Planetary magnetic field production mechanism may require consideration of fermi electrons. While avoiding the Boussinesq approximation and considering a presence of Fermi electrons in a planetary core, a new hypothesis how the planetary magnetic field may operate is proposed. The overall topology concerns both the core’s north hemisphere (NH) and south hemisphere (SH) that produce its own magnetic polarities due to a sense of the Earth’s rotation (Coriolis effect). Magnetism can be generated due to the electric current form the core’s fermi electrons that follow the more conducting spiraling plumes from the convection heat exchange. NH produces magnetic flux directed toward the north (reversed polarity) while SH produces magnetic flux directed to the south (normal polarity). When NH is more buoyant than SH, the overall dipolar reversed polarity is produced. When SH of the core is more buoyant, the overall normal magnetic polarity is produced. Overall planetary magnetic field is then generated from a core’s heat exchange competition between its NH and SH. For this hypothesis supports is found from the theoretical arguments, from the topology of finite element modeling, and from the evidence of a historical magnetic reversal record. Calculations considering the presence of Fermi electrons in the core allow for heat gradient generated magnetic flux estimate between 0.1 mT and 3 mT inside the liquid core. Finite element modeling topology of simulated magnetic dipoles near inner/outer core boundary (IOB) oriented only northward in NH and southward in SH supported that todays’ surface magnetic field observations are consistent with the outer core fields between 0.1 mT and 3 mT. Individual treatment of normal and reversed polarity durations supported that a predominance of magnetic polarity durations relates to the existing temperature models near the core/mantle boundary (CMB) that have a consistent effect on the heating exchange within the core.

How to cite: Kletetschka, G.: Origin of the Earth’s magnetic field from the Fermi electrons, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-2458, https://doi.org/10.5194/egusphere-egu23-2458, 2023.

Recent satellite missions provide accurate measurement of the time derivative of the Gaussian coefficients from which the secular variation spectrum can be calculated. The ratio of the magnetic energy spectrum to the secular variation spectrum gives a typical scale τ for the temporal variation of the geomagnetic field as a function of the spherical harmonics degrees l. There is much interest in the scaling of τ with l: τ ~ l ^β. Numerical simulations and the frozen flux hypothesis suggest the simple relation τ ~ l ^-1 while observational studies give a diverse range of value for β. A question here is whether the frozen flux hypothesis is applicable. It is plausible that magnetic diffusion can be neglected inside the outer core. However, the situation in a boundary layer under the core-mantle boundary (CMB) is less clear. A related question is whether τ observed at the Earth's surface is relevant to what is happening in the interior of the outer core as the form of the magnetic field above the CMB is constrained by the boundary conditions at the CMB. Here we use a numerical dynamo model to investigate these questions. We extend the definition of τ to the inside of the outer core. We find that in our simulations the exponent β undergoes a sharp transition just beneath the CMB, magnetic diffusion plays a role in the scaling of τ above the CMB and the frozen flux hypothesis is not applicable here.

How to cite: Tsang, Y.-K.: Scaling of the geomagnetic secular variation time scales, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-10439, https://doi.org/10.5194/egusphere-egu23-10439, 2023.

We investigate the dipole–multipole field transition in rapidly rotating dynamos in the low-inertia regime relevant to planetary cores. Here, the Rossby number is small on the planetary core depth as well as on the length scale of core convection. Attention is focused on the dynamics of slow Magnetic-Archimedean-Coriolis (MAC), or magnetostrophic, waves generated in the energy-containing scales of the dynamo. The suppression of the slow MAC waves in a strongly driven dynamo is dynamically similar to the excitation of these waves in a moderately driven dynamo evolving from a small seed magnetic field. While the former regime causes polarity reversals, the latter regime produces the axial dipole field from a multipolar state. For either polarity transition, a Rayleigh number based on the mean wavenumber of the energy-containing scales bears the same linear relationship with the peak Elsasser number measured at the transition. This self-similarity can provide an estimate of the Rayleigh number that admits polarity reversals.

How to cite: Majumder, D., Sreenivasan, B., and Maurya, G.: The dipole–multipole transition in planetary dynamos, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-15288, https://doi.org/10.5194/egusphere-egu23-15288, 2023.

