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GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,
Effective strength heterogeneity controlling slow slip
events on laboratory faults
Paul A. Selvadurai,1
and Steven D. Glaser,1
Corresponding author: Paul A. Selvadurai, Civil and Environmental Engineering, University
of California, Berkeley, California, USA. ([email protected])
1Civil and Environmental Engineering,
University of California, Berkeley,
California, USA.
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Rheological differences on natural faults are believed to be a controlling
factor of slow earthquakes. We characterized factors controlling behavior on
a PMMA laboratory fault, focusing on effects of normal stress and loading
velocity on slip and slip rate evolution building up to gross fault rupture. Faults
displayed lower strength heterogeneity at lower normal stresses compared with
greater strength and stiffness heterogeneity at high normal stresses. Slowly
expanding shear rupture originated from central, weaker and more compli-
ant sections of the fault, propagating outwards at speeds of Cslow/CRayleigh ∼
(6−191)×10−7, scaling directly to rates for actual slow earthquakes. Rup-
ture expansion, slip rates and stress drop were dependent on the shearing
velocity. Smaller number of larger patches in an area led to regular earth-
quakes, while larger number of smaller patches led to slow earthquakes. Smooth-
ing of the degree of fault complexity by slow earthquakes prepared the con-
dition for standard breakaway events.
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1. Introduction
For more than fifty years seismologists have reported the occurrence of slow earthquakes
[Beroza and Ide, 2011]. Slow earthquakes are characterized by relatively long-period ema-
nating seismic waves in relation to the short-period seismic waves that make up traditional
earthquake signals [Ide et al., 2007]. Denser earthquake-monitoring networks, which in-
clude borehole seismometer arrays and continuously recording global positioning system
(GPS) networks, have allowed for more accurate and frequent observations of slow fault
slip at a range of depths [Kawasaki et al., 1995; Kostoglodov et al., 2003; Igarashi et al.,
2003; Rogers and Dragert , 2003].
A variety of slow earthquake phenomena have been observed, such as, deep episodic
non-volcanic tremor [Obara, 2002], low-frequency earthquakes (LFEs) [Shelly et al., 2007],
very low-frequency earthquakes (VLFs) [Ito et al., 2007], episodic tremor and slip (ETS)
[Rogers and Dragert , 2003], and long-term/short-term slow slip events (SSEs) [Hirose
and Obara, 2010; Fukuda et al., 2014]. Some of these phenomena may be linked. For
example, tremor and LFEs may be the noisy expression from a small fraction of the fault
surface undergoing large-scale slow slip episodes [Bostock et al., 2015] but our mechanical
understanding of their interaction is limited. In the field, physical mechanisms causing the
differences between the various types of slow earthquake behavior (and their interactions)
are not well understood, but seem to be characterized by shear slip along interplate
boundaries.
Slow fault slip at shallow depth (above the seismogenic zone, i.e. < 10 km) are still not
well understood and reside up-dip from large earthquake ruptures. Less focus has been
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paid to shallow events but they are believed to occur along the plate interface and should
therefore be controlled by friction properties and conditions characterizing the fault zone
[Ikari et al., 2013]. Slow earthquakes at greater depths (below the seismogenic zone) are
also thought to be attributed to frictional heterogeneity and asperity interactions [e.g,
Ando et al., 2010; Nakata et al., 2011; Zigone et al., 2015]. Obara [2011], among others
[e.g., Saffer and Wallace, 2015], gives an intricate picture of the variety of faulting con-
ditions that may interact to cause slow earthquakes. It is thought that slow earthquakes
occur on rocks exhibiting appropriate hydrothermal conditions [Okazaki and Katayama,
2015] but to date, there has been no unifying mechanism to describe aseismic transients
(slow slip). One thought is that slow earthquakes are prematurely arrested large earth-
quakes due to frictional barriers [Ikari et al., 2013; Mele Veedu and Barbot , 2016].
We present laboratory experiments that examine features of slow slip accumulation that
appear analogous to slow slip events (SSEs) on natural faults. The investigation focuses
on the possible mechanical factors causing systematic changes in the evolution of slow slip.
