Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
10-year progress in study of motional induction by tsunamis
and ocean tides
Takuto Minami
Earthquake Research Institute, The University of Tokyo
Abstract
[1] Conductive sea water moving in the ambient geomagnetic main field generates electric currents in
the ocean and thereby causes related magnetic variations. While there are several kinds of oceanic
flows, it is noticeable in recent years that the progress in studies on motional induction caused by
tsunamis and ocean tides, although the reasons of them are somewhat different. The progress in
tsunami magnetic studies is triggered mainly by recent large earthquakes and tsunamis, e.g. the 2011
Tohoku earthquake and the 2010 Chile earthquake. These events provided rare opportunities to analyze
real tsunami-generated EM variation data obtained both on land and at the seafloor. On the other hand,
magnetic fields generated by ocean tides attract more attention because new satellite constellation,
Swarm, provides new opportunity to monitor tide-generated EM variations at the altitude of low orbit
satellites. Furthermore, for both tsunami and tide motional induction studies, advent of sophisticated
seafloor instruments provided new opportunities to exploit the motional induction phenomena: seafloor
magnetic sensors potentially contribute to reveal tsunami dynamic procedure, while exploration of
Earth’s interior utilizing seafloor EM data due to ocean tides became plausible. This paper aims at
reviewing and discussing the progress in motional induction studies associated with tsunamis and ocean
tides in the last 10 years.
1. Introduction
[2] Conductive seawater moving in the ambient magnetic fields generate electromotive forces (emfs)
and resulting electric currents in the ocean. This phenomenon is called “motional induction”, and the
origin of the related studies dates back to the speculation by Michael Faraday (1832). Since that, in all
ages, advent of new sophisticated instruments, which includes towed electrodes, submarine cables,
seafloor magnetometers, and the recent satellite-borne magnetometers, enabled researchers to detect
new exciting real electromagnetic (EM) signals caused by motional inductions, and promoted studies in
these fields. On the other hand, sometimes along with the increased observation techniques and new
observation results, at other times prior to observations, researchers have been developing new theories
and numerical simulation methods to explain or predict motional induction phenomena. Although many
oceanic flow causes motional induction, progress in motional induction studies related to tsunamis and
ocean tides are remarkable in the last 10 years. While the increment of magnetic data from seafloor
magnetometer helped the studies in both fields, there are slightly different reasons for each progress.
For tsunami motional induction, several large earthquake tsunamis, e.g. the 2010 Chilean earthquakes
and the 2011 Tohoku earthquake tsunami, occurred and provided rare opportunities to observe related
magnetic variations both on land and seafloor. As for ocean tides, a new satellite constellation project,
Swarm, provided a new possibility to obtain tide-generated magnetic data at the satellite altitude, while
exploration of Earth’s interior exploiting seafloor EM data associated with ocean tides became plausible.
In this paper, we focus on the 10-year advances in motional induction studies related to tsunamis and
ocean tides, with brief description of preceding important works.
[3] In the rest of this section, I first outline how the motional induction studies developed since Faraday’s
th
speculation until the end of 20 century. In particular, the advances of motional induction studies in the
late 1900s are important both for tsunami- and tide- motional induction studies. After this introduction
section, I sequentially review the studies on tsunami-generated EM studies in Section 2 and oceangenerated ones in Section 3 almost in the same scheme composed of observations (subsection 1),
theoretical works (subsection 2), numerical works (subsection 3), and application to other fields
(subsection 4), although the titles are variable to some degree. I hope, among these subsections, a
reader can jump to anywhere he/she is interested in and easily find the related studies.
1
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
1.1 Short history since Faraday’s prediction up to the end of 1950s
[4] Here, I briefly review the history of motional induction studies from Faraday’s prediction to the end of
th
the 20 century. We can roughly divide the period into those before and after the middle of 1900s. The
former can be referred to as the cradle age of motional induction studies and the latter as the age of
their first prosperity mainly for theories. It is well-known that although Michael Faraday speculated that
ocean flow generates electric currents in the ocean, he failed to detect any potential difference due to
motional induction in the Themes river when he suspended copper plates from the parapet of the
Waterloo bridge. It took almost a half century to see the first report of tide-generated electric potential
by Adams (1881), although C. Wollaston had already measured electric potential with a lunar period in
1851 (Wollaston, 1881). Both of them used telegraph cable earthed in or near ocean. One possible
reason for this late first report since Faraday’s prediction seems lacks of adequate instrumentation and
immature understanding on the effect of conductive seafloor (Young et al., 1920). In the early 1900s,
Young et al. (1920) first succeeded in experimentally measuring tide-generated electric potential
variations by both moored and towed electrodes. They found that the electric potential variations with
semidiurnal ocean tide period cannot be in phase with the local tide water velocity, but with a stronger
tidal stream in a remote position, which supports their idea that conductive seafloor enables strong emfs
to form broad electric circuits controlling electric potential variations beside remote weaker tidal stream.
Readers can find the detailed story of this cradle age of motional induction studies in Longuet-Higgins
(1949) and partly in Filloux (1973). In this age, magnetic fields associated with ocean tides were
recognized somewhat away from the ocean (e.g. Rooney, 1938). After this cardinal age, in the 1940s
to 1950s, many researchers got involved in theoretical studies on motional inductions (e.g., Stommel,
1948; Longuet-Higgins, 1949, 1954; Malkus and Stern, 1952), which was the opening of the first
prosperity age of motional induction studies. This was triggered by the development of observation
method using towed electrodes (e.g., von Arx, 1950), which enabled to indirectly measure seawater
velocities. This new instrument was named Geomagnetic electrokinetograph (GEK, e.g. Filloux, 1987).
After the advent of GEK, Longuet-Higgins et al. (1954) first comprehensively investigated the
relationship between the seawater velocity and the generated EM variations, in some particular cases
of stationary oceanic flows. The derived relationships are useful to estimate water mass movements
from electric potential data obtained by towed electrodes. The works in the 1940s and 1950s were
followed by many good theoretical works in the late 1900s.
1.2 Prosperity of theoretical motional induction studies since 1950s
[5] Most of the theories derived since 1950s are still useful for interpretation of realistic motional
induction phenomena. While the theoretical works in the 1950’s (e.g. Longuet-Higgins et al., 1954) dealt
with some practical cases of stationary oceanic flow, most of the following excellent theoretical works
since the 1960s consider EM variations caused by temporally variable oceanic flows with careful
treatment of the self-induction effect, i.e. the effect of temporal variations of the magnetic field. Including
the full expression of the self-induction effect, Weaver (1965) presented an analytical solution for EM
fields caused by short waves and swells, assuming that the ocean depth is much longer than the
wavelength of the surface wave. This solution was proved by comparisons with observations (e.g.
Maclure et al., 1964). Sanford (1971) theoretically investigated EM fields generated by long-scale waves,
focusing on the cases that the phase velocity is less than ~10 m/sec. Larsen (1971) derived analytical
solutions of EM fields generated by long and intermediate waves, which is still useful in interpreting
tsunami-generated EM fields. Cox et al. (1978) explained the nonlinear mechanism by which the wind
wave can cause magnetic field oscillation at the seafloor. Chave (1984) theoretically investigated
magnetic field generated by internal waves. As for motional induction by ocean tides, Larsen (1968) first
considered the importance of self-induction effect on the tide-generated magnetic field in the open ocean.
Chave (1983) furthermore pointed out the importance of galvanic connection between ocean layer and
conductive seafloor medium in the tide-generated EM fields, which is revealed by analytical investigation
using the representation based on Green’s functions and Toroidal/Poloidal mode separations. In the
1960s to 1980s, because of the advent of seafloor magnetic observations with torsion fiber (e.g. Filloux,
1967) or with fluxgate magnetometer (e.g. White, 1979), analyses of seafloor magnetic data started
concerning tide motional induction (e.g. Larsen and Cox, 1966, Larsen et al., 1968), as well as on-land
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
electric data (e.g. Harvey et al., 1977; Junge, 1988). Refer to Filloux (1987) and Constable (2013) for
more detailed description of developments of seafloor instruments in the late 1900s. As mentioned by
Constable (2013), along with the advent of seafloor magnetometers, seafloor Magnetotelluric (MT)
surveys started in the 1960s. Since that, motional induction phenomena are disliked as noise generator
of seafloor MT studies (e.g., Cox, 1980), while were sill useful for oceanographer to measure seawater
velocities. Electric field observation using submarine cables played important roles still in the 1980s and
1990s, especially in inferring oceanic mass transport, for example, of Florida straight (e.g., Larsen and
Sanford, 1985; Larsen, 1992) and Kuroshio at the Nankai Trough (Segawa and Toh, 1992). Chave and
Luther (1990) and Luther et al. (1991) showed that measurements of horizontal electric field at the
seafloor can serve as an efficient barotropic flow meter in the central North Pacific, in the Barotropic,
Electromagnetic and Pressure Experiment project (BEMPEX, Luther et al., 1987). In the 1990s,
furthermore, there appeared some studies also on Baroclinic ocean flow. Lilley et al. (1993) reported
magnetic variations generated by passage of ocean eddy. It follows that Tyler and Mysak (1995) derived
analytical solutions applicable to vertically and horizontally sheared plane-parallel flows. Palshin (1996)
reviewed oceanic electromagnetic studies in the 1990s, which includes most of the motional induction
studies mentioned above. At the end of the 1990s, seafloor EM observatories for long-time operation
which incorporates Fluxgate and Overhauser magnetometer is developed (Toh et al., 1998). This led to
the first detection of tsunami-generated EM signals in the early 2010s. In the 2000s, as well as the
sophisticated seafloor instruments, floating magnetometer was used to detect the magnetic field
generated by ocean swells (Lilley et al., 2004). The submarine cables are important to infer the mass
st
transport still in the 21 century. Nolasco et al. (2006) found that voltages measured on both sides of
Ria de Aveiro Lagoon, in Portugal, are dominated by semidiurnal ocean frequencies of M2, S2, K2.
1.3 Global numerical simulations and advent of satellite observations from the 1990s to 2000s.
[6] In the previous section, the development of theory and observations from the 1990s to 2000s are
outlined. Here we focus on a new observation tool of satellites and the development of numerical
simulation techniques in the 1990s and 2000s. Numerical simulations associated with motional induction
started mainly in 1990s. Most of the simulation works mentioned here are described in detail by the
good preceding review by Kuvshinov (2008), which comprehensively reviewed 3-D global simulation
studies including those for EM fields of oceanic origins.
[7] As for ocean circulations, since 1990s, we can see many numerical simulations related to steady
ocean circulations (e.g. Stephenson and Bryan, 1992; Flosadottir et al., 1997; Tyler et al., 1997; Vivier
et al. 2004; Manoj et al., 2006). Stephenson and Bryan (1992), Tyler et al. (1997), and Vivier et al. (2004)
applied the thin-shell approximation (Price, 1949) to calculate magnetic fields generated by steady
ocean circulation, where the conductivities above and beneath the ocean layer were insulators. It is
noteworthy that Vivier et al. (2004) showed the correlation between the Antarctic Circulation Current
(ACC) and the calculated magnetic field. On the other hand, Flosadottir et al. (1997) and Manoj et al.
(2006) conducted full 3-D simulations including realistic conductivity beneath the seafloor, adopting 3D finite difference method (Smith, 1996a, b) and Integral Equation method (Kuvshinov et al., 2002),
respectively. These were the opening of global motional induction studies.
[8] In the field of ocean tides, the advent of satellite magnetic observations promoted studies on tide
motional inductions in the early 2000s. Tyler et al. (2003) showed that the magnetic variations generated
by the M2 tidal component can be detected at the altitude of CHAMP satellite orbit, by comparing
observations with their global simulation results. Following this, Maus and Kuvshinov (2004), Kushinov
and Olsen (2005), and Kuvshinov et al. (2006) conducted the 3-D global simulations to reveal the
features of motional induction due to ocean tides. These studies are discussed later in subsection 3.3.
The advent of satellite observation and various numerical techniques applicable to global simulation led
to broad possibilities in studies of motional induction by ocean tides.
