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Towards quantitative assessment of the hazard from space weather. Global 3D modellings of the electric field induced by a realistic geomagnetic storm
Earth, Planets and Space volume 65, pages 1017–1025 (2013)
Abstract
In order to estimate the hazard to technological systems due to geomagnetically induced currents (GIC), it is crucial to understand the response of the geoelectric field to a geomagnetic disturbance and to provide quantitative estimates of this field. Most previous studies on GIC and the geoelectric field generated during a geomagnetic storm assume a 1D conductivity structure of Earth. This assumption however is invalid in coastal regions, where the lateral conductivity contrast is large. In this paper, we investigate the global spatiotemporal pattern of the surface geoelectric field induced by a typical major geomagnetic storm in a conductivity model of Earth with realistic laterallyheterogeneous oceans and continents. Exploiting this model makes the problem fully 3D. Data from worldwide distributed magnetic observatories are used to construct a realistic model of the magnetospheric source. The results of our numerical studies show large amplification of the geoelectric field in many coastal regions. Peak amplitudes obtained with 3D modelling exceed the amplitudes obtained in a 1D model by at least a factor 2, even if the latter makes use of the local vertical conductivity structure. Lithosphere resistivity is a critical parameter, which governs both amplitude and penetration width of the anomalous electric field inland.
1. Introduction
Eruptions at Sun’s surface (coronal mass ejections) blow large quantities of charged particles into space. The particle streams interact with Earth’s magnetic field, intensifying the westward directed magnetospheric ring current (Love, 2008). This phenomenon, leading to substantial temporal variations of the geomagnetic field, is known as geomagnetic storm. According to Faraday’s law of induction, the fluctuating geomagnetic field in turn generates an electric field and induces currents in Earth and grounded conducting networks, such as power grids and pipelines (Pirjola, 2000). These geomagnetically induced currents (GIC) can lead to severe damages of the power network, as happened, for example, 1989 in Quebec (Kappenman et al., 1997). Understanding the properties of the geoelectric field is a key consideration in estimating the hazard to technological systems from space weather (Pulkkinen et al., 2007).
So far, most studies of the geoelectric field in connection with GIC were performed on a regional or local scale, considering rather simplified models of the inducing geomagnetic source (see review paper of Thomson et al. (2009) for more details). In addition, most of the studies (except for the works by Beamish et al., 2002; Thomson et al., 2005 and Gilbert, 2005) employed the assumption of a onedimensional (1D) conductivity structure of Earth. But it is wellknown that the lateral conductivity contrast is large at oceanland interfaces, making the 1D assumption invalid in many coastal areas. The literature contains many publications (Parkinson and Jones, 1979; Cox, 1980; Fainberg, 1980; Rikitake and Honkura, 1985; Kuvshinov, 2008; among others) dealing with the study of the coastal (ocean) effect. However, these studies mainly concentrate on either the investigation of Earth’s mantle structure in the presence of oceans or the influence of the ocean effect on the geomagnetic field.
In this paper, we discuss a rigorous numerical scheme that aims to model on a global scale the geoelectric field induced by a geomagnetic storm as close to reality as possible. Based on this scheme, we investigate the global pattern of the geoelectric field during the main phase of the storm (when the largest amplitudes are expected), using a conductivity model of Earth with realistic laterallyheterogeneous oceans and continents, and exploiting a realistic model of the magnetospheric source. Note that estimating the geoelectric field during geomagnetic substorms (i.e. when the auroral currents are intensified, but not necessarily the ring current) is out of scope of this study. In Section 4.3 of this paper, we discuss how our approach could be modified in order to estimate the electric field induced by geomagnetic substorms.
The paper is organized as follows. Section 2 describes the conductivity model and explains the approach to construct the spatiotemporal model of the magnetospheric source and to calculate the geoelectric field. Section 3 presents the results of our numerical studies, both in terms of modelled time series at specific locations and of modelled snapshots of the global pattern. Discussion and conclusions are presented in Section 4.
2. Methods
For a given impressed source, j^{ext}, and a given 3D conductivity model of Earth, σ(r, ϑ, φ), where r, ϑ and φ are distance from Earth’s centre, colatitude and longitude, respectively, it is possible to calculate the time series of the electric field E (and the magnetic field B) by solving numerically Maxwell’s equations
where μ_{0} is the magnetic permeability of free space. In the following, we describe the conductivity model (Section 2.1), explain the construction of the source model (Section 2.2), and outline the scheme to estimate the geoelectric field (Section 2.3).
2.1 Conductivity model
Our model consists of a thin spherical layer of laterally variable conductance S(ϑ, φ) at Earth’s surface and a radially symmetric (1D) conductivity structure underneath. The shell conductance S (Fig. 1(a)) is obtained by considering contributions both from seawater and sediments. The conductance of seawater has been taken from Manoj et al. (2006) and accounts for ocean bathymetry, ocean salinity, temperature and pressure. Conductance of the sediments (in continental as well as oceanic regions) is based on the global sediment thicknesses given by Laske and Masters (1997) and calculated by a heuristic procedure similar to that described in Everett et al. (2003). The resolution of the model is chosen to be 1° × 1°. Note that calculations on a denser mesh with a resolution of 0.3° × 0.3° revealed only negligible differences in the final results.
The importance of the underlying conductivity structure was tested by simulating induction in models with different 1D sections. Our basic 1D profile consists of a resistive lithosphere with a thickness of 100 km and a layered model underneath, derived from 5 years of CHAMP, Ørsted and SACC magnetic data by Kuvshinov and Olsen (2006). Previous model studies that aimed to investigate the ocean effect in S_{q} and D_{st} geomagnetic variations (Kuvshinov et al., 1999) demonstrated that the resistivity of the lithosphere is a key parameter, which governs the behaviour of the magnetic field at oceanland contacts. In order to investigate the effect of this parameter, lithosphere resistivities of 300 Ωm and 3000 Ωm were tested. Note that we do not account for lateral variations in the thickness and resistivity of the lithosphere; the reasoning for this is discussed in Section 4.2.
Alternative 1D sections are based on the study by Baba et al. (2010). The authors derived models of the 1D conductivity structure beneath the Philippine Sea and the North Pacific using sea floor magnetotelluric data, which are more sensitive to structures in the upper mantle than satellite data. Additional computations were performed with 1D sections based on the results by Baba et al. (2010), but using a uniform resistivity for the lithosphere (constituting the upper 100 km). These additional models allow to investigate the importance of the shallow 1D structure by comparison with the results obtained in the original structures derived by Baba et al. (2010) and the importance of the deep 1D structure by comparison with the results obtained in the basic model. This yields the following six 1D sections under consideration:

(a)
Model derived by Kuvshinov and Olsen (2006) from satellite data with lithosphere of 300 Ωm (R = 3 · 10^{7} Ωm^{2})

(b)
Model derived by Kuvshinov and Olsen (2006) from satellite data with lithosphere of 3000 Ωm (R = 3 · 10^{8} Ωm^{2})

(c)
Model derived by Baba et al. (2010) for the Philippine Sea with lithosphere of 300 Ωm (R = 3 · 10^{7} Ωm^{2})

(d)
Model derived by Baba et al. (2010) for the North Pacific with lithosphere of 3000 Ωm (R = 3 · 10^{8} Ωm^{2})

(e)
Model derived by Baba et al. (2010) for the Philippine Sea (R = 5 · 10^{7} Ωm^{2})

(f)
Model derived by Baba et al. (2010) for the North Pacific (R = 4 · 10^{8} Ωm^{2})
Here, R stands for depthintegrated resistivity (transversal resistance) of the upper 100 km, representing the lithosphere. Figure 1(b) shows the 1D conductivity sections (b), (e) and (f).
2.2 Derivation of the source model
A major geomagnetic storm, which had its maximum on November 20, 2003 with amplitudes of about 300 nT at Earth’ surface, is used as basis to construct a spatiotemporal model of the magnetospheric source. We have selected this storm due to its classical temporal form with clearly distinguishable main and recovery phases. For a tenday time segment starting on November 18, 2003, we assembled minute mean magnetic data of 72 worldwide distributed observatories, situated at geomagnetic latitudes equatorward of ±55° (cf. Fig. 1(a)). What follows is an explanation how we derive the spatiotemporal structure of the source using these data.
We start with removing the mean value and a linear trend from the magnetic data. As all subsequent computations are done in frequency domain, we perform a Fourier transformation of the horizontal components of the data and obtain . Here a is Earth’s mean radius and ω is angular frequency. Frequencies range between the Nyquist frequency of two minutes and the length of the time segment, i.e. ten days. Next we estimate the spatial structure of the impressed source. In frequency domain, Maxwell’s equations (1)–(2) read
Here time dependence is accounted for by e^{−iωt}. Note that the dependence of B, E and j^{ext} on ω is omitted but implied. Equation (3) above Earth’s surface (in an insulating atmosphere and outside the source) reads
allowing the derivation of the magnetic field B in this region from the magnetic potential V,
By using the solenoidal property of the magnetic field,
the potential V satisfies Laplace’s equation
The general solution of Eq. (8) can be represented as a sum of external and internal parts, V = V^{ext} + V^{int}. The external part is (in spherical coordinates) given by
Here is a complexvalued function of ω, and the spherical harmonics are
where are Schmidt quasinormalized associated Legendre polynomials. We avoid a discussion on V^{int}, since it is not relevant for the further development. It is obvious that the external part of the magnetic field (above Earth’s surface) has the form B^{ext} = −∇V^{ext}.
Now we are equipped to introduce a formula for the impressed current j^{ext} in Eq. (3) in terms of the coefficients . It reads
with
where δ denotes Dirac’s delta function, e_{ r }, e_{ ϑ } and e_{ φ } are unit vectors of the spherical coordinate system, and is a short expression for the double sum in Eq. (9). The impressed current j^{ext} flows in a thin shell at r = b ≥ a and produces exactly the external magnetic field B^{ext} in the region a ≤ r < b. Note that b does not represent the distance from the centre of the Earth to the actual magnetospheric source; see Appendix G of Kuvshinov and Semenov (2012) for details.
By letting b approach a infinitesimally, i.e. setting b = a^{+}, we can represent j^{ext} as
