On the Nature of Earthquakes: From the Field to the Lab-1

oratory2

Francois X. Passelegue1,+, Michelle Almakari2, Pierre Dublanchet2, Fabian Barras3, Marie3

Violay14

1Laboratoire de Mecanique des Roches, Ecole Polytechnique Federale de Lausanne, Switzerland.5

2Centre de Geosciences, MINES ParisTECH, PSL Research University, Fontainebleau, France.6

3The Njord Centre for Studies of the Physics of the Earth, University of Oslo, 0371 Oslo, Norway.7

+To whom correspondence should be addressed: francois.passelegue@epfl.ch8

Modern geophysics highlights that the slip behaviour response of faults is variable in space9

and time and can result in slow or fast ruptures. Despite geodetical, seismological, experi-10

mental and field observations, the origin of this variation of the rupture velocity in nature, as11

well as the physics behind it, is still debated. Here, we first discuss the scaling relationships12

existing for the different types of fault slip observed in nature and we highlight how they13

appear to stem from the same physical mechanism. Second, we reproduce at the scale of the14

laboratory the complete spectrum of rupture velocities observed in nature. Our results show15

that when the nucleation length is within the fault length, the rupture velocity can range from16

a few millimetres to kilometres per second, depending on the available energy at the onset17

of slip. Our results are analysed in the framework of linear elastic fracture mechanics and18

highlight that the nature of seismicity is governed mostly by the initial stress level along the19

faults. Our results reveal that faults presenting similar frictional properties can rupture at20

both slow and fast rupture velocities. This combined set of field and experimental observa-21

tions bring a new explanation of the dominance of slow rupture fronts in the shallow part of22

the crust and in areas presenting large fluid pressure, where initial stresses are expected to23

remain relatively low during the seismic cycle.24

1

Scientific context25

Recent geophysical observations around the world have highlighted that faults release elastic strain26

energy stored in the wall rocks through different types of slip events. Faults generate slow (∼0.1-127

m/s)1, regular (∼3000 m/s, also called fast ruptures) and supershear (∼4200 m/s) earthquakes1–3.28

Understanding the physical parameters and the environmental conditions controlling the rupture29

velocity (Vr) is crucial because earthquake damage increases with this parameter4,5. While seis-30

mology allows estimating the size of the events and their durations1, the parameters controlling31

the nature of the slip events, as well as the reasons whether slow events obey different scaling laws32

from regular earthquakes (Fig. 1a), remain poorly understood. In particular, the seismic moment33

of regular earthquakes scales with the duration of the events as M0 ∝ δ3, whereas the seismic34

moment of slow ruptures, such as tremors, low-frequency earthquakes (LFE), or slow slip events35

(SSE), scales following M0 ∝ δ, suggesting different propagation dynamics (Fig. 1a)1,6–8. In36

addition, the nature of slip along a fault is variable in space and time9. This complexity around37

fault ruptures and slip behaviours results in difficulty of evaluating the seismic risk of seismogenic38

areas.39

However, recent seismological observations have demonstrated that, considering a single40

population of events presenting a large range in magnitude, the moment-duration of slow slip41

events scales as M0 ∝ δ3 (Fig. 1a)10. In this context, we analysed existing natural observations42

for which estimates of both the average rupture velocity Vr and the average stress drop (∆σ) were43

made using seismological or geodetical methods (Fig. 1b). Making the hypothesis that slow slip44

events consist of rupture propagating circularly at a constant rupture velocity, i.e., as most regular45

earthquakes, we normalise the seismic moment of each event by their average stress drops and46

multiply their durations (δ) by their average rupture velocities (Vr). We show that both slow and47

fast rupture phenomena follow the same scaling law (Fig. 1b), which implies three important48

2

consequences: (i) the stress drop during events is a function of the rupture velocity; (ii) since most49

SSEs present pulse-like behaviour, the rupture velocity increases during rupture propagation; and50

(iii) both slow and fast earthquakes are governed by similar physics.51

What are the parameters controlling the rupture velocity in nature? Along subduction in-52

terfaces, such as the Japanese trench, modern seismology has determined that the distribution of53

rupture phenomena is organised6,7,11–17. Slow rupture phenomena are generally observed at depths54

between 28-40 km, where they appear to be the dominant mode of slip, or in the shallow part of55

the accretionary prism, where they coexist with regular earthquakes (Fig. 1b). These slip phe-56

nomena seem to occur in environments presenting high seismic velocity ratios, suggesting high57

fluid pressure (Fig. 1c)18–21. Fluid overpressure is known to play a key role in the quasi-static58

reactivation of faults22, as well as in the nucleation23 and the propagation of slip instabilities24–26.59

