geomagnetic disturbances during the maule (2010) tsunami
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Geomagnetic Disturbances During the Maule (2010) Tsunami Detected by Four
Spatiotemporal Methods
V. KLAUSNER,1 H. M. GIMENES,1 M. V. CEZARINI,1 A. OJEDA-GONZALEZ,1 A. PRESTES,1 C. M. N. CANDIDO,1
E. A. KHERANI,1 and T. ALMEIDA1
Abstract—Separating tsunamigenic variations in geomagnetic
field measurements in the presence of more dominant magnetic
variations by magnetospheric and ionospheric currents is a chal-
lenging task. The purpose of this article is to survey the
tsunamigenic variations in the vertical component (Z) and the
horizontal component (H) of the geomagnetic field using four
spatiotemporal methods. Spatiotemporal analysis has shown enor-
mous potential and efficiency in retrieving tsunamigenic
contributions from geomagnetic field measurements. We select the
Maule (2010) tsunami event on the west coast of Chile and
examine the geomagnetic measurements from 13 ground magne-
tometers scattered in the Pacific Ocean covering a wide area from
Chile, crossing the Pacific Ocean to Japan. The tsunamigenic
magnetic disturbances are possibly due to two types of contribu-
tions, one arising from direct ocean motion and the other from
atmospheric motion, both associated with tsunami forcing. More-
over, even though the tsunami waves decrease considerably with
increasing epicentral distance, the tsunamigenic contributions are
retrieved from a magnetic observatory in Australia (� 13,000 km
radial distance from the epicenter). These results suggest that
various types of tsunamigenic disturbances can be identified well
from the integrated analysis framework presented in this work.
Keywords: Tsunami, geomagnetism, AGWs, wavelet trans-
form, Hilbert–Huang transform, signal processing.
1. Introduction
Over the past 20 years, several studies have
observed seismogenic and tsunamigenic magnetic
disturbances generated by lithosphere–atmosphere–
ionosphere (LAI) or tsunami–atmosphere–ionosphere
(TAI) coupling, respectively. These studies have
made an effort to cover all possible sources from
oceanic to atmospheric forcing including Rayleigh
waves, acoustic gravity waves, and gravity waves
(Balasis and Mandea 2007; Manoj et al. 2011; Toh
et al. 2011; Utada et al. 2011; Klausner et al.
2014a, 2016a, c, 2017).
On 27 February 2010, the Maule earthquake of
moment magnitude Mw 8:8 generated a tsunami in the
Pacific Ocean. The Maule tsunami was due to one of
the largest earthquakes since the beginning of the
century. A Pacific-wide tsunami warning was issued
for numerous countries, and the local effects on the
Chilean coast were particularly severe. As discussed
by Zubizarreta et al. (2013), the Maule tsunami
caused more than $30 billion in damage, damaging or
destroying 370,000 houses, 4013 schools, and 79
hospitals. More than 500 people were crushed,
drowned, or burned to death by fires. Offshore data
on the few DART buoys in service were also
impressive. The Maule tsunami is among the largest
known tsunamis prior to the Tohoku-Oki (2011)
tsunami.
A geomagnetic disturbance of � 1 nT in its ver-
tical component was observed by Manoj et al. (2011)
using data from the Easter Island magnetic observa-
tory (IPM). Klausner et al. (2014a) examined
geomagnetic disturbances associated with the Maule
tsunami, employing an improved methodology based
on continuous/discrete wavelet techniques using the
Morlet/Daubechies function of order 2 as the wavelet
for analysis. They found the wavelet techniques to be
useful tools for characterizing the tsunamigenic
contributions in the geomagnetic field. Schnepf et al.
(2016) also reported that the wavelet techniques were
effective for tsunami detection/identification.1 Physics and Astronomy, Vale do Paraiba University, Av.
Shishima Hifumi, 2911, IP&D, Sao Jose dos Campos, SP CEP
12244-000, Brazil. E-mail: virginia@univap.br
Pure Appl. Geophys. 178 (2021), 4815–4835
� 2021 The Author(s), under exclusive licence to Springer Nature Switzerland AG
https://doi.org/10.1007/s00024-021-02823-x Pure and Applied Geophysics
Klausner et al. (2014a) and Minami (2017) also
discussed two possible current sources giving rise to
these geomagnetic disturbances: first, the movement
of electrically conducting seawater through the
Earth’s magnetic field due to the tsunami waves,
which then generated an electromotive force that
induced electric fields, electric currents, and sec-
ondary magnetic fields; and second, the ionospheric
currents due to the atmospheric motion from the
tsunamigenic and acoustic gravity waves.
Intense seismic events (above magnitude 6 on the
Richter scale) can disturb the atmosphere, and con-
sequently, the ionosphere. The TAI and LAI coupling
mechanisms involve acoustic gravity waves (AGWs),
gravity waves (GWs), and Rayleigh surface seismic
waves. These mechanisms can be examined by
employing nonlinear simulation models (Tyler 2005;
Kherani et al. 2012, 2016; Minami and Toh 2013;
Zhang et al. 2014; Torres et al. 2019). Ichihara et al.
(2013) and Minami (2017) adopted magnetic transfer
functions to subtract magnetic variations of iono-
spheric origin, while Zhang et al. (2014) used only
high-pass-filtered magnetic data. Many authors have
applied wavelet techniques for time–frequency
extraction of tsunamigenic/seismogenic information
from tide gauges, magnetograms, and ionospheric
data (Chamoli et al. 2010; Kherani et al. 2012, 2016;
Toledo et al. 2013; Klausner et al.
2014a, 2016c, a, 2017; Heidarzadeh and Satake 2015;
Torres et al. 2019; Adhikari et al. 2020). The
knowledge of these disturbances can provide addi-
tional information about earthquake and tsunami
parameters, and perhaps in the near future, the pos-
sibility of early warning of natural hazard events.
However, there are prerequisites for that purpose,
especially in terms of short time delays—for exam-
ple, LAI coupling takes 7 min (Astafyeva et al.
2009). Therefore, the time factor should be consid-
ered for the early warning potential of a new
methodology.
