<?xml version="1.0" encoding="UTF-8"?>
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<article xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:oasis="http://docs.oasis-open.org/ns/oasis-exchange/table" xml:lang="en" dtd-version="3.0"><?xmltex \makeatother\@nolinetrue\makeatletter?>
  <front>
    <journal-meta><journal-id journal-id-type="publisher">ANGEO</journal-id><journal-title-group>
    <journal-title>Annales Geophysicae</journal-title>
    <abbrev-journal-title abbrev-type="publisher">ANGEO</abbrev-journal-title><abbrev-journal-title abbrev-type="nlm-ta">Ann. Geophys.</abbrev-journal-title>
  </journal-title-group><issn pub-type="epub">1432-0576</issn><publisher>
    <publisher-name>Copernicus Publications</publisher-name>
    <publisher-loc>Göttingen, Germany</publisher-loc>
  </publisher></journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.5194/angeo-36-1483-2018</article-id><title-group><article-title>Electromagnetic field observations by the DEMETER satellite in connection with the 2009 L'Aquila earthquake</article-title><alt-title>Electromagnetic emission during the 2009 L'Aquila earthquake</alt-title>
      </title-group><?xmltex \runningtitle{Electromagnetic emission during the 2009 L'Aquila earthquake}?><?xmltex \runningauthor{I.~Bertello et al.}?>
      <contrib-group>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Bertello</surname><given-names>Igor</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="yes" rid="aff2 aff3">
          <name><surname>Piersanti</surname><given-names>Mirko</given-names></name>
          <email>mirko.piersanti@aquila.infn.it</email>
        <ext-link>https://orcid.org/0000-0001-5207-2944</ext-link></contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Candidi</surname><given-names>Maurizio</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Diego</surname><given-names>Piero</given-names></name>
          
        </contrib>
        <contrib contrib-type="author" corresp="no" rid="aff1">
          <name><surname>Ubertini</surname><given-names>Pietro</given-names></name>
          
        </contrib>
        <aff id="aff1"><label>1</label><institution>INAF – Istituto di Astrofisica e Planetologia Spaziali, Rome,
Italy</institution>
        </aff>
        <aff id="aff2"><label>2</label><institution>INFN – University of Rome Tor-Vergata, Rome, Italy</institution>
        </aff>
        <aff id="aff3"><label>3</label><institution>Consorzio Area di Ricerca in Astrofisica, L'Aquila, Italy</institution>
        </aff>
      </contrib-group>
      <author-notes><corresp id="corr1">Mirko Piersanti (mirko.piersanti@aquila.infn.it)</corresp></author-notes><pub-date><day>29</day><month>October</month><year>2018</year></pub-date>
      
      <volume>36</volume>
      <issue>5</issue>
      <fpage>1483</fpage><lpage>1493</lpage>
      <history>
        <date date-type="received"><day>27</day><month>June</month><year>2018</year></date>
           <date date-type="rev-request"><day>6</day><month>July</month><year>2018</year></date>
           <date date-type="rev-recd"><day>11</day><month>October</month><year>2018</year></date>
           <date date-type="accepted"><day>19</day><month>October</month><year>2018</year></date>
      </history>
      <permissions>
        
        
      <license license-type="open-access"><license-p>This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">https://creativecommons.org/licenses/by/4.0/</ext-link></license-p></license></permissions><self-uri xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018.html">This article is available from https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018.html</self-uri><self-uri xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018.pdf">The full text article is available as a PDF file from https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018.pdf</self-uri>
      <abstract>
    <p id="d1e130">To define a background in the electromagnetic emissions above seismic
regions, it is necessary to define the statistical distribution of the wave
energy in the absence of seismic activity and any other anomalous input (e.g.
solar forcing). This paper presents a completely new method to determine both
the environmental and instrumental backgrounds applied to the entire DEMETER
satellite electric and magnetic field data over L'Aquila. Our technique is
based on a new data analysis tool called ALIF (adaptive local iterative
filtering, Cicone et al., 2016; Cicone and Zhou, 2017; Piersanti et al.,
2017b). To evaluate the instrumental background, we performed a multiscale
statistical analysis in which the instantaneous relative energy
(<inline-formula><mml:math id="M1" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), kurtosis, and Shannon entropy were
calculated. To estimate the environmental background, a map, divided into
<inline-formula><mml:math id="M2" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> latitude–longitude cells, of the averaged
relative energy (<inline-formula><mml:math id="M3" display="inline"><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula>), has been constructed,
taking into account the geomagnetic activity conditions, the presence of
seismic activity, and the local time sector of the satellite orbit. Any
distinct signal different (over a certain threshold) from both the
instrumental and environmental backgrounds will be considered as a case event
to be investigated. Interestingly, on 4 April 2009, when DEMETER flew exactly
over L'Aquila at UT <inline-formula><mml:math id="M4" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 20:29, an anomalous signal was observed at 333 Hz
on both the electric and magnetic field data, whose characteristics seem to
be related to pre-seismic activity.</p>
  </abstract>
    </article-meta>
  </front>
<body>
      

