The Pennsylvania State University

The Graduate School

CHARACTERIZING ACOUSTIC EMISSION SIGNALS THROUGHOUT THE

LABORATORY SEISMIC CYCLE: INSIGHTS ON SEISMIC PRECURSORS

A Dissertation in

Geosciences

by

David C. Bolton

© 2021 David Bolton

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

August 2021

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The dissertation of David C. Bolton was reviewed and approved by the following:

Chris Marone Professor of Geosciences Dissertation Advisor Chair of Committee

Charles J. Ammon Professor of Geosciences

Donald M. Fisher Professor of Geosciences Jacques Rivière Assistant Professor of Engineering Sciences and Mechanics

Mark E. Patzkowsky Professor of Geosciences Associate Head for Graduate Programs and Research Department of Geosciences

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ABSTRACT

Estimating the location and timing of future earthquakes has been a long-standing goal in

earthquake seismology. However, progress in this area has been limited due to a poor understanding

of earthquake nucleation and the connection between nucleation processes and precursory signals.

For example, it is unclear why some earthquakes contain strong foreshock sequences, while others

do not. In addition, it is not immediately clear how earthquake nucleation processes regulate the

evolution of foreshocks and the causal processes that drive foreshock sequences are poorly

constrained. In this dissertation, I seek to provide insights into some of these problems by using

acoustic emissions (AEs) and laboratory stick-slip experiments, as proxies to foreshocks/seismic

signals and tectonic earthquakes, respectively.

In this dissertation, I use a variety of techniques to probe the pre-seismic and co-seismic

properties of AE signals throughout the laboratory seismic cycle. A significant focus is devoted to

understanding the parameter space and physical processes that control the temporal evolution of

AE signals. To this end, I examine the effect of normal stress, shearing rate, and fault zone

morphology on temporal variations in AE characteristics. In addition, I document co-seismic AE

properties for both slow and fast laboratory earthquakes.

The introduction lays out the motivation and broader implications of this work, particularly

as it relates to earthquake nucleation processes and seismic precursors. In Chapter 2, I carry out an

extensive analysis on event detection and answer basic questions surrounding the temporal

variations in the Gutenberg-Richter b-value throughout the laboratory seismic cycle. Chapters 3-4

are focused on applying machine learning (ML) algorithms to study laboratory earthquakes. In

Chapter 3, I use an unsupervised ML approach to characterize continuous AE data and identify

precursors to lab earthquakes. In Chapter 4, I illuminate the driving processes that regulate the

acoustic energy release throughout the seismic cycle by linking its temporal evolution to systematic

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changes in measured fault zone properties. In addition, Chapter 4 provides insights into ML-based

predictions of laboratory earthquakes. Lastly, in Chapter 5 I focus on characterizing the AE

radiation properties of slow and fast laboratory earthquakes.

This work provides insights into acoustic signals and seismic precursors to laboratory

earthquakes. The observations documented in this work provide an important framework for

moving forward and should help guide future laboratory research in AE monitoring. In general, I

show that laboratory earthquakes are often preceded by AE precursors and these precursors are

modulated by fault slip rate and fault zone porosity. Lastly, I show that the acoustic radiation

properties of slow and fast laboratory earthquakes are quite similar, which provides additional

evidence that slow and fast events are controlled by similar physical processes.

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TABLE OF CONTENTS

LIST OF FIGURES ............................................................................................................ viii

LIST OF TABLES .............................................................................................................. xx

ACKNOWLEDGEMENTS................................................................................................. xxi

Chapter 1 Introduction ....................................................................................................... 1

1.1 Background and Motivation ........................................................................... 1 1.2 Key Questions ................................................................................................ 2

1.3 References ............................................................................................................. 4

Chapter 2 Frequency-magnitude statistics of laboratory foreshocks vary with shear velocity, fault slip rate, and shear stress ....................................................................... 6

2.1 Abstract ................................................................................................................. 6 2.2 Introduction ........................................................................................................... 7 2.3 Methods ................................................................................................................. 10

2.3.1 Friction Experiments and Acoustic Emission Monitoring ............................. 10 2.3.2 Acoustic Emission Catalog Development and b-value calculation ................ 12

2.4 Results ................................................................................................................... 15 2.5 Discussion ............................................................................................................. 19

