地磁気観測所テクニカルレポート 第14巻第 2 号 35-50頁 平成30年
Technical Report of the Kakioka Magnetic Observatory Vol.14, No.2, pp.35-50, 2018

Numerical modeling of spatial profiles of geomagneticallyinduced electric field intensity in and around Japanby
Shigeru FUJITA1, 2, Ikuko FUJII1, Arata ENDO3 and Hiroki TOMINAGA4
Meteorological College
National Institute of Polar Research
3
Global Environment and Marine Department, Japan Meteorological Agency
4
Tokyo Regional Headquarters, Japan Meteorological Agency
1

2

Received 27 November 2017; accepted 14 December 2017;
published 23 March 2018

Abstract
The nationwide intensity map of geomagnetically induced electric fields (GIEs) in Japanis presented by using a numerical modeling method. We estimate near-surface resistivity
distributions from bathymetry and sediment thickness data. GIE intensity distributions arecomputed for external geomagnetic variations at periods of 200, 800 and 3,600 sec. The GIE
intensity is normalized with respect to the magnetic variation of 100 nT at Kakioka Magnetic
Obser vator y. The GIE appears significantly enhanced mainly in coastal areas. In addition,
the enhancement penetrates a few tens of kilometers inland. From the present calculations,
we identify the areas where the GIEs can be largely enhanced, these are (1) the northeast
coast along the Sea of Okhotsk, in Hokkaido; (2) the west coast along the Sea of Japan, insouthern Hokkaido and Aomori Prefecture (Matsumae-Tsugaru area); (3) the northwest coast
along the Sea of Japan, in Niigata Prefecture and Toyama Bay; (4) the southwest coast of the
Pacific Ocean; and (5) the east coast of the Korean Peninsula. Further we need to know thegeomagnetically induced currents (GICs) in Japan. However, we cannot calculate the GICs in
Japan because the power line parameters are not disclosed by policy of Japanese power line
companies.

1. Introduction
The solar flares sometimes result in severe
geomagnetic disturbances called by the magnetic
storms. The storms are characterized by the geomagnetic variations with the amplitudes as large as several 1,000 nT in the high-latitudes and several 100 nT in
middle- and low-latitudes like Japan. The storm-timemagnetic disturbances in the middle- and low-lat©2018 Kakioka Magnetic Observatory, Japan Meteorological Agency

itudes tend to have large depression in the northsouth component. These geomagnetic disturbances
are caused by the westward current in the magnetosphere (the equatorial ring current). The current
understandings of the magnetic storm are referred to
Kamide et al (1997) and references therein.
The magnetic storms induce an electric ﬁeld in
the Earth. Then a potential difference between two

36

Shigeru FUJITA, Ikuko FUJII, Arata ENDO and Hiroki TOMINAGA

neutral points of transformers in an electrical powerline system. That causes the geomagnetically induced
currents (GICs). They sometimes damage electrical
power line systems in high-latitude countries [Kappenman, 2005]. For example, a severe GIC resulted
in a wide-area blackout in 1989 in Canada [Bolduc,2002]. Thus, many investigations have studied GICs
in high-latitude countries [Pulkkinen et al., 2008], but
few have examined GICs in middle-latitude countries[Gaunt and Coetzee, 2007; Torta et al., 2012].
Japan is among the low-latitude countries where
GICs have been rarely investigated. The unique report is the GIC intensity measurement at a transformer station in central Hokkaido (the northern part ofJapan) [Watari et al., 2009]. It was as small as several
Amperes during a moderate geomagnetic storm.
This value is negligibly small compared with the permissible current intensity of a typical transformer. It
is reported that GICs larger than 100 A sometimes
cause transformer accidents in the foreign countries[Tsuboi and Horiuchi, 1988]. In fact, there have been
no reports of serious GIC-induced power line failures
to date in Japan.
A few recent works have investigated the potential effects of an extreme geomagnetic disturbance[Pulkkinen et al., 2012; Baker et al., 2013]. Such an
event does not happen frequently, but could cause
serious damage in developed areas (e.g., widespread
blackouts). Furthermore, an extreme event could
affect not only high-latitude countries, but also middle- and low-latitude regions. For example, the hugemagnetic storm in 1859 induced the geomagnetic
variation larger than 1,600 nT at Bombay in India[Tsurutani et al., 2003]. (This storm is the biggest
one among those recorded scientifically in the histor y of the geomagnetism research. The intensityof this storm is roughly 3-times larger than the 1989
storm [Tsurutani et al., 2003].) After the 2011 Tohoku-oki Earthquake, which was the highest-intensity earthquake in Japan in the past 1,000 years, theJapanese government is aware of the importance of
preparing for such a rare but serious event. It should
be noted that Ministr y of Economy, Trade, and Industry announced importance of the basic researchof GICs in Japan [METI, 2015]. From this viewpoint,
we should not ignore the potential danger of GIC
disasters, even in low-latitude countries like Japan.
Although the results of GIC observation in Hokkaido[Watari et al., 2009] seem to indicate that Japan issafe from GIC disasters, we cannot simply generalize
their findings to any GIC accident, because we do
not know the theoretical maximum intensity of an extremely severe GIC. For this reason, it is important toevaluate the potential effects of an extremely severe
GIC in Japan.
Three matters must be investigated simultaneously in order to gauge the social effects of an
extremely severe GIC. First, the intensity and occurrence rate of extreme severe space weather must be
evaluated (the space science). Second, intensity of
the geomagnetically induced electric fields (GIEs)
must be calculated based on a realistic ground resistivity structure (the geomagnetism). Third, GICs due
to such extreme disturbances must be quantitatively
evaluated by using the circuit parameters of powerline systems are known (e.g., impedances of transmission lines, contact resistances of transformers)[Pirjola, 2008]. Thus, the GIC research is interdisciplinary.
Responding to the needs raised by [METI,
2015], we need to investigate basic information about
the GICs. For instance, we do not have a nationwide
intensity map of the GIE at the surface of the Earth.
The GIE is known to be ver y sensitive to a local
electrical resistivity distribution. (Rough estimationof GIE in Japan by the electrical engineering paper
assumed uniform resistivity [Tsuboi and Horiuchi,
1988]. This treatment is not justiﬁed in Japan.) Therefore, the heterogeneous resistivity structures of theground in Japan whose horizontal scales are comparable to the vertical skin depth (about 10 km for typical storm-time variations in the ground with resistivity of 10 Ωm) should be reﬂected in the estimation of
the GIE. It is also important to identify areas where
the GIE intensity is enhanced in Japan for fundamental investigation of the GIC issues in Japan. We therefore focus on estimating the GIE in this paper before
estimating the GICs.
Previous modeling studies of the GIE havegenerally assumed a horizontally uniform groundresistivity [Pulkkinen et al., 2010]. However, studies
on the structures of the inside of the Earth have revealed that ground resistivity is signiﬁcantly heterogeneous, both horizontally and vertically [Ferguson
et al., 2012]. These studies also found that the GIE isenhanced at a resistivity boundary, because electricNumerical modeling of spatial profiles of geomagnetically induced electric field intensity in and around Japan