<sec id="Ch1.S1" sec-type="intro">
  <title>Introduction</title>
      <p id="d1e190">The nature of the Earth's interior, in terms of the dynamics of the crust,
mantle, and core, can be
investigated through extended ground-based and space observations (Bell,
1982; Hayakawa and Molchanov, 2002; Pulinets and Boyarchuk, 2004; De Santis
et al., 2015). In the same way, it is possible to inquest the natural or
anthropogenic origin of the electromagnetic emissions (EMEs) using
measurements in the near-Earth space (Parrot and Zaslavski, 1996; Buzzi,
2006). In addition, several works (Parrot, 1995; Parrot and Zaslavski, 1996;
Buzzi, 2007) remarked that EMEs of both anthropogenic (such as HF
broadcasting stations and VLF transmitters) and natural (i.e. Earth's
surface) origin can influence the dynamics and the composition of the
ionosphere–magnetosphere region (Parrot and Molchanov, 1995; Parrot and
Zaslavski, 1996). Taking into account that extreme reliability is needed to
call for preseismic phenomena, a characteristic background for the regions on
Earth where we want to detect the effects of earthquake-related EMEs should
be available. <italic>In the interim</italic>, comprehensive study of both
magnetospheric and ionospheric disturbances driven by ground preseismic EME
waves has to be carried out. In this context, aseismic fault creep and EME
waves are expected to be the principal mechanical and electromagnetic
earthquake precursors, respectively (Buzzi, 2007, and references therein).
Parrot and Molchanov (1995) and Parrot and Zaslavski (1996) achieved the
first promising result analysing rare EME wave observations over the
ionosphere–magnetosphere region. In their studies, they first distinguished
between internal and external components of the geomagnetic field and, then,
gave an efficient measure of the electric field, the plasma temperature, and
the density of the ionosphere. Despite several theoretical models having been
developed, the physical mechanisms leading to the observation of these
effects both at<?pagebreak page1484?> ground and in space are as yet largely unexplained. That is,
the following remains to be understood: the genesis of EME waves over the
focal area (especially soon before a seismic event, if any); its propagation
through lithospheric layers characterized by fixed vertical conductivity; its
access into both the neutral atmosphere and ionosphere; and its arrival in
the magnetosphere and its relative interaction. It is worth noting that, when
a EME wave propagates through both the ionosphere and magnetosphere, the
medium has to be considered dispersive too (Chen, 1977). Recently, Perrone et
al. (2018) analysed ionosonde data and crustal earthquakes with magnitude <inline-formula><mml:math id="M5" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mo>≥</mml:mo><mml:mn mathvariant="normal">6.0</mml:mn></mml:mrow></mml:math></inline-formula> observed in Greece during 2003–2015 to check whether the
relationships obtained between precursory ionospheric anomalies and
earthquakes in Japan and central Italy are also valid for Greek earthquakes.
They identified the ionospheric anomalies as observed variations of the
sporadic E-layer parameters (<inline-formula><mml:math id="M6" display="inline"><mml:mrow><mml:msup><mml:mi>h</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>Es, <italic>fo</italic>Es) and <italic>fo</italic>F2 at the
ionospheric station of Athens and found similar corresponding empirical
relationships between the seismoionospheric disturbances and the earthquake
magnitude and the epicentral distance. Moreover, the large lead times found
for the ionospheric anomalies'
occurrence seem to confirm a rather long earthquake preparation period.</p>
      <p id="d1e225">The search for ionospheric disturbances associated with earthquakes relies on
thorough statistical studies to disentangle seismic effects from the
variations induced by the physical processes that control the ionosphere
dynamic and natural emissions. Several studies have been performed, in the
framework of the DEMETER (Detection of Electro-Magnetic Emissions Transmitted
from Earthquake Regions) mission, and one of them has shown a decrease in the
extremely low-frequency (ELF) wave intensity in the frequency range between 1
and 2 kHz a few hours before the shock (Parrot et al., 2006; Píša
et al., 2012 and 2013; Zhang et al., 2012; Walker et al., 2013). Nĕmec et
al. (2008) built a statistical map of electromagnetic wave intensity obtained
from DEMETER satellite ICE and IMSC data available at that time (2004–2007).
Then, they estimated the probability of occurrence during a seismic event of
signals with higher intensity with respect to the background level defined by
the map. Their study was the first attempt to generate a background map in
the electromagnetic emission above seismic regions for the determination of
the statistical distribution of the wave energy in the absence of seismic
activity.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F1" specific-use="star"><caption><p id="d1e230">Typical ELF data of a half-orbit (orbit no. 302630 on 2010/02/26
day-side). It is shown that data are not available along the whole orbit, but
only when the satellite was in “burst mode”.</p></caption>
        <?xmltex \igopts{width=497.923228pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018-f01.png"/>

      </fig>

      <p id="d1e239">The present paper uses a completely new method to determine both the
environmental and instrumental backgrounds in the electromagnetic emission
above seismic regions by using the DEMETER satellite electric and magnetic
field observations. This algorithm is based on a new data analysis technique
called ALIF (adaptive local iterative filtering, Cicone et al., 2016, 2017;
Piersanti et al., 2017b) and through a multiscale statistical analysis of the
electromagnetic observations. The results obtained with this technique
allowed the construction of an electromagnetic energy background map over the
L'Aquila seismic region from 2004 to 2011. In addition, on 4 April 2009,
2 days before the 6.3 <inline-formula><mml:math id="M7" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">w</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> earthquake (USGS Earthquake catalogue),
when DEMETER flew exactly over L'Aquila at UT <inline-formula><mml:math id="M8" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> 20:29, an anomalous
signal with respect to the background was observed.</p>
</sec>
<sec id="Ch1.S2">
  <title>Data and methods</title>
<sec id="Ch1.S2.SS1">
  <title>DEMETER data</title>
      <p id="d1e271">In our study, we used the data from French satellite DEMETER, launched in
2004 on a Sun-synchronous orbit at about 700 km in altitude. The orbits of
the satellite had an inclination of 98<inline-formula><mml:math id="M9" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula> and a local time of 10:30 on
the day-side and 22:30 on the night-side. The instruments were operational at
geomagnetic latitudes between <inline-formula><mml:math id="M10" display="inline"><mml:mo>-</mml:mo></mml:math></inline-formula>65 and <inline-formula><mml:math id="M11" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>65<inline-formula><mml:math id="M12" display="inline"><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:math></inline-formula>, thus providing a good
coverage of the Earth's seismic zones (Parrot et al., 2005). The data from
the ICE electric field experiment (Berthelier et al., 2005) and the IMSC
magnetic field experiment (Parrot et al., 2005) were used in order to detect
any electromagnetic waves. Among the four available DEMETER channels we
selected the ELF band, the only one which provides the wave
form of the
three components of the fields. The ELF specification is a data range in the
frequency from 15 Hz to 1 kHz, with a sample rate of 2.5 kHz. Due to the
high data transfer resources required, the ELF acquisition is operational
only in “burst mode”, so data are available only in a fraction of the
entire orbit (see Fig. 1). The DEMETER mission lasted from 2004 to March
2011, so we have a large dataset of almost 7 years of the satellite
observations, altogether representing 71 730 half-orbits (35 865 on the
day-side and 35 865 on the night-side). Within the entire available dataset,
we selected the orbits with ELF data that covered a squared area of <inline-formula><mml:math id="M13" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (latitude and longitude) centred over L'Aquila's geographic
coordinates.</p>
</sec>
<sec id="Ch1.S2.SS2">
  <title>ALIF</title>
      <p id="d1e330">The algorithm for the evaluation of both environmental and instrumental
backgrounds in the electromagnetic emission above seismic regions is based on
a recent data analysis technique called ALIF, developed by Cicone et
al. (2016) and Piersanti et al. (2017b). ALIF is able, through a
time-frequency analysis, to identify and quantify the variations across
different scales for non-stationary signals due to the complexity and
non-linearity of the system that generated them. The reason for using this
technique is that, unlike typical data analysis methods, such as fast Fourier
transform and wavelet, ALIF does not suffer from either limited resolution
(Cohen, 2001) and interferences in the time-frequency domain (Flandrin,
1998). Thus, ALIF does not require any further processing of the
representation. The key idea behind this method, very similar to the
empirical mode decomposition (EMD, Huang et al., 1998), is a “divide et
impera” approach. In fact, ALIF first decomposes a signal into several
functions oscillating around zero and characterized by<?pagebreak page1485?> frequencies variable
with time (intrinsic mode functions – IMFs). Then, for each IMF, it performs
a time analysis. The great difference with EMD is that ALIF has a strong
mathematical structure which guarantees the convergence and stability of the
algorithm, which in turn guarantees the physical significance of the
decomposition (Piersanti et al., 2017b).</p>
</sec>
<sec id="Ch1.S2.SS3">
  <title>Multiscale statistical analysis and standardized mean (SM) test</title>
      <p id="d1e339">In order to evaluate the instrumental and environmental background of a
signal <inline-formula><mml:math id="M14" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (such as the magnetic and electric field observations), we
study its multiscale properties. To accomplish this task, we first use ALIF
to decompose <inline-formula><mml:math id="M15" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> into functions <inline-formula><mml:math id="M16" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
characterized by a peculiar scale of variability <inline-formula><mml:math id="M17" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> (Wernik, 1997), so
that
            <disp-formula id="Ch1.Ex1"><mml:math id="M18" display="block"><mml:mrow><mml:mi>s</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>m</mml:mi></mml:munderover><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mi>r</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M19" display="inline"><mml:mrow><mml:mi>r</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the residue of the decomposition. The connection between each
IMF and the scale of variability <inline-formula><mml:math id="M20" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> of <inline-formula><mml:math id="M21" display="inline"><mml:mrow><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> has been analyzed by using
the Flandrin (1998) technique: a dataset characterized by an evident scale
separation can be decomposed into two contributions:
            <disp-formula id="Ch1.Ex2"><mml:math id="M22" display="block"><mml:mrow><mml:mi>s</mml:mi><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msub><mml:mi>s</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced><mml:mo>+</mml:mo><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M23" display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is named the baseline and <inline-formula><mml:math id="M24" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> represents the
variations around the baseline. To identify <inline-formula><mml:math id="M25" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, we applied the
method proposed by Alberti et al. (2016), by defining <inline-formula><mml:math id="M26" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>s</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as the
reconstruction of a subset <inline-formula><mml:math id="M27" display="inline"><mml:mrow><mml:msub><mml:mi>s</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M28" display="inline"><mml:mrow><mml:mi>k</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:math></inline-formula> modes,
            <disp-formula id="Ch1.E1" content-type="numbered"><mml:math id="M29" display="block"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:mi>s</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>k</mml:mi></mml:msubsup><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          characterized by a standardized mean (i.e. the mean divided by the standard
deviation) SM <inline-formula><mml:math id="M30" display="inline"><mml:mo>≈</mml:mo></mml:math></inline-formula> 0 and by IMF fluctuating at higher frequency.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F2"><caption><p id="d1e650">An example of the application of the SM test <bold>(b)</bold> to the
magnetic field observations <bold>(a)</bold> over l'Aquila on 11 February 2009
from 09:33 to 09:39 UT.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018-f02.png"/>