[9] Finally in this subsection, we here briefly mention the studies on tsunami-generated magnetic fields,
which restarted in the 2000s after long suspension since Larsen (1971) and Chave (1983). Important
contributions are made mostly by Tyler (2005) and by Manoj et al. (2010) in this age. Tyler (2005)
derived a very simple relationship between tsunami sea surface displacement and the generated
magnetic field. Although Tyler (2005) investigated whether they can be detected at the altitude of low
orbit satellites, e.g. CHAMP, or not, it is hard to expect observable amplitude of tsunami-generated
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
magnetic field at the satellite altitude of ~400 km, because the horizontal scales of tsunamis, ~10^2 km,
are much less than those of ocean tides, ~10^3 km. Manoj et al. (2010) investigated whether submarine
cables in Indian Ocean could detect the electric field generated by the 2004 Sumatra earthquake
tsunami, by applying their global induction technique to tsunami-generated magnetic fields, which
revealed that the electric voltages of observable amplitude of ~0.5 V were induced in the submarine
cable. However, it will be found in the 2010s that seafloor in situ EM observations can provide much
more information on tsunami propagation compared to submarine cables.
1.4 Overview of all the recent progress in motional induction after 2008 to date
[10] In this paper, we would like to focus on the studies on tsunami and tide related motional inductions
after the review by Kuvshinov (2008). Before moving to each review of tsunami and ocean tides related
studies, here, let us outline the motional induction studies after the review by Kuvshinov (2008),
comprehensively. There have been dramatic progresses especially in tsunami motional induction
studies, while there also appeared many attempts of utilizing the motional induction by ocean tides.
[11] For tsunami motional induction studies, it should be first noted that several large earthquakes in the
2000s and 2010s provided rare opportunities of case studies on tsunami-generated magnetic variations
observed both on land and at the seafloor. First report of observed tsunami magnetic signal is done by
Toh et al. (2011). They observed the magnetic variations generated by the 2006 and 2007 Kuril
earthquake tsunamis at the northwest Pacific seafloor. The magnetic signals due to the 2010 Chilean
earthquake tsunami are observed on the Eater Island (Manoj et al., 2011; Wang et al., 2015) and at the
Pacific seafloor (Suetsugu et al., 2012; Sugioka et al., 2014). The 2011 Tohoku earthquake tsunami
also generated observable magnetic signals on land (Utada et al., 2011; Tatehata et al., 2015) and at
the seafloor (Minami and Toh, 2013; Ichihara et al., 2013; Zhang et al., 2014a, b). Since tsunamis are
nonstationary event, it is sometimes hard to find the corresponding signals. Klausner et al. (2014, 2016a,
b) attempted to apply the wavelet analysis technique to highlight tsunami magnetic. See subsection 2.1
for the detail of the above observation reports.
[12] Many observation reports motivated researchers to revisit the tsunami magnetic theory (Shimizu et
al., 2015; Minami et al., 2015; see subsection 2.2) and to develop numerical modelling techniques of
tsunami-generated magnetic fields (Minami and Toh, 2013; Zhang et al., 2014a; Tatehata et al., 2015,
see subsection 2.3). Although it is found tsunami-EM fields are not useful in exploring Earth’s interior
(see section 2.4,1), there recently appeared several applications of tsunami magnetic signals to
constrain the dynamics of earthquakes and tsunamis (Ichihara et al., 2013; Kawashima and Toh, 2016,
see subsection 2.4.2). Furthermore, a new seafloor instrument, called “Vector TunaMeter (VTM)” has
been developed by a group of Japan Agency for Marine-Earth Science and Technology (JAMSTEC),
which is designed to exploit tsunami motional induction for tsunami early warning (see subsection 2.4.3).
[13] As for motional induction studies related to ocean tide, some of the recent progress are associated
with satellite observations while others with exploration of Earth’s interior mainly using the seafloor
magnetic data. For the former, Sabaka et al. (2015, 2016) provided a new sophisticated technique to
extract the tide-generated magnetic signals from satellite magnetic data, based on the so-called
“Comprehensive Inversion” technique (see subsection 3.4.1). For the latter, Schnepf et al. (2014, 2015)
showed possibilities that the seafloor tide-generated magnetic fields are exploited to infer the
conductivity structure beneath the seafloor. Although this idea has been lie in the ocean tide motional
induction studies, the plausibility was recently validated (see subsection 3.4.2).
2. Motional induction by Tsunamis
[14] Hereafter, recent progress in tsunami motional induction studies is discussed in Section 2, and that
in tide motional induction will be reviewed in Section 3, sequentially. For the tsunami motional induction,
a number of tsunami magnetic data observed at the time of large earthquake tsunamis dramatically
promoted recent studies. In this section, we shall see the detail of the recent observation reports in
subsection 2.1, the theoretical aspect in subsection 2.2, developments of numerical techniques in
subsection 2.3, and finally the possible applications of tsunami motional induction in subsection 2.4.
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
2.1 Reports of EM data due to tsunami motional induction in the 2010s
[15] In the last 10 years, there appeared many reports of tsunami-generated EM variations observed
both on land and at the seafloor. These are not only because several large tsunami earthquakes
occurred under relatively quiet solar activity (e.g. the 2006/2007 Kuril earthquakes, the 2010 Chilean
earthquake, and the 2011 Tohoku earthquake tsunamis), but also because many sophisticated ocean
bottom electro-magnetometers are deployed, especially in the Pacific Ocean during the tsunami events.
Here we review the tsunami-generated EM variations reported in the 2010s.
2.1.1 The 2006 and 2007 Kuril earthquake tsunami
[16] The first report of evident tsunami-generated EM fields was done by Toh et al. (2011). They detected
EM variations due to the 2006 and 2007 Kuril earthquake tsunamis, by the seafloor electromagnetic
station system (SFEMS, Toh et al., 1998, 2006). The left column of Fig. 1 shows the EM components
(top three panels) and tilts (bottom panel) observed at the time of the 2006 Kuril earthquake tsunami.
We can see the clear responses of EM components not to the seismic wave arrival (red vertical line),
but to the arrival of tsunami (blue vertical line). Toh et al. (2011) concluded that a single site seafloor
EM sensor can monitor both the tsunami propagation direction and the tsunami wave height. This idea
led to the attempt to the development of Vector TsunaMeter (VTM) by the JAMSTEC group (see
subsection 2.4.3).
2.1.2 The 2010 Chilean earthquake tsunami
[17] Manoj et al. (2011) first reported on-land magnetic variations generated by tsunamis. They reported
magnetic variations observed on Easter Island, at the time of the 2010 Chilean earthquake tsunami.
Although on-land tsunami magnetic signals are often severely contaminated by ULF waves originating
from magnetosphere, exceptionally quiet magnetic condition enabled on-land detection of tsunamigenerated magnetic variation with an amplitude of ~1 nT at that time. Wang et al. (2015) verified that
the Chilean tsunami definitely caused the magnetic variation observable on Easter island, by applying
the analytical solution of Tyler (2005) to the result of tsunami simulation.
[18] Suetsugu et al. (2012) and Sugioka et al. (2014) first reported the concurrent observation of the
seafloor pressure and seafloor tsunami magnetic signals at the time of the 2010 Chilean earthquake
tsunami, through the TIARES project, aiming at sounding the Society hotspot region in the French
Polynesia (Suetsugu et al., 2012). The right panel of Fig. 1 shows the clear correlation between the
tsunami-generated magnetic field (black line) and the pressure perturbation observed at the seafloor
(red line), which is proportional to the sea surface displacement. This clearly proves the theoretical
prediction by Tyler (2005) that the in-phase relationship between the vertical component of the magnetic
field and tsunami sea surface displacement in deep oceans.
[19] At the time of the 2010 Chilean event, a new data processing technique, the wavelet transform
technique, was first introduced to the analysis of tsunami-generated magnetic variations by Klausner et
al. (2014). By applygin the gapped wavelet analysis method (Frick et al., 1997), they succeeded in
highlighting the magnetic variations with periods of the tsunami in magnetic data observed at Easter
Island and at Papeete (Tahiti Island) during the 2010 Chilean tsunami event. The wavelet analysis
technique has an advantage in studying transient local regularities thanks to the utilization of both the
oscillatory and envelope wave forms. This technique can reduce the task of conventional visual
inspection of the original time series.
2.1.3 The 2011 Tohoku earthquake tsunami
[20] After the 2011 Tohoku earthquake tsunami, a number of tsunami-generated EM signals were
reported from both on-land and seafloor. Utada et al. (2011) comprehensively reported on-land magnetic
variations originating from the 2011 Tohoku earthquake tsunami. Minami and Toh (2013) reported the
tsunami magnetic variations as large as approximately 3 nT observed at the northwest Pacific seafloor
(see Fig. 3). Ichihara et al. (2013) provided the seafloor magnetic variation data just on the eastern side
of Japan Trough. Ichihara et al. was the first attempt to constrain the tsunami source region from the
magnetic data. The detail of this work is discueed in subsection 2.4.2. Zhang et al. (2014a, b) reported
the array seafloor EM observation data in the north Pacific, where the array of seafloor instruments was
installed by the Normal Oceanic Mantle project (NOMan, e.g. Kawakatsu et al., 2013). They succeeded
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
in accurately determining the tsunami propagation direction in that area. Since high frequency external
variation cannot reach the seafloor, most of EM signals from the seafloor were clear and easy to infer
the dynamic properties of the tsunami propagation. Tatehata et al. (2015) analyzed the magnetic
variations observed at Chichijima Island. All the above works except Ichihara et al. (2013) conducted
numerical EM simulations to explain the observed tsunami-generated seafloor magnetic variations. The
details of the numerical simulations are reviewed later in subsection 2.3.
2.1.4 Tsunami-generated magnetic signals due to gravity waves
[21] It should be noted in this section that, during tsunami events, magnetic variations are caused not
only by tsunami motional induction but by Tsunami-Atmosphere-Ionosphere (TAI) coupling (e.g.
Tsugawa et al., 2011; Kherani et al., 2016). Acoustic gravity waves (AGWs) excited by tsunamis,
especially large-scale ones, can reach the ionosphere, which causes ionospheric dynamo and thereby
secondary magnetic fields observable at ground magnetic observatories. Klausner et al. (2016b)
concluded that the on-land Z variations preceding the tsunami arrival at each location by 10 ~ 50
stemmed not from the motional induction but from the ionospheric current excited by tsunami-generated
AGWs at the time of the 2011 Tohoku earthquake tsunami. On the other hand, as for the on-land data
at CBI, Tatehata et al. (2015) demonstrated by numerical simulations that the on-land Z variation at CBT
approximately 20 minutes prior to the tsunami arrival was generated by tsunami motional induction.
2.1.5 Discussion: Identification of tsunami magnetic signals prior to tsunami arrivals
[22] As a remaining problem in the EM variations due to tsunamis, there is no obvious criterion to judge
whether the magnetic field variation of the tsunami period is due to the tsunami motional induction or
due to the ionospheric current excited by tsunami-generated AGWs. In the case of on-land data in CBT
at the time of the 2011 Tohoku tsunami, I can claim that the Z variation ~20 minutes prior to the tsunami
arrival was probably generated by motional induction in the ocean, since the simulations of motional
induction presented by Tatehata et al. (2015) and Zhang et al. (2014) agree with the observed variations
at CBI. However, it might be difficult to decline the possibility that the Z variation at CBI was generated
by TAI coupling, only from the information presented by Klausner et al. (2016b).
[23] In another case, Klausner et al. (2014) found that the magnetic variations with the tsunami period
at Papeete in Tahiti Island were observed approximately 2 hours prior to the tsunami arrival during the
2010 Chilean earthquake tsunami. As mentioned by Klausner et al. (2014), a broad current circuit in the
ocean due to motional induction could cause the magnetic signal 2 hours earlier than the tsunami arrival
at Papeete. However, in turn, there are not obvious reasons to decline the possibility that tsunamigenerated AGWs caused the magnetic variation at Papeete.