Using a direct shear friction apparatus we constrain the boundary and initial conditions
then shear a frictional interface formed between two blocks of polymethyl methacrylate
(PMMA). Prior to shearing, we measure the clustering of asperities along the interface
that represent strength heterogeneity, a property controlled by the topographic interaction
between the two samples. Increased density of asperities, representative of local fault
fluctuations, changed with increased far- field normal stress (σ0). Both an increase in
overall strength and fluctuations in strength were observed at higher σ0. This causes an
increased resistance to the expansion of a slow shear frictional rupture. At high levels of
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applied normal stress, we observe a slowly expanding rupture we refer to as slow events
(SEs). These events were not present when strength heterogeneity decreased (low σ0).
We believe that the generation of slow earthquakes could be controlled by large variations
in the plate’s interface shear strength and stiffness on sections of the fault that are not
entirely locked (i.e. exhibit some level slow slip beforehand).
2. Experimental procedure
The tests were carried out on a direct shear friction apparatus. Additional details of
the experimental facilities, material properties are found in Selvadurai and Glaser [2015a]
and surface preparation techniques are in Supporting Information S1. The apparatus
(Figure 1(a)) allowed us to monitor transition of sliding (from slow to rapid) along a
pre-existing frictional fault. The top slider block had dimensions 400 mm x 80 mm x
12 mm thick and the base plate was 610 mm x 300 mm x 50 mm thick. The sliding
material was PMMA (shear modulus µ = 2200 MPa and Poisson’s ratio ν = 0.32) and
has been often used as an analog for faulting rock due to its similar constitutive responses
and lack of plastic flow at lower applied stresses [e.g., Spetzler , 1978; Petit and Barquins ,
1988; Dieterich and Kilgore, 1994; Rubinstein et al., 2004; McLaskey and Glaser , 2011;
Svetlizky and Fineberg , 2014; Subramanian and Singh, 2015]. The validity if using PMMA
as a ductile rock analog is discussed in Selvadurai and Glaser [2015a]. A pressure sensitive
film (20 micron pixel size) was used to map the size, location and normal stress supported
by asperities along the interface before each test was performed [Selvadurai and Glaser ,
2015a]. Seven noncontact eddy current displacement sensors (NC1-NC7) were used to
measure differential slip along-strike (x-direction) of the fault.
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During an experiment asperities along the interface are measured using the pressure
sensitive film [Selvadurai and Glaser , 2015a]. The fault was carefully indexed to a datum
location then the pressure film was developed by pressing it in between the slider block
into the base plate. Normal loading was accomplished by pressing two hydraulic jacks
on the massive, rigid loading platen; inducing a far-field normal stress σ0. Normal stress
was maintained on the fault for thold = 900 s allowing film time to develop. The fault
was unloaded, and the film was removed, digitized and the signal processed (see Figures
1(b) and (c) for examples of the measured asperity distribution). The slider block was
then re-indexed back the datum position and reloaded, without the pressure film, to the
same σ0. The fault was held for thold = 900 s then the rigid loading platen was driven at
a constant far-field velocity VLP that simulated tectonic loading. Shear force Fs built up
and slip δ (relative motion of the slider block and base plate) variably accumulated along
the fault until a gross fault rupture. Apparatus stiffness was calculated to be 0.76 N/µm
from the sample averaged slip versus the shear force dropped during gross fault rupture
[McLaskey and Kilgore, 2013]. The compliant nature of the apparatus coupled with low
driving velocities allowed us to study the slow premonitory phase in more detail [Heslot
et al., 1994].
Slip measurement from the noncontact sensors (NC1-NC7) are shown in Figure 2. These
measurements represent local slip which varied non-uniformly in the x-direction as slow
slip accumulated. Linear interpolation was used to expand the local measurements to a
2D spatiotemporal grid for both slip δ(x, t) and slip rate δ(x, t) (Figure 3), discretized at
10 mm increments and 1 second time intervals. A total of twenty two run-ups to gross
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rupture of the fault were studied at two levels of far-field normal stress: Low (σ0 = 0.8
MPa for Fn = 4.0 kN) and High (σ0 = 0.4 MPa for Fn = 2.0 kN). The range of loading
rates VLP was 1 µm/s, 3 µm/s and 7 µm/s. After each fault rupture, the slider was
unloaded and re-indexed back to the datum location before the subsequent test.