current is continuous across the boundar y. Therefore, anomalously large GIEs are observed in boundaries between conductive sea and resistive land (thecoast effect ) [Parkinson, 1962]. Therefore, it is appropriate that evaluations of GIE heterogeneity havebeen performed in the U.K. [Beamish et al., 2002;
McKay, 2004]. Coastal resistivity contrasts substantially affect GIE estimates in the global-scale modeling [Püthe and Kuvshinov, 2013].
Because Japan is an island country, the GIE in
Japan might also be strongly inﬂuenced by the coasteffect. Geomagnetic transfer functions in Japan arestrongly affected by resistivity contrasts in coastal
areas [Fujiwara and Toh, 1996]. This fact means thatelectromagnetic induction patterns in Japan are predominantly inﬂuenced by resistivity heterogeneities.
In addition, GIE obser vations in Hokkaido, Japan
were made with a network of telecommunication cables a few tens to a hundred kilometers long [Uyeshima et al., 2001]. Because their GIE distribution was
resolved on spatial scales as small as several tens ofkm, they concluded that the spatial features of GIEs
in Hokkaido were roughly reproduced using the regional distributions of sea and land.
As ground resistivity structure could signiﬁcantly affect estimates of the GIE and GIC in Japan, GIC
models from Hokkaido alone [Watari et al., 2009] do
not generalize directly to the entire country. Thus, itis crucial to investigate GICs in other areas of Japan.
For this purpose, it is important to characterize the
GIEs using a three-dimensional model of ground resistivity in an appropriate scale.
The GIE in Japan is modelled by using a realistic
geomagnetic storm as the induction source, and anear-surface 3D resistivity structure estimated frombathymetr y and sediment thickness data [Püthe
et al., 2014]. This research found that GIEs in the
coastal region significantly exceeded estimates obtained from 1-D resistivity models. However, the 1
×1 °mesh size was too coarse to discuss the powerline-scale spatial heterogeneities that might affect the
GIE in Japan. This partly motivates the present study.
In this work, we employ a ﬁner mesh and a heterogeneous ground resistivity model to calculate the GIE
intensity map in Japan.
The remainder of this paper is organized asfollows. The next section consists of three sub-sections that explain the numerical modeling technique37

used in this work. The first sub-section describes
the numerical technique itself, the second covers theconstruction of the mesh system, and the third deals
with the ground resistivity structure. The third major
section describes our numerical results, with a focus
on local characteristics of GIE intensity. The fourth
section describes further efforts to characterize GIE
in detail. The last section summarizes the main results.
2. Method
2.1		Theor y
In order to resolve the spatial distribution of the
GIEs in and around Japan, we use the global electromagnetic induction code of Uyeshima and Schultz(2000), with a staggered mesh scheme for ﬁnite-difference calculation of the electric and magnetic ﬁelds.
The magnetic and electric fields are given at thecorner point of a mesh and at the center of the mesh,respectively, as shown in Fig. 1 of Uyeshima andSchultz (2000). Given an inductive source external to
the Earth (this region is henceforth simply referred
to as “the air”), this code solves for the electromagnetic induction of a spherical Earth in the frequency
domain. We use the global code to calculate regional
induction in order to avoid the difﬁculties caused byhorizontal boundaries. We note that this method ignores magnetospheric plasmas.
To obtain the practical GIE intensity map, it
is important to model the magnetospheric source
current in detail. On the other hand, it is sufficient
to employ one element of the source current for
fundamental studies of the GIE intensity map itself.
Each element has a speciﬁc frequency, spatial variations denoted by a unique spherical harmonic, and anormalized intensity. The latter approach is naturally
expanded to the former because any geomagnetic
ﬁeld variation can be represented by linear combinations of GIEs from the elementar y source current.
Therefore, we model induction due to a simple external source in the frequency domain; we calculate
the electromagnetic response of the ground based on
periodic external magnetic variations as a function of
frequency.
We now brieﬂy review how to calculate groundinduction via numerical modeling. Let the Fourier
amplitudes of magnetic ﬁeld variation and the electric~~
current variation be denoted B and J, respectively (the38