In this article, we focus on the survey of geo-
magnetic variations induced by the tsunami event of
27 February 2010 (Maule). The geomagnetic field
components, particularly the Z- and H-components,
are examined for the possible identification of the
tsunamigenic effects. To accomplished this we
employ the spatiotemporal data analysis framework
that integrates advanced tools including continuous
wavelet transform (CWT), discrete wavelet transform
(DWT), travel–time diagram (TTD) using the
intrinsic mode function (IMF) of the Hilbert–Huang
transform (HHT), and mean absolute percentage error
(MAPE) maps. These techniques were employed
separately and partially together in previous studies,
revealing their capacity to isolate tsunamigenic dis-
turbances in various types of measurements, even on
geomagnetically disturbed days (Rolland et al. 2011;
Utada et al. 2011; Kherani et al. 2012, 2016; Klaus-
ner et al. 2014a, 2016a, c; Zhang et al. 2014). The
novelty of this paper compared to others is that all of
these mathematical tools are combined to perform the
analysis.
2. Magnetic Data
The Maule seismic event occurred near the coast
of central Chile on 27 February 2010. The tsunami-
genic earthquake onset was at 06:34 UT, and its
epicenter was located at Lat. �36:1� and Long.
�72:6� at 35km depth. For the Maule tsunami study,
we used data from 13 magnetic observatories of the
International Real-time Magnetic Observatory Net-
work (INTERMAGNET) program (www.
intermagnet.org), and from 10 sea-level stations of
the Sea Level Station Monitoring Facility (SLSMF)-
UNESCO/IOC (www.ioc-sealevelmonitoring.org).
Table 1 shows the INTERMAGNET magnetic
observatories (name and IAGA code), the tide gauge
stations (code), epicentral distance of the magnetic
observatories in kilometers, and the computed tsu-
nami initial arrival time obtained from the US
National Tsunami Warning Center (National Oceanic
and Atmospheric Administration [NOAA]/National
Weather Service) at the magnetic observatory. It is
possible to observe that some tide gauge stations are
not at the same location as the magnetic observatory;
however, all paired stations of magnetometer and tide
gauge are in the same tsunami wavefront direction.
Moreover, the tide gauge data will only be used as a
reference to compare the geomagnetic disturbances
with the oceanic variations, while the computed
arrival time estimated by the MOST (Method of
Splitting Tsunami) numerical simulation model is
4816 V. Klausner et al. Pure Appl. Geophys.
based on the near-coastal location of the geomagnetic
observatories. Figure 1 displays their geographic
distribution and the tsunami travel time (TTT) map. It
is important to mention that the geomagnetic data
from the HUA, IPM, and PPT observatories were
previously analyzed by Manoj et al. (2011) to study
the geomagnetic contributions due to the Maule tsu-
nami. Therefore, we selected the same three
observatories and included ten additional magnetic
observatories belonging to the INTERMAGNET
network. Therefore, the tsunamigenic magnetic con-
tribution study will be extended to locations as far as
13,000 km from the epicenter, covering islands of the
Pacific Ocean.
Another fact important to mention about the
Maule tsunami is that it occurs during geomagneti-
cally quiet conditions. The magnetic disturbance
storm time (Dst) index showed a very smooth mag-
netic variation, i.e., magnetic variations between �2
and 4nT, and the Kp index, between 1- and 2�. These
Dst and Kp index ranges mean that the magneto-
sphere is quiet. Therefore, the tsunamigenic or
seismogenic magnetic effects should not suffer
interference from abrupt changes in the magneto-
spheric currents that occur during geomagnetic
storms, and consequently from the disturbed varia-
tions in the ionospheric currents (Campbell 1989).
3. Methodology
Previous works by Klausner et al.
(2014a, 2016a, c) showed that wavelet analysis is a
very useful tool for identifying tsunamigenic varia-
tions in the vertical component of the geomagnetic
field. In this sense, by using the continuous wavelet
transform (CWT) with a Morlet wavelet for analysis,
small tsunamigenic geomagnetic variations can be
detected. The CWT provides better local characteri-
zation of induced magnetic variations by GWs/
AGWs or electrical currents due to the tsunami. It
may be the most convenient mathematical method for
detecting the local periods (from 8 to 32 min) which
cover the oceanic gravity modes observed in the
atmosphere (� 10 min) during tsunami events (Oc-
chipinti et al. 2006, 2008, 2011; Rolland et al. 2010;
Galvan et al. 2012; Kherani et al. 2012, 2016).
Moreover, tsunamigenic ionospheric disturbances
� 10 to 60 min in advance of the tsunami wavefront
have been simulated by Kherani et al. (2016), which
Table 1
INTERMAGNET observatories and Intergovernmental Oceanographic Commission (IOC) Global Sea Level Observing System (GLOSS) Sea
Level Stations used in this work
Geomagnetic observatory, IAGA code Tide gauge, code Epicentral distance (km) Computed initiala arrival time (UT)
Huancayo, HUA Callao La Punta, call 2658.96 10:34, 27 Feb.
Easter Island, IPM Callao La Punta, call 3586.16 11:34, 27 Feb
Scott Base, SBA Rikitea, gamb 6774.95 15:36, 27 Feb.
Pamatai, PPT Papeete, pape 7712.84 17:33, 27 Feb.
Dumont d’Urville, DRV Dumont d’Urville, dumo 8281.12 18:34, 27 Feb.
Macquarie Island, MCQ Castlepoint, cpit 8823.28 19:34, 27 Feb.
Eyrewell, EYR Castlepoint, cpit 9013.74 19:34, 27 Feb.
Apia, API Apia, upol 9907.42 19:48, 27 Feb.
Honolulu, HON Honolulu, hono 10,971.27 21:34, 27 Feb.
Canberra, CNB Port Kembla, pkem 10,981.86 21:34, 27 Feb.
Sitka, SIT Stika, sitk 11,873.41 00:30, 28 Feb.
Charters Towers, CTA Sand Point, sdpt 12,561.17 01:04, 28 Feb.
Shumagin, SHU Sand Point, sdpt 13,078.56 01:30, 28 Feb.
aThe computed arrival time is the estimated time of arrival computed by the MOST (Method of Splitting Tsunami) numerical simulation
model developed by the Pacific Marine Environmental Laboratory (PMEL) of the National Oceanic and Atmospheric Administration (NOAA)
based on the origin time and location
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4817
were caused by the excitation of secondary AGWs.
Using the effectiveness wavelet coefficient (EWC—
see definition in Klausner et al., 2016a), we will be
able to detect periods induced by AGWs due to the
first three decomposition levels using a Daubechies
wavelet of order 2 (db2) related to 3, 6, and 12 min,
which cover acoustic resonance modes (� 3 to 12
min)—remembering that at the near field, the
tsunamigenic magnetic disturbances induced by
AGWs have periods of � 5 to 10 min, and at the far
field, � 10 min (Kherani et al. 2016). The EWC is
derived from the discrete wavelet transform (DWT—
see the works of Klausner et al., 2014b, 2016b, for
the mathematical description).
