Asperity formations and their relationship to seismicity on a

Transcription

1 submitted to Geophys. J. Int. Asperity formations and their relationship to seismicity on a planar fault in the laboratory P. A. Selvadurai 1 & S. D. Glaser 1 1 Civil and Environmental Engineering, University of California, Berkeley, 94720, USA Received 2015 September XX; in original form 201X SUMMARY Earthquake faults, and all frictional surfaces, are in contact through touching asperities. We offer an explanation for why certain asperities are more prone to foreshock, and why others would be more likely to slide aseismically. This increased knowledge of how asperities form will provide a better understanding of the manner in which they communicate with each other (i.e. static or dynamic stress transfer) during the foreshock failure sequences leading to the larger main shock. We present results of experiments where a pressure sensitive film was used to map, size, and measure the normal stresses of the asperities along the laboratory fault. As the surface roughness plays an important role in how asperities are formed, two Hurst exponents were measured to characterize the interface: (1) long length scale estimate (H 0.45) and (2) short length scale estimate that was present over asperity junction points (H 0.8 to 1.2). Macroscopically, the number of asperities, real contact area, and the mean asperity size increased with additional applied normal force while the mean normal stress remained constant. Larger asperities carried higher levels of normal stress on average and displayed higher levels normal stress heterogeneity than smaller ones. The critical slip distance on foreshocking asperities was estimated to be d µm using frictional stability theory. d 0 was 2.5 to 1.9% of the premonitory slip needed to initiate gross fault rupture of the interface, ranging from between 20 to 40 µm. The overall slip necessary to initiate gross fault rupture was

2 2 P. A. Selvadurai & S. D. Glaser between 77 to 87.5 % of average asperity radius which follows micromechanical theories in previous laboratory studies. Key words: Instability analysis Earthquake interaction, forecasting, and prediction Mechanics, theory, and modelling Dynamics and mechanics of faulting Rheology: crust and lithosphere 1 INTRODUCTION Laboratory experiments (e.g., Dieterich, 1978, 1994) have been used to improve our understanding of earthquakes and faulting (Scholz, 2002). Laboratory models have provided a phenomenological understanding of the dynamics surrounding the transition of friction from static to kinetic. These mechanistic models allow for estimates of the changing stress states on fault in nature inferred using standard seismological techniques. Over the last two decades, the level of detail from the field measurements has increased due to improved seismometer array coverage, broadband seismometers, down borehole seismometer and more accurate global positioning systems (GPS) among other factors. The mechanical model describing the transition of frictional sliding from slow (stable) to rapid (unstable) is described as a shear rupture where stress is broken down by the accumulation of slip (e.g., Ida, 1972; Andrews, 1976). Both laboratory (e.g., Dieterich, 1978; Ohnaka & Shen, 1999; McLaskey & Kilgore, 2013; Selvadurai & Glaser, 2015b) and numerical studies (e.g., Lapusta et al., 2000; Chen & Lapusta, 2009; Ampuero & Rubin, 2008; Kaneko & Ampuero, 2011) have shown that a premonitory (nucleation) phase exists where a region of slow aseismic accelerating fault slip precedes a large earthquake. Detection of the premonitory phase is extremely difficult using current geodetic measurements (Tullis, 1996; Roeloffs, 2006) due to array coverage and location constraints, and the small size and limited timing of the accelerating aseismic region. With recent advances in broadband seismometers, recorded events are becoming smaller and were previously undetected. This seismicity is generated at the fringe of the nucleation re- Corresponding Author

3 Foreshocks seismicity in relation to asperity formations 3 gion. Seismologists have begun looking at this seismic activity as an indicator of the otherwise aseismic preparatory phase (Chiaraluce et al., 2011; Marsan & Enescu, 2012; Kato et al., 2014; Yagi et al., 2014; Meng et al., 2015). In nature, localized and rapid failure of asperities within a growing nucleation zone, if large enough, are referred to as foreshocks and have been observed to precede larger earthquakes. With better seismological instruments, clusters and swarms of small earthquakes and/or foreshocks are now being detected weeks to minutes before and in close spatial proximity the eventual main shocks (e.g., Mogi, 1963; Jones & Molnar, 1979; Ohnaka, 1993; Nadeau et al., 1994; Dodge et al., 1995, 1996; Chiaraluce et al., 2011; Govoni et al., 2013; Tape et al., 2013). Recent studies show evidence that at least 50% of major interplate earthquakes have foreshocks (Brodsky & Lay, 2014), whereas Bouchon et al. (2013) believe it to be more in the range of approximately 70%. Foreshock sequences and slow slip processes prior to recent, wellmonitored large earthquakes, i.e. the 2011 Tohoku-Oki, Japan, (Kato et al., 2012) and the 2014 Iquique earthquakes (Brodsky & Lay, 2014; Yagi et al., 2014) are forcing scientists to reconsider original estimates of spatial and temporal scales over which preparatory phases occur. A priori detection of foreshocks is currently difficult (if not impossible) to distinguish from non-premonitory seismic activity much of this is the result of our lack of understanding of the mechanical processes controlling premonitory seismicity. Stress changes along faults due to preparatory seismicity is not well understood; in certain cases, earthquake swarms do not culminate in a major event (Holtkamp et al., 2011). The exact relation between foreshocks and the aseismic preparatory phase is also debatable (Mignan, 2014). Two concurrent conceptual models exist that explain the presence of preparatory seismicity: (i) the pre-slip and (ii) the earthquake cascade models (Ellsworth & Beroza, 1995; Beroza & Ellsworth, 1996; Vidale et al., 2001). In the pre-slip model, slow aseismic slip is responsible for foreshocks and other precursory seismic activity. If the slow slip is below the detection threshold of modern geodetic networks, the seismicity produced is a means to monitor the extent and growth rate of the slow slip region. The size of this region determines the frictional stability of the shear rupture once a nucleation region reaches a critical size, unstable rupture will ensue. Better estimates of the size and growth rate of the nucleation zone could lead to better estimates and the possible prediction of the larger impend-

