of 24
manuscript submitted to
Geophysical Research Letters
1
Constraining Fault Friction and Stability with Fluid
-
Injection Field Experiments
1
2
Stacy Larochelle
1
, Nadia Lapusta
1,2
, Jean
-
Paul Ampuero
3
, and Frédéric Cappa
3,4
3
1
Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena,
4
California 91125, USA.
5
2
Division of Engineering and Applied Science, California Institute of Technology, Pasadena,
6
California 91125, USA
7
3
Université Côte d’Azur, IRD, CNRS, Observatoire de la Côte d’Azur, Géoazur, 06560 Sophia
8
Antipolis, France
9
4
Institu
t Universitaire de France, Paris, France
10
11
Corresponding
author:
Stacy Larochelle (
stacy.larochelle@caltech.edu)
12
13
Key Points:
14
Multiple frictional models with different stability reproduce the slip observ
ed during the
15
pressurization stage of a field experiment
16
The depressurization phase provides additional constraints on hydromechanical
17
parameters and hence fault stability
18
Fault stability and the spatial extent of slip relative to the pressurized region de
pend on
19
residual friction vs initial stress levels
20
21
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2
Abstract
22
While the notion that injecting fluids into the subsurface can reactivate faults by reducing
23
frictional resistance is well established, the ensuing evolution of slip is still poorly understood.
24
What controls whether the induced slip remains stable and confined to the fluid
-
affected zone or
25
accelerates into a runaway earthquake? Are there observable indicators of the propensity to
26
earthquakes before they happen? Here, we investigate these questio
ns by modeling a unique
27
fluid
-
injection experiment on a natural fault with laboratory
-
derived friction laws. We show that
28
a range of fault models with diverging stability with sustained injection reproduce the slip
29
measured during pressurization. Upon depr
essurization, however, the most unstable scenario
30
departs from the observations, suggesting that the fault is relatively stable. The models could be
31
further distinguished with optimized depressurization tests or spatially distributed monitoring.
32
Our findin
gs indicate that avoiding injection near low
-
residual
-
friction faults and depressurizing
33
upon slip acceleration could help prevent large
-
scale earthquakes.
34
35
Plain Language Summary
36
Fluid injections into the Earth’s crust are common practice in the exploita
tion of
37
subsurface energy
resources
such as geothermal energy, shale gas and conventional
38
hydrocarbons. These injections can perturb nearby fault structures and hence induce earthquakes
39
and transient slow slip. Understanding what controls the sta
bility (i.e., the propensity to generate
40
earthquakes) and spatial extent of the fault response as well as identifying precarious faults is
41
crucial to minimize the seismic hazard associated with these industrial practices. Here, we take a
42
step towards this
goal by modeling a unique experiment in which water was injected into a
43
natural fault and the resulting slip measured directly at depth. We first show that multiple models
44
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3
can explain the observations equally well while pressure is increased in the experim
ent. In these
45
models, how stable the fault response is with further injection and how large of a zone is
46
reactivated compared to the fluid
-
affected region depends on frictional properties. We then
47
demonstrate that the slow slip response to a decrease in in
jection pressure further constrains the
48
range of admissible models. Our work suggests that it may be possible to identify potentially
49
hazardous faults with optimally designed injection tests without inducing damaging earthquakes.
50
51
1 Introduction
52
Earthqu
akes induced by fluid injection into the subsurface pose a major challenge for the
53
geoenergy industry and society in general
(Ellsworth, 2013; Grigoli et al., 2017)
. Tectonically
-
54
quiescent regions where dormant faults could be reactivated are particularly c
hallenging, as their
55
infrastructure
is often
not designed for large
-
magnitude induced earthquakes
(McGarr et al.,
56
2015)
. At the same time, some faults have been observed to slip stably at aseismic speeds of 10
-
7
57
10
-
2
m/s in response to fluid injection
(Cornet et al., 1997; Duboeuf et al., 2017; Guglielmi et
58
al., 2015; Scotti & Cornet, 1994; Wei et a
l., 2015)
.
While induced earthquakes have been located
59
anywhere from a few meters to tens of kilometers from injection wells
(Goebel & Brodsky,
60
2018)
, the spatial extent of fluid
-
induced aseismic slip is not as well characterized due to the
61
paucity of direct observations. Understanding what conditions lead to seismic versus aseismic
62
and l
ocalized versus widespread fault r
eactivation is central to physics
-
based hazard forecasting.
