Displays

The composition of Earth's mantle, when compared to experimentally determined partitioning coefficients, can be used to constrain the conditions of equilibration - pressure P, temperature T, and oxygen fugacity fO₂ - of the metal and silicates during core-mantle differentiation.
This places constraints on the thermal state of the planet during its accretion, and it is tempting to try to use these data to estimate the heat content of the core at the end of accretion. To do so, we develop an analytical model of the thermal evolution of the metal phase during its descent through the solid mantle toward the growing core, taking into account compression heating,   viscous dissipation heating, and heat exchange with the surrounding silicates. For each impact, the model takes as initial condition the pressure and temperature at the base of the magma ocean, and gives the temperature of the metal when it reaches the core. The growth of the planet results in additional pressure increase and compression heating of the core. The thermal model is coupled to a Monte-Carlo inversion of the metal/silicates equilibration conditions (P, T, fO₂) in the course of accretion from the abundance of Ni, Co, V and Cr in the mantle, and provides an estimate of the core heat content at the end of accretion for each geochemically successful accretion. The core heat content depends on the mean degree of metal-silicates equilibration, on the mode of metal/silicates separation in the mantle (diapirism, percolation, or dyking), but also very significantly on the shape of the equilibration conditions curve (equilibration P and T vs. fraction of Earth accreted). We find that many accretion histories which are successful in reproducing the mantle composition yield a core that is colder than its current state. Imposing that the temperature of the core at the end of accretion is higher than its current values therefore provides strong constraints on the accretion history. In particular, we find that the core heat content depends significantly on the last stages of accretion. 

How to cite: Deguen, R. and Clési, V.: Linking the core heat content to Earth's accretion history, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10540, https://doi.org/10.5194/egusphere-egu2020-10540, 2020.

How to cite: Mandea, M., Dehant, V., and Cazenave, A.: GRACEFUL: Probing the deep Earth interior by synergistic use of observations of the magnetic and gravity fields, and of the rotation of the Earth, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13515, https://doi.org/10.5194/egusphere-egu2020-13515, 2020.

Radio signals from distant quasars allow us to determine Earth's rotation variations with exquisite accuracy. These observations can be used to estimate the amplitudes, frequencies and damping constants associated with Earth's rotational modes, particularly the Free Core Nutation (FCN) and the Free Inner Core Nutation (FICN). These estimates suggest, however, fluid core viscosities many orders of magnitude higher than expected, or rms magnetic fields at the core-mantle boundary (CMB) incompatible with downward continuation of the observed surface field. Aiming at resolve this difficulty, we have developed a proof-of-concept model where we incorporate an approximate fluid-dynamical treatment of the core flow associated with the FCN and the FICN. We show that, at least for the FCN, no abnormally high viscosities or magnetic fields are required. The model might provide in fact a robust, independent estimate of the rms magnetic field strength in the fluid core. Additionally, the model illustrates the importance of considering inter-mode resonances involving inertial modes (i.e. Coriolis-restored) and the rotational normal modes.

How to cite: Triana, S., Trinh, A., Rekier, J., and Dehant, V.: Ohmic dissipation induced by Earth's nutation, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11740, https://doi.org/10.5194/egusphere-egu2020-11740, 2020.