4 4 P. A. Selvadurai & S. D. Glaser ing earthquakes. Conversely, the earthquake cascade model does not require an initial region of slow slip. Here, earthquakes trigger the subsequent event. Each event is a foreshock to the previous event the main shock thus has only one foreshock (not a sequence) and triggering is due to dynamic or after-slip stress perturbations. Epidemic-Type Aftershock Sequence models (ETAS) (Ogata, 1988) use empirically based laws (i.e. Gutenberg-Richter and Omori time diffusion law) to study after-slip triggering. This model implicitly assumes that any transient change in the overall seismicity is due to the triggering of an earthquake by another one. Prediction becomes futile for the breakaway earthquake model; there is a lack of understanding of the fundamental mechanics, which is unlike that describing the nucleation theory for the pre-slip model. The behavior of a fault is controlled by the nature of the contact surfaces. In this study, we perform laboratory tests to study interface contacts (i.e. asperities) formed between two rough surfaces that are direct byproducts of the global stress states and physical properties along the frictional fault. Surface roughness has influence on many facets of natural phenomena such as adhesion, friction, wear and electrical/thermal transmission (e.g., Popov, 2010; Pohrt & Popov, 2012), and geophysical problems such as rock friction leading to earthquakes(scholz, 2002). Asperities represent strength heterogeneity caused by the coming together of the rough surfaces and produce local stress fluctuations that dictates how slip accrues. We look to the laboratory to understand how asperities interact during the premonitory slip phase (Tullis, 1996) and the initial prestress states of the fault. We relate the findings presented here to results presented from the concerted study by Selvadurai & Glaser (2015b) in which foreshocks occurred within a nucleation zone of a frictional fault similar to how they appear on natural faults. 1.1 Asperity formation in terms of contact mechanics Understanding how asperities are formed, in terms of contact mechanics, is in large part due to seminal research by Hertz (1882). He calculated the contact area and displacements formed between interacting quadratic surfaces in elastic contact, most notably two spheres pressed together under normal loads. Real surfaces exhibit sparse sets of dilute contacts over a range of length scales (e.g. Persson, 2006). We call an isolated contact patch an asperity and the sum of all as-

5 Foreshocks seismicity in relation to asperity formations 5 perities along the interface equates to the real contact area (A r ). We limit ourselves to length scale variations of 20 µm due to a limitation of our experimental facilities discussed later. Bowden & Tabor (2001) first noted that the real contact formed along an interface were typically orders of magnitude lower than the nominal area (A 0 ) of the interface. Idealized models (e.g. Archard, 1957, 1961; Greenwood & Williamson, 1966) examined the contacts formed between rough elastic surfaces in terms of statistically prescribed smooth spherical bumps with a range of radii. These models take advantage of the foundations provided by the Hertzian contact solutions in superposition (Timoskenko & Goodier, 1970). Geophysical studies (e.g., Brown & Scholz, 1985; Power & Tullis, 1991) build on these idealized contact models and apply it to rough interacting rock surfaces. More recent studies describe self-affine roughness characterized by the Hurst exponent H (Bouchaud, 1997; Candela et al., 2009, 2011; Kirkpatrick & Brodsky, 2014; Brodsky et al., 2016). Using the Greenwood-Williamson model (GW), interaction of these self-affine surfaces cause scale-dependent heterogeneous normal stress fields (Hansen et al., 2000; Batrouni et al., 2002; Persson, 2006) when a purely elastic constitutive relation was employed. Bowden & Tabor (2001) realized that asperities are local stress concentrations and can grow while maintaining a constant pressure (P m ), equal to the materials indentation hardness, due to local yielding. Moreover, as the normal force is increased on a single smooth contact, the material undergoes a transition through an elastic to elastic-plastic, to fully plastic regime ( 3 P m ) (see p. 178 Johnson, 1985). The GW model can be used to model fully plastic deformation. During fully plastic deformation, three conditions must be satisfied (Baumberger & Caroli, 2006): (1) the real contact area must be proportional to the normal load and independent of the nominal faulting area, (2) the average contact radius ā is load independent and (3) asperity radii are of micrometric order. Dieterich (1994) directly confirmed that contacts were indeed experiencing plastic deformations via optical experiments performed on roughened Lucite-Lucite interfaces. This model is commonly used in geophysical studies. We present laboratory findings that show both conditions (2) and (3) are not well satisfied on a fault that exhibited interesting frictional features: i.e., a growing nucleation region that exhibited localized foreshocks (Selvadurai & Glaser, 2015b).

6 6 P. A. Selvadurai & S. D. Glaser Foreshocks are believed to be the sudden failure of an asperity cause by nearby stress perturbations. Their presence (or lack thereof) may hold information regarding the impending larger earthquake and provide information about the breakdown zone and overall growth of the nucleating shear rupture. More recent laboratory results (McLaskey & Kilgore, 2013; McLaskey et al., 2014) and the study directly linked to the results presented here (Selvadurai & Glaser, 2015b) showed that local asperities within the breakdown region can fail dynamically as the shear rupture expands and prior to gross fault rupture (main shock). 1.2 Nucleation of rapid slip Asperity interactions may have important features when trying to understand nucleation processes along a fault modeled in terms of an outwardly growing shear crack (e.g., Andrews, 1976; Ohnaka, 1992). Shear stress ahead of the crack-tipτ i is broken down to a residual levelτ r by accruing slip. The amount of slip necessary to reach breakdown shear stress is referred to as the critical slip distanced c and occurs over a finite breakdown/cohesive zone of sizex c. Once the crack has grown to a sufficient sizeh, it begins to propagate unstably and accelerates to speeds closer to the Rayleigh wave velocity of the material. This produces seismic waves we interpret as earthquakes. One factor controlling h is the effective normal stress field σ (Rice & Ruina, 1983; Dieterich, 1992; Rice, 1993). Effective normal stress is also a parameter controlling asperities formations that may cause local fluctuations in strength that inhibit the growth of the nucleation region. Consequently, asperity formations and interactions may shed light on how stress breakdown occurs within the cohesive zone (Ida, 1972) at the tip of the shear crack as it attempts to grows large enough to generate an earthquake. A major focus of this study is to examine the asperities within a breakdown region in more detail. A novel pressure sensitive film was used to characterize the unique features of the asperities: their locations, size, and local normal stresses distributions. Our goal is to provide a better understanding of two factors within the breakdown region: (i) how asperities communicate with each other based on their location and size and (ii) what measured features (e.g. size and normal

