geomagnetic disturbances during the maule (2010) tsunami

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: [email protected]

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

http://orcid.org/0000-0003-0250-5574

http://crossmark.crossref.org/dialog/?doi=10.1007/s00024-021-02823-x&domain=pdf

https://doi.org/10.1007/s00024-021-02823-x

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.

http://www.intermagnet.org


http://www.ioc-sealevelmonitoring.org

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


https://www.gfz-potsdam.de/en/kp-index/

https://www.gfz-potsdam.de/en/kp-index/

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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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

)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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

)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(c1) SBA - Z-component (c2) SBA - 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

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

)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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

)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(f1) MCQ - Z-component (f2) MCQ - H-component

Figure 2continued


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 20:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(i1) HON - Z-component (i2) HON - H-component

Figure 2continued


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


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)


2010-02-27 06:34:00.000 2010-02-28 06:33:00.000


(m1) SHU - Z-component (m2) SHU - H-component

Figure 2continued


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


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


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


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


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


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


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





http://nctr.pmel.noaa.gov/model.html

http://nctr.pmel.noaa.gov/model.html

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


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


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.

Publisher’s Note Springer Nature remains neutral

with regard to jurisdictional claims in published maps

and institutional affiliations.

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