and 1270 °C, respectively, while the third composition is molten down to 1150 °C. As the composition crystallizes, the residual liquid becomes enriched in S and C, but S enrichment is greater due to the incorporation of C (but not S) into solid metallic FeNi. Comparison of these results to thermal models for the Moon allow an evaluation of which composition is consistent with the geophysical data of an early dynamo and a currently solid inner and liquid outer core. Composition 1 has a high enough liquidus to start crystallizing early in lunar history (4.3 Ga), consistent with the possible core dynamo initiated by crystallization of a solid inner core. Composition 1 also stays partially molten throughout lunar history, and could easily explain the seismic data. Composition 2, on the other hand, can satisfy one or the other set of geophysical data, but not both and thus seems like a poor candidate for a lunar core composition. Composition 3 remains molten to temperatures that are lower than current estimates for the lunar core, thus ruling out the possibility of a C-rich (and S-poor) lunar core. The S- and C-poor core composition studied here (composition 1) is consistent with all available geochemical and geophysical data and provides a simple heat source and mechanism for a lunar core dynamo (core crystallization) that would obviate the need for other primary mechanisms such as impacts, core–mantle coupling, or unusual thermal histories.

Measurement of the Earth's rotation: 720 BC to AD 2015.

New compilations of records of ancient and medieval eclipses in the period 720 BC to AD 1600, and of lunar occultations of stars in AD 1600–2015, are analysed to investigate variations in the Earth’s rate of rotation. It is found that the rate of rotation departs from uniformity, such that the change in the length of the mean solar day (lod) increases at an average rate of +1.8 ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3 ms per century. Besides this linear change in the lod, there are fluctuations about this trend on time scales of decades to centuries. A power spectral density analysis of fluctuations in the range 2–30 years follows a power law with exponent −1.3, and there is evidence of increased power at a period of 6 years. There is some indication of an oscillation in the lod with a period of roughly 1500 years. Our measurements of the Earth’s rotation for the period 720 BC to AD 2015 set firm boundaries for future work on post-glacial rebound and core–mantle coupling which are invoked to explain the departures from tidal friction.

Short period ScP phase amplitude calculations for core–mantle boundary with intermediate scale topography

The core–mantle boundary (CMB) topography plays a key role in constraining geodynamic modeling and core–mantle coupling. It’s effective to resolve the intermediate lateral scale topography (hundreds of km) with short period core reflected seismic phases (ScP) due to their small Fresnel-zones at short epicentral distances (<3336km (30°)). We developed a method based on the ray theory and representation theorem to calculate short period ScP synthetics for intermediate lateral scale CMB topography. The CMB topography we introduced here is axisymmetric and specified with two parameters: H (height) and L (diameter, or lateral length scale). Our numerical computation shows that a bump (H>0) and dip (H<0) model would cause defocusing/weakening and focusing/amplifying effects on ScP amplitude. Moreover, the effect of frequency and combination of L and H are quantified with the amplification coefficients. Then we applied this method to estimate a possible CMB topography beneath northeastern Japan, and a CMB model with L=140km, H=1.2km overall matches the observed pattern of 2D PcP/ScP amplitude ratios. However, it is difficult to totally rule out other factors that may also affect PcP/ScP pattern because of limitation of ray-based algorithms we used here. A hybrid method combining ray theory and numerical method is promising for studying complicated 3D structure and CMB topography in the future.

What causes geomagnetic reversals?

