Parallel dynamics of slow slips and fluid-induced seismic swarms

Domain: earth_science
Published: 2024-10-17
Editorial outcome: minor_revision

Abstract
Earthquake swarms may be driven by fluids, through hydraulic injections or natural fluid circulation, but also by slow and aseismic slip transients. Understanding the driving factors for these prolific sequences and how they can potentially develop into larger ruptures remains a challenge. A notable and almost ubiquitous feature of swarms is their hypocenters migration, which occurrence is closely related to the processes driving the observed seismicity, in a similar way as seismicity accompanies slow-slip events at subduction zones. Here, we analyze global data on migrating sequences, and identify scaling laws for migration velocity, moment and duration measured on natural and injection-induced swarms, foreshock sequences, and slow slip events. We highlight two different behaviors among these sequences: one linked to slow slips, with elevated migration velocities and moments, and the other related to fluid-induced processes, featuring lower velocities and moments. These results provide metrics for distinguishing between the drivers of earthquake swarms, fluid or slow-slip related, and prompt a reevaluation of scaling laws of fault slip transients, especially for swarms.

Introduction
Slip along faults can be seismic or aseismic, and occurs at various scales of fault size, slip released or source duration. Ruptures can span hundreds to thousands of kilometers and last from seconds to months. To gain insights into the processes occurring during slip episodes, scaling laws have been widely used to compare observations at the micrometers scale in laboratory to slip events that extend for hundreds of kilometers. Typical representations of slip duration (T) as a function of released moment (M0) revealed two different scaling laws. Individual earthquakes follow the scaling law M0 / T3 across more than four orders of magnitude, whereas slow slip events and transient aseismic slip sequences observed in subduction zones, exhibit a M0 / T dependence, although recent observations indicate that locally, a M0 / T3 scaling can emerge in SSE sequences. Nevertheless, these scaling relations are of significant importance and subject to debate as they provide fundamental information about the physics of fault slip.

Another crucial parameter of interest lies in the velocity at which transient slip episodes migrate over time. In subduction zones, slow slip events have been observed to propagate at velocities of a few kilometers per day, occasionally accompanied by faster transients known as secondary slip fronts. Conversely, some episodes of seismicity migrate only a few meters per day. This phenomenon is also characteristic of earthquake swarms, which are prolonged sequences of seismic activity lacking a distinct mainshock. Swarms manifest in diverse settings, including subduction zones, rift areas, mountain ranges, and intraplate regions. They can also be induced by fluid injections during industrial activities such as Enhanced Geothermal System (EGS) development, carbon dioxide or wastewater storage. Some earthquake swarms exhibit complex migration patterns, where alongside the overall migration of the sequence, faster and shorter seismicity transients have been observed and interpreted as indicative of aseismic slip. Moreover, swarm-like seismicity can escalate into large earthquakes and is retrospectively identified as a foreshock sequence which also exhibits migration patterns that unveil its underlying driving processes.

Swarms or foreshock sequences can persist for days to years, suggesting the need of an external driving force to sustain the seismicity rate and its migration. Studying seismicity migration conventionally involves the use of distance-time plots and has led to various mechanisms proposed to explain it, including pore pressure diffusion, poro-elastic deformation, earthquakes interactions or transient aseismic loading. Understanding the relation between migration velocity (V) and duration (T) can provide insights into these processes. For instance, migration following a fluid pressure diffusion law may exhibit a scaling of V / T ~ 0.5, while linear migration may indicate fluid-induced aseismic slip. The absence of migration would be characterized by V / T ~ 1.

Recent studies focusing on swarms have revealed that their migration velocities scale across a wider range of magnitudes, notably with swarm duration for both natural and injection-induced sequences lasting from a few days to several years. Conversely, certain swarms observed in subduction or transform faults display significantly higher migration rates, and behave more like Slow-Slip Events (SSEs). Therefore, fluid-induced swarms and SSEs may represent the two extreme behaviors of migrating seismic sequences.

Echoing the substantial body of work existing on the scaling of duration with moment for SSEs and earthquakes, investigating potential scaling of migration velocity with duration is also crucial for understanding slip transients on a global scale. We here employ scaling laws to compare migrating sequences from a global dataset of swarms and foreshocks with slow-slip events, secondary slip front and other fast migrating seismic sequences. By doing so, we aim at identifying their common characteristics, shedding light on their triggering processes, and gaining a better understanding of their driving mechanisms.