The promotion of slow slip events rather than regular earthquakes in areas presenting high fluid60

pressure is generally explained by an increase in the nucleation length with increasing fluid pres-61

sure, as expected by both rate-and-state and slip weakening theories23,27–30. Such behaviour has62

been observed experimentally by the reproduction of a quasi-static rupture mode, such as stable63

slip31–34. However, these theories do not explain the quasi-dynamic propagation of slow fronts in64

nature or the radiation of low-frequency waves at their rupture tips.65

To explore these questions, we conducted laboratory experiments to trigger a rupture front66

along a critically loaded fault interface by locally increasing the pore fluid pressure. Our method67

allows us to study the influence of the initial stress distribution and the presence of fluid overpres-68

sure on rupture propagation. Experiments were conducted on saw-cut samples of crustal rock in69

tri-axial loading conditions (Fig. S1a) that reproduce natural pressure conditions. The hydraulic70

transmissivity of the fault decreases from 10−17 to 10−18 m3 between 20 and 100 MPa effective71

normal stress (Fig. S1b). The static friction of the fault is ≈ 0.62 (Fig. S1c), in agreement with72

3

Byerlee’s law35. The fault was first loaded to up to 90% of the peak shear strength of the fault73

(defined by the static friction coefficient). The larger the confining pressure, the larger the initial74

shear stress (approximately 20, 42 and 70 MPa during experiments conducted at 30, 60 and 9575

MPa confining pressure, respectively), i.e., the amount of energy available in the system (Fig. 2).76

Then, the fluid pressure was increased locally through a borehole (Fig. S1a) at a constant volume77

rate to trigger a succession of slip events, up to the complete release of the energy stored in the78

system prior to the injection (Fig. 2).79

Independent of the confining pressure, i.e., of the effective normal stress acting on the fault,80

a strong hysteresis is observed between the fluid pressure measured in the injection site and the81

fluid pressure measured at the opposite edge of the fault. For instance, at low confining pressure,82

the first reactivation is observed when the fluid pressure in the injection site reaches 23 MPa, while83

the fluid pressure at the opposite edge remains relatively low (Pf ≈ 12 MPa) (Fig. 2a). The84

fluid pressure gradient generally decreases over time and with slip events due to fault reactivation85

during injection, which enhances the diffusion of the fluid pressure (Figs. 2 and S2). We estimate86

the diffusivity enhancement along the fault during the experiment by inverting the pore pressure87

history measured in the observation site (See Methods). We used a 2D diffusivity model assuming88

time variable diffusivity. Therefore, we were able to determine the pore pressure history on the89

entire fault during the experiment. Expressed in terms of the average values of shear stress and90

pore pressure profiles, our experimental results highlight that the fault reactivates when the average91

stress distribution reaches the corresponding Mohr-Coulomb failure criterion (Fig. S3).92

Remarkably, a transition between fast to slow slip events is observed as the injection pro-93

gresses, and the average shear stress decreases on the fault (Figs. 3a and Fig. S4). For each fast94

or slow release of stress, we computed an average slip (u) and slip velocity (Vs) within the resolu-95

tion of our system. Both u and Vs increase with increasing stress drop associated with each event96

4

(Fig. 3b and Fig. S5), as observed in previous studies36. Second, using a strain gage array, we97

tracked the slip front associated with each slip event (Fig. 3c). Our experimental results show that98

the events that propagated at the highest stress level present the highest rupture velocities, up to99

values close to the shear wave velocity of the bulk form of the material tested. Subsequent rupture100

propagations, induced at lower stress levels, present slower rupture velocities, from one meter to a101

few millimetres per second (Fig. 3c). These slow rupture velocities are in agreement with natural102

observations1,6–8.103

At the scale of our experiments, a strong correlation is observed between the state of stress104

prior to the onset of a slip event and the rupture velocity37. For instance, for each confining pres-105

sure tested, the rupture velocity increases with the decrease in the ratio between the average fluid106

pressure and the average normal stress (λ = Pf/σn) acting on the fault at the onset of propagation107

