laboratory-developed contact models controlling ...glaser.berkeley.edu/glaserdrupal/pdf/jgr 1...

Laboratory-developed contact models controllinginstability on frictional faultsPaul A. Selvadurai1 and Steven D. Glaser1

1Civil and Environmental Engineering, University of California, Berkeley, California, USA

Abstract Laboratory experiments were performed on a polymethyl methacrylate (PMMA)-PMMA frictionalinterface in a direct shear apparatus in order to gain understanding of fault dynamics leading to gross rupture.Actual asperity sizes and locations along the interface were characterized using a pressure-sensitive film.Slow aseismic slip accumulated nonuniformly along the fault and showed dependency on the appliednormal force—increased normal force resulted in higher slip gradients. The slow slip front propagatedfrom the trailing (pushed) edge into a region of more densely distributed asperities at rates between 1 and9.5mm/s. Foreshocks were detected and displayed impulsive signals with source radii ranging between0.21 and 1.09mm; measurements made using the pressure-sensitive film were between 0.05 and 1.2mm.The spatiotemporal clustering of foreshocks and their relation to the elastodynamic energy released wasdependent on the normal force. In the region where foreshocks occurred, qualitative optical measurementsof the asperities along the interface were used to visualize dynamic changes occurring during the slow slipphase. To better understand the nucleation process, a quasi-static asperity finite element (FE) model wasdeveloped and focused in the region where foreshocks clustered. The FE model consisted of 172 asperities,located and sized based on pressure-sensitive film measurements. The numerical model provides a plausibleexplanation as to why foreshocks cluster in space and observed a normal force dependency and lendcredence to Ohnaka’s nucleation model.

1. Introduction

Laboratory earthquake simulations have been used to model the nucleation of interfacial failure and frictionalsliding on a fault [e.g., Dieterich and Kilgore, 1996b; Ohnaka and Shen, 1999; Nielsen et al., 2010; Kaproth andMarone, 2013; Latour et al., 2013]. Frictional phenomena are commonly described using the phenomenologicalrate and state frictional models, which define the stability of friction processes [e.g., Dieterich, 1978; Ruina, 1983;Berthoude et al., 1999; Baumberger and Caroli, 2006; Ampuero and Rubin, 2008]. It is believed that these modelscapture a wide variety of physical behaviors leading to fault rupture. Advances in experimental techniques allowfor the acoustic isolation of the discrete, asperity-level, dislocationmechanisms [Thompson et al., 2009;McLaskeyand Glaser, 2011; Goodfellow and Young, 2014; McLaskey and Kilgore, 2013; McLaskey et al., 2014], which arebelieved to accompany the nucleation phase of fault rupture [Ohnaka, 1992].

Regional-scale (approximately kilometers) seismological studies have sometimes identified slow, possiblypremonitory, phenomena embedded in the main shock seismograms [Iio, 1995; Ellsworth and Beroza, 1995;Beroza and Ellsworth, 1996]. However, these motions are difficult to detect [e.g., Tullis, 1996; Johnston et al.,2006], and whether they are intrinsic to an earthquake is yet unproven [Olson and Allen, 2005]. In certaincases, clusters and swarms of small earthquakes and/or foreshocks have been detected weeks to minutesbefore the eventual main shock [e.g., Mogi, 1963; Ohnaka, 1993; Nadeau et al., 1994; Dodge et al., 1995,1996; Ando and Imanishi, 2011; Bouchon et al., 2011; Chiaraluce et al., 2011; Chen and Shearer, 2013; Govoniet al., 2013; Tape et al., 2013]. Observations of these premonitory events are becomingmore frequent becauseof the increased sensitivity and array coverage of seismically active regions. It is now believed that atleast 50% of major earthquakes have foreshocks [Brodsky and Lay, 2014]. However, foreshocks are currentlydifficult (or even impossible) to distinguish from nonprecursory seismic activity. Interpretation of the impactof stress changes along faults [e.g., Dodge et al., 1995, 1996] is not well understood; in certain cases, earthquakeswarms do not culminate in a major event [Holtkamp et al., 2011]. Brodsky and Lay [2014] examined foreshocksequences for the 2011 Mw 9.0 earthquake in Tohoku [Ando and Imanishi, 2011] and the 1 April 2014 Mw 8.1earthquake in northern Chile [see also Yagi et al., 2014]. Brodsky and Lay [2014] found that foreshocks occurredon frictionally locked sections of the fault as indicated by the geodetic survey data. Both regions also had

SELVADURAI AND GLASER FORESHOCKS ON FRICTIONAL FAULTS 4208

PUBLICATIONSJournal of Geophysical Research: Solid Earth

RESEARCH ARTICLE10.1002/2014JB011690

Key Points:• Laboratory investigation of instabilityon frictional faults

• Asperity model derived from thecontact measurements is modeledcomputationally

• Model predicted potential locationsfor foreshocks and asperity failuredynamics

Correspondence to:P. A. Selvadurai,[email protected]

Citation:Selvadurai, P. A., and S. D. Glaser (2015),Laboratory-developed contact modelscontrolling instability on frictional faults,J. Geophys. Res. Solid Earth, 120,4208–4236, doi:10.1002/2014JB011690.

Received 29 OCT 2014Accepted 29 APR 2015Accepted article online 30 APR 2015Published online 2 JUN 2015

©2015. American Geophysical Union.All Rights Reserved.

http://publications.agu.org/journals/

http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2169-9356

http://dx.doi.org/10.1002/2014JB011690

http://dx.doi.org/10.1002/2014JB011690

considerable seismic gaps; they had not experienced a large earthquake for over a century, which suggeststhat large amounts of strain would have accumulated. In this study, we use the laboratory setting to simulatea frictionally locked section of a fault and monitor the stress conditions that give rise to localized foreshocksbefore a stick-slip instability (main shock).

When the shearing stress is increased along a frictional fault in a laboratory simulation, conditions canbecome favorable for the formation of a stick-slip instability. Slip transitions can vary from slow (quasi-static)to high speed (dynamic), yet the processes controlling this transition are still not well understood. Recentlaboratory studies show that foreshocks can occur immediately prior to rapid sliding [McLaskey and Kilgore,2013]. Moreover, these laboratory foreshocks exhibited double-couple source mechanisms with magnitudesranging fromMw�7 toMw�5.5 [McLaskey et al., 2014]. These foreshocks are believed to be scaled versions ofthe larger, regional earthquakes.McLaskey and Kilgore [2013] also determined that fault strength heterogeneityalong the interface was necessary for the formation of the foreshocks, which followed the model proposedby Ohnaka [1992]. They assumed that this heterogeneity was due to slight topographic mismatch of theinteracting fault surfaces. Fault strength variations in nature may arise from a variety of conditions: e.g., rockinhomogeneity, topography of fracture surfaces, fault damage zones, fluid/temperature interactions, andgouge zones (see reviews by Ben-Zion and Sammis [2003], Biegel and Sammis [2004], Rice and Cocco [2007],and Ben-Zion [2008]).

In our controlled laboratory environment, asperity locations induced strength heterogeneity—the mechanicalinteraction between the rough faces of the fault. When the surfaces were pressed together, the resulting faultplane was observed to have a dilute set of microcontacts commonly referred to as asperities. The transmissionof shear and normal stresses across the fault occurs only through these asperities. Themicromechanics of asperitycontact governing the frictional behavior along a fault has been investigated, in both geophysical [e.g., Boitnottet al., 1992; Dieterich and Kilgore, 1994; Yoshioka, 1997] and tribological studies [e.g., Bowden and Tabor, 2001;Persson, 2006]. These studies focus on understanding the bulk response of asperity populations based upon theirstatistical distributions. An increase in the density of asperities present has been related to an increase in bulkshear stiffness of the fault (i.e., the amount of relative shear displacement (or slip) per unit shearing force)[Berthoude and Baumberger, 1998].

Recent laboratory studies simulate the faulting surfaces as very smoothly interacting surfaces [Rubinsteinet al., 2007]. The focus in these studies is to develop an understanding of the physics surrounding a singlenanoscale roughness junction rheology [Baumberger and Caroli, 2006], and not the interactions betweenasperities (i.e., multiple junctions) as is presented here. Fewer studies exist that model the interactionsbetween asperities in which their distributions are not statistically prescribed but use the actual dilute setpresent on the fault. Predominantly, asperities in these models used three types of formulations: (i) the rateand state frictional formulation [e.g., Ide and Aochi, 2005; Ariyoshi et al., 2009; Chen and Lapusta, 2009;Dublanchet et al., 2013; Noda et al., 2013], where asperities are modeled as velocity weakening regions;(ii) fracture mechanics [e.g., Sammis and Rice, 2001; Johnson and Nadeau, 2002; Johnson, 2010], whereasperities are considered to satisfy the exterior crack problem; or (iii) asperities are defined as frictionallyunstable patches [Ando et al., 2010; Nakata et al., 2011]. The area surrounding the asperity (i.e., “creeping”region) is modeled as a velocity strengthening region for case (i), whereas in case (ii) this region holds noshear stress near the asperity and in case (iii) supports a residual background shear stress.

In this study, we propose to use contact mechanics, within the framework of a finite element (FE) scheme,to better estimate the asperity-level mechanisms leading to general rupture. Along our laboratory fault oneimportant frictionally “locked” section, which had the largest shear stiffness, consistently showed less slipduring shear. In addition, sequences of foreshocks were recorded from these frictionally locked sectionmoments (seconds to milliseconds) before the transition to rapid sliding. Therefore, we focused ournumerical modeling efforts on characterizing the strain accumulation in this section of the fault basedon the interaction of a complex spatially distributed asperity field. To characterize this field, a novel techniqueinvolving pressure-sensitive film was used to measure asperity distributions (i.e., size and locations) in thelocked region. Information regarding the actual locations and sizes of asperities was extracted from thefilm and imported into the FE model. In the model, each individual asperity was assumed to conformto a Cattaneo partial slip asperity model [Cattaneo, 1938]. This solution showed promising similaritiesto qualitative observations of individual asperities observed using digital photography within the locked

Journal of Geophysical Research: Solid Earth 10.1002/2014JB011690


section while being loaded to failure. For various stressing conditions, we calculated the heterogeneousdistributions of strain energy, caused by the interaction of 172 asperities. These were then compared tothe experimental observations.

2. Experimental Methods2.1. Experimental Setup

A schematic view of the direct shear friction apparatus used in the experiments is shown in Figure 1a.The reaction frame accommodated the larger polymethyl methacrylate (PMMA) base plate(600mm×300mm×50mm thick) and could apply a normal force (Fn) of 5.8 kN through two balancedhydraulic cylinders (Parker H3LLT28A) and a rigid loading platen to a PMMA slider block(400mm× 80mm× 13mm thick). The PMMA slider block was bonded to the rigid loading platen usingcyanoacrylate. The PMMA-aluminum shear bond, tested in a separate load frame, had a shear stiffnessof 28N/μm compared to the 0.42N/μm stiffness of the PMMA-PMMA interface determined subsequently.

Figure 1. Experimental configuration of the direct shear friction apparatus used for the experiments on a PMMA-PMMAinterface. (a) A side view of the apparatus and summary of the components. (b) Side view schematic depiction of theinterface created by compressing the slider block into the base sample through the rigid loading platen. General detailsregarding the placement of the noncontact displacement sensors (NC1–NC7) and piezoelectric acoustic emission sensors(PZ1–PZ16) are provided. The normal force, Fn, was applied through the rigid loading platen and driven at a constantvelocity VLP using the shear actuator. The shear actuator was located at the trailing edge (TE) of the slider block. Detail Aprovides a cartoon representation of the multicontact interface occurring along the solid-solid interface. (c) Detailedlocations of the noncontact sensors (red crosses) and piezoelectric sensors (black triangles) with respect to the interface(shaded region). (d) A small section of the interface (12.7mm× 20mm) showing regions of initial asperity contact along thesolid-solid multicontact interface measured using the pressure-sensitive film.



Gross interface stiffness was calculated as the total force released divided by the amount of rapid slip during astick-slip event [Beeler et al., 2001]. A maximum normal stress of σn≈ 1.14MPa can be applied to the nominalsurface area of the simulated fault (12.7mm×406mm). The normal force (Fn) was estimated from an in-linepressure transducer (OMEGADYNE PX329-2KG5V) measuring the pressure in the hydraulic cylinders. Toinduce a shear force along the fault we used an electromechanical shear actuator (Exlar Tritex II T2X115) withshear stiffness of 154N/μm operating at 1Hz. The shear actuator was used to drive the rigid loading platen at aconstant velocity VLP while maintaining a normal force Fn on the slider block. The shear force (Fs) was measuredusing a load cell (OMEGADYNE LC213-1K) placed between the shear actuator and the loading platen.

2.2. Material Properties and Surface Preparations

A glassy polymer, poly(methyl methacrylate), PMMA, was used as an analog to a ductile rock/rock interface[see also Wu et al., 1972; Dieterich and Kilgore, 1996a; Berthoude et al., 1999; McLaskey and Glaser, 2011;McLaskey et al., 2012]. Physical properties of PMMA at room temperature are as follows: densityρ= 1180 kg/m3, shear modulus G= 2277.1MPa, and Poisson’s ratio ν=0.32. The corresponding body andshear wave velocities are 2700m/s and 1390m/s, respectively. Differential scanning calorimetry determinedthe glass transition (Tg) to be approximately 114°C. The interacting faces of the PMMA base plate and sliderblock were sandblasted using 440–200μm particles of aluminum oxide (Al2O3) for a controlled time, pressure,and blasting distance. Sandblasting PMMA using similar sized particles [e.g., Schmittbuhl et al., 2006] inducedrandomly rough surfaces similar to those that could be found naturally along fault surface outcrops [Powerand Tullis, 1991; Candela et al., 2009, 2011].