Results
A plot of the migration velocities against the durations of earthquake sequences studied here shows two distinct trends despite having similar slopes. The first trend, characterized by high migration velocities, includes slow slip events (SSEs), secondary slip fronts (SSFs), as well as some swarms from subduction and transform fault zones. For clarity, we refer to this group as “slow slip driven” (SSD) sequences, given that the majority have an underlying slow slip trigger. The second trend corresponds to injection-induced swarms and swarms taking place in diverse contexts like rift zones or mountain ranges (see Table S1), labeled as “natural” earthquake swarms here, and certain foreshock sequences. We call this group “fluid-induced” (FI) sequences due to the presence of all injection-induced sequences. Note that we do not exclude the role of fluids in the dynamics of SSD sequences. In both cases, we observe a scaling relationship of V / T ~ α over a duration range spanning six orders of magnitude. For FI swarms, we find α = 0.75 ± 0.15 for a 95% confidence threshold computed assuming a Gaussian distribution of errors, while for SSD sequences, we obtain α = 0.81 ± 0.08.

Despite exhibiting a similar dependence of velocity with duration, the two groups display significantly distinct positions along the ordinate axis. Assuming an exponent α = 0.8, the distribution of the parameter φ = log V × Tα clearly exhibits a bimodal distribution, indicating two distinct and well-separated behaviors. On average, FI sequences have an intercept of φ mean = 1.5 ± 0.6, indicating velocities two orders of magnitudes lower than SSD sequences, which have an average φ mean = 3.7 ± 0.4. Therefore, SSD sequences show higher migration velocities compared to FI swarms, by two orders of magnitude. For instance, taking a week-long duration, SSD sequences can reach migration velocities of several tens of kilometers per day, whereas injection-induced swarms typically exhibit velocities in the range of hundreds of meters per day. If the mechanism controlling seismicity migration is common to SSD and FI, as shown by the slope values, such differences in the scaling intercept might be explained by a systematic difference in the parameters involved in migration dynamics. While prior research has already identified a distinction between swarms and SSEs, this study underscores a broader spectrum of behaviors within migrating sequences, leveraging a larger and more diverse dataset.

The apparent scattering of data points may arise from complexities in the migration patterns that are not captured by an average velocity or from a difference in velocity determination methodology. It might also reveal a 2nd order dependency on fault and hydraulic properties, such as fault criticality concerning the stress state, or physical factors like frictional properties, temperature and fluid pressure.

This parallel, but distinct, behavior provides a valuable observable for distinguishing between the two groups and for inferring their driving processes. Migration velocity alone cannot make this distinction, as previously done, since short-duration swarms may exhibit faster migration than long-duration SSD sequences. However, velocity-duration relations can be used to determine the main driving mechanisms of the swarm. For instance, the foreshocks of the 2008 Mw = 4.9 Mogul and those of the 2009 Mw = 6.3 L’Aquila earthquake sequences appear to behave like FI-swarms, indicating that their dynamics align with injection-induced seismicity episodes. This would also be the case of the seismicity preceding the 2023 and 2024 Noto earthquakes, which migrates of ~8 km in depth for ~650 days before the first Mw = 6.2 earthquake. Some fast seismicity transients occurring during earthquake swarms, within the global earthquake migration, have been thought to be a direct signature of underlying aseismic slip based on their elevated migration velocity alone. However, contrary to previous interpretations based solely on their elevated migration velocity, our results suggest that these fast seismicity transients share the same underlying driving mechanisms as those governing the overall sequence migration, as they scale within FI sequences rather than SSDs.

Conversely, the migration of the precursory events of the 2017 Mw = 6.9 Valparaiso earthquake and the 2014 Mw = 8.1 Iquique earthquake confirm that these sequences are driven by slow slip. Figure 2 also further confirms that swarms occurring on transform faults are primarily driven by slow slips rather than fluid-induced processes, as their migration behavior falls precisely within the patterns observed for SSEs.

The extensive dataset, encompassing numerous sequences with a wide range of durations and velocities, along with the diversity of tectonic contexts and types of sequences examined, results in a more robust estimate of α compared to previous studies. The inferred exponents (α ~ 0.8) for both FI and SSD sequences notably deviate from α = 0.5 which is characteristic of a diffusive pattern. This deviation is corroborated by the apparent diffusivity coefficient, derived from fitting a diffusion law to migration fronts, which exhibits a dependency on swarm duration. Such a dependence, in addition to the value of α ~ 0.8 determined here make a diffusive relationship between time and distance, leading to a V / T ~ 0.5, less plausible.