with
We solve Maxwell’s equations for each , i.e.
By exploiting the linearity of Maxwell’s equation with respect to the source, we can represent, with the use of Eq. (13), the horizontal components of B at a groundbased observatory j as the sum of “unit” magnetic fields scaled by the external coefficients that we want to determine:
We remark here that we work with horizontal component only, since they are less influenced by conductivity heterogeneities than the radial component.
Finally we estimate the external coefficients by fitting the available data from the global net of observatories using the system of equations (17). We use an iteratively reweighted least squares algorithm (e.g. Aster et al., 2005) to assure the stability of the solution.
Two comments are relevant at this point. First, note that the source of geomagnetic storm variations is assumed to be largescale (at least at nonpolar latitudes), and therefore external coefficients of relatively low n and m (≤ 3) are used to describe its spatial structure. Second, to solve numerically Maxwell’s equations (15)–(16), i.e. to calculate and at Earth’s surface on a 1° × 1° mesh, an integral equation approach (Kuvshinov, 2008) is used. Values of at observatory locations are obtained by interpolation of the results obtained on the 1° × 1° mesh.
An inverse Fourier transformation of the recovered coefficients yields their respective time series, which are depicted in Fig. 2. Note that in time domain, the depicted external coefficients correspond to an expansion of the magnetic potential V (at Earth’s surface) in the conventional form of cosine and sine functions,
As expected, the storm is mainly characterized by the coefficient , apparent from a comparison with the D_{st}index (cf. first plot of Fig. 2). The amplitude of the main event decreases with increasing n and m. The periodic S_{q} variations are, on the other hand, well visible in higher degree harmonics.
The presented scheme was used and verified before by Olsen and Kuvshinov (2004). The fit of our leastsquares analysis (Eq. (17)) is shown in Fig. 3 by a comparison between the observed and calculated horizontal components of B at two observatories. As expected, the fit at the inland observatory Lanzhou/China (LZH, distance to the closest coast 1500 km) is slightly better than the fit at the coastal observatory Hermanus/South Africa (HER, distance to the coast <1 km). Note that the red graphs in Fig. 3 were obtained with model (a).
2.3 Calculation of the electric field
Once the external coefficients are estimated, one can readily calculate—exploiting again the linearity of Maxwell’s equations with respect to the source—the electric field at any location on Earth’s surface as
A subsequent inverse Fourier transformation yields the time series of the electric field. It is noteworthy that the estimation of the geoelectric field for a different storm does not require a renewed solution of Maxwell’s equation. Only an estimation of using Eq. (17) is necessary.
3. Results
3.1 Time series of the electric field at observatory locations
Figures 4 and 5 show the modelled time series of both horizontal components of E at the coastal observatory Hermanus (Fig. 4) and the inland observatory Lanzhou (Fig. 5). Solutions are shown for models (a) and (b), cf. Section 2.1. The choice of these models will be justified in Section 3.2. We make the following observations:

The electric field is subject to highfrequency oscillations during the geomagnetic storm, a clear peak phase (as usually observed for the magnetic field, cf. Fig. 3) is in general not recognizable.