Earth’s core Physics inspires the magnetoconvection models. Turbulent state of the core can increase the viscosity, the thermal diffusivity and also the magnetic diffusivity. The change of magnetic diffusivity is also called β-effect and it is important in dynamo mechanisms. Moreover, the turbulence suggests that the dynamics can be more complicated than it is usually presented. For instance, due to turbulence the diffusivity coefficients could be anisotropic as it was described in some recent studies, which stress how anisotropy in many cases facilitate convection and in other cases inhibits it. For example, if there is anisotropy some types of convection can occur also with very small values of Ekman numbers, which are usual for the Earth’s core. This is important because the convection can be the main cause of dynamo action. We present several rotating magnetoconvection models in horizontal plane layer with gravity and rotation axis in vertical direction and homogeneous magnetic field in horizontal direction. Different models correspond to different cases of anisotropic diffusivities. In other words, we consider several anisotropic models: one with anisotropy in all diffusivities and other models with various combinations of anisotropic and isotropic diffusivities. Comparisons with other former models (e.g. with isotropic case, p-case, partial anisotropy case when only magnetic diffusivity is isotropic, and f-case, full anisotropy case with all diffusivities anisotropic) are thoroughly performed. In all models we consider two distinct kinds of anisotropy, Stratification Anisotropy – SA, determined by direction of single gravity (buoyancy) force and Braginsky-Meytlis one – BM, determined by directions of magnetic field and rotation axis. All systems described by these models are prone to instabilities, so analysis in term of normal modes and search for preferred modes are very useful to study such systems. We focus our attention on stationary modes and SA anisotropies. Furthermore, we distinguish two sub-cases of SA anisotropy: atmospheric – Sa, if the diffusion in the vertical direction is greater than in the horizontal ones and oceanic – So, if opposite holds. In Sa (So) anisotropy the convection is in major cases facilitated (inhibited). This fact suggests that it is important to study Sa as well as So anisotropies in the Earth’s core. Our main results concern cases of anisotropic diffusivities, when preferred modes give new dynamics (unexpected in isotropic case) in the system in which geodynamo can work. 

How to cite: Filippi, E. and Brestenský, J.: Anisotropic turbulent diffusivities and rotating magnetoconvection problems, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-875, https://doi.org/10.5194/egusphere-egu2020-875, 2020.

Nonlinear analysis in a rotating Rayleigh-Benard system of electrically conducting fluid is studied numerically in the presence of externally applied horizontal magnetic field with rigid-rigid boundary conditions [1, 2]. This DNS approach is carried near the onset of convection to study the flow behaviour in the limiting case of Prandtl number [2]. The flow topology is verified with respect to the Euler number. The fluid flow is visualized in terms of streamlines, limiting streamlines, isotherms and heatlines. The dependence of the Nusselt number on the Rayleigh number, Ekman number, Elsasser number is examined.

References:

[1] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, 1961, Oxford University Press, London.

[2] P.H. Roberts and C.A. Jones, The onset of magnetoconvection at large Prandtl number in a rotating layer I. Finite Magnetic Diffusion, Geophysical and Astrophysical Fluid Dynamics, 92, 289-325 (2000).

How to cite: Rani, H. P., Rameshwar, Y., Brestensky, J., and Filippi, E.: Nonlinear Convection of Electrically Conducting Fluid in a Rotating Magnetic System, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21322, https://doi.org/10.5194/egusphere-egu2020-21322, 2020.

The magnetohydrodynamics of Earth has been explored at the University of Maryland through experiments and numerical models. Experimentally, the interaction between Earth's magnetic fields and its outer core is replicated using a three-meter spherical Couette device filled with liquid sodium that is driven by two independently rotating concentric shells and a dipole magnetic field applied from external electromagnets. Currently, this experiment is being prepared for design modifications that aim to increase the helical flows in the poloidal direction in order to match the turbulence of convection-driven flows of Earth. The experiment currently has 33 hall probes measuring the magnetic field, 4 pressure probes, and torque measurements on each sphere. We supplement the experiment with a numerical model, XSHELLS, that uses pseudospectral and finite difference methods to give a full picture of the velocity and magnetic field in the liquid and stainless steel shells. However, its impracticable to resolve all the turbulence. Our ultimate goal is to implement data assimilation by synchronizing the experimental observations with the numerical model, in order to uncover the unmeasured velocity field in the experiment and the full magnetic field as well as to predict the magnetic fields of the experiment. Through numerical simulations (XSHELLS) and data analysis we probe the behavior of the experiment in order to (i) suggest the best locations for new measurements and (ii) find what parameters are most feasible for data assimilation. These computational studies provide insight on the dynamics of this experiment and the measurements required to predict Earth's magnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

How to cite: Burnett, S., Schaeffer, N., Ide, K., and Lathrop, D.: Exploring Alternative Instrumentation in the Three-Meter Spherical Couette Experiment, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-10723, https://doi.org/10.5194/egusphere-egu2020-10723, 2020.