63
An outstanding opportunity to investigate these questions is offered by a decametric
-
scale
64
fluid injection experiment recently conducted in an underground tunnel intercepting a dormant
65
fault in a
carbonate formation
(Guglielmi et al., 2015)
(Figure 1A). During the experiment, the
66
fluid pressure and fault slip were recorded at the injection site. Although the observed slip was
67
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4
mostly aseismic, it is import
ant to understand if the observati
ons contained sufficient information
68
to determine whether slip would have accelerated into an earthquake rupture if injection had
69
continued. Previous efforts to model the field experiment with a slip
-
weakening friction law
70
concluded that aseismic slip outg
rew the pressurized zone, potentially leading to a runaway
71
earthquake with continued injection
(Bhattacharya & Viesca, 2019)
.
72
Here, we use the data from the field experiment to examine the issue of slow and
73
confined v
s.
fast and runaway slip in models with more realistic, laboratory
-
derived rate
-
and
-
74
state friction laws
(Dieterich, 1979, 2007; Ruina, 1983)
consistent with laboratory results on
75
materials from this specific fault zone
(Cappa et al., 2019)
. Furthermore, we use the modeling to
76
identify promising avenues to quantify the fault properti
es and control injection
-
induced
77
seismicity hazard. We adopt a full
y
-
dynamic computational framework that resolves both
78
aseismic and seismic slip on faults. We keep other model ingredients relatively simple to better
79
understand frictional effects in the pr
esence of a diffusing fluid. For example, we do not
80
explicitly mode
l the change in fault permeability induced by slip as in previous studies
81
(Bhattacharya & Viesca, 2019; Cappa et al., 2019; Guglielmi et al., 2015)
. Nonetheless, we find
82
that multiple frictional scenarios of varying spatial behavior and pronene
ss to large earthquakes
83
match the slip observations of the field ex
periment equally well during fault pressurization. We
84
also find that depressurization provides further constraints that could help identify potentially
85
hazardous faults.
86
87
2 Data and Metho
ds
88
2.1
A unique fluid
-
injection experiment on a natural fault
89
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5
The un
precedented field experiment involved injecting water directly into the fault zone and
90
measuring the resulting fault slip at a depth of 280 m with a specially desig
ned borehole p
robe
91
(Guglielmi et al., 2015)
(Figure
1
A
). Prior to the experiment, the shear and normal stress acting
92
on the fault were estimated at 1.65 +/
-
0.5 and 4.25 +/
-
0.5 MP
a
,
and the permeability and bulk
93
modulus of the
initially dry fault at 7
x
10
-
12
m
2
and
13.5 +/
-
3.5 GPa, respectively.
Figure 1
B
94
summarizes the main observations of the experiment, including the deceleration of slip
95
associated with depressurization not d
iscussed in previous w
orks.
The slip measured during the
96
pressurization phase displays three distinct slip stages. At first
,
the fault is inactive and no
97
significant slip is recorded. The second stage initiates between 300 and 400 s when slip rates
98
attain
~10
-
7
m/s and the accumulated slip becomes measurable within the timeframe of the
99
experiment. Stage 3 corresponds to the sharp acceleration to slip velocities of ~10
-
6
m/s
without
100
any significant increase in injection pressure at ~1200 s.
Hydromechanical
modeling suggests
101
that 70% of the 20
-
fold increase in permeability during the experiment occurred prior to this
102
acceleration
(Guglielmi et al., 2015)
.
Laboratory experiments were also performed on gr
i
nded
103
materials from the fault zone to further c
onstrain the
rate
-
and
-
state
frictional properties
(Cappa et
104
al., 2019)
.
105
2.2 Diffusion of pore fluid pressure into the fault zone
106
We model the field experiment as a fluid injection into a planar fault embedded in an
107
elastic medium (Figure 1AC). We simulate the fluid injection by prescribing an evolution of pore
108
p
ressure at the center of the fault that approximates the pressure history of the field experiment
109
(Figure 1B, top). Simulations with a smooth pressure evolution result in similar but easier to
110
interpret simulation results than those with the exact pressure
history (Figures S1
-
S2).
