Fluid-induced anthropogenic and natural earthquake swarms driven by aseismic slip

Anthropogenic ﬂuid injections at depth induce seismicity which is generally organized as swarms, clustered in time and space, with moderate magnitudes. Earthquake swarms also occur naturally in diﬀerent tectonic contexts. While some similarities between natural and injection-induced swarms have already been observed, whether they are driven by the same mechanism is still an open question. Indeed, they are commonly related to ﬂuid pressure processes, while recent observations suggest the presence of aseismic slip driving seismicity. Based on such observations, we propose a simple model that combines ﬂuid and aseismic processes, in which seismicity is triggered by ﬂuid-induced aseismic slip. The model reconciles the seismicity migration observed in natural and anthropogenic swarms, and allows us to quantify the seismic-to-total moment ratio. By validating our approach using 22 earthquake swarms, both from natural and anthropogenic origins, our ﬁndings provide a generic explanation of the swarm driving


Introduction
Over the past 50 years, a number of studies have documented that fluid injection or extraction in subsurface reservoir formations can induce seismicity.These earthquakes can sometimes exceed magnitudes of 5 and have the potential to impact infrastructures and the public acceptance for geo-energy projects (Ellsworth, 2013;Keranen and Weingarten, 2018).The Rangely (US) experiment, conducted from 1969 to 1973, is one of the oldest and pioneering studies of seismicity caused by forced fluid injection (Raleigh et al., 1976).Another famous example is the 2006 Basel injection in Switzerland where 11.500 cubic meters of fluids were injected at about 5 km depth over the course of 6 days, leading to hundreds of earthquakes including a  =3.4 event just a few hours after the shut-in of the injection well was decided (Deichmann and Giardini, 2009).More generally, anthropogenic hydraulic injections are responsible for many seismic sequences, in association with geothermal heat reservoir development (Charléty et al., 2007;Albaric et al., 2014;Baisch et al., 2006;Kwiatek et al., 2019), hydraulic fracturing (Schultz et al., 2018), wastewater storage (Keranen et al., 2013), CO2 sequestration (Zoback and Gorelick, 2012) or, at a smaller scale, during controlled fault activation experiments (Guglielmi et al., 2015).This fluid-induced seismic activity is singular as it organizes as a swarm with earthquakes clustered in time and space with no distinguishable mainshock/aftershock pattern.
Interestingly, earthquake swarms are also found in nature in a diversity of geological contexts such as mountain ranges (Jenatton et al., 2007), rift zones (De Barros et al., 2020), subduction zones (Metois et al., 2016), along transform faults (Roland and McGuire, 2009), or in geothermal and volcanic areas (Hensch et al., 2008;Shelly et al., 2013).Fluids are thought to play a key role in those natural swarms, either because seismicity is associated temporally or spatially with fluid circulation (Montgomery-Brown et al., 2019;Kraft et al., 2006;Shelly et manuscript submitted to Journal of Geophysical Research : Solid Earth al., 2013) or because they share similarities with injection-induced sequences (Skoumal et al., 2015).Indeed, the propagation of a seismicity front has been observed in sequences of anthropogenic origin (Goebel and Brodsky, 2018;Goebel et al., 2016) as well as in natural swarms (De Barros et al., 2020;Ross et al., 2020).This seismicity migration can be attributed to fluid pressure diffusion (Shapiro et al., 1997), aseismic slip (Roland and McGuire, 2009), or a combination of both (De Barros et al., 2021), as well as cascading events (Fischer and Hainzl, 2021).Studying the seismic moment released spatially during natural and injection-induced sequences also revealed they behave in a similar way (Fischer and Hainzl, 2017).However, despite those numerous observations, the drivers of seismicity in natural and induced swarms are still unkown.
The importance of aseismic slip during earthquake swarms is supported by several observations and models.Recently, based on hydromechanical modeling of fluid injection in a fault, studies showed that the increase of the critical earthquake nucleation size (the minimum size of a slip zone required for self-sustained seismic slip) with increasing fluid pressure leads to aseismic slip (Cappa et al., 2019), which may outpace the diffusing pressure front (Bhattacharya and Viesca, 2019;Larochelle et al., 2021) and may trigger seismicity near its edges where shear stresses increase (Wynants-Morel et al., 2020).On the other hand, at first order, seismic moment is expected to scale with injected volume (McGarr, 2014).However, discrepancies to this scaling have been observed and can be explained by aseismic slip release (McGarr et Barbour, 2018;De Barros et al., 2019).This is in accordance with observations of aseismic slip using geodesy in the vicinity of a fluid injection site in the Brawley Basin (California) during an intense seismic swarm (Wei et al., 2015), with direct measurements of fault displacements during field injection experiments (Guglielmi et al., 2015), or indirectly by studying repeating earthquakes during the Soultz-Sous-Forêt (France) sequences associated with geothermal stimulation (Bourouis and Bernard, 2007;Lengliné et al., 2014).At the same time, natural manuscript submitted to Journal of Geophysical Research : Solid Earth swarms are also accompanied by aseismic slip release, as revealed by geodesy and slip inversions (Lohman and McGuire, 2007;Gualandi et al., 2017), or by studying dual velocity migrations and repeating earthquakes like during the 2015 swarm in the Gulf of Corinth (Greece) (De Barros et al., 2020).However, geodetic observations of aseismic slip associated with earthquake swarms remain rare and difficult to achieve, given the depth and low deformation rate of such sequences.Thus, important questions on the contribution of aseismic slip during swarm activity remain.
In this study, we aim at exploring if injection-induced seismic sequences and natural swarms may be explained by the same processes.We first explore the similarities between both types of swarms, which then allows us to introduce a simple but realistic framework to constrain the aseismic slip released.We finally propose a physical model, based on observations, in which both types of swarms are driven by aseismic slip, which in turn is triggered by a fluid pressure perturbation.