2.5.1 Verification of F/M statistics using continuous acoustic records ................... 20 2.5.2 Acoustic Emission Event Rates.................................................................... 21 2.5.3 Shear Stress, fault slip rate, and shearing velocity dependence of F/M

Statistics ....................................................................................................... 22 2.5.4 A micromechanical model for the velocity dependence of AE size and b-

value ............................................................................................................ 24 2.5.5 Pre-seismic Fault Zone Dilation and AE Size ............................................... 25 2.5.6 Enhanced porosity and grain mobilization as a mechanism for the shear

velocity dependence of AE size and b-value in granular fault zones .............. 26 2.5.7 The reduction in b-value prior to co-seismic failure for granular fault

zones ............................................................................................................ 28 2.5.8 The relationship between AE size and frictional healing processes ............... 29 2.5.9 Scaling up laboratory AEs to foreshock sequences of seismogenic fault

zones ............................................................................................................ 29 2.6 Conclusion............................................................................................................. 30 2.7 References ............................................................................................................. 44

Chapter 3 Characterizing acoustic signals and searching for precursors during the laboratory seismic cycle using unsupervised machine learning ..................................... 55

3.1 Abstract ................................................................................................................. 55 3.2 Introduction ........................................................................................................... 56

3.2.1 Precursors to Earthquakes ............................................................................ 56

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3.2.2 Machine learning and acoustic signals prior to failure .................................. 57 3.3 Methods ................................................................................................................. 59

3.3.1 Friction Stick-Slip Experiments ................................................................... 59 3.3.2 Unsupervised Machine Learning Analysis of Acoustic Signal ...................... 61 3.3.3 Clustering in Principal Component Space .................................................... 64

3.4 Results ................................................................................................................... 65 3.5 Discussion ............................................................................................................. 67 3.6 Conclusions ........................................................................................................... 69 3.7 References ............................................................................................................. 79

Chapter 4 Acoustic Energy Release During the Laboratory Seismic Cycle: Insights on Laboratory Earthquake Precursors and Prediction ........................................................ 85

4.1 Abstract ................................................................................................................. 85 4.2 Introduction ........................................................................................................... 86 4.3 Methods ................................................................................................................. 88 4.4 Results ................................................................................................................... 90

4.4.1 Acoustic Energy .......................................................................................... 91 4.4.2 The Influence of Normal Stress and Shear velocity on Acoustic Energy ....... 91 4.4.3 Slide-Hold-Slide Tests ................................................................................. 95 4.4.4 The Influence of grain size on acoustic energy ............................................. 96

4.5 Discussion ............................................................................................................. 97 4.5.1 The effect of normal stress and shearing velocity on acoustic energy ........... 97 4.5.2 The effect of grain size and contact junction size ......................................... 101 4.5.3 Machine Learning and Prediction of Failure ................................................ 103

4.6 Conclusion............................................................................................................. 103 4.7 References ............................................................................................................. 118

Chapter 5 The high-frequency signature of slow and fast laboratory earthquakes ................ 127

5.1 Abstract ................................................................................................................. 127 5.2 Introduction ........................................................................................................... 128 5.3 Slow and Fast Laboratory Earthquakes and Acoustic Emission Monitoring ............ 131 5.4 Results ................................................................................................................... 132

5.4.1 Geodetic source properties of Slow and Fast Laboratory Earthquakes .......... 132 5.4.2 Spectral characteristics of slow and fast laboratory earthquakes ................... 133 5.4.3 Time-domain and High-Frequency Characteristics ....................................... 136

5.5 Discussion ............................................................................................................. 138 5.5.1 The high-frequency signature of slow and fast laboratory earthquakes ......... 139 5.5.2 The origin of high-frequency energy in laboratory earthquakes .................... 141

5.6 Conclusion............................................................................................................. 143 5.7 References ............................................................................................................. 153

Chapter 6 Concluding Remarks .......................................................................................... 159

6.1 Research Summary ......................................................................................... 159 6.2 Future research directions ............................................................................... 161

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Appendix A Supplementary Information for Chapter 2 ....................................................... 163

A.1 Overview....................................................................................................... 163

Appendix B Supplementary Information for Chapter 3 ....................................................... 173