The similarity in α for FI and SSD sequences suggests that a common mechanism may be responsible for the migration of slip, seismicity or tremors in the two groups. Aseismic slip has been directly measured for SSD sequences such as SSEs, as well as in some earthquake swarms, foreshocks, and injection experiments, and is also expected based on numerical modeling. Theoretical findings for specific FI sequences have obtained similar α values to those determined here, assuming that aseismic slip drives seismicity migration. Therefore, the common V / T ~ α scaling observed for FI and SSD supports the idea that both types of sequences may be driven by aseismic slip. In FI sequences, this aseismic slip is fluid-induced, with the migration velocity actually corresponding to the rupture velocity of this aseismic transient.

While studying migration velocities provides insights into two distinct regimes, a more conventional approach for discriminating slip sequences involves analyzing moment and duration, as it also provides information about the magnitude of the deformation. However, representations that solely consider seismic moment as a function of duration for swarms are incomplete, as aseismic moment release occurs during swarms and can sometimes exceed seismic moment by several orders of magnitude. This was assessed in previous studies looking at the (T–M0) scaling for swarms where the absence of a clear scaling is explained by not taking into account aseismic moment released. Consequently, in our analysis, we consider the total moment (seismic and aseismic) in the scaling representations and compare it to duration. When deformation is too subtle to be detected by geodetic measurements, we estimate the total moment by drawing analogies with repeating events and creep episodes. Here, we assume that seismic slip serves as a proxy for the surrounding aseismic slip. By using the seismic slip associated with the largest event of a sequence, we can estimate the average slip over the entire swarm area. This approach enables the reconstruction of the total moment released during the studied sequence, overcoming the detectability challenges posed by conventional geodetic methods. This method has been validated using values from the literature or through injected fluid volume reconstruction.

From Fig. 4, it appears that, as for the migration velocity-duration relation, the FI swarms exhibit an alignment parallel to the SSD sequences, with a M0 / T scaling. It confirms that SSD and FI swarms share similarities in their driving processes. The M0 / T scaling has been commonly observed on compilations of slow slip events. While individual sequences of slow slip events or low frequency earthquakes may exhibit a scaling relationship of (M0 / T3), the global trend of M0 / T arises from the compilation of these individual scalings. Therefore, by analogy with SSD, one might actually wonder if M0 / T3 transients might be observed within individual FI sequences despite the observed global scaling.

The two groups are also distinctly separated, as the total moment released during FI swarms is approximately three to four orders of magnitude lower than that of SSD sequences for a given duration. This offset between both group scalings exceeds the estimated moment uncertainty of 1 order of magnitude here, and is not related to the size of the swarms or the background stress level. For example, the 2005 Salton Trough and 2013-2014 Apennines swarms share similar size and depth (indicating similar confining stress levels), yet they belong to SSD and FI sequences, respectively. The parallel scaling observed between the FI and SSD sequences in both moment and duration, along with the analogous pattern noted between migration velocity and duration, may also manifest in the relation between moment and migration velocity. However, this association might entail more underlying uncertainty due to the methods and assumptions employed to compute both parameters, resulting in a less distinctly discernible trend.

For most FI swarms, the total moment could only be estimated, which limits the depth of analysis. However, in specific cases where the total moment was precisely quantified through geodetic measurements, it confirms the aforementioned observation. For example, the 2013–2014 Apennines and 2012 Pollino range swarms, where the total moment was measured through geodesy, align with the FI swarms. Conversely, certain swarms, such as the 2005 Salton Trough sequence and the Iquique precursor foreshock sequence exhibit behavior similar to SSEs, which reinforces the dichotomy made in Fig. 2 based on their observed migration velocity and duration. In conclusion, Fig. 4 introduces the distinction of two slip modes, corresponding to sequences of migrating slip or seismicity, highlighted by different M0 / T scalings: slow-slip driven sequences and fluid-induced swarms. This indicates that previous scaling representations only considering earthquakes and SSEs in the slip spectrum are incomplete by missing all FI sequences.