In addition, we complement these results by
constructing travel–time diagrams (TTDs) or keo-
grams as done by Kherani et al. (2012), using the
same IMF methodology applied by Klausner et al.
(2017). Here, we also construct mean absolute per-
centage error (MAPE) maps as previously done by
Klausner et al. (2016c) in order to detect the
tsunamigenic signatures in the Z- and H-components.
These TTDs and MAPE maps are constructed by
distributing the time series of Z- and H-components
in time and space. The time variation is presented on
the X-axis, and the spatial variation on the Y-axis,
based on the geographic locations of 13 chosen
magnetic observatories, as will be further discussed.
All the mathematical tools presented in this arti-
cle, i.e., CWT, EWC, DWT, and MAPE, are
described in the Appendix.
4. Results and Discussion
The first step of our analysis consists of process-
ing the digital data to extract the tsunamigenic feature
from the Z- and H-components of the geomagnetic
data. To this end, we determine the solar quiet (Sq)
baseline for each magnetic observatory and its
respective Z- and H-components. The Sq baseline is
computed considering the five quietest days of
February 2010, which can be found at https://www.
gfz-potsdam.de/en/kp-index/. The five quietest days
of February 2010 used here are 5, 9, 20, 21, and 26.
Although 27 and 28 February were ‘‘quieter’’ than 9
and 26 February, these days included the tsunami
event of our choice, and therefore they cannot be used
to calculate the Sq baseline. The Sq baseline corre-
sponds to magnetic variations unrelated to
Figure 1a TTT map and the maps of the geographic localization of b magnetic observatories and c sea-level stations used here to study the Maule
earthquake/tsunami, 2010. Source: TTT map courtesy of the National Oceanic and Atmospheric Administration (NOAA)/National Weather
Service (NWS)/West Coast and Alaska Tsunami Warning Center
cFigure 2The residual magnetic signatures compared to the tide gauge and
the Sq baseline for the 13 magnetic observatories for both Z- and
H-components
4818 V. Klausner et al. Pure Appl. Geophys.
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-6
-4
-2
0
2
4
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-3
-2
-1
0
1
2
Z (n
T)
-0.5
0
0.5
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
20
40
60
80
100
120
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-5
0
5
H (n
T)
-0.5
0
0.5
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(a1) HUA - Z-component (a2) HUA - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
5
10
15
20
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-1
-0.5
0
0.5
1
Z (n
T)
-0.5
0
0.5
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-5
0
5
10
15
20
25
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-2
-1
0
1
H (n
T)
-0.5
0
0.5
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(b1) IPM - Z-component (b2) IPM - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
20
40
60
80
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-10
-5
0
5
10
15
Z (n
T)
-0.1
0
0.1
0.2
prs(
m) r
ad(m
)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-40
-20
0
20
40
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-20
-10
0
10
H (n
T)
-0.1
0
0.1
0.2
prs(
m) r
ad(m
)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(c1) SBA - Z-component (c2) SBA - H-component
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4819
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-10
-5
0
5
10
15
20
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-3
-2
-1
0
1
2
Z (n
T)
-0.2
-0.1
0
0.1
0.2
prs(
m) r
ad(m
)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
10
20
30
40
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-2
-1
0
1
2
H (n
T)
-0.2
-0.1
0
0.1
0.2
prs(
m) r
ad(m
)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(d1) PPT - Z-component (d2) PPT - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
50
100
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-40
-20
0
20
40
Z (n
T)
-0.1
-0.05
0
0.05
0.1
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-40
-20
0
20
40
60
80
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-10
0
10
20
30
H (n
T)
-0.1
-0.05
0
0.05
0.1
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(e1) DRV - Z-component (e2) DRV - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-20
-10
0
10
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-6
-4
-2
0
2
4
Z (n
T)
-0.2
0
0.2
0.4
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-40
-20
0
20
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-5
0
5
H (n
T)
-0.2
0
0.2
0.4
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(f1) MCQ - Z-component (f2) MCQ - H-component
Figure 2continued
4820 V. Klausner et al. Pure Appl. Geophys.
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-5
0
5
10
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-2
-1
0
1
Z (n
T)
-0.2
0
0.2
0.4
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-40
-30
-20
-10
0
10
20
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-4
-2
0
2
4
H (n
T)
-0.2
0
0.2
0.4
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(g1) EYR - Z-component (g2) EYR - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-5
0
5
10
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-1.5
-1
-0.5
0
0.5
1
1.5
Z (n
T)
-0.2
-0.1
0
0.1
0.2
0.3
prs(
m)
Residual EventSea Level Residual
2010-02-27 20:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
10
20
30
40
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-2
-1
0
1
2
H (n
T)
-0.2
-0.1
0
0.1
0.2
0.3
prs(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(h1) API - Z-component (h2) API - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-10
-5
0
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-2
-1
0
1
2
Z (n
T)
-0.2
-0.1
0
0.1
0.2
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
5
10
15
20
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-2
-1
0
1
H (n
T)
-0.2
-0.1
0
0.1
0.2
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(i1) HON - Z-component (i2) HON - H-component
Figure 2continued
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4821
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-5
0
5
10
15
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-1.5
-1
-0.5
0
0.5
1
1.5
Z (n
T)
-0.1
0
0.1
0.2
aqu(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-40
-30
-20
-10
0
10
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-4
-3
-2
-1
0
1
2
3
H (n
T)
-0.1
0
0.1
0.2
aqu(
m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(j1) CNB - Z-component (j2) CNB - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-4
-2
0
2
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-3
-2
-1
0
1
2
Z (n
T)
-0.1
0
0.1
0.2
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-10
-5
0
5
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-2
0
2
4
H (n
T)
-0.1
0
0.1
0.2
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(k1) SIT - Z-component (k2) SIT - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
0
10
20
30
40
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-1
-0.5
0
0.5
1
Z (n
T)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-10
0
10
20
30
40
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-4
-3
-2
-1
0
1
2
3
H (n
T)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(l1) CTA - Z-component (l2) CTA - H-component
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-8
-6
-4
-2
0
2
Z (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-1.5
-1
-0.5
0
0.5
1
Z (n
T)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-10
-5
0
5
H (n
T)
EventSq
2010-02-27 12:00:00 2010-02-27 18:00:00 2010-02-28 00:00:00 2010-02-28 06:00:00
Time (UT)
-3
-2
-1
0
1
2
3
H (n
T)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
wls
(m)