1D modelling yields peak amplitudes of about 50 mV/km for both components in LZH. Peak amplitudes in HER are about 50 mV/km for E_{ φ } and about 20 mV/km for E_{ ϑ }. 1D modelling here implies the use of the local normal 1D structure of the 3D model (including the local conductance of the surface shell S, cf. Fig. 1(a)) and an individual solution of Maxwell’s equations at each grid point according to the methodology first presented by Srivastava (1966).

3D modelling increases the amplitudes of both field components by roughly a factor 2 in HER, but has only minor effects in LZH.

An increase in lithosphere resistivity from 300 Ωm to 3000 Ωm has virtually no effect for the 1D modelling results and only minor effects for the 3D modelling results obtained in LZH. However, both field components obtained with 3D modelling in HER are amplified, roughly by a factor 1.5.
3.2 Snapshots of the global pattern of the electric field
In order to compare the results obtained in models with different 1D sections and thus to examine the influence of the conductivity stratification, snapshots of the global pattern appear more suitable than time series at selected sites due to the highfrequency oscillations of the electric field. Snapshots of E_{ ϑ } obtained in the six models described in Section 2.1 are presented in Fig. 6. Note that the numbering of the panels coincides with the numbering of the models in Section 2.1. All snapshots shown in Fig. 6 (and in subsequent figures) are taken at 17:00 UTC on November 20, 2003. This is in the buildup phase of the storm, i.e. prior to the peak magnetic phase.
The results obtained in models (a) and (c) are very similar. As both models have the same lithosphere conductivity, but a different 1D stratification at greater depths, we conclude that the conductivity structure at depths greater than 100 km has only minor effects on the field pattern. The same conclusions can be made when comparing the results obtained in models (b) and (d). The field pattern obtained in model (e) (the original model derived by Baba et al. (2010) for the Philippine Sea) is similar to those obtained in models (a) and (c), but amplitudes appear to be slightly lower. Similarly, the pattern obtained in model (f) (the original model derived by Baba et al. (2010) for the North Pacific) is slightly less pronounced than the patterns obtained in models (b) and (d), and amplitudes are slightly lower. We attribute this difference to the increase in conductivity at shallow depths in the models derived by Baba et al. (2010) (cf. Fig. 1(b)).
A crosscomparison of both rows in Fig. 6 indicates that stronger and more pronounced fields are obtained in models with larger transversal resistance of the lithosphere. As the differences between the rows are significantly larger than those within each row, we conclude that our basic models (a) and (b) are good representatives and will thus in the following concentrate on the results obtained in models (a) and (b). Note that a comparison of E_{ φ } in the various models leads to the same conclusions, as well as the examination of snapshots at different instants.
We are especially interested in investigating the effects arising from the laterally nonuniform surface layer S. To this purpose, we present results in form of the “anomalous” electric field, which is computed as difference between our 3D modelling results and results obtained in a “local 1D” model. Local 1D modelling here implies the use of the local normal 1D structure of the 3D model (including the local conductance of the surface shell S) and a solution of Maxwell’s equations separately performed at each grid point. Expressions for the (frequency domain) electric field emerging due to induction by a source of our type in 1D conductivity models are presented in Appendix H of Kuvshinov and Semenov (2012).
Snapshots of the anomalous E_{ ϑ } and E_{ φ } for the same instant as in Fig. 6, computed in models (a) and (b), are presented in Fig. 7. The black latitudeparallel lines through North America and Australia indicate the profiles of electric field versus longitude that are drawn in Fig. 8. We make the following observations:

As expected, the anomalous field is very small inside continents and oceans, but pronounced in regions where conductance varies laterally on short scales, especially at the coasts.