Natural and injection-induced catalogs
To explain the similarities between natural and injection-induced swarms, as well as their most remarkable features, we focus on a global dataset of 22 earthquake swarms, from either injection-induced or natural origin.For natural earthquake sequences, we focus on swarms in which fluid processes have been previously discussed.For example, we do not consider the swarm studied by Lohman and McGuire (2007) which is interpreted as driven solely by a slow slip event.Likewise, we do not consider swarms taking place near volcanoes or in subduction zones as they might involve different processes (Roman and Cashman, 2006).For simplicity, the injection-induced sequences studied here are limited to sites where there is only one main manuscript submitted to Journal of Geophysical Research : Solid Earth injection well and to swarms that present a simple geometry.The earthquake catalogs used are described in detail in the Supplementary materials (Text S2), but we present them briefly below (Figure 1).
The 8 natural swarms have diverse geological contexts.For instance, the 2003-2004 Ubaye (hereafter, named UBY) sequence (Jenatton et al., 2007) occurred in a near-zero strain-rate area in the southern French Alps, lasted ~2 years and comprised thousands of events (Daniel et al., 2011), while the 2014 Crevoux swarm lasted only one week and produced ~270 seismic events.
Most of the 14 injection-induced swarms we consider originate from geothermal exploitation.However, they span a wide range of characteristics, including the injected fluid volume and the injection depth.The Soultz-sous-Forêts (SZ) stimulations took place in 1993, 1995, 1996, 2000, 2003, and 2004 in Eastern France during a tenth of days, with injected volumes up to 37,000 m 3 along several distinct wells, each time inducing a prolific seismic response with hundreds of events or more (Bourouis and Bernard, 2007;Gerard et al., 1997;Cuenot et al., 2008;Calo and Dorbath, 2013;Dyer et al., 2004).Just nearby, the Rittershoffen seismic sequences were induced also by a hydraulic stimulation (Lengliné et al., 2017).The Paralana, Cooper Basin 2003 and 2012 injections (PAR, CB03, CB12) took place in Australia, and also exhibited an intense seismic activity associated with fluid injection (Albaric et al., 2014;Baisch et al., 2006;Baisch et al., 2015).Recently, the ST1 sequence in Finland corresponds to a control experiment aiming at mitigating the seismicity induced by fluid injection.In this case, 18,000 manuscript submitted to Journal of Geophysical Research : Solid Earth m 3 of fluids were injected during 49 days, leading to hundreds of events but successfully preventing the occurrence of earthquakes of magnitude greater than 2.0 (Kwiatek et al., 2019).
Finally, the Paradox Valley swarm (PRX) is induced by wastewater disposal, with several millions cubic meters of fluids injected since 1985 leading to a long-lasting earthquake activity with several events of magnitudes Mw>4 (Ake et al., 2005).