7 Foreshocks seismicity in relation to asperity formations 7 stress) may promote a foreshock on an asperity; i.e. what constitutes a seismic versus aseismic asperity. 2 EXPERIMENTAL METHODS 2.1 General We examine the mature faulting surface after a suite of experiments described by Selvadurai & Glaser (2015b). General experimental configuration, fault geometry and sample dimensions are shown in Fig. 1(a) and surface preparation techniques are described by Selvadurai & Glaser (2015b). The mature fault (i.e. one exhibiting negligible wear) in this study had previously accumulated approximately 58.4 mm of slip over 32 stick-slip events (SS) at a range of applied normal loads (F n = 2000 to 4400 N). During the premonitory phase (i.e. the time prior to SS) a total of 68 foreshocks occurred at asperity length scale determined acoustically by Selvadurai & Glaser (2015b). The polymethyl methacrylate (PMMA)-PMMA interface was held under simple normal load F n for t hold = 900 s then sheared by driving the rigid loading platen at a constant velocity (V LP = mm/s) until gross fault rupture (SS) occurred (Fig. 1(b)). Slip sensors (NC1-NC7) captured the slow accumulation of slider block slip along the fault, which accumulated non-uniformly in the loading (x-) direction. Typical observations of normal force F n, shear force F s and slip δ for a stick-slip event is shown in Fig. 1(b). Tests were performed at four levels of applied force: 4400 N, 3400 N, 2700 N and 2000 N. Macroscopic nucleation of gross rupture was found to occur in a repeatable manner. A slowly propagating shear rupture (between 1 to 9.5 mm/s) moved from the trailing (loaded) edge of the sample into a relatively locked region and its propagation speed was normal stress dependent. Foreshocks seismicity is generated by localized, rapid sliding as an asperity failed. This was captured by an array of absolutely calibrated Glaser-type piezoelectric acoustic emission sensors (PZ1-PZ15) (McLaskey & Glaser, 2012). Foreshocks emanated from a seismogenic region extending fromx=150 mm to 300 mm. The entire catalog of foreshocks from the seismogenic region (recorded by Selvadurai & Glaser (2015b)) is shown in Fig. 1(c). The event magnitudes are given as the average fault-normal peak ground displacements (PGD) over the three

8 8 P. A. Selvadurai & S. D. Glaser AE sensors nearest to the seismic hypocenter. An example of seismic data recorded from a single foreshock is shown in Fig. 1(d). Foreshocks occurred on length-scales of 0.4 to 2 mm estimated acoustically (Selvadurai & Glaser, 2015b). 2.2 Microscopy of asperity surfaces Microscopy was performed on the surface of the slider block from within the seismogenic region shown in Fig. 1(c). Full asperity surfaces were initially visualized using light microscopy (dark field illumination). To reconstruct the asperity, multiple images were stitched together manually in an image processing software. Two different optical profilometers (using white light interferometry) were used to characterize the surface roughness at different length scales. For longer wavelengths (millimetric), a Nanovea PS50 Profilomter with a 3000 µm optical pen was used. Scans sizes were 25 mm x 13 mm with 10µm spatial resolution and 0.5µm height resolution. For shorter wavelengths, higher magnification (micron length scales) roughness measurements were required. Non-contact interferometry measurements were performed using the ADE MicroXAM- 100 Optical Profilometer. The non-contact profilometry provided height measurements (0.01 µm resolution) over a scanning area of 256 µm x 196 µm (0.95 µm spatial resolution) in the x- and y -directions, respectively. 3 RESULTS 3.1 Size and location of asperities The size and location of the asperities formed during the initial contact between the slider block and base plate were measured using Fujifilm Prescale medium range (12-50 MPa) pressure-sensitive film (Selvadurai & Glaser, 2012, 2015b,a). The pressure film was independently calibrated independently by Selvadurai & Glaser (2015a). Detailed calibration performed in our laboratory show that the spatial resolution of the pressure film was about 20 to 30 µm and, for this study, the film was digitized using a pixel size of 20 µm x 20 µm (A pixel = 400 µm 2 = 4 x 10 4 mm 2 ) using a HD scanner (MUSTEK SE A3 USB 2400 Pro). The digitized image was converted to stress (proportional to the coloration of the film) and a lower threshold was used to determine real contact

9 Foreshocks seismicity in relation to asperity formations 9 versus film noise. As a check on the sum measured force, we calculated the total reactive normal force F r supported across the asperities in the seismogenic region (x = 150 to 300 mm). The total reactive normal force F r balancing the normal force in the seismogenic region was calculated by summing the reactive force on eachi th asperity, n F r = σ i A i. i=1 Regions without contact were prescribed null normal stress conditions (Persson, 2006). (1) Fig. 2 shows a section of the interface (x = 270 to 290 mm, y = -2 to 6 mm) for two different confining normal forcesf n = 4400 N (top) and 2700 N (bottom). The inset of each image shows an enlarged view of a few asperities at the two different load levels and the manner in which asperities grew with the application of normal force. Highlighted in Fig. 2 is the (i) full normal stress field σ i, (ii) average of the normal stress field σ i, (iii) the asperity area A i and (iv) the coefficient of variation CV i = std(σ i / σ i ) which is a measure of dispersion in the stress field. 3.2 Macroscopic contact properties for various levels of F n Using the pressure film we examined the number of asperities n formed in the seismogenic zone under various far-field normal loads F n. Fig. 3(a) shows the relationship between reactive normal force F r and real contact (A r orange stars) and the number of asperities (n blue circles). We found that real contact area in the seismogenic regiona r increased at mm 2 per Newton of reactive force (R 2 =0.996). The number of asperities did have an increasing trend with reactive normal force but did not observe the amount of linearity seen in real contact area. Variations in the numbers of asperities could be due to the contact processes (e.g., Archard, 1957, 1961; Greenwood & Williamson, 1966; Nayak, 1973) and also our inability to recreate the fault along very small length scales (Selvadurai & Glaser, 2012). In Fig. 3(b) we examine the relationship between mean asperity area ( A blue squares) and mean asperity normal stress ( σ orange triangles) with the normal reactive force F r. From this we can also calculate upper and lower limits of the mean asperity radius (assuming a circular representation) which ranges from a = 26 to 36 µm for lower and higher normal reactive force, respectively. We note that average asperity radius was not insensitive to normal force which should