Residual EventSea Level Residual
2010-02-27 06:34:00.000 2010-02-28 06:33:00.000
Start Time End TimeApply Reset
(m1) SHU - Z-component (m2) SHU - H-component
Figure 2continued
4822 V. Klausner et al. Pure Appl. Geophys.
ionospheric and magnetospheric disturbances. It is
defined as the mean variation in the five quietest
days; see Campbell (1989) for more details. Before
calculating the Sq baseline, the mean nighttime
average during 23:00–03:00 LT is subtracted from
each of these quietest days. This subtraction allows
daytime magnetic variations to be emphasized. As
will be seen shortly, the extraction of the Sq baseline
is very useful for the analysis of tsunamigenic mag-
netic disturbances. Figure 2 shows the residual
magnetic signatures compared to the tide gauge and
the Sq baseline for the 13 chosen magnetic observa-
tories for both Z- and H-components. For each
magnet component, the upper panel has two lines
representing the 24 h event from the tsunami onset (in
blue) and the Sq baseline (in black), respectively.
Note that the Sq baseline is subtracted from the event
magnetic data to emphasize the tsunamigenic mag-
netic variations. On the lower panel, the residual
magnetic data (blue line) is defined as the difference
between the geomagnetic data without the Sq. If the
residual still includes harmonic variations of the
Earth’s rotation, the signal is filtered using polyno-
mial fit. Although this signal processing accounts for
removal of signals due to the ionosphere (Sq), it does
not remove disturbed magnetospheric signals. For
this reason, its outputs should be interpreted in con-
junction with the spatiotemporal multi-data analysis.
The lower panel also contains the sea-level residual
(green line), allowing us to compare the residuals, i.e,
the magnetic and sea-level data without the long-term
variations. The residual sea-level data are obtained by
filtering the periods related to the Earth’s rotation and
harmonics, and consequently the long periods linked
to the oceanic tides.
In Fig. 2, the magnetic observatories are arranged
according to their epicentral distance from nearest to
farthest. The sea-level data obtained from the tide
gauge stations closest to the magnetic observatories
(see Table 1) are shown as green curves. In the
absence of any nearby tide gauge station for the
magnetic observatory, we have chosen the tide gauge
station located at the same tsunami wavefront when
possible. It is worth noting that the maximum loca-
tion difference between magnetic and tide gauge
observations is 1000 km, so the delay errors between
the sea-level and geomagnetic residual due to the
location difference can be up to approximately ± 1.5
h, assuming a tsunami wave velocity of approxi-
mately 200 m/s. There is also a difference in distance
between the tide gauge station located at the coast or
ocean and the magnetic observatory located inland,
which may lead to an error of approximately ± 2
min, as discussed by Klausner et al. (2016c).
As shown in the lower panel of Fig. 2a1, it is
possible to see that before the tsunami arrival, the
residual of the Z-component for the HUA observatory
had smoothed variations (less than � j2j nT). After
that, the variations appear as an amplified N-shaped
waveform with � j7j nT values, with a signature
pattern similar to the sea-level data related to tsunami
propagation. The ‘‘N’’ shape is defined as the dis-
turbance having an upward peak immediately
followed by downward and upward peaks.
In the Z-component, we also note the presence of
amplified magnetic disturbances a few minutes after
the tsunami arrival time at each magnetic observa-
tory. However, it was not very evident in the
H-component (see IPM, MCQ, API, HON, SIT, CTA,
and SHU). In these magnetic observatories, it is
possible to note N-shaped amplified magnetic dis-
turbances in the H-component a few hours in advance
of the arrival of the tsunami. Also, at the far field,
N-shaped disturbances are present in the Z-compo-
nent a few hours in advance of the tsunami arrival
(see PPT, DRV, MCQ, HON, CNB, SIT, CTA, and
SHU). A similar magnetic signature in the Z-com-
ponent at PPT was reported by Klausner et al.
(2014a). The amplified magnetic disturbances are
observed in all magnetic observatories for both Z-
and H-components. However, the delay time of
N-shaped disturbances from the tsunami wavefront
arrival time appears minutes to a few hours in
advance at far-field locations.
The similarities between the residual magnetic
and sea-level data raise the possibility of their asso-
ciation during the tsunami occurrence. Moreover, the
magnetic residual disturbances appear 6–100 min
after the tsunami arrival at magnetic observatories
located within 8000 km radial epicentral distance,
while at the far field they appear 30 min to 2 h in
advance. In summary, we note the presence of
amplified magnetic disturbances associated with the
tsunami arrival time at each magnetic observatory in
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4823
4824 V. Klausner et al. Pure Appl. Geophys.
both components, Z and H. Our results show that the
delay time of N-shaped disturbances from the tsu-
nami occurrence time decreases in far-field locations.
A variety of wavefronts are generated by the vertical
and horizontal motion of the ground surface associ-
ated with the earthquake and tsunami. The
atmospheric waves reach ionospheric altitudes and
produce magnetic disturbances, which propagate
horizontally in the thermosphere with acoustic wave
speed of � 600 to 1000 m/s, gravity wave speed of
� 250 m/s, and slower speed (� 200 m/s) than the
tsunami. Therefore, in far-field locations, the mag-
netic disturbances triggered by AGWs can appear
about 30–80 min before the tsunami arrival.
The CWT was first employed in this way by
Klausner et al. (2014a, 2016a, b, c), and it has
demonstrated promising results in tsunami-
genic/seismogenic signal identification with a period
range associated with GW propagation modes
induced by tsunamis/earthquakes. Figure 3 shows
periods between 8 and 32 min that might be related to
the tsunami magnetic induction mechanism. The
energy spectra are associated with the significant
magnetic field disturbances before and after the
arrival (see the TTT map presented in Fig. 1 for
tsunami arrival guidance purposes), which may be
due to the contribution from both oceanic and
tsunamigenic ionospheric disturbances. The period
range of 8–32 min was chosen because it is related to
wavefronts propagating in the atmosphere and TAI
coupling. Artru et al. (2005) detected gravity waves
with a period range of 10–30 min which propagated
horizontally at approximately the same speed as the
tsunami observed in Peru on 23 June 2001. For the
Sumatra (2004) tsunami, the same period ranges of
geomagnetic pulsations were detected by Iyemori
et al. (2005) due to tsunami-related gravity waves.