Geomagnetic reversal is known as one of the most dramatic changes on Earth in that the north and south poles of the geomagnetic field switch their positions every 0.1–1 million years. Since Bernard Brunhes and Motonori Matuyama identified the geomagnetic reversal in the early 20th century, remarkable progress has been made on understanding the causes that drive the geomagnetic flip-flops through paleomagnetic investigations, space/ground-based observations and theoretical/numerical/laboratory experimental studies. However, based on our limited knowledge of the Earth’s deep interior, we are still unable to answer the title question clearly and definitely, but we do have found some clues that could help revealing the underlying mystery. The geomagnetic field is thought to be generated by the fluid convection in the Earth’s outer liquid core through magnetohydrodynamic process which is called the geodynamo. This hypothesis was initially proposed by Joseph Larmor in 1919 and now is widely accepted. In 1995, Gray A Glatzmaier and Paul H Roberts accomplished the first numerical self-consistent geodynamo model which maintained an Earth-like magnetic field and produced spontaneous magnetic reversals without special priori setup on fluid motion, magnetic field or boundary conditions. Later, the spontaneous geomagnetic reversals are repeated in many numerical simulations and laboratory experiments by other research groups, but the spontaneity of reversals remains sceptical because the conditions of simulations are far from those of the real Earth. Further studies have shown that heat flux variations across the core-mantle boundary induced by mantle convection or superplumes could control the frequency of geomagnetic reversals through thermal core-mantle coupling. The preference of virtual geomagnetic pole (VGP) paths during reversals for longitudinal bands associated with the subduction zones surrounding the Pacific Ocean supports the hypothesis that geomagnetic reversals are controlled by the thermal structure of the lower mantle. Moreover, the magnetic diffusion effects of the lower mantle can alter the structure of geomagnetic field and change the geodynamo process via magnetoelectric core-mantle coupling. Some studies suggested that the plate tectonics, the distribution asymmetry of the continental plates, and the growth rate of the inner core can also influence geomagnetic reversals. Even the super-rotation of the inner core or the Earth’s precession can be a candidate of driving the fluid motion in the outer core instead of thermal or compositional buoyancy force in the classical geodynamo theory and, consequently, affects geomagnetic reversals. This manuscript describes the temporal and spatial features of the geomagnetic field as well as the geodynamo theory, reviews the recent progress in the study of geomagnetic reversals. It points out that the answer to what causes geomagnetic reversals depends on our knowledge of the entire Earth and a comprehensive model that treats the Earth as a whole dynamic system with all relevant spheres taken into account.

Free core nutation: new large disturbance and connection evidence with geomagnetic jerks

Variations in free core nutation (FCN) are connected with various processes in the Earth's fluid core and core-mantle coupling, which are also largely responsible for the geomagnetic field variations, particularly the geomagnetic jerks (GMJs). A previous study (Malkin, 2013) revealed that the epochs of the observed extremes in the FCN amplitude and phase variations are close to the GMJ epochs. In this paper, a new evidence of this connection was found. The large FCN amplitude and phase disturbance occurred at the epoch close to the newly revealed GMJ 2011. This event occurred to be the second large change in the FCN amplitude and phase after the 1999 disturbance that is also associated with the GMJ 1999. Moreover, the long-time FCN phase drift had changed suddenly in 1998--1999, immediately before the GMJ 1999, and seemed to change again at the epoch immediately preceding the GMJ 2011. The FCN amplitude showed a general long-time decrease before GMJ 1999, and it subsequently grew until GMJ 2011, and then seemed to decrease again. A smaller FCN change can be observed at the epoch around 2013, which is also suspected as the GMJ epoch. The latter confirms the suggestion that a rapid change in the FCN amplitude and/or phase can be used as an evidence of the GMJ that is not clearly detected from the geomagnetic observations.

The strength of gravitational core-mantle coupling

Gravitational coupling between Earth's core and mantle has been proposed as an explanation for a 6 year variation in the length-of-day (ΔLOD) signal and plays a key role in the possible superrotation of the inner core. Explaining the observations requires that the strength of the coupling, Γ, falls within fairly restrictive bounds; however, the value of Γ is highly uncertain because it depends on the distribution of mass anomalies in the mantle. We estimate Γ from a broad range of viscous mantle flow models with density anomalies inferred from seismic tomography. Requiring models to give a correlation larger than 70% to the surface geoid and match the dynamic core-mantle boundary ellipticity inferred from Earth's nutations, we find that 3 × 10 19 < Γ < 2 × 10 20 N m, too small to explain the 6 year ΔLOD signal. This new constraint on Γ has important implications for core-mantle angular momentum transfer and on the preferred mode of inner core convection.