        </fig>

      <?pagebreak page1486?><p id="d1e665">Figure 2 shows an example of the application of the SM test to the DEMETER
magnetic field observations (upper panel) over L'Aquila (<inline-formula><mml:math id="M31" display="inline"><mml:mrow><mml:mi mathvariant="italic">λ</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn mathvariant="normal">42.334</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M32" display="inline"><mml:mrow><mml:mi mathvariant="italic">φ</mml:mi><mml:mo>=</mml:mo><mml:msup><mml:mn mathvariant="normal">13.334</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>; LT <inline-formula><mml:math id="M33" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> UT<inline-formula><mml:math id="M34" display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula>1) on 11 February
2009 from 09:33 to 09:37 UT. The lower panel shows the SM test results. It
can be easily seen that IMFs from 1 to 30 represent the fluctuating part of
the signal (<inline-formula><mml:math id="M35" display="inline"><mml:mrow><mml:mi mathvariant="italic">δ</mml:mi><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>), while IMFs from 31 to 82 are the baseline
(<inline-formula><mml:math id="M36" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mrow><mml:msub><mml:mi>y</mml:mi><mml:mn mathvariant="normal">0</mml:mn></mml:msub></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>). To distinguish between instrumental origin fluctuations and
real signals, a multiscale statistical analysis is needed. For the different
scales <inline-formula><mml:math id="M37" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>s, we considered the statistics of the values
<inline-formula><mml:math id="M38" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. This technique, called multiscale statistical
analysis, calculates and studies the second (the variance <inline-formula><mml:math id="M39" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>,
third (the skewness Sk(<inline-formula><mml:math id="M40" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, and fourth (the kurtosis excess
<inline-formula><mml:math id="M41" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">ex</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mi>K</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>-</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>) moments of the probability distribution
<inline-formula><mml:math id="M42" display="inline"><mml:mrow><mml:mi>p</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> of <inline-formula><mml:math id="M43" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, the relative
energy <inline-formula><mml:math id="M44" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, and the Shannon information entropy
<inline-formula><mml:math id="M45" display="inline"><mml:mrow><mml:mi>I</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, respectively defined as