For the Tohoku-Oki (2011) tsunami, 5–10-min geo-
magnetic pulsations were detected by Kherani et al.
(2012), and these pulsations were shown to be asso-
ciated with the acoustic gravity waves.
In particular, the following features are evident
from Fig. 3a: (1) at IPM, SBA, PPT, MCQ, EYR,
API, HON, CNB, CTA, and SHU, these variations
appear after the arrival of the tsunami or a few hours
before it; (2) at DRV, there is a lower-frequency
phenomenon near the tsunami arrival (the dashed
white line) that looks similar to SBA and CNB; and
(3) at HUA, the amplifications are noted randomly
before the tsunami onset. In Fig. 3b, we note that the
periods between 8 and 32 min appear around the
tsunami arrival at the SBA, PPT, and DRV observa-
tories located at the epicentral near field. At far-field
locations, such as MCQ, API, and HON, these peri-
ods appear a few hours in advance of the tsunami
wavefront arrival, whereas at other observatories,
such periods are not conclusively related to the arri-
val of the tsunami waves or gravity waves. It is worth
mentioning that the phenomena between 8 and 32
min simultaneously detected at all magnetic obser-
vatories originate in the magnetosphere, which shows
that the physical phenomena responsible for these
pulsations affected the magnetosphere globally. It
was not a local phenomenon like the tsunami.
In the Z-component analysis (Fig. 4a), we note
that the EWCs are amplified within 2 h before or after
the tsunami arrival (the black dashed line can be used
as a guide for the tsunami arrival time) at observa-
tories HUA, IPM, SBA, PPT, DRV, MCQ, HON,
CNB, and CTA, while at other observatories such
amplifications are not evident. On the other hand, in
the H-component analysis (Fig. 4b), these EWC
amplifications appear at SBA, PPT, DRV, and MCQ,
while at other observatories, there are inconclusive
tsunamigenic amplifications. For both component
analyses, EYR and API present very noisy signals.
Therefore, DWT analysis is not recommended.
Moreover, magnetic disturbances that simultaneously
appear at several magnetic observatories may origi-
nate from ionospheric currents, and we can
distinguish the signal by tsunamigenic origin,
bFigure 3
Z-component (a) and H-component (b) data sets and their
respective wavelet spectrum with period band-pass between 8
and 32 min. The CWT was applied in the raw data centered at zero.
From top to bottom, the magnetic data and their respective
scalogram are ordered according to the magnetic observatory
epicentral distance, with the nearest at the top and the farthest at the
bottom. In each, the dashed line corresponds to the tsunami arrival
at the coastal locations nearest each magnetic observatory (black
dotted line in the data set or white dotted line in the scalogram).
The residual geomagnetic variation in nT for each magnetic
observatory is shown on the vertical axis, and the time in hours
with the onset of the tsunami as 0 h on the horizontal axis
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4825
comparing the H-component responses to the Z-
component (Kherani et al. 2012, 2016; Klausner
et al. 2014a, 2016a, b, c, 2017). An increase in EWCs
between 11 and 13 h from the tsunami onset appears
simultaneously in almost all magnetic observatories
in both Z- and H-components. As explained by
Klausner et al. (2014a), this EWC amplification may
be caused by the passage of the solar terminator (ST),
which causes the generation of gravity waves, tur-
bulence, and instabilities in the ionosphere plasma.
Another important fact worth mentioning is an
earthquake occurrence with Mw 6:3 in Salta, Argen-
tina, at 15:45 UT (� 9 h from the tsunami onset). In
this context, it is possible that this extra energy from
the seismic forcing amplified the tsunamigenic
ionospheric disturbances. In other words, the pre-
conditioned ionosphere rendered by tsunamigenic
ionospheric disturbances provides favorable condi-
tions for the seismic contribution to attain the
detectable EWC threshold. Therefore, the conditions
described earlier make it unlikely that the observed
magnetic disturbances are associated with the tsu-
nami, and from Figs. 3 and 4, the tsunamigenic
disturbances cannot be well identified. To identify the
tsunamigenic disturbances, Figs. 3 and 4 should be
complemented by constructing TTDs using IMFs (see
Klausner et al. (2017) for more details).
Here, we also show the magnetic signatures
obtained using the IMF analysis, which covers AGW
and GW modes (Klausner et al. 2016a, 2017). In
these TTDs (Fig. 5), we search for magnetic distur-
bance signatures (N-shaped—see dashed rectangles)
correlated with the tsunami arrival, because we would
not expect variations from the external origin, as it
Figure 4From top to bottom, the panels display the magnetic EWCs related to Z-component (a) and H-component (b) analysis. The magnetic
observatories are ordered according to their epicentral distance, with the nearest at the top, and the farthest at the bottom. In each panel, the
EWC values for each magnetic observatory are shown on the vertical axis, and the time in hours using ‘‘0’’ UT as the onset of the tsunami are
shown on the horizontal axis. The dashed red line corresponds to the approximate tsunami arrival at the nearest coast from the analyzed
magnetic observatory
4826 V. Klausner et al. Pure Appl. Geophys.
was a geomagnetically quiet day. If such correlated
N-shaped wave packets exist, we can determine them
to be tsunamigenic. In Fig. 5a, we can identify an
N-shaped magnetic variation in the normalized IMF
values at IPM, SBA, MCQ, HON, CNB, and SIT at
almost the same time as the tsunami wavefront arrival
(see black line for tsunami wavefront arrival). This
suggests that these N-shaped magnetic variations
have propagation characteristics similar to those of
the tsunami wavefront propagation, suggesting that
they may be of tsunami origin.
Both oceanic currents (Tyler 2005) and iono-
spheric currents driven by AGWs (Heki and Ping
2005; Kherani et al. 2012, 2016; Sanchez-Dulcet
et al. 2015) are able to excite tsunamigenic magnetic
disturbances with similar propagation characteristics
as tsunami wavefronts. However, the magnetic fields
by oceanic dynamo and perturbation of ionospheric
dynamo by AGWs have different spatiotemporal
evolution. To date, the contribution of the oceanic
and ionospheric currents to these tsunamigenic
magnetic disturbances has remained an unresolved
issue. One important difference between the magnetic
disturbances arising from these two sources is that the
ocean current-induced amplified disturbances appear
instantly at the time of tsunami arrival (Tyler 2005;
Sugioka et al. 2014), while the AGW- and GW-am-
plified disturbances appear with a time delay of
10–50 min from the tsunami arrival (Rolland et al.