2.3. Instrumentation

The general loading arrangements are shown in Figure 1b. Local macroscopic slip displacements alongthe interface were required to investigate the nucleation processes. Noncontact displacement eddy currentsensors (Shinkawa VS-020 L-1), referred to as slip sensors, were deployed across the fault at seven locations(NC1–NC7) along the x direction of the fault (see Figures 1b and 1c). From Figure 1c, we note that five slipsensors (NC1, NC3, NC5, NC6, and NC7) were placed on the upper face (y> 0) of the slider block, while twosensors (NC2 and NC4) were located on the lower face (y< 0). The spatial locations in both x and y directionswere important for interpreting the data. Two slip sensors, measuring slip in the y direction (vertical), wereplaced at the leading (LE) and trailing edge (TE) of the slider block. These measured any twisting the slidersample might undergo during the experiments and enabled accurate location of the slider block relativeto the base plate at the beginning of each test. Aluminum targets, similar to those employed by Ohnakaand Shen [1999, see Figure 5b], were attached to the slider block using cyanoacrylate glue. The voltageoutput of the displacement converter (Shinkawa VC-202N) was linearized between frequencies of DC to20 kHz (�3 dB) and yielded a displacement accuracy greater than 0.1μm at frequencies up to 10 kHz.

Acoustic emission sensors have been used in the past to study nucleation processes of rock failure in thelaboratory [e.g., Lockner, 1993; Thompson et al., 2009; Stanchits et al., 2010; Goodfellow and Young, 2014].An array of 13 Glaser-type conical piezoelectric acoustic sensors (PZ1–PZ13) was placed on the undersideof the base plate. We employed absolute calibration techniques and determined that the sensors had a<�3 dB response over the frequency band~ 5 kHz–2.5MHz, with ±1 pm noise floor [McLaskey and Glaser,2010, 2012]. The sensors were connected to a high-speed digitizer (ELSYS TraNET EPC 16-bit dynamic range,10MHz sample rate) and measured small dynamic stress waves (foreshocks) emitted before the blockexperienced a fault-wide dynamic rupture. During a full stick-slip event, the high-sensitivity sensor signalsbecame clipped immediately before rapid sliding ceased. Full waveforms of the acoustic emissionsassociated with individual stick-slip events were recorded using two passive piezoelectric sensors(OLYMPUS Panametrics V-103) at PZ14 and PZ15. Accurate locations of the noncontact sensor array areshown in Figure 1c (red crosses) and the seismic array (black triangles) placed on the top (z= 0mm) andbottom (z= 50.8mm) surfaces of the base plate.

3. Experimental Procedure3.1. Characteristic of the Pressure-Sensitive Film

In order to estimate the size and location of the asperities formed during the initial contact between the sliderblock and base plate (see Detail A of Figure 1b), we placed Fujifilm Prescale® medium range (12–50MPa)



pressure-sensitive film between the slider block and base plate and applied a known far-field normal force Fn.The film is polyethylene based (~100μm thick) and local pressure caused microcapsules to break and reactwith a precalibrated color developing agent. The color density formed by the developing agent had spatialresolution of ±5μm and pressure resolution of ±1.5 Pa. Using the factory-provided calibration data, mapsof the interfacial normal stress distributions were recorded. An example of the contact measurements for amature surface is shown in Figure 1d with a magnified asperity in Detail B. Due to the static nature of thismeasurement and the inherently dynamic nature of the test, the pressure-sensitive film was removed fromthe interface prior to the application of a shear load since our focus was not on the study of a film-mediatedsliding surface. Once the film was extracted from the interface, it was scanned to a spatial resolution of 5μmand processed using MATLAB image recognition algorithms. The image was converted to stresses, and alower threshold contact stress value was obtained in an iterative manner [Selvadurai and Glaser, 2012,2015]. We assumed that the contact occurred only along the x-y plane and that the force on each pixelwas exactly perpendicular to the plane of the fault. For all pixels experiencing stresses above the threshold,a total reactive force Fr was calculated (i.e., measured stress on pixel multiplied by the area of a pixel). Thethreshold was then varied iteratively until Fr balanced the applied far-field load, i.e., Fr= Fn. With the thresholddetermined, we were able to accurately measure the asperity contact area and normal stress, includingmappingof the actual size, shape, and spatial distributions observed over the entire fault [Selvadurai and Glaser, 2013].

3.2. Interface Preparation

Prior to performing the experiments, the slider block was pressed against the base plate, then sheared for atotal of ~36.1mm of total cumulative slip. During this shearing procedure, a range of normal loads wereapplied (2000N to 4400N) and stick-slip events (SS) were allowed to occur. After four stick-slip events, theslider block was unloaded and repositioned to the initial position before it was normally loaded and shearingensued. The lapping procedure was continued until laboratory foreshocks (and the acoustic signals theyproduced) became consistently observed during the transition from slow to rapid sliding.

3.3. Test Procedure

Once surface lapping was completed, a suite of direct shear experiments was performed within a range ofnormal loads. Tests were performed in two phases (Phases I and II) and at four levels of normal force(Fn= 2000 N, 2800 N, 3400 N, and 4400 N). Figure 2 shows a typical experimental result for a normal forceof Fn≈ 4400 N. During Phase I, the fault was indexed to a datum location relative to the base plate andstress aged for thold = 900 s using the same level of normal force used previously to develop thepressure-sensitive film at the identical location. Phase II consisted of a slide-hold-slide test in whichinstability along the fault was driven by the far-field movement of the rigid loading platen. The loadingplaten was driven at a constant velocity VLP = 0.010mm/s. This resulted in an increase in shear force (redin Figure 2a) along the interface until instability or a stick-slip event (SS) occurred. A SS is an instabilitywhere the ensuing dynamic rupture propagates throughout the interface. Dynamic rupture was accompaniedby a sudden shear force drop (ΔFs) and a rapid increase in slip (δ) in the direction of applied shear. DuringPhase II, three stick-slip events (SS1, SS2, and SS3) were induced, as shown in Figure 2a. The slider wasconsidered to be accelerating toward a dynamic (unstable) state if any slip sensor achieved velocities>10mm/s. Local velocities at each slip sensor were determined by differentiating the raw signal andapplying a low-pass filter at 10 kHz. The choice of Vthresh = 4mm/s was chosen arbitrarily, and as the resultsshowed, once any slip sensors had breached this velocity, a rupture always propagated throughout theinterface (i.e., a SS occurred).

3.4. Emissions Prior to a Stick-Slip Event (SS)

Figure 2c shows an example of the slow slip measurements from slip sensor NC7 before a SS. AE data (blue)were recorded at 10MHz over 209ms long sections, for each AE sensor (i.e., PZ1–PZ15). The acoustic emission(AE) amplitude trigger threshold was set to 6 pm of fault normal displacement, and a block of data was takenwhen breached. In Figure 2c, a total of five AE signal blocks are shown. Within these blocks we noticed thepresence of high-frequency (between 100 kHz–1000 kHz) acoustic emissions. We refer to the high-frequencyemission as a “foreshock” (FS). Detail A of Figure 2c shows some foreshock detections (green stars) for thefinal AE signal block. A total of 10 foreshocks were detected for this particular stick-slip event (SS3 atFn=4400N) using the method described below.



3.5. Foreshock Locations and Timing

Figure 2d shows typical foreshock measurement suite for the 13 fully calibrated sensors. Each foreshockcontained high-frequency information including pulse-shaped wave arrivals associated with P and S wavephases of the radiated energy. Location of the hypocenter and timing of the events were estimated usinga least squares method, minimizing the error between the first arrival P and Swave information from aminimumcombination of five sensors. Due to clustering of the foreshocks in the locked region (i.e., from x≈150mm to300mm), sensors PZ5–PZ7 and PZ9–PZ12 were primarily used for this calculation. Arrival times of the P waveswere determined using an amplitude criterion: the average amplitude of the differentiated signal within a smallwindow y2 (10 samples=1μs) was compared to that of a preceding larger window y1 (100 samples =10μs). Themean of the larger window y1 was subtracted from the smaller window and normalized by the largerwindow standard deviation σ1; this accounted for variations among different sensors during different runsand is given as

z2 ¼ 1s1

y2 � y1ð Þ; (1)

where z2 was the transformed amplitude of the smaller window (standard normal deviate). An event wasselected when the value of z2 exceeded 4. Hypocentral locations were restricted to the fault plane andresolved to an approximate spatial resolution of 1mm and temporal resolution of 1μs. The assumptionthat fracture occurred on the faulting plane (but not off-fault; within the intact material) follows theprevious findings on PMMA-PMMA frictional interfaces [Mutlu and Bobet, 2005; McLaskey and Glaser, 2011].

The current analysis that describes the overall size of a foreshock took advantage of the absolute calibrationof the AE sensors [McLaskey and Glaser, 2012]. We assumed that the magnitude of a foreshock could be

a)c)

d)b)

Figure 2. A typical result from the modified direct shear experiment performed at Fn ≈ 4400 N. The test consists of aholding Phase I and a slide-hold-slide Phase II. (a) Measurements of the shear (red) and normal forces (blue) duringthe experiment. During Phase II, three stick-slip events (SS1, SS2, and SS3) are created by increasing shear until aninstability is formed. (b) Slip measurements from sensor NC7 (black) where an SS (indicated by yellow stars) resultedin a shear force drop and a rapid increase of slip along the fault. (c) Enhanced view of slip prior to a SS3 from NC7. AEsignal blocks (blue) are shown in relation to the slow slip signal. Timing of the foreshocks for this SS are shown asgreen stars. In Detail A, an enhanced signal shows the three foreshocks (FS) detected in this window before theimpending main shock (MS). (d) A foreshock, from the sequence shown in Detail A, showing the high-frequencynature of these signals as measured by the acoustic emission arrays (PZ4–PZ12).



related to the maximum peak ground displace-ments (PGDs) occurring within the 100μs fromthe first arrival, averaged about piezoelectric sen-sors PZ5, PZ6, and PZ7 (see Figure 2d). In thesetests, measurements from the AE sensors werethe fault normal displacements due to the sensors’orientation. These sensors were located directlyunder the locked “region of interest” of the faultand at hypocentral distances ~50mm from themajority of foreshock locations. At these sensorlocations, we expected source to sensor attenua-tion to be minimal for both the amplitude andfrequency content [To and Glaser, 2005; McLaskeyand Glaser, 2011]. We note that sensors furtheraway (e.g., PZ4 in Figure 2d) were affected byattenuation and should be adjusted using meth-ods similar to those given in McLaskey and Glaser[2011], but they are not considered for the PGDmeasurements used in this study.

3.6. Visual Records of Asperities Within theRegion of Interest

The unique setup and transparent properties ofPMMA made it possible to directly observe thebehavior of the interface during the experiments.Figure 3 shows a schematic representation of thePMMA slider block pressed against the base platewhere the axis of a video camera (Canon VIXIA

HF M301) was oriented at a 35° angle to the faulting plane. Detail A in Figure 3 illustrates the theory, whichfollows normal load experiments in previous studies performed on PMMA-PMMA interfaces [Dieterichand Kilgore, 1996a]: (i) two nominally flat interfaces only touch on regions called asperities, (ii) the lightwas transmitted more effectively through these contacting asperities, and (iii) the light was diffracted onthe open regions in which there is no contact. The camera recorded images at 60 frames per second(Δtframe≈ 16.67ms). The square complementary metal-oxide-semiconductor (CMOS) array was 6.35mm,and images are obtained at a focal length of 4.1mm. The field of view was approximately 41mm, and imagesare 1080× 1920 pixels per frame, making the resolution ~21μm/pixel. No image correction was performedfor the optical distortion as light passed through the slider sample and into the camera lens. The field of view(FOV) of the camera was from x= 200mm to 241mm and captured the entire width (y direction) of the fault.During the slow slip phase, we monitored, frame by frame, changes of high-intensity light transmitted throughasperities within this FOV until failure occurred. Images became blurred due to the vibrations transmittedthrough the reaction frame to the camera mount during rapid sliding and a stick-slip event. The first blurredimagewas given the time stamp tfail, and images prior to this were used to study the qualitative changes in lightintensity during the slow slip phase of the experiment.

4. Results4.1. Asperity Formation Along the Fault Under Normal Loads

Developing a map of the asperity locations and geometries along the fault, independent of the surfaceroughness, enabled us to build a computational model (section 5) capable of determining asperityinteractions from sections of the fault that control rupture nucleation. Contact measurements obtainedfrom the pressure-sensitive film are shown in Figure 4 for the four levels of applied normal force. Theasperity contact points are shown along the interface for initial (black) and posttest measurements(magenta). Real contacts greater than 0.04mm2 are shown as scaled circular patches with areas proportionalto the actual measured contact area, enlarged 20 times for clarity. Asperities which supported normal stresses

Figure 3. The experimental facility used to qualitativelyobserve light intensity transmitted through asperities priorto stick-slip events. Detail A shows the theory (as detailed byDieterich and Kilgore [1996a]) for the manner in which light istransmitted and diffracted across the interface.



above 18MPa had areas ranging from Afilm ∈ (0.01, 4.97) mm2, which converted to an equivalent circularasperity representation with radii between Rfilm ∈ (0.06, 1.25) mm. The center of the circular patch waslocated along the x-y plane using the geometric centroid of the true contact area calculated using imageprocessing algorithms. Spatial histograms of the asperity distributions are shown in the margins anddiscretized into a grid of 2mm and 0.5mm along the x and y directions for visual aid.

4.2. Spatial Slow Slip Distributions Along the Fault

Figure 5a summarizes the fault asperities for a normal load of Fn=4400N and the locations of the slip sensors(NC1–NC7). The time at which slow slip transitioned to rapid sliding (tfail) was defined as when the local slip ratebreached Vthresh (=10mm/s) at any slip sensor during the loading cycle. Figure 5b shows the spatiotemporalprofiles of slow slip along the x axis at 1 s intervals leading up to tfail (thick blue line). A piecewise cubicHermite shape-preserving interpolation scheme [Fritsch and Carlson, 1980] was used to calculate the slip profiles(black lines) across the sensors attached to the upper surface y> 0 (NC1, NC3, NC5, NC6, and NC7) at 100mmseparation distance.

