U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2018–1043

On the Feasibility of Real-Time Mapping of the Geoelectric 

Field across North America
Cover. View from space of the nighttime lights of the northeastern United States. Aurora light, often seen during magnetic storms, is visible 

overhead. Image by the National Aeronautics and Space Administration. 

(URL for this image: https://www.nasa.gov/multimedia/imagegallery/image_feature_2167.html)
On the Feasibility of Real-Time Mapping of 

the Geoelectric Field across North America

By Jeffrey J. Love, E. Joshua Rigler, Anna Kelbert, Carol A. Finn, 

Paul A. Bedrosian, and Christopher C. Balch

Open-File Report 2018–1043

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

RYAN K. ZINKE, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2018

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Suggested citation:

Love, J.J., Rigler, E.J., Kelbert, Anna, Finn, C.A., Bedrosian, P.A., and Balch, C.C., 2018, On the feasibility of real-time 

mapping of the geoelectric field across North America: U.S. Geological Survey Open-File Report 2018-1043, 16 p., 

https://doi.org/10.3133/ofr20181043.

ISSN 2331-1258 (online)
iii

Acknowledgments

We thank S.W. Cuttler, J.A. Herrick, G.M. Lucas, J. McCarthy, and J.L. Slate (U.S. Geological Survey) 

for reading a draft manuscript. We thank Antti Pulkkinen (NASA) for useful conversations.
iv

Contents

Acknowledgments........................................................................................................................................iii

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Length and Time Scales................................................................................................................................2

Motivation for Parameterized Induction....................................................................................................2

Geomagnetic Monitoring..............................................................................................................................2

Geomagnetic Variation .................................................................................................................................3

Mapping Geomagnetic Variation ................................................................................................................4

Solid Earth Electrical Conductivity and Diffusion.....................................................................................5

Magnetotelluric Surveys .............................................................................................................................5

Impedance and Models of Earth Conductivity..........................................................................................6

Calculation of Geoelectric Fields from Earth Impedance .......................................................................6

Realistic 3D Versus Simplistic 1D Models of Earth Conductivity...........................................................6

Interpolation and Validation of Geoelectric Field Estimates ..................................................................7

Implementation...............................................................................................................................................8

Applications....................................................................................................................................................8

Gap Summary .................................................................................................................................................8

References Cited............................................................................................................................................8

Figures

1. Comparison of 1-minute north-south Bx geomagnetic variation time series

recorded at the Ottawa and Fredericksburg observatories during the Halloween

storm of October 29–31, 2003, and the difference between the OTT and FRD

time series......................................................................................................................................4

2. Map showing synthetic geoelectric amplitudes Ex

h

 (scalar impedances) at

EarthScope and U.S. Geological Survey sites for north-south geomagnetic

induction Bx with a sinusoidal amplitude of 1 nanotesla and a period of

240 seconds. (second, s; millivolts per kilometer, mV/km). Modified from

Love and Bedrosian, 2018, fig. 4A ..............................................................................................7

Conversion Factors

SI to Inch/Pound

Multiply By To obtain

Length

meter (m) 3.281 foot (ft) 

meter (m) 1.094 yard (yd) 

kilometer (km) 0.6214 mile (mi)
v

Abbreviations

Dst disturbance storm time

Ex

h Reference geoelectric field (mV/km) for reference magnetic field of 

unit amplitude (1 nT)

Hz hertz (frequency)

nT nanoTeslas

S/m siemens (S) per meter (m); electrical conductivity

SWAP U.S. National Space Weather Action Plan

USGS U.S. Geological Survey

On the Feasibility of Real-time Mapping of the Geoelectric 

Field across North America

By Jeffrey J. Love,1 E. Joshua Rigler,1 Anna Kelbert,1 Carol A. Finn,1 Paul A. Bedrosian,1

and Christopher C. Balch2

Abstract

A review is given of the present feasibility for accurately mapping geoelectric fields across North America in near-realtime 

by modeling geomagnetic monitoring and magnetotelluric survey data. Should this capability be successfully developed, it could 

inform utility companies of magnetic-storm interference on electric-power-grid systems. That real-time mapping of geoelectric 

fields is a challenge is reflective of (1) the spatiotemporal complexity of geomagnetic variation, especially during magnetic storms, 

(2) the sparse distribution of ground-based geomagnetic monitoring stations that report data in realtime, (3) the spatial complexity 

of three-dimensional solid-Earth impedance, and (4) the geographically incomplete state of continental-scale magnetotelluric surveys.