3. Results
3.1. Asperity distribution at low and high normal stress
The key focus of this study is the manner in which slow slip accumulated along the
fault before gross rupture occurred. Our results showed that slow slip accumulated non-
uniformly along the fault. We note that differential slip has been observed in the some
laboratory friction studies [e.g., Ohnaka and Shen, 1999; McLaskey and Kilgore, 2013;
McLaskey et al., 2015], but, we will see, the rupture propagation speeds observed in our
study are much slower and may be due to the unique choice of material and apparatus
configuration. To further understand the factors controlling slow slip along the fault, we
investigated the asperity distributions at different normal load levels. Asperities were
formed due to topographic surface variations of the slider block at various length scales
(see Supporting Information S2) – local clustering of asperities are the result of local
variations in topography [e.g., Archard , 1961; Persson, 1999]. Figures 1(b) and (c) show
the asperity distributions at the low (σ0 = 0.4 MPa) and high (σ0 = 0.8 MPa) levels
of applied normal stress, respectively. The spatial distributions are shown for asperities
whose individual areas Ai were greater than 4 x 10−3 mm2. Spatial histograms were
segmented into 4 mm increments along-strike (x-axis) and 0.5 mm increments across the
y-axis and showed the non-uniform distribution of the real contact area (Ar). Supporting
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Information S2 discusses the topographic length scale variations along the slider block
sample that can account for variations in asperity distribution (Figures 1(b) and (c)) and
real contact area (Figure 1(d)) at various length scales (λ). Asperities on natural faults
also appear at a variety of length scales having been reconstructed using coseismic slip
distributions [e.g., Mai and Beroza, 2002; Lavallee and Archuleta, 2005].
For low normal stress (σ0 = 0.4 MPa), the total real contact area Ar = 16.44 mm2 (∼
0.53 % of the nominal contact area) was composed of N = 836 large asperities. Higher
normal stress (σ0 = 0.8 MPa) increased the total real contact area to Ar = 99.26 mm2 (∼
2.07 % of the nominal contact area) and was composed of N = 5040 large asperities. From
Mindlin [1949], we can estimate the elastic shear stiffness κ = (8µ · a/(2− ν)) for a single
circular contact of radius a under the no-slip condition. Assuming that a is the equivalent
radius for an asperity with area Ar, we estimate the equivalent fault shear stiffness as κ =
25.0 N/µm at σ0 = 0.4 MPa and κ = 61.6 N/µm at σ0 = 0.8MPa. Figure 1(d) compares
the two distributions of real contact area along the x-axis. Overall levels of real contact
increased with σ0 and appear to cluster at length scales λ ∼ 50 mm, explained by coming
together of a surface with a topographic “waviness” described in Supporting Information
S2. For both high and low normal stress there is a significant amount of contacts at the
leading edge (LE) of the fault. Figure 1(e) examines the gradient in real contact area
along the x-axis at the two levels of normal stress σ0. There is more variability along
the fault for high normal stress. The results shown here were representative of asperity
distributions throughout the initial asperity distributions for the 22 tests at both normal
load levels.
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3.2. Non-uniform slow slip accumulation
Figure 2 shows slow slip evolution patterns observed along the interface during the suite
of experiments performed at low σ0 = 0.4 MPa (Figure 2(a)) and σ0 = 0.8 MPa (Figure
2(b)). (Both the results in Figures 2 and 3 are shown for an identical loading rate of VLP
= 3 µm/s.) For each normal stress level σ0, the friction coefficient µ (= Fs/Fn), local slip
(δ) and local slip rate (δ) are shown for all noncontact sensors (NC1-NC7) in descending
order. The methodology for slip rate calculations are detailed in Supporting Information
S3.