10 10 P. A. Selvadurai & S. D. Glaser be the case for plastic asperity deformations. The average asperity normal stress remained relatively constant σ = F r /A r = MPa and insensitive to the normal force. Converse to the previous observation regarding A, this supports the theory that asperities formed plastically at a flow pressure (Archard, 1957). The counteracting observations suggests that the random processes models (Nayak, 1973) for the rough surfaces of PMMA may be more complex than previously anticipated using standard contact theories. 3.3 Local variations asperity properties at various levels off n We can measure the normal stress fieldσ i from each asperity allowing the calculation of the scalar mean of the normal stress field σ i for all asperities within the seismogenic region. Fig. 4(a) shows the probability density functions (PDF) of σ i for various levels of F n. Catalogs were created at the four levels of applied load F n and load levels are indicated in the legend and is applicable throughout Fig. 4(a). The distributions have not been normalized since the number of n asperities varied as the normal force was increased (Fig. 3(a)). We see that the distributions of asperities supporting lower σ i is relatively uniform for all F n. However, for asperities with σ i > 16.2 MPa we seen that an increase amount of asperities support higher σ i for increased F n as seen by the decreasing slope ξ in Fig. 4(a). It is evident that no single value of mean normal stress (e.g. σ from Fig. 3(b)) is necessary and sufficient to characterize the distributions of σ i on all asperities a various normal loads. A single value would be the case for the plastic formation of asperities and we denote σ (dashed lines in Fig. 3) to show how the distributions deviate. The heterogeneity described by these distributions again suggests that formation of asperities is more complex than typical models for our fault. In Fig. 4(b) we plot relationship between σ i and the individual asperity area A i. We see that as the asperities increase in size A i they also tend to support more mean normal stress σ i, which was the case for all levels of applied normal force F n. The only variation in the distributions in Fig. 4(b) was that more large asperities were present at higher normal loads F n (inferred from the results in In Fig. 4(a)). A similar clustering of asperity sizes versus the coefficient of variationcv i is observed in Fig.

11 Foreshocks seismicity in relation to asperity formations 11 4(c). Asperities with lower values of CV i indicate a more uniform distribution, whereas higher values indicate a larger degree of heterogeneity in the normal stress field σ i. This parameter may have implications on the seismicity generated from a foreshock and will be discussed later. Fig. 4(c) shows that asperities of all sizes show some dispersion in the normal stress field (CV i = = 6.1%). As the normal force was increased the dispersion increased along asperities that were smaller and continued to increase as asperities became larger (dashed line in Fig. 4(c)). This might been due to the increased complexity in as asperities shape and normal stress grew as the normal force was increased as shown directly in Fig.2. Fig. 4(d) plots the relationship between the mean normal stressσ i and the coefficient of variationcv i for individual asperities. We see that as the average normal stress increases along the fault so does the level of dispersion. We estimate that dispersion in the normal stress field σ i increased by4.1% per 1 MPa rise in σ i along individual asperities. 3.4 Microscopy of asperity surfaces After the sequence of tests was performed, the slider block sample was examined using microscopy techniques. Fig. 5(a) shows a typical asperity located atx 235 mm andy 5.1 mm on the slider sample. The asperity surfaces appear flat on top, most likely due to wear processes that occurred during the surface preparation techniques. We noticed interesting features reminiscent of asperities on rock faults, such as visual striations that align with the direction of slip and what appeared to be slickensides-like features over portions of the asperity (Candela et al., 2011; Kirkpatrick & Brodsky, 2014; Brodsky et al., 2016). Two small section on the asperity was analyzed using optical profilometery and the results are shown in Fig. 5(b) and (c). The colorbars are indicative of the surfaces height but we have also normalized this by the scan length L = mm. We see that the height is ranges from L to L which was the case in the scans taken on 33 different locations using the ADE MicroXAM-100 optical profilometer. Transects of the roughness profile along slip (blue) and normal to slip (magenta) are shown in Fig. 5(d) and (e) for the optical scans in (b) and (c), respectively. Below (in Fig. 5(f) and (g)) are Fourier power spectrum estimates of the slip profiles in Fig. 5(d) and (e), respectively, in the sliding (blue)

12 12 P. A. Selvadurai & S. D. Glaser and normal to sliding (magenta) directions. The Hurst exponent H was calculated using the spatial power spectrum. In this study, we calculate H par (along slip) andh per (normal to slip) using P(k) k (1+2H), (2) where k is the wavenumber. The Hurst exponent was measured for longer and shorter wavelengths about the wavenumber k = mm 1. The longer wavelength (k mm 1 ) Hurst exponents, averaged over 33 surface scans similar to those shown in Fig. 5(b) and (c), was H par = (along slip) and H per = (normal to slip). Shorter wavelength (k > mm 1 ) Hurst exponents was H par = (along slip) andh per = (normal to slip). Fig. 6(a) gives measurements from the Nanovea PS50 Profilomter of a 25 mm x 12 mm section of the fault within the seismogenic region. Transects A and B are drawn through the lower (y = -4 mm) and upper (y = 4 mm) section of the fault, respectively. Fig. 6(b) shows the probability density function (PDF) for the surface height for the entire surface shown in Fig. 6(a). We note that the PDF is not gaussian and seems to be display some skew, which we have attributed to the wearing process; this possible anisotropy of the PDF needs to be investigated in more detail in future studies. Fig. 6(c) shows the height profile for the two transects A and B in Fig. 6(a). Along they = 4 mm Transect B the surface has wider, flatter surfaces that in the lowery = -4 mm Transect A. Fig. 6(c) shows valleys (with height h) and flat-topped sections (with width w) which were prominent features of the fault. The ratio of h/w 0.06, similar to faulting outcrops in nature (Kirkpatrick & Brodsky, 2014). We also show the height profile normalized by the length of the scan (L = 25 mm) for a relative height of 100µm, which corresponds toh = L that is also similar to natural faults (Brodsky et al., 2016). The Hurst exponent was again calculated but for length scales using the measurements obtained from the Nanovea PS50 optical profilometer. that spanned the valleys observed between the flat-topped sections of the surface. In Fig. 6(d), we analyzed the Fourier power spectrum (FPS) between length scales of 60 µm to 1000 µm for height profiles in the direction (black) and normal (red) to the direction sliding. Hurst exponent estimates wash par = (along slip) and H per = (normal to slip). This matched the longer wavelength (k mm 1 ) estimates made using the ADE MicroXAM-100 optical profilometer. The Fourier power spectrum for scans