Introduction

On March 13, 1989, an intense magnetic storm (for example, Allen and others, 1989) induced Earth-surface geoelectric 

fields of sufficient strength to interfere with the operation of Québec’s high-voltage electric-power-grid system, causing a blackout across the entire Canadian province (for example, Bolduc, 2002). The same storm caused numerous operational problems 

and anomalies for power-grid systems in the United States, and geomagnetically induced currents damaged a high-voltage 

transformer at a nuclear-power plant (North American Electric Reliability Corporation, 1990; Barnes and others, 1991). More 

recently, the magnetic storm of November 6, 2001, caused the failure of electric-power transmission systems in New Zealand 

(Béland and Small, 2005), and the Halloween magnetic storm of October 29–31, 2003, caused operational failures in Swedish 

systems (Pulkkinen and others, 2005). Some scenario analyses anticipate that the future occurrence of a rare magnetic superstorm could cause widespread and long-lasting loss of electric power (for example, Kappenman, 2012) and entail significant 

cost for national economies (for example, Barnes and Van Dyke, 1990; National Research Council, 2008; Eastwood and others, 

2017). In light of these events and possibilities, the U.S. Federal Energy Regulatory Commission (2013; Order No. 779) directed 

the North American Electric Reliability Corporation to assess the vulnerability of United States domestic power-grid systems to 

geomagnetic disturbance.

Time-dependent maps of ground-level geoelectric fields (for example, Thomson and others, 2009; Love and others, 2014) 

would enable estimation of geomagnetically induced currents in power-grid networks and thereby support vulnerability assessments of power-grid systems (for example, Molinski, 2002; Samuelsson, 2013; Piccinelli and Krausmann, 2014). Geoelectric 

maps could also inform operational decision making and management of power-grid systems during geomagnetic storms. There 

are, however, significant challenges in producing such maps, especially in realtime. Mapping the geoelectric field requires 

estimates of both the Earth's surface geomagnetic field variation and the Earth’s surface electromagnetic impedance. In particular, 

the accuracy of such modeling is limited by the sparseness of real-time geomagnetic monitoring stations and the incompleteness 

of magnetotelluric surveys.

The U.S. National Space Weather Action Plan (SWAP) contains directives for Federal government agencies involved with 

a disparate set of subjects related to space-weather operations, response, and mitigation. One of these directives calls for the 

Department of the Interior to “report on the feasibility” for providing the Department of Commerce with a “real-time service for 

geoelectric field maps” (National Science and Technology Council, 2015, Action 5.5.6). This directive, in turn, applies to the 

U.S. Geological Survey (USGS) and its Geomagnetism Program (Love and Finn, 2011). 

1

U.S. Geological Survey

2

National Oceanic and Atmospheric Administration
2 On the Feasibility of Real-time Mapping of the Geoelectric Field across North America

This report was developed to satisfy the SWAP directive. It is also consistent with what the U.S. National Research Council 

(2013, p. 146) has described as a “critical national need” to develop capabilities for estimating geomagnetically induced currents 

in power-grid systems; it is consistent with a collaborative study sponsored by Living With a Star Program of the National 

Aeronautics and Space Administration (NASA) (Pulkkinen and others, 2017); and, in general terms, it is consistent with the 

goals identified in the USGS Natural Hazards Mission for enhancing observations, fundamental understanding of hazards and 

their effects, improving assessment products and services, and providing effective situational awareness (Holmes and others, 2013).

Length and Time Scales

In designing a project for mapping geoelectric fields, it is useful to first consider the relevant characteristic length and 

time scales of power-grid systems themselves. The geomagnetically induced voltage on a power grid can be obtained by 

point-to-point line integration of the geoelectric field along the length of the grid line between grounding points. The distance 

between these substations is typically 100 kilometers (km) or so (for example, Horton and others, 2012, table II), and a 

network can consist of multiple connections stretching across 1,000 km or more. With respect to time scales, we note that the 

1989 Hydro-Québec collapse occurred over the course of about 1 minute with tripping of multiple compensators that resulted 

in system instability (Bolduc, 2002). Electric-utility companies have considered the vulnerability of high-voltage transformers 

to abnormal heating caused by quasi-direct, geomagnetically induced currents with durations from about 100 seconds to 

about 10,000 seconds (about 10˗2 to 10 ˗4 hertz [Hz]) (for example, North American Electric Reliability Corporation, 2014a; 

Pulkkinen and others, 2017). 