Shigeru FUJITA, Ikuko FUJII, Arata ENDO and Hiroki TOMINAGA

Fourier amplitude of each parameter is denoted by
the tilde.) The electromagnetic response of the external source current (Jext) is expressed by the equation,(1)
where r and μ0 are the position and magnetic permeability of a vacuum, respectively. We assume no additional permeability from other materials.
The source current, J ext, is given at 10 Ear thradii (63,710 km) as a boundary condition. It flows
circularly on the equatorial plane, with the flow direction changing as a function of angular frequency,
ω. This source current then induces the north-south
source magnetic field over Japan region. Note that
we choose this source current as an arbitrarily example of a large-scale simple source. This is eventuallysimilar to the equatorial ring current of the magnetic
storm, but we do not intend to simulate the GIEs inthe magnetic storm. To model magnetic sources with
arbitrary polarizations, the plane of the source current flow is assigned an arbitrary inclination α withrespect to the equatorial plane. The inclined planeintersects the equatorial plane at 137.5 E and 42.5 W
with inclination angle α: the sense of α is positive
when current is inclined anticlockwise from east to
west.
~
The induced current J in Eq. (1) yields an elec~
tric ﬁeld (E) in the resistive medium, with electricalresistivity ρ. Thus, we have(2)
Angular frequencies of storm-time magnetic
variations are so low that we can neglect polarization
current [Püthe et al., 2014]. In our modeling, ρ is assumed to be a scalar.
The induction equation,(3)
describes the relationship between the electric and~~magnetic ﬁelds. Here, E and B are numerically calcu~
lated from given values of ρ and Jext. A more detailed
description of the numerical technique can be foundin Uyeshima and Schultz (2000).

2.2		Mesh system
We employ a biased mesh system with finer
meshes in Japan and surrounding areas. The horizontal mesh size is 0.125 over 25-50 N and 125-150 E inorder to reproduce the realistic resistivity structure
in Japan; these are much ﬁner than the 1 ×1 mesh
employed by Püthe et al. (2014). The mesh size outside Japan is gradually widened to 5 .
In the vertical direction, a ﬁner mesh spacing isused near the Earthʼs surface (r＝6371 km denotedwith a broken line). The finest mesh spacing is 1.0
km around the Earthʼs surface, and mesh width increases with increasing distance from the surface of
the Earth. For instance, the second to fifth meshes
have widths of 1.5, 2.5, 2.5, and 5.0 km, respectively.
(So, the mesh positions from the surface are 1 km,
2.5 km, 5 km, 7.5 km, 12.5 km.) This mesh structure
guarantees that numerical results near the surface
have the highest accuracy of any values in the model,
because these mesh widths are sufficiently smaller
than the skin depths of the most conductive material(seawater) in this study at the periods considered.
For example, the skin depth of the 100 sec variationis 〜10 km in seawater with resistivity 0.33 Ωm.
The upper and lower altitude boundaries forthese calculations are 63,710 km (10 times of Earthʼsradius) and 3,479 km, respectively. Both boundaries
are far enough so that electric and magnetic variations near the Earthʼs surface do not reach theseboundaries. The resistivity below the lower boundary(the mantle-outer core boundary) is set to zero to ensure no induction beyond the boundary.
The mesh is divided into 189 total meshes inlongitude, 153 total meshes in latitude, and 81 total
meshes in altitude.
2.3		Resistivity model
In order to calculate local to the regional GIEs
in Japan, we need to consider the distribution ofground resistivity in three dimensions. Some 3-D
regional models of the ground resistivity distribution
in Japan have been reported recently, based on direct
measurements [Kanda and Ogawa, 2014; Hata et al.,2015]. However, measurements are not yet available
for the entire region. Therefore, it is necessary to use
an inferred model for ground resistivity.
In the present paper, we utilize land topography and bathymetr y data from ETOPO1 [Amante

Numerical modeling of spatial profiles of geomagnetically induced electric field intensity in and around Japanand Eakins, 2009], along with a global digital map ofsediment thickness [Laske and Masters, 1997], to estimate ground resistivity in the near-surface area. Using these two data sets, the near-surface area can bedivided into a seawater region, a sedimentary region,
and a rock region. We generate a 3-D near-surface
resistivity distribution by assigning typical resistivity
values to each region. Radially symmetric (1-D) layers are used underneath the heterogeneous near-surface layers.
This resistivity model mainly features a large resistivity contrast between sea water (0.2-0.5 Ωm) androck (typically, 100 to 10,000 Ωm for the crust). Inclusion of the sediment region gives better accuracy
to the resistivity model. The sea-land contrast is themost severe and has the relevant spatial scale for the
GIE of the power line in Japan. The crustal rock canhave a resistivity as small as 0.1-1 Ωm, however thoseextreme values are ʻanomaliesʼ and would not last in
the powerline scale.
It is noted that bathymetry data have a resolution of 1ʼ×1ʼ, but sediment data have a resolution of
1 ×1 . It is important to utilize a horizontal meshsize as small as several tens of kilometers to calculate
GIEs in Japan, due to the regionʼs complex geography. Thus, to match the spatial resolution of the sediment data to that of the bathymetry data, we use thebicubic interpolation method of the General Mapping
Tools software package [Wessel and Smith, 1998].
Fig. 1 shows the bathymetry–altitude map in the left
panel, and the interpolated sediment thickness map
in the right panel.
Here, we explain how we determine resistivity