                <disp-formula specific-use="align" content-type="numbered"><mml:math id="M46" display="block"><mml:mtable displaystyle="true"><mml:mlabeledtr id="Ch1.E2"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:mfrac style="display"><mml:mrow><mml:msub><mml:mo>∫</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mi mathvariant="normal">|</mml:mi><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced><mml:msup><mml:mi mathvariant="normal">|</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mo>∫</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mi mathvariant="normal">|</mml:mi><mml:mi>s</mml:mi><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:msup><mml:mi mathvariant="normal">|</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msup><mml:mi mathvariant="normal">d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr><mml:mlabeledtr id="Ch1.E3"><mml:mtd/><mml:mtd><mml:mstyle class="stylechange" displaystyle="true"/></mml:mtd><mml:mtd><mml:mrow><mml:mstyle class="stylechange" displaystyle="true"/><mml:mi mathvariant="normal">I</mml:mi><mml:mfenced open="(" close=")"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:mfenced><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:msub><mml:mo>∑</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mo>}</mml:mo></mml:mrow></mml:msub><mml:mspace linebreak="nobreak" width="0.125em"/><mml:mi>p</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi mathvariant="normal">t</mml:mi></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>⋅</mml:mo><mml:msub><mml:mi mathvariant="normal">log</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">p</mml:mi><mml:mfenced close=")" open="("><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="normal">t</mml:mi></mml:mfenced></mml:mrow></mml:mfenced><mml:mo>.</mml:mo></mml:mrow></mml:mtd></mml:mlabeledtr></mml:mtable></mml:math></disp-formula></p>
      <p id="d1e1031">These parameters measure the variability of the statistics of the signal in
the function of the scale considered (Strumik and Macek, 2008). That is,
<inline-formula><mml:math id="M47" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">ex</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> indicates how the different <inline-formula><mml:math id="M48" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>s are rich in rare
fluctuations (Frisch, 1995); <inline-formula><mml:math id="M49" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> measures how
“energetically strong” the <inline-formula><mml:math id="M50" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> component is in Eq. (1). <inline-formula><mml:math id="M51" display="inline"><mml:mrow><mml:mi>I</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
measures the “degree of randomness” of each
<inline-formula><mml:math id="M52" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">t</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> component of the signal. In our case the
scale <inline-formula><mml:math id="M53" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> corresponds to the peculiar frequency of each IMF of both
magnetic and electric field observations.</p>
</sec>
<sec id="Ch1.S2.SS4">
  <title>Instrumental background</title>
      <p id="d1e1121">We define <inline-formula><mml:math id="M54" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> as having an instrumental
origin if two conditions are satisfied at the same time.
<list list-type="order"><list-item>
      <p id="d1e1140">The SM test evaluates the <inline-formula><mml:math id="M55" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi mathvariant="normal">t</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> as a fluctuation;</p></list-item><list-item>
      <p id="d1e1158"><inline-formula><mml:math id="M56" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">ex</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M57" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is almost
null and correspondingly <inline-formula><mml:math id="M58" display="inline"><mml:mrow><mml:mi>I</mml:mi><mml:mo>(</mml:mo><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced close=")" open="("><mml:mi>t</mml:mi></mml:mfenced><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> presents a relative maximum.</p></list-item></list></p>
      <p id="d1e1207">Indeed, an <inline-formula><mml:math id="M59" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">IMF</mml:mi><mml:mi mathvariant="normal">ℓ</mml:mi></mml:msub><mml:mfenced open="(" close=")"><mml:mi>t</mml:mi></mml:mfenced></mml:mrow></mml:math></inline-formula> that satisfies these two
conditions can be represented as a Gaussian fluctuation characterized by a
high “degree of randomness”. Thus, it can be identified as instrumental
noise. Figure 3 shows an example of a multiscale statistical analysis of the
<inline-formula><mml:math id="M60" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> component of the DEMETER satellite for the same period of Fig. 2.
Figure 3a shows the <inline-formula><mml:math id="M61" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> behaviour as a function of the
scale <inline-formula><mml:math id="M62" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula> (i.e. the frequency). Two energy peaks, at 20 Hz (blue dashed
line) and 333 Hz (green dashed line), are clearly visible. Scales lower than
3 Hz have almost null energy (red dashed line), have <inline-formula><mml:math id="M63" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">ex</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">0</mml:mn></mml:mrow></mml:math></inline-formula>, and show the highest values of <inline-formula><mml:math id="M64" display="inline"><mml:mrow><mml:mi>I</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>. The IMFs corresponding to
these scales could be attributed to instrumental noise. In any event, a more
accurate analysis of each IMF in the interval <inline-formula><mml:math id="M65" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>&lt;</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> Hz will be done in
the next sections. On the other hand, the IMFs related to 20 Hz are not of
instrumental origin because, despite the almost null value of
<inline-formula><mml:math id="M66" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">ex</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>, the Shannon entropy proves to be concave-upward. In fact, <inline-formula><mml:math id="M67" display="inline"><mml:mrow><mml:mo>≅</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mn mathvariant="normal">20</mml:mn><mml:mspace width="0.125em" linebreak="nobreak"/><mml:mi mathvariant="normal">Hz</mml:mi></mml:mrow></mml:math></inline-formula> is one of the peaks
of Shumann resonance in the ELF portion of the Earth's electromagnetic field
spectrum generated and excited by lightning discharges in the cavity formed
by the Earth's surface and the ionosphere (Barr et al., 2000, and references
therein). A similar situation is obtained for <inline-formula><mml:math id="M68" display="inline"><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">333</mml:mn></mml:mrow></mml:math></inline-formula> Hz. In fact, the
relative <inline-formula><mml:math id="M69" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">ex</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula> (Fig. 3b) and <inline-formula><mml:math id="M70" display="inline"><mml:mrow><mml:mi>I</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> (Fig. 3c) prove to be
concave-upward. Thus, the signal associated with 333 Hz does not originate
from instrumental noise.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F3"><caption><p id="d1e1377">Example of a multiscale statistical analysis of the <inline-formula><mml:math id="M71" display="inline"><mml:mrow><mml:msub><mml:mi>B</mml:mi><mml:mi>y</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> component
for the same data of Fig. 2: <bold>(a)</bold> <inline-formula><mml:math id="M72" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> vs.
frequency; panel <bold>(b)</bold> <inline-formula><mml:math id="M73" display="inline"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mi mathvariant="normal">ex</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> vs. frequency; panel
<bold>(c)</bold> <inline-formula><mml:math id="M74" display="inline"><mml:mi>I</mml:mi></mml:math></inline-formula> vs. frequency. Two energy peaks, at 20 Hz and at 333 Hz
are clearly visible.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018-f03.png"/>

        </fig>

      <p id="d1e1436">By the use of those criteria, we can identify all the <inline-formula><mml:math id="M75" display="inline"><mml:mrow><mml:mi>n</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mi>m</mml:mi></mml:mrow></mml:math></inline-formula>
IMFs(<inline-formula><mml:math id="M76" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>) originating from instrumental noise. As a consequence, the
instrumental background can be defined as
            <disp-formula id="Ch1.Ex3"><mml:math id="M77" display="block"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:munderover><mml:mo movablelimits="false">∑</mml:mo><mml:mrow><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mi>n</mml:mi></mml:munderover><mml:mi mathvariant="normal">IMF</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>,</mml:mo></mml:mrow></mml:math></disp-formula>
          where <inline-formula><mml:math id="M78" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi>b</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> is the signal of instrumental origin.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F4" specific-use="star"><caption><p id="d1e1507">Environmental background for the L'Aquila cell as evaluated by ALIF
in terms of <inline-formula><mml:math id="M79" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> vs. time and frequency
for the reference quiet period (<inline-formula><mml:math id="M80" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>, Kp <inline-formula><mml:math id="M81" display="inline"><mml:mrow><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M82" display="inline"><mml:mrow><mml:mi>L</mml:mi><mml:mo>=</mml:mo></mml:mrow></mml:math></inline-formula> night-side). <bold>(a)</bold> shows the
<inline-formula><mml:math id="M83" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for the three components of the
electric field; <bold>(b)</bold> shows the <inline-formula><mml:math id="M84" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> for the three components of the magnetic field.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018-f04.png"/>

