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\begin{document}

\title{Fluid-induced anthropogenic and natural earthquake swarms driven by
aseismic slip}



\author[1,1,1]{Philippe DANRE}%
\author[2,2,2]{Louis De Barros}%
\author[3,3,3]{Frédéric Cappa}%
\author[4,4,4]{Jean-Paul Ampuero}%
\affil[1]{Géoazur}%
\affil[2]{Université Côte d'Azur, CNRS, Obervatoire de la Côte d'Azur, IRD, Géoazur}%
\affil[3]{Université Côte d'Azur, CNRS, Observatoire de la Côte d'Azur, IRD, Géoazur}%
\affil[4]{Institut de Recherche pour le Développement}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
Anthropogenic fluid injections at depth induce seismicity which is
generally organized as swarms, clustered in time and space, with
moderate magnitudes. While some similarities between swarms have already
been observed, whether they are driven by the same mechanism is still an
open question. Pore fluid pressure or aseismic processes are often
proposed to explain observations, while recent models suggest that
seismicity is triggered by fluid-induced aseismic slip. Using 22 natural
and anthropogenic swarms, we observe that duration, migration velocity
and total moment scale similarly for all swarms. This confirms a common
driving process for natural and induced swarms and highlights the
ubiquity of aseismic slip. We propose a method to estimate the
seismic-to-total moment ratio, which is then compared to a theoretical
estimation that depends on the migration velocity, the effective stress
drop and the slip velocity. Our findings lead to a generic explanation
of swarms driving process.%
\end{abstract}%



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\emph{Geophysical Research Letters}

Supporting Information for

\textbf{Fluid-induced anthropogenic and natural earthquake}

\textbf{swarms driven by aseismic slip}Philippe
Danr\selectlanguage{ngerman}é\selectlanguage{english}\textsuperscript{*}, Louis de Barros, Frederic Cappa, Jean-Paul
Ampuero

\selectlanguage{english}\textsuperscript{*}To whom correspondence should be addressed;
E-mail:\emph{danre@geoazur.unice.fr}

\textbf{This document includes:}

Supplementary Text S1 to S5 Figs. S1 to S3 Tables S1

\textbf{Other Supplementary Materials for this manuscript include the
following:}



\section*{Introduction}

{\label{introduction}}

This Supplementary Material presents information about the data used in
our study, the methods chosen to estimate the parameters of interest as
well as their limits, and additional figures to help the understanding
of the paper.

Text S1. Data

In our study, we used datasets of earthquake swarms from natural and
injection-induced origins. Among all the swarms available, we did not
consider swarms associated with volcanic activity as they might involve
more complex processes (magma circulation, high temperature effects,
etc.). We also focus on swarms with suspected fluid-driven processes,
excluding swarms that are thought to be purely driven by slow-slips.
Furthermore, we did not consider ``complex'' swarms, i.e. swarms with
several phases of activity (bursts of seismicity separated by periods of
quiescence for instance) or with several faults involved, as it would
make our assumptions for parameter estimations less reliable. We limited
our work to simple swarms, with well-located events on a planar
structure. Studying complex swarms with our methods could be done by
decomposing them into more simple subsets.

The data required for our study only consists in standard earthquake
catalogs, which contain origin time, localization and magnitude. For the
Soultz 2004 and Cahuilla swarms,~we do not have a moment magnitude but
only a local magnitude. We assumed, following \emph{(} Edwards and
Douglas, 2014\emph{)} that for the first case Mw=Ml-0.2 while we use the
relation in Hawthorne et al. (2017) for the Cahuilla swarm.

For some of the swarms studied, the largest event static stress drop
value was available in the literature. In this case, we used this value
in our work. Otherwise, we assumed a default value of 10MPa.

Some of the sequences have incomplete data. Indeed, for the Soultz 1993
and 1995 swarms, instrumental deficiencies lead to gaps in seismicity.
However, given the small temporal duration of those gaps
(\textless{}10\% of the total duration), we chose not to correct for
them, and consider the missing seismic moment as negligible at first
approximation.

Text S2. Description of the data used.