[24] One possible reason of precedence of the Z component variation to tsunami arrival is that the Z
component theoretically precedes tsunami sea surface displacement by approximately 𝜋/4 in phase in
very shallow oceans (Tyler, 2005; Minami et al., 2015), which can be the case in the vicinity of island
coasts. This theoretical prediction and the distance between the magnetic observatory and the tide
gauge at CBI could accounts for the 20-minute precedence of magnetic variation at CBI in the case of
the 2011 Tohoku tsunami. However, at the present, identification of the preceding magnetic variation
with a tsunami period requires numerical simulations of both or at least either of tsunami motional
induction and tsunami-generated AGWs.
2.2. Theory of EM fields caused by tsunami motional induction
[25] Here let us briefly outline the theoretical aspect of EM variations due to tsunami motional induction.
To investigate the theory of tsunami motional induction, the most commonly adopted governing equation
is the magnetic induction equation,
𝜕𝐁
= 𝛁× 𝐯×𝐁 − 𝛁× 𝐾𝛁×𝐁 ,
𝜕𝑡
(1)
where 𝐾 = 𝜇𝜎 01 is the magnetic diffusion coefficient, where 𝜇 and 𝜎 are the magnetic permeability
and the conductivity, respectively. 𝐁 and 𝐯 are the magnetic field and the sea water velocity. If we
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
decompose the magnetic field, B, into the ambient geomagnetic main field, F, and the tsunamigenerated magnetic field, b, eq. (1) is reduced to
𝜕𝐛
= 𝛁× 𝐯×𝐅 − 𝛁× 𝐾𝛁×𝐛 ,
𝜕𝑡
(2)
where 𝐅 ≫ |𝐛|, |𝛁×𝐅| ≪ 1, and 𝜕𝐅/ ∂t = 0 are assumed. These assumptions are acceptable when we
assume 𝐯 as the tsunami seawater velocity, and 𝐅 as Earth’s main magnetic field at the Earth’s surface.
Almost all the theoretical studies of tsunami motional induction begin with eq. (2) with the exception of
Chave (1983). In many theoretical works on tsunami motional induction, assumed are the onedimensional (1-D) layered Earth with a homogeneous conductivity in each layer, including ocean layer
with a constant ocean depth, which leads to the conductivity is represented by 𝜎 = 𝜎(𝑧), where z is the
vertical coordinate and upward positive through this paper. By further assuming that 𝛁 ⋅ 𝐯 = 0, 𝛁 ⋅ 𝐅 = 0,
and 𝐯 ⋅ 𝛁 𝑭 ≪ | 𝑭 ⋅ 𝜵 𝐯|, this 1-D configuration, where the horizontal gradient of conductivity equals
to 0, enables us to separate a simple equation in terms of the vertical component 𝑏B from eq. (2),
𝜕𝑏B
= 𝐅 ⋅ 𝛁 𝐯 + 𝐾𝛁 D 𝑏B .
𝜕𝑡
(3)
Note that 𝛻× 𝐯×𝐅 = 𝛁 ⋅ 𝐅 𝐯 − 𝜵 ⋅ 𝐯 𝑭 + 𝑭 ⋅ 𝜵 𝐯 − (𝐯 ⋅ 𝛁)𝑭 is used. Eq. (3) indicates the so-called
Poloidal Magnetic (PM) mode equation (e.g. Chave, 1983). The other components of tsunamigenerated EM fields can be calculated from 𝛻 ⋅ 𝐛 = 0 and 𝛻×𝐞 = −𝜕H 𝐛 , where 𝐞 is the tsunamigenerated electric field.
[26] As for toroidal magnetic (TM) mode, Larsen (1971) clearly showed that TM mode is not excited by
tsunami motional induction. When we consider a tsunami propagating in the y direction, expressed as
𝐯 = 𝑣J , 𝑣K , 𝑣B with 𝑣J = 0, a loop integral of the emf along an arbitrary closed circuit in the y,z plain, 𝐶KB
with the area of 𝑆KJ , vanishes as
𝐯×𝐅 ⋅ 𝑑𝒔 =
PQR
𝛁× 𝐯×𝐅
SQR
J
𝑑𝑦𝑑𝑧 =
SQR
𝐅 ⋅ 𝛁 𝑣J 𝑑𝑦𝑑𝑧 = 0,
(4)
by Stokes’ theorem. Eq. (4) shows that the emf shorts out along any circuits in the y,z plain so that no
vertical electric field is induced by plain wave tsunamis. As a result, there are no needs to consider TM
mode for tsunami motional inductions, thanks to the conditions of 𝛻 ⋅ 𝐯 = 0, 𝛻 ⋅ 𝐅 = 0, and 𝐯 ⋅ 𝛁 𝑭 ≪
| 𝑭 ⋅ 𝜵 𝐯|. Note that this is not the case in tide motional induction because 𝐯 ⋅ 𝛁 𝑭 cannot be ignored
under much longer wavelengths of ocean tides.
[27] Thus, all the existing analytical solutions for tsunami-generated EM fields are involved only in PM
mode and are derived by solving eq. (3) with preferred levels of assumptions. The simplest expression
is presented by Tyler (2005), while the most comprehensive (complicated) expression is given by Larsen
(1971) and Shimizu and Utada (2015). Many other midst expressions are also presented (Ichihara et
al., 2013; Sugioka et al., 2014; Minami et al., 2015). The degree of assumptions and characteristics of
the analytical solutions are summarized in Table 1. There are the two kinds of tsunami seawater velocity
models, the linear dispersive wave model,
𝐯 = 0, 𝜔
cosh 𝑘 𝑧 + ℎ
sinh 𝑘ℎ
𝜂, −𝑖𝜔
sinh 𝑘 𝑧 + ℎ
sinh 𝑘ℎ
𝜂 (−ℎ < 𝑧 < 0),
(5)
and the linear long wave model,
𝜂
z+h
𝐯 = 0, 𝑐 , −𝑖𝜔
𝜂 −ℎ < 𝑧 < 0 ,
ℎ
ℎ
(6)
where I assumed the tsunami propagates only in the y-direction and sea surface displacement can be
expressed as 𝜂 ∝ exp 𝑖 𝑘𝑦 − 𝜔𝑡 with the wavelength k and the angular frequency 𝜔. The sea surface
and seafloor are represented by𝑧 = 0 and 𝑧 = −ℎ, respectively. Eq. (6) is easily derived from eq. (5) by
considering the wave length much longer than the ocean depth, say, 𝑘ℎ → 0.
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
[28] Here we focus on the analytical solutions by Tyler (2005) and Minami et al. (2015). First, Tyler’s
expression is noticeable because of its very simple form of
𝑏B
𝑐 𝜂
=
,
𝐹B 𝑐 + 𝑖𝑐j ℎ
𝑧 = 0or − ℎ ,
(7)
where, 𝑐 = 𝑔ℎ is the tsunami phase velocity, 𝑐j = 2𝐾/ℎ is the lateral magnetic diffusion velocity. Tyler
(2005) simplified the relationship derived by Larsen (1971), by adopting the linear long wave model of
eq. (6), insulating earth model beneath the seafloor, and the assumption that the skin depth of seawater
is much longer than the ocean depth, 2𝐾/𝜔 ≫ ℎ. These assumptions result in the form of eq. (7),
which is independent of frequency. Although it looks too simple, eq. (7) is surprisingly able to explain
most of the features of tsunami-generated magnetic fields. Eq. (7) indicates that, in deep ocean, 𝑏B is in
phase with 𝜂 , as represented by 𝑏B /𝐹B ~𝜂/ℎ . This feature is clearly identified, for example, in the
comparison between seafloor magnetic and pressure data shown in the right column of Fig. 1, reported
by Suetsugu et al. (2012). Another noticeable feature is that the analytical expressed of eq. (7) neglects
the effect of earth’s conductivity beneath the seafloor, which is also validated by many other analytical
studies. For example, Fig. 2 shows the comparison between eq. (7) (red line) and the solutions derived
by Minami et al. (2015) (the other colored lines), where the horizontal axis is the ocean depth regularized
by the scale length, 𝐿 = 2𝐾/ 𝑔
D/p
~2.7km. Discrepancy between Tyler’s solution (red) and the other
color lines are trivial, which demonstrates that the assumption adopted in Tyler (2005) is reasonable.
Figure 3 implies difficulty in using tsunami-magnetic fields as a tool to infer the conductivity beneath the
seafloor, which was thoroughly investigated by Shimizu and Utada (2015). Let us discuss later in
subsection 2.4.1.
[29] As well as the effect of sub-seafloor conductivity, Fig. 2 expresses another interesting feature of
tsunami-generated magnetic field, namely the dependence on the ocean depth. Relative phase of 𝑏B to
𝜂 differ from 90 to ~10 degrees as the ocean becomes deep, while the amplitude of 𝑏B has a peak at a
depth of approximately ℎ/𝐿 = 201/p . As pointed by Minami et al. (2015), the diffusion term 𝐾𝛁 D 𝑏B is
much larger than the self-induction term 𝜕H 𝑏B in shallow oceans, and vice versa in deep oceans, which
leads to the phase variability and amplitude peak at the midst ocean depth. It is expected from Fig. 2
that the signal to noise ratio of tsunami-generated magnetic signals are dominantly controlled by the
ocean depth. Minami et al. (2015) also showed that the peak of 𝑏B amplitude is shifted to in shallower
oceans when considering conservation of the dynamical energy of tsunamis, i.e. 𝑔ℎ× 1/2 𝜌𝑔 𝜂 D =
𝑐𝑜𝑛𝑠𝑡.through the propagation. Features mentioned here should be taken into account in designs of
future tsunami observations.
[30] All the above analytical solutions are very useful in predicting the tsunami-generated EM fields.
However, difficulty rises in evaluating the effect of bathymetry, which requires the need of numerical
modeling with realistic bathymetry.
2.3. Numerical simulations of tsunami-generated EM fields
[31] We can regard tsunami motional induction problems as an analogy of controlled source
electromagnetics (CSEM), where the source electric current, 𝑗y , is replaced by the product of the ocean
conductivity and emf due to tsunamis, 𝜎(𝐯×𝐅). Thus, many existing EM modelling techniques can be
applied to simulations of tsunami-generated EM fields with small adjustments. Recently, more and more
variety of numerical methods appeared for simulations of the tsunami-generated EM variations.
[32] Manoj et al. (2008) is the first attempt to simulate tsunami-generated EM variations. They applied
the integral equation technique of Kuvshinov et al. (2002) to 3-D global numerical simulations of tsunamigenerated EM variations, in order to investigate whether submarine cables in the Indian Ocean could
detect the voltage difference caused by the 2004 Sumatra-Andaman earthquake tsunami. This study
was partly motivated by Thomson et al. (1995), which found the voltage variations across an undersea
cable that had time associations with the 1992 Cape Mendocino earthquake tsunami. Manoj et al. (2008)
show that the 2004 Sumatra earthquake tsunami have produced electric voltages of the order of ±500
mV across the existing submarine cable in the Indian Ocean, which may be measurable (c.f. Fujii and
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Chave, 1999). On the other hand, the resolution of simulation by Manoj et al. was 1°×1°, which is too
coarse when we compare numerical results with in-situ observed EM data.
[33] After Manoj et al. (2010), many tsunami-generated EM variations were reported in the early 2010s,
which required accurate numerical simulations that can reproduce tsunami-generated EM variations.
Utada et al (2011) first conducted a numerical simulation of the magnetic field generated by the 2011
Tohoku earthquake tsunami, although it was not accurate enough because they used the Biot-Savart
law, neglecting the self-induction effect, i.e. 𝜕𝒃/𝜕𝑡.
[34] Minami and Toh (2013) developed a 2-D time-domain simulation code to reproduce the magnetic
variations generated in the northwest Pacific at the time of the 2011 Tohoku earthquake tsunami, by
adopting the finite element method and Crank-Nicolson method for spatial and time discretization,
respectively. They calculated the tsunami oceanic flow from the fault slip model of Maeda et al. (2011),
and thereby used the velocity field to calculate the tsunami-generated magnetic fields. Figure 3 shows
their result, where both the sea surface displacement data at DART observatories operated by NOAA
(e.g. Bernard and Meinig, 2011) and the generated magnet variations are well reproduced by the 2-D
simulation. In Fig. 3, it is noteworthy that the initial rise in the horizontal component, 𝑏K , apparently
precedes the arrival of tsunami peak by approximately 5 minutes at NWP, while the peak of the vertical
component is almost in phase with the sea surface displacement.
