地震予知連絡会会報第 110 巻

11 － 62023 年 9 月発行

Instantaneous Tracking of Earthquake Growth With Elasto-Gravity Signals inJapan and Application to Historical Data from the Tohoku Oki Earthquake.
ROUET-LEDUC Bertrand (DPRI, Kyoto University)

Rapid and reliable magnitude estimation for large earthquakes (Mw >= 8) is key to mitigate the risk associatedwith strong shaking and tsunamis. Early warning systems based on seismic waves often fail to rapidly
estimate the size of very large earthquakes, and tend to saturate and be unable to distinguish between Mw 8earthquakes and Mw 9 earthquakes. GNSS-based approaches can provide better estimations, but suffer fromlarge uncertainties and latency associated with the slowness of seismic waves, and require to make a priori
constraints that may be diﬃcult to determine. The recently discovered speed-of-light Prompt Elasto-Gravity
Signals (PEGS) has raised hopes to overcome these limitations, but has never been tested for operational
early warning, in part to the very low signal to noise ratio they suffer from. In this research, PEGS is usedin real-time to track earthquake growth without delay once the event reached a certain magnitude. A deeplearning model is developed that leverages the information carried by PEGS recorded by regional broadband
seismometers in Japan before P-waves. After training on a database of synthetic waveforms augmented with
empirical noise, the first example of instantaneous tracking of an earthquake source time function is presented
on real data. This model unlocks real time access to the rupture evolution of large earthquakes using a portionof seismograms that is routinely treated as noise, and could immediately be used to supplement existing
methods, by refining Mw estimates for very large earthquakes.
Because of the rarity of PEGS observations (they are only observed for very large earthquakes), PEGSNet istrained on a database of synthetic PEGS waveforms to which real noise recorded at each station in the seismic
network is added. The training database is made of 500,000 synthetic earthquake sources distributed along theJapanese megathrust, with location, strike and dip angles following the Slab2.0 model. Random magnitude
and rake angles are drawn. The Gutenberg-Richter distribution for Mw is deliberately not used, to avoid
sampling bias during training.
Random source time functions (STF) are generated using a model designed to mimic empirical laws andstatistical observations to produce three-component waveforms representing the source characteristics of all
expected large megathrust earthquakes along the Japanese subduction zone. Empirical noise recorded at eachstation is then added to the generated waveforms.
PEGSNet is a deep convolutional neural network (CNN) that combines convolutional layers and fully
connected layers in sequence (Fig. 1). Mw is time-dependent, therefore noted as Mw(t), and corresponds
to the equivalent time-integrated STF at a given time. In order for PEGSNet to learn Mw(t), it is given
the network-wide data for 300 seconds and is tasked with estimating Mw(t) at the end of this 300 seconds
window, that parses the data, as explained in Fig. 2.
Figure 3 summarizes the results on the synthetic test set (data the model has never seen in training) forestimating Mw(t) using PEGSnet. For each example in the test set, the end time of the input data is shiftedwith a time step of 1 s from the earthquake origin time (t=0) to t=315 s, and PEGSNet predicts Mw at each－ 465 －地震予知連絡会会報第 110 巻