111
The imposed pressure diffuses axisymmetrically into the fault plane as follows:
112
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휕푝
(
,
)
휕푡
=
*
+
(
,
)
+
+
1
휕푝
(
,
)
휕푟
.
(1
)
w
here
is the pore pressure,
is the radial distance from the
injection interval
,
is time,
and
113
is the hydraulic diffusivity. The diffusion is numerically implemented using a forward finite
114
difference scheme.
Injection p
ressure is prescribed at a distance
of
/01
=
0.05
m from the center
115
of the fault to m
imic the experimental procedure.
Although we prescribe zero pressure boundary
116
conditions to emulate the initially dry fault, the choice of boundary condition is not essential here
117
because the size of the simulated fault
(250 m)
is larger than that of the p
ressure diffusion.
118
Models with larger fault domains produce nearly identical results (Figure S3).
119
Although both pressure and flow rate are reported as part of the field experiment, the
120
exact value of
the hydraulic diffusivity
is still uncertain because the spatial extent of the
121
pressurized zone and the
fault
thickness over which the diffusion occurs,
, are poorly
122
constrained.
The v
olumetric flow rate,
, depends on
as
:
123
=
푘푏
(
2
/01
)
휕푝
휕푥
(2)
w
here
is the permeability of the fault zone,
/01
is the injection radius and
the dynamic
124
viscosity of water.
Hence, for
a given
flow rate, there is a trade
-
off between
the fault thickness
b
125
over which the fluid diffusion occurs and
the permea
bility
k
(and hence hydraulic diffusivity
=
126
:;<
=
>
?
,
where
>
is
the
specific
storage
)
of the fault zone.
In
Section 3
,
we
use
hydraulic
127
diffusivities of 0.04, 0.20
,
and 0.85 m
2
/s
to match field experimental measurements of slip for
128
different friction regimes
.
A
ssum
ing
the
specific storage of
>
=
2
x
10
-
4
m
-
1
as in Bhattacharya
129
and Viesca (2019)
, these hydraulic diffusivities
correspond to
the
permeability values of 0.8
,
4
,
130
and
17
x
10
-
12
m
2
that
are within the ranges presented in previou
s studies that considered
131
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7
permeability enhancement: 0.8 to 1.3
x
10
-
12
m
2
(Bhattacharya and Viesca, 2019) and 7 to 100
132
x
10
-
12
m
2
(Guglielmi et al., 2015). These permeability values
are also consistent with the flow
133
rates measured in the field experiment
,
fo
r reasonable values of the
fault thickness
b
of 2
9
, 6.7,
134
and 1.8 cm, respectively
(
Figure 1B
)
.
While
considering
permeability enhancement
may be
135
necessary to match the finer features of the pressure and flow rate histories
(un
less the fault
136
thickness
b
affected
by fluid flow
varies with time or with space)
,
all three combinations
of the
137
parameters we use
reproduce the hydrologic observations to
the
first order. We therefore
138
consider a range of
constant
hydraulic diffusivity (an
d
hence
permeability) values in our search
139
for models that reproduce the main features of the experimental observations.
140
141
2.3 Numerical modeling of fluid
-
induced fault slip
142
As fluid pressure
increases and
diffuses into the fault plane, fault friction eve
ntually
143
decreases and measurable slip ensues (Figure 1C). We model this induced fault slip using a fully
-
144
dynamic 2D antiplane boundary integral method capable of simulating the complete seismic
145
cycle including both aseismic and seismic deformation
(Lapusta et al., 2000; Noda & Lapusta,
146
2013)
. Fault slip is governed by the following elastodynamic equation
:
147
(
,
)
=
[
(
,
)
]
=
/0/
+
[
(
,
)
]
2
X
(
,
)
(
3)
w
here
is the shear stress,
the friction coefficient,
the normal stress,
/0/
the initial
(i.e.,
148
background)
shear stress,
a linear functional which depend
s on the slip history,
,
the shear
149
modulus of the elastic medium,
X
the shear wave speed
and
the slip rate. The friction
150
coefficient in (
3
)
follows an empirical rate
-
and
-
state formulation derived from laboratory
151
experiments which describes th
e dependence of
on the slip rate and a state variable
152
(Dieterich
, 1979, 2007; Ruina, 1983)
:
153
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(
,
)
=
+
ln
+
ln
`>
(
4)
w
here
and
are the direct and evolutionary rate
-
and
-
state parameters,
`>
is the critical slip
154
distance
and
is
a reference coefficient of friction at reference slip r
ate
.