We briefly describe below the datasets used, the context of injection or
of seismic activity as well.

\textbf{Basel, Switzerland :} In 2006 a fluid injection took place in
the underground of the city of Basel, in Switzerland. It aimed at
developing an Enhanced Geothermal System (EGS). More than 11,000 cubic
meters of fluids were injected at a depth of around 5km, during 6 days.
After an intense seismic activity, the injection was stopped. Despite
that, a Ml=3.4 event took place a few hours after well shut-in, and
seismicity was still intense a few days after that. Mainshock stress
drop has been to 2MPa (Goertz-Allmann et al., 2011). In our work, we use
the relocated catalog from Herrmann et al., 2019.

\textbf{Soultz-Sous-Foret, France~:} The 1993, 1995, 1996, 2000, 2003,
2004 Soultz-Sous-Foret fluid injections took place in Alsace, France.
Those injections also aim at developing a deep geothermal system. Using
several well with time, GPK1-4, injections of 9400 (in 2004) to 37000
(in 2003) cubic meters took place at about 5km, during 4 to 15 days. The
largest earthquake induced range from Mw=0.8 for the 1993 sequence to
Mw=2.9 for the 2003 sequence. Data for those sequences are provided by
the CDGP services
(\emph{https://cdgp.u-strasbg.fr/geonetwork/srv/fre/catalog.search\#/home}).

\textbf{Rittershoffen :} In June 2013, an hydraulic stimulation took
place in Eastern France at a depth of 2580m. It lasted 2 days, and lead
to a few hundreds of events, separated into two phases both temporally
and spatially (Lengline et al., 2017). We consider both phases as
injection-induced sequences, but analyze them independently. We get
migration velocities of 251m/day and 1161 m/day, over durations of 0.48
and 0.05 days respectively.

\textbf{ST1, Finland~:} This fluid injection is the most recent of our
dataset. It took place in June and July 2018 during 49 days. The goal
was to control the injection parameters in order to mitigate the
associated risk. A volume of fluids of more than 18,000 cubic meters was
injected at a depth of around 6.1 km. It led to several events of
magnitude greater than 1 and one of magnitude 1.9. The value of the
largest event static stress drop (taken as 20MPa) and the earthquake
data comes from \emph{(} Kwiatek et al., 2019\emph{)} .

\textbf{Paralana, Australia~:} This injection took place at about 4km
below the surface, in the South of Australia, in July 2011. More than
3,000 cubic meters of fluids were injected to create a geothermal
reservoir. The induced seismicity presented a mainshock with a magnitude
of Mw=2.5.~ The data are provided by J. Albaric (Albaric et al., 2014)
and the static stress drop value for the biggest earthquake is 1.8MPa
(\emph{Pers. Communication} . \emph{from J. Albaric} ).

\textbf{Cooper Basin, Australia :} In 2003, an injection was performed
in the Cooper Basin injection site in Australia. During
\textasciitilde{}45 days, 20000 cubic meters of fluids were injected at
a depth of \textasciitilde{}4250m in the granitic crust, during two
phases. We only consider here the seismicity between 29/11/2003 and
22/12/2003.

In 2012, around 34000 cubic meters of fluids were injected during two
injections (a small one then the main one) in a new well, at
\textasciitilde{}4000m depth. We focus here only on the main injection,
going on from 17/11/2012, with around 20000 events.

The data for Cooper Basin come from the EPOS repository
(\emph{https://tcs.ah-epos.eu/\#episodes}:).

\textbf{Paradox Valley, USA :} This sequence is one of the longest
injection-induced seismic sequence, as injection activities in this area
of the Colorado began in 1985. About 7.7 million cubic meters have been
injected at a depth between 4 and 5 km. This tremendous injection lead
to several Mw\textgreater{}4 earthquakes like in May 2000 and January
2013. Yeck et al., 2015 estimate the largest event static stress drop as
being 5MPa.

\textbf{Corinth, Greece :} The Gulf of Corinth is an extension zone
prone to earthquake swarms. The swarm considered here occurred in 2015
and lasted 10 days, with a magnitude culminating at 2.5. The data used
come from De Barros et al., 2020.

