Geoelectric Field Estimations During Geomagnetic Storm in North China From SinoProbe Magnetotelluric Impedances

Evaluating the impact of geomagnetic disturbances on power grid infrastructure is critical to mitigate the risk posed by geomagnetically induced currents (GICs). In this paper, the geoelectric field and induced voltage distribution in North China were estimated from the SinoProbe magnetotelluric (MT) impedance data together with the geomagnetic observatory data of six INTERMAGNET stations recorded during the significant geomagnetic storm of 17th March 2015. The measured impedances from 119 SinoProbe MT sites were convolved with geomagnetic observatory data to account for the Earth's complex three‐dimensional electrical resistivity structure. The resultant geoelectric field was then used to model the induced voltage distribution across the regional power transmission network in North China. Due to the large inter‐site distances of the SinoProbe MT program, the derived geoelectric field is mostly homogeneous, except in the Ordos Basin that displays a polarization of the geoelectric field, and with higher magnitudes in the orogenic belts. The estimated geoelectric fields in Taihang‐Lvliang, Yanshan, and Luxi orogenic belts of North China were large (>1 V/km) during the storm, due to high‐resistivity lithosphere resulting in large voltage gradients in the Earth. However, in relation to locations of major power transmission lines, only the central part of North China experienced induced voltages exceeding 100 V.


Introduction
Violent solar activity can form strong solar winds that interact with the Earth's magnetic field.This interaction will result in large geomagnetic disturbances, such as geomagnetic storms, inducing geoelectric fields at the surface and interior of Earth (Balasis et al., 2018;Daglis et al., 2003).The ground electric field can couple with grounded technological infrastructure, such as power systems and pipelines, and produce geomagnetically induced currents (GICs) that can cause partial saturation of transformers leading to a variety of power system effects and significant socioeconomic damages (Albertson & Thorson, 1974;Allen et al., 1989;Baker et al., 2004;Molinski, 2002).
Large GICs in electrical transmission lines were generally regarded as only occurring in high-latitude areas (>60°) during geomagnetic storms, such as Finland (Pirjola & Lehtinen, 1985), North America (Cliver & Svalgaard, 2004), Norway (Myllys et al., 2014), Ireland (Blake et al., 2016), and Russia (Kozyreva et al., 2020).However, although geomagnetic disturbances at middle and low latitudes are weaker, recent studies have showed that large GICs can be also generated during strong geomagnetic storm, for example, in New Zealand (Béland & Small, 2004), Spain (Torta et al., 2012), Australia (Marshall et al., 2011), South Africa (Joo et al., 2018), and Brazil (Espinosa et al., 2023).GICs in electrical transmission lines are proportional to the induced voltages calculated from the resultant geoelectric field, together with the spatial layout of the electrical transmission lines (Kelbert et al., 2019).Moreover, the induced geoelectric field depends on not only the geomagnetic disturbances but also the regional lithospheric electrical structure (Bedrosian & Love, 2015).Therefore, estimating geoelectric fields and induced voltages during geomagnetic storms is crucial for GIC hazard evaluation, future disaster prevention and early warning.
In North China, 1,000 kV long transmission lines are prevalent in densely populated areas, which increases the potential for hazards from GICs during strong geomagnetic storms.Previous studies are mostly based on 1-D resistivity models in North China (Liu et al., 2015;Zheng et al., 2013) and with a few simplified 3-D models of local areas (Liu, Fu, et al., 2023;Liu, Li et al., 2023;Wang et al., 2015;Zhang et al., 2015).This paper presents and discusses the induced geoelectric field in North China during a large geomagnetic storm on 17th March 2015, estimated from interpolated geomagnetic field variations coupled with 119 MT impedance tensors from the SinoProbe project.The geoelectric hazards in 1,000 kV ultra-high-voltage (UHV) transmission lines are comprehensively evaluated by combining the geoelectric field and induced voltage.