(Fig. S6 and Fig. 4a). While this trend depends slightly on the confining pressure, all data collapse108

when comparing the average rupture velocity to the average slip velocities reached during each109

instability (Fig. 4a). Note that the slip velocity increases linearly with increasing rupture veloc-110

ity achieved during the event, a behaviour that is predicted by linear elastic fracture mechanics111

(LEFM)38,39. Regarding the slip mode, we observed a strong correlation between Vr and λ and112

with the average shear stress profile (τ0) at the onset of the slip event. In our experiments, the113

nucleation length was systematically smaller than the length of the fault, allowing preferentially114

for fast rupture propagation. From these conditions and the observation that the slip front process115

zone remains much smaller than the specimen dimensions, the rupture velocity is expected to be116

a function of the energy available at the rupture tip. Indeed, following LEFM predictions for a117

dynamic shear crack, Vr can be expressed following Vr = CR(1 − Gc/Γ) for sub-Rayleigh rup-118

tures, where CR is the Rayleigh wave velocity, Gc is the fracture energy required to advance the119

slip front, and Γ is the energy release rate. Assuming that Gc depends only on the effective normal120

stress before the rupture, this relation can be written as a function of the initial stress acting on the121

5

fault:122

Vr = CR

(1− (σn − Pf )

∆τ 2d

Ω

πLE∗)

(1)

where ∆τd is the dynamic stress drop during rupture, L is the length of the crack, and E∗ is the123

dynamic Young’s modulus (E∗ = E/(1− ν2) in plane strain). Ω is a term describing the effect of124

frictional weakening with slip. For a linear slip-weakening model of friction, Ω = (fs−fd)dc, with125

dc being the characteristic slip for frictional weakening and fs and fd are respectively the static and126

dynamic friction coefficients. This relation sheds light directly on the dependence between the ini-127

tial state of stress acting on the fault and the rupture velocity observed. Considering that Ω is not128

a function of the initial stress, the rupture velocity is expected to decrease with increasing fluid129

pressure (Methods, Equation 10) or with decreasing initial stress acting on the fault (σn and τ0 in130

our experiments) because both lead to a decrease in ∆τd during events40 (i.e., to an increase in the131

ratio (σn− Pf )/(∆τd)2). We now compare our experimental results to LEFM predictions29. First,132

we compute the stress terms in equation (1) for each event using direct measurements. For each133

confining pressure tested, Vr increases with decreasing (σn−Pf )/∆τ 2d , although some exceptions134

exist (Fig. 4b). Note that our experimental results are strongly consistent with the theoretical pre-135

dictions computed for two different values of strength drop (fs − fd) and assuming dc ≈ 10 µm29136

and L = Lf = 0.08 cm (Lf being the length of the experimental fault). Both experimental re-137

sults and theoretical predictions highlight that a low stress level promotes the propagation of slow138

rupture phenomena. It is interesting to note how the supershear ruptures observed in previous139

experiments under dry conditions36 extend the scaling predicted by the equation of motion 1 for140

sub-Rayleigh velocities41.141

So why do slow ruptures not accelerate to seismic wave velocities in nature? Along low-142

stress areas, the fluid overpressure or far field loading rate can be sufficient to reach the critical143

6

energy release rate and to nucleate the rupture front. However, the low level of shear stress at which144

the fault is operating prevents the emergence of a significant dynamic stress drop and enables only145

quasi-static rupture propagation. This explanation is supported by recent theoretical and numerical146

studies42 as well as by the evolution of ∆τd observed in the experiments for lower values of shear147

stress and higher fluid pressures. Finally, the low initial stress conditions may not be enough to148

extend the rupture length L, limiting and buffering the rupture front velocity (Equation 9).149