on the computational mesh. In our staggered meshsystem, resistivity is given at the center of a meshreﬂecting the portion of sea water, sediment and rockin it.
Let bathymetry and sediment thicknesses at θ
(co-latitude) and Ψ (longitude) be zb(θ,Ψ) and zs(θ,Ψ),respectively. θ and Ψ locate the center of the top
surface of a mesh which represents the uppermost
ground (Fig. 2). Altitude is neglected in this study;i.e., zb(θ,Ψ)＝0 on land. The bathymetr y and sediment thickness data are given on ﬁner meshes thanour computational mesh at the surface of the Earth.
Thus, some surface computational meshes have multiple bathymetry and sediment thickness values. To
compensate, we arrange the data onto the horizontal
computation mesh by averaging values included ineach mesh.
For the sea region, let zb(θ,Ψ) denote the depthof the seawater. We set zb(θ,Ψ) equal to the depth of
the top of the sediment; thus, zb(θ,Ψ)+zs(θ,Ψ) gives
the depth of the top of the crustal rock. Therefore,
the boundaries between seawater and sediment, as
well as between sediment and rock, are determinedon the computational mesh. We then assign eachmesh to the portions of seawater, sediment, and rockby computing the widths of seawater, sediment, androck included in that mesh. Let dw(θ,Ψ,r), ds(θ,Ψ,r)and dr(θ,Ψ,r) denote the widths of seawater, sedimentand rock, respectively, for the mesh centered on θ,Ψ
and r. When the mesh is occupied by one or two regions, the width(s) of excluded region(s) is zero. The

Fig. 2

Fig. 1(a) Bathymetry and altitude, and (b) sediment
thickness, in and around Japan. Sediment
thickness is interpolated to a 1’×1’ mesh.

39

Schematic view of the computational meshand distributions of seawater, sediment androck. rk means the k-th node in the r direction.
The depths of sea water and sediment zb(θ,Ψ)
and zs(θ,Ψ) are given at the center of the top
surface of the uppermost mesh for the groundθ(co-latitude) and Ψ(longitude). The widths ofseawater, sediment and rock, dw(θ,Ψ,r), ds(θ,Ψ,r)and dr(θ,Ψ,r), respectively, are computed fromzb(θ,Ψ) and zs(θ,Ψ) for each subsurface mesh.

40

Shigeru FUJITA, Ikuko FUJII, Arata ENDO and Hiroki TOMINAGA

conductivity σ(θ,Ψ,r) of the mesh is the average ofthe conductivities of the three regions, weighted by
the relative proportions of each:(4)

where ρw, ρs, and ρr denote the resistivities of seawater, sediment, and rock, respectively. d is the widthof the mesh. In this work we assume ρw＝0.33 Ωm,
ρs＝10 Ωm, and ρr＝1,000 Ωm, respectively. The resistivity, ρ(θ,Ψ,r), is simply the reciprocal of conductivity; i.e., ρ(θ,Ψ,r)＝1/σ(θ,Ψ,r).
Fig. 3 shows the resistivity distribution of theuppermost mesh of the ground (1 km width) in andaround Japan. It is evident from Figs. 2 and 4 thatlower-resistivity areas in the deep sea invoke striking contrasts with higher resistivity areas on land. It
is noted that these contrasts are reproduced by thepresent the 1ʼ×1ʼ mesh calculation. We also noticecomparatively low-resistivity patches that reﬂect geological structures on land and in the shallow-water
region. For example, depressed resistivity appears in
the Kanto Plain and in Akita Prefecture of Honshu, aswell as the Ishikari and Tokachi plains of Hokkaido;

Fig. 3

Resistivity distribution from the surface to 1 km.

these low-resistivity areas are associated with thicksediment. The low-resistivity area in Akita Prefectureis also seen in the 3-D resistivity model of Kanda andOgawa (2014). It is expected that these low-resistivity
areas act like shallow sea areas in terms of electromagnetic induction.
Fujiwara and Toh (1996) and Uyeshima et al.
(2001) performed thin sheet modeling with resistivity models that consisted of seawater and rock. Since
we include sediment, our resistivity model shows
spatially smooth variations. Such a ﬁne-scale groundresistivity structure is important in evaluating GIEs.
The rock region extends to a depth of 42 km.
The region beyond this depth is the upper mantle,
with 500 Ωm resistivity and a thickness of 758 km; i.e.,
extending from 42 km to 800 km below the surface.
The lower mantle, with resistivity 0.5 Ωm, has a thickness of 2,092 km (extending from 800 km to 2,892
km below the surface). The outer core, at r＜3,479
km (extending from 2,892 km below the surface), is
assumed to be a perfect conductor. It is noted thatthese deeper parts of the Earth do not significantly
affect induction for the geomagnetic variations concerned.
3. Results
3.1		GIE induced by north-south magnetic variation
We now show numerical estimates of GIE intensity in and around Japan. The GIEs induced by external magnetic variations with periods of 200, 800, and3,600 sec are discussed in the present report. The
200 sec variations roughly correspond to the timescale of the geomagnetic sudden commencement
which is invoked by sudden compression of the magnetosphere due to the solar wind shock [Araki, 1997].
The 3,600 sec variations represent the magnetic substorm associated the severe auroral activity in the polar region [Akasofu, 1964]. First, we show GIE intensity for external magnetic variations polarized in thenorth–south direction (i.e., the source current ﬂowing in the equatorial plane). Subsequently, we discuss
GIE intensity caused by external magnetic variations,with horizontal vectors declined from north (i.e., thesource current inclined from the equatorial plane).
Fig. 4 shows the GIE intensity map in andaround Japan at a period of 200 sec, when the source
current induces north–south magnetic variations on