13 Foreshocks seismicity in relation to asperity formations 13 from the ADE MicroXAM-100 optical profilometer is shown in Figure 6(d) for comparison. The larger sampling region displayed less anisotropy in Hurst exponents between the direction and normal to the direction of sliding. It is possible that wearing processes affected shorter wavelengths (<60µm). The effect of surface roughness on the manner in which asperities are formed has been studied (Greenwood & Williamson, 1966; Nayak, 1973; Hansen et al., 2000; Batrouni et al., 2002; Schmittbuhl et al., 2003; Persson, 2006); these features may play an important role in determining how resistive a patch of asperities are to shearing when perturbed with a slowly growing nucleation front. The increased number of flat-topped sections, measured on the upper (y < 0) portion of the seismogenic zone, may be a prerequisite for the generation of foreshocks in the premonitory sliding phase. 3.5 Asperity separation distances A major assumption in the GW model is that contacts are sparse and separated - elastically independent and do not communicate through the substrate. Here we investigate the average asperity separation distances in the seismogenic within uniformly discretized sections of the fault. Neighboring contacts must be much further away than the average asperity radius. From a visual inspection of the small section of the pressure sensitive film shown in Fig. 2(a) and (b), it appears that this is not the case. To calculate the average asperity separation distance in the seismogenic region, we discretized the region into square cells with a side length of L grid = 4 mm. Fig. 7(a) shows the asperity distribution within the gray seismogenic region when the fault was loaded to F n = 4400 N. In Fig. 7(a), we see a square gridded region composed of 40 x 3 cells. Fig. 7(b) shows a cartoon representation of the actual asperities distributed within a single cell. Each cell has two parameters: the total number of asperities N grid and the total sum of the real contact area A grid. Using these values we can calculate the average asperity radius in the specified grid cell ā grid = A grid /πn grid. To calculate the average asperity separation distance we must distribute the N grid equal sized asperities (having constant radius ā grid ) evenly throughout the square cell. This was achieved using optimization techniques. Optimal packing of equally sized circles into a square is a non-trivial problem (e.g., Goldberg, 1970). Specht (2015) has calculated the average

14 14 P. A. Selvadurai & S. D. Glaser separation distances d sep to this problem from a range (1 to 10,000) of equally sized asperities (N grid ) occupying a unit square. Fig. 7(c) show an example schematic of the separation distance d sep calculated from the pressure film measurements. Using the metrics for each cell in the seismogenic zone, we calculated the asperity separation distances at normal forces off n = 4400 N. The average number of asperities over all 120 cells was N grid = 117 (ranging from 43 to 251 asperities). The average equivalent radius of the asperities in all cells was a grid = mm = 53 µm (ranging from 31 µm to 120 µm) mm. Using these measurements and the tabular packing data (Specht, 2015) we found on average d sep /a grid = 9.33 (ranging from 3.95 to 19.75). At lower normal forcesf n =2000 N, we found on averaged sep /a grid = (ranging from 4.97 to 76.90). As expected, the ratio of separation distance to average asperity radius increased as the fault was unloaded. 4 DISCUSSION 4.1 General contact observations Fig. 3 shows that the real contact area increased with increase of normal force F n increased. This is a typical observation in contact mechanics studies where A r << A 0 (Johnson, 1985; Bowden & Tabor, 2001). These observations can be interpreted in context of the GW model (Greenwood & Williamson, 1966) a standard model employed in geomechanical studies (Boitnott et al., 1992; Yoshioka & Iwasa, 1996; Yoshioka, 1997; Selvadurai & Yu, 2005). We appear to observe more complexity than in previous studies regarding the manner in which asperities form from the measurements obtained from the pressure film. Overall we observe a constant average asperity normal stress σ = MPa (Fig. 3(b)) that was independent of the applied normal force F n. According to Archard (1953) this promotes the idea that the deformations forming the asperities are plastic. For plastic deformation, the real contact area A r is such that A r A 0 P app P m, (3) wherea 0 is the apparent contact area,p m is the flow pressure (where asperity deformations occur

15 Foreshocks seismicity in relation to asperity formations 15 plastically) and P app is the apparent pressure (Baumberger & Caroli, 2006). Assuming that the flow pressurep m = MPa, we can evaluate both sides of eq. 3, within the seismogenic region independently using the results from Fig. 3. We use the apparent areaa app = 1800 mm 2 to estimate the apparent pressure P app = F r /A app. For F r 1600 N, the apparent pressure becomes P app = 0.88 MPa and the ratio of P app /P m At the same reactive normal force, we measure the real contact area A r 93 mm 2 and the ratio A r /A This calculation promotes the idea that contact deformation was plastic as interpreted from the film. However, plastic (and elastic) deformation on nominally flat rough surfaces predicts that the average size of asperities should remain constant (Greenwood & Williamson, 1966; Johnson, 1985) a feature that was not the case for our interface (see Fig. 3(b)). The GW model has limiting features that seem to be violated: (1) asperities must deform independently of each other and (2) the roughness profile must be isotropic gaussian. Separation distances were small within the seismogenic region (see Fig. 7) and the distribution of height on the slider block were not gaussian (see Fig. 6(b)) both of which violates this standard model. These atypical features, describing the frictional fault reported here, may lead to increased complexity at the microscopic level. 4.2 Asperity separation relating to nucleation processes One question which remains unanswered is the impact of a failing (foreshocking) asperity on the manner in which the stress is transferred to its surroundings. Foreshock sequences have been studied as precursory phenomena to a larger main shock (e.g., Yagi et al., 2014; Kato et al., 2012; Brodsky & Lay, 2014). Two predominant theories surrounding foreshock sequences have been postulated: the cascade and preslip models. A better understanding of stress states along asperities and the range of their elastic interactions may help scientists understand the implications of foreshock(s) and how they relate to the larger main shock. Whether asperities on the fault communicate elastically or are isolated will affect the local stiffness of the fault and may be important when attempting to understand breakdown processes in the cohesive zone of the shear rupture. The interactions between asperities through the off-fault material becomes an issue at small separation distances. This elastic interaction probably affects

