Deriving the geomagnetically induced electric field at the Earth’s surface from the time derivative of the vertical magnetic field

Abstract

We present a new method for estimating the geomagnetically induced electric field at the Earth's surface directly from the time derivative of the vertical magnetic field, without any need for additional information about the Earth's electric conductivity. This is a simplification compared to the presently used calculation methods, which require both the magnetic variation field and ground conductivity model as input data. The surface electric field is needed e.g. in modeling Geomagnetically Induced Currents (GIC) that flow in man-made conductor systems, such as gas and oil pipelines or high-voltage power grids. We solve the induced electric field directly from Faraday's law, by representing the magnetic variation field in terms of external equivalent current and taking time derivative of the associated vector potential. This gives an approximative solution, where the divergencefree part of the electric field is reproduced accurately (at least in principle), but the curl-free part related to lateral variations in ground conductivity is completely neglected. We test the new calculation method with several realistic models of typical ionospheric current systems, as well as actual data from the Baltic Electromagnetic Array Research (BEAR) network. We conclude that the principle of calculating the (divergence-free part of the) surface electric field from time derivative of the vertical magnetic field is sound, and the method works reasonably well also in practice. However, practical applications may be rather limited as the method seems to require data from a quite dense and spatially extended magnetometer network.

Use of spherical elementary currents to map the polar current systems associated with the geomagnetic sudden commencements on 2013 and 2015 St. Patrick's Day storms

“…After the work of Pulkkinen et al . [], SECS have been extensively used to model rapidly varying ionospheric currents with the interest put into the effects they have on technological conductor systems at the Earth's surface due to geomagnetically induced currents (GICs) [e.g., Viljanen et al ., ; Bernhardi et al ., ; Wik et al ., ; Beggan et al ., ; Vanhamäki et al ., ; Caraballo et al ., ; Wei et al ., ; Liu et al ., ; Barbosa et al ., ; Viljanen et al ., ; Juusola et al ., ]. The method can also be used as a means to interpolate magnetic field variations over large areas [ McLay and Beggan , ] and has found its application to reduce geomagnetic repeat station surveys [ Vujić and Brkić , ].…”

“…Accordingly, it served to combine field-aligned currents (FACs) from the Cluster II fleet of satellites with two-dimensional ground magnetic data so as to calculate actual (not equivalent) ionospheric currents [Amm, 2001] or, recently, to derive maps of ionospheric conductances, currents, and electric field in the area between the trajectories of the two Swarm lower spacecraft [Amm et al, 2015]. After the work of Pulkkinen et al [2003b], SECS have been extensively used to model rapidly varying ionospheric currents with the interest put into the effects they have on technological conductor systems at the Earth's surface due to geomagnetically induced currents (GICs) [e.g., Viljanen et al, 2004;Bernhardi et al, 2008;Wik et al, 2008;Beggan et al, 2013;Vanhamäki et al, 2013;Caraballo et al, 2013;Wei et al, 2013;Liu et al, 2014;Barbosa et al, 2015;Viljanen et al, 2015;Juusola et al, 2015]. The method can also be used as a means to interpolate magnetic field variations over large areas [McLay and Beggan, 2010] and has found its application to reduce geomagnetic repeat station surveys [Vujić and Brkić, 2015].…”

Low Geo‐Effectiveness of Fast Halo CMEs Related to the 12 X‐Class Flares in 2002

“…The predicted time of occurrence of geo‐effective events in the Earth environment depends on the effects studied. The common transit time from Sun to Earth for CME/ICMEs and coronal hole high‐speed wind streams can be estimated up to 2 to 4 days (Gopalswamy et al, ; Scolini et al, ); that is, only after this time, the related effects such as geomagnetic storms, energetic particle enhancements, and geomagnetic induced currents are measured at Earth (Vanhamäki et al, ). Impulsive SPEs (from a few keV) up to relativistic energies (few GeV), accelerated by magnetic reconnection‐driven processes during the impulsive phases of solar flares, have a transit time as low as 10 min while large gradual SPE events are produced by fast CME‐driven shock waves and can last a few hours or even days depending on their trajectories and their orientation in the interplanetary magnetic field (IMF) (Zurbuchen & Richardson, ). SPEs can penetrate down to the upper atmosphere leading to solar array degradation, single event effects in electronics, and potential health risks for manned spaceflight and air travelers (Lario & Simnett, ). …”

Rapid prediction of electric fields associated with geomagnetically induced currents in the presence of three‐dimensional ground structure: Projection of remote magnetic observatory data through magnetotelluric impedance tensors

“…[] to determine GIC causes and test how certain prediction methods would have worked if used at the time. Recent studies have been aimed at detecting GICs through means such as solving coupled ionospheric and surface equations [ Love and Swidinsky , ], vertical magnetic effects [ Vanhamaki et al ., ], and inversion [ de Villiers and Cilliers , ]. These techniques have typically been accurate, although too slow and computationally intensive for direct application by industry.…”