Methods
We have compiled a comprehensive global dataset that encompasses seismic catalogs of various migrating sequences. This dataset contains twelve sequences induced by injection activities in geothermal systems and wastewater disposal, as well as over fifty natural swarms occurring in diverse tectonically active regions like mountain ranges, rift zones, subduction zones and transform faults. Additionally, we have included two examples of fast seismicity bursts occurring during swarms as well as notable sequences of foreshocks, observed in subduction areas and transform and normal fault systems. We have also incorporated observations of slow-slip events from subduction zones based on the SSEs catalogs from Gao et al. and secondary slip fronts (SSF) as documented by Bletery et al. The diversity of tectonic or industrial fluid injection contexts, combined with a wide range of durations (spanning over 6 orders of magnitude), velocities (also covering over 6 orders of magnitude) and moments (encompassing over 7 orders of magnitude), alongside the various natures of migrating slip sequences (including SSEs, SSFs, swarms, fast transients, foreshocks), as well as the potential mechanisms proposed to explain such migrations (pressure diffusion, aseismic slip, poro-elastic effects), collectively contribute to a dataset that offers a more comprehensive representation of migrating slip sequences compared to previous works. From all these studies, we compile values of the migration velocity of seismicity and tremors, the duration of the migrating sequence and, when available, the total moment associated. Error estimates for velocity and moment are often unavailable or challenging to compute from the works considered, as these values are derived using various methods (like for velocity: direct fitting, seismicity front fitting, direct estimate). To maintain consistency across all datasets used in this study and align with previous research on scaling laws facing similar challenges, we adopt a conservative approach. We assigned a migration velocity uncertainty of 25% and a total moment error of up to 1 order of magnitude. However, it is likely that the error is lower for geodetical moments, especially in more recent studies, due to improvements in GPS coverage and the quality of InSAR data. Errors in duration are neglected as they are likely to be small compared to those of velocity and moment. Indeed, migration duration is almost identical to injection duration for injection-induced sequences while seismicity duration and geodetic duration are also closely correlated. This correlation makes the determination of transient slip episodes duration reliable through the compiled values here. Detailed information on data sources, corresponding values, and uncertainties used in our analysis can be found in Supplementary Tables S1 and S2 and Text S1.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "Review of the paper NCOMMS-24-15148 submitted to Natural Hazards\nParallel dynamics of slow slips and fluid induced seismic swarms\nby Philippe Danré et al\nThe present paper studies the scaling of migration velocity versus duration for several types\nof swarms and slow slip events observed in different tectonic environments. The main result\nin figure 1 is that slow-slip-driven sequences, scale differently from fluid induced swarms\nthat occur when the swarm is forced” by fluid flow as has been identified in several\nexamples in the literature. The effort to collect a large collection of data is excellent and the\nseparation of the two families of swarms is quite convincing. The main problem that I find is\nthat there is no estimate of error in this data collection. One can find discussions about\nmany sources of error in the paper and in its supplement, but there is no quantification of\nerrors something that in my opinion is really essential.\nMajor comments\n1. The estimation of duration (T) and Velocity (V) in figure 2 have no hint of the errors\ncommitted in evaluating duration and velocity. The authors discuss several sources of errors\nin the text, but they do not provide estimates of these errors in figures 2 and 4. It is clear\nfrom these figures that SSD sequences are very different from FI but the errors in the\nestimation of velocity are not shown in the figures. The authors discuss in the text that\nerrors in the determination of velocity may be large. I think the authors should revise the\nmanuscript to give at least some hint of the errors involved, and how they could affect their\nestimates.\nMinor comments\n1. This is briefly mentioned in line 40: both refs. 7 and 8 have found that the scaling of\nindividual events in SSE sequences do not follow the scaling shown in Fig 4 for SSDs, but\nrather the classical M ~ T3 shown in the green band of Figure 4. If th authors cared to plot\nearthquakes along with SSD and FI sequences, they should discuss why did the authors of\nrefs, 7 and 8 find a different result, as well as Supino et al (2020).\nRef: Supino, Poiata, Festa, Vilotte, Satriano, et al.. Self-similarity of low-frequency\nearthquakes. Scientific Reports, 2020, 10, p.367-371.\n2. Figures 3 and 4 need changes so as toke them easier to read. The color and symbol choice\nis very difficult to read. Foreshocks are in a shade of purple that is difficult to distinguish\nfrom blue circles. In my version of Figure 4, the pink area is gray. The origin of earthquake\ndata (Denolle et al) is not clearly described.