Motivation for Parameterized Induction

It is tempting to consider continental-scale mapping of geoelectric fields through straightforward interpolation of data 

acquired from geoelectric observatories. In fact, long-term geoelectric field monitoring is maintained at only a few locations 

around the world (for example, Fujii and others, 2015), and data from these stations are useful for validating geoelectric estimation 

methods. However, because of the complexity of solid-Earth conductivity structure, a geoelectric field induced at one location 

can differ significantly from that induced less than a hundred kilometers away (for example, McKay and Whaler, 2006; 

Bedrosian and Love, 2015). This means that accurate mapping of geoelectric fields by interpolation of direct measurements 

would require a very dense network of geoelectric observatories. Unfortunately, it is relatively difficult to operate geoelectric 

monitoring systems for long durations of time (for example, Ferguson, 2012). A more practical approach for mapping of 

geoelectric fields would utilize an empirical parameterization of induction (for example, Bonner and Schultz, 2017; Kelbert and 

others, 2017; Weigel, 2017)—this amounts to muliplication in the frequency domain or convolution in the time domain of 

a real-time map of horizontal-component geomagnetic variation, derived from ground-level magnetometer data, with a map 

of the Earth’s surface impedance, derived from magnetotelluric survey data. In what follows, we summarize some of the technical 

issues, challenges, and opportunities of this approach for operational mapping of geoelectric fields in realtime.

Geomagnetic Monitoring

Magnetometer stations are operated by a variety of institutes for a variety of purposes (for example, Love, 2008). Some of 

these stations are full-fledged observatories and are, as such, dedicated to the long-term acquisition of accurate magnetometer 

time series (for example, Rasson and others, 2011); other stations are simpler variometers, for which acquired time series are not 

necessarily calibrated for absolute accuracy. Many observatory institutes “adjust” their real-time data so that they have a rough 

calibration. Often, this is a rotation that compensates for magnetometer orientation defined by the local magnetic meridian (the 

deviation from geographic north is declination); many variometer institutes do not report magnetometer orientation. Some 

magnetometers are operated with high levels of temporal continuity, whereas others are operated more intermittently. Data 

from only a subset of the world’s magnetometer stations are available in what might be considered “near-realtime.” Improving 

ground-level geomagnetic monitoring is an important goal of the SWAP (National Science and Technology Council, 2015, 

Action 6.2.1), one that would bring significant benefit to the space-weather community but which also comes with significant 

challenges (for example, Love and Finn, 2017).

With respect to North America, inspection of the INTERMAGNET (www.intermagnet.org; for example, Love and 

Chulliat, 2013) and SuperMAG (http://supermag.jhuapl.edu; Gjerloev, 2009) databases for 1-second holdings identified data 
Geomagnetic Variation 3

for January 2015 from about 45 stations in Canada, including observatories operated by Natural Resources Canada (NRCan) 

(Lam, 2011) and variometers that are parts of the AUTUMN (Connors and others, 2009), AUTUMNX (Connors and others, 

2016), CARISMA (Mann and others, 2008), and MACCS (Engebretson and others, 1995) projects; 15 stations in the continental 

United States, including observatories operated by the USGS (Love and Finn, 2011) and variometers that are part of the McMac 

project (Chi and others, 2013); and 10 stations in Alaska, including observatories operated by the USGS and variometers that 

are part of the GIMA project (Wilkinson and Heavner, 2006). The geographic distribution of these stations is far from uniform, 

and the distance between many of them exceeds 1,000 km. Data from all the observatories operated by the USGS are available 

within about 15 minutes of acquisition, either directly from the USGS or through INTERMAGNET; NRCan data are available 

to selected users, including the USGS, National Oceanic and Atmospheric Administration, Space Weather Prediction Center, and 

the U.S. Air Force in near-realtime, though only after a 1-day delay through INTERMAGNET; data from the variometer stations 

are available on a range of schedules, from a few minutes up to a day or so after acquisition. 

Geomagnetic Variation

Geomagnetic field variation is a superposition of numerous signals generated by source electric currents that are both above 

the Earth’s surface and within the Earth’s interior. So, for example, although magnetic storms have their source currents in the 

Earth’s ionosphere and magnetosphere, they induce telluric currents in the Earth’s interior, and these, in turn, generate magnetic 

fields that contribute to the totality of the field measured at the surface. During periods of solar-terrestrial quiescence, quasi-periodic 

geomagnetic variation is sustained by tides in the ocean and ionosphere (for example, Matsushita, 1967). Geomagnetic variation, 

such as that realized at a particular geographic site, encompasses a wide range of frequencies (periods) (for example, Olsen, 2007). 