Largest amplitudes are observed at long east and west coasts, e.g. the Americas or southern Africa. This reflects the geometry of the source (the magnetospheric ring current).

An increase of lithosphere resistivity from 300 Ωm to 3000 Ωm leads to an amplification of the components of the anomalous electric field by roughly a factor 2 at coastal sites.

The penetration width of the anomalous field is also governed by lithosphere resistivity. Dependent on the site, massive enhancements are observed up to 400 km inland in the case of a 300 Ωm lithosphere and up to 600 km inland in the more resistive case (Fig. 8; note that 1° of longitude corresponds to 100 km in the profile through Australia and to 85 km in the profile through North America).

In latitudeparallel profiles through continents, the anomalous E_{ φ } exhibits an axial symmetry, while the anomalous E_{ ϑ } is antisymmetric. This observation confirms previous results by Kuvshinov et al. (1999) obtained in simplified conceptual models. Note that there is no enhancement of E_{ ϑ } at the Australian west coast for the chosen moment, cf. Fig. 8.
Our results stress the need of 3D modelling in an environment with large lateral variations in conductivity. The amplifications observed at coasts are at least on the same level as the maximum amplitudes obtained in 1D models. As previously shown in Fig. 4, using a 1D model might results in an underestimation of the peak amplitudes of the geoelectric field during a geomagnetic storm by a factor 2–3 at coastal sites. Due to the high temporal variability of the geoelectric field, coastal enhancements vary significantly during a geomagnetic storm.
4. Discussion and Conclusions
4.1 Summary
We have presented a numerical scheme for a time domain estimation of the global electric field induced by a geomagnetic storm with realistic spatiotemporal structure, derived from measurements of the horizontal component of the magnetic field at worldwide distributed observatories. A conductivity model of Earth’s interior with a realistic laterally heterogeneous surface layer representing oceans and continents was used.
The results could be obtained within a few hours, if the observatory data were available and preprocessed (edited, checked for consistency etc.). It is noteworthy that this estimate does not depend on the complexity and resolution of the 3D conductivity model, since the responses for induction in a given 3D model by elementary sources (in case of a geomagnetic storm described by spherical harmonics) can be calculated beforehand and archived. To obtain the geoelectric field for a specific storm, it is just necessary to reconstruct the spatiotemporal form of the external source responsible for this storm and to convolve the source field with the precomputed 3D responses. We believe that our numerical scheme would be a useful tool to estimate quantitatively the space weather hazard associated with excessive GIC arising in groundbased conductor networks (such as power lines) during major geomagnetic storms.
4.2 Effect of oceans and lithosphere
Model studies based on our numerical scheme revealed substantial differences between the electric fields generated in 3D and 1D models, even if the 1D model makes use of the local vertical conductivity structure. As expected, the differences are mainly marked at the coasts. The anomalous electric field, computed as difference between the electric fields obtained in 3D and 1D models, can penetrate up to more than 500 km inland (depending on the site and the local conductivity structure). Anomalous amplitudes are at least as large as the amplitudes calculated in a 1D model. Peak amplitudes of a geomagnetic storm at coastal sites are hence underestimated by a factor 2–3 when using a 1D model. The 3D modelling results state that coastal areas are in danger of experiencing electric field amplitudes of up to 200 mV/km during a typical magnetic storm. Long east and west coasts like the Americas, southern Africa or Australia and narrow land bridges like Panama seem to be especially endangered.
The resistivity of the lithosphere is a critical parameter when estimating amplitudes of the electric field. Resistivities of 300 Ωm and 3000 Ωm, representing realistic boundary values for Earth’s lithosphere, were tested in this study. Lithosphere resistivity mainly affects the electric field at coastal sites. The amplitudes of the anomalous electric field were doubled in the model with a lithosphere of 3000 Ωm, and the “coastal region”, in which the anomalous field shows enhanced amplitudes, was significantly wider. The influences of the conductivity distribution at greater depths and the precise stratification within the lithosphere on the results were minor in comparison with the integrated lithosphere resistivity.