[35] Zhang et al. (2014b, JGR) recently adopted the integral equation technique (Koyama, 2002) and
succeeded in performing 3-D numerical simulations of the seafloor EM variations due to the 2011
Tohoku earthquake tsunami. They prescribed realistic 3-D conductivity structure beneath the seafloor,
based on the reported 1-D conductivity structure in the Pacific Ocean (Baba et al., 2010). One drawback
of their simulation is that the calculation is conducted in the frequency domain, which requires the source
sea water velocities in the frequency domain although the adopted tsunami simulations are performed
in the time-domain (Maeda et al., 2011). To exert Fourier transform against the sea water velocity in all
the numerical space consumes additional computational time, compared to the time-domain simulations
like Minami and Toh (2013). Figure 4 shows the summarized results of Zhang et al. (2014b). While the
peak time at CBI (Chichijima Island) and at NM04 (seafloor site) are well reproduced by the 3-D
simulations, discrepancy becomes large after the first peak at NM04. These can be attributed to the
elimination of the dispersive properties in linear long wave approximation (Zhang et al., 2014b). On the
other hand, at the land magnetic observatory ESA, the discrepancy between the 3-D simulation result
(red) and observation (black) is very large. As the authors mention, the significant variation in the
observed field starting at about 10 min after the origin time was probably caused by the ionospheric
disturbance (e.g., Tsugawa et al., 2011) and therefore should not be compared with the present
simulation result of tsunami motional induction. This discrepancy at ESA remains an existing problem
to be solved by future works.
[36] Tatehata et al. (2015) adopted another unique numerical approach in their simulation of tsunamigenerated EM variations. They improve the Biot-Savart simulation method of Utada et al. (2011) by
applying the analytical solution of Tyler (2005). They assumed at every grid point of their simulation
space that 1) tsunamis can be approximated by plain waves, 2) seafloor is flat, and calculated resulting
net current element, i.e. ~(ω) = 𝜎(𝐄(ω) + 𝐯(𝜔)×𝐅), at all the grid points, where a hat denotes frequencydomain component and 𝑬 is calculated by Tyler’s (2005) method. Then, the magnetic field at any grid
point is obtained by superposition of magnetic fields from ~(ω) at all the grid points through Biot-Savart
law. This method is very simple and allows to calculate the magnetic field on land as well as in the ocean.
They demonstrated by their simulations that the magnetic variation in Z component at CBI, which
preceded tsunami arrival at Chichijima Island by approximately 20 minutes, was surely generated by
the 2011 Tohoku earthquake tsunami. Although their numerical results are consistent with the
observation at CBI for the magnetic field by the 2011 Tohoku tsunami, possible errors due to bathymetry
gradient and the curvature of tsunami wave form should be assessed in the future.
[37] Recently, Kawashima and Toh (2016) adopted the thin-shell numerical calculation technique
(Dawson and Weaver, 1979; McKirdy et al., 1985) and succeeded in reproducing the magnetic field
variation observed in the northwest Pacific at the time of 2007 Kuril earthquake tsunami. This work
includes an aspect of constraining the mechanism of tsunami/earthquake. The detail of this study is
mentioned later in subsection 2.4.2.
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
[38] In the last 10 years, there appeared variety of tsunami EM simulation methods. However, most of
them are frequency-domain methods except for the work by Minami and Toh (2013). Since most of the
tsunami simulations are performed in the time domain, advent of more time-domain tsunami EM
numerical techniques would promote corroborations between tsunami motional induction studies and
conventional tsunami simulation studies in the future.
2.4 Applications of tsunami electromagnetic signals
[39] We here discuss the possibility of practical application of tsunami-generated EM variations. In the
following, we discuss applications of tsunami EM variations to explore the internal Earth in subsection
2.4.1, review the usage of tsunami EM fields to infer the tsunami dynamic properties in subsection 2.4.2,
and finally review the possibility of new seafloor instrument “Vector TsunaMeter (VTM)”, developed by
a group of JAMSTEC, in subsection 2.4.3.
2.4.1 Possibility of Earth’s interior sounding by tsunami motional induction
[40] First, we should mention the possibility of exploring the Earth’s internal structure by using EM
variations caused by tsunamis. While many researches have been interested in the possibility, it was
recently found difficult by Shimizu and Utada (2015) to utilize the tsunami-generated EM fields for
exploration of the Earth’s conductivity structure. Shimizu and Utada (2015) thoroughly investigated the
possibility to use EM fields generated by surface gravity waves to sound the conductivity structure
beneath the seafloor. Actually, as the poloidal magnetic mode is dominant in tsunami magnetic
phenomena as shown in subsection 2.2, the Earth’s structure can influence only through the mutual
induction between the ocean layer and conductive layers below. From analytical investigations, Shimizu
and Utada (2015) finally concluded that EM variation observed at the seafloor is suitable only for
exploring the tsunami wave properties rather than the Erath’s structures.
[41] One can see the evidence of above in Figs. 5.1 and 5.2. Shimizu and Utada (2015) compared the
amplitudes and phase of tsunami-generated electric/magnetic fields between the case where the
realistic 1-D conductivity structure (Fig. 5.1) is assumed and the case where the half-space insulator is
set beneath the seafloor. In Fig. 5.2, solid and dashed lines denote the case of 𝐹B = 30000nT (no 𝐹„ ),
and that of 𝐹„ ＝30000nT (no 𝐹B ), respectively. As they mentioned, we can recognize the difference in
amplitude only in the period greater than ~5000s (~83 min), which is extremely longer than usual
tsunami periods ranging from ~10 to ~50 min. As for the comparison of phase, in the period less than
5000s, we can see only the small discrepancy between red (insulator case) and the other lines (case
with conductivity structure of Fig. 5.1) only in magnetic components. The results in Fig. 5.2 evidently
show tsunami-generated EM variations are not useful to infer conductivity structures beneath the
seafloor (Shimizu and Utada, 2015).
2.4.2 Application to reveal/constrain dynamic properties of earthquake/tsunami
[42] As concluded by Shimizu and Utada (2015), tsunami EM signals are suitable not for exploring
Earth’s interior but for investing the tsunami properties. At the present, we can find two noticeable
examples of practical applications in the aspect of inferring tsunami/earthquake parameters, in Ichihara
et al. (2013) and Kawashima and Toh (2016).
[43] Ichihara et al. (2013) first tried to constrain tsunami source region from the three components of the
seafloor magnetic variation data. This sounds a highly feasible application, because seafloor vector
tsunami magnetic sensor can monitor the tsunami propagation direction from a single site alone (Toh et
al., 2011). By adopting a back propagation method, Ichihara et al. (2013) found that the tsunami reaching
the seafloor OBEM site, B14, originated in the region with the latitude of approximately 39 degN, which
was rather northern area compared to the previous work using only sea surface displacement (Maeda
et al., 2011). Figure 6 summarizes the backpropagation results (left panels) and the final fit between the
observation and simulated results (right panels). Recent tsunami source inversion by Satake et al.
(2013) validated the tsunami source region constrained by Ichihara et al. (2013).
[44] The other remarkable application was performed by Kawashima and Toh (2016). They utilized the
linear relationship between tsunami-flow and magnetic signals shown in eq. (2), and inferred the best
fault slip model of the 2007 Kuril earthquake that can explain the magnetic field variations observed at
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
the north Pacific seafloor. Figure 7 shows the results. As described in Tyler (2015), the ocean is quite
unlike the fluid core or upper atmosphere in that the energy density of the EM field is quite small in
comparison to that contained in kinetic and other forms. From this energy disparity, we may regard
oceanic flows as just EM sources which is not influenced by EM inductions. This appears as the linear
form in terms of both 𝐯 and 𝒃 in induction equation of eq. (2). The resulting linear relationship allows to
calculate Green’s functions of magnetic field at observation sites due to a unit slip of each divided fault
(Fig.7b). As a result, a linear combination of Green’s functions that explains the observed magnetic data
provides a best fault model. This method allows the magnetic data to easily join the conventional tsunami
source inversions (e.g. Maeda et al., 2011), which will be one of powerful methods to accurately
determine the tsunami source mechanism in the future.
2.4.3 Application of the seafloor tsunami EM signals to tsunami early warning
[45] Recently, a JAMSTEC group developed a seafloor instrument, called “Vector TunaMeter (VTM)”
(e.g. JAMSTEC, 2014; Marine Technology, 2014), to apply the tsunami-generated EM signals to
tsunami early warning. A VTM consists of a fluxgate magnetometer for three components of the
magnetic field, a differential pressure gauge (DPG) for the pressure at the seafloor, and the acoustic
module to transfer data to the sea surface, shown in Fig. 8. A single VTM observation can monitor the
tsunami propagation direction by the vector magnetic observation and detect the sea surface
displacement by DPG. The most attractive feature of VTMs is that the VTM is designed to communicate
with an unmanned wave glider floating at the sea surface (e.g. Manley et al., 2010), by using the
equipped acoustic module, which allows a VTM to transfer real-time data to land stations via satellites.
[46] Hamano et al. (2014a, b) have already reported some successful detections of tsunami EM signals
by a VTM installed in the Philippine Sea, at the time of the Solomon Islands tsunami (Mw 8.0) on
th
February 6 , 2013. Although the altogether long-term operation of a VTM and a wave glider cost much,
this technique intrinsically has a great advantage in determining the tsunami propagation direction,
therefore may be adopted as a new strategy to prepare for coming destructive tsunamis in the future.
3. Motional induction studies by ocean tides
[47] In the early 2000s, Tyler et al. (2003) explored a new research field by demonstrating that the tidegenerated magnetic variations are observable at the low orbit satellite altitude. On the other hand, the
recent accurate seafloor EM observations seemingly provide opportunity to use seafloor tide-generated
magnetic data for the exploration of Earth’s interior. In this section, we comprehensively review the
studies on tide generated EM fields as follows: the observations of tide-generated magnetic field and
comprehensive geomagnetic field model (CM5) derived by Sabala et al. (2015) (subsection 3.1), the
brief history of the theory of tide-generated magnetic field (subsection 3.2), the numerical simulations of
tide motional inductions (subsection 3.3), and the recent application to the other fields (subsection 3.4).
In the subsection 3.4, we focus on two applications: 1) Earth’s interior sounding (subsection 3.4.1) and
remote monitoring of ocean via tide-generated magnetic fields (subsection 3.4.2).
3.1 Observations and extraction of motional induction due to ocean tides
[48] The history of observation of tide-generated magnetic fields is much longer than that of tsunamigenerated magnetic fields. For the comprehensive history, please refer to the story written in Section 1.
Here we focus on the story after Larsen (1968). Larsen (1968) reported magnetic signals of M2 ocean
tide observed both on land and at the seafloor, which was the first report of seafloor magnetic variation
due to ocean tides. Since the seafloor magnetic data started to be used in MT studies in the 1960s,
ocean tides have been often regarded as noise generators in MT surveys (e.g. Cox, 1980), because the
seafloor EM variations in the period of ocean tides consist of not only signals suitable for MT studies but
variations of ocean tides, quasi-periodic solar daily variation (Sq), etc., which are difficult to exclude from
MT data. Conventional methods use the night time data to identify the amplitude and phase of the tidegenerated magnetic field (e.g. Chapman and Miller, 1940; Malin and Chapman, 1970), while some MT
studies exclude tidal components directly by sinusoids fitting (e.g. Baba et al., 2010). However, there
still exists some remaining originating from tides in many MT data.
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
[49] Partly for this problem, Sabaka et al. (2015) recently added the M2 source parameters in their fifth
version of comprehensive geomagnetic field model (CM5, Sabaka et al., 2015). The CM5 was derived
from CHAMP, Orsted, and SAC-C satellite and observatory hourly-means data from 2000 August to
2013 January by using the Comprehensive Inversion (CI) technique. By using both the satellite and onland data, the CI technique can decompose the observed magnetic fields into variations originating from
sources in the three regions, i.e. 1) sources beneath the Earth’s surface, e.g. electric currents in the
core or induced currents in the Earth, 2) sources between the ground and the satellite altitudes, e.g.
ionospheric sources, and 3) sources above the satellite altitude, e.g. sources in the magnetosphere.