Figures 5b and 5c show the slow slip accumulation along the fault for two levels of normal load (Fn= 4400Nand 2700N) and two stick-slip events (SS2 and SS3), respectively. SS1 did not display any foreshocks, and slowslip profiles are not shown. Slow slip profiles along the fault at tfail–50 s or tfail–25 s before failure are shown asthe thick red line. Accumulation of slip at different locations on the fault can be easily visualized: (i) sectionsof the fault that showed more compressed slip profiles indicate a relatively locked section of the fault and(ii) increased spacing between subsequent slip profiles indicated accelerating slip.

Slow slip initially accumulated relatively uniformly along the fault. This can be seen by the flat (low spatialslip gradient) red lines in Figures 5b and 5c, which represent the slip profiles at 50 s and 25 s before failure,respectively. As time goes on (loading continues) the gradient becomes larger at the side near the thrust;the amount of gradient depends on the normal force Fn. The amount of slip across the fault forms an elbowwith time and flattens out between 100mm to 200mm past the loaded edge depending on the normal load.An example of the “elbow” is shown for SSE 3 at Fn=4400N in Figure 5b. As time to failure decreased, (i) thelevel of slip gradient (between the TE and LE) increased and (ii) the elbow propagated away from the trailingedge (TE) into the region containing a more dense distribution of asperities (Figure 5a). We refer to the more

4.97

Asperity area (mm2)

10

-10

0

-10

0

10

Fn

Fn

Fn

Fn

4400 N 3400 N

LE TEy-di

rect

ion

(mm

)y-

dire

ctio

n (m

m)

-10

0

-10

0

10

10

LE TE

2700 N 2000 N

10

-10

0

-10

0

10

10

-10

0

-50 0 50 100 150 200 250 300 350 400

-50 0 50 100 150 200 250 300 350 400-10

0

10

x-direction (mm)

-50 0 50 100 150 200 250 300 350 400

-50 0 50 100 150 200 250 300 350 400

x-direction (mm)

LE TE LE TE

0.0448

Figure 4. Asperity contact area at various levels of normal force Fn, measured using the pressure-sensitive film, before (black) and after (magenta) four modifieddirect shear experiments. Spatial histograms of asperities larger than 0.04mm2 are shown on the x (discretized into 2mm sections) and y (discretized into0.5mm sections) margins.



densely distributed asperities as the “relatively locked” section of the fault. We estimated the speed at whichthe elbow propagated into the relatively locked section by taking the approximate location of the elbow atfailure, we then assumed it began at the loading point edge and took 25 s or 50 s (depending on the normalload Fn) to propagate to the locked section. We show the estimates of the average elbow propagation speedas the dashed magenta lines depicted on the slip profiles at time tfail (blue lines) in Figure 5b. We used thelocation of the elbow to define the location of the rupture tip of the breakdown zone [Ohnaka, 1992] sincethe sudden breakdown of shear stress behind the rupture tip results in an increase in slip as described bythe slip-weakening model.

The average speed at which the rupture tip (or breakdown tip) moved into the relatively locked regionranged from 2mm/s to 9.5 mm/s over the last 25 to 50 s before failure and was dependent on the normalconfining force Fn. At higher Fn, the breakdown tip did not penetrate as far into the locked region andmoved at a slower speed than measured at lower normal confining loads. Detail A in Figure 5b showsthe increased detail used to estimate the location and propagation speed of the elbow. Estimates show

y-di

rect

ion

(mm

)-10

-5

0

5

10

(a)

LE TE

NC6 NC7NC5

NC4

NC3

NC2

NC1y > 0

y < 0

Direction of slip

0 50 100 150 200 250 300 350 400

x-direction (mm)

m)

(S

low

slip

,µ

m)

(S

low

slip

,µ

x-direction (mm) x-direction (mm)

0 100 200 300 4000

10

20

30

40

50

60

0 100 200 300 4000

10

20

30

40

50

60

0 100 200 300 4000

10

20

30

40

50

60

0 100 200 300 4000

10

20

30

40

50

60

-25 s

12 mm/s 6 mm/s2 mm/s

-25 s-50 s

6 mm/s3 mm/s

1 mm/s

-50 s

“elbow”

2 mm/s4

68

Detail A

Fn = 2700 N, SS2Fn = 4400 N, SS2

Fn = 2700 N, SS3Fn = 4400 N, SS3

(b) (c)Propagation of slow rupture

PZ5 PZ7

PZ6

6 mm/s3 mm/s

1 mm/s

12 mm/s 6 mm/s

2 mm/s

Figure 5. Slow slip measurements prior to the onset of rapid sliding. Slip profiles in the x direction were interpolatedfrom the noncontact displacement sensors at times 25 s to 50 s before failure (tfail). (a) Contact estimates along thefault and locations of the slip sensors with respect to the upper (y> 0) and lower (y< 0) surface. (b) Interpolated slowslip data from upper surface (black) for the 50 s before rapid sliding for the stick-slip events SS2 and SS3 at Fn = 4400 N.(c) Interpolated slow slip data from upper surface (black) sensors for 25 s before failure for the stick-slip events SS2and SS3 at Fn = 2700 N. Estimates of the elbow propagation speed away from the trailing edge (TE) were calculatedusing the velocity measurements shown in magenta. Detail A in Figure 5c shows the increased detail used to betterestimate elbow location and propagation speed.



that the tip progressed ~100mm to 150mm awayfrom the TE at speeds between ~1mm/s–3mm/sfor higher Fn and ~150mm to 200mm away fromthe TE at speeds between~6mm/s–9.5mm/s forlower Fn.

Examining the measured slip profiles at failure(tfail) for the events shown in Figures 5b and 5c,we see that the gradient in slow slip along the xdirection increased (δ) with additional confiningnormal force Fn. The gradient in slip profiles(∂δ/∂x) at failure due to higher Fnwould, by defi-nition, result in proportional increase in strain εand the amount of locally stored strain energy.While the strain energy has not been calculatedin this study, theoretical, efforts are currentlybeing developed to understand the near-faultvolume of material, encompassing the faultplane, which controls the release of strainenergy and the resulting effects on the devel-opment of foreshocks.

4.3. Foreshock Characteristics4.3.1. Foreshock Size Versus AppliedNormal ForceFigure 6 shows details of the AE measurementsfor foreshocks observed from PZ6 during theloading cycle for the third stick-slip event (SS3)at all four normal load levels. Only the largestforeshock that was plotted within each sequenceis shown. In general, we observed a dependence

between the foreshock size, measured as the peak ground displacement (PGD as described in section 3.5),and applied normal stress: for larger applied loads, we noticed an increase in size (PGD) of the foreshock.This result is also visible in the spatiotemporal plots of the foreshock sequences seen in Figures 7b and 8b.In foreshock sequences at higher normal loads we still observed small foreshocks; our numerical model offersan explanation for the potential of larger events due to the faults ability to locally store more shearstrain energy.4.3.2. Foreshock Source RadiusWe used a form of the Brune relationship [Brune, 1970, 1971] and estimated the source dimension forindividual foreshocks. The corner frequency of the radiated seismic energy was used to calculate thesource radius R0 of the given event using the relationship:

R0 ¼ 2:34β= 2ϖ f 0ð Þ; (2)

where β is the shear wave velocity of PMMA (1390m/s), f0 is the corner frequency given in kHz, and R0 is thesource radius in millimeter. The elastodynamic energy released, due to local rapid sliding on singleasperities, occurs over a finite time t0 and is observed as foreshocks. The width of the S wave pulse, inBrune’s relationship, describes the duration of moment rate function and can be used to approximatethe corner frequency f0. We used the duration of the first S wave pulse to determine the ruptureduration t0 whose inverse is approximately the corner frequency f0 (i.e., f0~1/t0) [McLaskey et al., 2014].Rupture duration ranged from 0.4 μs (standard deviation = 1.3 μs) to 2.1 μs (standard deviation = 0.5 μs)for the total catalog of 68 foreshocks. The source radii ranged from R0~0.21mm to 1.09mm accordingto the Brune relationship. These estimates of source radii are similar to the actual measurementsprovided by the pressure-sensitive film (Figure 4) which ranged from Rfilm~0.06mm to 1.25mm. Fromthe Brune relationship in equation (2) we can evaluate the corner frequency f0 as a function of thecircular asperity radius: i.e., f0 = 2.34β/(2ϖR0). According to the Brune relationship, the range of asperity

0 20 40 60 80 100

Fn = 4400 N

Fn = 3400 N

Fn = 2700 N

P wave

S wave

Time (µs)

0 20 40 60 80 100

Time (µs)

Rel

ativ

e no

rmal

dis

plac

emen

t (nm

)

Sensor PZ6, SS3

0

0.5 nm

Detail A

P wave0

0.0125 nm

Detail A

Fn = 2000 N

Figure 6. Actual waveforms of the largest foreshocks in the SS3sequences (for all normal load levels), recorded fromAE sensor PZ6.



radii recorded from the film Rfilm~0.06mm to 1.25mm may result in small earthquakes with cornerfrequencies ranging from 414 kHz to 8.6MHz if the asperities were to fail dynamically. The smaller asperities(R0 = 0.06mm) fall outside of the flat broadband range of our acoustic sensors (5 kHz–2.5MHz) and aretherefore limited to observing asperity failure with minimum source radii of R0~0.21mm.

4.4. Spatiotemporal Distributions of Foreshock Sequences

For the experimental campaign no foreshocks occurred during the first stick slip event (SS1) at any normalload. In this section, we present the foreshock sequences recorded during the second and third stick-slipevents (i.e., SS2 and SS3). Figure 7a shows the slip (solid black) and slip rate (gray) measured from each slipsensor for all four load levels during SS2. The time history of the slip signal is differentiated numerically toobtain the slip velocity. The pulse was due to shear rupture moving through the fault during the rapid slidingphase. Once the fault decelerated, new populations of asperity contacts were formed along the interface.Full rupture was also measured acoustically, using the low-sensitivity PZ15 AE sensor (light gray). Thesemeasurements are given in voltage since the low-sensitivity AE sensors had not been absolutely calibrated.Foreshocks were determined using the high-sensitivity AE array (PZ1-PZ13), and their timing is plottedin Figure 7b. Figure 7a shows only the foreshocks close to the main shock while Figure 7b shows the fullforeshock catalog. No foreshocks were observed for SS2 at Fn=2700N, and the reasons will be discussedin the section 4.7. Figure 8 shows the spatiotemporal evolution of foreshock sequences in SS3, which

b)a)

Figure 7. Spatiotemporal distributions of foreshocks during SS2 at various normal loads. (a) Slip (black) and slip rate (gray)measurements calculated from displacement transducers prior to and during the rapid sliding phase and AE signals (lightgray) of rapid sliding were captured using the low-sensitivity sensor PZ15. Foreshocks (red arrows) and main shock (MS,magenta arrow) are shown for a window of ~10ms before rapid slip. Inmost cases, the foreshock sequences began before thistime window and the red fraction indicates the amount of foreshocks visible in FIgure 7a. (b) Full foreshock sequences duringSS2. The color code highlights the temporal evolution of the sequence (from blue to red) and the main shock hypocenterlocation is the star. Foreshocks are shown as circles with sizes proportional to peak ground displacements (PGD).



produced more foreshocks for each normal load level and is presented for the sake of catalog completeness.(Note that an error occurred with the AE data acquisition system, and it did not trigger for the SS3 atFn=3400N; therefore, no main shock was located).

4.5. Foreshock Recurrence Rates

Figure 9a examines the timing of foreshocks from each SS (see legend on bottom right). In general, timebetween foreshocks decreased as the main shock drew closer, an observation that has beenmade in the field[e.g., Jones and Molnar, 1979]. In tests Fn=4400N SS3 and Fn= 3400N SS3 foreshock sequences began atupward of 10 s prior to the main shock. In all other tests, the locatable foreshocks (described in the nextsection) began at times of 1 s or less before the impending main shock. Figure 9b shows the overall peakground displacement (PGD) of each foreshock sequence. As previously mentioned, the size of a foreshockappears to depend on the normal force Fn.

4.6. Foreshocks Distance in Relation to Main Shock

Figure 9c shows the foreshock distance to the main shock (Lm) in relation to the timing of the main shockfor each sequence of foreshocks. Recent studies propose that the main shock (or subsequent foreshocks)may be triggered by foreshock afterslip which propagates in a diffusional manner from the hypocenterof the foreshock [Ando and Imanishi, 2011; Yagi et al., 2014]. In nature, postseismic transients can result fromprocesses associated with time dependence such as viscoelasticity, creep, and poroelasticity [Barbot andFialko, 2010]. If postforeshock transients are present in our experiment, these would only be caused by thefault creep (i.e., viscoelastoplastic deformations). Ando and Imanishi [2011] studied the 2011 earthquake in

a) b)

Figure 8. Spatiotemporal distributions of foreshocks during SS3 at various normal loads. Detailed description is similarto Figure 8.



the Pacific Coast of Tohoku, Japan, and found that afterslip propagated away from the foreshock followingthe relationship:

Lm ¼ DTð Þ1=2 (3)

where T (s) is the event occurrence time and Lm (mm) is the distance of migration, and the constantD (mm2 s�1) is a coefficient identified with underlying diffusional processes. The basic hypothesis is thatafterslip from individual foreshocks propagates away from the source and slows down (in a diffusionalmanner). The main shock (or subsequent foreshocks) is then triggered when the diffusional wave reachesthe main shock hypocenter. We do see, in some cases, that subsequent foreshocks can occur along adiffusional line: e.g., the final two foreshocks in the Fn= 4400N SSE3 along the D=104mm2 s�1 diffusion

10-4 10-2 100 1020

10

20

30

40

50

60

70

80

90

100D

=10

D=

10

D=

10

D=

10

D=

10D

= 1

0

Fn

= 4400 N, SS2

Fn

= 4400 N, SS3

Fn

= 3400 N, SS2

Fn = 3400 N, SS3

Fn

= 2700 N, SS2

Fn

= 2700 N, SS3

Fn = 2000 N, SS2

Fn = 2000 N, SS3

Time to main shock (s)

Dis

tanc

e fr

om m

ain

shoc

k, L

m (m

m)

a)

Tim

e be

fore

mai

n sh

ock

(s)

0 5 10 15 20 2510-4

10-3

10-2

10-1

100

101

Foreshock

10-3

10-2

10-1

100

Fn =

4400 N, S

S2

Fn =

2700 N, S

S2

Fn =

3400 N, S

S3

Fn =

2700 N, S

S3

Fn =

2000 N, S

S3

Fn =

4400 N, S

S3

Fn =

2000 N, S

S2

Fn =

3400 N, S

S2

Pea

k G

roun

d D

ispl

acem

ent (

nm)

b)

c)

Figure 9. (a) Foreshock time before main shock for all SS sequences. (b) Overall peak ground displacement (PGD) for eachforeshock sequence. (c) The time to main shock in relation to the foreshocks distance from the main shock hypocenter (seealso Figures 7b and 8b for spatiotemporal foreshock distributions). Various values of the diffusional coefficient (mm2/s)describing the rate at which diffusional afterslip [e.g., Ando and Imanishi, 2011] would propagate away from a prior foreshock.The size of the symbols are proportional to the peak ground displacements (PGD) as described in section 3.5. Time to mainshock (x axis) decrease from right to left on a log10 scale.



line. While there seems to be little correlation, in field study conclusions of diffusional slip triggering the mainshock have been found from so few as one or two large foreshocks beforehand [Ando and Imanishi, 2011; Yagiet al., 2014] and the migrating swarms of smaller earthquakes. While diffusional slip may trigger subsequentforeshock (or main shock), the general disorder observation suggests that more processes are drivingforeshocks. A discussion to this effect is presented in section 6.3.4.