\textbf{Ubaye, France :} This earthquake swarm began in 2003 in the Alps
region in France. It lasted 2 years. The data used is an earthquake
catalog of relocated events from Daniel et al., 2011 of more than 1,000
events (more than 16,000 were initially detected by (enatton et al.,
2007).

\textbf{Crevoux, France :} This small swarm also occurred in the Alps
region, in 2014, just near the Ubaye Valley. It took place during the
aftershock sequence of the 07/04/2014 Barcelonette earthquake (Ml=4.8),
6km North of the main cluster of seismicity (De Barros et al., 2019)

\textbf{SWX, Iceland~:} The Husavik--Flatey Fault has experienced
numerous earthquake swarms (Passarelli et al., 2018). From Passarelli's
study, we considered 3 swarms, in 2001, 2008 and 2013, taking place in
different zones of the same transform fault. We chose those swarms among
the other swarms they studied because of their spatial and temporal
simplicity (Passarelli et al., 2018).~\textbf{Cahuilla, USA~:} Similarly
to the Ubaye swarm, this swarm is unexpectedly long, lasting more than 2
years and with a highest magnitude of Mw=4.4. It took place near the San
Jacinto fault, an area prone to earthquake swarms. Composed of more than
19000 events, the catalog from Ross et al., 2020 was used here.

Text S3. Migration velocity of the swarms

In our study, we estimate the migration velocity of the swarms using the
same methodology for both natural and injection-induced sequences.
Indeed, if for the latest the injection location can be known and used
as the origin for distance computation, it is not available for natural
swarms. We therefore decided to take as a spatial origin the median of
the coordinates of the first 10 events. Indeed, those 10 first events
can be considered close spatially and temporally to the injection point
given that hundreds or thousands of events will then migrate from there.

With this spatial origin, and taking the occurrence time of the first
event as the t=0s reference, we compute the distance and time of each
event. We define the migration front of the swarms based on the
90\textsuperscript{th} percentile of distance bins with time. Indeed,
some events, likely background seismicity or mislocated events, occurred
isolated at large distances early in the swarm. Choosing the
90\textsuperscript{th} percentile of distance allows us not to take into
account those events for the migration velocity computation. For the ST1
swarm velocity fitting, we removed the events happening at a
\textgreater{}750m distance very early in the swarm, as they do not seem
triggered by the same mechanisms as the other events. The percentiles
were computed over sliding 50 events bins, to get a reliable estimate of
the position of the seismicity front with time.

For each swarm, we empirically defined a migration period. Indeed, in
the case of injection-induced swarms, the seismicity front migration
decelerates when the injection is stopped. It is likely to be the case
for natural earthquake swarms, but the injection duration is unknown in
this case. As we did not find a criterion for natural and
injection-induced swarms to separate the migrating and non-migrating
part and avoid a bias in the fitting, we empirically defined the
migration period as the time during which the migration front
propagates. In all cases, this period lasts most of the swarm.

Over the migration period, we then just performed a linear regression
over the 90\textsuperscript{th} percentiles of distance with time. The
value of the slope is the migration velocity of the swarm. We do not
force the fit of the seismic front to pass by the origin~as 1) the
injection might not be purely punctual, but may originate from a 1D/2D
structure, such as an open borehole and 2) the origin time is
arbitrarily fixed to occurrence time of the first event time, but the
injection might have started before.

This method allows us to get an average migration velocity for all
swarms.

We added, on Figure 2, some data from literature. Those sequences come
from Kim et al., 2013; Seeber et al., 2004; Duverger et al., 2015~;
Yoshida et al., 2018~; Duboeuf, 2018.

Text S4. Effective stress drop

Following Fischer et Hainzl, 2017, we compute the effective stress drop
of the studied seismic sequences. Some catalogues (Rittershoffen) do not
have moment available. In this case, we did not consider them in the
computation of the effective stress drop or further for the total moment
estimation.