        </fig>

</sec>
<sec id="Ch1.S2.SS5">
  <title>Environmental background</title>
      <p id="d1e1625">The environmental background has been evaluated through the following steps.
<list list-type="order"><list-item>
      <p id="d1e1630">We divided the entire electric and magnetic DEMETER dataset into two subsets
depending on the local time sector of the satellite orbit (i.e. day-side or
night-side). Each subset has again been divided into two more subsets
characterized by different seismic conditions. The first one (<inline-formula><mml:math id="M85" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>)
is defined for low seismic activity (<inline-formula><mml:math id="M86" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mo>≤</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="M87" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula> being the earthquake
magnitude) and the second (<inline-formula><mml:math id="M88" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) for high seismic activity
(<inline-formula><mml:math id="M89" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>). This procedure is crucial to take into account the
nature of the earthquake and the different ionospheric response.</p></list-item><list-item>
      <p id="d1e1687">As in Perrone et al. (2018), all <inline-formula><mml:math id="M90" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">L</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M91" display="inline"><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi mathvariant="normal">H</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> subsets were again
divided into three subsets according to the level of geomagnetic activity.
This division is important to take into account possible signals associated
with geomagnetic activity. To accomplish this task, we used either the Sym-H
index or the AE index. The first one is<?pagebreak page1487?> the ring current activity index,
which takes into account possible low-latitude geomagnetic activity
(McPherron et al., 1986). The second is the
auroral electrojet activity index, which takes
into account possible high-latitude geomagnetic activity induced by the
loading–unloading process from the magnetotail current (Akasofu,
2017). The three subsets correspond to three
intervals, which are <inline-formula><mml:math id="M92" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>: Sym-H <inline-formula><mml:math id="M93" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> [10 nT, <inline-formula><mml:math id="M94" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> nT) and
AE &lt; 100 nT; <inline-formula><mml:math id="M95" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>: Sym-H <inline-formula><mml:math id="M96" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> [<inline-formula><mml:math id="M97" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> nT, <inline-formula><mml:math id="M98" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> nT) and
AE &lt; 150 nT; and <inline-formula><mml:math id="M99" display="inline"><mml:mrow><mml:msub><mml:mi>I</mml:mi><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>: Sym-H <inline-formula><mml:math id="M100" display="inline"><mml:mo>≤</mml:mo></mml:math></inline-formula> <inline-formula><mml:math id="M101" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">80</mml:mn></mml:mrow></mml:math></inline-formula> nT and AE <inline-formula><mml:math id="M102" display="inline"><mml:mo>≥</mml:mo></mml:math></inline-formula> 150 nT. I<inline-formula><mml:math id="M103" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>, I<inline-formula><mml:math id="M104" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula>, and I<inline-formula><mml:math id="M105" display="inline"><mml:msub><mml:mi/><mml:mrow><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> correspond to quiet,
moderate, and high geomagnetic activity. Since both the Sym-H and AE indices
have 1 min resolution, to assign each orbit to the correct “geomagnetic
activity” interval, we considered their behaviour 24 h before the event
under analysis.</p>
      <p id="d1e1872">As a consequence, we finally obtained a total of 12 intervals (hereafter
<inline-formula><mml:math id="M106" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi mathvariant="normal">M</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, where the subscripts M, K, and L correspond to the
magnitude interval, geomagnetic activity interval, and local time interval of
the satellite orbit, respectively).</p></list-item><list-item>
      <p id="d1e1896">The world map has been divided into <inline-formula><mml:math id="M107" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> latitude–longitude cells.
Each <inline-formula><mml:math id="M108" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi mathvariant="normal">M</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula> will be decomposed by ALIF. For each cell, after the
removal of instrumental noise by applying the technique described above, a
time-frequency <inline-formula><mml:math id="M109" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> will be calculated. Then, a mean
<inline-formula><mml:math id="M110" display="inline"><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> will be calculated and stored for each
frequency scale. Averaging has been applied only if the ratio <inline-formula><mml:math id="M111" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="false"><mml:mfrac style="text"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mfrac></mml:mstyle><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, where <inline-formula><mml:math id="M112" display="inline"><mml:mrow><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> is the standard deviation of
<inline-formula><mml:math id="M113" display="inline"><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover></mml:math></inline-formula> evaluated at the single frequency scale <inline-formula><mml:math id="M114" display="inline"><mml:mi mathvariant="normal">ℓ</mml:mi></mml:math></inline-formula>.</p></list-item></list></p>
      <?pagebreak page1488?><p id="d1e2064">For each <inline-formula><mml:math id="M115" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi mathvariant="normal">M</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>, we defined
<inline-formula><mml:math id="M116" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow><mml:mo mathvariant="normal">‾</mml:mo></mml:mover><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> as the environmental background.
This kind of background gives a representation of both the magnetospheric and
ionospheric electric and magnetic field activity directly driven by the
geoelectric and geomagnetic field variations induced by solar forcing. As a
consequence, any distinct signal (over the threshold <inline-formula><mml:math id="M117" display="inline"><mml:mrow><mml:mn mathvariant="normal">1</mml:mn><mml:mo>±</mml:mo><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">σ</mml:mi><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>
could be reasonably studied as an anomalous event.</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F5"><caption><p id="d1e2132">DEMETER electromagnetic observation on 4 April 2009 in the ELF band.
<bold>(a)</bold> shows the satellite orbit (red) as a function of the geographic
latitude and longitude. Lower panels show the electric <bold>(c)</bold> and
magnetic <bold>(b)</bold> field observations as a function of the universal time
(UT). The blue circle identifies the L'Aquila geographic position.</p></caption>
          <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018-f05.png"/>