The state variable is
155
assumed to evolve according to the aging law
(Marone, 1998; Ruina, 1983)
.
156
As the fault in the experiment is inactive prior to the fluid stimulation, the modeled fault
157
is not loaded tectonically. Fault slip is thus purely fluid
-
induced
, i.e., no significant slip would
158
occur without the injection within the time scales considered in the simulations.
To initialize the
159
models, we impose shear and normal stresses in agreement with the values reported at the field
160
site prior to the experimen
t
(Guglielmi et al., 2015)
and initial state variable values consistent
161
with a dormant, highly healed fault (Text S1; Figures S4
-
S7). The corresponding initial slip rate
162
is then computed from
Eq.
(
4
).
163
164
3. Results
165
3.1 Models in agreement with the
slip
observations during pressurization
166
By first l
imiting our analysis to t
he
pressurization stage of the experiment (up to 1400 s
)
,
167
we find that t
he observations
are
equally well reproduced by a family of models.
Three
168
representative cases, which we denote lower
-
, intermediate
-
and higher
-
friction models,
are
169
shown in Figures 2A
-
C and S
8 to S11
a
n
d
T
a
b
l
e
S
1
. Below we expla
in how we constrained these
170
models by examining how the various parameters govern the transitions between the different
171
slip stages and considering the trade
-
off between friction and fluid pressure.
172
At the beginning of all simulations, slip rates are low
and both inertial effects and elastic
173
stress transfers are negligible. Eq. (3) then reduces to:
174
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(
,
)
[
(
,
)
]
=
/0/
(
5
)
As
increases and
/0/
remains constant over time,
must increase via growing slip rates in
175
order for
(5)
to remain true, resulting in a balance between the direct frictional effect and
176
changes in po
re pressure
(Dublanchet, 2019)
. Slip rate and friction continue increasing until slip
177
becomes significant a
t
~ 10
-
7
m/s. The onset of significant slip thus approximately coincides
178
with the maximum friction reached during the simulations (Figures 2
A
B
, S
8
)
. The peak friction,
179
a
, can be approximated as:
180
a
~
+
ln
X
+
ln
/0/
`>
(
6
)
where
X
= 10
-
7
m/s. The state variable remains at its initial value,
/0/
, as it has not
evolved
181
significantly yet due to negligible slip and short healing time compared to its large initial value.
182
Moreover, becaus
e the fluid pressure at the injection site is known at all times, we can relate
a
183
to the timing of slip initiation,
X
:
184
a
=
/0/
[
(
0
,
X
)
]
(
7
)
It is thus possible to control
X
by computing the corresponding
a
with Eq.
(7)
and selecting
,
185
,
,
/0/
and
`>
such that Eq.
(6)
is satisfied.
The three example models have
X
between
300
186
and 400s and
a
between 0.84 and 0.99
(Figure
s 2B, S
8
)
.
187
Once significant slip starts accumulating
, the fault begins weakening until it reaches
188
steady state and friction reaches its
quasi
-
static residual
value of
d
=
+
(
)
ln
/
at
189
the latest stage of the fault pressurization experiment
(Figure 2B, S
8
). As in Dublanchet (2019)’s
190
rate
-
st
rengthening models, we find that this transition to steady state is accompanied with a
191
marked acceleration in slip rate (Phase II in Dublanchet
,
20
19)
which we assume to explain the
192
acceleration observed at 1200s.
193
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The critical slip distance,
f
, over which friction weakens from
a
to
d
can be
194
approximated as:
195
f
a
d
/
`>
(
8
)
since
hi
hj
k
l
m?
. Furthermore, from elasticity, slip is related to stress drop by:
196
(
9
)
where
is the length
of the slipping zone
. By equating Eq. (
8
) and (
9
) at the center of the fault,
197
we can estimate the slipping zone size,
qf
, at which steady state is reached and
Stage 3
initiates:
198
qf
`>
a
d
(1
0
)
Moreover, by choosing
to be
on the same order of magnitude as the
fastest slip rate measured
199
during the field experiment (
= 10
-
6
m/s), we can approximate
d
with
since
the
200
contribution of
(
)
ln
/
be
comes small compar
ed to that of
.