16 16 P. A. Selvadurai & S. D. Glaser local variations in fault stiffness (Campaña et al., 2011; Ciavarella et al., 2008; Yastrebov et al., 2012). In-plane asperities separation distances in the seismogenic zone, even at the lower normal loads, were too small (results relating to Fig. 7) to neglect the elastic interactions (Baumberger & Caroli, 2006). Tribological studies of the local interactions between closely packed asperities are now being more often investigated (e.g., Ciavarella et al., 2008; Afferrante et al., 2012). These interactions may affect sliding dynamics during the premonitory phase and therefore cannot be ignored, as is the case for the standard GW model. The work pioneered by Bowden & Tabor (2001) and Archard (1953) suggest that typical separation distances for multicontact interfaces are much larger, approximately 100 radii which has been confirmed by direct observations (Dieterich & Kilgore, 1994, 1996b). Discrepancies between these studies and that presented here may be influenced by the surface roughness; surfaces in the aforementioned studies are much smoother ( 0.1 µm RMS) than the long length scale roughness ( 5 µm RMS roughness) seen in this study (see Fig. 6). 4.3 What constitutes a foreshock susceptible asperity? Asperity interactions at longer length-scales, i.e. the length of the seismogenic region 150 mm, may account for the large amounts of macroscopic slip (from 20 to 40 µm) observed experimentally before gross fault rupture (see figure 5 from Selvadurai & Glaser, 2015b). Here we use frictional stability theory to estimate features of asperities that may have allow localized foreshocks. We know that foreshocks observed in this study are the sudden localized failure of an individual asperities that form at length-scales from tens of microns to a few millimeters. This was determined by Selvadurai & Glaser (2015b) using the acoustic emission signals and the standard Brune relationship (Brune, 1970) for the sudden failure of a circular asperity. McLaskey & Kilgore (2013) suggested that foreshocks in their laboratory experiments arose as local slip rates increased in close proximity to a local strength heterogeneity (i.e. asperity). They attributed this strength variation to the geometric interaction of the two faulting surfaces and in our experiments we quantified these interactions using the pressure film (see Fig. 4). It is possible for an asperity to

17 Foreshocks seismicity in relation to asperity formations 17 be seismogenic, independent of the rate at which it slides or how fast sliding occurs nearby. The potential for seismicity here depends on the contact size and normal stress measurements along asperities and takes advantage of frictional stability theory (Rice & Ruina, 1983; Ruina, 1983; Baumberger et al., 1994). We first assume frictional stability theory scales to the length-scales at which asperities form. This assumption implies that along an asperity a small nucleation region grows outwards from a relatively weak section along the asperity. The asperity exhibits an initial shear stress distribution that is broken down to residual levels by allowing characteristic amount of slipd c to accrue across the asperity junction. A critical nucleation half-lengthh describes the maximum size at which the asperity-level nucleation region can achieve before frictional instability occurs (i.e. a foreshock). For eachi th asperity, we examine the theoretical foreshock nucleation size using two formulations (Kaneko & Ampuero, 2011): h RR i = π G D c 4 σ i (b a), h RA i = 1 π G σ i D c b (b a) 2, (4) (5) where the Poissons ratio ν 0.32, G is the shear modulus (G = G/(1 ν)) for in-plane sliding, G is the shear modulus of PMMA (1410 MPa (Saltiel et al., 2016)), D c is the characteristic slip distance over which the state parameter evolves, σ i is the average normal stress on an individual asperity (measured using the pressure sensitive film) andaandbare the rate and state constitutive parameter for steady-state velocity weakening friction capable of forming an instability (i.e. b a > 0). The estimate h RR i was derived from the linear stability analysis of steady sliding by Rice & Ruina (1983), while h RA i was obtained for (a/b) >= 0.5 by Rubin & Ampuero (2005) on the basis of energy balance for a quasi-statically expanding crack governed by the aging law. We used values of a = 0.01 and b = in conjunction with a numerical study Kaneko & Ampuero (2011) that attempts to explain nucleation processes in a frictional laboratory study between two blocks of Columbia Resin (polymer) (Nielsen et al., 2010). In Fig. 8(a) we plot eqs 4 (solid line) and 5 (dashed line) for a range of normal stresses assuming the constants mentioned on the graph. The cartoon in Fig. 8(a) describes the relationship between asperity radiusr i (shaded

18 18 P. A. Selvadurai & S. D. Glaser region) to the critical nucleation size h (green circle) and how to interpret these curves when the experimental data provided from the pressure sensitive film is introduced (blue dots). From Fig. 4 we obtain the average normal stress σ i and radius r i (assuming a circular representation). For each asperity we can compare whether it lies above or below the h estimates provided by eqs 4 or 5. If an asperity radius is smaller than critical nucleation size, i.e. r i < h, we expect these asperities to be aseismic they would be incapable of developing foreshocks since linear stability is not violated (within the lower limits of our instruments). Asperities with radii greater than the critical nucleation length, i.e. r i > h, could potentially generate a local foreshock according to nucleation theory. Selvadurai & Glaser (2015b) estimated source length scales from foreshocking asperities to range from R to 1.09 mm. In Fig. 8(b) we enlarge the experimental pressure film data and include the range of foreshock sizesr 0 (shaded gray region). We see that using the parameters shown on Fig. 8(a), eq. 5 predicts that more asperities should be susceptible to foreshock seismicity based on the size and normal stress on asperities measured experimentally. They also seem to bound the lower estimates of foreshock sizes (i.e.r mm) determined experimentally. Typical laboratory values D c have been reported between 24 µm (calculated from curves in Dieterich & Kilgore, 1996a) to 100 µm (Marone, 1998) for a range of materials sometimes with the presence of gouge. This is significantly higher than the low critical slip distance predicted here D c = 0.65 µm and may be explained by variations in the surface roughness. Laboratory tests have shown that critical slip-weakening distance D c decreases as the interacting surfaces become smoothed (Dieterich, 1994; Yoshioka & Iwasa, 1996; Yoshioka, 1997; Ohnaka & Shen, 1999). Ohnaka (1992) suggested that strength inhomogeneities (i.e. asperities) are local barriers to an expanding nucleation front that can have lower characteristic slip displacements (d 0 ) than the critical displacement D describing the spatially larger breakdown processes along the fault. Each laboratory experiment studying nucleation processes on pre-existing faults is unique. Distinct foreshock sequences observed in our experimental study may have been caused by the unique surface roughness that varied at shorter (Fig. 5(f) and (g)) and longer wavelengths (Fig. 6(d)). In Fig. 6(d), we see that the mature faulting surface can be characterized using a Hurst