\n3. Figure 3d is very interesting since it shows that data is broadly dispersed, but clearly\nseparate FI and SSD sequences. Its interpretation in terms of fault parameters should be\ninteresting.", "reviewer_2": "This manuscript investigates scaling laws between migration velocity, sequence duration,\nand the total seismic moment of migrating slow slip events, earthquake swarms, and\nforeshock sequences. They compile previously reported migration velocities and durations\nof such events and either use previously reported seismic moments or a relatively new way\nto estimate seismic moment. They examine two scaling laws to compare the different types\nof earthquakes: migration velocity versus sequence duration and total moment versus\nduration. The authors find that slow slip events have higher velocities and total moments\nwhen compared with swarms induced by fluids (fluid-induced sequences). This manifests as\nslow slip and fluid-induced sequences having different intercept values in the scaling laws.\nNotably, the scaling laws for both the slow slip and fluid induced groupings have a near-\nidentical slope. The authors interpret that this indicates that similar physical mechanisms\ncause these two different classes of earthquakes. More specifically, the authors argue that\naseismic slip is the primary driver of both classes of earthquakes, including fluid-induced\nswarms. Similar scaling relationships are initially reported in Figures 4 and 6a of Danre et al.,\n(2022", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports.\nThis is part of the Nature Communications initiative to facilitate training in peer review and\nto provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "This paper compiles several studies at a global scale on migrating sequences of seismicity in\nvarious context: injection-induced swarms, slow slip events, natural swarms and foreshock\nsequences. The authors analyse various scaling relations : migration velocities versus\nduration; Moment versus Duration. They reveal two different behaviors for the sequences,\nthat they attribute to different dynamics, either fluid induced swarms (FI) or slow slip driven\n(SSD). They show that the scaling of migration velocity versus duration (V ~ T^α) evolves\nwith the same trend for FI and SSD (with α around 0.75 to 0.83), but with a different\nintercept, SSD being 2 to 3 orders of magnitude faster for a similar duration. The scaling of\nMoment versus duration is linear for both type of sequences, but also evolves on two\nparallel trends for FI and SSD sequences. The proposition of two different behaviors for\nthose sequences (FI and SSD) was already presented in an earlier work from the same group\n(Danré et al. 2022 (JGR)), however, the current paper uses a more complete dataset and\nprovides more details on the scaling analysis and its interpretation. This paper provides an\nimportant perspective for the understanding of the drivers of seismic and aseismic fault\ntransients, and discards the diffusive process as the driving mechanism for FI sequences.\nThe paper is generally well written and figures are clear. I recommand publication after\nminor revisions.\nMain comments:\nI think the authors should better clarify the added value of the current study with respect to\nthe previous work by Danré et al. 2022 (JGR). In particular, a significant part of the points\nshown in Figure 2 were already present in Fig. 4 from Danré et al. 2022 (JGR), and that\nearlier paper also investigated the scaling between velocity and duration. The current work\nremains an important contribution since (1) new datasets have been compiled and used to\nestimate scaling relations in the current study and (2) the authors go further in the\ninterpretation of the results. Nevertheless, a clarification of the differences and\nimprovement with respect to previous work would be useful.\nOn the same note, the scaling coefficient α (in the relation V ~ T^α) estimated in the current\nstudy differs from Danré et al. 2022 (JGR), and this has implication for the physical\ninterpretation since the new coefficients are not compatible with fluid diffusion. The\nauthors did not clearly explain the origin of this discrepancy: does it come from the addition\nof new datasets over larger temporal scales ? On that point, see also my detailed comments\nassociated to l.104-106.\nSome studies have revealed the existence of migration velocities at different\nspatial/temporal scales (rapid tremor reversals, i.e. Houston. et al. 2011, and/or dual\nmigration velocities [DeBarros et al. 2020, Dublanchet & De Barrow, GRL 2020]). These\nstudy show that the migration velocities can be defined at different time scales. This brings\nseveral questions: (1) how is the time-scale at which the observations are made selected,\nand how can we be sure that all datasets have been analyzed the same way ? (2) Could both\nmigrations velocities be represented in the Figure 2 ? (global events with slow migration and\nsmaller events within clusters with faster velocities) (3) Would the proposed mechanisms (FI\nand SSD) hold to explain events with dual migration velocities ?\nI think this could be discussed at some point in the paper.