Eq.
(1
0
) can
then be
201
rewritten in terms of known parameters as:
202
qf
`>
ln
X
+
ln
/0/
`>
/0/
[
(
0
,
qf
)
]
(1
1
)
w
here
qf
denotes the o
nset of Stage 3.
For all the simulations presented in this work, we find
203
that adding a pre
-
factor of 3
to Eq. (1
1
) provides a good estimate of the slipping zone
size at
qf
204
(Text S2)
.
Remarkably,
qf
only depends on quantities at the injection s
ite. We can
thus control
205
the initiation of Stage 3 in our simulations by tuning the model parameters such that the slipping
206
zone reaches length
qf
at ~1200s as is the case for our three representative models in Figure 3.
207
Another critical aspect in
these simulations is the balance between friction and the pore
208
pressure forcing. Figures S
2
0
-
S2
3
illustrate how
the aseismic slip zone grows with decreasing
209
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and increasing
, respectively. In particular, during Stage 3, the spatial extent of the sl
ipping
210
zone with respect to the pressurized zone and the slip rate at the injection site depend on the
211
difference between the residual and initial friction,
d
/0/
,
which
controls the elastic energy
212
available to drive fault rupture once initia
ted
(Bhattacharya & Viesca, 2019; Dublanchet, 2019;
213
Galis et al., 2017; Garagash & Germanovich, 2012)
(Figure S
19
A
-
C
)
. Note
that this is distinct
214
from the
difference between peak and initial frict
ion,
a
/0/
(e.g., Gischi
g, 2015)
, which
215
controls the timing of fault reactivation
as discussed above
.
216
Given all
these
consideration
, for each diffusion scenario presented in Figure 1B, we find
217
a corresponding frictional model by adjusting
such that
the simulated slip matches the
218
observations during the first 2 slip
stages and produces a sufficiently large slip transient during
219
Stage 3. To be able to use
values in
agreement with the range
d
=
0.55
-
0.65 inferred from
220
lab
oratory experiments on the grinded fault zone material
(Cap
pa et al., 2019)
, we
set
/0/
to 0.5
4
221
(
/0/
= 2.15 MPa
,
= 4.00 MPa), which is within the uncertainty range of the initial stress
222
measurements.
The selected values of
restrict the range of possible values for the term
223
ln
/0/
/
`>
in Eq.
(6) in order for slip to initiate between 300 and 400 s
, which in turn
224
restricts
factor
휇퐷
`>
/
in Eq. (11) in order for Stage 3 to initiates at 1200s. The factor
휇퐷
`>
225
which appears in estimates of critical nucleation lengths also needs to b
e large enough to avoid
226
nucleation of dynamic events within the experimental time
(
e.g.,
Rice & Ruina, 1983;
Rubin &
227
Ampuero, 2005)
.
Finally
, we fine tune parameters
and
/0/
to adjust the slope and timing of the
228
acceleration
, respectively
. Note that decreasing
while keeping
constant increases the slope of
229
the slip acceleration
-
due to the (weak) dependence of
d
on
(
)
and eventually leads
to
230
the nucleation of a dynamic event right at
qf
(Figure
S1
6
and
S
19
D
-
F
).
This procedure
results in
231
a family of models with
=
0.48
to 0.60,
=
-
0.001 to
-
0.005
(
= 0.016)
,
/0/
= 1.2
x
10
12
232
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12
to 7.0
x
10
12
s and
= 0.04 to 0.85 m
2
/
s that
match the slip observations
equally well during
233
pressurization.
234
Although the three models exhibit comparable slip histories at the injection site, they
235
differ in features that were not directly accessible to field observation. In particular, their
spatial
236
behaviors differ qualitatively (Figure 3,
S
9
-
S1
1
). Defining the pressurized zone with 0.5 MPa
237
pressure contours
as in previous works, the lower
-
friction scenario produces an aseismic front
238
that outruns the pressurized region, within 1400 s, a
s in slip
-
weakening models
(Bhattacharya &
239
Viesca, 2019)
(Figure 3D). By contrast, in the higher
-
friction model, which reproduces the
240
observations equally well, aseismic slip remains confined well within the pressurized area
241
(Figure 3F).