4.7. Nonlocated Foreshocks and Additional Seismic Activity

The foreshock sequences described in Figures 7 and 8 are composed of a catalog of 68 total foreshocks andeight full ruptures. Figure 10 examines the raw AE signals from sensors PZ5–PZ7 directly below the centralregion for SS2 at Fn~2700N (0 foreshocks) and SS2 at Fn~2000N (9 foreshocks). The foreshocks are indicatedby the green lines. The arrival picking algorithm (equation (1)) detected additional events during the test(black circles). These events were very small in amplitude (see Details A and B in Figure 10) and presentedimpulsive P and S wave arrivals similar to the larger events. The location algorithm, however, was unableto locate them due to the lack of manifestation over a sufficient number of sensors. These signals werereferred to as “foreshocks (which were) detected only.” (This lack of signal strength was most likely due tothe amplitude attenuation in PMMA.) For all eight SSs, the number of events that could not be accuratelylocated was 85 for PZ5, 59 for PZ6, and 133 for PZ7. This gives an indication of the variations in local activityat the leading and trailing edge of the seismically active region. PZ7, which was located at the trailing edge ofthe locked region, accounted for ~49% of the increased activity, while the central (PZ6) and leading edge(PZ5) sensors composed of 21% and 30%.

Figure 10, Detail C, shows a “foreshock (which was) detected and located” (green line). Another event (red)occurred ~74.7μs later but went machine unpicked. Between these two events, there was an approximateS minus P wave difference of ~0.15μs, suggesting that the second event happened ~0.2mm away andhad source radii of ~1.5mm for both events, suggesting that some overlaps in source areas were possible.Bouchon et al. [2011] observed Sminus P travel times corresponding to separations of 5m on foreshocks priorto the 1999 Mw 7.6 Izmit earthquake.

36.3 36.32 36.34 36.36 36.38 36.40.04

0.05

0.06

0.07

0.08

29.8 29.82 29.84 29.86 29.880.04

0.05

0.06

0.07

0.08

PZ7

PZ6

PZ5

PZ7

PZ6

PZ5

Fn = 2000 N, SS2 (9 Foreshocks located)

Fn = 2700 N, SS2 (0 Foreshocks located)

Foreshock detected + located

Foreshock detected only

Time (s)

Foreshocknot picked

Foreshock detected only

Time (s)

Rel

ativ

e no

rmal

dis

plac

emen

ts (

nm)

100 sµ

0.5 pm

2 ms

2 pm

50 sµ1 pm

P

S

Detail A

Detail B

Detail C

Figure 10. Increase in seismic activity measured for SS2 at Fn = 2700 N and SS2 at Fn = 2000 N. The former experienced nolocatable foreshocks but the picking algorithm was able to detect events (black circles) which displayed pulse-like P andS wave characteristics (Details A and B). SS2 at Fn = 2000 N experienced a total of 9 locatable foreshocks (green lines)and had 21 nonlocatable foreshocks between sensors PZ5–PZ7. Detail C shows an enhanced view of a located foreshockthat was quickly followed by an unpicked event (red).



4.8. Asperity Interactions During Slow Slip Phase

The images obtained using the movie camera provided a unique insight into processes that in normallaboratory frictional tests are concealed due to the nontransparent nature of rock in friction experiments.While the visualization of asperities under normal loads is not a novel technique [e.g., Dieterich and Kilgore,1994; Dieterich and Kilgore, 1996a], doing so under combined normal and shear loading (as in this experiment) isa relatively new development [Nagata et al., 2014]. Figure 11 shows frames taken from the slip-deprived regionduring the slow loading phase. At failure, the camera image becomes blurred due to the rapidmotion along theinterface. The first blurred frame was called the “tfail–0 frame” (Figure 11d). Figures 11a–11c represent imagestaken, 300, 60, and 6 frames before the first blurred image. Each image contains an unmagnified imageand two levels of digital magnification (4X and 20X). In these images, color was converted from RGB tointensity [Gonzalez et al., 2004]. Dark to light colors are represented by blue to red coloration, respectively.The unmagnified image contains the interface (blue region) as well as portions of the base plate thatreflect incident light from the room (appearing red). Magnifying the interface, we observe small brightspots that we assume are the asperities in contact. We note that these bright spots only appeared whenthe samples were pressed together and therefore were due to the roughness and normal stiffness of theslider block surface itself.

Using the photographic technique, Selvadurai and Glaser [2014, 2015] have begun to study the concomitantlight changes and foreshock signals emanating from similar regions on the fault, between subsequent framesmeasured. In this study, we examined the large asperity shown in the 20X magnified image. We observedthat the light intensity transmitted across the asperity decreased as time increased to failure (betweenFigures 11c and 11d). These images are (currently) not meant for any quantitative analysis. However, theydo provide unique qualitative insight into the slip-deprived region on a fault during the slow slip phase.We observed that (i) the larger asperities transmitted light relatively constantly for a large portion of the slow

0 10 mm

Interface

0 2.5 mm

0.5 mm

tfail - 0 frames (0 s)

Base plateRapid slip

tfail - 6 frames (~ 99.96 ms)

0 10 mm

Interface

0 2.5 mm

0.5 mm

tfail - 300 frames (~ 5000 ms)

Base plateDirection of applied

shear

0 10 mm

Interface

0 2.5 mm

0.5 mm

Base plate

0 10 mm

Interface

0 2.5 mm

0.5 mm

tfail - 60 frames (~1000 ms)

Base plate

a) b)

c) d)

20X

4X

1X

20X

4X

1X

20X

4X

1X

20X

4X

1X

Asperities

Figure 11. CMOS images obtained during the slow slip phase of the loading cycle from x = 200 to 241mm. (d) Framerepresented the first image to become blurred—a characteristic we assumed to be representative of the onset of rapidsliding along the fault. (a–c) Images represent 300, 60, and 6 frames before rapid sliding shown in Figure 11d. Image color isfrom blue to red which translated to dark to light in physical terms. Unmagnified images contained both the dark (blue)interface and the light (red) base plate. Digital magnifications of 4X and 20X show “bright spots” along the interface that weassume to be the light transmitted across an asperity. Larger asperities remained in contact throughout this portion of theloading cycle and light transmission varied in the later stages (differences between Figures 11b and 11c).



slip cycle and (ii) the light intensity decreased along the periphery of the large asperity as imminent failureapproached. Using this information, we developed a numerical model that captured these two phenomena.

5. Quasi-Discrete Asperity Model

The finite element modeling was performed using the commercial software ABAQUS/implicit [ABAQUS, 2004]to improve our understanding of the experimental contact conditions measured using the pressure-sensitivefilm as well as the observable phenomena (section 4.8) associated with the transition from slow to rapidsliding on the fault (i.e., slow slip heterogeneity and foreshock generation). We employed contact mechanicsto study the constitutive response of a single asperity and further our understanding of asperity interactionsby modeling multiple asperities whose geometry and locations are described by the pressure-sensitive film.Our numerical study focused on the transient evolution of slow slip heterogeneity within the central region ofthe fault, with respect to the applied normal stresses along the asperities.

5.1. Geometry and Boundary Constraints of a Single Asperity

Figure 12a shows the finite element domainwhich consisted of two areas: an elastic region (slider=10a×10a×10a)and a rigid base. We assumed a frictionless response, i.e., the shear stress is zero (τ =0), for all interfacial regionsoutside the circular asperity patch with radius a. Boundary conditions along the interfacial surface are given incylindrical coordinates (r2 = x2 + y2) as follows:

σzz r; θ; 0ð Þ ¼ �p; r∈ 0; a½ �; θ∈ 0; 2π½ �; (4)

where the pressure p is applied from the rigid base plate to the elastic slider region. The elastic region wasprescribed a shear modulus and Poisson’s ratio applicable to PMMA (section 2.2). The analysis wasperformed in the following three steps: (i) the elastic region is brought into perfectly/mated contactwith the rigid base, (ii) a pressure p was applied within the circular boundary which simulated thepressure transferred normally between the contacting asperities, (iii) a far-field displacement boundary

Figure 12. Discrete quasi-static asperity calibration model. (a) A circular asperity was prescribed a finite frictional relationship,and the surroundings were frictionless. Normal pressure p (blue arrows) was applied to the asperity followed by thequasi-static far-field displacements (red arrows). (b) Constitutive frictional relations prescribed within the asperity (blue)and the surroundings (green). (c) Constitutive response for a circular asperity composed of 20 elements along itsperiphery for various levels of normal stress. As the far-field displacement Δstep increased, so did the total shearing forceFTOT and the asperity experienced partial slip from its periphery to the center. (d) Slip deficit caused by the asperity dueto Δstep = 100 μm for a variety of applied normal pressure.



condition was applied in the x direction at the top surface (z = 10a), and (iv) the side surfaces wereprescribed traction free boundary conditions. The displacement boundary condition was applied insteps (Δstep) of 1 μm from 0 to 100 μm and can be expressed as

ux x; y; 10að Þ ¼ Δstep; x ∈ �5a; 5a½ �; y ∈ �5a; 5a½ �; Δstep ∈ 0; 1; 2; 3;…; 100f gμm: (5)

5.2. Constitutive Modeling

The elastic region was modeled as a classical Hookean isotropic elastic medium [Timoskenko and Goodier,1970; Davis and Selvadurai, 1996]. The incremental elastic strains are given by

dεij ¼ dσij2G

� λ� � dσkkδij2G 3λ� þ 2Gð Þ ; (6)

where λ* is the Lamé’s first parameter and G is the shear modulus and summation over the repeated indicesis implied.

Contact elements were given two types of constitutive responses. These relations, shown in Figure 12b,accounted for the frictional shear stress (τ) response and are defined through the relative tangential slip(δs) and a shear stiffness (ks). Element interior to the asperity domain was given a Coulomb-type frictionalresponse, whereas the surrounding regions were maintained zero frictional shear stress. The ABAQUS codeadopted a finite sliding computational algorithm to compute the slip displacements occurring along theinterface. The relationship between the contact shear stress and relative shear deformation was

τ ¼ ksΔs for τ < μ�σ�; (7)

where σ* is the normal stress on the individual element and the shear stiffness ks=μ*σ*/γcrit. The localcoefficient of friction μ* was chosen to be 0.5, and the maximum elastic slip distance γcrit was specified tobe a function of the characteristic length of the element (length scale). In our model, maximum elastic slipdistance (γcrit) was set to 0.005 times the element characteristic dimension (i.e., length scale of anelement [ABAQUS, 2004]). Asperities were constrained to have 20 elements along the periphery. Themaximum elastic slip distance was therefore a function of the asperity size. We investigated the variationin asperity shear versus its radius (section 5.4). For simplicity, deformations experienced along theinterface were constrained to movements only along the interface (x and y directions) with out-of-planedeformations (z direction) set to zero (i.e., the surface remained perfectly mated throughout the simulations).

5.3. Results for Calibration Model

According to planar contact theory [Cattaneo, 1938; Ciavarella, 1998a, 1998b], when a shear force is monotonicallyincreased along the discontinuity, a circular asperity under a constant normal load experiences partial slipbeginning at the outer edge of the contact circle and propagating inward as the shear stress is increased[Cattaneo, 1938]. In Figure 12c contact elements initially remain unloaded and in a “stuck” (red) regime. Asthe far-field displacement (Δstep) is increased, the total force supported by the asperity increases and basedon equation (6), when the element shear stress exceeds μ*σ*, that element enters a “sliding” (green) regime.Due to the geometry and loading conditions on the asperity, elements entered the sliding regime from theperiphery toward the center. Once all elements had entered the sliding regime, the asperity was consideredto be “steadily sliding” and a further increase in the far-field displacement would not result in increased shearstress along the contact region. We therefore defined the “partial sliding” regime to be when an asperityhad any element that remained stuck. For Figure 12b, slip at the center of the asperity was measured versusthe total shear force integrated along the fault. A total of four levels of pressure were applied and thecorresponding shear responses recorded. As expected increased asperity pressure resulted in increasedasperity stiffness. Similar to the potential energy stored in a spring, that which was stored by the asperitywas taken as the area under the curve in Figure 12b. As the normal pressure increased the potential energystored by the asperity grew linearly, the asperity under p = 70MPa, 50MPa, and 30MPa stored 77.17%,54.7%, and 32.5% of the energy capable of being stored by the asperity subjected to p = 90MPa. As anestimate for the validity of the model, the total force supported in the steadily sliding regime was comparedto the maximum theoretical shearing force of a uniformly loaded asperity of radius a subjected to a squeezingpressure p (i.e., μ*pπa2) which varied between 4.2 and 1.5%. Figure 12d shows the displacements along thetransect bisecting the contact region, along the x axis, at the final loading step (i.e., Δstep= 100μm). At this step,



the asperity had entered the steadilysliding regime for each level of normalpressure. The asperity caused a slipdeficit due to its ability to supportshear loads, both of which increased asa function of the normal pressure.