Ground magnetometers are used to define the time evolutionary phases of magnetic storms (for example, Nishida, 1978; 

Loewe and Prölss, 1997). Many of these commence suddenly, with the arrival at Earth of interplanetary shocks driven by 

coronal-mass ejections (for example, Tsurutani and Gonzalez, 1997). Storm commencements and related intrastorm impulses 

(for example, Joselyn and Tsurutani, 1990) are seen globally in ground-magnetometer time series as abrupt changes in geomagnetic field across a broad range of latitudes with time scales ranging from seconds (Araki and others, 1997) to a few minutes (for 

example, Araki and others, 2004). After storm commencement, geomagnetic disturbance is roughly organized by geomagnetic 

latitude (for example, Ngwira and others, 2013; Woodroffe and others, 2016). Storm main-phase is characterized by the reduction in low-latitude intensity that is generated by an intensification of the magnetospheric ring current (for example, Gonzalez 

and others, 1994; Cowley, 2007). During a magnetic substorm, abrupt rearrangements of the plasma and fields in the Earth’s 

magnetotail divert electric currents into and out of the high-latitude ionosphere (for example, McPherron, 1991; Kamide and 

others, 1998). These substorm currents can generate both auroral light and localized ground-level geomagnetic disturbance. 

During an intense magnetic storm, the auroral oval and associated geomagnetic disturbance can drift down to lower latitudes 

(Nagata, 1950), such as those of the continental United States.

Small-scale ionospheric currents at a height of about 100 km will, by geometric attenuation, generate ground-level geomagnetic disturbance having horizontal length scales exceeding 100 km. This expectation is supported by analyses of data acquired 

from closely spaced, high-latitude magnetometers: geomagnetic disturbance with periods longer than 10 seconds has a horizontal-length scale greater than about 200 km (for example, Watermann and others, 2006; Ngwira and others, 2015). Ground-level 

substorm disturbance typically lasts for an hour or two (for example, Akasofu, 1964), interspersed by quieter periods of a few 

hours (for example, Borovsky and others, 1993), but occasionally, long bouts of substorm disturbance can persist for days or a 

week or more (for example, Tsurutani and others, 2004).

Although these general observations can guide our project for mapping geomagnetic variation, we also recognize that the 

spatiotemporal details of geomagnetic disturbance (for example, Valdivia and others, 1999; Pulkkinen and others, 2006) are 

unique for each storm. Some storms exhibit complicated geomagnetic disturbance, whereas for others it can be relatively simple. 

Sometimes, over the course of a storm, disturbance can evolve from simple to complex and back to simple. Indeed, it is sometimes said that “if you have seen one storm, you have seen one storm” (Friedel and others, 2002, p. 266). Furthermore, physicsbased models of the coupled solar-wind-magnetospheric-ionospheric system cannot yet accurately predict the idiosyncratic, 

storm-time, spatiotemporal details of ground-level geomagnetic disturbance, especially at mid- and auroral-zone latitudes (for 

example, Pulkkinen and others, 2013; Rastätter and others, 2013; Tóth and others, 2014).

A straightforward, empirical demonstration of some of the challenges faced in mapping the storm-time geomagnetic field 

is given in figure 1, where we plot north-south (Bx) disturbance during the Halloween storm of October 2003 as recorded with 

1-minute sampling by magnetometers at two observatories, Ottawa (OTT, Ontario, Canada) and Fredericksburg (FRD, Virginia, 

United States), that are on nearly the same magnetic longitude but different magnetic latitudes. From this figure, we see that the 

time series are similar for about 2 hours during the initial phase of the storm, but afterward, large-amplitude variation with time 

scales shorter than a couple of hours are not well correlated for the remaining duration of the storm.
4 On the Feasibility of Real-time Mapping of the Geoelectric Field across North America

Mapping Geomagnetic Variation

Careful consideration needs to be given for the methods used to construct maps of geomagnetic variation with the data that are 

presently available from ground-based magnetometer stations. Simple, nearest-neighbor and two-dimensional interpolation methods do 

not use well-defined correlation lengths, and the resolution of the model’s field is not better than the spacing of stations (too sparse). 

Statistical interpolation, such as kriging (for example, Armstrong, 1998), is somewhat better, but it requires prior understanding of 

correlation lengths. Better are methods based on physically realistic assumptions. Specifically, one can assume that the field below 

the ionosphere and above the Earth’s surface is free of currents and solve for the magnetic field potential in the region. With this, 

it is conventional to construct maps of geomagnetic variation using regularized least-squares fitting (for example, Menke, 2012) of 

mathematical basis functions to magnetometer data. Three types of basis functions are in common use: for global mapping, spherical 

harmonics (for example, Winch, 1981); for regional mapping, spherical cap (for example, Haines and Torta, 1994); and spherical 

elementary current systems (SECS) (for example, Amm and Viljanen, 1999; Weygand and others, 2011). Development of an operational capability for near-realtime mapping of geomagnetic variation (for example, Rigler and others, 2014) using SECS algorithms 

(for example, Pulkkinen and others, 2003) is part of an ongoing interagency collaborative project between the USGS, NASA, and the 

National Oceanic and Atmospheric Administration (National Science and Technology Council, 2015, Action 5.5.6).