Migration velocity
The average migration velocity of each swarm is estimated by fitting the seismicity front with a linear model.The spatial origin of the swarm is chosen as the median of the hypocentral manuscript submitted to Journal of Geophysical Research : Solid Earth coordinates of the 10 first events.The origin time is defined as the time of the first event.
Migration duration is defined as the time during which the envelope of distance to the spatial origin increases continuously.We compute the seismicity front as the 90 th percentile of event distances in a sliding window containing 50 events (Figure 2).Seismicity fronts have been modelled by either a diffusive law, constant speed or more complex relationships (Goebel and Brodsky, 2018;De Barros et al., 2021).However, here, the shape of the migration is not investigated, as we only focus on estimating an average migration velocity, in order to make first-order comparisons among swarms.We fit a linear model over the seismicity front during the migration period of each sequence, leading to consistent and similar r² values compared to other classical migration models like pressure diffusion (Supplementary Figures S1 and S2).
This procedure yields an average migration velocity for each sequence.The complete migration fits can be found in the Supplementary materials.

Effective stress drop
Following the approach of Fischer and Hainzl (2017), the seismicity area is computed by fitting a 2D plane over the 3D distribution of hypocenters, after removing the few outliers in the catalogs but not in the swarm area.Hypocenters are then projected over the plane, and a convex manuscript submitted to Journal of Geophysical Research : Solid Earth hull is fitted to delineate and return the seismicity area S. We then compute the radius of the seismicity area, assuming it is circular at first order, with  = /.
By analogy with the moment-size relationship for circular ruptures, the effective stress drop of a swarm is defined as (Fischer and Hainzl, 2017): where  , is the cumulative seismic moment during the swarm.A low effective stress drop suggests seismic asperities are far apart, whereas values close to earthquake stress drops, typically around 1-100 MPa (Cocco et al., 2016), suggest that seismic asperities cover most of the slipping area.The former has been proposed to indicate a large contribution of aseismic slip during swarms (Fischer and Hainzl, 2017).

Total moment estimation
The total moment is defined as the sum of the seismic and aseismic moments.Aseismic slip quantification is difficult for injection-induced sequences because the associated deformations are small and extend over long durations, leading to small strain rates that are hard to observe.
The same issue affects natural swarms, in addition to the instrumental limitations, the distance between sensors and the source depth.For instance, during the Icelandic swarms, despite the substantial aseismic slip expected, no corresponding signal was detected on the neighboring GPS stations (Passarelli et al., 2018).
We propose a simple way to estimate, roughly, the amount of aseismic slip in a swarm in the absence of geodetic data.Studies of slow slip transients in subduction zones and on creeping faults have shown that the cumulative slip of repeating earthquake sequences equals the surrounding aseismic slip (Matsuzawa et al., 2004;Uchida, 2019).Based on recent works manuscript submitted to Journal of Geophysical Research : Solid Earth demonstrating that the migration front of seismicity can be directly triggered by the shear stress perturbation induced by aseismic slip (Cappa et al., 2019;Wynants-Morel et al., 2020; Figure 3), we make an analogy with slow slip transients.We suppose that the slip released seismically over discrete asperities equals the surrounding aseismic slip.We neglect the contribution of afterslip given that it represents only ~20% of the slip occurring over the seismically slipping area for simulations of small repeating earthquakes (Chen et Lapusta, 2009).Assuming that the asperity associated with the largest earthquake in the swarm only ruptures once, its slip gives an order of magnitude of the slip over the whole area.For each sequence, we isolate the largest event, with moment  , =       , assuming a circular rupture of radius   , a shear modulus G=30GPa (a conventional value for crustal rocks) and a static stress drop (Madariaga, 1976) of 10 MPa (unless a more precise value is provided in the literature, see Supplementary Materials), in order to compute the slip   over this asperity as (Madariaga, 1976): (2) Given that seismic moment is released over brittle asperities and aseismic slip is released in between them, we estimate the total moment over the seismicity area as: While the effective stress drop qualitatively indicates the importance of aseismic slip during a swarm, the rough quantification approach proposed here allows us to better constrain aseismic moment release for each sequence.