Figure 3 illustrates an example of spatio-temporal slip and slip rate evolution along
the fault throughout the loading phase. Time was discretized at one-second intervals and
the fault discretized at 10 mm intervals along-strike. The values of slip and slip rate are
taken from individual noncontact sensors (Figure 2) and used to interpolate and visualize
the spatio-temporal evolution during the loading phase. This was done for low (Figure
3(a)) and high (Figure 3(b)) levels of normal stress σ0 allowing us to visualize two distinct
patterns in slow slip evolution – arrested slow slip events and sudden breakaway events
leading to rupture.
3.3. Variations in slow slip
During all tests, slow slip accumulation initiated from the center of the specimen where
the density of asperity contacts were lower (see along-strike histogram in Figures 1(b)
and (c)), shown in the spatio-temporal plots of Figure 3. Slow slip evolved in two distinct
manners and depended on the far-field normal stress σ0. The two types slow slip evolution
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patterns are described as: (1 ) a breakaway event (BE only in Figures 2(a) and 3(a)) and
(2 ) a slow event followed by a breakaway event (SE + BE in Figures 2(b) and 3(b)).
Slip evolution pattern (1 ) (BE only) is observed only when the fault was loaded to a
lower applied normal stress (σ0 = 0.4 MPa). Nucleation was characterized by an outwardly
growing shear rupture originating from the center of the fault. The slow shear rupture
propagated to both LE and TE edges (i.e. along-strike) at speeds CBE ∼ 5.1 mm/s
at VLP = 1 µm/s to CBE ∼ 60.94 mm/s at VLP = 10 µm/s. Within the rupture, slip
gradually accelerated and, upon reaching the ends of the fault, gross fault rupture ensued
characterized by an average shear force drop ∆FS ∼ 109.5 N.
Slip evolution pattern (2 ) (SE+BE) is only observed during tests performed at higher
applied normal stress (σ0 = 0.8 MPa). During the SE portion of slip evolution pattern
(2 ), the shear rupture nucleated from the center of the fault, propagating outwards at
rates between Cslow ∼ 0.8 mm/s at VLP = 1 µm/s to Cslow ∼ 26.10 mm/s at VLP = 10
µm/s. Upon reaching the ends of the fault, the interface decelerated releasing a partial
shear force drop ∆Fslow = 12.4 N (see inset of Figure 2(b) and arrows on slip and slip rate
plots). After the partial stress drop, the fault began reloading itself and was followed by
an ensuing BE similar to that in slip evolution pattern (1 ). Nucleation of the consequent
BE originated from the central section of the fault and expanded at rates of CBE ∼ 3.2
mm/s at VLP = 1 µm/s to CBE ∼ 31.7 mm/s at VLP = 10 µm/s. The BE events in
slow slip evolution pattern (2 ) grew outwardly at slower rates than those observed during
slip evolution pattern (1 ). All expanding shear ruptures were dependent on the far-field
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loading velocity (VLP ) – higher loading velocities resulted in faster expansion of both the
SE and BE portion of evolution pattern (2 ).
3.4. Rupture growth during slow events (SE)
Spatio-temporal slip rate plots in Figure 3 are used to examine rupture growth rate Cslow
and duration tslow for SEs at various loading rates VLP . The dashed white lines in the slip
rate evolution (bottom panels in Figure 3) indicate the region along the x-direction of the
fault where slip rate increased beyond a lower threshold. The threshold for approximating
the nucleation region was set to δ/VLP ∼ 0.02. The propagation rate Cslow was calculated
as the slope from the nucleation point to the LE. Results from calculating Cslow for various
loading rates are shown in Supporting Information S4.
Table S1 in Supporting Information S4 shows the propagation rate Cslow of SEs, du-
ration tslow and propagation rate normalized by the Rayleigh wave speed of the material
(Cslow/CR) for each loading rate VLP . The Rayleigh wave velocity for PMMA was CR =
1297 m/s. The SEs propagated at speeds of Cslow/CR ∼ (6–191) x 10−7; these speeds are
much lower than the slow rupture fronts (Cslow/CR ∼ 0.05) observed during breakaway
events in other laboratory direct shear friction experiments [e.g., Rubinstein et al., 2004].