We have studied theoretically the weakly nonlinear analysis in a rotating Rayleigh-Benard system of electrically conducting fluid in the presence of applied horizontal magnetic field with free-free boundary conditions [1]. This theoretical approach is carried near the onset of convection to study the flow behavior at the occurrence of cross rolls, which are perpendicular to the applied magnetic field. The nonlinear problem is solved by using the Fourier analysis of perturbations up to the O(ε⁸) to study the cross rolls visualization [2,3]. The dependence of the Nusselt number on the Rayleigh number, Ekman number, Elsasser number is extensively examined. The fluid flow is visualized in terms of kinetic energy, potential energy, streamlines, isotherms, and heatlines.

References :

[1] P. H. Roberts and C. A. Jones , The Onset of Magnetoconvection at Large Prandtl Number in a Rotating Layer I. Finite Magnetic Diffusion, Geophysical and Astrophysical Fluid Dynamics, Vol. 92, pp. 289-325 (2000).

[2] H.L. Kuo, Solution of the non-linear equations of the cellular convection and heat transport,  Journal of Fluid Mechanics,  Vol.10, pp.611-630 (1961).

[3] Y. Rameshwar, M. A. Rawoof Sayeed, H. P. Rani, D. Laroze, Finite amplitude cellular convection under the influence of a vertical magnetic field, International Journal of Heat and Mass Transfer, Vol. 114, pp.  559-577 (2017).

How to cite: Rameshwar, Y., Srinivas, G., Rani, H. P., Brestensky, J., and Filippi, E.: Convection of Electrically Conducting Fluid in a Rotating Magnetic System: Cross rolls, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-21632, https://doi.org/10.5194/egusphere-egu2020-21632, 2020.

The Earth is submitted to the gravitational effect of different objects,  resulting  in  small  variations  of  the  orientation  of  its  axis  rotation.   The  precession corresponds to the rotation of the body spin axis around the normal to the elliptic plane. The primary flow forced by precession in a sphere is mainly a tilted solid body rotation, a flow of uniform vorticity. In this study we focused on the pseudo-resonance between the precessional forcing  and  the  spin-over  mode,  detected  as  a  peak  of  amplitude  of  the  norm  of the  vorticity  of  the  fluid.   We  show  the  influences  of  both  the  geometry and the application of an uniform external magnetic field on the external boundary, onto this pseudo-resonance.  The major purpose is to validate a semi-analytical model to allow its interpolation to planetary bodies.  We compared the semi-analytical model [Noir and C ́ebron, 2013] with numerical simulations performed with XSHELLS [Schaeffer, 2013],  which give us the components of the fluid vorticity in a precessing frame. We compared also the spin-over mode coefficients, used to simulate the viscous  effect  on  the  model,  with  two  methods :  an  empirical  equation  and  the numerical solver Tintin [Triana et al., 2019], taking into account the solid inner-core size (η=RI/R).  The differential rotation between the flow and the container, obtained with the model and the XSHELLS simulations, show us a verygood agreement especially for a small Ekman number (E= 10^−5), thus the spin-over mode coefficients for small E and η≤0.5.  An increase of the inner-core size  implies  a  decrease  of  the  resonance  amplitude  caused  by  the  supplementary Ekman layer added at the Inner Core Boundary (ICB); nevertheless thecolatitude (αf) and the longitude (φf) of the fluid don’t change significantly.The  application  of  a  uniform  magnetic  field  at  the  CMB  implies  a  decrease of the resonance amplitude, but also a modification of the mean rotation axis direction.  Indeed, the coupling between the viscous flow and the magnetic field induces a modification of the αfand φf, which follow the main direction angle of the magnetic field axis.  We observe small discrepancies between the simulations (XSHELLS and Tintin) and the model but the behavior following different parameters (Po,α angle,Ro,η,β angle, Λ) is well understood.  As a result, we applied the models at few parameter ”realistic values” of planetary objects like terrestrial planets but also ice’s satellites.