Seismic to total moment ratio
manuscript submitted to Journal of Geophysical Research : Solid Earth By considering the total (seismic and aseismic) slip is equivalent to a single slip event over a circular area of radius R and stress drop   (Figure 3), we have (Madariaga, 1976): The rupture velocity of a slow slip event is related to its stress drop and to its maximum slip velocity   by (Ampuero and Rubin, 2008;Rubin, 2008;Passelègue et al., 2020): where n is the ratio between the strength drop (peak minus residual stress) and the stress drop,   (initial minus residual stress).In several numerical simulations of slow slip, n~10 (Hawthorne and Rubin, 2013;Lambert et al., 2021).
We hypothesize that seismicity is triggered by fluid-induced aseismic slip.Therefore, the

Aseismic slip drives natural and induced swarms
The estimated velocities of the 22 swarms studied here range from a few meters per day, like for the Cahuilla swarm (Ross et al., 2020), to more than 1 km/day, like for the Rittershoffen sequence (Lengliné et al., 2017).Figure 4 shows the migration velocity V as a function of swarm duration T, for induced and natural swarms.We included velocity measurements from the literature for additional cases (Kim et al., 2013;Seeber et al., 2004;Duverger et al., 2015;Yoshida et al., 2018;Duboeuf, 2018).For the sake of comparison, we also show the migration velocity of slow slip events in subduction zones (Gao et al., 2012).For these events, velocities correspond to the propagation of aseismic slip, which is characterized either with geodesy (Schmidt and Gao, 2010) or with tremor migration (Bartlow et al., 2011;Ito et al., 2007).
manuscript submitted to Journal of Geophysical Research : Solid Earth  Gao et al., 2012).Filled triangles and pentagons represent injection-induced and natural swarms, respectively, for which we determined migration velocity and duration based on seismicity catalogs.Empty symbols represent migration velocities and durations directly taken from the literature (Kim et al., 2013;Seeber et al., 2004;Duverger et al., 2015;Yoshida et al., 2018;Duboeuf, 2018).Black line represents the best-fitting power-law relation between velocities and durations of natural and induced swarms (R² = 0.76).
Two main observations can be made.First, injection-induced and natural swarms follow the same scaling    , with  = . and  = . for each swarm subset, respectively.In addition to the other similarities discussed beforehand, the continuous scaling of velocity with duration for all swarms is direct evidence that both types of sequences, natural and injectioninduced, obey the same physics for all velocity ranges (from a few meters per day in the Ubaye and Cahuilla years-long sequences, to ~1100 m/day for Rittershoffen which barely lasts a day).
As anthropogenic seismicity is induced (though indirectly) by fluid injection (Bentz et al., 2020), this similar scaling suggests that natural swarms studied here are also a consequence of fluid pressure perturbations.
Second, the velocity-duration scaling is similar for swarms (  . ) and for the SSEs (  . ) reported by Gao et al. ( 2012), despite higher velocities for the latter, typically around 1 to 10 km/day.The small difference of scaling exponents can be explained by different velocity measurements methods for swarms and SSEs.The scaling similarity indicates that the migration of swarms globally behaves like the propagation of aseismic slip, supporting our assumption that Vrupt = Vmigr.The observed scaling for swarms,   . , is compatible with fluid pressure diffusion.However, a similar scaling is obtained for SSEs, which exhibit manuscript submitted to Journal of Geophysical Research : Solid Earth individual linear migrations (Houston et al., 2011) and are not directly driven by fluid diffusion.
Other mechanisms have been proposed to explain such scaling for SSEs, like a uniform stress drop or a uniform slip over the ruptured area (Ide et al., 2007).These mechanisms might also be valid for swarms, explaining then the observed continuum of characteristics (Figure 4).
Therefore, a general scaling compatible with diffusion does not imply that individual swarms are directly driven by fluid diffusion, but its similarity with SSE scaling suggests that swarm migration velocity behaves like an aseismic slip migration velocity.
The effective stress drop   for the swarms studied is found to range between 1 kPa and 1 MPa (Figure 5).Those values are lower than typical values of static stress drop for earthquakes, which usually range between 1 and 100 MPa (Cocco et al., 2016), and are more similar to the stress drop values of SSEs (Brodsky and Mori, 2007).Thus,   values may indicate an aseismic component in the swarm processes.For instance,   = 1 kPa for the Soultz-sous-Forêt stimulations (1993,1995,1996) could suggest an important aseismic moment release, while   = 1 MPa for the Basel injection might mean that aseismic slip is relatively less important in this case.  ranges are similar for natural and injection-induced sequences (Figure 5), indicating once again similar processes for both.Based on similar velocity-duration scaling and effective stress drop values, natural and injection-induced swarms appear to share the same driving processes, in which aseismic slip seems ubiquitous, like depicted on Figure 3.The seismicity front delineates the aseismic slip rupture front and the seismicity area corresponds to the aseismic slip area, in a similar way as tremors locations in SSEs zones delineate slip migration and area (Bartlow et al., 2011).
However, as suggested by the variability of   values, the aseismic contribution might be different from one swarm to another.