Numerical modeling of spatial profiles of geomagnetically induced electric field intensity in and around Japanthe ground. GIE intensities shown in this ﬁgure arenormalized with respect to a geomagnetic intensity at
Kakioka of 100 nT. Hereafter, all GIE intensity maps
use the same normalization. Fig. 4 also shows that
GIE intensity varies locally across Japan; the GIE is
uniform and very small in the ocean, whereas patchy
patterns are resolved on land. The GIE amplitude on
land ranges from about 500 to 2500 mV/km. Thesevariations reflect the heterogeneous distribution ofground resistivities in Fig. 3.
The GIC and GIE have been previously estimated under the assumption of a horizontally homogeneous surface resistivity [Pulkkinen et al., 2010].
Thus, it is interesting to compare the GIE in the heterogeneous resistivity case (i.e., Fig. 4) with that of
the homogeneous resistivity case. This comparison
will emphasize the coast effect. Fig. 5 shows the ratioof GIE estimated from a heterogeneous model (Fig.
4) to that estimated from a homogeneous model withuniform (1,000 Ωm) surface layers. We use the same

equatorially flowing (east–west) source current for
both cases. This figure clearly shows that the GIEs
are enhanced when coastlines trend north–south.
These coastlines are perpendicular to the directionof the source current, which is perpendicular to thedirection of the primary current induced in a uniform
medium. This GIE enhancement penetrates a few
hundred kilometers onto land, especially when theland is narrow or resistive (i.e., shallow sediment).
Peaks of enhanced-GIE regions have widths as narrow as a few tens of kilometers.
We notice intensified GIEs (as large as 2500mV/km, for the 100 nT magnetic variation at Kakioka) along the west coast of Matsumae Peninsula,
Hokkaido, and on the west coast of Tsugaru Peninsula (labeled “A” in Fig. 4). The GIE is also enhancedon the conjugate coastlines of Iwate Prefecture, on
the Paciﬁc Ocean (labeled B in Fig. 4), but the in-Fig. 5
Fig. 4

GIE intensity in and around Japan for theequatorial source current at a 200 sec period.
GIE intensity is normalized to match the 100 nT
magnetic intensity at Kakioka. The white arrow
indicates the direction of the source current.
The GIE is enhanced along the west coast of
Matsumae Peninsula and Tsugaru Peninsula (A),and along the east coast of Iwate Prefecture(B). The GIE is depressed in Ishikari Plain (C),Tokachi Plain (D), in Kanto Plain (E), and Akita
Prefecture (F).

41

Ratio of GIE modeled with a heterogeneous
surface to GIE modeled with a homogeneous
surface. A source current is placed on theequatorial plane and oscillated with a 200 sec
period. Absolute values of the complex ratio areshown. Areas where the heterogeneous GIE islarger/smaller are shaded red/blue, respectively.
Green solid curves are isolines corresponding toa ratio of unity. Heterogeneous areas reflect theland–sea distribution and sediment thickness inthe area, while homogeneous areas are made ofrock. Rock resistivity is fixed at 1,000 Ωm.

42

Shigeru FUJITA, Ikuko FUJII, Arata ENDO and Hiroki TOMINAGA

tensity is smaller than that of the Matsumae-Tsugaru
region. This asymmetry comes from differences in
the resistivity structures of each regionʼs respective
coastal areas. In the Matsumae-Tsugaru region, thedeep sea is close to the coast, whereas this is not thecase for Iwate Prefecture (Fig. 1a). The concentration of GIEs due to the deep seaʼs proximity can beseen in a cross-section of GIE and electric current
distributions in Matsumae Peninsula (Fig. 6). Fig. 6
illustrates the electric current vectors in an arbitraryscale at t＝0 in the cross section. (As the current~
is expressed as J (r,ω)eiωt, the current at t＝0 is thereal part of J.) The sea depth is 〜 1 km next to thecoastal mesh in the peninsula. The electric current
has a large vertical component just offshore, whichconverges in the horizontal direction at the coastal
mesh. Although the electric current has no verticalcomponent at the sur face (air has almost infinite
resistivity), the vertical component can propagate to
subsurface layers. Thus, due to the resistivity distribution, the induced electric current is distributed
three-dimensionally in Matsumae Peninsula, givinga wide range of GIE values at the surface. It is notedthat the mountains above the sea level do not affectsignificantly the GIE distribution because currents
induced in the mountains can ﬂow along the ground.
It is evident from Fig. 4 that reduced surface
GIEs appear in the Ishikari Plain (“C” in the ﬁgure)and Tokachi Plain (“D”) regions of Hokkaido, andin Kanto Plain (“E”) and in Akita Prefecture (“F”) of
Honshu. All of these regions are characterized by

Fig. 6

Cross-section of GIE intensity (color contours)
and electric current (white arrows) in Tsugaru
Peninsula at t＝0. The current vectors areshown in an arbitrary scale. Cross-section
latitude is 41.875°N. Bathymetry and altimetry
are indicated by black lines. Altimetry above
sea level is ignored in this study.

low resistivities due to great sediment thicknesses(Fig. 1b). Slightly enhanced GIEs appear at the rimsof these low-GIE regions, caused by the resistivity
contrast between sediment and rock. This feature
was already reported that an enhanced GIE should
be seen at the margin of the Kanto Plain, because thesediment-basement rock boundar y causes a weakcoast-like effect [Honkura, 1985]. We also note thata strongly enhanced GIE is observed along the east
coast of the Korean Peninsula.
Fig. 7 shows the GIE intensities for external
magnetic variations with periods of 800 sec and 3,600
sec, assuming external magnetic variations are oriented north–south. Naturally, the net GIE intensity
is reduced (relative to that of 200 sec variations),
which follows directly from Faradayʼs law. However,
the general spatial pattern of enhanced GIE intensities in coastal areas does not change. Thus, the GIEs
responsible for GICs on power line systems are substantially affected by near-surface resistivity structure in and around Japan, for magnetic variations
with time scales of 200-3,600 sec. These are typicaltime scales for external geomagnetic disturbances.
Spatial variations in GIC intensity will be strongly
affected by sharp changes in surface resistivity along
the routes of power lines.
3.2		GIEs from various source polarizations
Since geomagnetic disturbances in the magnetosphere are not only polarized in the north–south
direction, we need to investigate the dependence of
GIE intensity on polarization direction. In this analy-

Fig. 7

GIE intensity in and around Japan for externalcurrent with (a) 800 sec period and (b) 3,600s
period. The source current is placed on theequatorial plane.