3.5. Stress drop (∆σ) during slow events (SEs)
It is possible to estimate the amount of stress drop across the expanding slow slip
region of the SE in terms of linear elastic fracture mechanics [e.g., Andrews , 1976; Ida,
1972; Svetlizky and Fineberg , 2014]. Stress drop ∆σ can be determined from the ratio
between the slip rate and rupture propagation velocity, which is then scaled by the shear
modulus (i.e. ∆σ = µ · (δ/Cslow)). We provide an estimate of the stress drop using the
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rupture propagation calculations Cslow (calculated before) and estimates of the maximum
slip rate during the SE. These values are reported in Table S1. We found that stress
drop varied between ∆σ = 0.25, 0.52, and 0.97 MPa for experiments at loading rates
of VLP = 1, 3 and 7 µm/s. The stress drop increased as loading rate increased. These
may be overestimates of ∆σ since the maximum slip rate during the entire SE was used.
The stress drop during these tests may have varied spatially due to fluctuations in the
fault shear strength (Figure 1) defined by the fault prestress. With respect to the applied
normal stress σ0, shear stress drop (∆σ) appears relatively large; however, it is only a
fraction (1 to 4%) of the normal stress supported on the asperities, estimated using the
pressure sensitive film [σasperity ∼ 23 to 32 MPa from Selvadurai and Glaser , 2015b].
4. Discussion
4.1. Slip evolution pattern and its relation to fault strength
While the underlying mechanism remains elusive, slow earthquakes are believed to ob-
serve in situ frictional conditions that promote a transitional state between the stick-slip
and steady aseismic sliding regimes [Ikari et al., 2013; Mele Veedu and Barbot , 2016; Lee-
man et al., 2016]. Part of this transitional state is believed to occur due to elevated pore
pressures causing low effective stress or variations in frictional properties that promote
slow transient slip [Segall et al., 2010; Liu and Rice, 2005, 2009; Okazaki and Katayama,
2015]. Numerical simulations of slowly propagating slip fronts into regions of frictional
heterogeneity [Ando et al., 2010; Nakata et al., 2011; Zigone et al., 2015] have shown
similarities to natural observations [e.g., Rogers and Dragert , 2003; Ghosh et al., 2010]
but realistic distributions of this heterogeneity are not well known. Saffer and Wallace
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[2015] examined frictional properties of a few well known subducting plates (Pacific Plate,
Philippine Sea Plate and Cocos Plate) and found that the subduction of the rough seafloor
may promote both compositional and geometrical heterogeneity – presenting physical con-
ditions that are likely met on many shallow megathrust faults. In this study we found
similarities with SSEs in nature and the SEs described when the fault was loaded to higher
applied normal stresses. We specifically observe rupture growth rates that scale directly
(via the Rayleigh wave speed) to the rock in nature where slow earthquakes propagate
at rates of 1 - 10 km/day (Cslow/CR ∼ (34–340) x 10−7)[Bartlow et al., 2011; Fukuda
et al., 2014; Kostoglodov et al., 2003; Obara, 2011; Wech and Bartlow , 2014]. We find
that changes in slow slip are a function of locally varying frictional properties, i.e. in-
creased fault strength and evolving complexity. Similar conditions are believed to occur in
natural settings [Saffer and Wallace, 2015]. The topography of our faults bodies caused
heterogeneous variations in the manner in which asperities form and interact. While pore
fluids are not present in our experiments, the number of asperities (Ar) and local cluster-
ing of asperities became more pronounced when the fault was confined to higher far-field
normal stresses σ0. This may produce analogous complexity to that observed in nature
[Schmittbuhl et al., 2006; Candela et al., 2011; Brodsky et al., 2016].
Combining elastic dislocation with friction theory [Scholz , 2002] gives us insight of how
local variations in effective normal stress will proportionally change the local variation
in effective fault stiffness (κ ∝ σn). Variations in local stiffness, controlled by the scale
dependent interaction of asperities, appear to control the differences the evolution of slip in
this laboratory study. On our laboratory fault, heterogeneous stiffness seems to directly
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affect the faults ability to resist shear rupture expansion. Dieterich [1978] described
this heterogeneity in terms of effective strength: a property that limits the dimensions
of slip and, therefore, affects the complexity of the fault being tested. It is possible
that the material used, surface preparation techniques and apparatus imposed boundary
conditions allowed for dimensions of slip that mimic more closely a natural settings. The
direct scaling of the expanding slow rupture rates may be a realization of up-scaling
relationships that require more extensive investigations.