2011). These disturbances are referred to as coseis-
mic traveling ionospheric disturbances (CTIDs),
which propagate in the ionosphere with similar hor-
izontal velocity in the ocean and appear within 10
min at any tsunami arrival location (Astafyeva et al.
2009; Liu et al. 2011; Kherani et al. 2012, 2016). Liu
et al. (2011) demonstrated the presence of iono-
spheric disturbances during the Tohoku-Oki (2011)
tsunami that propagated faster than the tsunami and
appeared earlier than the tsunami arrival at a remote
location. These disturbances were found to propagate
horizontally at 600 m/s to 1.2 km/s, which is the
range of acoustic speed in the thermosphere, and
therefore they propagated ahead of the tsunami,
appearing 30 min to 2 h earlier than the tsunami
arrival at epicentral far-field locations (Astafyeva
et al. 2009; Liu et al. 2011; Kherani et al.
4 5 6 7 8 9 1011121314151617181920Time (hours)
2000
4000
6000
8000
10000
12000
14000
Epi
cent
ral d
ista
nce
(km
)
4 5 6 7 8 9 1011121314151617181920Time (hours)
HUAIPMSBAPPTDRVMCQEYRAPIHONCNBSITCTASHUN-shaped
(b)(a)
Figure 5a Z-component data set filtered using IMFs, and b the H-component. The distance between the earthquake epicenter and the magnetic
observatory is shown on the vertical axis, and the universal time is show on the horizontal axis. The black dotted box highlights the N-shaped
magnetic disturbances, and the black line is a rough approximation of the tsunami wave-field propagating in the Pacific Ocean
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4827
2012, 2016). This range of speed may be due to a
mode mixing between Rayleigh and acoustic waves
near the epicenter, as discussed by Astafyeva et al.
(2009).
In the TTD (Fig. 5b), the N-shaped amplified
pulses can be examined with such distinction. We
note that these N-shaped amplified pulses do not
appear instantly at the arrival time of the tsunami.
These pulses appear with a time delay of 30–80 min,
which covers the range suggested by thermospheric
AGWs driven by the TAI coupling mechanism.
Therefore, the delayed N-shaped amplified pulses
inside the identified wave packets may arise from the
forcing in the thermosphere through AGWs, as can be
observed in HUA and IPM. It should also be noted
that over SBA, PPT, DRV, MCQ, EYR, and API,
another N-shaped amplified pulse appears instantly at
the arrival time of the tsunami, which may be
attributable to the forcing from the ocean currents
associated with the tsunami. On the other hand, at the
far field, N-shaped amplified pulses appearing in
advance of the tsunami arrival, as in the case of CNB,
SIT, CTA, and SHU, are probably attributable to
secondary AGWs, which propagate with high
acoustic speed in the thermosphere (Kherani et al.
2016).
Figure 6MAPE map of Z-component (a) and H-component (b) between the magnetic observatories along the propagation of the Maule tsunami
wavefront. The solid continuous line corresponds to the tsunami wavefront simulated by the tsunami wave model
4828 V. Klausner et al. Pure Appl. Geophys.
To validate the TTD results, we construct a
MAPE map between all the 13 magnetic observato-
ries. The same wave packet found in TTD for the
nearest magnetic observatory (HUA) to the epicenter
was used to construct the fitted time series values for
each piece of the magnetic series filtered with the
same length of the tsunamigenic wave packet. Then,
the HUA wave packet was shifted forward with a step
of 1 min in each data set from the 13 chosen magnetic
observatories to calculate the MAPE value at this
point, and this procedure was repeated over the entire
data length. The contour MAPE maps were con-
structed through an interpolation method using a
spline because of the irregular distribution of the
magnetic observatory epicentral distance, and con-
sequently their data. Also, the MAPE values are
affected by border effects, and for this reason, the
border distortions were removed from the analysis
(the data set used had a length of 2 days). According
to Eq. (15) (Appendix), the lower the MAPE value,
the better the forecast. However, we normalize the
MAPE values to match the color map in Fig. 3.
Therefore, the value ‘‘1’’ indicates the best forecast,
and ‘‘0’’ the worst. Figure 6 shows the MAPE map
considering the period after the tsunami onset and
epicentral distance in kilometers for each magnetic
observatory. The continuous black line represents the
tsunami wavefront (� 250 m/s), and it can be used as
a reference to search for similar MAPE values par-
allel to this line after the tsunami arrival. In Fig. 6a,
b, it can be seen that the highest MAPE values show
the same trend observed in the tsunami wave-field,
which may indicate that the magnetic disturbances
are induced by the tsunami wavefront. It is reasonable
to consider that these magnetic disturbances are
possibly related to the two types of coupling evoked
(through AGW or oceanic coupling).
5. Final Remarks
In this paper, we analyze the Maule (2010) tsu-
nami, an event previously analyzed by other authors
(Manoj et al. 2011; Klausner et al. 2014a). However,
we complemented and improved the previous studies
by increasing the number of analyzed data and the
methods for analyzing them. To this end, we used 13
ground-based magnetic measurements obtained on 27
February 2010 (geomagnetically quiet day). To
identify the tsunamigenic feature extraction from the
magnetic data, we take advantage of well-known
wavelet techniques complemented by TTDs and
MAPE maps. These mathematical and computational
tools have recently shown great potential as alterna-
tive tools for tsunamigenic disturbance identification,
even during geomagnetically disturbed days (Klaus-
ner et al. 2014a, 2016a, c, 2017; Kherani et al.
2012, 2016). The following results can be highlighted
in the present study:
1. We were able to identify amplified N-shaped
waveforms in the magnetic data with a signature
pattern similar to the sea-level data related to the
tsunami propagation. At near-field magnetic
observatories, these magnetic signatures appear
6–100 min after the tsunami arrival, while at far-
field locations they appear 30 min to 2 h in
advance. The presence of amplified magnetic
disturbances was detected in Z- and H-compo-
nents associated with the tsunami arrival time at
each magnetic observatory.
2. Using the wavelet methodologies, we were well
able to identify the tsunamigenic disturbances at
the near-field locations. However, at the far field
(epicentral distance � 8000 km), using only the
wavelet methodologies, we were not able to
identify the tsunamigenic disturbances.
