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 ( Edwards and Douglas, 2014) 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 (<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.
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.
Soultz-Sous-Forêt, France : The 1993, 1995, 1996, 2000, 2003, 2004 Soultz-Sous-Forêt 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 (https://cdgp.u-strasbg.fr/geonetwork/srv/fre/catalog.search#/home).
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 (Lengliné 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.
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 ( Kwiatek et al., 2019) .
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 (Pers. Communication . from J. Albaric ).
Cooper Basin, Australia : In 2003, an injection was performed in the Cooper Basin injection site in Australia. During ~45 days, 20000 cubic meters of fluids were injected at a depth of ~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 ~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 (https://tcs.ah-epos.eu/#episodes:).
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>4 earthquakes like in May 2000 and January 2013. Yeck et al., 2015 estimate the largest event static stress drop as being 5MPa.
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.
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).
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)
SWX, Iceland : The Húsavík–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). 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 90th 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 90th 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 >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 90th 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 ∆σe is given by (24) following :
\(\text{Δσ}_{e}=\frac{16*M_{0,seismic}}{7*R^{3}}\) (Equation S1)
where \(M_{0,seismic}\)  is the cumulative seismic moment. We find similar values to the ones previously determined by (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) 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 ~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 \(V_{\max}/n\).