Effect of core–mantle and tidal torques on Mercury’s spin axis orientation

The rotational evolution of Mercury’s mantle plus crust and its core under conservative and dissipative torques is important for understanding the planet’s spin state. Dissipation results from tidal torques and viscous, magnetic, and topographic torques contributed by interactions between the liquid core and solid mantle. For a spherically symmetric core–mantle boundary (CMB), the system goes to an equilibrium state wherein the spin axes of the mantle and core are fixed in the frame precessing with the orbit, and in which the mantle and core are differentially rotating. This equilibrium exhibits a mantle spin axis that is offset from the Cassini state by larger amounts for weaker core–mantle coupling for all three dissipative core–mantle coupling mechanisms, and the spin axis of the core is separated farther from that of the mantle, leading to larger differential rotation. Relatively strong core–mantle coupling is necessary to bring the mantle spin axis to a position within the uncertainty in its observed position, which is close to the Cassini state defined for a completely solid Mercury. Strong core–mantle coupling means that Mercury’s response is closer to that of a solid planet. Measured or inferred values of parameters in all three core–mantle coupling mechanisms for a spherically symmetric CMB appear not to accomplish this requirement. For a hydrostatic ellipsoidal CMB, pressure coupling dominates the dissipative effects on the mantle and core positions, and dissipation with pressure coupling brings the mantle spin solidly to the Cassini state. The core spin goes to a position displaced from that of the mantle by about 3.55arcmin nearly in the plane containing the Cassini state. The core spin lags the precessing plane containing the Cassini state by an increasing angle as the core viscosity is increased. With the maximum viscosity considered of ν∼15.0cm2/s if the coupling is by the circulation through an Ekman boundary layer or ν∼8.75×105cm2/s for purely viscous coupling, the core spin lags the precessing Cassini plane by 23arcsec, whereas the mantle spin lags by only 0.055arcsec. Larger, non-hydrostatic values of the CMB ellipticity also result in the mantle spin at the Cassini state, but the core spin is moved closer to the mantle spin. Current measurement uncertainties preclude using the mantle offset to constrain the internal core viscosity.

The interior structure of Mercury constrained by the low-degree gravity field and the rotation of Mercury

Among all the planets of the solar system Mercury stands out, because it has a relatively high average density compared to its size. To account for this high density, Mercuryʼs core radius is thought to be larger than 34 of its radius. Here, we use recent data about the second-degree gravity field coefficients and measurements about Mercuryʼs rotation – obliquity and 88-day libration amplitude – to obtain constraints on Mercuryʼs interior structure. By combining the gravity field data and the obliquity measurements, the mean moment of inertia of Mercury can be determined. If the coupling between the core and the mantle is neglected then the gravity field data together with the libration amplitude provide an estimate of Mercuryʼs silicate shell moment of inertia. However, since the effect of core–mantle coupling on the 88-day libration amplitude can be about as large as the libration amplitudeʼs uncertainty (Van Hoolst et al., 2012) we use as data the mean moment of inertia and the 88-day libration amplitude to infer knowledge about Mercuryʼs interior structure.We use two different interior modeling approaches. The first one is based on Rivoldini et al. (2009) and uses a set of 5 mantle mineralogies, a crust with a given thickness and density, and two mantle temperatures. In the second setting the density of the mantle, the thickness, and density of the crust, and the temperature of the core mantle boundary are parameters of the model. In both cases, we assume that the core is made of iron and the light element sulfur and use the temperature, pressure, and the concentration of sulfur in the core together with the melting temperature of iron–sulfur to determine the radius of the inner core.Our results show that the data provide a strong constraint on the radius of the core and on its average density or equivalently on the fraction of sulfur in the core if sulfur is the only light element in the core. We find that Mercury has a core radius of 2004±39 km, an average core density of 7233±267 kg/m3, and a sulfur fraction of 4.5±1.8 wt%. The other parameters of the model, in particular the density of the mantle are however, only weakly constrained by the data. The geodesy data can also not distinguish between a fully liquid core and the existence of an inner core.

A Test of Recent Inferences of Net Polar Ice Mass Balance based on Long-Wavelength Gravity

Abstract A comprehensive analysis of satellite datasets has estimated that the ice sheets of Greenland, West Antarctica, the Antarctic Peninsula, and East Antarctica experienced a net mass loss of −100 ± 92 Gt yr−1 over the period 1992–2000 and −298 ± 58 Gt yr−1 over the period 2000–11, representing an increase of −198 ± 109 Gt yr−1 between the two epochs. The authors demonstrate that the time rate of change of the degree-four zonal harmonic of Earth's gravitational potential provides an independent check on these mass balances that is less sensitive to uncertainties that have contaminated previous analyses of the degree-2 zonal harmonic [e.g., due to ongoing glacial isostatic adjustment (GIA), solid Earth body tides, and core–mantle coupling]. For the period 2000–11, the signal implied by the ice sheet mass flux cited above is (3.8 ± 0.6) × 10−11 yr−1, whereas the change in the harmonic across the two epochs is (2.3 ± 1.1) × 10−11 yr−1. In comparison, using satellite laser ranging (SLR) data, the authors estimate a GIA-corrected value of (3.8 ± 0.6) × 10−11 yr−1 for the epoch 2000–11 and a change across the two epochs of (5.3 ± 1.6) × 10−11 yr−1. The authors conclude that the former supports recent estimates of melting over the last decade, whereas the latter suggests either that estimated melt rates for the earlier epoch were too high or that the uncertainty associated with the SLR-based inference of during the earlier epoch is underestimated.