Methodology
For GIC sources, the plane wave approximation of external source fields is assumed (Kelbert & Lucas, 2020;Kelbert et al., 2017;Wang et al., 2020).The MT impedance tensor, calculated at a site from natural time varying geomagnetic fields and induced geoelectric fields, can be used as a predictor of temporal geoelectric fields in time and space for specific geomagnetic storms (Lucas et al., 2020).
As geomagnetic observatory sites are typically spaced hundreds of kilometers apart, it is necessary to interpolate them spatially.Such methods include nearest neighbor interpolation, Delaunay triangulation and other linear interpolation methods, and methods with physical background, including magnetic scale potential (Düzgit et al., 1997) and the Spherical Elementary Current Systems (SECS) method (Amm & Viljanen, 1999).At middle and low latitudes, nearest neighbor interpolation or magnetic scale potential methods are generally good (Torta et al., 2017).
In this paper, nearest neighbor interpolation of the geomagnetic field is used to simulate the variational fields at each of the SinoProbe sites.The MT impedance refers to the frequency domain transfer function between electric and magnetic fields at the same measuring point r, and impedance Z r can be expressed as (Cagniard, 1953): where E r and H r are the electric field and the magnetic field in the frequency domain, respectively.
For a hypothetical geographic region where Earth conductivity is only a 1-D function of depth, the impedance tensor is antisymmetric (Simpson & Bahr, 2005): If the Earth conductivity structure is assumed to be 2-D, the impedance tensor is asymmetric: However, in reality, the subsurface conductivity structure of the Earth is 3-D.Consequently, the impedance Z r is a 2 × 2 fully filled and asymmetric tensor (Chave & Jones, 2012): For any geomagnetic storm event, the interpolated geomagnetic field at each SinoProbe MT site is then convoluted with the MT impedance tensor for that site in time domain, from which the geoelectric field can be expressed as (Unsworth, 2007): The problem can be defined in the frequency domain using the Fourier Transform as: where μ 0 is the permeability in vacuum.The inverse Fourier transform of the electric field E(ω) yields the geoelectric field in the time domain E(t), as: To determine the effect of the induced geoelectric field to a transmission line, we utilize a Delaunay triangulation to calculate barycentric interpolation weights between three sites forming a triangle around the point at each moment for the geoelectric field at every point along the transmission line, so as to generate the induced voltage of transmission line (Boteler & Pirjola, 2017;Lucas et al., 2018): where dl is a path segment along the transmission line and L is the length of transmission line.

Geomagnetic Storm
A geomagnetic storm is the causal response of the Earth's coupled magnetospheric-ionospheric system to the variable and dynamic action of the solar wind (Bedrosian & Love, 2015).To estimate a magnetic-storm intensity, the D st index is widely used, which is a 1-hr time sequence index that is an average of geomagnetic disturbance measured at low-latitude observatories relative to the quiet-time variation of the geomagnetic field (Sugiura & Kamei, 1991).The D st index can be interpreted as a strength indicator of the westward-directed equatorial ring current in the magnetosphere (Daglis, 2006), which increases during a geomagnetic storm's main-phase (Gonzalez et al., 1994;Loewe & Prölss, 1997).
Based on the D st index, we screened all the intense storms ( 100 nT as G4 intensity on the five-level NOAA space weather scale and adopted as the geomagnetic source in this study (Zhang et al., 2015).
It has been well established that the main phase of a geomagnetic storm, associated with ring-current intensifications, is the primary cause of large GICs and hence a risk factor for electrical power networks and other major infrastructure.However, at middle latitudes, magnetospheric shocks due to large-scale interplanetary pressure pulses give rise to storm sudden commencement (SSC) determined as the first response in the D st index, which have been regard as a potential driver for large GICs (Boutsi et al., 2023;Espinosa et al., 2019;Kappenman, 2003;Zhang et al., 2015).For the geomagnetic storm on 17 March 2015, the SSC started at 04:45 UT along with the sudden increase to 62 nT of the SYM-H index (Figure 1), an index displaying ring current strength like the D st index but with 1-min resolution (Wanliss & Showalter, 2006).Besides, the auroral electrojet currents can also affect the mid-latitude regions during very intense or super geomagnetic storms.To estimate the auroral electrojet currents, the AE index was used, which is calculated from the horizontal magnetic field component recorded with 1-min time resolution at magnetic observatories located under the average auroral oval in the Northern hemisphere (Kauristie et al., 2017).From the AE index shown in Figure 1, the auroral electrojet currents were intense between 13:00-24:00 UT and the index reached a maximum of 2,155 nT at around 14:27 UT.
Compared with the Beijing geomagnetic observatory, the effects of the SSC and auroral electrojets are obvious (Figure 1).Anyway, the magnetopause currents and the auroral electrojet currents are quite far from the midlatitude regions (Carter et al., 2015), so the plane wave theory is still available in our research area.