\nMinor comments:\nl. 26-28: The authors should reformulate their One-sentence summary, the sentence\nstructure is odd, and the second part of the sentence (« and what we learn… ») should be\nself-contained.\nl. 39: a more recent reference (Beroza and Ide 2023) exist on the M0~T scaling, with the\nsame authors. It could be cited here as well. That paper also provides a possible\nexplanations for the observed scaling M0-T^3 on restricted datasets that could be due to\ndetection bias.\nl. 97-99: The distinction between these two groups « slow slip driven » and « fluid induced »\nwas already introduced in Danré et al. 2022. This could be mentioned here.\nFigure 3A and l.104-106: How are the error bar determined on the value of the slope here ?\nI have the same question for the Intercept (Fig.3B), and l. 115-116.\nl. 104-106: Here the authors should compare more explicitly the values of the parameters\nobtained in this study with the previous work from Danré et al. 2022. I understand that\n« makes it less likely a diffusive process » refer to the higher exponents in this study\ncompared to Danré et al. 2022, but this could stated more clearly. The reason for the\nchange in scaling could also be discussed (how many orders of magnitudes have been added\nwith respect to the previous work) ?\nL. 154-155: « by assuming seismic slip as a proxy for the surrounding aseismic slip. »: You\ncould be more specific here in describing the approach on how to estimate the total\nmoment from swarm data. Reference 27, where the method is described, should be\nassociated to the last part of the sentence.\nL. 1999-200: shallow SSEs have also been detected at shallow depth in several subduction\nzones (Japan, Hikurangi …)\nL. 205-206: the authors point out the uncertainties in estimating the migration velocity and\ntotal moment. It seems to me that uncertainties in the determination of the event duration\nis also large. This is especially true for geodetically detected SSEs, where the duration is\ndefined from a noisy-emerging signal and is subject to large uncertainties due to noisy daily\ndata that often require temporal smoothing. These uncertainties were evaluated in Michel\net al. 2019 (Fig. 3a). In the catalog from Gao et al. 2012, even if not mentioned,\nuncertainties on the evaluation of the duration for SSE also exist and should probably be\nmentioned here as well here.\nl. 224: Observations made Figures 2 and 4. => Observations made in Figures 2 and 4.\nl.224-227: The authors could detail more how they deduce the alpha values from the two\nmodels proposed in Ide et al. 2007. In the sentence (l.225-226), it could be stated that the\nuniform slip model implied L^2 ~ T while the constant stress drop model implies L^3~T. This\nwill help the reader to understand more clearly the relationship between the proposed\nmodels and the alpha values, without having to refer in details to Ide et al. 2007.", "reviewer_author_response": "Below, we provide detailed responses to the reviewers’ comments. Our direct answers are\nhighlighted in blue, while red text indicates additions or modifications in the manuscript and\nsupplementary materials. Additionally, we have included a tracked changes document where\nall revisions to the initial manuscript are highlighted in yellow.\nReview of the paper NCOMMS-24-15148 submitted to Natural Hazards\nParallel dynamics of slow slips and fluid induced seismic swarms\nby Philippe Danré et al\nThe present paper studies the scaling of migration velocity versus duration for several types of\nswarms and slow slip events observed in different tectonic environments. The main result in\nfigure 1 is that slow-slip-driven sequences, scale differently from fluid induced swarms that\noccur when the swarm is forced” by fluid flow as has been identified in several examples in\nthe literature. The effort to collect a large collection of data is excellent and the separation of\nthe two families of swarms is quite convincing. The main problem that I find is that there is\nno estimate of error in this data collection. One can find discussions about many sources of\nerror in the paper and in its supplement, but there is no quantification of errors something that\nin my opinion is really essential.\nWe thank the reviewer for their helpful and constructive comments.\nMajor comments\n1. The estimation of duration (T) and Velocity (V) in figure 2 have no hint of the errors\ncommitted in evaluating duration and velocity. The authors discuss several sources of errors\nin the text, but they do not provide estimates of these errors in figures 2 and 4. It is clear from\nthese figures that SSD sequences are very different from FI but the errors in the estimation of\nvelocity are not shown in the figures. The authors discuss in the text that errors in the\ndetermination of velocity may be large. I think the authors should revise the manuscript to\ngive at least some hint of the errors involved, and how they could affect their estimates.\nThe reviewer raises an important yet challenging point, particularly when using works that\ncompile results from various studies. As noted in other research (e.g., Passarelli et al., 2021;\nGao et al., 2012), compiling observations from diverse sources complicates error estimation\nbecause (1) errors are not always computed, (2) data may not always be available, and (3)\nvalues are derived from different methods, leading to varying uncertainties.