Our models
demonstrate that slip did not necessarily extend beyond the pressure
242
perturbation during the experiment; that explaining a slip history at a single point in space is a
243
non
-
unique problem; an
d that further hydro
-
mechanical complexity is not required to explain the
244
observed slip to first order. Monitoring fault slip and fluid pressure along the length of the fault,
245
directly with additional probes or remotely with geophysical methods, would help
distinguish
246
between these different scenarios and would allow to study additional
fault processes such as
247
permeability evolution and inelastic dilatancy
(Segall & Rice,
1995)
.
248
3.2
Distinguishing between models with depressurization
249
We find that the depressurization stage of the field experiment, which was not discussed
250
or modeled in previous studies
(Bhattacharya & Viesca, 2019; Cappa et al., 2019; Derode et al.,
251
2015; Guglielmi et al., 2015)
, contains valuable information on fault pro
perties.
In this pressure
-
252
reduction stage, the lower
-
friction model features a pronounced delayed slip response that is not
253
observed in
the experiment or in the other two cases (Figure 2A). The intermediate
-
and higher
-
254
friction models, which also have high
er hydraulic diffusivities, thus explain the entire set of
255
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13
observations better than the lower
-
friction model. Further discriminating between these two
256
models is not possible with the current dataset because, by the time depressurization is initiated,
257
the s
lip rates in these simulations are too low to produce a detectable difference in incremental
258
sli
p
.
However, if the injection
pressure is decreased more gradually and earlier in the
259
acceleration phase
at which point the intermediate
-
and high
er
-
friction scenarios have
260
approximately the same (and higher) slip rate
the three scenarios lead to diverging levels of
261
incremental slip (Figure 2D).
As we only investigate a limited portion of the rate
-
and
-
state
262
parame
ter space in this study, we cannot conclude that
timely depressurization
can uniquely
263
discriminate between all possible frictional scenarios.
However,
it is clear that timely
264
depressurization can
provide additional constraints on the frictional and hydromechanical
265
properties of
fault
zone
s
.
266
In addition to fitting the entire set of
slip observations better, models with
f*
of 0.55 and
267
0.60
are also
more
consistent with
the rang
e of residual friction values of 0.55 to 0.65 derived
268
from
laboratory experiments on
grinded fault
gouge
(Cappa et al., 2019)
.
Moreover
, the initial
269
fault conditions implied by these
higher
-
friction cases are fully consistent with those of a
270
dormant fault whereas the low
-
friction case is not (
Text S1).
Our preferred model for the site of
271
the injection experiment is thus a rate
-
weakening fault with 0.55 <
f*
< 0.
60,
0.20 <
<
0.85
272
m
2
/s,
= 0.011 and
= 0.016.
This is in contrast to the original Guglielmi et al.
(2015)
study
in
273
which
the authors
inferred
a rate
-
strengthening fault from a spring
-
slider model with
274
permeability enhancement. Within the limited parameter space that we explored through the
275
procedure outlined in section 3.1, we could only find rate
-
strengthening models with relatively
276
low
f*
and hence
ones that
only match
the pressurization stage of the
experiment (Figure S2
4
).
It
277
is possible that there are 2D models with rate
-
strengthening parameters that match the entire slip
278
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14
history
that
we have not consid
ered here, which would further
strength
en our conclusions that
279
the
field measurements can be match
ed with multiple friction scenarios and that the
280
depressurization stage provides further constraints than pressurization alone.