Magnetotelluric and Geomagnetic Data
Impedance tensors from 119 sites of the SinoProbe MT program were used in this project between 35°and 41°N (geomagnetic latitude 29°-36°N) and 104°-126°E in North China (Figure 2).The sites were collected on an approximately 1°grid (about 110 km spacing) with overall high-quality response bandwidth of 10-2,000 s (Dong  1c).The variations of ΔB x and ΔB y between 13:00 and 24:00 UT are related to the intense auroral electrojet currents as indicated from AE index (Figure 1d).Moreover, a typical feature for middle and low geomagnetic latitudes is that north-component geomagnetic field variations are much larger than the east component.In addition, at these latitudes, magnetic field variations for the six geomagnetic stations are quite similar, with only slight variation.

Frequency-Domain Geoelectric Field
The induced geoelectric field at 0.01 and 0.001 Hz are shown in Figure 4.The geoelectric field has large amplitude in the north-west, south-west, central, north-east and south-east parts of North China, corresponding to the Wula-Daqing, Qilian, Taihang-Lvliang, Yanshan, and Luxi orogenic belts, respectively.Besides, the geoelectric fields at 0.01 Hz in the Ordos Basin displays a polarization, mostly pointing to south.

Time-Domain Geoelectric Field
The average peak amplitude of the geoelectric field for each time step for all MT sites was calculated, where maximum amplitude at each MT site occurred at 13:57 (UT) on 17th March 2015.The geoelectric field vectors at this moment are shown in Figure 5, where the amplitudes of 18 vectors exceed 1 V/km limit, generally predicted for a once-per-century geomagnetic storm (Love et al., 2015).
The amplitude distribution of the time-domain geoelectric field is similar to frequency-domain, while the direction roughly points to the northeast.We note that due to the ocean effect, geoelectric fields close to the coast are significantly distorted, as shown at sites Hb30, Hb16, Hb32, Hb118, and Hb119 in Figure 5.The maximum and minimum geoelectric field amplitudes for all sites range from 2.05 V/km to 0.01 V/km at sites Hb24 and Hb10, respectively.
The geoelectric field time series at four typical MT sites in Figure 2 are shown in Figure 6.The east-west component (E y ) of the geoelectric field has a much larger amplitude than that of south-north component (E x ), corresponding to stronger north geomagnetic variations.Moreover, corresponding to the geomagnetic fields in Figure 3, the geoelectric fields also present sudden increases at 04:45 UT and intense variations between 13:00 and 24:00 UT.

Discussion
During the geomagnetic storm on 17 March 2015, the typical features of geoelectric fields are the sudden increases at 04:45 UT and the intense variations between 13:00 and 24:00 UT (Figure 6), which are consistent with the variations of the geomagnetic fields (Figure 3).From the D st and SYM-H indexes, the shock-triggered SSC started at 04:45 UT.Oliveira et al. (2018) observed intense variations of geomagnetic fields caused by impacts of nearly head-on shocks on the magnetosphere.This is the case of the 17 March 2015 shock, with a shock normal deviation with respect to the Sun-Earth Line less than 20°.Such shock is more geoeffective and can cause intense magnetopause current intensifications, which will cause intense variations of geomagnetic fields at middle and low latitudes (Oliveira et al., 2018).Moreover, the AE index indicates the auroral electrojet currents were intense between 13:00 and 24:00 UT.Therefore, considering drivers of space weather, large impulsive geomagnetic disturbances from auroral electrojet currents and high intensifications of magnetopause currents due to large-scale interplanetary pressure pulses, are the main factors of high geoelectric hazards during the geomagnetic storm on 17 March 2015.Besides, although the scale of SSC events in middle latitudes is quite small compared with auroral electrojet currents (Figure 1), such low-amplitude disturbance can provide a considerable geoelectric field (Figure 6).On the other hand, it has been argued by several authors that the large-scale tectonic units are the most significant factor in determining the low frequency geoelectric field amplitude (Bedrosian & Love, 2015;Cordell et al., 2021;Love et al., 2016Love et al., , 2018)).Simpson and Bahr (2020) show evidence that lithospheric thickness may have a positive correlation with the amplitude of induced geoelectric field.
Figure 7 shows the main tectonic units (Chen, 2009(Chen, , 2010;;Wei et al., 2003) and the amplitude of the maximum geoelectric field during the geomagnetic storm.The lithosphere of North China has a thickness range of 50-90 km and tends to be generally thinner from west to east (Chen, 2009(Chen, , 2010;;Pasyanos et al., 2014).However, this cannot be accounted for the small geoelectric field in the western Ordos Basin and the large geoelectric field in the eastern Yanshan and Luxi orogenic belts (Figure 5).In general, there is reasonable spatial correlation: highamplitude geoelectric fields were mainly distributed in the high-resistivity Taihang-Lvliang, Yanshan and Luxi orogenic belts, while low-amplitude geoelectric fields were mainly distributed in the low-resistivity Ordos Basin and Huang Huai Basin.Within the Ordos Basin, Wei et al. (2010) and Lv et al. (2020) show that the volcanic-sedimentary package in the northern Ordos Basin is quite electrically homogeneous and the geoelectric field amplitude are quite uniform.Variations in the geoelectric field occur mainly in the crystalline basement under the basin.Moreover, the coast effect distorts the geoelectric field (Love et al., 2018), and may affect the estimated geoelectric fields in the Luxi and Jiao Liao orogenic belts, as shown in Figures 5 and 7. To evaluate the geoelectric hazards on UHV transmission lines, the induced voltages in 17 1,000 kV transmission lines were calculated at 13:57 (UT) 17th March 2015, as shown in Figure 8.Among 17 lines, lines 10 and 13-15 have induced voltages larger than 100V regarded as vulnerable lines susceptible to geomagnetic interference (Federal Energy Regulatory Commission, 2013).Besides, different from large geoelectric fields distributed in the SHAO ET AL.
central, northeastern and southeastern parts of North China, large geoelectric hazards on transmission lines are only concentrated in the central part.This difference can be ascribed to the spatial structure of transmission lines and the directivity of geoelectric field.