Our new results demonstrate that seismogenic faults can be activated by stress perturbations150

by all possible modes of slip independently of the frictional properties. The slip mode depends151

only on the initial stress acting along the fault ahead of the rupture tip, i.e., the energy stored along152

the fault. Note that in nature, large values of Pf may imply small values of τ0 because of the slow153

far field loading rate compared to the rate of fluid pressure accumulation. For instance, assuming154

certain hypotheses (Methods, Equation 11), slow rupture velocities (Vr < 0.1 m/s) are expected155

to occur when faults are subjected to an initial effective normal stress of 10 MPa, which implies156

almost lithostatic fluid pressure at depth, in agreement with natural observations21,43,44. Our results157

explain why slow ruptures are promoted in over-pressurised areas or at shallow depths (Fig. 1c),158

where the stress is expected to remain low during the seismic cycle. Finally, our results also support159

the spatio-temporal variability of the mode of slip in nature since the stress acting on faults evolves160

both in time and in space.161

Methods162

Sample preparation163

Cylindrical samples (diameter: 40 mm, length: 90 mm) were cored from andesite blocks from164

the Dehaies quarry, located in Guadeloupe (France)45. This andesite was found to have a density165

of 2690 kg/m3 and a porosity ranging from 1.1 and 2.3 %, in agreement with a previous study45.166

7

This rock was chosen due to (i) anticipated future exploitation of the reservoir by a geothermal167

project and (ii) the negligible permeability of the bulk of the intact specimen (<10−21 m−2)45,168

which ensures purely in-fault fluid diffusion during the injection experiments.169

Prior to experiments, the rock cylinders were saw-cut to create an experimental fault at an170

angle of 30o with respect to σ1 (the principal stresses are denoted σ1 > σ2 = σ3). The fault surfaces171

were roughened first with grinder and then with coarse sandpaper (grit number P240, ≈ 50 µm172

roughness) using ethanol to avoid frictional heating during sample preparation. All experiments173

were conducted on a fault surface presenting the same initial geometry and roughness. To induce174

injection along the artificial fault interface, boreholes were drilled at both edges of the fault (Fig.175

S1a). The bottom borehole was used as the injection site, while the top borehole was used only as176

a measurement site (Fig. S1a).177

Triaxial apparatus and strain gauge array178

The apparatus used in this study is a tri-axial oil medium loading cell (σ1 > σ2 = σ3) built by179

Sanchez Technologies. The confining pressure is directly applied by a volumetric servo-pump up to180

a maximum of 100 MPa. The axial stress is controlled independently by an axial piston controlled181

by a similar servo pump. The axial stress can reach 680 MPa on 40 mm diameter samples. Both182

confining and axial pressure are controlled and measured with a resolution of 0.01 MPa. Axial183

contraction is measured by averaging the values recorded on three capacitive gap sensors located184

outside of the vessel. These sensors record both the sample deformation and that of the apparatus.185

The resolution of these measurements is 0.1 micron. Both pressure and displacement data were186

recorded at the maximum sampling rate during experiments (2.4 kHz). Note that because of our187

sample geometry, increasing the differential stress leads to an increase in both shear and normal188

stresses. In addition to the record of regular mechanical data (σ1, σ3, axial strain ε1, radial strain189

ε3, and axial contraction), eight strain gauges equally spaced at 0.8 cm and recording preferentially190

8

axial strain were glued 3 mm from the fault plane along the fault strike (Fig. S1a). This strain191

gage array is used to monitor the propagation of the rupture front during episodic slip events and192

to image the evolution of the stress distribution profile along the fault during experiments. The193

local shear stress was computed from the resolved stresses accounting for the transient changes in194

the axial stress recorded by the strain gage array. Transient changes in the confining pressure were195

neglected, which is justified by the relatively high compliance of the confining medium36.196

Hydraulic and frictional properties of the experimental fault197

Prior to the injection experiments, the hydraulic transmissivity of the fault was measured over the198

complete range of effective pressure tested using constant flow methods. The hydraulic trans-199

missivity was estimated assuming non-linear flow lines along the fault interface46. The in-plane200

hydraulic transmissivity is estimated directly from the volumetric flux following201

ζhy = kw =Jηlog(2a

r0− 1)

Bπ dPdx

(2)

where k is the permeability of the fault, w is the fault thickness, a is half of the distance between202

the boreholes, r0 is the borehole diameter, dPdx

is the imposed pressure gradient, J is the volumetric203

fluid flux, η is the fluid viscosity and B is a constant of order unity. Based on this estimate, the204

hydraulic transmissivity of the fault is observed to decrease from 10−17 to 10−18 m3 between 20205

and 100 MPa effective normal stress (Fig. S1b). These results are compatible with experimental206

faults presenting the same geometry46 and suggest a fault permeability between 10−13 and 10−14207

m−2 assuming a fault aperture ranging from 10 to 100 microns. This range of permeability is208

comparable to that of previous studies on similar fault geometry46 and initial and final roughness209

levels of the fault. The peak shear strength of the fault at the onset of slip is determined at three210

different confining pressures (30, 60 and 95 MPa). At each confining pressure, the initial pore211

pressure along the fault is set to 10 MPa and is regulated to remain constant during the axial212