B.1 Statistical Features ......................................................................................... 173 B.2 Sensitivity analysis of the moving window:.................................................... 173 B.3 Influence of the Bandwidth parameter ............................................................ 174 B.4 Scaling of Variance and Kurtosis ................................................................... 175 B.5 Clustering in Variance-Kurtosis Space vs PC Space ....................................... 176 B.6 Principal Component Analysis (PCA): ........................................................... 177 B.7 Clustering results with respect to PC 2 ........................................................... 177 B.8 Variance and Kurtosis Clustering Results ....................................................... 178

Appendix C Supplementary Information for Chapter 4 ....................................................... 189

C.1 Overview ....................................................................................................... 189

Appendix D Supplementary Information for Chapter 5 ....................................................... 194

D.1 Overview....................................................................................................... 194

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LIST OF FIGURES

Figure 2-1: A Shear stress and AE amplitude plotted as a function of time. Open symbols represent AE amplitudes and are color coded according to the sensor they were detected on. Top left inset shows double-direct shear configuration with acoustic blocks. Top right inset shows 2D schematic of acoustic block and the locations of the three sensors used in this study. Acoustic amplitude increases throughout the seismic cycle and larger AEs nucleate during the inter-seismic period for higher shear velocities. B-C. Shear stress and continuous AE data plotted as a function of time for one entire seismic cycle at 3 µm/s and 100 µm/s. Spikes in the continuous acoustic data are AEs that are cataloged according to their peak amplitude and plotted in panel A. ................................................................................. 32

Figure 2-2: A-D Shear stress and AE rate (per unit displacement) as a function of time for different shear velocities explored in this study (see Figure 2-1). AE rate is calculated using a time window whose width corresponds to 10% of the recurrence interval of the seismic cycle. For each window we count how many events were detected and normalize each time window by the amount of slip displacement covered. Event rates are high after a failure event, decrease to a minimum, and subsequently increase until co-seismic failure. ............................................................. 33

Figure 2-3: A-D Frequency-magnitude plots are shown for each shear velocity at different locations in the seismic cycle. F/M plots represent AE statistics derived from our cataloging approach from Experiment p5363. Curves are color coded according to their location within the seismic cycle and the black dashed line represents the magnitude range used to compute b-values. Note, each inset shows the specific seismic cycle from which the F/M curves are derived from. The color coded squares in the inset corresponds to the time window associated with each F/M curve. F/M curves are plotted using a constant number of events, and thus, windows vary in time at each location within the seismic cycle and become smaller as time to failure approaches zero due to higher event rates (see Figure 2-2). B-value decreases as failure approaches and scales inversely with shear velocity. ..................................... 34

Figure 2-4: A-D Shear stress, fault slip velocity, and b-value as a function of time for different shear velocities. B-values are averaged across three channels and the error bars represent one standard-deviation among the channels. The pre-seismic changes in fault slip rate show that the fault unlocks very early on in the seismic cycle and increases continuously until co-seismic failure. B-value decreases systematically throughout the seismic cycle for each shearing velocity. .............................................. 35

Figure 2-5: A. B-value plotted as a function of shear stress. Note, b-values correspond to the same data plotted in Figure 4. B-value scales inversely with shear stress once the fault surpasses ~ 60% of its peak stress and is inversely correlated with shear velocity. B. B-value versus true fault slip velocity. Note, the strong correlation between b-value and slip rate for a given shearing velocity. C. F/M statistics derived from stacking multiple F/M curves at 90% of the peak stress, resulting in a total of ~ 7,400 AEs for each F/M curve. D. B-value scales inversely with shear

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velocity for data at 90% of the peak stress. Note, b-values are estimated from F/M curves in C. ................................................................................................................. 36

Figure 2-6: Mean acoustic amplitude derived from the continuous AE data. Amplitudes are averaged across all the slip cycles shown in Figure 4 for a given shear velocity and location within the seismic cycle. 1 µm windows are used to compute mean values. AE amplitude increases as the fault approaches failure and scales inversely with the shear velocity. ................................................................................................ 37