Conclusion
We convolved measured impedances of 119 SinoProbe MT sites with time series from six geomagnetic observatories in North China to obtain an estimated geoelectric field response during the large geomagnetic storm on 17 March 2015 during Solar Cycle 24.The large geoelectric fields (>1 V/km) occur in the central, north-eastern and south-eastern parts of North China, corresponding to the resistive Taihang-Lvliang, Yanshan, and Luxi orogenic belts, respectively.The high GIC hazard on 1,000 kV transmission lines is concentrated in the central region of North China, where the induced voltages exceed 100 V.
Our estimated geoelectric field models are useful on a regional scale, but with SinoProbe station spacing of 1°( about 110 km) the models are limited for any given transmission line.We recommend additional MT sites coupled with higher-resolution 3D resistivity models that capture topography and bathymetry to provide greater certainty in estimating natural hazard effects of GICs in power networks.Moreover, the shock-triggered SSC can provide a considerable geoelectric field, indicating the importance of forecasting interplanetary shocks for predicting geoelectric effects and GICs at middle latitudes.This study is supported by the National Natural Science Foundation of China with Grants 41904079 and 42174090.The authors appreciate Institute of Geophysics, China Earthquake Administration for observing and sharing the geomagnetic data.The authors appreciate Prof. Wencai Yang of Zhejiang University, and Professors Wenbo Wei, Gaofeng Ye, and Sheng Jin at China University of Geosciences (Beijing), for providing the magnetotelluric data.Collection of MT data was supported by SinoProbe-01.The authors also appreciate Prof. Jennifer Gannon, and two anonymous reviewers for their constructive suggestions that have improved the quality of the manuscript.

Figure 1 .
Figure 1.The Beijing geomagnetic observatory recording and geomagnetic indices of the geomagnetic storm on 17th March 2015.(a) Two days variations of ΔB x (red) and ΔB y (blue) with 1-min resolution; (b) the Kyoto 1-hr D st time series; (c) SYM-H index; (d) AE index.The storm sudden commencement (SSC) and the storm maximum are labeled.

Figure 3 .
Figure 3. Geomagnetic field time-series for north (ΔB x ) and east (ΔB y ) components at six geomagnetic stations during the geomagnetic storm of 17th March 2015.

Figure 6 .
Figure 6.Geoelectric field E x (red) and E y (blue) time series at four typical MT sites.The site location is indicated in Figure 2.

Figure 7 .
Figure 7. Map of geoelectric amplitude and geoelectric features in North China.Resistive and conductive geologic domains are shown in red and green shading, respectively.Resistive units include the Jiao Liao, Yanshan, Luxi, and Taihang-Lvliang orogenic belts, while the Huang Huai and Ordos sedimentary basins are nore conductive.Dashed contour represents the lithosphere thickness from Pasyanos et al. (2014).

Figure 8 .
Figure 8. Snapshot at 13:57 (UT) 17th March 2015 of the induced voltages across transmission lines.The induced voltages are calculated from integrating the spatial distribution of geoelectric fields with the transmission line paths between junctions in the power grid.