Thus the CI technique co-estimates parameters shown in Table 2, which are composed of the spherical
harmonic coefficients for the given time harmonics, for magnetic sources in the magnetosphere,
ionosphere, ocean, solid earth, and core. Figure 9.1. shows the results of the inverted magnetic field of
M2 origin in CM5 (bottom panels), with comparison to the two forward modelling results of Kuvshinov
(2008) (middle panels) and Tyler et al. (2003) (top panels). Note that CM5 and the forward modeling
by Kuvshinov (2008) used the 1-D conductivity model presented by Kushinov and Olsen (2006), shown
in the left panel of Fig. 9.1, while the Tyler et al. (2003) assumed insulating Earth beneath the surface
inhomogeneous conductance layer.
[50] Figure 9.1 and 9.2 show well agreement among the three magnetic models of M2 origin.
In Fig. 9.2, profiles of the three spectra agree quite well up to approximately 𝑛 = 18. The fact that M2
field powers of CM5 and Kushinov model are less than that of Tyler’s model make sense because Tyler
model eliminated the effect of upper mantle conductivity. The extracted M2 magnetic component in CM5
can be one of the important reference in broad study scope associated with M2 ocean tide.
3.2 Theoretical works of tide-generated EM fields in the late 1900s
[51] Theoretical works on tide-generated EM fields are thoroughly conducted in the late 1900s. Larsen
(1968) first applied the Kelvin wave model and thin-sheet approximation to the tide-generated EM fields
assuming an insulating crust and mantle beneath the seafloor. Chave (1983) derived general forms of
ocean-generated EM fields based on PM/TM modal representation and Green’s function representation
and applied them to the Kelvin wave model. In contrast to tsunamis, it was pointed out by Chave (1983)
that the importance of TM mode related to galvanic connection between the ocean layer and the
underlying medium, which implies a possibility of tide-generated magnetic fields to Earth’s interior
exploration.
3.3 Numerical simulations of tidally-induced magnetic field
[52] Since Tyler et al. (2003) found that tide-generated EM fields are detectable at altitude of satellites,
global simulation became a main stream of motional induction studies associated with ocean tides. Tyler
et al (2003) calculated the magnetic field of M2 tidal origin with a tidal model of Egbert and Erofeeva
(2002), by adopting the thin-shell approximation with the assumption of insulating Earth’s interior, and
compared the numerical prediction with the magnetic data observed by CHAMP satellite. Following Tyler
et al. (2003), Maus and Kuvshinov (2004), Kushinov and Olsen (2005), and Kuvshinov et al. (2006)
comprehensively investigated magnetic fields generated by other tidal components of N2, K1, P1, and
O1 as well as the M2 semidiurnal component, using the realistic conductivity structure beneath the
seafloor. Kuvshinov and Olsen (2005) used the Integral Equation method (Kuvshinov et al, 2002) to
simulate the magnetic fields observed at the altitude of CHAMP satellite, and revealed the effect of
realistic conductivity structure on M2 tidal magnetic field. Refer to Kuvshinov (2008) for the detail of 3D global simulations for tide-generated magnetic fields in the 2000s. Adopting the same manner as
Kuvshinov, Schnepf et al. (2014) recently compared the seafloor observed data with numerical results
of magnetic fields generated by M2, N2 and O1 components of ocean tides, by using variable
conductivity structure models (Baba et al., 2010; Kuvshinov and Olsen, 2006; Shimizu et al., 2010).
Figure 9 shows the result for M2 tidal component, where the difference in 1-D conductivity (shown in left
panel of Fig. 9) influence the estimated magnetic components at the seafloor observatories.
Furthermore, Schnepf et al. (2015) investigated the sensitivity of tide-generated magnetic fields
observed at the seafloor and at satellite altitude, by gradually changing the 1-D conductivity structure.
See the detail in subsection 3.4.1.
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
3.4 Application of EM variations generated by ocean tides
[53] Here we discuss two applications of tide-generated magnetic EM variations: 1) the Earth’s interior
sounding by the tide-generated EM fields (subsection 3.4.1), and 2) the monitoring of ocean remotely
from satellite altitude via tide-generated magnetic fields (subsection 3.4.2).
3.4.1 Earth’s interior sounding by tide-generated EM fields
[54] Larsen (1968) has already pointed out that, “Electromagnetic variations induced by oceanic tides
depend on the distribution of tidal currents and on the distribution of electrical conductivity beneath the
ocean. If either were known perfectly, the measurements would serve to give some precise information
of the other.” In contrast to tsunami magnetic signals, there remains great possibilities in exploring
earth’s interior by using magnetic fields generated by ocean tides. Chave (1983) pointed out the
importance of toroidal magnetic mode in the tidally-induced magnetic field. This point is becoming more
and more noteworthy in the recent studies on tidally induced EM variations, while the toroidal magnetic
component cannot leak to the air. Dostal et al. (2012) performed a numerical modeling only for the
toroidal component of magnetic field associated with the M2 component of ocean tide, and revealed
that the energy of the toroidal magnetic component is concentrated in short-wavelength spatial patterns
over shallow water coastal regions.
[55] Schnepf et al. (2015) implemented numerical experiments to investigate whether the motional
induction due to ocean tides are useful in exploring earth’s interior. The results of this study is
summarized in Fig. 10. They compare Frobenius norms of tide-generated EM components,
𝑆†,‡
ˆ
†,‡
†,1
𝐹‰,Š
− 𝐹‰,Š
=
D
,
(8)
‰,Š
among the several 1-D conductivity structure scenario. In eq. (8), F denotes the corresponding field
component, i, j label grid points in or above oceanic regions, k represents the conductivity scenario (C1,
C2, C3, C4, C5) shown in the Fig.10B, and l denotes the layer being analyzed. This sensitivity
investigation revealed that the horizontal magnetic field at the seafloor is remarkably sensitive to the
lithospheric conductivity. The reason can be attributed to the galvanic coupling between the source
region, i.e. ocean layer, and the sub-seafloor medium. Although Schnepf et al. (2015) don’t show the
spatial distribution of the sensitivity of the seafloor horizontal magnetic component (𝐵Œ ), it is expected
that the sensitivity of seafloor 𝐵Œ are relatively high in the coastal regions, because of the insight from
Dostal et al. (2012). This implies that ocean tidal flow might be efficient source to infer the conductivity
structure especially in some coastal regions. As far as I know, attempts to invert the conductivity
structure from the tidally induced EM data have been under way. We could see some results in the near
future.
3.4.2 Monitoring ocean by satellite magnetic observations
[56] In this last subsection, I would like to mention new possibilities recently presented by Sabaka et al.
(2016), i.e. remote ocean monitoring by satellite magnetic field of M2 tidal origin. They demonstrated
that Swarm satellite constellation enables us to extract the tide magnetic signals at satellite altitude from
much shorter interval of observation compared to the previous CHAMP satellites (CM5, Sabaka et al.,
2015).
[57] A new marvelous satellite mission, Swarm, was launched by the European Space Agency (ESA)
on 22 November 2013, which consists of a trio of three satellites: a pair of satellites flying side by side
at a relatively low altitude of approximately 455 km and a single satellite at higher altitude of
approximately 515 km (Olsen et al., 2015). This satellite mission enables the use of not only along-track
but also cross-track magnetic field differences in analyses of geomagnetic fields. Benefitting from this
cross-track magnetic difference between the Swarm low altitude satellite pair, Sabaka et al. (2016)
succeeded in extracting magnetic fields generated by semidiurnal M2 (period = 12.42060122h) and N2
(period = 12.65834751h) tidal components from the first 20.5-month SWARM data, by using the CI
technique (Sabaka et al., 2015). It was confirmed that extracted magnetic fields of M2 origin agree well
with the Tyler’s theoretical prediction with a tidal model of Egbert and Erofeeva (2002). Figure 12 shows
the summarized result of extraction of M2 magnetic field from Swarm or CHAMP satellite data. By using
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Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
both the along-track and cross-track gradient data from Swarm constellation, it takes as short as 20.5
months to extracted M2 field. It is noteworthy that 20.5 months is much shorter than over ten years that
is required to achieve the same accuracy when using only CHMAP data. This result implies possibilities
of monitoring seasonal/annual ocean variability remotely by observations of M2-generated magnetic
field at satellite altitudes.
[58] This promising satellite observations recently attract attentions of oceanographers and
climatologists, because of the possibilities of monitoring ocean parameters dependent on climate
changes by satellite magnetic observations. Recently, Saynisch et al. (2016) investigated the effect of
Antarctic Meridional overturning circulation (AMOC) decay on the magnetic field generated by the M2
tidal component, by conducting 3-D forward modeling. AMOC decay is expected as a result of additional
freshwater input by Greenland glacier melting (e.g. Stouffer et al., 2006). Saynisch et al. (2016)
demonstrated that the tide-generated magnetic fields are likely to be influenced not by the climate
variability induced deviations in the tide system, i.e. the change in seawater velocities, but by the
changes in sea water salinity and temperature. The expected variability of outward magnetic field at the
sea surface was ~0.7 nT. This kind of investigations of effects of possible climate change scenario on
magnetic fields can provide us important information for predicting the future M2 magnetic signals.
4. Summary
4.1 Summary of progress in studies on motional induction due to tsunamis
1. A number of EM data associated with tsunami motional inductions were reported in the last 10
years (e.g. Toh et al., 2011; Manoj et al., 2011; Suetsugu et al., 2012).
2. Many analytical solutions were derived recently. (e.g. Ichihara et al., 2013; Minami et al., 2015;
Shimizu et al., 2015)
3. Minami et al. (2015) revealed the strong dependence of tsunami EM signals on the ocean depth.
4. There appeared several types of numerical techniques for tusnmai-generated magnetic fields:
2-D time-domain method (Minami and Toh, 2013), 3-D frequency-domain IE technique (Zhang
et al., 2014b), Combination of Biot-Savart and Tyler’s analytical solution (Tatehata et al., 2015),
thin-shell 3-D frequency technique (Kawashima and Toh, 2016).
5. Shimizu and Utada (2015) thoroughly investigated possibility of applying tsunami-magnetic
variation to exploration of Earth’s interior. They concluded that tsunami motional induction is not
useful for the Earth’s interior exploration.
6. A JAMSTEC group developed and operated VectorTunaMeter (VTM) and Wave glider, which
is one of important approach to apply tsunami-generated magnetic fields to tsunami early
warning. A single VTM observation can monitor both the tsunami propagation direction and
tsunami height, while the wave glider is able to transfer real-time VTM data to land via satellite
communication.
7. Ichihara et al. (2013) and Kawashima and Toh (2016) succeeded in apply seafloor tsunami
magnetic data to constrain the earthquake and tsunami mechanism. Linear relationship
between seawater velocity and generated EM fields enables us to easily apply magnetic data
to conventional tsunami source inversion.
4.2 Summary of progress in studies on motional induction due to ocean tides
1. Sabaka et al. (2015) added M2 tidal source parameters in their comprehensive geomagnetic
field model (CM5).
2. Many global simulation studies have been conducted associated with ocean tides (Maus and
Kuvshinov, 2004; Kushinov and Olsen, 2005; and Kuvshinov et al., 2006; Dostel et al., 2012;
Saynisch et al., 2016), since Tyler et al. (2003).
3. Motional induction by ocean tides has a possibility to be used to explorer the Earth’s interior
(Schnepf et al., 2014; 2015).
4. The horizontal magnetic component of M2 tidal origin is the most sensitive one to the
conductivity beneath the seafloor, because of the galvanic (TM mode) coupling between ocean
layer and the sub-seafloor medium (Schnepf et al., 2015)
14
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
5. Swarm constellation mission allows us to extract the M2 tidal magnetic component from Swarm
and on-land observatory magnetic data much earlier than CHAMP satellite data, which may
provide us a new opportunity to monitor seasonal/annual variations of temperature and salinity
of seawater through the M2 tidal magnetic signals at satellite altitudes (Sabaka et al., 2016;
Synisch et al., 2014).