9

loading tests up to the reactivation of the fault.213

Numerical modelling of the pore pressure distribution214

The model assumes a homogeneous diffusivity along the fault, which is modelled as an ellipsis.215

Neumann boundary conditions are assumed at the edge of the ellipsis in agreement with our exper-216

imental conditions (i.e., no fluid flow outside of the ellipsis). Because of the low permeability of217

the bulk of the sample (≈ 10−21 m−2 (Fig. S1b), we assume purely in-fault fluid diffusion between218

the injection site and the measurement borehole. We assume that the hydraulic diffusivity along the219

fault is spatially constant but changes over time. The pressure is then estimated using the diffusion220

equation221

∂p(x, y, t)

∂t= D

(∂2p(x, y, t)

∂x2+∂2p(x, y, t)

∂y2

)(3)

The 2D diffusion equation is evaluated using the finite volume method. The fault is discre-222

tised into 64 cells and 32 cells in the length and width of the fault, respectively. The stability of the223

system is ensured since224

∆t =∆x2∆y2

2D(∆x2 + ∆y2)=

∆x2

4D(4)

where ∆t and ∆x and ∆y are the time and spatial steps, respectively. Note that in our calculation,225

we assume that ∆x = ∆y. The pressure at the injection and measurement boreholes are then used226

to invert the spatial evolution of the fluid pressure along the entire fault plane. To improve our227

estimates, we allow an increase in diffusivity over time. The results regarding the evolution of the228

hydraulic diffusivity during the experiments are beyond the scope of this paper but are partially229

presented in Fig. S2a, which presents the comparison between the experimental measurements230

10

and the prediction, as well as the evolution of the hydraulic diffusivity required to invert the exper-231

imental data. This numerical modelling provides an estimate of the fluid pressure along the fault232

during the experiments, which is used to estimate the average fluid pressure at instability in the233

manuscript (Fig. 4).234

Slip front equation of motion from LEFM235

The dynamic energy release rate for a mode II crack in the sub-Rayleigh regime can be written236

as38:237

GII(L, Vr) = g(Vr)GII(L, Vr = 0). (5)

In the equation above, g(Vr) is a universal function of the rupture velocity, and GII(L, Vr =238

0) is the energy release rate for a static crack of the same length L, which can be expressed as47:239

GII(L, Vr = 0) = χ(∆τ)2πL1

2E∗ (6)

where χ is a dimensionless variable in the range of unity accounting for the geometry of the crack,240

∆τ is the dynamic stress drop, and E∗ = E/(1 − ν2) is the plane strain condition. The crack241

tip energy balance implies that the dynamic energy release rate should always equal the fracture242

energy Gc during the rupture. Using Freund’s approximation38 g(Vr) = (1−Vr/CR) and equation243

5, the energy balance leads to the following crack tip equation of motion:244

Vr(L) = CR

(1− Gc

GII(L, Vr = 0)

). (7)

In the context of frictional rupture, the fracture energy can be expressed as245

11

Gc =1

2(σn − Pf )Ω (8)

with Ω being a generic function describing frictional weakening with slip. For the linear slip-246

weakening model47, Ω = (fs − fd)dc with fs and fd as the static and dynamic friction coef-247

ficients, respectively, and dc the slip-weakening distance. For rate-and-state models of friction,248

Ω = α ln2(Vs/V0)48, with Vs and V0 being the slip velocity behind and ahead of the front, respec-249

tively, and α a constant depending only on the rate-and-state parameters.250

Combining equations 6, 7, 8 and taking χ = 1, the rupture velocity can be expressed as a251

function of the initial effective normal stress, the dynamic stress drop and the length of the crack,252

which are directly measured through our experiments:253

Vr = CR

(1− (σn − Pf )

∆τ 2d

Ω

πLE∗). (9)