\nError estimates for velocities are not available in many studies. For instance, Roland and\nMcGuire (2009) provide only direct velocity estimates without precise fitting. Gao et al.,\n(2012), values for SSEs we use, suggest a velocity uncertainty of about 25% across the\nnumerous SSE studies they compile. Similarly, Kuna et al. (2019), which we also reference,\nreport velocity errors around ~10% of their values, noting that their velocity fits are based on\nrelatively few points per sequence. Conversely, velocities determined for swarms with more\ndata points and well-defined seismicity fronts, such as those in Danré et al. (2022), exhibit\nlower uncertainties. We have added these error values to the Supplementary Materials in\nTable S2 and provided more detail in Supplementary Materials Text S1. To maintain\nconsistency across all datasets and ensure conservative observations, we have chosen to\nassume a 25% error margin for all velocity values considered in this study. As discussed in\nGao et al. (2012), this approach also indirectly accounts for errors in duration. Also, errors in\nduration are expected to be small compared to the ones for velocity and moment as (1) it is\neasier to determine and (2) migration duration and injection duration are almost identical (see\nDanré et al., 2023) as well as seismicity duration and geodetical duration (citation). It\n2\ntherefore seems that determining transient slip episodes duration does not carry significant\nuncertainty compared to velocity or moment.\nError estimates for moment are also crucial. There are two types of errors to consider: those\nrelated to the estimated total moment for swarms, and those pertaining to moment\nmeasurements using geodesy. In the first case, Danré et al. (2023) discussed that total moment\nestimates are generally consistent with their theoretical expectations based on injected fluid\nvolume, assuming a factor of 10 uncertainty. For moment obtained using geodesy, Gao et al.\n(2012) suggest that the uncertainty should be less than an order of magnitude. To maintain a\nconservative approach, we have opted to consider the error for moment to be up to an order of\nmagnitude for both estimated or geodetic moments. However, it is likely that the error is\nlower for geodetical moments, especially in more recent studies, due to improvements in GPS\ncoverage and the quality of InSAR data.\nFollowing reviewer’s comment, we added in the manuscript (Lines 101-114):\nError estimates for velocity and moment are often unavailable or challenging to compute from\nthe works considered, as these values are derived using various methods (like for velocity :\ndirect fitting39, seismicity front fitting30, direct estimate32). To maintain consistency across all\ndatasets used in this study and align with previous research on scaling laws facing similar\nchallenges, we adopt a conservative approach. We assigned a migration velocity uncertainty of\n25% and a total moment error of up to 1 order of magnitude2. However, it is likely that the error\nis lower for geodetical moments, especially in more recent studies, due to improvements in GPS\ncoverage and the quality of InSAR data. Errors in duration are neglected as they are likely to\nbe small compared to those of velocity and moment. Indeed, migration duration is almost\nidentical to injection duration for injection-induced sequences40 while seismicity duration and\ngeodetic duration are also closely correlated35. This correlation makes the determination of\ntransient slip episodes duration reliable through the compiled values here. Detailed information\non data sources, corresponding values, and uncertainties used in our analysis can be found in\nSupplementary Tables S1 and S2 and Text S1.\nAnd in the Supplementary Materials, Text S1 we also provide more detail:\nGiven the diversity of sources used in this work, accounting for uncertainties in both velocity\nand moment (total or geodetic) is challenging, as these were either not computed in the\nstudies considered or determined using different methods. To address this inconsistency,\nprevious research on scaling laws has often used reasonable, conservative error estimates\nbased on observations and theoretical results. For instance, Gao et al. (2012) suggest that the\ngeodetic moment for SSEs should be constrained within a 1 order of magnitude of its value.\nTotal moment estimates for natural and fluid-induced swarms, as found in Danré et al. (2022\nand 2023), are consistent with limited geodetic observations and theoretical expectations,\nalso\nconsidering a maximal error factor of 10. The error in moment was therefore considered as up\nto 1 order of magnitude here. Velocities determined from fitting the distance of earthquakes\nover time, such as in Kuna et al. (2019), carry an uncertainty of about 10%. According to\nDanré et al. (2022), most velocities uncertainties are below 10%, except for one sequence at\n25% (see Table S2). Gao et al., 2012 estimate that SSE velocities should have an error below\n25%. In contrast, velocities determined without fitting, such as those by Roland and McGuire\n(2009), lack available error estimated due to the low number of data points and absence of\n3\ndirect fitting. Consequently, we chose to adopt conservative uncertainties in our studies,\nassigning a 25% uncertainty to velocities and constraining moment (total or geodetic) within a\n1 order of magnitude range.