Acknowledges
T. M. would like to thank The Working Group for inviting me as a reviewer at the EM Induction Workshop
2016 in Chiang Mai, Thailand. T. M. would express sincere thanks to Hisashi Utada, Hisayoshi Shimizu,
and Hiroaki Toh, for their helpful comments on this review through seminars and personal
communications, which made this review comprehensive. This review was produced while working in
Earthquake Research Institute, the University of Tokyo, as a Japan Society for the Promotion of Science
(JSPS) postdoctoral fellow (PD). Production of this review was supported by Grant-in-Aid for Scientific
Research, Ministry of Education, Culture, Sports, Science and Technology, Japan (No. 26282101).
15
Keynote review: Takuto Minami
Larsen (1971)
Tyler (2005)
Ichihara et al.
(2013)/ Sugioka
et al. (2014)
Minami et al.
(2015)
Shimizu
and
Utada (2015)
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Tsunami
velocity
Linear
dispersive wave
Below seafloor
Linear
wave
Linear
wave
long
Insulator
long
Homogeneous
space
half-
Only 𝐹B
Linear
dispersive wave
Homogeneous
space
half-
Only 𝐹B
Linear
dispersive wave
Arbitrary 1-D Earth
Three
model
layer
Main field
𝐹„ and𝐹B
Earth
Only 𝐹B
𝐹„ and𝐹B
Characteristics
Shallow
and
deep
mantle
models
are
investigated
Independent of
frequency
Homogeneous
earth model
Conservation of
dynamic energy
is considered.
General form of
Larsen (1971)
Table 1. The papers presenting the analytical solutions for tsunami-generated EM fields. Tsunami
velocities are either of linear long wave or linear dispersive wave, defined by equations (5) and (6),
iii
respectively. D. SUETSUGU et al.: TIARES—SEAFLOOR ARRAY FOR SOCIETY HOTSPOT
B02104
TOH ET AL.: TSUNAMI SIGNALS AT SEAFLOOR OBSERVATORY
B02104
Fig. 3. (a) BBOBS on board R/V “MIRAI” just before installation. (b)
OBEM recovered by the fishing boat “Fetu Mana.”
Figure 4. The 3 h plots of the observed time series at the time of the two Kuril earthquakes in (left) 2006
5. 19 h(b
records
(a) vertical
(b) horizontal
northward
andofeastward
(b
) geomagnetic
com2007. of
(toptsunami-generated
to bottom) The downward EM
(bz),Fig.
x), (Left:
Figureand
1. (right)
Reports
variations
Toh2010
etycomponent,
al., 2011;
Right: component,
Suetsugu et al.,
(c)horizontal
water pressure
earthquake.
and
tilts of
(Txthe
and Ty).Chilean
The two
vertical R1, R2, ... and
ponents, horizontal geoelectric components (Ex and Ey),and
2012). solid
Leftlines
panel
shows
time
series
of
tsunami-generated
EM
components
(bz,bx
and
by,
Ex) and tilt
G1,
G2,
...
denote
successive
arrivals
of
Rayleigh
and
Love
waves,
indicate the estimated time of arrival (ETA) of seismic and tsunami waves at NWP, respecwhich
circled and
the
threedenote
panels: the
tively.
Note time
that major
variations
the seafloor
EM respectively,
components
commenced
onlyEarth’s
after surface.
those
of Bottom
tiltslines
variation
at the
of the
2006ofKuril
earthquake
tsunami.
Red
blue
vertical
(d) in
EW
(e)
NS component,
and (f) vertical component of
ceased. occurrence
The tsunami ETAs
well with the
peaks
thecomponent,
horizontal
geomagnetic
components.
earthquake
andcoincide
the tsunami
arrival
at therecords
seafloor
site,
respectively.
Right panel
3-htime
geomagnetic
of the tsunami
generated by the earthquake
corresponding
water
pressure
record
(red) isat
superimposed.
shows the three magnetic components (black (black).
lines)The
and
pressure
data
(red
lines)
the time of the
where Ex, Ey, bx and by are the northward electric, eastward
[7] The contribution of sediments can be argued negligi2011
earthquake
respectively.
electric,Chile
northward
magnetic andtsunami,
eastward magnetic
com- ble as follows: because the thickness of sedimentary layers
ponents of the tsunami‐induced EM field, respectively [see
Sanford, 1971]. m and k are the magnetic permeability and the
leakage constant [Chave and Luther, 1990] that is the ratio of
the seafloor conductance to the ocean conductance.
Equations (1) and (2) are valid when conductivity of the crust
and the mantle is small enough. To evaluate their validity, let
us assume the subseafloor conductivity, s, be 10−2 S/m
(somewhat too conductive crust and uppermost mantle) and
the time scale of the tsunamis, T, be 103 s (very long tsunami
duration). p
These
"
# us the upper limit of conductance
ffiffiffiffiffiffiffiffi values give
3
¼ !" ¼ 10!T
2# " 10 ½S$ for the crust and the mantle, where
beneath NWP is as thin as 375 m [Shipboard Scientific
2001], the
leakage
is as small toasdetermine
less
ofParty,
teleseismic
body
wavesconstant
will bek employed
than 2% (0.0168). This means that the motionally induced
the
seismic velocity structure in the mantle transition zone
electric currents are mostly confined within the ocean in the
(MTZ),
a depth
from 400
km, and
the lower
present case.
It is range
worth arguing
whattois700
expected
for larger
mantle.
topography
of the mantle
discontinuities
k. WhileThe
the negligible
k maximizes
the contribution
of the (the
seafloor and
electric
field todiscontinuities)
the particle motion
estimates
(see as a
410-km
660-km
could
be used
equations (1) and (2)), a k as large as unity makes the par“mantle
thermometer”
because
they
are
interpreted
as minticle motions irrelevant to the seafloor electric field. This
eral
phase
changes
controlled
by
temperature
and
pressure.
implies that the vector geomagnetic measurements become
Previous
studies
(e.g.,
et al.,
2002; Suetsugu
much more
important
forNiu
seafloor
observatories
in coastalet al.,
regions with thick and conductive sediment accumulation
16
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Figure 2. Relative phase of the magnetic vertical component (bz) to tsunami sea surface displacement
(left), where 𝜃 = 90° means the 𝜋/4 phase lead of 𝑏B to 𝜂, and normalized amplitude of bz (right), with
respect to the ocean depth (Minami et al., 2015). Lines titled LDW(𝜎, 𝑇) is the solution by Minami et al.
(2015), where LDW stands for “Linear Dispersive Wave”, and 𝜎 is the half-space conductivity beneath
the seafloor and T is the period of tsunami, while red line indicates Tyler’s solution.
MINAMI AND TOH: 2-D TSUNAMI DYNAMO FEM SIMULATIONS
OH: 2-D TSUNAMI DYNAMO FEM SIMULATIONS
Figure 1. The epicenter of the 2011 Tohoku earthquake that occurred on 11 March 2011 (open red star), its W-phase MT
solution by USGS, and the seafloor EM observatory installed in the northwest Pacific (red rectangle). The epicentral distance
f 4 S/m and
a (41.1026°N, 159.9518°E) is approximately 1500 km. Two DART stations operated by NOAA (yellow squares) are
to NWP
also depicted. Sea level changes at the DART stations were fitted by our 2-D hydrodynamic simulations in order to calculate
the ocean.
the In
magnetic signals observed at NWP.
o EM simula∂η ∂Φ
operated by NOAA at DART21401 and
#
¼ 0 at sea surface
(3)
adopted. gauges
We (OBPs)as shown
∂t
∂z
DART21419,
in Figure 1. It was found that profiles
the sea level changes at the two DART stations are very
∂Φ
ulated for ofsimilar
slip
¼0
at sea bottom
(4)
to the downward magnetic component observed at
∂n
NWP. In the present paper, we try to explain both the sea level
nd 6.6 m from
changes at the DART stations and the magnetic variations at
[7] Here, Φ, g, and η denote the velocity potential, the
ges at the NWP
twoby 2-D tsunami dynamo simulations, assuming that gravity
acceleration, and the sea surface elevation, respectsunamis can be approximated by plane waves.
tively. Operators, ∂/∂ t, ∂/∂ z, and ∂/∂ n, denote differentia2-D hydrodytions with respect to time, the vertical coordinate, and the
3. Simulation Method
i arrival times
direction normal to the seafloor, respectively. Note that η
[5] We developed a 2-D FEM tsunami dynamo simulation and z are upward positive throughout this paper. The leapfrog
M components,
code in order to explain the sea level changes at DART21401 method was adopted to solve equations (2) and (3), while
DART21419 and the tsunami-induced magnetic varia- equation (1) is solved by FEM in order to calculate Φ with
produced. and
The
tions at NWP simultaneously. We adopted simulations in the given boundary values.
[8] In the second step, we calculated the tsunami-induced
gnetic compothe time domain, because transient waves such as solitary
waves cost a lot to reproduce in the frequency domain. EM fields using the tsunami flows of the first step as
he subsequent
Furthermore, we adopted FEM because unstructured triangu- follows: We began with equation (9) in Tyler [2005], the
lar meshes can express actual bathymetry, which may virtu- induction equation in terms of the tsunami-induced vertical
onent as large
ally be impossible using rectangular meshes [Minami and magnetic component,
Toh, 2012]. Our simulation method consists of two steps.
ed.
∂b
In the first step, oceanic flows associated with tsunami prop(5)
¼ #∇ • ðF u Þ þ K∇ b :
∂t
d EM field agation
dis- are calculated. Second, the induction equation in
terms of the magnetic field is solved numerically for given
mi. The figure
[9] K = (μσ) is the magnetic diffusivity, where μ and σ
oceanic flows. In order to obtain consistent results between
two steps, the same numerical mesh was used for both are the magnetic permeability and the conductivity, respecmately 104 the
min
tively. b , u , and F denote the tsunami-induced vertical
finite element calculations.
magnetic
component,
the horizontal
velocity, and
[6] In the Figure
first step, the4.
Laplace
equation was solved
in
that an initial
Generation
mechanism
of an initial
riseoceanic
in seaterms of the velocity potential, assuming the oceanic flows the vertical component of the geomagnetic main field,
e seafloor, are
had
2-D configuration
with tsunamis
propagating
tsunami
magnetic simulations for the 2011 Tohoku earthquake tsunami,
floor
bpresent
the Two-dimensional
peak
of brespectively.
itself
(blue
circles
irrotational.
In theFigure
paper,to
we3.
focused
mainly on
y prior
z. The Inemf
propagation observable at NWP. We there- only in the y direction, we can set the x component of ∇ and
arrival ofoffshore
the tsunami
crosses
inside)
is
driven
the
coupling
of(2013).
horizontal
v by
to nil.
Under
this circumstance,
equation
(5) is reduced
fore adoptedwith
linear boundary
conditions
on the by
sea surface.
conducted
Minami
and
Toh
Theto map shows the locations of the epicenter (open star), DART
As for the seafloor,
we assumed
negligible
!
ise in seafloor
tsunami
flows
withbottom
thefriction.
vertical component
of∂ "the geomag$
∂
∂
∂#
The governing equation to be solved and the related boundb ¼ μσ
F u :and (6)
þrectangles),
# μσ
observation
sites (yellow
seafloor EM observatory (red open rectangle). The right panel
∂y
∂z e slightly
e induced elecary conditions
are summarized
follows:Tsunami-induced bz ∂y
netic
main asfield.
and
precede
x ∂t
cing v × B field the sea
shows
the comparisons
the wherever
sea thelevel
(top) and the magnetic fields (bottom), where colored
level
change
in deep
oceans
due(6)of
to
self-induction
ef- change
[10] Equation
is applicable
conductivity
is
ΔΦ ¼ 0
(1)
homogeneous,
the regions
andthe
beneath the
Although the fects
of the tsunami itself. Because
e isincluding
opposite
to vabove
×in B,
data
∂Φ lines indicate observed
ocean layer.x When
equation and
(6) is used the
the air,black
σ = 0 and lines are the simulation results. Here the z axis is upward
þ
gη
¼
0
at
sea
surface
(2)
, difference in slight
∂t
u =causes
0 are substituted
to make equation
the Laplace
phase lead of ex to v × B
the initial
rise in(6)seaandthethepeak
y axis
is in
front of v × B, floor positive
by preceding
of the
sea the
leveltsunami
change. propagation direction. (After Minami and Toh, 2013). The left
4561
lower
panel
shows
mechanism
of how the initial rise in by is generated by tsunami propagation.
