university of california, berkeley - e ective strength heterogeneity...

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.

D R A F T May 20, 2016, 9:43am D R A F T

X - 2 SELVADURAI & GLASER: LABORATORY SLOW SLIP EVENTS

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.


SELVADURAI & GLASER: LABORATORY SLOW SLIP EVENTS X - 3

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



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



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.



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



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



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.



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



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



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



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



[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



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



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



[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



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].



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



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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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.



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.



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).



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.



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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