        </fig>

      <p id="d1e2150">Figure 4 shows the background components of both the electric (left panels)
and magnetic (right panels) fields over the L'Aquila cell
(<inline-formula><mml:math id="M118" display="inline"><mml:mrow><mml:msub><mml:mi>C</mml:mi><mml:mrow><mml:mi mathvariant="normal">M</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">K</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="normal">L</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math></inline-formula>: <inline-formula><mml:math id="M119" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> in latitude and <inline-formula><mml:math id="M120" display="inline"><mml:mrow><mml:msup><mml:mn mathvariant="normal">1</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> in longitude
centred at the L'Aquila geographic coordinate) with <inline-formula><mml:math id="M121" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mi mathvariant="italic">&lt;</mml:mi><mml:mn mathvariant="normal">3</mml:mn></mml:mrow></mml:math></inline-formula>,
<inline-formula><mml:math id="M122" display="inline"><mml:mrow><mml:mo>-</mml:mo><mml:mn mathvariant="normal">10</mml:mn></mml:mrow></mml:math></inline-formula> nT &lt; Sym-H &lt; 0 nT and AE &lt; 100 nT,
<inline-formula><mml:math id="M123" display="inline"><mml:mi>L</mml:mi></mml:math></inline-formula> <inline-formula><mml:math id="M124" display="inline"><mml:mo>=</mml:mo></mml:math></inline-formula> night-side, which we defined as being the quiet background
condition. For the evaluation we used 72 satellite orbits. The results are
presented in the satellite reference framework<fn id="Ch1.Footn1"><p id="d1e2232"><inline-formula><mml:math id="M125" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula> is directed along
the nadir direction; <inline-formula><mml:math id="M126" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula> is directed along the satellite velocity vector; <inline-formula><mml:math id="M127" display="inline"><mml:mi>y</mml:mi></mml:math></inline-formula>
is perpendicular to the <inline-formula><mml:math id="M128" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> plane</p></fn> (Berthelier et al., 2005).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F6" specific-use="star"><caption><p id="d1e2271">Anomalous event detected over L'Aquila on 4 April 2009. <bold>(a)</bold>
shows the <inline-formula><mml:math id="M129" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> vs. time and frequency
for the three components of the electric field; <bold>(b)</bold> shows the
<inline-formula><mml:math id="M130" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> vs. time and frequency for the
three components of the magnetic field. A clear anomalous energy peak at
333 Hz, with respect to the quiet reference conditions (Fig. 4), appears in
both magnetic and electric fields.</p></caption>
          <?xmltex \igopts{width=341.433071pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018-f06.png"/>

        </fig>

</sec>
</sec>
<sec id="Ch1.S3">
  <title>4 April 2009 case event</title>
      <p id="d1e2327">Figure 5 shows the characteristics of the DEMETER orbit (upper panel) that
occurred on 4 April 2009 (2 days before a 6.3 magnitude earthquake), in terms
of latitude and longitude position, and the relative electric (left panels)
and magnetic (right panels) field observations. This orbit was identified as
anomalous by our technique. In fact, Fig. 6, exhibiting <inline-formula><mml:math id="M131" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> for both the electric and magnetic field components, shows an
anomalous signal (<inline-formula><mml:math id="M132" display="inline"><mml:mrow><mml:msup><mml:mi>s</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>) at frequency <inline-formula><mml:math id="M133" display="inline"><mml:mrow><mml:mi>f</mml:mi><mml:mo>*</mml:mo><mml:mo>=</mml:mo><mml:mn mathvariant="normal">333</mml:mn></mml:mrow></mml:math></inline-formula> Hz, which is not present
in quiet conditions (see Fig. 4). It is worth noting that the time of
<inline-formula><mml:math id="M134" display="inline"><mml:mrow><mml:msup><mml:mi>f</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> onset corresponds exactly to the DEMETER passage through the
L'Aquila geographic footprint. <inline-formula><mml:math id="M135" display="inline"><mml:mrow><mml:msup><mml:mi>s</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> has a peculiar
electromagnetic (e.m.) polarization, characterized by a
magnetic field oscillating principally in the <inline-formula><mml:math id="M136" display="inline"><mml:mrow><mml:mi>y</mml:mi><mml:mo>-</mml:mo><mml:mi>z</mml:mi></mml:mrow></mml:math></inline-formula> plane and an electric
field (less clear situation) oscillating principally along the <inline-formula><mml:math id="M137" display="inline"><mml:mrow><mml:mi>x</mml:mi><mml:mo>-</mml:mo><mml:mi>y</mml:mi></mml:mrow></mml:math></inline-formula> plane
(in the satellite reference frame).</p>
      <p id="d1e2413">Since ALIF extracts both the electric and magnetic field wave forms at each
frequency, we were able to calculate the instantaneous phase difference
between the two signals, resulting in <inline-formula><mml:math id="M138" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:msup><mml:mn mathvariant="normal">90</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>. This condition
allowed the evaluation of the Poynting vector
<inline-formula><mml:math id="M139" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">S</mml:mi><mml:mo>=</mml:mo><mml:mi mathvariant="bold-italic">E</mml:mi><mml:mo>×</mml:mo><mml:mi mathvariant="bold-italic">B</mml:mi></mml:mrow></mml:math></inline-formula>,
showing the following characteristic angles with respect to the satellite
coordinate system: <inline-formula><mml:math id="M140" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϑ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:msup><mml:mn mathvariant="normal">167.1</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M141" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">1</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">15.4</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> (<inline-formula><mml:math id="M142" display="inline"><mml:mi mathvariant="italic">ϑ</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M143" display="inline"><mml:mi mathvariant="italic">φ</mml:mi></mml:math></inline-formula> being the angles
between <inline-formula><mml:math id="M144" display="inline"><mml:mi mathvariant="bold-italic">S</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M145" display="inline"><mml:mi>x</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M146" display="inline"><mml:mi mathvariant="bold-italic">S</mml:mi></mml:math></inline-formula> and <inline-formula><mml:math id="M147" display="inline"><mml:mi>z</mml:mi></mml:math></inline-formula>, respectively). The
direction of <inline-formula><mml:math id="M148" display="inline"><mml:mi mathvariant="bold-italic">S</mml:mi></mml:math></inline-formula> confirms that <inline-formula><mml:math id="M149" display="inline"><mml:mrow><mml:msup><mml:mi>s</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> is directed toward the
satellite, coming from the ground.</p>
      <p id="d1e2544">Interestingly, the same peculiar frequency, <inline-formula><mml:math id="M150" display="inline"><mml:mrow><mml:msup><mml:mi>f</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>, was found on 11
February 2009, with lower (<inline-formula><mml:math id="M151" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> %) <inline-formula><mml:math id="M152" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> (see
Fig. 2) and comparable polarization in both magnetic and electric fields (not
shown). Also for this case event, the evaluated direction of <inline-formula><mml:math id="M153" display="inline"><mml:mi mathvariant="bold-italic">S</mml:mi></mml:math></inline-formula>
confirms a signal coming from the ground
(<inline-formula><mml:math id="M154" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϑ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">154.6</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M155" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">6.4</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula>).</p>

      <?xmltex \floatpos{t}?><fig id="Ch1.F7"><caption><p id="d1e2627">Geomagnetic field observations at L'Aquila ground station:
<bold>(a)</bold> shows the <inline-formula><mml:math id="M156" display="inline"><mml:mi>H</mml:mi></mml:math></inline-formula> (north–south) component; <bold>(b)</bold> shows the
<inline-formula><mml:math id="M157" display="inline"><mml:mi>D</mml:mi></mml:math></inline-formula> (east–west) component; <bold>(c)</bold> shows the <inline-formula><mml:math id="M158" display="inline"><mml:mi>Z</mml:mi></mml:math></inline-formula> (vertical) component.
The observations show the typical Sq daily variations.</p></caption>
        <?xmltex \igopts{width=236.157874pt}?><graphic xlink:href="https://angeo.copernicus.org/articles/36/1483/2018/angeo-36-1483-2018-f07.png"/>