Numerical modeling of spatial profiles of geomagnetically induced electric field intensity in and around Japansis, the source current at 63,710 km is inclined relative to the equatorial plane, so that induced magnetic
variations in the Japan region have arbitrarily polarized directions with inclination angle α. Fig. 8 shows
GIE intensity plots forα＝－30 and 60 . When theseresults are compared with Fig. 4, we notice that the
GIE is enhanced in different locations. For example,
with α＝60 the GIE is greater in the western half ofHonshu than in the eastern half; this is the oppositeof the pattern in Fig. 4. For α ＝－30 , the GIE is generally large in most of the Japanese islands. In bothcases, an enhanced GIE appears along the Pacificcoast of southwest Japan (“A” in Fig. 8). These differences may arise because the induced electric current

Fig. 8GIE intensity distributions in and around Japanfor inclined source currents with a period of
200s. Source current is inclined (a) 60° and (b)–30° relative to the equatorial plane.

Fig. 9GIE intensity and electric current at Toyama
Bay for inclined source currents. GIE intensity(color contours) and electric current (whitearrows) are computed at a period of 200 sec.
The source current is inclined (a) 0° and (b) 60°
with respect to the equatorial plane. Snap shots
when the GIE and current amplitudes are near
their maximum values are shown: (a) t＝150
sec and (b) t＝50 sec. The electric current
vectors in each figure are shown in an arbitraryscale.

43in the ocean has a component perpendicular to thecoast when the inducing magnetic ﬁeld has a component parallel to it.
The GIE shows a sharp peak at the coast of
Toyama Bay (“B” in Fig. 8a). Toyama Bay is the terminus of a deep, narrow bay structure formed by
Honshu and Noto Peninsula. This geography results
in a conductive narrow path along the coast, and a
sharp resistivity boundar y at the coast of Toyama
Bay (Fig. 4). When the source electric current ﬂows
parallel to the axis of the bay structure (α＝60 ), theinduced electric current in the ocean is concentrated
in the narrow conductive path, and reaches Toyama
Bay (Fig. 9b). The same mechanism seen in Fig. 6
enhances the GIE at the coast of Toyama Bay. If thesource electric current is not parallel to the axis of
the bay structure, then intensiﬁcation of the electric
current and GIE is only moderate (Fig. 9a). A similar
resistivity structure to that of Toyama Bay is seen
at Suruga Bay in Fig. 3; therefore, there may be enhanced GIEs at the coast of Suruga Bay when thesource electric current ﬂows parallel to the bay axis.

Fig. 10 Maximum GIEs in and around Japan for an
external current with an oscillation period of
200 sec. The maximum GIE at each site istaken from five inclination angles (–60°, –30°, 0°,30°, and 60°). Areas of enhanced GIE intensity
tagged with 1～5 are explained in the text.

44

Shigeru FUJITA, Ikuko FUJII, Arata ENDO and Hiroki TOMINAGA

Fig. 11 Maximum GIE maps in and around Japan for
external currents with periods of (a) 800 sec
and (b) 3,600 sec.

As noted above, GIE intensity depends on thehorizontal polarization of the external magnetic
field. Thus, GIE intensity reaches its maximum atsites where declination changes continuously. The
superposed envelope of the maximum GIEs of allsites yields a map showing theoretical maximum GIE
intensity in and around Japan (e.g., Fig. 10). These
values can be obtained by changing the inclination
angle of the source current. Fig. 10 shows the maximum GIE map for the 200 sec magnetic variation forinclination angles of a＝60 , 30 , 0 , 30 , and 60 . Thisﬁgure indicates ﬁve areas of intensiﬁed GIE: (1) thenortheast coast along the Sea of Okhotsk, in Hokkaido; (2) the west coast along the Sea of Japan, insouthern Hokkaido and Aomori Prefecture (Matsumae-Tsugaru area); (3) the northwest coast along the
Sea of Japan, in Niigata Prefecture and Toyama Bay;(4) the southwest coast of the Paciﬁc Ocean; and (5)the east coast of the Korean Peninsula. An intensiﬁed
GIE appears in the same areas for 800 sec and 3,600
sec GIEs (Fig. 11).
4. Discussions
4.1		Resistivity in the rock region
We estimated GIE intensity using heterogeneous
near-surface resistivity, with typical values of resistivity for seawater, sediment, and rock. The resistivities
of seawater and sediment are appropriately typicalvalues, because seawater resistivity ranges from 0.25
to 0.5 Ωm (depending on temperature and salinity),and sedimentary resistivity ranges from 1 to 50 Ωm.
On the other hand, the resistivity of crustal rock canvary from 〜 0.1 to 10,000 Ωm, and resistivity in theFig. 12 Maximum GIE maps in and around Japan for arock resistivity of 100 Ωm, with an applied 200
sec current.