Modern observations show that the fast fluctuations in geomagnetic acceleration and fluid core surface flow motions always occur at the equatorial regions, which may arise from the rapidly hydromagnetic waves atop the Earth’s core. But, the exact origins of these waves are still unclear, though the so-called eMAC waves may provide a potential mechanism. Given that the physical expressions of describing the physical properties (e.g., equatorial confinement and latitudinal distribution, damping rate, eigen-period) and the perturbed magnetic fields of the eMAC waves have not been given before, this work carefully revisits the currently eMAC wave theory and firstly gives the systematically analytical expressions for these physical properties. Importantly, the perturbation analysis indicates that the eMAC wave model can own the high accuracy (i.e., the relative errors are less than 5%) to describe the low-latitude waves with latitude below 25 degrees, which can cover the regions where the equatorial waves mainly locate. In summary, this work provides an important complement for the currently eMAC wave theory. The results of this work are significant to understand the physical mechanism responsible for the origins of the inferred equatorial waves, their physical properties and the dynamics of the Earth’s equatorial regions.

How to cite: Duan, P.: Analytical model of the equatorial Magnetic-Archimedes-Coriolis waves propagating at Earth’s core surface and the potential implications, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-12751, https://doi.org/10.5194/egusphere-egu23-12751, 2023.

Core surface flow inversion using physics-informed neural networks

Jinfeng Li (1) and Yufeng Lin (1)

(1) Department of Earth and Space Sciences, Southern University of Science and Technology, Shenzhen 518055, China.

Physics-informed neural networks (PINNs) have recently been widely used to solve PDEs or ODEs. An attractive feature of this method is that it can calculate the derivatives without truncation errors by the automatic differentiation method (Lu et al., 2021). Another advantage is that it can solve the inverse problem with slightly modified code for solving the forward problem (Raissi et al., 2020). In this study, we use the PINN to inverse the core surface flow from the geomagnetic observations. We start from the radial component of the induction equation under the frozen-flux approximation (Robert and Scott, 1965) and tangentially geostrophic flows assumption (Hills, 1979). Instead of using the large-scale approximation, which assumes the flows that generate the observed secular variation (SV) are large-scale, we model the flow field in the physic space and construct the unobserved magnetic field based on the power spectrum of numerical dynamo simulations. We examine the nonuniqueness of the inversion results by pre-setting the different initial parameters of the neural network. Our tests show that the uncertainty of large-scale flow field is small and the inversion scheme is robust.

We retrieve the core surface flow field between 2000 and 2020 using the core magnetic field model CHAOS-7 (Finlay et al., 2020). We then perform the dynamic mode decomposition method (DMD) (Schmid, 2010) of the retrieved core flow. This method decomposes the flow field and SV into several eigenmodes with time evolution. The consistency time evolution between the flow and the SV modes indicates the inversion algorithm is stable. Moreover, we calculate the secular acceleration (SA) of the magnetic field for each dynamic modes and find the mode with 8 years period can match the jerk events occurred in the equatorial region.

Reference

• C. Finlay, C. Kloss, N. Olsen et al. 2020, The CHAOS-7 geomagnetic field model and observed changes in the South Atlantic Anomaly, Earth Planets Space, 72, 156.
• G. Hills, 1979, Convection in the Earth’s Mantle Due to Viscous Shear at the Core-Mantle Interface and Due to Large-Scale Buoyancy. PhD Thesis, New Mexico State University, Las Cruces.
• Lu, X. Meng, Z. Mao and G. E. Karniadakis, 2021, DeepXDE: A Deep Learning Library for Solving Differential Equations, SIAM Review, 63, pp. 208-228.
• Raissi, A. Yazdani and G. E. Karniadakis, 2020, Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations, Science, 367, pp. 1026-1030.
• H. Robert and S. Scott, 1965, On analysis of the secular variation. 1: A hydromagnetic constraint: Theory, Journal of Geomagnetism and Geoelectricity, 17, pp. 137-151.
• J. Schmid, 2010, Dynamic mode decomposition of numerical and experimental data, J. Fluid Mech, 65, pp. 5-28.

How to cite: Li, J.: Core surface flow inversion using physics-informed neural networks, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-3710, https://doi.org/10.5194/egusphere-egu23-3710, 2023.

The energy dissipation in the fluid flow near the boundary separating the core and the mantle (i.e. the CMB) of a planet or moon with a fluid interior is a crucial parameter to understand its rotational dynamics. This boundary layer is typically very small compared to the core radius, and can become turbulent under certain conditions, which presents a challenge for global scale simulations of the flow in the fluid core. Here we construct a local Cartesian model to study the boundary layer of a precessing planet or moon. The solutions we derive in the laminar regime, i.e. where the Reynolds number Re is small and the non-linear term is neglected, are consistent with previous studies. This gives us confidence to push the model further into the turbulent regime. We solve numerically the governing equations, i.e., the Navier-Stokes equation and the continuity equation for an incompressible fluid in a rotating frame. We observe that, when the flow is turbulent, the boundary layer dissipation is increased, compared to its laminar counterpart, as expected. Moreover, we found that the velocity profile agrees with the law of the wall, a theory developed to study turbulent flow near a solid boundary. Based on our numerical results, we further construct a turbulence model using similarity theory. Last but not least, due to chemical interaction on the planetary core-mantle boundary, small-scale topography or surface roughness might exist. To investigate this topographic effect, we impose a sinusoidal topography in our local model. Preliminary results show further increase of the dissipation. Our results may provide valuable insight into the boundary layer dissipation near the CMB for both the Earth and the moon.