281
3.3
Diverging fault stability with sustained injection
282
Modeling what would have happened
if the fluid injection had continued for longer
283
highlights why distinguishing between the three qualitatively different scenarios identified in this
284
study is crucial. In response to an extended constant
-
pressure injection (Figure 4, Figures
S
3,
285
S25
-
S2
7
), the low
-
friction fault nucleates an earthquake almost immediately, while the
286
intermediate and higher
-
friction faults decelerate and continue slipping aseismically before
287
eventually transitioning to seismic slip rates. Once a seismic rupture initia
te
s, whether it is self
-
288
arrested or run
-
away depends on the
dynamic
residual friction,
r
,
which is generally slightly
289
lower than
d
(Galis et al., 2017; Garagash & Germanovich, 2012)
. If
r
<
/0/
,
as in the low
-
290
and intermediate
-
friction cases (Figure 4B), the rupture may release enough elastic energy to
291
propagate beyond the fluid
-
affected regions and would only be stopped by less favorably
292
stressed fault patches, geometrical bar
riers, or more stable materials not present in the current
293
model (Figures 4C,D). Such runaway ruptures may be preceded by smaller ruptures or aseismic
294
slip transients (Figures
S1
5
and
S
19
A
); indeed, in fracture mechanics models
(Galis et al., 2017)
,
295
the transition to runaway rupture requires a certain balance between fluid pressurization and
296
background stress to be reached. If
r
<
/0/
,
as in the high
-
friction case, the rupture self
-
arrests
297
once out of the pressurized zone (Figure 4E). For low
-
to intermediate
-
friction faults, the
298
maximum expected earthquake magnitude,
uqv
,
is thus controlled by hydro
-
mec
hanical and
299
geometrical fault properties as opposed to injection attributes (e.g., cumulative volume injected)
300
(van der Elst et al., 2016; Galis et al., 2017; Gischig, 2015; McGarr, 2014)
.
For example, varying
301
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the injection rate in our simulations does not alter the event size (
Figure
S
28
). In the
302
intermediate
-
friction
case, the fault ultimately undergoes a runaway earthquake despite having
303
stably released energy for over an hour, thus demonstrating that aseismic slip does not signify an
304
absence of earthquake hazard.
Fortun
ately, comparing the depressurization and prolonged
305
injection scenarios reveals that reducing the injection pressure might be sufficient to suppress
306
earthquake nucleation at the injection site. The lower
the
friction
on
the fault, the faster the rate
307
of t
his depressurization needs to be (Figure
S
2
9
). Note, however, that earthquakes could still be
308
triggered by aseismic slip itself on more unstable heterogeneities away from the injection site
309
(Eyre et al., 2019; Guglielmi et al., 2015)
.
310
4 D
iscussion and Conclusions
311
To summarize, our modeling of a fluid
-
injection experiment into a fault zone reveals that
312
the difference between fault prestress and quasi
-
static or dynamic fault friction controls whether
313
slip is confined to the fluid
-
affected zo
ne or outruns it. We find that: (i) multiple scenarios
with
314
different
hydrologic assumptions and
friction levels are consistent with the measured slip at the
315
injection site during the pressurization phase, (ii) the low
-
friction scenario in which slow sli
p
316
outruns the pressurized region is inconsistent with slip during the depressurization phase, and
317
(iii) the high
-
friction scenario, in which the slipping zone is well confined within the pressurized
318
region, is most consistent with the full range of informa
tion from the experiment, including the
319
fault behavior during fault depressurization and laboratory friction measurements on the
320
materials from the fault zone. Key hydro
-
mechanical parameters such as the
difference between
321
quasi
-
static friction
a
nd
initial normalized prestress,
d
/0/
,
the rate dependence of friction,
322
,
and the hydraulic diffusivity,
,
exercise a first
-
order control on the stability and spatial
323
extent of a fault response to fluid injections. Further
constraining these parameters is thus critical
324
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16
for seismic hazard management. In the geoenergy industry, test injections with timely
325
depressurization and spatiotemporal monitoring of fluid pressure and aseismic slip could be
326
performed prior to exploitatio
n to ensure that there are no low
-
friction faults nearby. Our
327
findings s
how
that augmenting fault
-
pressurization experiments with suitably designed
328
depressurization phases and multiple monitoring locations along the fault
c
ould
provide
329
invaluable ins
ight into the physics of both induced and natural earthquakes
(Savage et
al., 2017)
330
and friction properties of dormant faults. Such more advanced injection experiments and
331
corresponding modeling work will potentially be able to assess the effects and relative
332
importance of additional mechanisms (e.g., poroelastic stresses
(Deng et al., 2016; Goebel et al.,
333
2017; Segall & Lu, 2015)
, slip
-
induced dilatancy
(Cappa et al., 2019; Segall & Rice, 1995)
, bulk
334
fluid diffusion, and enhanced dynamic weakening) and complexity (e.g., material heterogeneities
335
(Eyre et al., 2019)
).
336
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