Changes in nominal normal stress σ0 affect the near-fault (effective) normal stress along
the fault. These stress fields have been found to control shear slip dynamics along frictional
faults in the laboratory [e.g., Ohnaka and Shen, 1999; Ben-David et al., 2010; McLaskey
and Kilgore, 2013; Leeman et al., 2016]. Shear rupture in these studies have been modeled
as an expanding shear crack with a slip-weakening zone controlled by the stress field,
which can be determined to establish the transition of sliding from stable to unstable
[e.g., Andrews , 1976; Chen and Knopoff , 1986]. Initiation of the shear rupture occurs at
the weakest location along the fault [Ohnaka, 1992]. In our experiments, nucleation of
slow shear rupture originates near the sparsely populated (Figure 1(d)) center of the fault
for both types of slip evolution patterns. This follows standard theory.
Similarities compared to field observations, in the manner that all our experimental
ruptures initiate (SEs and BEs) may indicate they share similar mechanisms and are
controlled by evolving frictional processes. Recent studies suggests that shallow slow
earthquakes may indeed nucleate in a similar manner to regular earthquakes but their ex-
pansion is prematurely arrested [Ikari et al., 2013] or may follow a complicated frictional
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response that cycles between slow and fast earthquakes [Mele Veedu and Barbot , 2016].
In our experiments the exact cause of rupture arrest is not well known but Saffer and
Wallace [2015] note that high complexity persists in shallow subduction zones due to geo-
metric complexity and heterogeneous lithology in natural shallow settings and rheological
differences from these factors may be responsible for slow earthquakes at these depths.
4.2. Similarities of laboratory to field studies
Slow earthquakes and non-volcanic tremor migrate at velocities varying between ∼1
km/day to ∼ 10 km/day along-strike [Kostoglodov et al., 2003; Obara, 2002; Bartlow et al.,
2011; Fukuda et al., 2014; Wech and Bartlow , 2014]. Global positioning system (GPS)
networks, have been used to map the spatio-temporal progression of a cohesive zone of
a very slowly propagating shear rupture believed to be a slow earthquake. Assuming a
Rayleigh wave speed of rock about 3450 m/s, we calculate expansion of a shallow slow
earthquake in nature ranges between 34 to 340 x 10−7 · CR, results comparable to those
observed in this study (Table S1). It is possible that the PMMA at these stress levels
and experimental boundary conditions create a degree of strength heterogeneity that can
provide slow transients that propagate at speed directly consistent to those on faults in
the Earth.
Slow earthquakes may have common mechanisms, i.e. an outwardly expanding shear
rupture from weak and compliant zones with a breakdown region at the crack-tip [Bartlow
et al., 2011; Ikari et al., 2013]. For both low and high normal stress states we observe:
(i) the level of premonitory sliding before gross fault rupture is comparable (which is
expected if the characteristic slip distance Dc is independent of the applied normal stress
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[Dieterich, 1979]) and (ii) nucleation initiates at similar locations for both SEs and BEs.
We also know that the stiffness of the gross sample (from the geometry) and the apparatus
remains unchanged between tests – only the interfacial stiffness (κ) is changed when σ0 is
increased. Increased shear stiffness is proportional to the distributions of asperities along
the fault [Berthoude and Baumberger , 1998]. Complexity, we interpret as large gradients
in real contact along-strike, grew with an increase in applied normal stress σ0. We believe
this could be a factor that allows a fault to hold back rupture, such that expansion speeds
and slip rates were similar to natural settings for this configuration and material.