According to our modelling results, a precise estimate of the lithosphere resistivity in the region of interest is crucial in order to obtain a trustworthy estimate of the actual electric field. In this study, we considered a model with a lithosphere of laterally uniform thickness and resistivity. While the chosen lithosphere thickness of 100 km agrees with the global average, it is wellknown that lithosphere thickness is very variable on Earth and ranges from few km at midocean ridges to several 100 km below old continental shields. The choice of a laterally uniform lithosphere is thus a limitation of our work; it was however necessary, since thickness and resistivity of the lithosphere are poorly resolved on a global scale. We want to stress in this context that the numerical solution discussed in this paper is fully 3D and thus can readily adopt models with a laterally variable lithosphere once reliable information about such variability is available.
4.3 Estimates of the electric field at polar latitudes
In this paper, we discussed the geoelectric field induced by a largescale magnetospheric source that dominates in midlatitudes. However, it is well known that one can expect larger signals in polar regions due to substorm geomagnetic disturbances (Pirjola and Viljanen, 1994). The recovery of the spatiotemporal structure of the auroral ionospheric source, which is responsible for this activity, is more challenging due to the large variability of the auroral source both in time and space.
One of the ways to determine realistic auroral currents on a semiglobal scale (in the whole polar cap) consists of collecting the data from highlatitude geomagnetic observatories and polar magnetometer arrays (e.g. IMAGE and MIRACLE arrays in Scandinavia, DTU and MAGIC arrays in Greenland, CARISMA array in Canada etc.) and then reconstructing the auroral current, for example by exploiting an approach based on elementary current systems (e.g. Amm, 2001; Sun and Egbert, 2012). Note that this approach was used by Pulkkinen and Engels (2005), who analysed the influence of 3D induction effects on ionospheric currents during geomagnetic substorms.
Once the auroral source is quantified, a similar numerical scheme as described above, however with two modifications, can be implemented in order to calculate the geoelectric field caused by a geomagnetic substorm. One modification concerns the description of the substorm source— instead of using a spherical harmonics representation, one can mimic the auroral ionospheric current by elementary current systems. Another modification applies to the 3D conductivity model. Since substorm magnetic variations are characterized by periods between a few tens of seconds and tens of minutes, one cannot exploit a model in which the surface layer is approximated by a thin shell, as it was done in this paper. The variable thickness of this layer is important in this period range, thus a full 3D model (including bathymetry) should be considered. However, as mentioned in Section 4.1, the complexity and resolution of the 3D conductivity model has no effect on the computational cost of the source modelling for a specific substorm. As in the case of a largescale geomagnetic storm, a model of the electric field due to a specific substorm for the whole polar cap could be obtained within a few hours when using a standard workstation for computations. Note again that this estimate does not account for the efforts of collecting and preprocessing the data and for the 3D calculations of the magnetic field due to elementary sources.
Semiglobal estimates of the geoelectric field induced by a realistic geomagnetic substorm in a realistic 3D conductivity model accounting for bathymetry and nonuniform lithosphere will be the subject of a subsequent publication.
References
Amm, O., The elementary current method for calculating ionospheric current systems from multisatellite and ground magnetometer data, J. Geophys. Res., 106, 24843–24855, 2001.
Aster, R. C., B. Borchers, and C. H. Thurber, Parameter Estimation and Inverse Problems, Elsevier Academic Press, 2005.
Baba, K., H. Utada, T. Goto, T. Kasaya, H. Shimizu, and N. Tada, Electrical conductivity imaging of the Philippine Sea upper mantle using seafloor magnetotelluric data, Phys. Earth. Planet. Inter., 183, 44–62, 2010.
Beamish, D., T. D. G. Clark, E. Clarke, and A. W. P. Thomson, Geomagnetically induced currents in the UK: Geomagnetic variations and surface electric fields, J. Atmos. Sol. Terr. Phys., 64, 1779–1792, 2002.