3. When the wavelet analyses are complemented
with the TTDs or keograms and MAPE maps, the
tsunamigenic magnetic signatures may be identi-
fied in locations as far as � 13; 000 km from the
epicenter.
4. In TTDs and MAPE maps, the wave packets are
observed after the tsunami arrival time, and they
are found to propagate with a velocity similar to
the principal tsunami wavefront. For this reason,
these magnetic signatures may be identified as
tsunamigenic disturbances.
5. Inside the tsunamigenic packets, two kinds of
amplified N-shaped pulses are observed: one
occurring instantaneously with the tsunami, and
another occurring 10–50 min after the tsunami
arrival at any location. The instantaneous and
delayed pulses are identified as possibly due to the
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4829
oceanic and ionospheric currents, respectively,
both arising from the tsunami forcing. In other
words, the instantaneous and delayed tsunami-
genic pulses may be associated with the oceanic
sources (Tyler 2005; Sugioka et al. 2014) and
ionospheric currents driven by AGWs (Rolland
et al. 2010; Occhipinti et al. 2011; Kherani et al.
2012), respectively.
6. The tsunamigenic magnetic disturbances in
advance of the tsunami wavefront may be
attributable to secondary AGWs propagating hor-
izontally with acoustic wave speed in the
thermosphere (Kherani et al. 2012; Klausner et al.
2016a, c).
7. In summary, we presented a detailed observational
work regarding tsunamigenic magnetic distur-
bances possibly arising from oceanic and
ionospheric currents due to TAI coupling through
a variety of wavefronts propagating with a veloc-
ity ranging from acoustic to GW velocity.
Acknowledgements
The authors wish to thank CNPq (process number
165873/2015-9, 300894/2017-1) and FAPESP (pro-
cess number 11/21903-3 and 15/50541-3). The
authors would like to thank the National Oceanic
and Atmospheric Administration (NOAA) and the
International Real-time Magnetic Observatory Net-
work (INTERMAGNET) and Sea Level Station
Monitoring Facility-UNESCO/IOC for the data sets
used in this work.
Author Contributions VK and HGM developed the
MAGNAMI software; MVC contributed to MAGNAMI
validation and data analysis; VK, HGM, and EAK
contributed to methodology development, implementation
and analysis; and all authors contributed to writing and
reviewing the manuscript.
Funding
This research was supported by FAPESP (11/21903-3
and 15/50541-3) and CNPq (147392/2017-9, 118040/
2017-0, 305249/2018-5, 431396/2018-3).
Data Availability
The data sets generated and analyzed during the
current study are available in the INTERMAGNET
program (www.intermagnet.org) and Sea Level Sta-
tion Monitoring Facility—UNESCO/IOC (www.ioc-
sealevelmonitoring.org) sites. The NOAA tsunami
travel time map was generated by the MOST (Method
of Splitting Tsunami) model and distributed by the
NOAA Center for Tsunami Research (http://nctr.
pmel.noaa.gov/model.html). The MAGNAMI soft-
ware is made available to users as supplementary
material.
Code Availability
The MAGNAMI software is made available to users
as supplementary material.
Declarations
Competing interests The authors declare that they have no
competing interests.
Ethics approval Not applicable.
Consent to participate All authors voluntarily agreed to
participate in this research manuscript.
Consent for publication All authors give their consent to
publish this manuscript in the journal Pure and Applied Geo-physics.
Appendix: Mathematical Tools
Continuous Wavelet Transform
A wavelet is an oscillating function of time which
has finite energy, and is very suitable for analysis of
nonstationary data. This class of functions is well
localized in both time and frequency, which allows
one to perform simultaneous time and frequency
analysis (Morlet et al. 1982a, b; Grossmann and
Morlet 1984). Mathematically, a wavelet is a function
w in the Hilbert Space L2ðRÞ that satisfies the
admissibility condition, that is,
Cw ¼Z 1
0
jwðxÞj2
xdx\þ1; ð1Þ
where w denotes the Fourier transform of w. To
4830 V. Klausner et al. Pure Appl. Geophys.
guarantee that the integral in (1) is finite, w must have
zero average (wð0Þ ¼ 0) and w must be a continu-
ously differentiable function (Mallat 2008). The zero
average requirement implies that a wavelet must
oscillate in such a way that the net area below the
curve is zero. There are several types of wavelets that
are used for data analysis, and the choice of wavelet
depends on the purpose of the analysis. Wavelets
equal to the second derivative of a Gaussian occur
frequently in applications and are called Mexican
hats (Mallat 2008), defined as
wðtÞ ¼ 2
p1=4ffiffiffiffiffiffi3r
p t2
r2� 1
� �exp
�t2
2r2
� �; ð2Þ
where r[ 0. Another type of wavelet that appears
frequently is the complex Morlet wavelet, commonly
defined as
wðtÞ ¼ 1
p1=4eix0te�t2=2; x0 ¼ 2pf0; ð3Þ
where f0 is the center frequency of the wavelet. As
can be seen from Eq. (3), the Morlet wavelet consists
of a complex wave within a Gaussian envelope that
has unit standard deviation. The factor p�1=4 ensures
that the wavelet has unitary energy.
There are two types of operations that one can do
over wavelets: translation and dilation. For the first
one, the central position of the wavelet along the time
axis is shifted, whereas for the second, the wavelet is
compressed or dilated. Strictly speaking, if w denotes
a wavelet, then it will be called the mother wavelet,
and the family of functions wa;b spanned by those
operations is known as daughter wavelets and is
given by
wa;bðtÞ ¼1ffiffiffia
p wt � b
a
� �; ð4Þ
where a[ 0 and b 2 R are called dilation and
translation parameters, respectively. It is important to
note that the factor 1=ffiffiffia
pensures that all daughter
wavelets have the same energy. Thus, relative to
every wavelet w, the continuous wavelet transform
(CWT) of a signal f for an instant of time b and scale
a is defined by
Wf ða; bÞ ¼Z 1
�1f ðtÞ 1ffiffiffi
ap w� t � b
a
� �dt
¼Z 1
�1f ðtÞw�
a;bðtÞdt
¼ hf ;wa;bi
ð5Þ
where h�; �i denotes the usual inner product of L2ðRÞ.Equation (5) can be thought of as an analysis equa-
tion, since it represents the projection Wf(a, b) of f
over a daughter wavelet centered at b with scale a.