In assessing the errors in SECS maps of geomagnetic variation over North America, it is helpful to examine two related analyses. 

Using data recording a magnetic storm of modest intensity (maximum ˗Dst = 101 nanoteslas [nT]; where Dst refers to disturbance 

storm time) acquired from a relatively dense magnetometer network operated in Scandinavia, Pulkkinen and others (2003) found 

misfit errors in estimates of local geomagnetic variation of about 10 percent (approximately 100 nT) during disturbance (their fig. 9); 

750 OTT FRD

A

B

500

250

0

–250

–500

–750

750

8

Hours from 00:00 29 Oct 2003

16 24 32 40 48 56 64 72

Diff (nT)

Bx (nT)

500

250

0

–250

–500

–750

Figure 1. Comparison of (A) 1-minute north-south Bx geomagnetic variation time series recorded at the Ottawa (red, OTT, magnetic 

55.37°N, 355.88°E) and Fredericksburg (blue, FRD, magnetic 48.14°N, 353.93°E) observatories during the Halloween storm of October 

29–31, 2003, and (B) the difference between the OTT and FRD time series. These observatories are separated by 814 kilometers. Bx, in 

nanoteslas; Difference, in nanoteslas. FRD data from Love and Bedrosian, 2018, fig. 2.
Magnetotelluric Surveys 5

misfit errors in their estimates of the time derivative of the field exceed a factor of 2 (their fig. 10). Using data recording relatively 

quiescent conditions (maximum ˗Dst = 55 nT) acquired from a sparse distribution of observatories in Northern Canada and Alaska, 

McLay and Beggan (2010) found misfit errors in estimates of local geomagnetic variation of approximately 50 nT but also occasionally more than 300 nT, or an amount comparable to the amplitude of variation in the field itself (see their fig. 2, and compare 

with our fig. 1). These results are sobering, and they are cause for caution in concluding that geomagnetic variation can be easily 

mapped. They indicate a need for systematic assessment of uncertainties in the results from such methods.

Solid Earth Electrical Conductivity and Diffusion

The electrical conductivity of the Earth has a complicated spatial distribution, this being reflective of the Earth’s geological 

history and tectonic structure. The most complicated conductivity structure is concentrated in the Earth’s crust, which extends to 

a depth of approximately 20–50 km in North America (for example, Bally and Palmer 1989; Chulick and Mooney, 2002); over 

lateral spatial scales of interest to the power-grid industry (several kilometers to thousands of kilometers), crustal conductivity 

spans at least 4–6 orders of magnitude—from highly conducting to effectively insulating (or resistive)—depending on a myriad 

of factors, including mineralogy, partial melt, water and aqueous fluid content, clay content, volatile content, porosity, and so forth 

(for example, Yoshino, 2011; Evans, 2012). Deeper down, the continental lithosphere (extending to depths of approximately 50 to 

approximately 200 km) followed by the asthenosphere (below the lithosphere) extend down to the upper transition zone boundary at 

410 km depth, and these have complicated conductivity structure; indeed, even the Earth’s upper to mid-mantle down to 1,200 km 

or so is known to exhibit significant spatial structure spanning several orders of magnitude (for example, Kelbert and others, 2009). 

Time-dependent geomagnetic field variation, such as that generated in geospace and measured at the Earth’s surface, propagates into the Earth’s interior in a manner that is, essentially, diffusive for the frequency (period) range of interest (for example, 

Stratton, 1941, chap. 5; Weidelt and Chave, 2012). The Earth’s structure affects the characteristic length scale across which these 

electromagnetic signals are attenuated in the Earth’s interior; the diffusive “skin depth” is proportional to the square root of the 

period of geomagnetic variation and inversely proportional to the square root of the conductivity. For example, for bulk conductivity of 10-3 siemens per meter (S/m), which might correspond to dry continental craton, and for a 240-second (4-minute) 

electromagnetic variation, the diffusive length scale is about 250 km; correspondingly, for bulk conductivity of 10-1 S/m, which 

might correspond to a sedimentary basin, the diffusive length scale is about 25 km. In other words, a 240-second electromagnetic 

variation can plumb the depths of continental crust and even the continental lithosphere. We note that these scales of several tens 

to several hundred kilometers also correspond, very approximately, to the typical lateral distance between neighboring electricpower-grid substation ground points in North America. Longer periods of interest, out to a few hours, can propagate as deep as a 

thousand kilometers.

