・ 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;
in which VTEC(t) is the VTEC value at time t andypre (t ) is the fitted septic function, andε is the fitting error. Then, the VTEC during the prediction
period is predicted by substituting t = T-15 to T into the
obtained ypre (t ). Figures S2 and Movies S1
show the VTEC(t ) and ypre (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
< T-15 min, the prediction period is T-15 min ≤ t ≤ T, and the
VTEC(t ) - ypre (t ) of the prediction
period is anomaly X(t ). The prediction functionypre (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(t )
and ypre (t ) for various T for the 0214
central station. We can see how ypre (t ),
or X (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.