The effective stress drop is defined following the same formalism as the
static earthquake stress drop, but at the scale of the swarm and not of
the individual earthquake. Therefore, it depicts the cumulative seismic
moment release over the seismicity area to the power 3/2 (see Equation
S1).~ Effective stress drops are usually lower than classical values of
static earthquake stress drop (1-10 MPa). A low effective stress drop
value indicates a low seismic moment release on a large seismicity area,
and therefore a strong aseismic deformation.~ On the contrary, an
effective stress drop value that gets close to an earthquake one
indicates that most of the slip is seismic. We here do not focus on the
possible time variations of the effective stress drop during the swarm
but on its final value.

To compute the effective stress drop, we use a similar method as in
Fischer et Hainzl, 2017. First, given a set of hypocenters in 3D, we
remove the few points too far away from the rest of the seismicity.
Then, using a least square fitting method, we find the best plane
fitting the 3D distribution of the events.~ Assuming that all events
occured on a single fault, we then project the hypocenters on this
plane, and after removing once again the points too far away, we compute
the area of seismicity using a Convex Hull.

Note that it is important to remove the outliers as (i) they could bias
the plane fitting and (ii) they can lead to an overestimation of the
seismicity area and radius (especially given that to compute the
effective stress drop we need a cubic power of the radius).

We then sum the seismic moment of the events within the area, and
compute a radius by assuming the area of seismicity is circular,
following :

\begin{equation}
R=\sqrt{S/\pi}\nonumber \\
 \end{equation}

The effective stress drop [?]\selectlanguage{greek}σ\selectlanguage{english}e is given by (24) following :

\(\selectlanguage{greek}\text{Δσ}\selectlanguage{english}_{e}=\frac{16*M_{0,seismic}}{7*R^{3}}\) (Equation S1)

where \(M_{0,seismic}\)~ is the cumulative seismic moment. We find
similar values to the ones previously determined by \emph{(24),} ~like
0.95 MPa and 3 MPa for Basel, or 0.36 MPa and 0.34 MPa for Soultz 2000
(our analysis and Fischer et Hainzl, 2017 respectively\emph{)} Those
differences can come from the difference in the catalogs used (i.e.
differences in cumulative moment values, localization of the events,
etc.) or from the implemented methods.

Text S5. Total moment

To compute the total moment, we consider the slip\(\mathbf{D}_{\mathbf{\max}}\) over
the main event asperity. We compute\(\mathbf{D}_{\mathbf{\max}}\) based on the main
event moment and stress drop. We neglect the afterslip given that
aseismic slip represents only \textasciitilde{}20\% of the slip
occurring over the seismically slipping area for simulations of small
repeating earthquakes (Chen et Lapusta, 2009). Therefore, we can still
get the good order of magnitude for the slip occurring over the
seismically slipping area by not considering aseismic slip.

On Figure 4 in the main text, the indicative black lines were computed
assuming a G value of 30GPa and \(V_{\max}/n\ \)values
of\(10^{-9},\ 10^{-8}\ \text{and\ }10^{-7}\)m/s values. To see the influence of the value of G
on the estimated values of \(V_{\max}\ \) we plot below the same
figure but with G=15GPa. Despite a lateral shift, we still find similar
values, consistent, for \(V_{\max}/n\).

\section*{Fig. S1.}

{\label{fig.-s1.}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure S1 :} Map with the locations of the swarms studied.
Symbols and color are the same as in the main manuscript. When swarm
location is redundant, only one symbol is represented.



\section*{Fig. S2.}

{\label{fig.-s2.}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure S2 :} Area computation in the case of the Cooper Basin
sequence. After removing the too far away points (none here), area is
computed using a Convex Hull algorithm, which computes the smallest
convex envelope that encloses all the seismic events, projected on the
best-fitting fault plane.

\section*{Fig. S3.}

{\label{fig.-s3.}}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure S3:} Seismic to total moment ratio as a function of the
product of the swarm migration velocity and its effective stress drop.
Here a value of G=15GPa is assumed.