      </fig>

</sec>
<sec id="Ch1.S4">
  <title>Discussion and conclusions</title>
      <p id="d1e2673">The correct identification of a background in the e.m. emission over seismic
regions has a crucial role for the detection of possible signals related to
earthquake or pre-earthquake activity. The algorithm presented here
represents a new and very efficient technique to distinguish between
instrumental, environmental, and external source signals from satellite
observations. The efficiency of ALIF for both non-linear and non-stationary
signal analysis, and peculiar frequency onset identification, has been proved
in several works (i.e. Piersanti and Villante, 2016; Alberti et al., 2016,
and references therein). In any event, its possible application to identify
correctly the instrumental origin noise has never been presented before.
Here, we showed that the coupling between ALIF and MSA represents a powerful
tool to identify and remove noise from a signal. In fact, our method was able
to determine all the noise frequencies declared in electric and magnetic
field experiments of the DEMETER satellite (Lagoutte et al.,<?pagebreak page1489?> 2005), such as
1 Hz in the E field (see Fig. 4). This signal is an effect of the
instrumental disturbance, i.e. the sweeping voltage of the Langmuir probe
(Lagoutte et al., 2005). Concerning the continuous 20 Hz signal detected in
the magnetic field observations, we speculated that it can be attributed to
one of the peaks of Shumann resonance in the ELF portion of the Earth's
electromagnetic field spectrum generated and excited by lightning discharges
in the cavity formed by the Earth's surface and the ionosphere (Barr et al.,
2000, and references therein). In any event, Lagoutte et al. (2005) in their
DEMETER satellite user guide manual certificated <inline-formula><mml:math id="M159" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">20</mml:mn></mml:mrow></mml:math></inline-formula> Hz as a BANT
(Boîtier Analogique et Numérique de Traitement) noise.</p>
      <p id="d1e2686">On the other hand, this paper presents a useful method for the correct
selection of anomalous signals with respect to the evaluated background. The
choice of using the ratio <inline-formula><mml:math id="M160" display="inline"><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mi mathvariant="italic">ϵ</mml:mi></mml:msub><mml:mo>(</mml:mo><mml:mi mathvariant="normal">ℓ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula> was to take into
account possible anomalous energy enhancements as well as a new signal onset.
In addition, the choice of a threshold equal to <inline-formula><mml:math id="M161" display="inline"><mml:mrow><mml:mn mathvariant="normal">3</mml:mn><mml:mi mathvariant="italic">σ</mml:mi></mml:mrow></mml:math></inline-formula> makes the
anomaly selection as strong as possible and should exclude possible false positives. In any event, at this stage, a visual inspection of each
anomalous signal detected is needed. Last but not least, an analysis of the
geomagnetic index behaviour associated with a possible e.m. anomaly detected
by our method is crucial. In fact, it is worth remarking that the external
origin perturbations, in terms of solar activity, represent the principal
disturbance of both the Earth's ionospheric electric and magnetospheric
fields (Vellante et al., 2014; Piersanti et al., 2017a, and references
therein).</p>
      <?pagebreak page1490?><p id="d1e2716">In this context, the 333 Hz component, appearing when the DEMETER flew
exactly over L'Aquila (Fig. 6), is not visible in the corresponding
background (in terms of Kp and <inline-formula><mml:math id="M162" display="inline"><mml:mi>M</mml:mi></mml:math></inline-formula> indices – Fig. 4) and then may be an
interesting anomaly. In fact, 4 April 2009 was characterized by very low
geomagnetic activity, since the Sym-H index was between 8 and 10 nT, and the
AE index was less than 95 nT. This confirms that 4 April 2009 was a solar
quiet (Sq) day (Matsushida and Maeda, 1965; Chulliat et al., 2005). Sq is
caused by the concurring contribution of a current system flowing in the
so-called ionospheric dynamo region and of the induced telluric currents in
the Earth's upper mantle. Briefly, their interaction gives rise to two pairs
of vortices: two in the sunlit hemisphere and the other two in the dark one
(Richmond et al., 1976; Shinbori et al., 2014). This is confirmed by the
behaviour of the geomagnetic field observation at L'Aquila ground station
(Fig. 7), which presents the typical Sq daily variation at middle/low
latitude in April (De Michelis et al., 2010). In addition, the inspection of
the solar wind conditions coupled with a map of auroral oval emission from
the DMSP satellite taken at 20:34 UT (not shown) confirmed the absence of
any disturbance of solar origin, such as substorm activity, that could affect
the low–middle latitudes' magnetic and electric fields. Indeed, L'Aquila
geomagnetic trace (Fig. 7) did not show any Pi2 wave activity for the entire
day (Olson, 1999; Piersanti et al., 2017a). Moreover, no ELF perturbations
are observed between 20:30 and 20:40 UT. As a consequence, we can reasonably
assert that <inline-formula><mml:math id="M163" display="inline"><mml:mrow><mml:msup><mml:mi>s</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> cannot be related to any solar perturbation.</p>
      <p id="d1e2737">As a matter of fact, the relative Poynting vector <inline-formula><mml:math id="M164" display="inline"><mml:mi mathvariant="bold-italic">S</mml:mi></mml:math></inline-formula> indicates a wave
propagating from the ground to the ionosphere. The <inline-formula><mml:math id="M165" display="inline"><mml:mrow><mml:msup><mml:mi>s</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> peculiar
polarization might be associated with a horizontal current system flowing at
the ground, switched on by an anomalous ground impedance generated by the
fault break. It is thought that the low-frequency components (ULF/ELF) of
seismo-electromagnetic emission (SEME) waves generated by pre-seismic sources
(such as local deformation of fields, rock dislocation and micro-fracturing,
gas emission, fluid diffusion, charged particle generation and motion,
electro-kinetic, piezo-magnetic and piezoelectric effects, and fair weather
currents) are transmitted into the near-Earth space (Dobrovolsky, 1989;
Teisseyre, 1997; Pulinets and Kirill, 2004; Sorokin, 2001). During their
propagation through the solid crust, the SEME waves characterized by lower
periods are attenuated. As a consequence, only low-frequency waves (in the
ULF/ELF band) can go over the Earth's crust and propagate through the
ionosphere–magnetosphere system with moderate attenuation (Bortnik and
Bleier, 2004). Observations from the low-Earth orbit (LEO) satellite seem to
confirm this scenario. In fact, pre-seismic variations of electric and
magnetic fields and of ionospheric plasma temperature and density (Parrot,
1993; Chmyrev, 1997, Buzzi, 2007) have been observed from a few minutes to
several hours (2–6 h) prior to earthquakes of moderate or strong magnitude
(<inline-formula><mml:math id="M166" display="inline"><mml:mrow><mml:mi>M</mml:mi><mml:mi mathvariant="italic">&gt;</mml:mi><mml:mn mathvariant="normal">4.0</mml:mn></mml:mrow></mml:math></inline-formula>). Unfortunately, no magnetotelluric measurements that
could confirm or contradict our hypothesis were available for the event under
investigation. In any event, it is interesting to emphasize that, repeating
the same analysis for cells further north and south than the L'Aquila cell
(not shown), no anomalous signal centred at 333 Hz was found. So, we are
confident that what is seen on 4 April only occurred above L'Aquila and not
elsewhere.</p>
      <p id="d1e2771">Interestingly, on 11 February 2009, a similar signal, characterized by lower
(<inline-formula><mml:math id="M167" display="inline"><mml:mrow><mml:mo>∼</mml:mo><mml:mn mathvariant="normal">60</mml:mn></mml:mrow></mml:math></inline-formula> %) <inline-formula><mml:math id="M168" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϵ</mml:mi><mml:mi mathvariant="normal">rel</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula> and comparable polarization, was
observed on both electric and magnetic field components. Despite the
direction of <inline-formula><mml:math id="M169" display="inline"><mml:mi mathvariant="bold-italic">S</mml:mi></mml:math></inline-formula> confirming that this signal also comes from the ground
(<inline-formula><mml:math id="M170" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">ϑ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">154.6</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="M171" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="italic">φ</mml:mi><mml:mn mathvariant="normal">2</mml:mn></mml:msub><mml:mo>=</mml:mo><mml:mn mathvariant="normal">6.4</mml:mn><mml:msup><mml:mi/><mml:mo>∘</mml:mo></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math></inline-formula>, nothing can be speculated as to its physical causes
in this case. In fact, first of all, it is characterized by different solar
activity conditions, with Sym-H between 40 and 50 nT, and AE between 150 and
200 nT. Last but not least, the satellite orbit was diurnal. Hence, to be
consistent with our cell division method, 11 February 2009 cannot be compared
to our quiet background or to the 4 April 2009 case event. In any event, its
peculiar characteristics need to be investigated in a companion paper
containing a statistical approach.</p>
      <p id="d1e2842">The analysis of the 4 April 2009 event showed that only through a
multi-instrumental and multi-disciplinary approach can a reliable
disentanglement of the earthquake effects from changes due to the physical
processes that govern the ionosphere dynamic and natural EME be obtained.</p>
      <?pagebreak page1491?><p id="d1e2845">This work could be considered as a suggested analysis approach for the
forthcoming scientific phase of the first CSES mission (launched in February
2018, and still in the commissioning phase) aiming to reduce the lack of
knowledge of lithosphere–ionosphere coupling. As soon as further
applications, performed on different seismic events, reach the expected
reliability, the proposed method could be used to compute the global
background level (with 1 squared degree of resolution) for a direct real-time
comparison of CSES in-flight data.</p>
</sec>