5.4. Asperity Size and Shear Response

The effect of asperity size is examined inthis section, and asperities with radiiof r=2.5mm and r= 0.25mm are com-pared in Figure 13. The maximum elasticslip distance γcrit was 0.005 times that ofthe characteristic surface dimension,and the coefficient of friction was

μ*= 0.5 for both cases. Figure 13 shows the log-log result between the slip at the center of the asperity versusthe total shearing force FTOT. We defined the critical slip distance, Lc, as the amount of slip sustained at thecenter of the asperity for it to enter the steadily sliding regime. Smaller asperities experienced a scaledresponse to their respective applied pressures: (i) they accommodated less shear force, (ii) they caused lessslip deficit, and (iii) they entered the steadily sliding regime at lower levels of shear displacements.

5.5. Multiple Asperity Interface

During modeling shear response of individual asperities behaved according to the results described in theprevious sections. Information on the geometry and locations of asperities measured from the pressure-sensitivefilm (section 3.1) were imported directly into ABAQUS. Individual asperities were given an “equivalent circulararea” representation. Due to computational constraints, only a small section of the interface (dimensions75mm× 12.7mm) was numerically modeled. Pressure-sensitive film measurements of the initial contactdistribution between x=182.5mm and 257.5mm were used to define the asperities in the numerical model.

Figure 14a shows the interface composed of 172 circular asperities (black) surrounded by the frictionlessinterface (white). Due to computational restrictions, only larger asperities with areas exceeding 0.2mm2 weremodeled. Simulations for a range of normal asperity pressures were conducted (p= 50, 70, 90MPa) whereeach asperity had the same prescribed pressure across the whole interface. For each applied normal stresslevel, we were able to induce steadily sliding conditions (i.e., no stuck elements) by increasing the far-fielddisplacement Δstep from 0 to 100μm in 1μm increments.

5.6. Numerical Results5.6.1. Local Quasi-Static Transition From “Stick” to “Slip”Figure 14b shows snapshots of the quasi-static evolution of contact patches from stick (red) to sliding (green)for various levels of far-field displacements (Δstep) for a contact pressure p= 90MPa. While this simulation isstrictly quasi-static, we defined the transient portion of the simulation as loading steps where any singleelement along the interface remained in a stuck state. A steady state was defined when all elements on allasperities experienced the steadily sliding regime discussed previously. Once the system had attained a steadystate, no changes in the deformation gradient were observed since any increase in far-field displacement resultedin no change in shear force along the interface. The locations and sizes of asperities were taken directly from thepressure-sensitive film; smaller asperities occupied the lower (y< 0) section of the fault. From section 5.4, we knowthat these smaller contacts exhibit smaller critical slip distances, Lc, and these asperities entered a steadily slidingregime before the larger asperities, which dominated the upper section of the fault (y> 0).

For the loading step corresponding to Δstep = 36μm, the lower section of the fault had entered the steadilysliding regime while the upper section remained partially locked. At this time, the locked upper section of thefault was loaded by twomechanisms: (i) the increase in far-field displacement Δstep and (ii) the increase in slipacross the asperity populations along the lower section (seen as the isocontour lines in Figure 14b). As thefar-field displacement increased, individual contacts in the upper locked region entered the steady slidingregime. The numbered asperities in Figure 14a represent the ascending sequence of the last 10 asperitiesto enter the steady sliding regime as the far-field displacement was increased. In this model, the spatial

10-2 10-1 100 101 102100

101

102

103

FT

OT (

N)

Slip at center of the asperity ( m)µ

p = 90 MPa

p = 70 MPa

p = 50 MPa

p = 30 MPa

r = 0.25 mm

r = 2.5 mm

Lc

Lc

Figure 13. Separate numerical results for two asperities of different sizes atvarious normal pressures p and subjected to the far-field displacementsdefined by equation (6).



ordering did not align itself sequentially in the direction of shear loading due to the heterogeneity of asperitydistributions (sizes and locations).5.6.2. Variations in the Slip Displacement FieldsFigure 15a shows values of slip ux, in the direction of applied shear, along three transects: A (y=5mm),B (y=0.5mm), and C (y=�3mm), at the contact pressure p=90MPa, for a far-field displacement stepΔstep= 91μm. At this displacement step the fault was in the steadily sliding regime. The locations of transectsA, B, and C are shown graphically in Figure 15a. Transect C bisected the lower section of the fault composed ofsmaller contacts, which transitioned to steadily sliding conditions more rapidly than Transects A and B. TransectC also displayed a smoother distribution of slip and accrued more total slip. Transect A displayed a more tortuousdistribution of slip ux due to the larger slip shadow caused by larger asperities located along this transect.

A

B

C0

7

Direction of applied shear

-7

y-di

rect

ion

(mm

)

Transect

(a)

10987 6 54 32 1

182.5 192.5 202.5 212.5 222.5 232.5 242.5 252.5

0

7

-7

x-direction (mm)

0

7

-7

0

7

-7

0

7

-7

0

7

-7

y-di

rect

ion

(mm

)Contact pressure p = 90 MPa ’(b)

2

10

6

14

18

22

30

26

34

38

u1 (µm)

= 36 mµ

= 65 mµ

= 87 mµ

= 91 mµ

= 0 µm

‘Stick‘Slip’

Figure 14. Results from the multiple asperity simulation in which locations and sizes of asperities were defined using thecontact information obtained from the pressure-sensitive film. (a) The model consisted of 172 equivalent-area circularasperities along the interfacial region between x = 182.5 to 257.5 mm. The numbered asperities correspond to thefinal 10 asperities that transitioned from partial to steady sliding in ascending order with increasing quasi-static stepdisplacements. (b) Results of the simulation calculated at a constant contact pressure of p = 90MPa. The isocontour linesdefine the displacement field at four far-field displacement steps (Δstep).



Figure 15b examines the effect of the normal pressure on the scalar valued function strain energy density(SED= (1/E)σ2), where σ is the stress field and E is the Young’s modulus) that accumulated along Transect Afor asperity normal pressures (p=50 and 90MPa). These calculations were made once the interface hadentered the steadily sliding regime. At this point the strain energy density could not change (deformationgradient was zero and was higher for the larger contact pressure. This was expected since larger pressuresresult in more distortion to the displacement field (see section 5.3).

6. Discussion

We will examine and interpret factors controlling nucleation in the experiment and our position in theresearch in relation to the slip-weakening nucleation model [Ohnaka, 1992] (referred to as Ohnaka’s model).Insights into distributions of asperities, from the experimental and computational results, are discussed inrelation to their ability to resist a slowly propagating rupture front.

6.1. Source Dimensions of Foreshock

In this study, we used the Brune relationship to seismically estimate foreshock source radii. These estimatesranged between R0~0.21mm and 1.09mm calculated from the rupture risetime obtained from the acousticforeshock signal. These sizes were congruent with the estimates provided from the pressure-sensitivefilm shown in Figure 4. Asperities which supported normal stresses above 18MPa had areas ranging fromAfilm ∈ (0.01, 4.97) mm2 that converted to an equivalent circular asperity representation had radii betweenRfilm ∈ (0.06, 0.12) mm. In a Brune model interpretation, our foreshocks are the result of the failure of asingle circular patch, occurring smoothly over time trise. Discrepancies between the maximum source areameasured acoustically (i.e., π(1.09mm)2 = 3.73mm2) and found that using the pressure-sensitive film(~4.97mm2) may be attributed to the irregular formation of asperities along the interface such as thedistributions seen in Figure 1 (Detail B). Failure of an asperity may be due to the failure of a single, large(millimeter length scale), irregularly formed asperity, or the failure of the larger patch and its surroundinglocal microcontacts, or the failure of multiple closely spaced medium-sized asperities (multiple submillimeterlength scale). Acoustically, foreshock signals were not smooth at times predicted by Brune’s model. The

µm1

C

B

A

(a)Contact pressure = 90 MPap

µm19=

182.5 192.5 202.5 212.5 222.5 232.5 242.5 252.5

x-direction (mm)

Slip

, ux

(µm

)S

ED

p = 90 MPap = 50 MPa

(b)

0

0.1

0.2

Along transect A

182.5 192.5 202.5 212.5 222.5 232.5 242.5 252.5

x-direction (mm)

MPa

Figure 15. Numerical results from the multiple asperity model. (a) Slip in the x direction along three transects taken atΔstep = 91 μm. (b) An increase in strain energy density (SED), in the x direction along transect A, with an increase inapplied normal pressure p.



incoming P wave pulse (e.g., for the foreshock marked as Fn=4400N in Figure 6) displayed pulse-like featuresandwas irregularly shaped, whereas Brune’s model predicts that the incomingwave (P or S) be a smooth. Theseadditional features may be due to the local variations in strength and junction rheology on a failing asperity;strength is given using Amontons’s law [see, e.g., Bowden and Tabor, 2001]. Across larger asperities, such as thatdepicted in Figure 1 Detail B, asperities formed are not circular and do not exhibit normal stress distributionsconsistent with many theoretical studies, which analyze the failure of asperities in the context of fracturemechanics [e.g., Johnson and Nadeau, 2002; Johnson, 2010]. It appears that the roughness on individual asperitiespromotes the idea of smaller asperities within asperities [Archard, 1961; Nayak, 1973; Persson, 2006] and that thesecause variations in strength that may promote/suppress the amount of stress dropped during failure, which isrelated to the high-frequency component in the radiated earthquake [McLaskey et al., 2012].

McLaskey et al. [2012] found that increased number of asperities formed between a PMMA-PMMA interface,controlled by varying interseismic hold times, increased the high-frequency content of the acoustic signals.We see an increase in the amount and density of asperities along the interface at increased levels of normalforce Fn (Figure 4). We expect that at larger normal forces the distribution of normal stress of individualasperities (and hence its local strength) becomes more heterogeneous and promotes HF components inthe foreshock signal. The magnitude and frequency content of the displacement signal produced by theforeshocks may be linked to the manner in which larger asperities form, their proximity to each other, andthe amount of near-field microcontacts. A study is currently being prepared to investigate the formation ofasperities from both film measurements and microscopy of the interacting surfaces (P. A. Selvadurai, andS. D. Glaser, Asperity formations and their relation to seismicity on a planar fault, submitted to Journal ofGeophysical Research: Solid Earth, 2015). Numerical studies have been performed [Boatwright and Quin,1986; Ripperger et al., 2007] to study the effects of fault strength heterogeneity defined in a statistical mannerin relation to the source time function of the shear rupture. Variations in statistical distributions of strengthalong the fault resulted in variations in the HF content of the resulting P and S wave arrivals.

6.2. Foreshock Magnitude and the Dependence on Normal Stress

We see in Figures 6, 7b, 8b, and 9b that the peak ground displacement (PGD) for foreshocks are, for themost part, larger when higher amount of normal force Fn was applied to the fault. Acoustically, determinedforeshock source radii were calculated from the pulse duration of the foreshock signals, having values from~0.21 to 1.09mm. Peak ground displacements (PGDs) for each recorded foreshock sequence were shown inFigure 9b. As noted in section 5.6.2, an increase in normal stress on an asperity would increase local stiffnessand its ability to store potential energy. Consider two asperities of identical radii, each subjected to a high andlow normal stress. By forcing each asperity to identical ratios of partial sliding, the shear force FTOT sustainedalong the interface would be less for lower normal stresses p. Furthermore, the potential for an asperity toaccommodate strain energy was proportional to the level of normal stress applied. If these two independentasperities suddenly failed at this point, the asperity under higher normal stress would have more potentialenergy. Assuming that the seismic efficiency (i.e., the amount of potential energy transformed into dynamicallyradiated stress waves [Aki and Richards, 2002]) was equal in both cases, asperities which stored more strainenergy released more energy during an event.

6.3. Nucleation Processes6.3.1. Breakdown ModelOhnaka’s [1992] slip-weakening source nucleation model, which is based on physical principles, is importantfor interpreting the data in our experiments and for developing an understanding of factors contributing tothe observed foreshocks. The theory follows that as slip on a fault transitions from quasi-static to quasi-dynamic rupture, a localized nucleation zone gradually grows based on the ability of the fault to resist therupture. During earthquake nucleation, premonitory slip from within the localized nucleation zone graduallyincreases while shear stress within this region decreases. The region where shear stress is broken down froman original value to a residual value is the breakdown region. Slow slip initially nucleates where the resistanceto rupture is at a minimum along the fault or where shear stress is locally high. Nucleation proceeds in threesteps: (i) the tip of the breakdown region grows steadily, followed by (ii) stable but accelerating progressionof the tip until a critical state where (iii) a dynamic instability forms (i.e., main shock).