19 Foreshocks seismicity in relation to asperity formations 19 exponent at smaller and longer wavelength. Smaller estimates of D c = 0.65 µm (Fig. 8) promotes the idea that foreshocks from on smoother junctions of the fault (see Fig. 5) if lower values of D c are characteristic of the interaction between smoother surfaces (Yoshioka & Iwasa, 1996). Selvadurai & Glaser (2015b) measured approximately 20 to 40 µm of slow premonitory slip leading up to gross fault rupture. A standard interpretation of the critical slip distanced c has been that of the slip necessary to renew surface contacts (Dieterich, 1979; Marone, 1998) and usually is on the order of the mean contact diameter (Dieterich, 1994; Yoshioka & Iwasa, 1996). From Fig. 3(b) we see that mean contact radius ranges from 26 to 35 µm. The overall premonitory slip was approximately 77 to 87.5 % of the average asperity radius in the seismogenic region. Comparing D c = 0.65µm (Fig. 8) to the mean asperity radii, we obtain a critical slip distance that is 2.5 to 1.9% of the mean asperity radius. This supports Ohnakas theory that the two length scales of critical slip distances may be affecting the nucleation processes along fault. Foreshocks may be attributed to smoother localized sections of the fault, i.e. asperity top, that exhibit a lower critical slip distance (d 0 ) than the overall critical slip distance (D ) defined by a longer length scale roughness. While this mechanism could explain the presence of foreshock, more numerical studies may be necessary to determine the effect of rate and state parameters (a and b), locally varying normal stress states and the ratio of asperity-level to overall critical slip distance (d 0 /D ) during nucleation processes (Higgins & Lapusta, 2014, 2015). 4.4 Local variations in normal stress on individual asperity junctions Looking at the image of a smoother section of the fault (Fig. 5(a)) we see features (slickensides, striations) that would suggest that normal stress variations would vary along a given asperity. This was confirmed using the pressure film visually (Fig. 2) and quantified using the coefficient of variationcv i (Figs 4(b) and (c)). The normal stress field along an individual asperities (which fluctuates due to the asperities on asperity concept (Archard, 1957, 1961; Persson, 2006)) is then indicative of local variations in shear strength along the individual asperity. Variation seismicity can be directly indicative of the strength fluctuations along the fault (Bouchon et al., 1998; Boatwrigth & Quin, 1986; Mai & Beroza, 2002; Ripperger et al., 2007). Reasons for the increased dispersion in

20 20 P. A. Selvadurai & S. D. Glaser the normal stress field (i.e. the increasedcv i shown in Fig. 4(c) and (d)) on asperities could be related to the local contact processes of asperities formed between the rough-rough interfaces (e.g., Nayak, 1973). Using the techniques here it may be possible to study characteristics of foreshocks seismicity (e.g. the high-frequency content of the elastodyamic signals) and its relationship to how asperities form and their local stiffness along the natural fault. Using seismicity (foreshocks or swarms) to help develop a better understanding of the local strength heterogeneity prior to gross fault rupture (main shock) could help better estimate seismic hazard but would require increased laboratory efforts. 4.5 Effects of multiscale roughness on contact formation Surfaces forming the asperities on our fault appeared to be flat-topped islands amongst a large flat sea, as seen in Fig. 6, and were characterized over longer length scales with a Hurst exponent of 0.41 to Along the tops of individual asperities themselves, such as the images seen in Fig. 5(a), the surfaces were smoother at smaller length scales. The two varying levels of roughness may be important during earthquake nucleation: (i) longer length scale roughness may define the inter-asperity spacing (d sep ) and the manner in which asperities interact during the slow slip process and (ii) the shorter length scale roughness may defines how/if foreshock(s) will be present and may dictate the elastodynamic radiation patterns released upon failure. The larger asperities, which were more likely to form a foreshock according to the model proposed in Fig. 8, appear to contain non-uniform normal stress distributions and are irregularly shaped (containing perforations on the periphery) perhaps more appropriately described contact processes involving two roughness profiles (Nayak, 1973). 5 CONCLUSIONS Selvadurai & Glaser (2015b) observe a number of foreshocks occurring as premonitory slip accumulated and transitioned from slow to rapid sliding (Selvadurai & Glaser, 2015b). Foreshocks in that study were constrained to a seimsogenic section of the fault. In this study, we investigated (in more detail) the measurements from a pressure sensitive film that mapped the location of asperities

21 Foreshocks seismicity in relation to asperity formations 21 and their local normal stress. Macroscopically the contacts formed in the seismogenic region in a standard manner; maintaining an average normal stress of P m = MPa for different levels of applied nominal normal force (F n ). Closer inspection showed that asperities formed in a more complicated manner than standard geophysical contact models. Larger asperities accrued higher normal stress levels than smaller asperities. The variability in normal stress along the asperities also varied with both size A i and average normal stress σ i they supported. Separation distances between asperities within the seismogenic region, appeared to be small. Traditional models (e.g. the GW model) assume that the formation of asperities are independent of each other and the long range elastic interactions between asperities (via the material substrate) can be neglected. This may be an oversimplification and future investigations into frictional breakdown may need to include asperity interactions in the cohesive breakdown zone of a slowly growing shear rupture. Upon examining the surface roughness, we found that asperity formation was likely controlled by two levels of surface roughness. On asperity length scales (micron to sub-millimeter length scales) a smoother surface was measured (H par = 0.8 (along slip) and H per = 1.2 (normal to slip)) than at longer length scale variations (tens of millimeter) where the fault was characterized by a Hurst exponent of H = We proposed that asperities forming at the smaller length scales are responsible for localized foreshocks. Frictional stability theory was used in conjunction with measurements of asperity radius and normal stress to determine a critical slip distanced 0 required to generate a foreshock on the smoother asperity surface itself. We found a d 0 = 0.65 µm and was 2.5 to 1.9% of the mean asperity radius along the interface. The global level of slip need to induce gross fault rupture was closer to the mean asperity radius (77 to 87.5 %), a value that agrees with traditional laboratory estimates (Marone, 1998). From these findings, we proposed that two critical slip distance may be controlling nucleation processes on our frictional fault small d 0 is responsible for the generation of foreshocks (that represent localized barriers resistant to shear rupture) and large (D ) that control the general growth of the nucleation zone. The variations in critical slip distance can be related to the smoother and rougher estimates of surface roughness at smaller and longer length scales, respectively.