Difference
in phase
between
the the
peak of
bz and the secondary
peak of by becomes approximately T/4 due to the current
composed of ex and v × B.
z
H
z H
2
z
#1
z
H
z
H
H
2
2
2
2
z
z y
y
which causes an initial rise in seafloor by prior to bz variations. It was also found by our additional simulation that
the induced EM field variations around the first arrival look
very similar to those induced by a solitary wave (see section
4 in the supporting information). It therefore is probable that
the initial rise in seafloor by and the subsequent main peaks
in by and bz result from the mechanism described in the
solitary first wave. This small rise in seafloor by needs further
investigation because it may enable us to detect tsunami
arrivals by seafloor magnetic observations before actual
arrivals of tsunami peaks.
[17] Although our simulation results successfully reproduced
17
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Figure 4. The results of 3-D numerical simulation of the 2011 Tohoku earthquake tsunami, conducted
by Zhang et al. (2014b). a) The locations of the epicenter, the on-land magnetic observatories, CBI and
ESA, and seafloor site, NM04. b) Comparison of the downward component, Bz, at ESA among the
observation (black), the prediction using Biot-Savart law by Utada et al. (2011) (red), and the result by
3-D simulation by Zhand et al. (2014b, JGR) (blue). c) Comparison of Bz at CBI between the observation
(black) and 3-D simulation result (red). d) Comparison of By, Bz, and Ex between the observation (black)
and the simulation (red).
Motional impedance
(a)
(b)
0
0
393
2.2 Evaluation of the electromagnetic field at the seafloor
due to motional induction
We suppose a four-layer electrical conductivity model beneath the
seafloor to examine the typical features of a motionally induced
electromagnetic field at the seafloor (Fig. 3). A sediment layer that
40
2
contains a large amount of seawater is supposed as the first layer.
The thickness of the layer is assumed to be 400 m and its electrical
conductivity is taken to be 1.1 S m−1 (e.g. Flosadóttir et al. 1997;
3
60
Bourlange et al. 2003; Shankar & Riedel 2011), which is one-third
of that of seawater. The second layer consists of the oceanic crust
4
80
with a conductivity of 10−3 S m−1 . The layer is assumed to extend
down to 6 km deep from the seafloor (e.g. Cox et al. 1986). The
100
5
third layer is the lithospheric mantle. Its conductivity is expected to
10−5 10−4 10−3 10−2 10−1 100
10−5 10−4 10−3 10−2 10−1 100
be very low (e.g. Larsen 1971; Cox et al. 1986); we suppose here
electrical conductivity [S/m]
electrical conductivity [S/m]
the conductivity to be 10−5 S m−1 (Cox et al. 1986). The thickness
Figure
3.
Supposed
electrical
conductivity
model
beneath
the
seafloor.
of this(2015).
low-conductivity
layer increases
with S/m
increasing age of the
Figure 5.1 Electric conductivity profile used in Shimizu and Utada
The sediment
layer 1.1
(b) ais thickness
a magnification
the electrical
profileis
near
the seafloor.
seafloor (Filloux
1980;
Baba
et al.
2010, 2013),
with
ofof400
m, the conductivity
oceanic crust
1.d-3
S/m and extended
to 6 km
deep
from
seafloor.
The but we suppose
bottom depth
layer to be 70
km. The layer beneath
lithospheric mantle is 1.d-5 S/m down to 70 km from here
the theseafloor.
Theof the
conductive
mantle
-2
the
resistive
layer
is
the
conductive
mantle
(asthenosphere)
and its
(asthenosphere) is 2*10 S/m below the lithosphere. The depth of ocean depth is set 4000 m with 3.3
electrical conductivity is taken to be 2 × 10−2 S m−1 (see, e.g. Baba
S/m conductivity seawater.
et al. 2010, 2013). The depth of the sea is assumed to be 4000 m.
Using the obtained coefficients calculated by eqs (18), (20) and
Fig. 4 shows the amplitude and phase of by , bz and Ex at the
(21), we can evaluate the magnetic and electric fields at an arbitrary
seafloor for the conductivity model shown in Fig. 3. The phase is
position between the sea surface and seafloor from the informadetermined with respect to that of the surface gravity wave. The vertion of the ocean current (surface gravity wave) and the electrical
tical displacement amplitude of the surface gravity wave is assumed
conductivity structure.
1
depth [km]
100
360
10−1
270
10−2
10−3
by bz phase [degree]
by bz amplitude [nT]
depth [km]
20
180
90
18
360
10−1
270
10−2
10−3
10−4
10
Ex amplitude [micro V/m]
by bz phase [degree]
100
−1
102
103
10−2
10−3
10−4
10−5
102
103
period [sec]
104
180
90
0
104
360
Ex phase [degree]
by bz amplitude [nT]
Using the obtained coefficients calculated by eqs (18), (20) and
(21), we can evaluate the magnetic and electric fields at an arbitrary
position between
the sea
surface
and Minami
seafloor from the informaKeynote
review:
Takuto
tion of the ocean current (surface gravity wave) and the electrical
conductivity structure.
electrical conductivity is taken to be 2 × 10−2 S m−1 (see, e.g. Baba
et al. 2010, 2013). The depth of the sea is assumed to be 4000 m.
Fig. 4 shows the amplitude and phase of by , bz and Ex at the
seafloor
for the conductivity model shown in Fig. 3. The phase is
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
determined with respect to that of the surface gravity wave. The vertical displacement amplitude of the surface gravity wave is assumed
102
103
104
102
103
104
270
180
90
0
period [sec]
Figure 4. Relative amplitude and phase of the induced magnetic field (by and bz , top panels) and electric field (Ex , bottom panels) due to a surface gravity wave
Figure
Relative
amplitude
and
phase
induced
(by and
bzthe, top
panels)
and
of 1 cm amplitude
for the 5.2
conductivity
models
shown in Fig.
3. The
by andof
bz the
components
are magnetic
shown by bluefield
and black
lines in
top panels,
respectively.
electric
(ExnT, (θ
bottom
panels)
to a surface
gravity
1 000
cmnT
amplitude
conductivity
= 30 000
= 90◦ ) and
B0z = 0due
nT (dashed
lines) or B0H
= 0 nT wave
and B0z of
= 30
(solid lines).for
For the
comparison,
those with
The ambient field
was B0H field
the case in which
subseafloor
is insulator
are shown
by redblines.
models
shown
in Fig.
5.1. The
and b components are shown by blue and black lines in the top
y
z
panels, respectively. The ambient field was FH = 30 000 nT (𝐹B = 0nT ) (dashed lines) or 𝐹B =
30000𝑛𝑇 (𝐹„ = 0nT)(solid lines). For comparison, those with the case in which subseafloor is
insulator are shown by red lines. (After Shimizu and Utada, 2015).
19
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
120
H. Ichihara et al. / Earth and Planetary Science Letters 382 (2013) 117–124
121
H. Ichihara et al. / Earth and Planetary Science Letters 382 (2013) 117–124
over each other, suggesting the travel times have been overestimated (Fig. 6a). We then assumed a delay time of 1 min between
tsunami generation and the initial fault rupture. In this case, the
back-propagation curves indicate the source area is located along
the Japan Trench axis and between latitudes 39.0◦ N and 39.5◦ N
(the gray area in Fig. 6b), which is consistent with the tsunami
source area inferred from the magnetic data alone. These results
suggest that the impulsive tsunami generation was likely delayed
with respect to the initiation of the rupture, possibly by around
1 min, as predicted by previous seismic studies, in which it was
estimated that the fault rupture near the tsunami-generation area
occurred between 45–90 s after the initial rupture (e.g. Ide et al.,
2011; K. Yoshida et al., 2011a; Y. Yoshida et al., 2011b). The result
also indicates that the source area is narrow, with a width less
than 20 km in the across-trench direction.
As a further check, we simulated the tsunami waveforms at the
5. Estimated location of the t
stations by inputting the estimated source area, and thenFig.
comof the magnetic field data (red ar
tsunami
pared it with the observed sea level and magnetic changes.
Thepropagation direction base
The red thick curve denotes the ba
waveforms were calculated based on the finite-difference program
rival time of 05:51 UTC for the cur
the back
Cornell Multi-grid Coupled Tsunami Model (COMCOT, Version
1.7)propagation curves in 2-m
(Wang and Liu, 2006), which can solve nonlinear equations for
4. Estimation
of tsunami so
shallow-water. The 500-m-mesh bathymetric data by the JCG
are
used for the sea depth distribution. We began by assuming seafloor
Assuming the impulsive
uplift in an area 90 km long and 20 km wide (Fig. 1), field
which
is fully induced by the
allow us to estimate t
is based on the back-propagation estimation. The seafloor(2)uplift
OBEM
started 50 s after the initial fault rupture at the south end of thedata. The propagatio
θ , can be calculated from
uplift area and propagated to the north at the speed of 0.8 km/s.
magnetic field variation, by
◦ –115
At each grid, the seafloor showed constant uplift from 0 m to9613
m ◦ was obtained fro
within 2 min rise time.
which indicates the azimut
◦
from site
The resulting tsunami waveforms for this model are shown
in B14 was −65 to
The distance from the tsun
Fig. 4. The calculated waveforms come close to fully explaining the
travel time and propagation
impulsive waves at the stations, with the exception of DART21418
of the vertical geomagnetic
(Fig. 4). At DART21418, a dispersion effect, which cannot of
bethe
eximpulsive tsunami at
vertical
plained using the simulation code, is obviously present (Saito
et magnetic anomaly
tude change, the total mag
al., 2011). The propagation azimuth calculated from the horizontsunami arrived at site B14
tal velocity components in the result of COMCOT also explains
time of the total magnetic
Fig. 6. Estimation of the tsunami source area based on back-propagation curves of
Figure
6. Left: The focal area inferred by back propagation
the
vector
magnetic
field
data
at the
theFig.propagating
azimuth
at (red)
sitesea-level
B14 based
onthehorizontal
magnetic
4.using
Observed (blue)
and
calculated
changes
at
offshore seatsunami arrival based on E
the OBEM and the sea level stations, assuming that the impulsive wave was generlevel gauge and the
B14 4).
OBEMItstation.
The sea-level
change
at sitethe
B14 isnorthward
estimated
components
(Fig.
isand
worth
noting
that
propa- tsunami arrival is
ated 0 and 1 min
after initialization
of the
rupture ((a)observed
and (b), respectively).
seafloor.
Right:
The final
fit fault
between
sea surface
displacement
seafloor
magnetic
dataimpulsive
from the vertical magnetic field variation based on Eq. (1). The horizontal axis in the
ture (05:46:18 UTC).
For the DART21418 station, the curve is represented as a thick curve because of the
gation
of the tsunami
was
necessary
to rupture.
explain
graphs represents
the time fromsource
the initiation
of the
earthquake fault
(For the arrival
(blue
lines)
with
those
obtained
by
numerical
calculations
(red
lines)
(after
Ichihara
et
al.,
2013).
Based on the tsunami tr
1-min uncertainty caused by its sampling rate. The gray-shaded area denotes the
interpretation
the references
to color inIf
thiswe
figure,
reader
is referred the
to the northward
time
at theofIwate_N
station.
dothenot
assume
ric data distributed by the
web version of this article.)
estimated source area.
propagation, the peak time of the impulsive wave is delayed
by
the back-propagation
distan
90ins the
at NOAA
this station.
using the Tsunami Travel T
DART21418 station (Fig. 4). Based on Eq. (3), we caldistance to the source may be shorter than 70 km, because the
tributed
by
Geoware
Corpor
culated b H from the observed b z . The impulsive feature of the
tsunami may have been generated after the rupture, as we will distsunami.html). The TTT calc
very well with that of the observed b y , which
b H agrees
5. calculated
Discussion
and conclusions
ing the long-wave assumpt
cuss later. The estimations of the azimuth and distance constrained
is the dominant horizontal component (shown by green dashed
construction method to dete
the position of the nearest tsunami source from the OBEM site in
and
solid
red
lines
in
Fig.