\nNote that despite considering upper bound values for errors in velocity and moment, our\nresults remain consistent : the distinction between FI and SSD sequences is still evident, as\nthey are separated by 2-3 orders of magnitude, while the errors are up to 1 order of magnitude.\nWe added accordingly (Lines 219-220):\nThis offset between both group scalings exceeds the estimated moment uncertainty of 1 order\nof magnitude here (see Supplementary Materials Text S1),\nWe do not consider the error in moment – duration for earthquakes, as these values are\nincluded solely to illustrate their distinct behavior and are not the focus of this work.\nWe have updated Figures 2 and 4 to include error bars accordingly.\nMinor comments :\n1. This is briefly mentioned in line 40: both refs. 7 and 8 have found that the scaling of\nindividual events in SSE sequences do not follow the scaling shown in Fig 4 for SSDs, but\nrather the classical M ~ T3 shown in the green band of Figure 4. If th authors cared to plot\nearthquakes along with SSD and FI sequences, they should discuss why did the authors of\nrefs, 7 and 8 find a different result, as well as Supino et al (2020).\nReferences 7-8 and Supino et al. (2020) examined specific sequences and identified cubic\nscaling between duration and moment within individual sequences. In contrast, we investigate\na broader range of diverse slip sequences, revealing a more global trend. This broader trend is\nalso illustrated in Ide and Beroza (2023) where the global trend emerges from the compilation\nof all individual scalings. These individual scalings might also result from observational gaps\nor interpretation of biased data. Consequently, our results are not incompatible with\nobservations from References 7-8 and others; rather, they are complementary.\nWe have added in the manuscript (Lines 213-215):\nWhile individual sequences of slow slip events or low frequency earthquakes may exhibit a\nscaling relationship of 7,8,56, the global trend of arises from the\ncompilation of these individual scalings5,47.\n3\n(𝑀0 ∝ 𝑇 ) 𝑀𝑂 ∝ 𝑇\nAlso we have added in the discussion the importance of FI sequences in the scaling laws\nstudies, as they are situated above the bounds of observability defined in Ide and Beroza,\n2023\n(Lines 277-279).\nMoreover, incorporating fluid-induced sequences (FI) in our study adresses observational\ngaps identified in the litterature55, thereby defining a new ensemble that runs parallel to SSEs.\n4\n2. Figures 3 and 4 need changes so as toke them easier to read. The color and symbol choice\nis very difficult to read. Foreshocks are in a shade of purple that is difficult to distinguish\nfrom blue circles. In my version of Figure 4, the pink area is gray. The origin of earthquake\ndata (Denolle et al) is not clearly described.\nWe enhanced Figure 3 by adjusting the colors to improve the clarity of distinguishing\nbetween the FI and SSD domains. Additionally, in Figures 2 and 4, we replaced the markers\nfor foreshock sequences with diamond shapes to enhance their visibility. Furthermore, we\nupdated the color for the FI sequences in Figure 4 to ensure they no longer appear gray.\nFor the earthquake data’s origin, we have added more detail in the caption of Figure 4:\nSquares represent seismic moment and duration data obtained from a global earthquake\ndataset. The duration is determined through corner frequency analysis of nearly a thousand of\nearthquakes3.\n3. Figure 3d is very interesting since it shows that data is broadly dispersed, but clearly\nseparate FI and SSD sequences. Its interpretation in terms of fault parameters should be\ninteresting.\nWe have added a sentence to highlight that the scattering of points may reveal differences in\nfault and hydraulic properties (Lines 145-147):\nIt might also reveal a 2nd order dependency on fault and hydraulic properties, such as fault\ncriticality concerning the stress state41, or physical factors like frictional properties,\ntemperature and fluid pressure35.\nThis manuscript investigates scaling laws between migration velocity, sequence duration, and\nthe total seismic moment of migrating slow slip events, earthquake swarms, and foreshock\nsequences. They compile previously reported migration velocities and durations of such\nevents and either use previously reported seismic moments or a relatively new way to\nestimate seismic moment. They examine two scaling laws to compare the different types of\nearthquakes: migration velocity versus sequence duration and total moment versus duration.\nThe authors find that slow slip events have higher velocities and total moments when\ncompared with swarms induced by fluids (fluid-induced sequences). This manifests as slow\nslip and fluid-induced sequences having different intercept values in the scaling laws.\nNotably, the scaling laws for both the slow slip and fluid induced groupings have a near-\nidentical slope. The authors interpret that this indicates that similar physical mechanisms\ncause these two different classes of earthquakes. More specifically, the authors argue that\naseismic slip is the primary driver of both classes of earthquakes, including fluid-induced\nswarms. Similar scaling relationships are initially reported in Figures 4 and 6a of Danre et al.,\n(2022"}, "author_response": ""}]

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