While not all slow earthquakes experience a sudden deceleration, the 2013-2014 shallow
slow earthquake (see Figure 4(b)) near the Boso peninsula, Japan [Fukuda et al., 2014],
had remarkably similar moment and moment rates to the SEs observed in our experiments
Figure 4(a). Fukuda et al. [2014] showed that the Boso SSE exhibited two distinct phases:
Phase I and Phase II. The slow event associated with VLP = 3 µm/s in Figure 4(a) was
decomposed into P1 and P2 for visual purposes. The phases P1 and P2 appear visually
similar a to the Phase I and Phase II described by Fukuda et al. [2014] as shown in Figure
4(b). They cite that the transition between phases Phase 1 and Phase 2 occur due to the
sudden acceleration of an expanding rupture from ∼ 1 km/d or less (Phase 1) to ∼ 10
km/d (Phase 2) which was also accompanied with an increase in seismicity (blue bars in
Figure 4(b)). The acceleration of an expanding rupture is observed in standard earthquake
nucleation theory, again promotes the idea that slow and regular earthquakes share similar
mechanisms and this further promotes the idea that slow earthquakes are the results of
spatial heterogeneity in friction along the fault which can prematurely arrested rupture. In
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Figure 3(b) a black dash-dotted line was added to the slip rate plot to show that Cslow may
actually be characterized using multiple propagation velocities (as described by Fukuda
et al. [2014]) but more study with better resolution in slip sensor and acoustic emission
measurements is necessary. The inversion of GPS data performed by Fukuda et al. [2014]
also showed that the faults suddenly underwent and rapid deceleration similar to what
was observe experimentally here (Figure 4(a)) – a possible indication of rheologic changes
along the fault.
If we are assuming slow and regular earthquakes have similar mechanisms, why do
the laboratory slow events (SEs) not result in a gross fault rupture? An explanation
may be the geometric length scales of the velocity-weakening (VW) region is surrounded
by a velocity-strengthening (VS) zone. Noda and Hori [2014] found that if the critical
nucleation size was larger than the VW region where the slow earthquake originated,
there may exist fluctuations in the slip velocity (increases followed by a sudden drop)
in the later stages of the interseismic cycle. Here, the mechanism is the same for slow
and regular earthquakes but rupture is arrested prematurely for the slow. While the
extent of our laboratory fault may be limiting certain aspects of our understanding of
slow earthquakes, the sudden deceleration of the fault may be better explained as if the
slow rupture moved into velocity-strengthening region on the fault – on our fault this was
the free edge boundary condition.
From standard frictional stability theory, an increase in effective normal stress σ0 should
decrease critical nucleation size. One would similarly expect slow slip evolution patterns
at both levels of normal stress, each leading to gross fault rupture [Latour et al., 2013].
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However, if the increasing σ0 varied the rate-and state-dependent parameters A and B
[see Noda and Hori , 2014], this could allow for a change in slow slip evolution patterns
seen here. It is possible that the sharp gradient in real contact area near the leading edge
constitutes a rheological change in frictional properties, imposed here by the experimental
facilities, that mimics the movement of shear rupture from a VW to VS regime. More
laboratory studies should be conducted since our understanding of asperity distributions
and its relationship to frictional properties (in terms or the rate and state variables) are
not well understood. A better understanding of asperity distribution, in terms of the
the contrasting local rheology, could help better understand the complicated dynamic
evolution of slip and conditions leading to slow earthquakes.
5. Conclusion
A fault was sheared in a direct shear configuration in the laboratory. Slow slip was
observed to accumulate non-uniformly along the fault before gross fault rupture occurred.
For some configurations slow slip stalled before becoming gross rupture. Pressure sensitive
film was used to visualize changes in asperity distributions caused by the increasing σ0.
Distributions of asperities along the shearing interface were a direct indication of the
initial bulk stress level along the fault that primarily control frictional processes. During
the shearing experiments, two levels of applied normal stress σ0 caused distinct (and
repeatable) dynamic response slip evolution patterns (1 ) breakaway events and (2 ) slow
earthquakes leading to breakaway events. Only when higher normal load σ0 was applied
did we observe slow events – characterized by the increased local slip rates within an
expanding shear rupture that culminated in partial stress drop and slip deceleration. Slow
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SELVADURAI & GLASER: LABORATORY SLOW SLIP EVENTS X - 19
earthquakes nucleated from the central (weaker) section and proceeded to grow towards
of the (stiffer) leading edge fault end. Growth occurred at propagation speeds much lower
than anything seen in typical laboratory studies Cslow/CR ∼ (6–191) x 10−7 similar to
rates observed for shallow slow earthquakes. Upon reaching the end, a partial stress drop
was observed, accompanied by the deceleration of the fault.
