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\begin{document}

\title{Reanalysis of the ionospheric total electron content anomalies around
the 2011 Tohoku-Oki and 2016 Kumamoto earthquakes: Lack of a clear
precursor of large earthquakes}



\author[1,1,1]{Ryoya Ikuta}%
\author[1,1,1]{Ryoto Oba}%
\author[1,1,1]{Daiki Kiguchi}%
\author[1,1,1]{Tomoya Hisada}%
\affil[1]{Faculty of Science, Shizuoka University}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
We investigate the veracity of the reports by Iwata \& Umeno (2016,
doi:10.1002/2016JA023036) and Iwata \& Umeno (2017,
doi:10.1002/2017JA023921), both of which claimed that the observed
perturbations in GNSS-based ionospheric total electron content (TEC)
could serve as a ``precursor'' of large earthquakes based on correlation
analysis. Iwata \& Umeno (2016) defined a spatial correlation of
residuals between the observed and predicted TEC time series. They
reported that the correlation value is significantly larger before large
earthquakes than those observed during non-earthquake periods. Iwata \&
Umeno (2017), who applied the same method to other large earthquake,
claimed that the preseismic ionospheric disturbances can be
distinguished from other non-earthquake phenomena based on the small
percentage of area where the correlation value exceeds the criterion.
They also claimed that the low propagation velocity of the correlation
peaks is also a pre-seismic characteristic. Here we tested their claims
using a larger dataset. As a result, these three characteristics they
claimed to have captured as evidence of earthquake precursors are not
significant being frequently observed during normal (non-earthquake)
days. In addition to that, the criteria of Iwata \& Umeno (2017) cannot
be applied to the large earthquake discussed by Iwata \& Umeno (2016),
and vice versa. Therefore, we can find no basis for claiming that they
detected precursors to the earthquakes. The calculation procedure of the
correlation function shows that the value is more of an indicator that
amplifies small variations synchronized between nearby stations, like
medium-scale traveling ionospheric disturbances rather than earthquake
precursors.%
\end{abstract}%



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\selectlanguage{english}
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\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

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\emph{Journal of Geophysical Research}

Supporting Information for

\textbf{Reanalysis of the ionospheric total electron content anomalies
around the 2011 Tohoku-Oki and 2016 Kumamoto earthquakes: Lack of a
clear precursor of large earthquakes}

R. Ikuta\textsuperscript{1}, R. Oba\textsuperscript{1}, D.
Kiguchi\textsuperscript{1}, T. Hisada\textsuperscript{2}

1. Faculty of Science, Shizuoka University, 2. Graduate School of
Integrated Science and Technology, Shizuoka University

\textbf{Contents of this file}

Text S1 Figures S1 to S4

\textbf{Additional Supporting Information (Files uploaded separately)}

Caption for Movies S1 and S2

\textbf{Introduction}

Supplementary materials are composed of one body text, four Figures, and
one Movie that help readers understand the manuscript better.

Figure S1 shows a diagram of Iwata and Umeno 2016 drawn with our data,
confirming the reproducibility of the method.

In the text part Text S1, the calculation process of C(T) is described
in detail and its properties are explained. Figures S2 and S3 and the
Movies S1 and S2 are the material for this part.

Figure S4 shows the correlation between Kp index and C(T).

\textbf{* Text S1.}

This section supplements the procedure to calculate C(T) described in
the main text. First of all, for the central GNSS station and the 30
surrounding stations, the VTEC during the training period of 120 minutes
from T-135 minutes to T-15 minutes is approximated by septic function as
follows;

(S1)