upper mantle can vary from 10 to 1,000 Ωm [Evans,2012]. A resistivity value of 1,000 Ωm for rock regions
above 42 km was chosen in the present study as arepresentative value for the resistive lithosphere (i.e.,
crust and brittle upper mantle) in the region. Therefore, we also calculated GIE intensity based on the
conductive lithosphere (100 Ωm), to investigate thepossible effects of changing resistivity on GIE intensity. Fig. 12 shows the maximum GIEs for a 200 sec
current. This ﬁgure indicates that rock resistivity signiﬁcantly affects GIE amplitude in coastal areas. On
the other hand, spatial patterns of GIEs are roughly
the same as for 1,000 Ωm, because the GIE spatial
patterns are mainly characterized by enhancement at
resistivity boundaries.
4.2		Magnetotelluric impedance tensors
As the numerical results described above are
not confirmed by real obser vation, it is important
to compare the numerical results with the observed
one. However, the direct measurements of the GIEs
all over Japan have not been conducted yet. Instead,
we treat the magnetotellulic induction vectors whichwere measured by Uyeshima et al. (2001).
As shown above, the GIE is highly sensitive toNumerical modeling of spatial profiles of geomagnetically induced electric field intensity in and around Japan

45

Fig. 13 Magnetotelluric impedances for a 3,600 sec equatorial source current in Hokkaido (a, b) and Kanto (c, d).
Vectors of Re(Zxx) and Re(Zyx) are shown in (a) and (c), and vectors of Re(Zxy) and Re(Zyy) are shown in (b) and(d), respectively. The arrow in (e) denotes a scale reference impedance vector of 5.0×10－3 Ω.

the resistivity distribution of the Earth. Therefore,
it exhibits a complicated pattern at the surface. Thisfacts indicates that a 1-D model does not fully reproduce the full complexity of true GIEs in Japan. As often shown in magnetotellurics (hereafter MT) [Cagniard, 1953], the 1-D assumption breaks down when
MT impedances are considered. MT impedance,
Zij(i,j＝x,y), appears in the following expression,(5)components illustrate how Bx relates to Ex and Ey.
Fig. 13b and d shows the corresponding components
Re(Zxy) and Re(Zyy), to illustrate how By relates to Ex
and Ey. These ﬁgures clearly show that the magnetic ﬁeld correlates to the electric ﬁeld in the parallel
direction (i.e., the diagonal component of MT impedance). This reﬂects the resistivity distribution of the
Earth. For instance, in Fig. 13a and b we can recognize the following characteristics of MT impedance
at Memambetsu: (1) responses to B y have larger

Zij (i,j=x,y) is also the transfer function of thegeoelectric field Ei to the geomagnetic field Bj. Fig.
13 shows estimates of MT impedances in the Hokkaido and Kanto Plains at 3,600 sec periods, using
our computations of the GIE and magnetic field at
the Earthʼs surface. Fig. 13a and c shows the vector
components Re(Zxx) and Re(Zyx), respectively. These

amplitudes than responses to Bx; and (2) responses
to Bx are relatively 1-D, but responses to By are not.
The second feature is consistent with impedances
observed by Fujii et al. (2015), and with observationsof a strong correlation between the GIC and By near
Memambetsu [Watari et al., 2009]. Fur thermore,when the impedances in Hokkaido (Fig. 13) are compared with obser ved values reported by Uyeshima

46

Shigeru FUJITA, Ikuko FUJII, Arata ENDO and Hiroki TOMINAGA

et al. (2001), their spatial patterns are similar. For
example, both the measured and calculated induction
vectors are directed toward the coastline in the coast
area of the Okhotsk Sea and south-east in the central
part of the Hokkaido and in the coast area of Paciﬁc
Ocean. Thus, the present calculation is independently validated by existing observations. However, theobserved impedances show smaller-scale variations
than our computations. This indicates that the observed impedances are influenced by smaller-scalegeological structures than present models can consider.
The MT impedance estimates for Kanto Plain(Fig. 13c and d) are a serendipitous consequence ofthe present study: anthropogenic noise interfereswith ﬁeld measurements of the GIE or geomagnetic
ﬁeld in such highly industrialized, densely populatedareas. Yet the same high population density makes it
important to estimate GIE in this area. Our numericalresults show that the coast effect is seen along the
Pacific Ocean, and at the margins of the thick sediment layer. This result is consistent with Honkura(1985). However, their anomalously large Ey values
at Kakioka and patchy distributions of GIEs near
Kakioka are not reproduced in Fig. 13. Thus, several
key local geological structures might be missed byour model because our model aims at the GIE in the
power line scale.
4.3		Future issues
We note that the present fine-mesh (0.125 ×
0.125 ) calculation is capable of reproducing the local
GIE enhancement in Japan better than the coarsemesh (1 ×1 ) calculation by Püthe et al. (2014) is. In
addition, the local GIE enhancements obtained in thispaper are mainly associated with the sharp resistivity
contrasts in the sea-land boundary; these contrasts
are essentially determined by the bathymetry data.
Therefore, the local GIE enhancements in the GIC
map seem to be realistic. However, it is noted that the
GIE map with much finer mesh configurations may
be still desirable in order to conﬁrm convergence ofthe numerical calculation; this is the future work. In
addition, as the 3D resistivity distribution is not conﬁrmed by the measurement of the resistivity. Therefore, the measured resistivity distribution is strongly
required for the realistic estimation of the GIEs.
Thus, the second future work is to calculate the GIE