2023 年 9 月発行

time step. In other words, a running time window of 315 s parses the data, and is fed to PEGSNet, that makes
its Mw(t) estimate for the end of the window.
In addition, PEGSNet makes a prediction only if at least 10 stations are active at a given time and a
successful prediction is defined as within ± 0.4 magnitude units from the ground truth. Figure 3a indicatesthat PEGSNet is able to track the moment released by earthquakes with final Mw above 8.5/8.6 with good
accuracy (above 90%) and low errors (below 0.25 in Fig. 3b), starting roughly after 40 s from origin time. For
earthquakes with final Mw between 8.1 and 8.6, early tracking of the moment release is more diﬃcult andonly the final Mw can be estimated (with accuracy around 75% and errors above 0.25) after 150 s from origin
time. Any predicted Mw below 8.1 is poorly constrained by the data. A conservative lower limit on PEGSNet
sensitivity to Mw is between 8.0 and 8.2.
In order to examine the time-dependent performance of PEGSNet more closely, Figure 3c shows all thepredictions (on the test set) associated with events with a final Mw of 9.0 ± 0.05. The system latency ofabout 30 s is related to the ten-station constraint and to the initial lack of PEGS sensitivity below Mw(t)=8.1.
However, after 40 s (when the true Mw is generally above 8.0 according to the STF database) PEGSNet isable to track the evolution of the moment release instantaneously as indicated by the mode of the distributionof the predictions. These results show that PEGSNet is able to exploit the key features of PEGS data: 1) PEGS
sensitivity to magnitude for large earthquakes allows the model to distinguish between a Mw = 8 and a Mw
= 9 earthquake and 2) the information about Mw is effectively propagated at the speed of light, which results
in instantaneous tracking of the moment release. Although P-wave triggering is needed at each station (andtherefore some latency in the system exists), the instantaneous information about the source (carried by PEGSat the speed of light) is readily available in the pre P-wave time window. This allows PEGSNet to estimate
Mw(t) with zero delay once the magnitude exceeds ~ 8.3.
PEGSNet has been tested on real data from the 2011 Mw=9.0 Tohoku-Oki earthquake (Fig. 4). The raw
seismograms are processed as described in Vallée et al.1 and fed to PEGSNet. As for the test set, a Mw
prediction is made at each time step starting at the earthquake origin time. Figure 4a shows the results ofthis retrospective analysis compared with a “true” STF calibrated against a variety of different data types2.
PEGSNet is able to instantaneously track the evolving moment release of the Tohoku earthquake, starting atabout 55 s from origin time when Mw is about 8.2. PEGSNet reaches a correct prediction of the final Mw
around 150 s when the rupture is over. Note that the predicted values are almost constant after 150 s, although
new stations are added to the input data until 176 s after origin time (Fig. 4c). This highlights the robustness ofthe prediction even with an incomplete dataset. Consistently with synthetic tests (Fig. 3), predictions after 55 s(corresponding to the time the earthquake reaches Mw ~ 8.3) provide robust snapshots of the evolution of thesource at that exact time because PEGS carries information about the source at the speed of light.
To assess the robustness of the model’s Mw estimation on the Tohoku data, a test is performed in which
the P-wave arrivals information is kept but the actual recorded waveforms in the pre P-wave time window
is substituted with noise, and the resulting prediction of Mw(t) never exceeds the lower sensitivity limit of
PEGSNet (i.e. 8.1) and remains constant at about 6.5, which provides a baseline value for noise.

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2023 年 9 月発行

PEGSNet requires few modifications to be implemented in real time. Predictions are fast to obtain, but somelatency may be introduced by the preprocessing step. The model relies on P-wave arrival times which areassumed to be known, but any existing triggering algorithms can be used before feeding the data to the model.
These results provide the first example of instantaneous tracking of moment release for large earthquakes
and promote PEGS data as a new class of observables for practical application in early warning systems,
which are intrinsically limited by the speed of P-waves. For this reason, to-be-developed holistic approaches
to EEWS that leverage the benefit of multiple data types may consider the advantage of including PEGS data.
In general, PEGSNET could come in complement to existing EEW warning systems, and would provide
additional and independent estimates for very large magnitudes. Moreover, PEGSNet could immediately prove
useful for tsunami early warning for which Mw estimation within a few minutes is vital.
This research has been published in:
Licciardi, A., Bletery, Q., Rouet-Leduc, B., Ampuero, J. P., & Juhel, K. (2022). Instantaneous tracking ofearthquake growth with elastogravity signals. Nature, 606(7913), 319-324.
ROUET-LEDUC Bertrand
Other references:
1.

Vallée, M. et al. Observations and modeling of the elastogravity signals preceding direct seismic waves,
Science, 358(6367), 1164-1168 (2017).

