Time‐Domain Modeling of Three‐Dimensional Earth's and Planetary Electromagnetic Induction Effect in Ground and Satellite Observations

Grayver, Alexander; Kuvshinov, Alexey; Werthmüller, Dieter

doi:10.1029/2020ja028672

Cited by 16 publications

(19 citation statements)

References 45 publications

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“…(2019), and Grayver et al. (2021), current loops in Sun et al. (2015), or eigenmodes from the Principal component analysis (PCA) of the physics‐based models in Egbert et al.…”

Section: Methodsmentioning

confidence: 99%

“…Note also that the form of j i (r) (and their number, L) varies with application. For example, j ext (r, ω) is parameterized via spherical harmonics in Püthe and Kuvshinov (2013), Honkonen et al (2018), Guzavina et al (2019), and Grayver et al (2021), current loops in Sun et al (2015), or eigenmodes from the Principal component analysis (PCA) of the physics-based models in Egbert et al (2021) and Zenhausern et al (2021).…”

Section: Governing Equations In the Frequency Domainmentioning

confidence: 99%

“…An important note here is that, according to Equation B13, one does not need to compute E i (r s , ω; σ) for 𝐴𝐴 𝐴𝐴 𝐴 𝜋𝜋 Δ𝑡𝑡 . This may be obvious, however, this is not the case if one uses piece-wise constant (PWC) approximation of c i (t) as it is done, for example, in Grayver et al (2021). With PWC approximation, one is forced to compute the fields at very high frequencies irrespective of Δt value; this can pose a problem from the numerical point of view.…”

Section: (B8)mentioning

confidence: 99%

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Real‐Time 3‐D Modeling of the Ground Electric Field Due To Space Weather Events. A Concept and Its Validation

2022

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We present a methodology that allows researchers to simulate in real time the spatiotemporal dynamics of the ground electric field (GEF) in a given 3‐D conductivity model of the Earth based on continuously augmented data on the spatiotemporal evolution of the inducing source. The formalism relies on the factorization of the source by spatial modes (SM) and time series of respective expansion coefficients and exploits precomputed GEF kernels generated by corresponding SM. To validate the formalism, we invoke a high‐resolution 3‐D conductivity model of Fennoscandia and consider a realistic source built using the Spherical Elementary Current Systems (SECS) method as applied to magnetic field data from the International Monitor for Auroral Geomagnetic Effect network of observations. The factorization of the SECS‐recovered source is then performed using the principal component analysis. Eventually, we show that the GEF computation at a given time instant on a 512 × 512 grid requires less than 0.025 s provided that GEF kernels due to pre‐selected SM are computed in advance. Taking the 7–8 September 2017 geomagnetic storm as a space weather event, we show that real‐time high‐resolution 3‐D modeling of the GEF is feasible. This opens a practical opportunity for GEF (and eventually geomagnetically induced currents) nowcasting and forecasting.

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“…(2019), and Grayver et al. (2021), current loops in Sun et al. (2015), or eigenmodes from the Principal component analysis (PCA) of the physics‐based models in Egbert et al.…”

Section: Methodsmentioning

confidence: 99%

Section: Governing Equations In the Frequency Domainmentioning

confidence: 99%

Section: (B8)mentioning

confidence: 99%

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Real‐Time 3‐D Modeling of the Ground Electric Field Due To Space Weather Events. A Concept and Its Validation

2022

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“…Efficient calculation and properties of these integrals for a general case are discussed in Grayver et al (2021). Further, when σ(r) ≡ σ(r), and σ(r) is given by a set of concentric shells with laterally uniform conductivity values, Equations (A15)-(A16) can be solved analytically.…”

Section: Appendix a Electromagnetic Induction In Rocky Planetsmentioning

confidence: 99%

Interior Heating of Rocky Exoplanets from Stellar Flares with Application to TRAPPIST-1