Magnetotelluric Surveys 

Magnetotellurics is a passive geophysical exploration method for estimating the electrical conductivity structure of 

the Earth’s crust, lithosphere, and upper mantle (for example, Unsworth, 2007). Magnetotelluric surveys are performed 

for purposes of geothermal and mineral exploration, for the study of earthquake and volcano hazards, and for fundamental 

geophysical research (for example, Ritter, 2007). A survey of a given geographic region is accomplished through temporary 

deployment of electromagnetic sensors (magnetometers and grounded electrodes) with which simultaneous measurement 

is made of natural geomagnetic variation and geoelectric field variation at the Earth’s surface (for example, Simpson and 

Bahr, 2005; Ferguson and others, 2012). 

In the United States, the National Science Foundation’s EarthScope program (Williams, and others, 2010) has, since 2006, 

supported a magnetotelluric survey that has covered about half of the continental United States to date (Schultz, 2010). The 

EarthScope magnetotelluric survey is being accomplished with a transportable set of measurement systems, installed at a quasiregular 70-km spacing and operated for about 2–4 weeks at each site. The EarthScope impedance tensors can be obtained from 

the Data Management Center of the Incorporated Research Institutions for Seismology (http://ds.iris.edu/ds/products/emtf; 

Kelbert and others, 2011). The tensors (Schultz and others, 2006–2018) are roughly limited to a frequency band of 10-4 to 10-1 Hz 

(10 to 10,000 seconds). In a separate, smaller project, the USGS performed a magnetotelluric survey of the Florida peninsula in 

2015 consistent with EarthScope magnetotelluric protocols. In Canada, the Natural Sciences and Engineering Research Council 

has supported magnetotelluric surveys of southern Canada through its Lithoprobe program (for example, Hammer and others, 

2011), though these surveys have not been performed on a broad geographic scale like that made through EarthScope.
6 On the Feasibility of Real-time Mapping of the Geoelectric Field across North America

Impedance and Models of Earth Conductivity

It is conventional to summarize the Earth-surface relation between the geomagnetic field and the induced geoelectric field 

in terms of a complex-valued, frequency-dependent impedance tensor. Physically, impedance is determined by the conductivity structure of the Earth’s interior (for example, Weidelt and Chave, 2012). An empirical impedance tensor can be constructed 

(for example, Egbert, 2007a; Chave, 2012) by Fourier transforming the magnetotelluric time series using a regularized leastsquares fitting method (for example, Menke, 2012). Empirical impedance tensors can, in turn, be inverted for models of Earth 

conductivity structure (for example, Egbert, 2007b; Rodi and Mackie, 2012) using regularized nonlinear inverse methods along 

with standard numerical packages (for example, Kelbert and others, 2014). Earth conductivity models obtained by magnetotelluric inversion methods are usually parameterized in terms of either finite-difference or finite-elements computational grids (for 

example, Kelbert and others, 2014), and these usually show that Earth conductivity is three-dimensional (3D) in structure (for 

example, Hermance, 2011).

Conductivity models obtained using the EarthScope magnetotelluric tensors inform fundamental understanding of North 

American geology and tectonic history (for example, Bedrosian and Feucht, 2014; Meqbel and others, 2014; Yang and others, 

2015; Bedrosian 2016; Murphy and Egbert, 2017). They also provide us with important insight on the feasibility of mapping 

geoelectric fields. In particular, synthetic analyses of the EarthScope magnetotelluric impedance tensors show that some geographic regions would realize significant site-to-site differences in induced geoelectric fields during magnetic storms, sometimes 

as large as 2 orders of magnitude over distances of about 100 km, whereas other regions would realize relatively uniform geoelectric fields over broad areas (Bedrosian and Love, 2015). Beyond certain rules of thumb, and without a significant computational cost, error estimates on model impedance can be obtained by comparing the modeled magnetotelluric impedances with 

local empirical impedances coming from auxiliary finer scale survey installations.