References

[Noir and C ́ebron, 2013]  Noir,  J.  and  C ́ebron,  D.  (2013).    Precession-driven flows in non-axisymmetric ellipsoids.Journal of Fluid Mechanics, 737:412–439.

[Schaeffer, 2013]  Schaeffer, N. (2013).  Efficient spherical harmonic transforms aimed  at pseudospectral numerical  simulations.Geochemistry, Geophysics,Geosystems, 14(3):751–758.

[Triana et al., 2019]  Triana, S. A., Rekier, J., Trinh, A., and Dehant, V. (2019).The coupling between inertial and rotational eigenmodes in planets with liq-uid cores.Geophysical Journal International.

How to cite: Laguerre, R., Houliez, A., Cébron, D., and Dehant, V.: Steady flows in the core of precessing planets : effects of the geometry and an applied magnetic field. , EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-14058, https://doi.org/10.5194/egusphere-egu2020-14058, 2020.

Traditionally, searching the Slichter mode (the longest-period mode of the Earth's free oscillations ₁S₁) is based on the data of the superconducting gravimeters of the international GGP network. Currently this network is included in the International Geodynamics and Earth Tide Service (IGETS).

The sensitivity limit of the best superconducting gravimeters is about 1 nGal and not sufficient for direct observation of the Slichter mode even after the significant earthquakes. To reduce the detection threshold, the researchers used the “stacking” procedure — an joint data processing of the several instruments, but the different sensitivity level of the gravimeters prevents the achievement of maximum efficiency.

We have developed an asymptotically optimal algorithm based on the maximum likelihood method that takes into account the features of the Slichter mode and seismic noise. An important feature of the algorithm is its ability to evaluate the splitting parameter b which determines the distance between the side singlets of the triplet, simultaneously with the mode period T. The use of a non-linear inertial converter allows to take into account the non-Gaussian noise of real data. The use of the Neumann-Pearson criterion makes also possible to determine confidence level of detection: the false alarm probability and the correct detection probability, depending on the signal-to-noise ratio).

The algorithm was tested on synthetic data. A computer experiment has shown that the algorithm can detect the Slichter mode for a signal-to-noise ratio of 10^-4. The algorithm was used to search the Slichter mode after the largest earthquakes based on the data of the IGETS network.

The results of the analysis are reported.

This work is supported by the Russian Foundation for Basic Research under Grant No Grant No 19-05-00341.

How to cite: Milyukov, V., Vinogradov, M., Mironov, A., and Myasnikov, A.: Detection and estimation of the Slichter mode based on the data of the IGETS superconducting gravimeters network using the asymptotically optimal algorithm, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-11614, https://doi.org/10.5194/egusphere-egu2020-11614, 2020.

The release of latent heat and lighter materials during inner core solidification is the driving force of the liquid iron flow in the outer core which generates the Earth's magnetic field. It is well known that the behaviour of the magnetic field varies over long time scales. Two clearly identifiable regimes are recognized, (i) superchrons and (ii) periods of hyperactivity (Biggin et al. 2012). Superchrons are characterized by an exceptionally low reversal rate of the magnetic pole and are associated with a low core mantle boundary (CMB) heat flux. Hyperactive periods are defined by a high reversal rate and have a high CMB heat flux.