How to cite: Shih, S.-A., Triana, S. A., and Dehant, V.: Turbulent Dissipation in the Boundary Layer of Precession Driven Flow in a Sphere, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-10448, https://doi.org/10.5194/egusphere-egu23-10448, 2023.

Seismological observations of J-phases, the seismic waves traversing the Earth’s inner core (IC) as shear waves, are critical to understanding the inner core shear properties. That, in turn, will shed light on the solidification process and the evolution of the inner core and our planet. Most body-wave detections of the J waves have been controversial due to their small amplitudes, which involve energy conversion from P- to S- and vice versa at the inner core boundary. Recent advances in understanding the nature of the late coda correlation offer a new way to sample the deep Earth, including the shear properties of the Earth’s inner core. The correlation-based features provide the sensitivity of the periods between 15 and 50 s, placing it between the body waves and normal mode data. Therefore, the observations of late coda correlation are vital in refining the shear properties of the IC, such as velocity, anisotropy, and attenuation.

This study employs several uninvestigated J-wave correlation features detected in the global coda-correlation wavefield building on the study of Tkalčić and Pham (2018) that determined the shear wave speed reduction of 2.5% relative to PREM. The correlation features observed in the coda-correlation wavefield arise from similar seismic phases in which one contains a shear-wave leg in the IC. Improved data selection process and knowledge acquired from recent theoretical and observational developments in understanding the anatomy of coda correlation wavefield enable significant improvements in the data quality. We benchmark the waveforms of observed correlation features using numerical modeling, confirm the observations of J waves and inner core solidity and update its shear properties’ values, including shear-wave speed and Poisson’s ratio.

How to cite: Costa de Lima, T., Pham, T.-S., Ma, X., and Tkalčić, H.: New constraints on shear properties of the Earth’s inner core from the global correlation wavefield, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-16047, https://doi.org/10.5194/egusphere-egu23-16047, 2023.

The thermal conductivity values through Earth’s core and planetary cores have important implications for the thermal evolution and magnetism of these bodies. For the outer cores of small terrestrial planetary bodies, this study constrains the thermal conductivity of liquid Fe-8wt%S-4.5wt%Si at pressures 2-5 GPa. Thermal conductivity was estimated using the Wiedemann-Franz Law from electrical resistivity measurements of a small Fe alloy sample at high pressures and high temperatures in a 1000-ton cubic anvil press. The powder samples were prepared by mixing powders of three compositions: Fe, FeS, and Fe-9wt%Si. Electron microprobe analysis and micro X-ray diffraction verified the elemental composition and crystallographic structure of the sample material both before and after pressurization.

Resistivity-temperature plots of the Fe-8wt%S-4.5wt%Si data display trends common to Fe mixed with significant amounts of Si: a general rise in resistivity to a peak, a drop in resistivity through the melt, and a leveling of resistivity through the liquid state. Two reversals in slope occur between 800 K and 1000 K. At each integral pressure value between 2-5 GPa, an electrical resistivity in the range 300±100 μΩ·cm was found. Using the Sommerfeld value of the Lorenz number, thermal conductivities in the range 15±5 W/m/K were estimated. Comparative plots including resistivity data of Fe, Fe-4.5wt%Si, Fe-17wt%Si, and Fe-20wt%S are instructive to illuminate the relative effects of S and Si on the resistivity and thus the thermal conductivity and adiabatic heat flow of core mimetic Fe alloys. If the pressure at the top of the core is constrained using the assumptions of hydrostatic equilibrium and a bulk silicate mantle, then these thermal conductivity results may be applied to a number of known small terrestrial bodies, such as Io, in the case of a dominantly Fe-S-Si liquid outer core.

How to cite: Lenhart, E., Yong, W., and Secco, R.: Outer Core Heat Flux in Small Terrestrial Bodies from Electrical Resistivity Measurements of Liquid Fe-8S-4.5Si at High Pressure, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-10229, https://doi.org/10.5194/egusphere-egu23-10229, 2023.