We utilize the notations from Ohnaka’s study (see Figure 1 from Ohnaka [1992]) to interpret our data. Prior toloading, the fault remains at the initial shear stress level given as τi. Three parameters are used to describe the



slip-dependent constitutive relation: the peak shear stress (breakdown strength) τp, the residual fault shearstress τr, and the critical slip displacement Dc. The breakdown stress drop Δτb is defined as the differencebetween the peak τp and the residual frictional stress τr. The drop of Δτb occurs over the critical slip distanceDc, and these parameters can be seen as controlling factors of rupture growth resistance. The region whereshear stress breakdown occurs is the breakdown region Xc. Our interpretation of this model is that thesemacroscopic parameters will be controlled by the asperities as discussed in the previous sections.6.3.2. Experimental Bulk Rupture Growth ResistanceFrom the slow slip data shown in Figures 5b and 5c, breakdown begins at the trailing edge (TE) as more slipaccumulates in this region leading up to failure. We observed a slowly propagating slip front which grewbetween ~1mm/s to 9mm/s into the central region of the fault—a region with a large clustering of asperities(Figure 5a). The amount of slow slip increased with increased normal confining load Fn, as did the gradient inslip along the x direction. From Figures 5b and 5c we see that the leading edge (LE; x=0mm) experiencedsimilar amounts of slow slip at all load levels while the trailing edge (TE; x=400mm) experienced more slipat higher normal confining loads. In this approximation, the gradient in slip profile, along the x direction,increased with the applied confining normal load. Figures 5b and 5c show that the slip gradient (∂δ/∂x)over the entire length of the fault (i.e., ∂x= 400mm) was ~4.52 × 10�5 at Fn=4400N and decreased to~2.41 × 10�5 at Fn= 2700N. Additional slip sensors, along the x direction, allowed us to identify an elbowshape in the signal, observed in the slow slip distribution leading up to failure. This elbow showed a dependenceon the normal confining load. The slow slip front propagated further into the interface (i.e., from 100 to 200mm)as the normal force decreased. A better estimate of the elbow location at failure was the epicentral location of themain shock (shown as stars in Figures 7b and 8b), identified using the acoustic emission sensors, where the mainshock moved away from the trailing edge at lower confining normal loads.

At higher normal loads the bulk shear stress (i.e., the total shearing force over the nominal contact area Fs/Anom)along the fault increased. The additional increase in normal force resulted in proportionally higher levels oftotal bulk shear force (Fs) at failure while the nominal contact area Anom (≈400mm× 12.7mm) remainedconstant. From Figures 5b and 5c, we see that for an increase in applied normal force the gradient in slipincreased (∂δ/∂x). The gradient in slip is also a measure of the bulk shear strain εs along the fault of length L.The bulk shear stress τs (assuming a basic linearly elastic model) is given as τs =G · εs, where G is the shearmodulus. Under classical assumptions of frictional contact, the breakdown shear stress Δτb may beexpressed as a function of the normal stress (σ) and the peak (μp) and residual (μr) coefficient of friction,i.e., Δτb= (μp�μr) · σ. Assuming constant coefficients of friction and shear modulus, the observed increasein shear strain within the breakdown zone can be attributed to the increase in normal stress divided by theshear modulus εs= (μp�μr) · (σ/G).

The elbow in the slip data is likely the location of the rupture tip of the quasi-stably growing nucleation zone.Again, the elbow in the curve indicated a normal force dependence as the tip propagated further intothe relatively locked section with decrease in normal force. Estimates of the size, the nucleation zone, andits dependence on the normal force are discussed in more detail in section 6.3.4. From our macroscopicobservations, we expect that as the normal force was increased, the ability of the fault to resist shear rupturealso increased. A schematic of the resistance of the fault to rupture, which captures the observed trendsdescribed above, is shown in Figure 16. For further insight into the location of the elbow, we look toAndrews [1976] whom provided an analytical solution for the stability of a growing crack on a frictional fault.Assuming the simple slip-weakeningmodel described by Andrews [Andrews, 1976, equations (12) to (14)], theeffective surface energy Gc can be expressed as a function of the normal stress (σ), the peak (μp) and residual(μr) coefficient of friction, and the critical slip displacement (Dc):

Gc ¼ 14Δτb � Dc ¼ 1

4μp � μr

� �σDc: (8)

The critical length scale Lc* for this particular version of the slip-weakening model becomes [Andrews, 1976]

L �c ¼ 4

πG � Gc

τi � τrð Þ2 ¼1π

G � Dcð Þ τp � τr� �τi � τrð Þ2 : (9)



From before, we know that peak andresidual shear stresses can be repre-sented in terms of the normal stress,i.e., τp=μp σ and τr=μd σ. Substitutingthis into equation (9), we get a relationfor the critical nucleation length in termsof the normal stress, i.e.

L �c ¼ 1

πG � Dc

σ

� � μp � μr

� �τiσ � μr

� �2 : (10)

We see that the critical nucleation lengthis inversely proportional to the normalstress, which explains why at lowernormal applied normal Fn, the elbowin the slip profiles (Figures 5b and 5c)moved further along the interface thanat higher normal force.

While the bulk properties of the fault are characterized by the slip-weakening model, we are interested indetailed aspects that control the ability of the fault to resist rupture, specifically those at the asperity leveland their dependence on the normal force Fn. The quasi-discrete asperity model was used to link thesetwo scales in this study. The ability of a single asperity to store potential energy is directly influenced by bothits stiffness (which is controlled by the applied normal force) and the amount of slip which has accrued atthat point of the loading cycle (Figure 12). Multiple asperities behaved in a similar fashion as shown by thenumerical simulation in Figure 14. The distribution of asperities was acquired from the pressure-sensitivefilm in a region of the fault where the slowly propagating shear front (described above) would have had topenetrate. Numerical results (Figure 14) show that slow slip accumulated nonuniformly across the faultand even when some larger asperities remained stuck, other sections of the fault experienced a bulk slipdeficit of ~36μm (see Δstep = 87μm in Figure 14b). The maximum difference in slip along the interface oncethe fault had entered full sliding represents a slip deficit along the interface, which was controlled by theamount of normal force. Due to the unknown coefficient of friction μ* at the asperity level, the values of slipare somewhat arbitrary; however, the shear response helps explain how populations of asperities resist shearrupture. When we decreased the asperity pressure to p=40MPa, we observed that asperities entered slidingmore easily (at Δstep = 38μm) and the slip deficit was reduced to 16μm; the bulk stiffness of the fault wasreduced as was its ability to resist the slow slip front. The bulk slip deficit measured in themultiasperity modelis similar to the critical slip distance Dc in Ohnaka’s nucleation model. The ability of an asperity to create slipdeficit (Figure 12d) is, in effect, its ability to resist shear rupture, which was normal force dependent.

The breakdown stress drop Δτb in Ohnaka’s model is also well explained by the numerical model. As thenormal pressure increased we observed an increased potential of the fault to store shear strain energy(Figure 15b). Consider twomultiasperity surfaces, with identical asperity distributions, at high and low normalasperity contact pressures, respectively. To force all asperities along the interface into full sliding, a largeramount of critical slip Dc is required and as a result, more strain energy (proportional to Δτb) accumulatedalong the fault at higher normal pressure p. For a slow rupture to break down the stuck asperities, a specificheterogeneous distribution of slip was required. As macroscopic slip increased, the potential for the faultto resist rupture decreased. Similarly, local potential to store shear strain energy also dropped as localslip increased.6.3.3. Local Rupture Growth Resistance and Foreshock ClusteringLocal stress changes during nucleation are explained in more detail using the numerical model. Experimentsshowed that foreshocks were observed in a region of the fault near to where a slowly propagating shearrupture migrated into an asperity rich, locked section of the fault. Foreshocks (FS) are assumed to be local,dynamic failure of individual [McLaskey and Glaser, 2011] or local clusters of asperities. While Figure 16qualitatively depicts the fault resistance to rupture as smooth, in reality they are more likely to be irregularlyshaped and determined by the heterogeneous distributions of asperity contacts. Numerically, we observed

Figure 16. Qualitative variations in rupture growth resistance determinedfrom the experimental observations. A slow shear rupture frontpropagated away from the trailing edge (TE) and its distance Lc

*, beforethe fault slipped unstably, depended on the applied normal force Fn.Below is the along-strike spatial histogram of asperities at the twonormal load levels Fn = 4400 N (black) and 2000 N (magenta), takenfrom Figure 4.



that increasing the normal pressure on the fault increased the magnitude of potential energy stored inindividual asperities (see section 5.3). Once the fault was forced into “steady sliding” regime, at lower pressurep, the magnitude and spatial distribution (i.e., degree of heterogeneity) in the shear strain energy field werelower. Consider a fault composed of asperities under similar levels of normal stress with similar materialproperties and which behave as described by the quasi-discrete asperity model. If only one asperity withinthe asperity field failed, the static stress change [Stein, 1999] would cause local perturbations in the stressfield [Lin and Stein, 2004]. The distance that these static stress perturbations propagate away from the sourcedepends on the stress dropped, the radius (assuming a circular source), and on the ability of the fault toresist shear rupture—a normal force-dependent parameter in the quasi-discrete asperity model. A faultexhibiting higher rupture resistance has the ability to support sharper gradients in the shear strain energyfield, suggesting that closer populations of asperities would be able to accommodate static stress changesresulting from the sudden failure of a single asperity. Spatiotemporal foreshock distributions (Figures 7and 8) support this idea, and tighter clustering of foreshocks was observed at higher normal forces Fn.6.3.4. Breakdown Tip ProgressionExperimental evidence shows that a slow shear rupture propagated into a relatively locked region and wasnormal load dependent (Figures 5b and 5c). At higher normal forces, the break-down tip velocity propagatedat a slower velocity (1–3mm/s over the last 50 s before tfail) than at lower forces (6–9.5mm/s at the last 25 sbefore tfail). This observation is similar to the conceptual model put forward by Ohnaka [1992] where theslowly growing crack has a breakdown zone (Xc), which includes a number of local asperities. Prior to rapidsliding sequences of foreshocks were observed and showed a normal load dependence (sections 6.3.2 and6.3.3). In this section, we examine the manner in which foreshocks occurred and the information they carryin relation to the main shock.

Foreshock sequences have been studied as precursory phenomena to a larger main shock. Three predominanttheories surrounding foreshock sequences have been postulated. In the cascademodel, a small foreshock occurswhich triggers the next event, which eventually culminates into the main shock. In the cascademodel foreshocksare triggered by static stress changes, pore fluid changes, or dynamic effects. In the preslip model, nucleationoccurs due to an aseismic slippage region that grows until at a certain size when failure occurs. Foreshocks areinterpreted as localized failure within or along the fringe of the nucleating region. Our experimental observationsseem to support preslip since the macroscopic motions show slip patterns that are well explained by Ohnaka’snucleation model—asperities within the growing breakdown zone fail locally based on the ongoing slippagearound them. In the preslipmodel, the stress changes from the foreshocks are incidental to the main shock failuremechanism [Dodge et al., 1996], the foreshock failure mechanism is likely to be similar to the main shock (in ourexperiment, foreshocks released stress in shear along the planar fault [McLaskey and Glaser, 2011]). Relatively,recent studies have examined the diffusional afterslip from foreshocks as the mechanism which triggersthe main shock [Ide, 2010; Ando and Imanishi, 2011]. Barbot and Fialko [2010] discuss the time-dependentrelaxation controlling afterslip after an earthquake (or foreshock) and find that postseismic deformationmay be due to a combination of poroelastic response, fault creep, and viscous shear. In our dry-frictionexperiment, the poroelastic effects are absent (PMMA is nonporous glassy polymer [Arruda et al., 1995])and any purely viscous processes would not allow for the generation of foreshocks—in our experimentsany triggering of subsequent foreshocks (or main shock) due to postseismic deformation is due to faultcreep. Fault creep following a foreshock is, in mechanical terms, localized viscoelastoplastic deformation.Ando and Imanishi’s [2011] studied the foreshock sequence prior to the 2011 Tohoku-Oki, JA earthquake.They found that the Mw 9.0 main shock, 11 March 2011, 14:46, was triggered by the diffusional afterslip fromthe Mw 7.3 foreshock, 9 March 2011, 11:45 (Japan standard time). The mechanism proposed was controlledby the ratio of brittle to ductile areas (i.e., strongly coupled patches to decoupled stable regions), which inour experiment would be analogous to ratios of the strong asperity patches to the noncontact regions.

In all foreshock sequences (except Fn= 2700N, SS3) the first foreshock was located behind the mainshock hypocenter in the direction of the slowly propagating rupture (Figures 7b and 8b). This is similar towell-analyzed foreshock sequences during the 2011 Tohoku-Oki, Japan earthquake [Ando and Imanishi,2011] and the 2014 Iquique, Chile earthquake [Brodsky and Lay, 2014; Yagi et al., 2014]. Additional seismicitywas recorded in our experiments; it was unlocatable but showed some spatial organization (section 4.7). Themajority of the additional seismicity (~48% of the observed increased seismicity) originated within thetrailing edge of the locked section of the fault. We believe that this background seismicity in our experiment



is similar to that present behind theMw 7.3 foreshock, with respect to the direction of the diffusely expandingrupture front, in the Tohoku-Oki sequence [Ando and Imanishi, 2011]. These smaller, unlocatable signals maybe some form of background seismicity that is indicative of macroscopic slow slip of the relatively lockedregion. While this observation does not distinguish between the various mechanisms triggering foreshocks,it does show unique similarities to observations in nature.

We look at the result shown in Figure 9c to examine the possible factors contributing to (or controlling) theingress of slip into the relatively locked section of our experiment. We plot the diffusion coefficient D (mm2/s)(according to equation (4)) on top of the time to main shock versus the hypocentral distance to the mainshock (Lm) in order to help us investigate whether diffusional afterslip was a possible trigger of a subsequentforeshock or perhaps even the eventual main shock. The result show a dispersed behavior. As we see fromFigure 9a, foreshocks generally tend to increase in frequency and spatially coalesce (Figures 7b and 8b)toward the main shock hypocenter as the time to main shock decreases. This observation is similar to thatmade by Jones and Molnar [1979], who observed increased foreshock activity before major earthquakes(between 1914 to 1973). This observation supports the preslip model in that as nucleation, characterized inpart by Ohnaka’s slip-weakening model, of the accelerating slow slip front (and larger shear stress gradients[McLaskey and Kilgore, 2013]) may promote foreshocks on individually stiffer asperities. Moreover, in Figures7b and 8b we see that subsequent foreshocks span distances greater than 10 times their source radius. Thelargest source size, measured acoustically, was R0~1.09mm. Since the shear stress perturbation (dS) along theplanar fault decays proportional to d�3 [Aki and Richards, 2002; Chen et al., 2013], where d is the hypocentraldistance between subsequent foreshock; shear stress perturbations (dS) are relatively weak at distancesgreater than ~10 radii from the previous foreshock (i.e., 10 · R0~10.9mm). This detracts from the possibilityof a cascading style foreshock sequence. Furthermore, since the tip of the slowly propagating slip front onlygrows in the direction away from the trailing edge (Figures 5b and 5c), we would expect foreshocks to occurin a more organized manner if the cascade model was correct, expecting that the breakdown shear stress(Δτb) across the breakdown zone (Xc) would drive the first foreshock and the subsequent foreshocks wouldappear further ahead of the slowly propagating rupture tip. In contrast, spatiotemporal observations of foreshocksequences (Figures 7b and 8b) show that foreshocks appear both ahead and behind of the propagating slowrupture tip after the first foreshock was recorded. This observation is consistent with our numerical model,specifically the manner in which asperities enter a full sliding regime (Figure 16a). The ingress of slip into thelocked region of the numerical model promotes the preslip model, it also demonstrates that stress shielding[Kato, 2004] is likely a contributing factor to the manner in which foreshock sequences are realized.