Here we investigate whether the occurrence of these two regimes is related to radial variations in inner core seismic structure. Using seismic body-wave observations of compressional PKIKP-waves (Irving & Deuss 2011, Waszek & Deuss 2011, Lythgoe et al. 2013)., we construct a model of inner core anisotropy by comparing the difference between travel times for polar and equatorial rays. Anisotropy is the directional dependence of wave velocity and is determined by the structure of iron crystals in the inner core, hence changes in seismic anisotropy are due to changes in inner core crystal texture. We invert for radial changes in anisotropy while allowing for lateral variations and find that a model of the inner core containing five layers best fits our data. The model contains an isotropic uppermost inner core and four deeper layers with varying degrees of anisotropy.

Texture differences of the inner core iron crystals have been linked to changes in the solidification process of the inner core (Bergman et al. 2005), i.e. the motor of outer core flow. Therefore, the observed anisotropy variation, caused by variations of inner core solidification, might be related to changes in the behaviour of the magnetic field. Using an inner core growth model (Buffett et al. 1996) we convert depth to time for a range of inner core nucleation ages between 3.0 and 0.5 Ga (Olsen 2016). We find a remarkable correlation between the solidification time of the seismically observed layers and the occurrence of the magnetic regimes for two inner core ages; one with a nucleation at 1.4 Ga and one at 0.6 Ga, corresponding to an average CMB heat flux of 7.6 TW and 16.7 TW respectively.

Although we currently cannot differentiate between these two inner core ages considering our results alone, they do show that a relation between inner core structure and the behaviour of the magnetic field is possible, and suggest that seismic observations of inner core structure might provide new and independent insights into the magnetic field and its history.

How to cite: de Jong, J., de Groot, L., and Deuss, A.: Observing the signature of the magnetic field's behaviour in the radial variation of inner core anisotropy, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-20504, https://doi.org/10.5194/egusphere-egu2020-20504, 2020.

Lateral variations in structure and composition with a scale length of about several kilometers are thought to be one of the reasons for strong seismic attenuation in the Earth’s solid inner core. These fine-scale heterogeneities are probably best constrained by scattered coda of body waves pre-critically reflected from the inner core boundary (PKiKP). Here we analyze 9 arrays of sources and receivers to detect weak PKiKP coda on short-period and broadband seismic records in the range of epicentral distances from 6 to 94 degrees. 6 PKiKP bounce points scan the IC surface below Central Asia, 2 – under the Arctic region, and one – under Southeastern Asia. We observe the IC scattered coda in the Hilbert envelope of the PKiKP beam built by linear summation of 1.3 – 5 Hz bandpass frequency filtered vertical records of array channels. Assuming the detected PKiKP codas result from scattering through the volume of the uppermost inner core, we estimate the Qc quality factor by fitting of the observed PKiKP codas with a standard model – the classical method invoked in crust and mantle studies. We find the quality factors are between 400 and 500 with no distinct geographical dependence.

How to cite: Krasnoshchekov, D.: Inner core scattering estimates inferred from PKiKP coda waves, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-13416, https://doi.org/10.5194/egusphere-egu2020-13416, 2020.

Determining the high pressure and temperature behavior of iron (Fe) provides valuable insight into the evolution and dynamics of the Earth’s core. Shock compression using lasers can achieve extreme pressure and temperature conditions simultaneously. The duration of the extreme conditions state is on the order of nanoseconds. This is a challenge for in situ measurements of the shocked material’s properties. In this work, we shock-compressed polycrystalline iron at the Matter in Extreme Conditions End Station at the Linac Coherent Light Source, SLAC National Accelerator Laboratory and performed in situ X-ray diffraction (XRD) measurements with sub-picosecond time resolution. The final aim of these experiments is the study of stress of texure in Fe under extreme conditions of pressure and temperature. The presentation will highlight the strategies for such experiment and data processing and present our premilinary results.

How to cite: Merkel, S., Hok, S., Bolme, C., Gleason, A., and Mao, W.: Understanding strength and texture in Fe at planetary core pressures and temperatures: insights from laser compression experiments, EGU General Assembly 2020, Online, 4–8 May 2020, EGU2020-22379, https://doi.org/10.5194/egusphere-egu2020-22379, 2020.