Figure 2-7: A. AE amplitude and shear stress plotted as a function of time for a stable-sliding friction experiment. AE amplitude increases with shearing velocity. B. Histogram of AE amplitudes for 500 µm windows. Higher shearing velocities produce fewer small events (M < 1.4) and show a net increase in larger events relative to lower shearing rates. C. Histogram of AE amplitudes derived from stacking multiple seismic cycles at 85%, resulting in ~ 7,400 AEs for each shear velocity. F/M data show an increase in bigger events relative to smaller events at higher shearing rates. ................................................................................................... 38

Figure 2-8: A. Layer-thickness and shear stress plotted for one seismic cycle. Pre-seismic dilation is computed as the change in layer-thickness across the inter-seismic period. B. Dilation plotted as a function of stress drop for each shearing velocity explored in Experiment p5363. Dilation scales systematically with stress drop and inversely with shearing velocity. .................................................................................. 39

Figure 2-9: A 2D schematic of a micro-mechanical model describing the velocity dependence of AE size and b-value in granular fault zones. This simplistic view suggests that sub-parallel structures (shear bands/force chains) support the bulk of the stress and strain throughout the inter-seismic period. Highly stressed regions (depicted by darker particles) are separated by spectator regions (light shaded particles) that accommodate very little strain throughout the seismic cycle. Upon step increase in loading velocity, the fault zone width increases by ∆H. The increase in fault zone width, increases fault zone porosity (decreases density), and permits the nucleation of large AEs and lower b-values. ................................................................. 40

Figure 2-10: Histogram of AE amplitudes located at 85% of the peak stress for 10,000 AEs from 20 seismic cycles. The average number grains across each gouge layer (GAL) was systematically modified by varying the fault zone thickness and/or particle size (see Table 2-1). F/M curves show an inverse relationship between AE size and the number of grains across each gouge layer. ................................................ 41

Figure 2-11: Acoustic energy of AEs as a function of AE duration. Larger AEs radiate more energy and contain longer time-domain signals. .................................................. 42

Figure 3-1: (a). Biaxial shear apparatus with the double-direct shear configuration. Normal and shear forces on the fault are measured with strain-gauge load cells mounted in series with the horizontal and vertical pistons. Displacements parallel and perpendicular to the fault are measured with direct-current displacement transformers (DCDT) coupled to the vertical and horizontal pistons respectively. (b).

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Sample configuration with two gouge layers placed between three steel loading platens. Piezoceramic sensors (PZT) are embedded within steel blocks that transmit the fault normal stress. ................................................................................................. 71

Figure 3-2: (a). Shear stress evolution for one entire experiment. Slip events transition from periodic to aperiodic to stable sliding as a function of load-point displacement. We focus on the section of aperiodic lab earthquakes shown in panel (b). Note that inter-event times vary and that large events are often preceded by small foreshocks. (c). Zoom of three seismic cycles with aseismic creep and foreshocks prior to the main event. .................................................................................................................. 72

Figure 3-3: (a). Shear stress and acoustic amplitude plotted for one slip cycle within the aperiodic section of the experiment (see Figure 2.). Grey box shows a 1.36-s moving window used to compute statistical features of the acoustic signal. (b). Zoom of the window. Note that the signal is dominated by spikes that look like noise at this scale. (c). Small AEs occur frequently throughout all stages of the seismic cycle. (d). Large AEs occur during all stages of the laboratory seismic cycle; however, they are more commonly associated with the inelastic loading stage just prior to failure (see Figure 3-2). ................................................................................................................. 73

Figure 3-4: Shear stress as a function of time (red dashed line) plotted with the machine learning prediction (blue line) for experiment p4679. Here, a supervised ML algorithm (gradient boosted tree algorithm) is used to estimate the instantaneous shear stress based on similar statistical features used in this study (see Supplement). The tight correlation between measurements and the ML prediction shows that the acoustic signal contains important information regarding the physical state of the fault during all stages of the lab seismic cycle. (After Hulbert et al., 2018) ................... 74

Figure 3-5: (a) Shear stress evolution and acoustic amplitude for one stick-slip cycle in experiment p4677. Grey box shows a moving window that slides through the continuous time series (4 MHz sampling rate) and is used to compute statistical features of the acoustic signal. We use the end time of each window for the time stamp associated with the window. (b) Temporal evolution of PC 1 (black) and PC 2 (red) throughout one stick-slip cycle shown in (a). Grey box with circles shows the time stamp derived from the moving window in (a). (c) Cumulative eigenvalue percentage plotted versus number of principal components. The first two principal components account for about 85% of the data variance. (d) Data for all slip cycles between 2067-2337 s (Figure 3-2b) in PC 1-PC 2 space (black symbols). Highlighted in red are data for the slip cycle shown in panel a...................................... 75