Aseismic contribution differs among swarms
manuscript submitted to Journal of Geophysical Research : Solid Earth Once the total moment  , for each swarm is computed (Equations 2 and 3), we compare it to the seismic moment released by using the seismic to total moment ratio r.A value of r close to 1 indicates that moment release is mainly seismic, while a low value shows that moment release is significantly aseismic.As shown in Figure 6a, r ranges from 0.001 to almost 1.For the Basel injection-induced sequence, r = 0.97, suggesting that aseismic deformation is low in this case, while for the Ubaye natural swarm, r = 0.005, indicating an important aseismic moment release.
For the Soultz 1993 sequence, despite an injected fluid volume of the same order of magnitude as in the Basel injection (Deichmann and Giardini, 2009), the cumulative seismic moment is 3 orders of magnitude lower than the Basel one.This can be explained by an important aseismic moment release (r ~ 0.001) during the Soultz sequence.Therefore, our computations seem to validate that the strong difference of seismic moment release for similar injected volumes observed for injection-induced earthquake swarms can simply reflect the amount of induced aseismic deformation (McGarr and Barbour, 2018;De Barros et al., 2019). , assuming G = 30 GPa (see Equation 8).
Interestingly, one can also note that the scaling of duration with estimated total moment (Figure 6b) seems to be close to 1:1, similarly to the scaling between event duration and aseismic moment observed for SSEs (Ide et al., 2007;Peng and Gomberg, 2010).This correlation is quite weak, but seismic moment versus duration does not exhibit such a scaling (Passarelli et al., 2018).Our total moment estimate accounts for the "hidden" aseismic slip release occuring during swarms : in the compilation of duration versus moment observations by Peng and Gomberg (2010), many swarms have much longer duration than expected for slow slip events 20 manuscript submitted to Journal of Geophysical Research : Solid Earth whose aseismic moment equals the swarm's cumulative seismic moment.This difference can be explained if the aseismic moment contribution in swarms, which has not been accounted for, is significant.
Using Equation 8, we can relate the seismic to total moment ratio to two observables, the effective stress drop and migration velocity (see Figure 6c).We estimate   / being between   and   m/s, which corresponds to   values consistent with expected orders of magnitudes (Roland and McGuire, 2009;Glowacka et al., 2001) if we consider a value of n~10 (Hawthorne and Rubin, 2013;Lambert et al., 2021).Variability in   explains why the observed scaling between  and   *   is not as linear as expected.
As the general trend shows a scaling different than the isovalues of Vmax/n, it means that Vmax also depends, through fault and stress properties, on the seismic-to-total seismic ratio.