Grayver

Bower

Saur

et al. 2022

ApJL

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Many stars of different spectral types with planets in the habitable zone are known to emit flares. Until now, studies that address the long-term impact of stellar flares and associated coronal mass ejections (CMEs) assumed that the planet’s interior remains unaffected by interplanetary CMEs, only considering the effect of plasma/UV interactions on the atmosphere of planets. Here, we show that the magnetic flux carried by flare-associated CMEs results in planetary interior heating by ohmic dissipation and leads to a variety of interior–exterior interactions. We construct a physical model to study this effect and apply it to the TRAPPIST-1 star whose flaring activity has been constrained by Kepler observations. Our model is posed in a stochastic manner to account for uncertainty and variability in input parameters. Particularly for the innermost planets, our results suggest that the heat dissipated in the silicate mantle is both of sufficient magnitude and longevity to drive geological processes and hence facilitate volcanism and outgassing of the TRAPPIST-1 planets. Furthermore, our model predicts that Joule heating can further be enhanced for planets with an intrinsic magnetic field compared to those without. The associated volcanism and outgassing may continuously replenish the atmosphere and thereby mitigate the erosion of the atmosphere caused by the direct impact of flares and CMEs. To maintain consistency of atmospheric and geophysical models, the impact of stellar flares and CMEs on atmospheres of close-in exoplanetary systems needs to be studied in conjunction with the effect on planetary interiors.

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“…Two types of unstructured grids can be used to approximate the curved shell structure of the Earth, which are hexahedral grids (Grayver et al, 2019(Grayver et al, , 2021 and tetrahedral grids (Everett et al, 2003;Everett & Schultz, 1996;Ribaudo et al, 2012;Weiss & Everett, 1998;Yoshimura & Oshiman, 2002). Although hexahedral grids can obtain a good adaptivity for shell structures by using a high-order mapping function, tetrahedral grids can well approximate complex subsurface structures with a curved shape, even working in low-order mapping mode.…”

mentioning

confidence: 99%

A Multi‐Resolution Finite‐Element Approach for Global Electromagnetic Induction Modeling With Application to Southeast China Coastal Geomagnetic Observatory Studies

et al. 2022

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We present a multi‐resolution finite‐element approach for three‐dimensional (3D) electromagnetic (EM) induction modeling in spherical Earth. First, the secondary electric field approach is employed so that both magnetospheric and ionospheric current sources are naturally considered. Second, the multi‐resolution tetrahedral grids are used to approximate the heterogeneous crust and mantle, so that the local ocean effects at coastal and island observatories can be accurately simulated. Furthermore, a parallel goal‐oriented hp‐adaptive finite‐element method with Nédélec vector elements is employed to guarantee the accuracy of solutions for arbitrary 3D conductivity distributions. Finally, two synthetic models are used to verify the accuracy and efficiency of our newly developed forward modeling solver. Results show that accurate solutions can be obtained for problems with several million to hundreds of millions of unknowns in a few minutes using 128 cores on a cluster. We apply this approach to correct the near‐surface ocean effects for several unused Chinese coastal observatories by performing multi‐resolution 3D modeling. The corrected data are inverted for the subsurface layered mantle conductivity structures. The conductivity model beneath southeast China is more resistive than that beneath northeast China by more than half an order of magnitude. By comparing the inverse models with the latest laboratory conductivity‐depth profiles, the estimated transition zone water content is less than 0.01 wt% beneath southeast China irrespective of which laboratory data is used. Considering the low‐velocity anomalies in this region, which suggest high‐temperature structures, less water is expected. We, therefore, infer that the mantle transition zone beneath southeast China is dry.

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Time‐Domain Modeling of Three‐Dimensional Earth's and Planetary Electromagnetic Induction Effect in Ground and Satellite Observations

Cited by 16 publications

References 45 publications

Real‐Time 3‐D Modeling of the Ground Electric Field Due To Space Weather Events. A Concept and Its Validation

Real‐Time 3‐D Modeling of the Ground Electric Field Due To Space Weather Events. A Concept and Its Validation

Interior Heating of Rocky Exoplanets from Stellar Flares with Application to TRAPPIST-1

A Multi‐Resolution Finite‐Element Approach for Global Electromagnetic Induction Modeling With Application to Southeast China Coastal Geomagnetic Observatory Studies

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