in which VTEC(t) is the VTEC value at time \emph{t}
and\emph{y\textsubscript{pre}} (\emph{t} ) is the fitted septic
function, and\selectlanguage{greek}\emph{ε} \selectlanguage{english}is the fitting error. Then, the VTEC during the
prediction period is predicted by substituting \emph{t} = T-15 to T into
the obtained \emph{y\textsubscript{pre}} (\emph{t} ). Figures S2 and
Movies S1 show the VTEC(\emph{t} ) and \emph{y\textsubscript{pre}}
(\emph{t} ) calculated with the central station of 0214 and satellite
PRN26 for T = 5:20 on the day of Tohoku-Oki earthquake (same with Figure
S1). In this case, according to I\&U16, the training period is T-135 min
[?] t \textless{} T-15 min, the prediction period is T-15 min [?] t [?] T, and
the VTEC(\emph{t} ) - \emph{y\textsubscript{pre}} (\emph{t} ) of the
prediction period is anomaly X(\emph{t} ). The prediction
function\emph{y\textsubscript{pre}} (\emph{t} ) shows a pronounced
temporal variation, far from the natural extension of the VTEC of
training period, which may be the result of overfitting the faint
variation that appears during the training period (circled in the Figure
S3a). As a result, X(t) seems not to be an indicator of whether VTEC is
as predicted during the prediction period, but rather an indicator of
small fluctuations during the training period. Then, the correlation is
calculated between anomalies of the central GNSS station and its
surrounding 30 stations. The correlations are averaged over 30 station
pairs to be C(T) as expressed in Equation 1 in the main text. Figure
S2-b shows C(T) calculated with the PRN26 satellite and 0214 central
station. Movie S1 shows C(T) and temporal variation of VTEC(\emph{t} )
and \emph{y\textsubscript{pre}} (\emph{t} ) for various T for the 0214
central station. We can see how \emph{y\textsubscript{pre}} (\emph{t} ),
or \emph{X} (\emph{t} ), magnifies the faint VTEC change during the
training intervals. The large C(T) fluctuation corresponding to the
large X(t) variation means that the faint VTEC changes are coherent
between 30 stations in this case. The C(T) in Figures S2, S3 and Movies
S1, S2 show large oscillation with a period of about 15-20 minutes. This
oscillation period is about half of a typical MSTID period, reflecting
the fact that C(T) folds the negative side of the VTEC sinusoidal
variation, thus halving the period. Contrary to I\&Us' claim that C(T)
can extract VTEC variation of seismic origin, it is an indicator that
amplifies small fluctuations synchronized between nearby stations, such
as MSTID.\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
Figure S1. Reproduction test of Figure 1 and Figure 3 in I\&U16 using
the same satellite-central station pair as theirs. The central station
is Kitaibaraki (0214), the satellite is PRN26. The regression curves are
septic functions. (a) The day of Tohoku-Oki earthquake. The time of the
mainshock is indicated by the vertical line. (b) Forty days (DOY30), (c)
30 days (DOY40), (d) 20 days (DOY50), and (e) 10 days (DOY60) before the
earthquake. They are good reproductions of I\&U16.\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
Figure S2. C(T) calculation for the day of the Tohoku-Oki earthquake.
(a) Snap shot of training (green) and prediction (red) based on the
observed VTEC (black dots) at station 0214 for T = 5:20 UT (vertical
gray line) on March 11, 2011 (DOY70). The time of the mainshock is shown
with vertical black line. The polarities of the VTEC curvature are shown
with broken lines. (b) Calculated C(T) using the 31 stations with the
central station 0214.\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
Figure S3. Same as Figure S2 but for a non-earthquake day. (a) Snap shot
for T = 4:26 UT (Vertical line) on Feb. 19, 2011 (DOY50). VTEC variation
in the circle is supposed to be the cause of the oscillation of C(T)
(see text S1). (b) Calculated C(T) using the 31 stations with the
central station 0214.\tabularnewline
\bottomrule
\end{longtable}\selectlanguage{english}
\begin{longtable}[]{@{}l@{}}
\toprule
Figure S4. Histograms of hourly maximum C(T). (a) C(T) calculated for 14
non-earthquake periods (2:15-10:00 UT on DOY30, DOY31, DOY40, DOY49,
DOY50, DOY60, DOY63, DOY72 and DOY73 in 2011, DOY96 and DOY116 in 2016,
12:15-20:00 UT on DOY96 and DOY116 in 2016). Colors corresponds to Kp
indexes. (b) Normalized histogram of Figure S4a. Lines connecting bars
show boundary between Kp=1+ and 2-, and Kp=4 and 5-.\tabularnewline
\bottomrule
\end{longtable}

\section*{Caption for Movie S1}

{\label{caption-for-movie-s1}}

Movie S1. C(T) calculation movie corresponding to Figure S2 with time
range of 3:45 [?]T[?] 6:00.

\section*{Caption for Movie S2}

{\label{caption-for-movie-s2}}

Movie S2. Same with Movie S1 but corresponding to Figure S3 with time
range of 3:45 [?]T[?]5:38.

\textbf{Hosted file}

\verb`essoar.10506732.3.docx`  available at \url{https://authorea.com/users/549855/articles/607920-reanalysis-of-the-ionospheric-total-electron-content-anomalies-around-the-2011-tohoku-oki-and-2016-kumamoto-earthquakes-lack-of-a-clear-precursor-of-large-earthquakes}

\selectlanguage{english}
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\end{document}