\section*{Table S1.}

{\label{table-s1.}}\selectlanguage{english}
\begin{longtable}[]{@{}lllllll@{}}
\toprule
\textbf{Name} & \textbf{Data source} & \textbf{Migration duration
(days)} & \textbf{Velocity (m/day)} & \textbf{Seismic moment
(N.m)\textsuperscript{*}} & \textbf{Effective stress drop (MPa)} &
\textbf{Ratio of seismic to aseismic moment}\tabularnewline
\midrule
\endhead
Basel (BAS) & Herrmann et al., 2019 & 6.7 & 81 & 2.6E14 & 0.95 &
0.97\tabularnewline
Soultz 1993 (SZ93) & \emph{EOST \& GEIE EMC. (2017), CSMA;} Bourouis and
Bernard, 2007 & 15.5 & 48 & 2.2E11 & 0.0006 & 0.003\tabularnewline
Soultz 1995 (SZ95) & \emph{EOST \& GEIE EMC. (2017), CSMA;} Gerard et
al., 1997 & 11.6 & 18 & 1.5E11 & 0.001 & 0.01\tabularnewline
Soultz 1996 (SZ96) & \emph{EOST \& GEIE EMC. (2017), CSMA;} Gerard et
al., 1997 & 2.1 & 122 & 2.6E11 & 0.001 & 0.01\tabularnewline
Soultz 2000 (SZ00) & \emph{EOST \& GEIE EMC. (2018),} Cuenot et al.,
2008 & 7.3 & 37 & 2.1E14 & 0.37 & 0.34\tabularnewline
Soultz 2003 (SZ03) & \emph{EOST \& GEIE EMC. (2018),} Calo and Dorbath,
2013 & 17.9 & 67 & 2.1E14 & 0.06 & 0.07\tabularnewline
Soultz 2004 (SZ04) & \emph{EOST \& GEIE EMC(2018);} Dyer et al., 2004 &
2.4 & 151 & 5.6E13 & 0.54 & 0.47\tabularnewline
Paralana (PAR) & Albaric et al., 2014 & 6.0 & 39 & 8.9E13 & 0.03 &
0.16\tabularnewline
ST1 & Kwiatek et al., 2019 & 47.3 & 2.0 & 2.4E13 & 0.04 &
0.05\tabularnewline
Cooper Basin 2003 (CB03) & Baisch et al., 2006 & 11.6 & 47 &
1.1\textsuperscript{E}15 & 0.36 & 0.15\tabularnewline
Cooper Basin 2012(CB12) & Baisch et al., 2015 & 15.8 & 74 & 1.2E15 &
0.47 & 0.39\tabularnewline
Paradox (PRX) & \emph{US Bureau of Reclamation} & 8815 & 1.7 & 1.3E16 &
0.007 & 0.02\tabularnewline
Ubaye (UBY) & Daniel et al., 2011 & 658 & 6.0 & 1.7E14 & 0.001 &
0.005\tabularnewline
Corinth 2001 & Duverger et al., 2018 & 150 & 18 &
3.2\textsuperscript{E}15 & 0.08 & 0.07\tabularnewline
Corinth 2015 (CRT) & De Barros et al., 2020 & 5.0 & 105 & 1.4E14 & 0.97
& 0.54\tabularnewline
Crevoux (CRV) & De Barros et al., 2019 & 6.3 & 73 & 9.4E12 & 0.2 &
0.13\tabularnewline
SW2 & Passarelli et al., 2018 & 20 & 89 & 4.0E14 & 0.046 &
0.047\tabularnewline
SW4 & Passarelli et al., 2018 & 12.8 & 106 & 3.6E14 & 0.003 &
0.009\tabularnewline
SW6 & Passarelli et al., 2018 & 11.4 & 280 & 2.2E15 & 0.02 &
0.02\tabularnewline
Cahuilla (CHA) & Ross et al., 2020 & 1073 & 3.4 & 1.0E16 & 0.22 &
0.12\tabularnewline
\bottomrule
\end{longtable}

Table S1 : Results of our computations. * = Cumulative seismic moment
within the area determined for the effective stress drop. It might
differ from the cumulative seismic moment of the whole catalog.

\selectlanguage{english}
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