An interesting foreshock sequence is Fn=4400N, SS3 (red squares in Figure 9c) with respect to the possibility ofdiffusional afterslip as a triggering mechanism. Two pairs of foreshocks, i.e., first two and last two foreshocks ofthis sequence, fall on the diffusion curves given by D≈ 10mm2/s and 1000mm2/s. From the spatial distributionof the first pair (Figure 8b) we see that the first foreshock originated closer to the trailing edge of the sample(as mentioned this observation was common). The second foreshock was located slightly ahead of the firstforeshock, in the direction of slip, but was unlikely caused by static stress perturbations dS due to the lengthytime between events (~8 s). In the second foreshock pair (occurring just prior to failure) the foreshocks appearedahead of the main shock with respect to the direction of the slowly propagating rupture—if diffusional aftersliptriggered the subsequent foreshock it propagated against the direction of the slowly propagating rupture atD≈ 1000mm2/s. The change in the diffusion parameter D may be associated with changes in the ability ofthe fault to resist rupture (i.e., as it weakened due to increased slip). In nature this value has been observedto be constant [Ando and Imanishi, 2011]; however, if the final foreshocks in the sequences discussed heremay be caused by a diffusional type back slip (propagating against the direction of the slow rupture), theconstant value of D may only be applicable over shorter timescales just prior to the main shock. Finally, wealso observe the possibility of diffusional afterslip triggering the main shock for the foreshock sequenceFn=3400 SS2. Similar to the Tohoku, Japan earthquake it only had one substantial foreshock but this diffusionalvalue was similar to the estimate made earlier (D=1000mm2/s).

Evolution of foreshock sequences impetus (or not) to the main shock is due to a variety of factors: the static(Coulomb) stress transfer from a foreshock (i.e., stress drop and source radius dependent [Stein, 1999]),diffusional propagation of foreshock afterslip (i.e., diffusion coefficient D dependent [Ando and Imanishi,2011]), the ability of small asperities to suppress slip (i.e., increased resistance to rupture [Kato, 2004]), and



stiffness and density of asperities in the transitional “crack-tip” region. These represent multiple mechanismswhich may be driving the breakdown of shear stress (i.e., increase of slip) over the crack-tip region. Whileobservations in nature may promote one model relative to another, the reality is that numerous factorsmentioned above are likely to be fault dependent and may be occurring in a concurrent manner. In thelaboratory we are beginning to observe foreshock sequences and to discuss their relation to the mainshock—the mechanisms can begin to be examined in a controlled environment.

7. Conclusions

The transition from slow to rapid sliding along the fault is of interest to geophysicists, engineers, and scientistsalike. In our direct shear experiment, we observe a number of foreshocks as slip transitioned from slow to rapidsliding. Foreshocks showed similar acoustic characteristics and spatiotemporal evolution as those detected innature. Slip sensors were placed along the fault, and nonuniform slip profiles leading up to failure wererecorded. In our experimental model, the only manner for stress to be transmitted across the frictional faultwas through asperity contacts. These contacts were characterized from the experiments by using apressure-sensitive film. Prior to dynamic instability (i.e., main shock), the bulk stress states (controlledthrough asperity contacts) varied and we measured the propagation of a slow rupture into a relativelylocked region of the fault composed of an increased density of asperities. We found that the propagationof the slow rupture into the locked region was dependent on the normal force Fn. Higher Fn was found toslow the propagation of the slow shear rupture into the locked region. Within the relatively locked region, anoticeable increase in size and more compact spatial-temporal distributions of foreshocks were measuredwhen Fn was increased.

To develop an understanding between Fn and the resistance of the fault to the slow shear rupture front, aquasi-static finite element (FE) model was developed. The model used distributions of asperities directlymeasured from the pressure-sensitive film in a small section of the interface where foreshocks coalesced;i.e., the locked section of the fault, specifically the region where the slowly propagating slip front met themore dense distribution of asperities (x= 182.5 to 257.5mm). Physics from the numerical model followedthe qualitative observations made using the photographic methods on the experiment, which visualizedasperities in the locked region—larger asperities remained stuck throughout the loading cycle and the lighttransmitted through individual asperities constricted throughout the loading cycle. A single asperity wasmodeled and followed the Cattaneo partial slip asperity solution. As the shear force increased along the fault,the asperities in this model accommodated for tangential slip by entering a partial sliding regime, the centralcontact of the asperities remained stuck while sliding accumulated along its periphery. Partial slip on theasperity propagated inward as the shear force was incrementally increased. Further increase of the shearforce caused the asperity to enter a full sliding condition. Increasing confining loads showed increasedstiffness and increased capacity to store potential shear strain energy—a possible measure of the “degreeof coupling” between the fault surfaces. Potential energy stored by the asperity increased relative to thenormal pressure p. Multiple asperities were modeled along the interface using a quasi-static analysis.Progression of slip into the asperity field was inhibited as the normal confining force Fn was increased. Thecomputational model provided an explanation as to why an increased confining force Fn would result fromboth an increased resistance to slow rupture as well as an increased potential for larger foreshocks within theresistive, locked section of a fault. In all, the numerical and experimental results imply the validity of Ohnaka’s[1992] nucleation model.

ReferencesABAQUS, Inc. (2004), ABAQUS/Standard Version 6.4. ABAQUS Theory Manual, (n.d.).Aki, K., and P. G. Richards (2002), Quantitative Seismology, 2nd ed., Univ. Science Books, Sausalito, Calif.Ampuero, J.-P., and A. M. Rubin (2008), Earthquake nucleation on rate and state faults: Aging and slip laws, J. Geophys. Res., 113, B01302,

doi:10.1029/2007JB005082.Ando, R., and K. Imanishi (2011), Possibility of Mw 9.0 mainshock triggered by diffusional propagation of after-slip from Mw 7.3 foreshock,

Earth Planets Space, 63(7), 767–771.Ando, R., R. Nakata, and T. Hori (2010), A slip pulse model with fault heterogeneity for low-frequency earthquakes and tremor along plate

interfaces, Geophys. Res. Lett., 37, L10310, doi:10.1029/2010GL043056.Andrews, D. J. (1976), Rupture propagation with finite stress in antiplane strain, J. Geophys. Res., 81, 3575–3582, doi:10.1029/

JB081i020p03575.Archard, J. F. (1961), Single contacts and multiple encounters, J. Appl. Geophys., 32(8), 1420–1425.

AcknowledgmentsThis paper was improved by thehelpful reviews by Jean Paul Ampueroand an anonymous reviewer. All datasets required to reproduce the resultspresented here are freely availableto the reader upon request. Pleasecontact the corresponding author foraccess. Funding for this research wasprovided by the National ScienceFoundation grant (CMMI-1131582) tothe University of California and the JaneLewis Fellowship (University of California,Berkeley) and the National Scienceand Engineering Research Council ofCanada (PGSD3-391943-2010) providedto P.A. Selvadurai.



http://dx.doi.org/10.1029/2007JB005082

http://dx.doi.org/10.1029/2010GL043056

http://dx.doi.org/10.1029/JB081i020p03575


Ariyoshi, K., T. Hori, J.-P. Ampuero, Y. Kaneda, T. Matsuzawa, and R. Hino (2009), Influence of interaction between small asperities on varioustypes of slow earthquakes in a 3-D simulation for a subduction plate boundary, Godwana Res., 16, 534–544.

Arruda, E. M., M. C. Boyce, and R. Jayachandran (1995), Effects of strain rate, temperature and thermomechanical coupling on the finite straindeformation of glassy polymers, Mech. Mater., 19, 193–212.

Barbot, S., and Y. Fialko (2010), A unified continuum representation of post-seismic relaxation mechanisms: semi-analytic models of afterslip,poroelastic rebound and viscoelastic flow, Geophys. J. Int., 182(3), 1124–1140, doi:10.1111/j.1365-246X.2010.04678.x.

Baumberger, T., and C. Caroli (2006), Solid friction from stick–slip down to pinning and aging, Adv. Phys., 55, 279–348.Beeler, N. M., D. A. Lockner, and S. H. Hickman (2001), A simple stick–slip and creep-slip model for repeating earthquakes and its implication

for microearthquakes at Parkfield, Bull. Seismol. Soc. Am., 91(6), 1797–1804.Ben-Zion, Y. (2008), Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes, and

different dynamic regimes, Rev. Geophys., 4, RG4006, doi:10.1029/2008RG000260.Ben-Zion, Y., and C. G. Sammis (2003), Characterization of fault zones, Pure Appl. Geophys., 160(3–4), 677–715.Beroza, G. C., and W. L. Ellsworth (1996), Properties of the seismic nucleation phase, Tectonophysics, 261(1–3), 209–227.Berthoude, P., and T. Baumberger (1998), Shear stiffness of a solid–solid multicontact interface, Proc. R. Soc. London A, 454(1974), 1615–1634.Berthoude, P., T. Baumberger, C. G’Sell, and J.-M. Hiver (1999), Physical analysis of the state- and rate-dependent friction law: Static friction,

Phys. Rev. B: Condens. Matter Mater. Phys., 59(22), 14,313–14,327.Biegel, R. L., and C. G. Sammis (2004), Relating fault mechanics to fault zone structure, Adv. Geophys., 47, 65–111.Boatwright, J., and H. Quin (1986), The seismic radiation from a 3-D dynamic model of a complex rupture process. Part I: Confined ruptures, in

Earthquake Source Mechanics, Geophys. Monogr. Ser., edited by S. Das, J. Boatwright, and C. H. Scholz, AGU, Washington, D. C., doi:10.1029/GM037p0097.

Boitnott, G. N., R. L. Biegel, C. H. Scholz, N. Yoshioka, and W. Wang (1992), Micromechanics of rock friction 2: Quantitative modeling of initialfriction with contact theory, J. Geophys. Res., 97(B6), 8965–8978, doi:10.1029/92JB00019.

Bouchon, M., H. Karabulut, M. Aktar, S. Ozalaybey, J. Schmittbuhl, and M. P. Bouin (2011), Extended nucleation of the 1999 Mw 7.6 Izmitearthquake, Science, 331(6019), 877–880.

Bowden, F. P., and D. Tabor (2001), The Friction and Lubrication of Solids, Oxford Univ. Press, New York.Brodsky, E. E., and T. Lay (2014), Recognizing foreshocks from the 1 April 2014 Chile earthquake, Science, 344(6185), 700–702.Brune, J. N. (1970), Tectonic stress and spectra of seismic shear waves from earthquakes, J. Geophys. Res., 75(26), 4997–5009, doi:10.1029/

JB075i026p04997.Brune, J. N. (1971), Correction [to “Tectonic stress and the spectra, of seismic shear waves from earthquakes”], J. Geophys. Res., 76(20), 5002,

doi:10.1029/JB076i020p05002.Candela, T., F. Renard, M. Bouchon, D. Marsan, J. Schmittbuhl, and C. Voisin (2009), Characterization of fault roughness at various scales:

Implications of three-dimensional high resolution topography measurements, Pure Appl. Geophys., 166, 1817–1851.Candela, T., F. Renard, M. Bouchon, J. Schmittbuhl, and E. E. Brodsky (2011), Stress drop during earthquakes: Effect of fault roughness scaling,

Bull. Seismol. Soc. Am., 101(5), 2369–2387.Cattaneo, C. (1938), Sul contatto di due corpi elastici: Distribuzione locale degli sforzi, Reconditi Accad. Naz. Lincei, 27, 342–348, 434–436,

474–478.Chen, K. H., R. Bürgmann, and R. M. Nadeau (2013), Do earthquakes talk to each other? Triggering and interaction of repeating sequences at

Parkfield, J. Geophys. Res., Solid Earth, 118, 165–182, doi:10.1029/2012JB009486.Chen, T., and N. Lapusta (2009), Scaling of small repeating earthquakes explained by interaction of seismic and aseismic slip in a rate and

state fault model, J. Geophys. Res., 114, B01311, doi:10.1029/2008JB005749.Chen, X., and P. M. Shearer (2013), California foreshock sequences suggest aseismic triggering process, Geophys. Res. Lett., 40, 1–6,

doi:10.1029/2012GL054022.Chiaraluce, L., L. Valoroso, D. Piccinini, R. Di Stefano, and P. De Gori (2011), The anatomy of the 2009 L’Aquila normal fault system (central Italy)

imaged by high resolution foreshock and aftershock locations, J. Geophys. Res., 116, B12311, doi:10.1029/2011JB008352.Ciavarella, M. (1998a), The generalized Cattaneo partial slip plane contact problem. I - Theory, Int. J. Solids Struct., 35(18), 2349–2362.Ciavarella, M. (1998b), The generalized Cattaneo partial slip plane contact problem. II - Examples, Int. J. Solids Struct., 35(18), 2363–2378.Davis, R. O., and A. P. S. Selvadurai (1996), Elasticity and Geomechanics, 206 pp., Cambridge Univ. Press, Cambridge.Dieterich, J. H. (1978), Preseismic fault slip and earthquake prediction,” J. Geophys. Res., 83(B8), 3940–3948, doi:10.1029/JB083iB08p03940.Dieterich, J. H., and B. D. Kilgore (1996a), Imaging surface contacts: power law contact distributions and contact stresses in quartz, calcite,

glass and acrylic plastic, Tectonophysics, 256, 219–239.Dieterich, J. H., and B. D. Kilgore (1996b), Implications of fault constitutive properties for earthquake prediction, Proc. Natl. Acad. Sci. U.S.A.,