3,
respectively).
These
facts
support
the
We estimated the source area of the impulsive tsunami
gen- error in the calcula
expected
contention that the impulsive magnetic change observed by the
the fan-shaped area shown in Fig. 5. Because the earthquake ocmodel
erated by the 2011 Tohoku earthquake using the magnetic
fieldand the accuracy of
OBEM
was
likely
to
have
been
induced
by
the
impulsive
tsunami
curred at the plate boundary between the Pacific plate and the NE
travel
time based on 1 arcvariation
observed
onindicate
the seaward
slope change
of the(ηJapan
Trench.
The
wave. Eqs.
(1) and (2)
that sea-level
) at site
is almost identical to that
Japan arc, the tsunami source area should be distributed on the
source
location
was from
reasonably
constrainedchange.
to the
the
B14 can
be estimated
observed geomagnetic
Wearea
ob- near
ric data. When we assume t
landward slope of the trench. Based on this constraint, the source
trench
the the
latitude
39◦ N, even
thoughnT),observation
η = 1.around
8–2.9 m from
peak amplitude
of b z (12–19
tained axis
immediately after the ruptu
of the impulsive tsunami was tentatively located near the trench
F z (38570 nT)
andnot
h (5830
using
(1), which
comparable
timated within 70 km of sit
conditions
were
idealm)for
theEq.analysis
ofisthe
tsunami-induced
◦
axis at around latitude 39 N (the red area in Fig. 5).
η =terms
1.4–2.7 of
m, obtained
from the
(4–5 nT) sampling
with the estimate,
the travel time more precise
magnetic
signal in
the number
ofb xstations,
the distance estimation sho
and b y (8–17 nT), F z , and h using Eq. (2).
We further attempted to refine of the source location of the
intervals,
or measurement of the instrumental attitude, because
impulsive tsunami wave by using the back-propagation distances
the OBEM had originally been emplaced as part of an electrical
from six offshore observatories in addition to the OBEM station.
structure study. Furthermore, joint analyses utilizing the sea-level
These include three GPS buoys emplaced and operated by the
change data supported the estimation and constrained the tsunami
Nationwide Ocean Wave Information Network for Ports and Harsource area to a narrow area along the trench axis, and a tsunami
bours (NOWPHAS) along the northeastern coast of Japan (Iwate_N,
origin time of about 1 min after the initial rupture. These results
Iwate_M, and Iwate_S, 3-s interval sampling). Additionally, there
suggest the potential of using magnetic observations of the seafloor
are two cabled ocean bottom pressure gauges operated by the Unifor tsunami observations.
versity of Tokyo and Tohoku University (Maeda et al., 2011) (TM1
Koketsu et al. (2011), Gusman et al. (2012), and Satake et al.
and TM2, 1-s interval sampling) and a buoyed pressure gauge oper(2013) estimated that the tsunami source was located between
ated by US NOAA (DART21418, 1-min interval sampling) (Gonzalez
38°N and 39◦ N latitude. Our estimation is consistent with the
et al., 2005). When we assume that the impulsive tsunami ocnorthern portion of the area outlined by these studies. Satake
curred immediately after the initial rupture, the back-propagation
et al. (2013) recently presented a precise tsunami source model
considering a temporal change of the source, in which they
curves for the stations emplaced east and west of the trench cross
20
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Figure 7. Best fault model B for the 2007 Kurill earthquake tsunami is inferred by 3-D tsunami EM
simulations adopting thin-sheet approximation (Kawashima and Toh, 2016). a) Map of observatory
distribution used for tsunami source inversion by Fujii and Satake (2008). b) The left shows the northwest dipping fault model (model A), while the right is south-east dipping fault plane models (model B
and C). c) The fault plane parameters of models A, B, and C. d) Fault slip distributions of models A and
B, optimized to fit the seafloor magnetic field at NWP. e) Seafloor magnetic data and those calculated
using optimized fault slip distributions of models A and B. From top to bottom, the downward, the
northward, the eastward component comparisons are shown. In each component, calculated field in top
and bottom panels indicate that model A (north-west dipping) and B (south-east dipping) were used,
respectively.
Combination)of
OBEM)(Bx,By,Bz,)Ex,)and)Ey)
and
DPG)(Pressure)change)
Figure 8. Vector TsunaMeter developed by the JAMSTEC group. The observed seafloor tsunami EM
signals and seafloor pressure data are transferred via the wave glider to satellite, which enables to apply
the vector EM signals to tsunami early warnings. (After JAMSTEC, 2014)
21
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Table 2. CM5 parametrization (after Sabaka et al., 2015). Spherical harmonic coefficients up to degree
of 36 are included to represent M2 tidal signal with the prescribed M2 period.
22
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Figure 9.1. The outward component of the magnetic field at the altitude of 430 km, generated by the
M2 tidal component. From top to bottom, the panels show the prediction by Tyler et al. (2003), the
simulation by Kuvshinov (2008), and the fields obtained by CM5 (Sabaka et al., 2015). The left and
right columns indicate the amplitude and phase of Br, respectively. While Tyler’s calculation assumed
the insulator beneath the ocean layer, modeling by Kuvshinov and CM5 adopted the 1-D conductivity
structure of Kuvshinov and Olsen (2006), shown on the left side. (After Sabaka et al., 2015).
23
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
CM5, a pre-Swarm comprehensive model
1615
0.2
Tyler model
Kuvshinov model
CM5 model
0.18
0.16
0.14
2
Rn [nT ]
0.12
0.1
0.08
0.06
0.04
0
0
5
10
15
20
25
30
35
40
degree n
Downloaded from http://gji.oxfordjournals.org/ at NASA Goddard Space Flight Ctr on February 5, 2015
0.02
Figure 11. The
Rn spectra9.2.
(Lowes
1966)
of the time-averaged
oceanic
M2 tidal of
magnetic
at the Earth’s surface from
n = 1−36M2
for thetidal
theoretical
forward
Figure
Rn
spectra
(Lowes,
1966)
thefield
time-averaged
oceanic
magnetic
field at Earth’s
models of Tyler (blue), Kuvshinov (green) and the estimate from CM5 (red). The vertical dashed line at n = 18 shows the approximate point beyond which the
surface
(r=6371.2
km)
from
n=1
-36
for
the
three
model
shown
in
Figure
11.1.
Three
color lines
spectral power begins to increase in the CM5 estimate and the profile begins to diverge from the theoretical predictions.
corresponds to the models by Tyler, Kuvshinov, and CM5 in Fig. 9.1. (After Sabaka et al., 2015)
The spatial features of the predicted and extracted M2 fields shall now be discussed. Because the tidal signal is temporally periodic and
the wave shape (sinusoid) known, there are only two numbers (amplitude/phase or, alternatively, the real/imaginary components) required to
completely specify the signal at a given location. Here the convention in ocean tidal literature is followed where amplitude/phase are used and
referenced to zero (for the amplitude) and Greenwich phase (for the phase). The sense of propagation of the features is towards increasing
values in the phase contours. The propagation circles around the so-called ‘amphidromes’, where the phase values become undefined.
In Fig. 12 are shown the M2 radial magnetic fields from each of the two prediction models, and the CM5 extraction. In keeping with the
spectral results, all fields shown have been truncated at degree n = 18. Furthermore, the fields are presented for a spherical surface at altitude
430 km. This represents the approximate mean-altitude of CHAMP over the first 4 yr of the mission. The satellite data, because they cover
the oceans, are expected to be primarily responsible for the M2 resolving power in CM5 and so the choice of presenting the comparison at
430 km is aimed at collocating predicted and observed fields. Note, however, that at this altitude the smaller-scale features are further reduced
due to geometric attenuation.
One immediately sees that the amplitude distributions (Fig. 12, left-hand panels) agree very well to within the coarse comparison
attempted here. The global correlation coefficients between the maps of Tyler and CM5, Kuvshinov and CM5 and Tyler and Kuvshinov
are 0.879, 0.921 and 0.929, respectively. That is, the two forward models, despite their different formulations and representations of the
conductive mantle, produce similar M2 predictions; these predictions also independently agree with observations as extracted through CM5.
This provides validation for the CM5 recovery as well as mutual validation between the forward models. Recall that the M2 tidal basis
functions in CM5 have no information about continental versus oceanic regions, and the weak strength of the signal over the continents is a
strong indication that the extracted signal is indeed of oceanic origin. More specifically, these basis functions presently include only temporal
information and are given no a priori spatial information. The correlation in the spatial distributions then surely confirms the ocean tides as
the source. The maximum amplitude of the radial component of the CM5 M2 at 430 km is about 2.11 nT, but near the end of the mission
CHAMP had descended to an altitude of about 250 km at which point the maximum value is about 2.58 nT. This is a very promising result
given that much of the recovered signal is on the order of 1−2 nT in strength over this satellite altitude range and represents the next largest
Figure
10.theComparison
of magnetic amplitude generated by the M2 tidal component, 𝐁 ⋅ 𝐁 ’ /|𝐁 “ |,
magnetic field
source after
lithosphere.
where 𝐁
is distributions
the tide-generated
magnetic
and agreement
𝐁 ’ is the
field. note
Color
The Greenwich
phase
(Fig. 12, right-hand
panels) alsofield,
show coarse
onceambient
some caveatsmain
are observed:
that bars indicate the
the conceptobserved
of phase becomes
undefined
the associated
amplitude
vanishes. Hence,
not surprising
thatconductivity
reasonable agreement
between shown in the left
(red),
andasthe
numerical
prediction
usingit isthe
four 1-D
structure
predicted and
CM5 fields
is found
the amplitudes
are large. Alsoand
note that
in the continental
regions,and
agreement
in phase
is not
panel,
where
KOonly
is where
the model
of Kuvshinov
Olsen
(2006), PAC
PHS
are Pacific
and Philippine
expected between the two forward models as the Tyler model employs a thin-shell induction approximation, which may become inaccurate
sea
model
presented
by
Baba
et
al.
(2010),
and
SM
is
the
model
by
Shimizu
et
al.
(2010).
All the
as the assumed thin conductor vanishes.
°
°
4.5
numerical predictions are calculated on a global grid of 0.25 ×0.25 resolution, except for SM2 model,
where the SM model (Shimizu et al., 2010) is used on a grid of 1° ×1° resolution. (After Schnepf et al.,
Ionospheric field
2014).
The ionospheric E-region current system is modelled as a sheet current at an altitude of 110 km (Sabaka et al. 2002) and the corresponding
equivalent current (stream) function for the primary (left) and secondary (right) systems are shown in Fig. 13 during vernal equinox centred
on noon MLT, but at different magnetic universal times. The primary function shows the distinctive counter-clockwise/clockwise flow in the
24
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
Figure 11. Investigation of sensitivity of tide-generated EM variation to the underlying conductivity
structure. A) From a) to e), the five panels show the sensitivity of the outward and horizontal component
(𝐵” and 𝐵Œ ) at a satellite altitude of 430 km, 𝐵” and 𝐵Œ at the seafloor, the horizontal component of the
electric field (𝐸Œ ). The sensitivity, S, is defined by Frobenius norm as eq. 8. (Schnepf et al., 2015).
Figure 12. A) Comparison of Br amplitude generated by M2 tidal component at a altitude of 430 km
among the forward calculation by Tyler et al. (2003) (top left), Comprehensive Inversion (CI) with
CHAMP data (top center), CI with Swarm data with full gradients data (top right), CI with Swarm data
without along-track gradients (bottom left), CI without cross-track gradient (bottom center), CI without
any gradients (bottom right). B) The life-time of CHAMP and Swarm satellites with solar activity by F10.7
index. C) The amplitudes of each spherical harmonic degree, n, among the six presented in A. (After
Sabaka et al., 2016)
25
Keynote review: Takuto Minami
23rd Electromagnetic Induction Workshop, Chiang Mai, Thailand
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Keynote review: Takuto Minami
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Keynote review: Takuto Minami
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