Since the projections are computed to every value of
b and a, at the end of the process one obtains a two-
dimensional transform plane with all the projections
or wavelet coefficients, which represents the decom-
position of the signal f over a family of daughter
wavelets. Each of these coefficients has an energy
which is given by
Eða; bÞ ¼ jWf ða; bÞj2; ð6Þ
and the plot of E(a, b) is called a scalogram. The
CWT preserves the total energy of a signal f and can
be recovered by integrating (6) for all values of a and
b:
E ¼ 1
Cw
Z 1
0
Z 1
�1jWf ða; bÞj2db
da
a2: ð7Þ
The main feature of the CWT is time–frequency
localization (Soman et al. 2004). So, to obtain a
time–frequency plane it is necessary to convert the
scales to so-called pseudo-frequencies, which can be
done using the equation
f ¼ fca; ð8Þ
where fc is the center frequency of the mother
wavelet (a ¼ 1) defined by
fc ¼1
2p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiR10
x2jwðxÞj2dxR10
jwðxÞj2dx
vuut ; ð9Þ
as discussed in Addison (2002). Specifically, the
CWT measures the local matching between a signal f
and the daughter wavelet at a particular instant of
time b and scale a. A large coefficient value means
that f and wa;b correlate well in the vicinity of b,
whereas a low value indicates the opposite. Similarly
Vol. 178, (2021) Geomagnetic Disturbances During the Maule (2010) Tsunami 4831
to the Fourier transform, from the wavelet coeffi-
cients one can recover the original signal f with the
synthesis equation defined as
f ðtÞ ¼ 1
Cw
Z 1
0
Z 1
�1Wf ða; bÞwa;bðtÞdb
da
a2; ð10Þ
which is also called inverse continuous wavelet
transform (ICWT) (Mallat 2008).
Discrete Wavelet Transform
In this work, we use the Daubechies (db2) wavelet
function of order 2, and therefore the nonzero low
filter values are hu 1þffiffi3
p
4ffiffi2
p ; 3þffiffi3
p
4ffiffi2
p ; 3�ffiffi3
p
4ffiffi2
p ; 1�ffiffi3
p
4ffiffi2
ph i
, and the
high-pass are g ¼ ð�1Þkþ1hð1 � kÞ. Also, we only
study the discrete scales j ¼ 1; 2; and; 3 which are
associated with the center frequencies of 3, 6, and 12
min, respectively. These center frequency values are
obtained due to our analysis wavelet choice and to the
data sample rate of 1-min time resolution; see
additional details in Klausner et al.
(2014b, 2016a, b, 2017).
Moreover, we use the EWC method to narrow the
period band by choosing the first three wavelet
decomposition levels according to the physical pro-
cess in which we intend to highlight. Here, the EWC
corresponds to the weighted geometric mean of the
square wavelet coefficients per 8 min, as shown in the
following equation
EWC ¼ 1
7
XN
k
dj¼1k
������2þ2
XN
k
dj¼2k
������2þX
N
k
dj¼3k
������2
!
ð11Þ
where N is equal to 8.
Hilbert–Huang Transform
The Hilbert–Huang transform (HHT) is an empir-
ical method for analyzing nonstationary data that
come from nonlinear processes (Huang and Shen
2005). This transform consists of two main parts:
empirical mode decomposition (EMD) and Hilbert
spectral analysis (HSA). Despite the importance of
HSA, only EMD will be discussed in this article. It is
important to note that the main difference between
HHT and the conventional transforms is that for the
former, the signal under analysis is expanded in terms
of an adaptive basis (a basis that comes from the
data), whereas for the others the expansion occurs in
terms of a prior established basis (Huang and Shen
2005), e.g, sines and cosines for Fourier transform
and various translated and dilated versions of the
mother wavelet for CWT. Moreover, it can be said
that HHT is more an algorithm than a transform, due
to the absence of an analytical foundation that will
require significant time and effort to accomplish
(Huang and Shen 2005).
The EMD method assumes that any data consist
of intrinsic modes of oscillations, and those intrinsic
modes are obtained by an algorithm called the sifting
process, which decomposes a given signal in a set of
intrinsic mode functions (IMF), which are functions
that satisfy the following conditions (Huang and Shen
2005):
• The number of maxima and minima points and the
number of roots must either be equal or differ at
most by 1.
• At any point, the mean value of the envelope
defined by the local maxima and the envelope
defined by the local minima is zero.
To perform the sifting process over a given signal f,
the first step is to find its extrema points (minimum or
maximum) and connect them through a cubic spline,
conceiving an upper and a lower envelope for the
signal. The second step is to calculate an average
envelope from those obtained in the first step and
subtract it from the original signal. After these two
steps, a test is applied to the resulting signal to
determine whether it satisfies the IMF conditions or a
stoppage criterion. If it does not, then these steps are
applied to the resulting signal until an IMF is
obtained. Finally, this IMF is subtracted from f,
producing a residue. At this point, the steps are
applied to the residue until another IMF is obtained,
yielding another residue. This process of obtaining
successive residues stops when the last one becomes
a monotonic function from which no further IMFs
can be extracted.
Suppose that the sifting process stops at the n-th
iteration. So, for a residue rj with 0� j� n � 1, an
IMF is extracted by the following recurrence relation
4832 V. Klausner et al. Pure Appl. Geophys.
h0 ¼ rj
hi�1 � mi ¼ hi
�; i� 1; ð12Þ
where mi is the average envelope computed from the
upper and lower envelope of hi�1 and r0 ¼ f ðtÞ.Considering that hi converges to an IMF for some
value of i, then the IMF associated with the residue j
will be denoted by cj, and the following equation
holds
rj ¼ rj�1 � cj; 1� j� n: ð13Þ
Therefore, from Eq. (13), one can write the original
signal f in terms of n IMFs obtained at the end of the
sifting process, as follows
r1 ¼ f ðtÞ � c1
r2 ¼ r1 � c2
..
.
rn ¼ rn�1 � cn
)f ðtÞ ¼Xn
i¼1
ci þ rn: ð14Þ
Mean Absolute Percentage Error (MAPE)
The MAPE is a statistical measure, given in
percentage terms, of the accuracy of a forecasting
model and is defined by
M ¼ 1
n
Xn
i¼1
Ai � Fi
Ai
��������; ð15Þ
where Ai is the actual value and Fi is the forecast
value. Because of the simplicity of Eq. (15), the
MAPE is widely used to indicate the accuracy of a
forecasting model, but it is scale-sensitive and should
not be used with low-volume data.
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with regard to jurisdictional claims in published maps
and institutional affiliations.
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