93(9), 3787–3794.Dodge, D. A., G. C. Beroza, and W. L. Ellsworth (1995), Foreshock sequence of the 1992 Landers, California, earthquake and its implications for

earthquake nucleation, J. Geophys. Res., 100(B6), 9865–9880, doi:10.1029/95JB00871.Dodge, D. A., G. C. Beroza, and W. L. Ellsworth (1996), Detailed observations of California foreshock sequences: Implications for the earthquake

initiation process, J. Geophys. Res., 101(B10), 22,371–22,392, doi:10.1029/96JB02269.Dublanchet, P., P. Bernard, and P. Favreau (2013), Interactions and triggering in a 3-D rate-and-state asperity model, J. Geophys. Res. Solid

Earth, 118, 2225–2245, doi:10.1002/jgrb.50187.Ellsworth, W. L., and G. C. Beroza (1995), Seismic evidence for an earthquake nucleation phase, Science, 268(5212), 851–855.Fritsch, F. N., and R. E. Carlson (1980), Monotone piecewise cubic interpolation, SIAM J. Numer. Anal., 17, 238–246.Selvadurai, P. A., and S. D. Glaser (2012), Direct measurement of contact area and seismic stress along a sliding interface, in ‘46th U.S. Rock

Mechanics/Geomechanics Symposium’.Gonzalez, R. C., R. Woods, and S. L. Eddins (2004), Digital Image Processing Using MATLAB, Pearson Prentice-Hall, Upper Saddle River, N. J.Goodfellow, S. D., and R. P. Young (2014), A laboratory acoustic emission experiment under in situ conditions, Geophys. Res. Lett., 41,

3422–3430, doi:10.1002/2014GL059965.Govoni, A., et al. (2013), Investigating the origin of seismic swarms, Eos Trans. AGU, 94(41), 361–362, doi:10.1002/2013EO410001.Holtkamp, S. G., M. E. Pritchard, and R. B. Lohman (2011), Earthquake swarms in South America, Geophys. J. Int., 187(1), 128–146.Ide, S. (2010), Striations, duration, migration and tidal response in deep tremor, Nature, 466, 356–359.Ide, S., and H. Aochi (2005), Earthquakes as multiscale dynamic ruptures with heterogeneous fracture surface energy, J. Geophys. Res., 110,

B11303, doi:10.1029/2004JB003591.Iio, Y. (1995), Observations of the slow initial phase generated by microearthquakes: Implications for earthquake nucleation and propagation,

J. Geophys. Res., 100(B8), 15,333–15,349, doi:10.1029/95JB01150.



http://dx.doi.org/10.1111/j.1365-246X.2010.04678.x

http://dx.doi.org/10.1029/2008RG000260

http://dx.doi.org/10.1029/GM037p0097

http://dx.doi.org/10.1029/GM037p0097

http://dx.doi.org/10.1029/92JB00019




http://dx.doi.org/10.1029/2012JB009486

http://dx.doi.org/10.1029/2008JB005749

http://dx.doi.org/10.1029/2012GL054022

http://dx.doi.org/10.1029/2011JB008352

http://dx.doi.org/10.1029/JB083iB08p03940



http://dx.doi.org/10.1002/jgrb.50187

http://dx.doi.org/10.1002/2014GL059965

http://dx.doi.org/10.1002/2013EO410001

http://dx.doi.org/10.1029/2004JB003591


Johnson, L. R. (2010), An earthquake model with interacting asperities,” Geophys. J. Int. 182(3), 1339–1373.Johnson, L. R., and R. M. Nadeau (2002), Asperity model of an earthquake: Static problem, Bull. Seismol. Soc. Am., 92(2), 672–686.Johnston, M. J. S., R. D. Borcherdt, A. T. Linde, and M. T. Gladwin (2006), Continuous borehole strain and pore pressure in the near field of the

28 September 2004 Mw 6.0 Parkfield, California, earthquake: Implications for nucleation, fault response, earthquake prediction, andtremor, Bull. Seismol. Soc. Am., 96(4B), S56–S72.

Jones, L. M., and P. Molnar (1979), Some characteristics of foreshocks and their possible relationship to earthquake prediction and premonitoryslip on faults, J. Geophys. Res., 84(B7), 3596–3608, doi:10.1029/JB084iB07p03596.

Kaproth, B. M., and C. Marone (2013), Slow earthquakes, preseismic velocity changes, and the origin of slow frictional stick-slip, Science,314(6151), 1229–1232.

Kato, N. (2004), Interaction of slip on asperities: Numerical simulation of seismic cycles on a two-dimensional planar fault with nonuniformfrictional property, J. Geophys. Res., 109, B12306, doi:10.1029/2004JB003001.

Dieterich, J. H., and B. D. Kilgore (1994), Direct observation of frictional contacts: New insights for state-dependent properties, Pure Appl.Geophys., 143(1–3), 283–302.

Latour, S., A. Schubnel, S. Nielsen, R. Madariaga, and S. Vinciguerra (2013), Characterization of nucleation during laboratory earthquakes,Geophys. Res. Lett., 40, 5064–5069, doi:10.1002/grl.50974.

Lin, J., and R. S. Stein (2004), Stress triggering in thrust and subduction earthquakes and stress interaction between the southern SanAndreas and nearby thrust and strike-slip faults, J. Geophys. Res., 109, B02303, doi:10.1029/2003JB002607.

Lockner, D. A. (1993), The role of acoustic emission in the study of rock fracture, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 30(7), 883–899.McLaskey, G. C., and S. D. Glaser (2010), Hertzian impact: Experimental study of the force pulse and resulting stress waves, J. Acoust. Soc. Am.,

128, 1087–1096.McLaskey, G. C., and S. D. Glaser (2011), Micromechanics of asperity rupture during laboratory stick slip experiments, Geophys. Res. Lett., 38,

L12302, doi:10.1029/2011GL047507.McLaskey, G. C., and S. D. Glaser (2012), Acoustic emission sensor calibration for absolute sourcemeasurements, J. Nondestr. Eval., 31(2), 157–168.McLaskey, G. C., and B. D. Kilgore (2013), Foreshocks during the nucleation of stick–slip instability, J. Geophys. Res. Solid Earth, 118, 2982–2997,

doi:10.1002/jgrb.50232.McLaskey, G. C., A. M. Thomas, S. D. Glaser, and R. M. Nadeau (2012), Fault healing promotes high-frequency earthquakes in laboratory

experiments and on natural faults, Nature, 491, 101–105.McLaskey, G. C., B. D. Kilgore, D. A. Lockner, and N. M. Beeler (2014), Laboratory generated M �6 earthquakes, Pure Appl. Geophys.Mogi, K. (1963), Some discussions on aftershocks, foreshocks and earthquake swarms: the fracture of a semi-infinite body caused by an inner

stress origin and its relation to the earthquake phenomena (third paper), Bull. Earthquake Res. Inst., 41, 615–658.Mutlu, O., and A. Bobet (2005), Slip initiation on frictional fractures, Eng. Fract. Mech., 72, 729–747.Nadeau, R. M., M. Antolik, P. A. Johnson, W. Foxall, and T. V. McEvilly (1994), Seismological studies at Parkfield III: Microearthquake clusters in

the study of fault-zone dynamics, Bull. Seismol. Soc. Am., 84(2), 247–263.Nagata, K., B. Kilgore, N. Beeler, and M. Nakatani (2014), High-frequency imaging of elastic contrast and contact area with implications for

naturally observed changes in fault properties, J. Geophys. Res. Solid Earth, 119, 5855–5875, doi:10.1002/2014JB011014.Nakata, R., R. Ando, T. Hori, and S. Ide (2011), Generation mechanism of slow earthquakes: Numerical analysis based on a dynamic model

with brittle-ductile mixed fault heterogeneity, J. Geophys. Res., 116, B08308, doi:10.1029/2010JB008188.Nayak, P. R. (1973), Random process model of rough surfaces in plastic contact, Wear, 26, 305–333.Nielsen, S., J. Taddeucci, and S. Vinciguerra (2010), Experimental observation of stick–slip instability fronts, Geophys. J. Int., 180(2), 697–702.Noda, H., M. Nakatani, and T. Hori (2013), Large nucleation before large earthquakes is sometimes skipped due to cascade—

Implications from a rate and state simulation of faults with hierarchical asperities, J. Geophys. Res. Solid Earth, 118, 2924–2952,doi:10.1002/jgrb.50211.

Ohnaka, M. (1992), Earthquake source nucleation: A physical model for short-term precursors, Tectonophysics, 211(1–4), 149–178.Ohnaka, M. (1993), Critical size of the nucleation zone of earthquake rupture inferred from immediate foreshock activity, J. Phys. Earth, 41(1),

45–56.Ohnaka, M., and L. F. Shen (1999), Scaling of the shear rupture process from nucleation to dynamic propagation: Implications of geometric

irregularity of the rupturing surfaces, J. Geophys. Res., 104(B1), 817–844, doi:10.1029/1998JB900007.Olson, E. L., and R. M. Allen (2005), The deterministic nature of earthquake rupture, Nature, 438, 212–215.Persson, B. N. J. (2006), Contact mechanics for randomly rough surfaces, Surf. Sci. Rep., 61(4), 201–227.Power, W. L., and T. E. Tullis (1991), Euclidean and fractal models for the description of rock surface roughness, J. Geophys. Res., 96(B1),

415–424, doi:10.1029/90JB02107.Rice, J. R., and M. Cocco (2007), Seismic Fault Rheology and Earthquake Dynamics, chap. 5, pp. 99–137, MIT Press, Cambridge, Mass.Ripperger, J., J. -P. Ampuero, P. M. Mai, and D. Giardini (2007), Earthquake source characteristics from dynamic rupture with constrained

stochastic fault stress, J. Geophys. Res., 112, B04311, doi:10.1029/2006JB004515.Rubinstein, S. M., G. Cohen, and J. Fineberg (2007), Dynamics of precursors to frictional sliding, Phys. Rev. Lett., 98, 226,103.Ruina, A. (1983), Slip instability and state variable friction laws, J. Geophys. Res., 88(B12), 10,359–10,370, doi:10.1029/JB088iB12p10359.Sammis, C. G., and J. R. Rice (2001), Repeating earthquakes as low-stress-drop events at a border between locked and creeping fault patches,

Bull. Seismol. Soc. Am., 91(3), 532–537.Schmittbuhl, J., G. Chambon, A. Hansen, and M. Bouchon (2006), Are stress distributions along faults the signature of asperity squeeze?,

Geophys. Res. Lett., 33, L13307, doi:10.1029/2006GL025952.Selvadurai, P. A., and S. D. Glaser (2013), Experimental evidence of micromechanical processes that control localization of shear rupture

nucleation, in ‘47th U.S. Rock Mechanics/Geomechanics Symposium’.Selvadurai, P. A., and S. D. Glaser (2014), Insights into dynamic asperity failure in the laboratory, in ‘48th US Rock Mechanics / Geomechanics

Symposium’, Minneapolis, Minn.Selvadurai, P. A., and S. D. Glaser (2015), Novel monitoring techniques for characterizing frictional interfaces in the laboratory, Sensors, 15,

9791–9814, doi:10.3390/s150509791.Stanchits, S., S. Mayr, S. Shapire, and G. Dresen (2010), Fracturing of porous rock induced by fluid injection, Tectonophysics, 503(1–2), 129–145.Stein, R. S. (1999), The role of stress transfer in earthquake occurrence, Nature, 402, 605–609.Tape, C., M. West, S. Vipul, and N. Ruppert (2013), Earthquake nucleation and triggering on an optimally oriented fault, Earth Planet. Sci. Lett.,

363, 231–241.Thompson, B. D., R. P. Young, and D. A. Lockner (2009), Premonitory acoustic emissions and stick–slip in natural and smooth-faulted Westerly

granite, J. Geophys. Res., 114, B02205, doi:10.1029/2008JB005753.




http://dx.doi.org/10.1029/2004JB003001

http://dx.doi.org/10.1002/grl.50974

http://dx.doi.org/10.1029/2003JB002607

http://dx.doi.org/10.1029/2011GL047507


http://dx.doi.org/10.1002/2014JB011014

http://dx.doi.org/10.1029/2010JB008188


http://dx.doi.org/10.1029/1998JB900007


http://dx.doi.org/10.1029/2006JB004515


http://dx.doi.org/10.1029/2006GL025952

http://dx.doi.org/10.3390/s150509791

http://dx.doi.org/10.1029/2008JB005753

Timoskenko, S. P., and J. N. Goodier (1970), Theory of Elasticity, McGraw-Hill, New York.To, A. C., and S. D. Glaser (2005), Full waveform inversion of a 3-D source inside an artificial rock, J. Sound Vib., 285, 835–857.Tullis, T. E. (1996), Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes, Proc. Natl. Acad.

Sci. U.S.A., 93(9), 3803–3810.Wu, F. T., K. C. Thomson, and H. Kuenzler (1972), Stick-slip propagation velocity and seismic source mechanism, Bull. Seismol. Soc. Am., 62,

1621–1628.Yagi, Y., R. Okuwaki, B. Enescu, S. Hirano, Y. Yamagachi, S. Endo, and T. Komoro (2014), Rupture process of the 2014 Iquique Chile earthquake

in relation with the foreshock activity, Geophys. Res. Lett., 41, 4201–4206, doi:10.1002/2014GL060274.Yoshioka, N. (1997), A review of the micromechanical approach to the physics of contacting surfaces, Tectonophysics, 277, 29–40.



http://dx.doi.org/10.1002/2014GL060274

laboratory-developed contact models controlling ...glaser.berkeley.edu/glaserdrupal/pdf/jgr 1...

Documents