2.

Bletery, Q. et al. A detailed source model for the M w 9.0 Tohoku-Oki earthquake reconciling geodesy,seismology, and tsunami records. J. Geophys. Res. Solid Earth, 119, 7636-7653 (2014).

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地震予知連絡会会報第 110 巻○○年○月発行

2023 年 9 月発行

Figurearchitecture.
The Theinputinput
data forconsistsconsists
in a three
image ofimage
shape MN, where
Figure1 1| PEGSNet| PEGSNetarchitecture.
dataoneforexample
one example
in channela three channelof xshape
M xM
N, where M isisthethenumbernumber of
N isnumberof seismicstations.
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samplesandandN theis thenumberof seismicstations.
Only
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vertical component
the isinput
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forsimplicity.
simplicity.
Eachconvolutional
is composedof a convolutional
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witha ReLu (orange),
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with a ReLu
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layer(lightblue).
pooling(red) reduceeach dimensionof thefactor
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MaxMaxpoolinglayerslayers(red) reduceeach dimensionof the input
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Theofnumberof number offilters
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Thelastconvolutionalblock
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activationfunction),
withdropout(lightblue).
Theoutputlayer
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latitude(φ)
andlongitude(λ).
w(using a ReLu activation function), with dropout (light blue). The output layer estimates Mw, latitude (φ) and longitude (λ).

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地震予知連絡会会報第○巻
地震予知連絡会会報第 110 巻 2023 年 9○○年○月発行
月発行

Figure 2 | PEGSNet training strategy. a, The input data for one example consists in a three-channel image of shape M x N,
where M is the number of time samples and N is the number of seismic stations. Only the vertical component of the input data isdisplayed for simplicity. Each convolutional block is composed of a convolutional layer (yellow) with a ReLu activation (orange),a spatial dropout layer (light blue). Max pooling layers (red) reduce each dimension of the input data by a factor of two. The
number oftraining
filters usedstrategy.
in each convolutional
layer isindicatedfor clarity.
The last
convolutional
block is connectedimage
to denseof shape M x N
Figure 2 | PEGSNet
a, The input
datafor one
exampleconsists
in a three-channel
layers(purple)(usinga
ReLu
activationfunction),
withdropout(lightblue).
Theoutput
layer
uses
atanh
activation
functionwhere M is the number of time samples and N is the number of seismic stations. Only the vertical componentof the input datato predict values of Mw, latitude (φ) and longitude (λ). b, The value of the Huber loss is plotted as a function of epochs for theisplayed for simplicity. Each convolutional block is composed of a convolutional layer (yellow) with a ReLu activation (orange
training and validation sets. The red star indicates the epoch with the minimum value of the loss on the validation set and thespatial dropout
layer (lightblue).
poolingonlayers
dimensionof thefrom
input
data bydatabasea factor of two. Th
corresponding
modelis usedMaxfor predictions
the test(red)set andreducereal data.eachc, Data
from one example
the training
umber of filters
used component).
in each convolutional
is indicatedforclarity.
last convolutional
block
connected(verticalThe grey shadedlayer
area corresponds
to theinput
data forThePEGSNetshown in (a). T1 andT2 areisthe
beginning to dense layepurple) (using anda ReLu
activationfunction),
withdropout(lightblue).
Theoutput
layer
uses
atanh
activation
function to predi
end of the selected input window. During training, T1 is selected at random and T2= T1 + 315 s. d, Moment rate (blue) andMw(t) (darkthe selected(λ).
event.
the randomly
the correspondinglabel
alues of Mw, latitude(φ)grey)
andforlongitudeb, Given
The valueof theselected
Hubervalue
lossforisTplotted
as a functionof epochs
foris the training an
1 for this example,
at theend of thethe
selected
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compared withthe predicted
Mw estimatedPEGSNet in2), i.e.
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The(TredstarindicatesepochwithThis
theisminimumvalueof the loss
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seta andandused
the correspondin
fortraining.
model is used for predictions on the test set and real data. c, Data from one example from the training database (vertical componen