In figure 2, we show a map of synthetic geoelectric amplitudes (scalar impedances) that would be induced by spatially 

uniform north-south geomagnetic variation having unit amplitude (1 nanotesla [nT]) and varying in time as a sinusoid with 

a period of 240 seconds. Geographic differences in the induced geoelectric fields are due solely to geological and deeper 

tectonic structure. Generally speaking, synthetic amplitudes are large above the resistive igneous craton, such as in northern 

Minnesota (MN), and small above conductive sedimentary rocks, such as in Florida (FL). Significant differences in amplitude 

between neighboring northern Minnesota sites are consistent with a complex 3D subsurface conductivity structure (for example, 

Yang and others, 2015; Bedrosian, 2016), including a failed continental rift that convulsed the continent 1.1 billion years ago 

(for example, Stein and others, 2016). The spatial resolution of maps such as this are, of course, limited by the station spacing 

of the EarthScope magnetotelluric survey; resolving smaller scale conductivity features is possible, but it would require a denser 

magnetotelluric survey.

Calculation of Geoelectric Fields from Earth Impedance

The geoelectric field at the Earth’s surface can be obtained by convolving a map of horizontal-component geomagnetic 

variation with a map of the Earth’s surface impedance. This convolution can be performed, for a given location, in the frequency 

domain, by applying an inverse discrete Fourier transform to the geomagnetic variation time series (for example, Bonner and 

Schultz, 2017; Weigel, 2017), or in the time domain, after converting the local impedance to a discrete impulse response function (for example, Marti and others, 2014; Kelbert and others, 2017). Analyses using these methods show that peak geoelectric 

field variation can be estimated with an error of within 15 percent (Kelbert and others, 2017). 

Realistic 3D Versus Simplistic 1D Models of Earth Conductivity

In contrast to analyses based on magnetotelluric surveys, some studies of storm-time geoelectric fields (for example, 

Boteler, 1997; Pulkkinen and others, 2008; Gannon and others 2012; Wei and others, 2013; Marti and others, 2014; North 

American Electric Reliability Corporation, 2014b; Viljanen and others, 2014; Boteler and Pirjola, 2017; Torta and others, 2017; 

Winter and others, 2017) have been based on impedances calculated from simplistic one-dimensional (1D) or 1D piecewise 

assemblies of regional depth-dependent conductivity profiles estimated indirectly and qualitatively from geological and geophysical 

information (for example, Ferguson and Odwar, 1997; Ádám and others, 2012; Fernberg, 2012; Blum and others, 2015). We also 

note that the geoelectric field time series that Natural Resources Canada makes available on their website are obtained using 1D 

impedances (Trichtchenko and others, 2016). 
Interpolation and Validation of Geoelectric Field Estimates 7

Independent of the details of these analyses and their accuracy, because induction occurs within a continuous volume, for 

sites above 3D Earth structure, a 1D impedance will not generally be a good approximation of the corresponding impedance—

the amplitude, polarization, and phase of the geoelectric fields induced in a realistic 3D structure will differ, often significantly, 

from those induced in an idealized 1D structure (for example, McKay and Whaler, 2006; Bedrosian and Love, 2015; Bonner and 

Schultz, 2017; Kelbert and others, 2017; Weigel, 2017). Furthermore, piecewise induction of geoelectric fields in piecewise 1D 

impedances cannot resemble the induction of geoelectric fields from a fully 3D impedance. For these reasons, it would be worthwhile to reexamine the accuracy of geoelectric field results derived from qualitative 1D impedances. 

Interpolation and Validation of Geoelectric Field Estimates

To map geoelectric fields by parameterized induction, two alternative methods are available. The first might be described 

as physically motivated: a plausible 3D conductivity model is constructed from the magnetotelluric impedance tensors, and 

from this, and for a chosen geographic location, the model magnetotelluric impedance is calculated as a forward problem (for 

example, Avdeev, 2007; Weiss, 2012). The model impedance can then be convolved with a geomagnetic field time series taken 

from a variation map to obtain a map of the geoelectric field as a function of time. The second method is more computationally 

convenient, though it probably requires good survey coverage for a chosen geographic location. Here, a closely spaced set of 

magnetotelluric impedance tensors are convolved with geomagnetic time series. The resulting geoelectric time series are interpolated to a chosen location (for example, Bonner and Schultz, 2017). A comparison of the two computational methods has not 

yet been performed. 

Maps of storm-time geoelectric fields obtained by parameterized induction are likely to show localized areas of complexity that is the result of a combination of spatially complicated geomagnetic disturbance and spatially complicated impedance. 

An important spot-check on the accuracy of the estimated geoelectric fields can be made by comparing them directly against 

measured data, such as those now being acquired at the USGS Boulder magnetic observatory in Colorado (Blum and others, 

2017); residual differences between measured and modeled geoelectric fields can be continuously updated and made available 

in realtime. Comparisons with geoelectric field measurements obtained with temporary magnetotelluric deployments or from 

longer operating observatories provide a valuable validation opportunity for geoelectric field modeling (for example, Bonner and 

Schultz, 2017; Kelbert and others, 2017; Weigel, 2017).