Figure 3-6: a-b. Data for all stick-slip cycles analyzed in this study (see Figure 3-2b) after clustering with a mean-shift algorithm. (a) Results for acoustic variance and kurtosis. The red cluster encompasses all data that are not associated with a lab earthquake, while the cyan cluster classifies the acoustic data associated with both foreshocks and mainshocks. (see Figure 3-2c). (b) Results for PC 1 and PC 2 after clustering in principal component space. Each point represents a linear combination of the 43 statistical features and each color corresponds to a single cluster. The yellow and purple cluster classify the acoustic signal associated with the linear-

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elastic and inelastic loading stages of each seismic cycle, while the green and blue clusters classify the acoustic data associated with the co-seismic phase. c-d. Results after clustering with a k-means algorithm. In each case, we determine the number of clusters by optimizing the Silhouette Coefficient as a function of the number of clusters (see Supplement). Note, that the results are identical for k-means and mean-shift when clustering in variance-kurtosis space. When clustering in PC space the acoustic data associated with the inter-seismic period (i.e yellow and purple clusters) are independent of the choice of clustering algorithm. However, the co-seismic data are partitioned differently by the two clustering algorithms (i.e green and blue cluster). ....................................................................................................................... 76

Figure 3-7: (a) Temporal evolution of clusters with respect to PC 1 (see supplement for results for PC 2). Shear stress curves are color coded corresponding to their respective cluster color defined by PC 1 and PC 2. The clusters reveal a distinct and systematic temporal trend as failure approaches. (b) Zoom showing details of how the clusters evolve as failure approaches. The early stages of the inter-seismic period are mapped to the yellow cluster, while the latter stages are mapped to the magenta cluster. The co-seismic phase is further divided into the green and blue clusters. .......... 77

Figure 3-8: Comparison of PC 1 and PC 2 as a function of shear stress. In both panels, we plot data for all seismic cycles analyzed in this study (Figure 3-2b), color coded by cluster. Note that the partitioning of data into clusters by the ML algorithm is reproducible across multiple lab seismic cycles and labquakes. Plotting the acoustic data as a function of shear stress illuminates the relationship between cluster transitions (e.g yellow to purple) and it becomes clear that the transition from yellow to magenta occurs once the fault has reached its peak strength. Acoustic data associated with the co-seismic phase are mapped to the green and blue clusters. .......... 78

Figure 4-1: A. Data for one complete experiment (p5198) showing measured stresses as a function of load-point displacement. Inset in A shows double-direct shear configuration with acoustic sensors (orange squares) and on-board displacement transducer. Shear and normal forces are measured with strain gauge load cells mounted in series with the vertical and horizontal rams respectively. Horizontal and vertical displacements are measured with direct current displacement transformers (DCDT) and are referenced to the loading frame. B. Zoom of shear stress and acoustic energy during a series of lab earthquakes. Note the systematic evolution of acoustic variance throughout the seismic cycle. For the ML analysis (see Hulbert et al. 2019), we use the first 60% of the data for training and the remaining 40% for testing. C. Comparison of measured and predicted shear stress (r2 = .87) using ML. ..... 105

Figure 4-2: A-B. Shear stress plotted as a function of time for data at different shear velocities and normal stresses (A 2-60 µm/s; B 6-11 MPa). Note that the lab seismic cycle changes systematically with shear velocity and normal stress. The stress drop during failure events decreases as fault normal stress decreases, and sliding becomes stable at the lowest normal stress. C. Shear stress normalized by the peak value prior to failure is plotted as a function of time for three different driving velocities. Note that stress drop scales inversely with shear velocity. D. Normalized shear stress during failure events at four normal stresses. Slip duration decreases and stress drop