This equation can then be directly related to the effective normal stress by considering that254

∆τd = (σn − Pf )(f0 − fd), where f0 is the background friction coefficient along the fault. Based255

on this hypothesis, the rupture velocity can be approximated by256

Vr = CR

(1− 1

(σn − Pf )(f0 − fd)2Ω

πLE∗)

(10)

and the effective stress leading to a sub-Rayleigh rupture velocity can be expressed as follows:257

(σn − Pf ) =

(1

(1− Vr

CR)(f0 − fd)2

(fs − fd)κπ

E∗

)(11)

where κ = dc/L (≈ 10−5 in our experiments). Note that if we assume that dc is a linear function258

12

of L, which is assumed in seismology, this last relation can be used to estimate the initial effective259

stress that leads to a given rupture velocity independent of the crack length. For instance, assuming260

fixed values for (f0− fd) = 0.1 and (fs− fd) = 0.5, slow rupture velocities (Vr < 0.1 m/s) should261

be promoted when faults are subjected to an initial effective normal stress of approximately 10262

MPa, which implies lithostatic fluid pressure at depth.263

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Acknowledgements FXP acknowledges funding provided by the Swiss National Science Foundation380

through grant PZENP2/173613. FXP is grateful to A. Kato for providing him the teleseismic dataset. FXP381

acknowledges J. Fortin and A. Nicolas for providing the andesite sample through the grant GEOTREF ob-382

tained by J. Fortin. FXP thanks A. Schubnel and R. Madariaga for introducing him to this topic and F.383

Paglialunga and M. Acosta for continuing to explore it with him. This work benefits from discussions with384

F. Cappa, J. Fineberg, J-P. Avouac and H. Leclere.385

Competing Interests The authors declare that they have no competing financial interests.386

Correspondence Correspondence and requests for materials should be addressed to francois.passelegue@epfl.ch.387

18

1.pdf

1015 1020 1025

Seismic moment M0 [N.m]

100

105

1010

Dur

atio

n [s

econ

ds]

1010 1015 1020

M0 / [L3]

103

104

105

106

107

x V

r [L]

LFE (Bletery et al., 2017)Tremor (Bletery et al., 2017)

SSE (Gao et al., 2012)SSE (Michel et al., 2019)

SCARDEC (Vallee & Douet, 2016)Earthquakes (Denolle et al., 2017)

LFE (Takemura et al., 2019)

a. b.

Slow ea

rthqu

akes

3

Regular earthquakes

c.

0 5 10 15Earthquake percentage [%]

0

10

20

30

40

50

Dep

th [k

m]

1.2 1.4 1.6 1.8 2C p / Cs

Standard deviation

Each profiles accross the through

Average profile

SSE epicenters

SSE, LFE, VLFEEarthquakes

Scaling relation between the different modes of slip. (a.) Scaling law for natural earthquakesobserved from seismological or geodetical measurements. Blue circles correspond to slow slipevents (so-called SSEs), deep low-frequency earthquakes (LFEs) and very-low-frequency earth-quakes (VLFEs)6,8,10–13,17,49. Regular earthquakes are presented by the red circles. The source timefunctions used were downloaded from the SCARDEC database14,50. Most of the data for regu-lar earthquakes were taken from recent studies49,50. The dashed lines correspond to the regulartrend deduced from natural observations for both slow (blue dashed lines) and fast earthquakes(red dashed lines)1,6. (b.) Normalised scaling low assuming the average rupture velocity andthe average static stress drop as determined in previous work for both regular49,50 and slow slipevents1,6,8,10,13,17. (c.) Hypocentral distribution of both slow and fast earthquakes in Japan6,7,11–17.Lines present the wave velocity profiles obtained from the analyses of seismic and teleseismicwaves in the subducting Philippine Sea plate in the Tokai district, Japan18,21. The blue dashed linecorresponds to the profile cross-cutting LFE hypocenters21. The black dashed line corresponds tothe average of all grey profiles obtained along the subduction trench21. The grey area correspondsto the standard deviation.