–130

50

MN

MI

MD

VA

NC

SC

FL

WI

240 – s Ex

h

 (mV/km) for Bx =1 nT

45

40

35

30

25

Longitude (°E)

Latitude (°N)

–120

10.0 < E

3.0 – 10.0

1.0 – 3.0

0.3 – 1.0

0.1 – 0.3

E < 0.1

–110 –100 –90 –80 –70

Figure 2. Map showing synthetic geoelectric amplitudes Ex

h

 (scalar impedances) at EarthScope and U.S. Geological Survey 

sites for north-south geomagnetic induction Bx

 with a sinusoidal amplitude of 1 nanotesla and a period of 240 seconds. 

(second, s; millivolts per kilometer, mV/km). Modified from Love and Bedrosian, 2018, fig. 4A.
8 On the Feasibility of Real-time Mapping of the Geoelectric Field across North America

Implementation

Geoelectric maps, be they in realtime or otherwise, can be provided on a spatial grid (such as latitude-longitude). To 

minimize quantization error, geoelectric values would sensibly be reported with a grid spacing that is finer than that afforded 

by measured data. Alternatively, the geomagnetic mapping algorithms could be provided along with gridded estimates of Earth 

impedance so that a user agency could, with real-time geomagnetic data streams, produce (locally) their own maps of geoelectric 

field. In some cases, it might be useful to use a finely spaced grid in regions where it is required by auroral-zone concentration 

of geomagnetic variation and localized complexity in Earth impedance. As new magnetotelluric data become available, gridded 

estimates of Earth impedance might be periodically updated. To facilitate reproducibility, data, models, and algorithms should be 

referenced by version numbers, digital object identifiers, and metadata.

Applications

For direct calculation of the geomagnetically induced current at transformer-ground point in a power-grid network, two 

quantities are needed (for example, Pirjola, 2002; Horton and others, 2012; North American Electric Reliability Corporation, 

2013): (1) the network admittance, which is a function of ground-point resistivities that can be directly measured (for example, 

Gill, 2009, chap. 11), and (2) the geomagnetically induced voltages on the network lines between the ground points, which can 

be obtained by line integration of the geoelectric fields obtained by the empirical mapping methods discussed here. Real-time 

estimation of geomagnetically induced currents could support real-time assessments of power-grid systems, which have, so far, 

relied on 1D Earth impedances (for example, Boteler and others, 2007; Marti and others, 2013). Geoelectric maps of historical 

magnetic storms would inform the design of power-grid systems that are resilient to geomagnetic disturbance.

Gap Summary

The routine mapping of geomagnetic variation over North America certainly presents significant practical challenges. Additional magnetometer stations (National Science and Technology Council, 2015, Action 5.3.6), supported by modest amounts of 

dedicated support, would certainly improve what is expected to be the relatively poor spatial resolution of real-time geomagnetic 

variation maps. These stations would sensibly be concentrated between about 45° and 65° north magnetic latitude, a zone that 

experiences intense and spatially complex storm-time disturbance and that encompasses several large North American urban 

centers (New York, Chicago, Washington, Philadelphia, Boston, Toronto, and others). The resolution of the geomagnetic variation maps can also be improved by incorporating additional physics that might be brought to the modeling of the magnetometer 

data; most promisingly, using assimilative methods (for example, Schunk and others, 2004; Kihn and Ridley, 2005; Qian and 

others, 2014) and accommodating spherical-Earth geometries (for example, Kelbert and others, 2009; Sun and others, 2015).

The other glaring need is completion of U.S. magnetotelluric surveys (National Science and Technology Council, 2015, 

Action 5.5.5)—only about half of the continental United States has been covered. Very importantly, recent survey work has 

included the northeastern United States, a region that includes major metropolitan centers and substantial electric-power-grid 

infrastructure and is situated on top of old and complicated geological and tectonic structures and at latitudes where geomagnetic disturbance can be intense. By 2018, it is anticipated that the EarthScope magnetotelluric survey will have been completed 

across the Dakotas and Nebraska. Funding has not yet been secured to complete the survey across the southwestern and southcentral United States, though this would certainly be extremely useful. Extending the magnetotelluric survey into southern 

Canada would also facilitate real-time mapping of geoelectric fields of importance for assessing magnetic-storm interference on 

integrated North American power-grid networks.

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