22 22 P. A. Selvadurai & S. D. Glaser ACKNOWLEDGMENTS All data sets required to reproduce the results presented here is freely available to the reader upon request. Please contact the corresponding author for access. The National Science Foundation Grant CMMI provided funding for this research, P.A. Selvadurai received funding from the Jane Lewis Fellowship (University of California, Berkeley) and the National Science and Engineering Research Council of Canada (PGSD ). References Afferrante, L., Carbone, G., & Demelio, G., Interacting and coalescing Hertzian asperities: A new multiasperity contact model, Wear, (0), Ampuero, J. P. & Rubin, A. M., Earthquake nucleation on rate and state faults: Aging and slip laws, Journal of Geophysical Research, 113, B Andrews, D. J., Rupture propagation with finite stress in antiplane strain, Journal of Geophysical Research, 81(20), Archard, J. F., Contact and rubbing of flat surfaces, Journal of Applied Physics, 24(8), Archard, J. F., Elastic deformation and the laws of friction, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 243(1233), Archard, J. F., Single contacts and multiple encounters, Journal of Applied Geophysics, 32(8), Batrouni, G. G., Hansen, A., & Schmittbuhl, J., Elastic response of rough surfaces in partial contact, EPL (Europhysics Letters), 60(5), 724. Baumberger, T. & Caroli, C., Solid friction from stick-slip down to pinning and aging, Advances in Physics, 55, Baumberger, T., Heslot, F., & Perrin, B., Crossover from creep to inertial motion in friction dynamics, Nature, 367, Beroza, G. C. & Ellsworth, W. L., Properties of the seismic nucleation phase, Tectonophysics, 261(1-3),

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30 30 P. A. Selvadurai & S. D. Glaser a) c) y-direction (mm) Loading platen PMMA slider block PMMA base plate Piezoelectric sensors (PZ1 - PZ15) z F N / 2 Seismogenic region [ Selvadurai and Glaser, 2015] x-direction (mm) F N / 2 LE TE Slip sensors (NC1 - NC7) mm PGD (nm) M F S b) d) 20 nm kn Stick-slip event (SS) 0 kn 0 μm Time (s) μs F N (kn) F S (kn) Slip, δ ( μ m) PZ12 PZ11 PZ10 PZ9 PZ8 PZ7 PZ6 PZ5 PZ4 Relative displacement (nm) Figure 1. Experimental configuration of the direct shear friction apparatus used for the experiments on a PMMA-PMMA interface. (a) Side view schematic depiction of the interface created by compressing the slider block into the base sample through the rigid loading platen. The normal force,f n, was applied through the rigid loading platen and driven at a constant velocity V LP using the shear actuator. The shear actuator was located at the trailing edge (TE) of the slider block. (b) Measurements from a typical stick-slip event (SS) during a single loading cycle. Slip (δ) accumulated slowly in the interseismic phase and transitioned to rapid sliding during the seismic phase of the loading cycle. (c) Total catalog of foreshock seismicity from Selvadurai & Glaser (2015b). A total of 68 foreshocks were observed over 8 stick-slip events and the size of the event was determined from the peak ground displacements (PGD) averaged over local sensors. (d) An individual seismic event (black event from (c)) as measured by the sensors in the acoustic emission array.

31 Foreshocks seismicity in relation to asperity formations 31 Figure 2. Normal stress distributions recorded from the pressure sensitive film for a small section (x = 270 to 290 mm,y = 6 to -2 mm) of the interface atf n = 4400 N (top) and 2700 N (bottom). The inset shows how the asperities vary with changing normal forcef n is changed over the mature faulting surface. For eachi th asperity, we measure the normal stress field σ i (MPa), the mean normal stress σ i (MPa), the asperity area A i (mm 2 ) and the coefficient of variation CV i. a) Number of asperities, n Real contact area, A r (mm ) Ar = Fr 2 R = Reactive normal force, F r (N) Reactive normal force, (N) b) 2 Mean asperity size A ( mm ) MPa F r Mean asperity normal stress, σ (MPa) Figure 3. (a) Changes in the amount of asperities n (blue circles) and real contact area A r (orange stars) as the reactive normal force F r increased within the seismogenic region (x = 150 to 300 mm). Reactive normal force was calculated as the summation of forces on all i asperities within the seismogenic region. (b) Changes in the mean asperity area A (blue squares) and mean asperity normal stress σ (orange triangles) as the reactive normal forcef r in the seismogenic region was increased.

32 P. A. Selvadurai & S. D. Glaser a) b) σ 10 5 Counts Fn = 4400 N Fn = 3400 N Fn = 2700 N Fn = 2000 N ξ Mean asperity normal stress, si (MPa) c) Mean asperity normal stress, si (MPa) d) Coefficient of Variation 10 Asperity area Ai (mm2) σ 10 2 Asperity area Ai (mm2) % Coefficient of Variation %/MPa Mean asperity normal stress, si (MPa) Figure 4. Normal stress measurements from individual asperities within the seismogenic region of the fault (x = 150 mm to 300 mm) compiled into a catalog for various levels of far-field normal force Fn. (a) The probability distribution function (PDF) for the distribution of the mean asperity normal stress σ i. Relationships between (b) asperity mean normal stress σ i and contact area Ai, (c) asperity coefficient of variation CVi and contact area Ai and (d) asperity mean normal stress σ i and coefficient of variation CVi.

33 Foreshocks seismicity in relation to asperity formations 33 Figure 5. (a) Optical microscopy images of an asperity, on the slider block surface, located in the highly seismogenic region of the fault (approximately x = 235 mm andy = 5.1 mm) after the suite of experiments were performed. Stitching four sub-images created the image. We see evidence of features similar to geological features on natural faulting surfaces (Candela et al., 2011), such as, striations and slickensides. (b and c) show separate 2D surface profiles using the ADE MicroXAM-100 optical profilometer. (d) and (e) shows height profiles along transects from (b) and (c), respectively, in the direction of slip (blue) and normal to slip (magenta). (f and g) Fourier power spectrum P(k) of the 1D profiles from (d and e), respectively, in the direction and normal to slip on the interface. The Hurst estimate H (eq. 2) was used to measure the self-affinity of the surface.

34 34 P. A. Selvadurai & S. D. Glaser Figure 6. (a) A large section (25 mm x 12 mm) of the seismogenic region is shown. (b) The Power Density Function (PDF) of surface heights is shown for (a). (c) Surface profiles from Transect A (y= -4 mm) and Transect B (y= 4 mm) are shown for the section shown in (a). Transect B has more and larger flat-topped surfaces than the lower region. A small section of Transect B was examined to better see the flat-topped feature. We see that this feature has a widthw 0.7 mm and heighth 0.03 mm (h/w = 0.04). (d) Fourier power spectrum P(k) of the height profiles using the Nanovea PS50 optical profilometer are shown in the direction (red) and normal to slip (black) on the interface. These are compared with the smaller and more spatially resolved measurements taken using the ADE MicroXAM-100 and shown for comparison (blue and magenta lines).