The grey shaded area corresponds to the input data for PEGSNet shown in (a). T1 and T2 are the beginning and end of the selectnput window. During training, T1 is selected at random and T2= T1 + 315 s. d, Moment rate (blue) and Mw(t) (dark grey) for telected event. Given the randomly selected value for T1 for this example, the corresponding label is Mw (T2), i.e. at the end of telected window. This is compared with the predicted Mw estimated by PEGSNet in a and used for training.
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地震予知連絡会会報第○巻

Figure 3Figure| Timelinessof Mwofestimationfrom fromPEGSPEGS
data.data.
Resultsof predictions
on onthethetesttestset.
3 | TimelinessMw estimation
Resultsof predictions
set.(a)(a)Model
Modelaccuracy
accuracy as
as a function
calculated
as asthethenumberof successful
predictions
dividedby the total
function ofof time
time andandMw.
Mw.ForForeacheachpixel
pixelininthe
theimage,
image,accuracyaccuracyis iscalculated
numberof successful
predictions
dividednumberof samples.
A prediction
is definedsuccessful
if theif distancewithwiththe groundtruth truth
is within±0.4 magnitudeunits. Dashedby the total
numberof samples.
A prediction
is definedsuccessful
the distancethe groundis within±0.4 magnitudelines indicates the average values of the ground truth Mw(t) for events with different final magnitude the lower limit of PEGSNet
units. Dashed lines indicates the average values of the ground truth Mw(t) for events with different final magnitude the lower
sensitivity is between 8.0 and 8.2. (b) Same as in (a) but the average residuals (|Mw[true]-Mw[pred]|) for each pixel are shown.
limit of PEGSNet
sensitivity
is between
8.0 and 8.2.for(b)allSame
as in (a)but test
the averagefor redeachline is the(c) Probability
densityof Mw predictions
the eventsin theset with residuals
true final(|Mw[true]-Mw[pred]|)Mw of 9±0.05. The solid
pixel aremodeshown.
(c)
Probability
densityofMw
predictions
foralltheevents
inthetest
setwithtruefinalMwof9±0.05.
The and theof the distribution. The red dashed lines bound the 95-25 interquartile range. The white lines are the mean (solid)solid red95-5
line interquartileis the mode rangeof the (dashed)distribution.
The
reddashedlines
boundthe95-25
interquartile
range.
The
whitelines
aretheof the ground truth.
mean (solid) and the 95-5 interquartile range (dashed) of the ground truth.

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地震予知連絡会会報第 110 巻

2023 年 9 月発行

Figure 4 | Instantaneous moment tracking of the 2011 Mw=9.0 Tohoku-Oki earthquake. (a) PEGSNet Mw(t) predictions
are represented by the mean (solid blue line) and one standard deviation (dashed blue lines) of the posterior distribution of thepredictions at each time step. Predictions are displayed only if ten stations are available at a given time. The source time function
4 | Instantaneous
momenttracking
the 2011(a) PEGSNetpredictions
areofFigure
the Tohoku-Oki
earthquake(orangeline) isoftaken
fromMw=9.0
Bletery Tohoku-Oki
et al.2. (b) andearthquake.
(c), PEGSNet
input dataMw(t)(verticalcomponent)
atrepresentedtime steps of54and176s
respectively.
Thetoppanels
show
thewaveform
ofthelaststations
includedintheinput
dataattheby the mean (solid blue line) and one standard deviation (dashed blue lines) of the posterior distribution of thecorresponding time step.
predictions at each time step. Predictions are displayed only if ten stations are available at a given time. The source time functionof the Tohoku-Oki earthquake (orange line) is taken from Bletery et al.2. (b) and (c), PEGSNet input data (vertical component)
at time steps of 54 and 176 s respectively. The top panels show the waveform of the last stations included in the input data at thecorresponding time step.

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