Cox, C. J., Electromagnetic induction in the oceans and inferences on the constitution of the earth, Geophys. Surv., 7, 137–156, 1980.
Everett, M. E., S. Constable, and C. G. Constable, Effects of nearsurface conductance on global satellite induction responses, Geophys. J. Int., 153, 277–286, 2003.
Fainberg, E. B., Electromagnetic induction in the world ocean, Geophys. Surv., 4, 157–171, 1980.
Gilbert, J., Modeling the effect of the oceanland interface on induced electric fields during geomagnetic storms, Space Weather, 3, doi:10.1029/2004SW000120, 2005.
Kappenman, J., L. Zanetti, and W. Radasky, Geomagnetic storms can threaten electric power grid, Earth in Space, 9, 9–11, 1997.
Kuvshinov, A., 3D Global induction in the oceans and solid Earth: recent progress in modeling magnetic and electric fields from sources of magnetospheric, ionospheric and oceanic origin, Surv. Geophys., 29, 139–186, 2008.
Kuvshinov, A. and N. Olsen, A global model of mantle conductivity derived from 5 years of CHAMP, Ørsted, and SACC magnetic data, Geophys. Res. Lett., 33, doi:10.1029/2006GL027083, 2006.
Kuvshinov, A. and A. Semenov, Global 3D imaging of mantle electrical conductivity based on inversion of observatory Cresponses I. An approach and its verification, Geophys. J. Int., 189, doi:10.1111/j.1365–246X.2011.05349.x, 2012.
Kuvshinov, A. V., D. B. Avdeev, and O. V. Pankratov, Global induction by Sq and Dst sources in the presence of oceans: bimodal solutions for nonuniform spherical surface shells above radially symmetric Earth models in comparison to observations, Geophys. J. Int., 137, 630–650, 1999.
Laske, G. and G. Masters, A global digital map of sediment thickness, Eos Trans. AGU, 78, F483, 1997.
Love, J. J., Magnetic monitoring of Earth and space, Physics Today, 61, 31–37, 2008.
Manoj, C, A. Kuvshinov, S. Maus, and H. Luehr, Ocean circulation generated magnetic signals, Earth Planets Space, 58, 429–437, 2006.
Olsen, N. and A. Kuvshinov, Modeling the ocean effect of geomagnetic storms, Earth Planets Space, 56, 525–530, 2004.
Parkinson, W. D. and F. W. Jones, The geomagnetic coast effect, Rev. Geophys., 17, 1999–2015, 1979.
Pirjola, R., Geomagnetically induced currents during magnetic storms, IEEE Trans Plasma Sci, 28, 1867–1873, 2000.
Pirjola, R. and A. Viljanen, Geomagnetically induced currents in the Finnish highvoltage power system, a geophysical review, Surv. Geophys., 15, 383–408, 1994.
Pulkkinen, A. and M. Engels, The role of 3D geomagnetic induction in the determination of the ionospheric currents from the ground geomagnetic data, Ann. Geophys., 23, 909–917, 2005.
Pulkkinen, A., M. Hesse, M. Kuznetsova, and L. Rastatter, First principles modeling of geomagnetically induced electromagnetic fields and currents from upstream solar wind to the surface of the Earth, Ann. Geophys., 25, 881–893, 2007.
Rikitake, T. and Y. Honkura, Developments in Earth and planetary sciences, in Solid Earth Geomagnetism, vol. 5, edited by Rikitake, T., Terra Scientific Publishing Company, 1985.
Srivastava, S. P., Theory of the magnetotelluric method for a spherical conductor, Geophys. J. R. Astron. Soc., 11, 373–387, 1966.
Sun, J. and G. Egbert, Spherical decomposition of electromagnetic fields generated by quasistatic currents, Int. J. Geomath., 3, 279–295, 2012.
Thomson, A. W. P., A. J. McKay, E. Clarke, and S. J. Reay, Surface electric fields and geomagnetically induced currents in the Scottish Power grid during the 30 October 2003 geomagnetic storm, Space Weather, 3, doi:10.1029/2005SW000156, 2005.
Thomson, A. W. P., A. J. McKay, and A. Viljanen, A review of progress in modelling of induced geoelectric and geomagnetic fields with special regard to induced currents, Acta Geophys., 57, 209–219, 2009.
Acknowledgments
The authors express their gratitude to the staff of the geomagnetic observatories who have collected and distributed the data. We thank Dr. Alan Thomson for discussion on the manuscript and Dr. Ikuko Fujii and an anonymous reviewer for helpful comments. This work has been supported by the Swiss National Science Foundation under grant No. 2000021140711/1.
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Püthe, C., Kuvshinov, A. Towards quantitative assessment of the hazard from space weather. Global 3D modellings of the electric field induced by a realistic geomagnetic storm. Earth Planet Sp 65, 1017–1025 (2013). https://doi.org/10.5047/eps.2013.03.003
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DOI: https://doi.org/10.5047/eps.2013.03.003
Key words
 Geomagnetic storms
 GIC
 geoelectric field
 3D modelling