Discussion and conclusions
In addition to the numerous observations in the literature made on the similarities between natural and injection-induced earthquake swarms, our global analysis of both types of sequences helps to better understand the processes taking place during those phenomena.
Indeed, based on the velocity versus duration scaling continuity, the drivers of natural and anthropogenic swarms appear to be the same.Aseismic slip is a solid candidate to explain seismicity propagation, as it has already been observed for particular sequences of both types, but also as the scaling of migration velocity versus duration of swarms is similar to that of slow slip events (Figure 4).This is of particular interest given that for anthropogenic sequences aseismic slip is thought to have a significant importance in the relation between moment and injected fluid volume, on which anticipation of the seismic moment released is often based (McGarr and Barbour, 2018;De Barros et al., 2019).Therefore, it appears that the role of aseismic slip is not limited to slip release but might be responsible for the dynamics of swarms, through shear stress transfer at its tips triggering a migrating seismicity (Figure 3).Such a stress transfer originating from an aseismic slip zone and seismicity triggering has been observed in different contexts like in the Boso Peninsula in Japan where two SSEs lead to two earthquake swarms at their tips (Hirose et al., 2014).
As mentioned above, our migration velocity measurements return us average velocities, but some information might be left out.De Barros et al. ( 2021) indeed showed that seismic fronts have a complex time-dependent shape, revealing the seismogenic state of faults.However, we still get reliable results depicting the behavior of swarms, not on an individual but on a global scale.
If aseismic slip provides an explanation for the observations on swarms, making parallels with existing aseismic transients gives more information on its importance.Using observations made on repeating earthquake sequences, we were able to compute total (and therefore aseismic) moment released during swarms.While our quantification of total moment is rough and relies on several simplifying assumptions, we hope that further systematic study of relevant parameters like stress drop will help confirm our findings.Still, our results indicate that the importance of aseismic slip differs among swarms; even though it always drives seismicity, it can sometimes represent a small fraction of the deformation (like for the Basel case) or actually be the main slip mode (like for the Soultz 1993 sequence).Our approach overcomes the difficulties caused by the low and long deformations occurring during those sequences, preventing geodetic observations in most cases.
Based on the studies of slow slip events, we introduced a simple mechanical model to relate different observables (Equation 8).This allows to give a physical sense to their measurements and provides a first order physical approach to the slip dynamics during swarms.Further work manuscript submitted to Journal of Geophysical Research : Solid Earth on earthquake swarms might help identifying or better constraining the relevant parameters to model and understand in detail swarm dynamics.
Here, we also show that the slip velocity, together with the migration velocity and the effective stress drop, are the crucial parameters to characterize the seismic and aseismic moment partitioning in swarms.Among other properties, these three parameters depend on the stress state and on the proximity of the fault to failure (Hainzl and Fischer, 2002;Fischer and Hainzl, 2017;Passelègue et al., 2020;Wynants-Morel et al., 2020;De Barros et al., 2021).These relationships therefore deserve to be investigated in order to anticipate the swarm evolution, especially given that similarities are found between swarms and foreshock sequences of some major earthquakes (Chen and Shearer, 2013).
We here worked on catalogs selected for their simplicity (simple injection history and geometry) and removed from the analysis swarms from different contexts (e.g., subduction, volcanoes).However, we have reconciled observations made since decades on the two types of swarms, injection-induced and natural, by proposing a realistic scenario involving aseismic slip triggering seismicity, based on multiple observations made on 22 sequences.This opens interesting perspectives to better understand seismic swarms, their propagation, and improve their monitoring in order to anticipate potential large earthquakes.It also paves a way to studying natural and injection-induced swarms as the same phenomena.
manuscript submitted to Journal of Geophysical Research : Solid Earth by Z. Ross and D. Trugman (Ross et al., 2020)

Figure 1 .
Figure 1.World map of the location of studied seismic sequences.Pentagons indicate natural Figure 2. Distance-time plot of seismicity and average migration speed estimates for (A) Basel, seismicity front follows the aseismic slip front(Bhattacharya and Viesca, 2019;Wynants- Morel et al., 2020;De Barros et al., 2021) like observed with tectonic tremors migration and slow slip propagation in subduction zones(Bartlow et al., 2011).The migration velocity of the swarms is then equal to the rupture velocity of the aseismic slip (Vrupt = Vmigr).Our hypothesis and the previously discussed observations are summarized in Figure3.Combining Equations 4 and 5 we then have: to the following expression for the ratio r of seismic to total moment: the ratio of the cumulative seismic moment to total moment to the product of the migration velocity and the effective stress drop of the swarm.

Figure 3 .
Figure 3. Schematic view of the model considered here, based on observations and hypothesis

Figure 4 .
Figure 4. Scaling of propagation velocity with duration for swarms and slow slip events Figure 5. Seismicity area (m²) as a function of the cumulative seismic moment released during

Figure 6 .
Figure 6.(A) Seismic to total moment ratio, as a function of the seismic moment released . Data for the Soultz fluid injections are available on the CDGP web services (https://cdgp.u-strasbg.fr/).Data for the Cooper Basin injections are available on the EPOS platform (https://tcs.ah-epos.eu/).Data for the Paradox Valley fluid //www.usbr.gov/uc/progact/paradox/index.html).Rittershoffen data was made available by O. Lengliné(Lengliné et al., 2017).