Breakaway events, which followed slow events, nucleated from the same location but
culminated in gross fault rupture. Breakaway events propagated faster than slow earth-
quakes suggesting that the partial stress drop had weakened the relatively locked leading
edge section of the fault sufficiently to allow for the subsequent gross fault rupture. We
believe that shallow slow earthquakes may have a similar mechanism to large earthquakes.
Slow earthquake may be shear ruptures that nucleate on a velocity-weakening section of
the fault; they become suddenly arrested as the shear rupture moves into a large velocity-
strengthening section of the fault. SSEs present in the upper lithosphere may be due
to the mechanical differences in local fault strength and, while further investigation is
necessary, the findings presented here show promise that the study of these controlling
features are attainable in the laboratory.
Acknowledgments. Funding for this research was provided by the National Science
Foundation Grant CMMI-1131582, the Jane Lewis Fellowship (University of California,
Berkeley) and the National Science and Engineering Research Council of Canada some-
thing grant (PGSD3-391943-2010) provided to P. A. Selvadurai.
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X - 20 SELVADURAI & GLASER: LABORATORY SLOW SLIP EVENTS
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Copyrighted Material
The authors ensure that this is an original study and that no material presented here has
been published elsewhere in any form and nor has it been submitted elsewhere for consideration
for publication. We give the American Geophysical Union the rights for the distribution of the
material in its current and future formats.
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Figure 1. (a) The direct shear friction apparatus used to study the onset of dynamic sliding
along a pre-existing frictional interface. (b) Pressure sensitive film measurements showing the
asperity distributions when the interface was loaded to σ0 = 0.4 MPa. The real contact area
Areal is shown in the spatial histograms along the x- and y-axis. Locations of the noncontact
slip sensors (NC1-NC7) are shown in relation to the interface. (c) The same as (b) with the
fault loaded to σ0 = 0.8 MPa. (d) Comparison of the real contact area Ar along the fault for the
different levels of σ0. (e) Comparison in the gradient in real contact area ∇Ar along the x-axis
for two levels of σ0.
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Figure 2. Experimental results during the preslip phase of the loading cycle. Both interfaces
were subjected to a loading rate VLP = 3 µm/s, but the left-hand side (a) and right-hand ride
(b) were subjected to normal stresses of σ0 ∼ 0.4 MPa and 0.8 MPa, respectively. The panels
in (a) and (b) show the tribological coefficient of friction along the fault µ(t), slip, slip rate for
individual noncontact sensors in decending order. The thick dashed-dot line is the average slip
and slip rate in the respective panel. The arrows in (b) indicate the partial stress drop associated
with the termination of the slow event (SE).
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Figure 3. The interpolated spatiotemporal slip distribution (top panels) and slip rate (bottom
panels) distributions for the loading conditions seen in Figures 2(a) and (b). Two types of
slow slip evolution patterns were observed: slow slip evolution pattern (1 ) (BE) and slow slip
evolution pattern (2 ) (SE+BE). SEs where observed only in tests loaded to higher normal stress
σ0. Estimates for the nucleation point are shown as stars and the rate at which the slow event
grew is indicated by the dashed lines whose slope is Cslow . Total slow slip occurs over time tcycle,
SE over time tslow and BE over time tb.
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Figure 4. (a) Laboratory slow events (SE) from two independent tests at σ0 = 0.8 MPa and
VLP = 3 µm/s. P1 and P2 are phases determined (approximately) by the change in average slip
rate. (b†) Results of the moment release (left) and moment rate (right) for the SSE near the Boso
Peninsula, central Japan, from Dec. 2013 to Jan. 2014 [from Fukuda et al., 2014]. Seismicity per
day, shown in blue, increased during Phase II sliding.
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