19

2.pdf

0 200 400 600 800 1000Time [sec]

0

10

20

30

Shea

r Str

ess,

Pf [M

Pa]

0

0.1

0.2

0.3

0.4

0 400 800 1200 1600 2000

20

40

60

0

0.2

0.4

0.6

0.8

0 1000 2000 3000 4000 50000

20

40

60

80

0

0.2

0.4

0.6

Slip

[mm

]

Time [sec] Time [sec]

τ [MPa]δ [mm]

Pfinj [MPa]

Pfedge [MPa]

events

a. Pc = 30 MPa b. Pc = 60 MPa c. Pc = 95 MPa

Triggering of instabilities along a critically loaded crack. Evolution of the macroscopic shear stressand of the slip along the fault during experiments conducted at 30 (a. ), 60 (b.) and 95 (c.) MPaconfining pressure. In each case, the shear stress first increased at 90% of the peak strength of thefault. Then, fluid was injected at a constant volume rate into the injection borehole (Fig. S1a), upto the release of the energy stored in the system. Black, red, cyan and blue solid lines correspondto the evolution of the shear stress, the fault slip, the fluid pressure in the injection borehole, andthe fluid pressure in the measurement borehole, respectively. Black circles correspond to each slipinstability treated in this study.

20

3.pdf

0 1000 2000 3000 4000 5000 60000

20

40

60

80

100

120

0 1000 2000 3000 4000 5000 600010-4

10-2

100

102

Slip

rate

[mm

/s]

Shea

r Str

ess,

Pf [M

Pa]

Time [seconds] Time [seconds]

a. b.#1

#2

#3

#4#5 #6

#1

#2

#3

#4#5

#6

Slip

[mm

]

0

0.5

1

1250.65 1250.7 1250.75Time [seconds]

1774 1774.2 1774.4 1774.6 1774.8Time [seconds]

3401 3401.5 3402 3402.5Time [seconds]

3505 3510 3515 3520Time [seconds]

3845 3850 3855 3860Time [seconds]

4570 4580 4590 4600Time [seconds]

c.Vr

min≈ 120 m/s Vr ≈ 20 m/s Vr ≈ 0.5 m/s

Vr ≈ 0.05 m/s Vr ≈ 0.05 m/s Vr ≈ 0.01 m/s

#1 #2 #3

#4 #5 #6

Transition from fast to slow slip events. (a.) Mechanical results obtained during the experimentconducted at 95 MPa confining pressure. The evolution of the local shear stress along the fault ateach strain gage location as a function of time is displayed by the grey-to-black solid lines. Theevolution of the average slip along the fault is displayed by the red solid line and the evolution ofthe fluid pressure in the injection site by the cyan solid line. (b.) Slip velocity burst associated witheach slip instability. The peak slip velocity reached during instability decreases over time, i.e., withan increasing number of events and with the progressive release of the initial shear stress. Numbersdisplayed in (a.) and (b.) refer to events for which the slip front propagation is presented in figure(c.). (c.) Propagation of rupture along the interface during slip events. The rupture velocity isestimated using an equidistant strain gage array along the fault. The average rupture velocity iscomputed using the average travel time for the rupture front.

21

4b.pdf

10-8 10-6 10-4 10-2 100

Vs [m/s]

10-2

100

102

104

Vr [m

/s]

0

0.2

0.4

0.6

0.8

1

10-2 100 102 104

Vr [m/s]

10-8

10-7

10-6

10-5

10-4

( n-P

f ) /

d2 [M

Pa-1

]

0

0.05

0.1

0.15

0.2

/ n

P f ( f

s-fd )

a. b.fs-fd =0.01

fs-fd =0.2

n = 1

Pc= 30 MPa

Pc= 60 MPa

Pc= 95 MPa

Pc= 30 MPa

Pc= 60 MPa

Pc= 95 MPa

Control of the nature of the seismicity. (a.) Scaling relation between the rupture velocities and theslip velocities reached during each slip event. White, grey and dark grey correspond to slip eventsobserved at 30, 60 and 95 MPa confining pressures, respectively. The colour bar displays the ratiobetween the average fluid pressure and the average normal stress along the fault at the onset ofthe slip events. (b.) Influence of the stress parameters derived from equation 9 on the rupturevelocity achieved during slip events. White, grey and dark grey symbols correspond to slip eventsobserved at 30, 60 and 95 MPa confining pressures, respectively. Red symbols correspond to dryexperiments conducted on Westerly granite36. Blue and red dashed lines correspond to LEFMpredictions using strength drops of 0.01 and 0.2, respectively.

22