map with the measured 3D resistivity distribution in
Japan.
The present study manifested the maximum
GIE intensity map. The intensity does not refer to theabsolute values, but the relative one corresponding
to the normalized magnetic variation (100 nT at Kakioka magnetic observatory). To access the absolutevalue and discuss the possible vulnerability of thetransformers in Japanese powerline system, we need
information of the magnetic variations of the hugemagnetic storm occurring once in 1,000 years. At thesame time, it is important to investigate the criticalintensity of the GIC that can damage a transformer.
However, there is no deﬁnite report about the critical
GIC. The transformers used in Japan are safe for the
GIC of 30 A [Takasu et al., 1993]. On the other hand,
there is a report that the GICs more than 100 A may
cause damages of transformers in foreign countries[Tsuboi and Horiuchi, 1988]. Recently, it is reported that the Japanese transformers seem to work insafe for the GIC with more than 100 A [METI, 2015]
which occurred in Nov. 2003 (the Halloween storm).
The intensity of this storm ( 〜400 nT) is about 1/4 of
the 1859 storm intensity ( 〜1600 nT). Therefore, thevulnerability of the Japanese transformers is not settled when the huge magnetic storm occurring once
in 1,000 years is considered. It is noted that we might
predict the huge storm from observations of the sun
with a lead time of about 1day.
As a next step, it is important to calculate GICs
from the GIE distribution obtained in this paper. To
that end, system parameters of the power grid in Japan are required. However, as the information is notdisclosed by Japanese electric companies, it is difﬁcult to calculate GICs at the present time.
5. Conclusions
After the 2011 East-Japan great Ear thquake,
the Japanese government acknowledged that the enhanced GICs due to the extremely severe magnetic
storms are regarded to be investigated seriously. On
the other hand, as the GICs in Japan are not sufficiently investigated, we perform the basic researches
about the GIE intensity map in Japan by using a modelled ground resistivity structure.
We constructed a 3-D resistivity model of the
Earth surface, estimated from bathymetry and sediment thickness data. We then calculated the intensity

Numerical modeling of spatial profiles of geomagnetically induced electric field intensity in and around Japanof the GIE based on the inferred resistivity model.
Based on our work, several areas of Japan appear
prone to enhanced GIEs: (1) the northeast coast of
Hokkaido, along the Sea of Okhotsk; (2) the west
coast of southern Hokkaido and Aomori Prefecture(Matsumae-Tsugaru area), along the Sea of Japan; (3)the northwest coast of Niigata Prefecture and Toyama Bay, on the Sea of Japan; and (4) the southwest
coast of the Paciﬁc Ocean in the Japan islands. Notably, all enhanced areas are located on the coast.
From the discussions in Fig. 6, the GIE variations in the coastline of the Japan Sea and that in the
Paciﬁc Ocean side become anti-phase. Therefore if atransformer station is located in the Japan-Sea areawith enhanced GIEs (for example, Tsugaru Peninsula) and the neighboring station is located in the Pacific-Ocean side (for example, the coastline of the Iwate
Prefecture), the potential difference between the twostations may be very large. Thus, the GIE map presented here can be used as a preliminary hazard map
for the GIC disasters.
MT impedance vectors obtained from our modeling work are comparable to obser ved values in
Hokkaido. In addition, we obtained MT impedancesfor Kanto Plain, where anthropogenic noise makes
accurate ﬁeld measurements impossible. The map ofMT impedance vectors in Japan may provide a usefulreference for electric and magnetic measurementsin the future, when more detailed resistivity models
become possible.
Resistivity in the crust and mantle control GIE
intensity. Therefore, it is important to use ﬁne-scale
resistivity distributions in modeling work. If resistivity structure can be directly measured, the GIE map
will be improved greatly. We also stress that simulated GIEs must be compared with observed values inorder to validate any modeled maximum GIE map.
Finally, in order to accurately estimate hazards, GIC
values must be calculated using data from power line
systems and transformer stations.
Acknowledgments
The authors are grateful to M. Uyeshima of The
University of Tokyo for his assistance with the computational code and discussions. We are also thankful to A. Pulkkinen of NASA for useful discussions.
Figures were drawn with the Generic Mapping Tools
software package [Wessel and Smith, 1998]. This

47

work was supported by JSPS KAKENHI Grant Number JP15H05815 (PSTEP).
Some of the results of this paper already appeared in the report of http://www.meti.go.jp/meti_
lib/report/2015fy/000095.pdf (in Japanese) [METI,
2015]. This paper is a full paper describing all scientiﬁc matters obtained by the present research.
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Shigeru FUJITA, Ikuko FUJII, Arata ENDO and Hiroki TOMINAGA

日本および周辺領域における地磁気誘導電場分布の数値計算
藤田 茂1, 2，藤井郁子1，遠藤 新3，富永博紀4
気象大学校，2国立極地研究所，3気象庁地球環境海洋部，4東京管区気象台1

2017年11月27日受領，2017年12月14日受理，2018年 3 月23日刊行

要旨

日本の地磁気誘起電場（GIE）の全国強度マップを，数値モデリング手法を用いて求めた。
地球表面近傍の電気抵抗率分布は，地下深度と堆積物の厚さデータから推定する。GIE 強度分布は，200, 800，および3,600秒の周期を持つ外部地磁気変化に対して計算した。GIE 強
度は，地磁気観測所における100 nT の磁気変動に対して正規化されている。GIE は主に沿岸域で大幅に増大しているように見える。加えて，数キロメートルの内陸部まで及んでいる。
現在の計算から，GIE が大幅に増強される可能性のある地域を特定する。これは，（ 1 ）北海道オホーツク海の北東海岸域，（ 2 ）北海道および青森県（松前津軽地域）の日本海沿岸の西海岸域，（ 3 ）新潟県から富山湾にかけての日本海北西部域，（ 4 ）太平洋の南西海岸域，（5）
朝鮮半島の東海岸域である。さらに我が国の地磁気誘起電流（GICs）を知る必要がある。しかし，日本の電力会社は電力線のパラメータを公開していないため，日本の GIC を計算することはできない。