      
      </body>
    <back><notes notes-type="dataavailability">

      <p id="d1e2853">The DEMETER mission data can be downloaded at
<uri>http://demeter.cnrs-orleans.fr/</uri> (last access: 25 October 2018), according to the user type as
expressed in the website. The INTERMAGNET data can be downloaded at
<uri>http://www.intermagnet.org/</uri>  (last access: 25 October 2018). The ALIF data analysis tool is freely
available at <uri>http://www.cicone.com/</uri>  (last access: 25 October 2018).</p>
  </notes><notes notes-type="competinginterests">

      <p id="d1e2868">The authors declare that they have no conflict of
interest.</p>
  </notes><notes notes-type="sistatement">

      <p id="d1e2874">This article is part of the special issue “Dynamics and
interaction of processes in the Earth and its space environment: the
perspective from low Earth orbiting satellites and beyond”. It is not
associated with a conference.</p>
  </notes><ack><title>Acknowledgements</title><p id="d1e2880">The authors thank Fabrizio Capaccioni for useful scientific discussion and
comments. The authors want to thank the CNES teams in charge of the DEMETER
project and its in-flight operations, and Dominique Lagoutte, Jean-Yves Brochot,
and Stephanie Berthelin for their remarkable work at the DEMETER Science Mission
Centre. The results presented in this paper rely on the data collected at
L'Aquila. We thank INGV (Istituto Nazionale di Geofisica e Vulcanologia) for
supporting its operation and INTERMAGNET for promoting high standards of
magnetic observatory practice (<uri>http://www.intermagnet.org/</uri>, last
access: 25 October 2018). The authors also thank the Italian Space Agency
(ASI) for the financial support under contract ASI “LIMADOU scienza” no.
2016-16-H0.<?xmltex \hack{\newline}?><?xmltex \hack{\newline}?> Edited by: Georgios
Balasis<?xmltex \hack{\newline}?> Reviewed by: Angelo De Santis and one anonymous
referee</p></ack><ref-list>
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    <!--<article-title-html>Electromagnetic field observations by the DEMETER satellite in connection with the 2009 L'Aquila earthquake</article-title-html>
<abstract-html><p>To define a background in the electromagnetic emissions above seismic
regions, it is necessary to define the statistical distribution of the wave
energy in the absence of seismic activity and any other anomalous input (e.g.
solar forcing). This paper presents a completely new method to determine both
the environmental and instrumental backgrounds applied to the entire DEMETER
satellite electric and magnetic field data over L'Aquila. Our technique is
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filtering, Cicone et al., 2016; Cicone and Zhou, 2017; Piersanti et al.,
2017b). To evaluate the instrumental background, we performed a multiscale
statistical analysis in which the instantaneous relative energy
(<i>ϵ</i><sub>rel</sub>), kurtosis, and Shannon entropy were
calculated. To estimate the environmental background, a map, divided into
1° × 1° latitude–longitude cells, of the averaged
relative energy (<span style="text-decoration: overline;"><i>ϵ</i><sub>rel</sub></span>), has been constructed,
taking into account the geomagnetic activity conditions, the presence of
seismic activity, and the local time sector of the satellite orbit. Any
distinct signal different (over a certain threshold) from both the
instrumental and environmental backgrounds will be considered as a case event
to be investigated. Interestingly, on 4 April 2009, when DEMETER flew exactly
over L'Aquila at UT&thinsp; = &thinsp;20:29, an anomalous signal was observed at 333&thinsp;Hz
on both the electric and magnetic field data, whose characteristics seem to
be related to pre-seismic activity.</p></abstract-html>
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