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increases as normal load increases. E. Shear stress and slip velocity as a function of load-point displacement for one seismic cycle. Grey line shows elastic loading when the fault is locked. The onset of fault slip (inelastic creep) is marked with the red dot. Note that the onset of inelastic creep varies with normal stress and shear velocity. The fault reaches its peak slip velocity during co-seismic failure. Stress drop is calculated as the difference between the peak shear stress and the minimum shear stress. ................................................................................................................. 106

Figure 4-3: A. Shear Stress, acoustic amplitude, and acoustic variance plotted as a function of time for one seismic cycle. The dashed rectangle shows our moving window (0.636 s) used to compute the acoustic variance. At this scale acoustic data look like noise, however the signal is composed of individual AEs (some identifiable as small spikes) that grow in size and number as failure approaches (see B). The acoustic variance first decays following a failure event, reaches a minimum during the inter-seismic period and finally begins to increase prior to failure. B. Zoom of an AE that nucleated during the inter-seismic period. C. Zoom of the acoustic signal during co-seismic failure. Note the broad, low amplitude nature of the envelope with superimposed high-frequency AEs. ...................................................................... 107

Figure 4-4: A. Shear stress and acoustic variance plotted as a function of time and load-point displacement for one complete experiment (p5201) with detail at (B) 2µm/s and (C) 60 µm/s. Note, the variance in A is a discrete time series signal computed at all times throughout the seismic cycle. When plotted on the same scale the acoustic variance time series shows distinct differences as a function of velocity. At low shear velocity the acoustic variance stays low for most of the seismic cycle and only begins to increase once the fault has reached its peak strength. In contrast, at high drive velocities the acoustic variance decays, reaches a minimum and begins to increase before the fault reaches its peak stress. D. Average cumulative acoustic energy and stress drop plotted as a function of shear velocity. The cumulative acoustic energy is computed from the variance time series data in Figure 4-4A. Variance is integrated from peak shear stress to minimum shear stress for each slip cycle shown in Figure 4-4A. Square symbols represent mean values and error bars represent one standard deviation. Cumulative acoustic energy scales directly with stress drop and inversely with shear velocity. ............................................................... 108

Figure 4-5: Normalized peak slip velocity during failure as a function of stress drop for all events in two experiments. Symbols are color coded according to the cumulative acoustic energy. Note the strong correlation between peak slip velocity, stress drop and cumulative acoustic variance radiated from the fault during failure. ....................... 109

Figure 4-6: Shear stress, acoustic variance, and slip velocity as a function of time for one seismic cycle in experiment p5198 (8 MPa normal stress). Dashed rectangle shows the moving window used to compute the acoustic variance. Initially, the fault is locked, with near zero slip velocity. The fault begins to unlock about half way through the cycle, and the fault slip rate increases dramatically prior to failure. The acoustic variance mimics the slip velocity and reaches a peak during co-seismic failure. Acoustic variance is color coded based on the following: black to blue shows

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the onset of inelastic creep, blue to green coincides with the peak shear stress, and green to black corresponds to the peak slip velocity. .................................................... 110

Figure 4-7: Acoustic variance as a function of slip velocity plotted for four different normal stresses from Experiment p5198. Plots show data from multiple slip cycles at each load (see Figure 4-1). For each slip cycle, we plot data from the onset of inelastic creep until peak-slip velocity. Blue shows data from the onset of inelastic creep until peak shear stress. Green shows data from peak shear stress until peak slip velocity (see Figure 4-2E and Figure 4-6). A-B At low normal loads (8-9 MPa) the acoustic variance increases with slip velocity during the inter-seismic period (blue data). Also note that the acoustic variance increases only as the fault reaches a slip rate of ~ 10 µm/s. At higher normal loads (10-11 MPa) the fault slip rate is < 10 µm/s for most of the inter-seismic period and the acoustic variance only increases during the latter stages (green) of the seismic cycle. ..................................................... 111

Figure 4-8: Acoustic variance as a function of slip velocity for data at six different shear velocities from Experiment p5201 (same color coding as Figure 4-7). At low shear velocities (2-5 µm/s) the acoustic variance does not increase during the inter-seismic period (e.g., blue data). In contrast, at high shear velocities (>= 20 µm/s), the acoustic variance increases systematically with slip velocity during the inter-seismic period. ......................................................................................................................... 112

Figure 4-9: A. Friction and acoustic variance plotted as a function of time for a series of SHS tests for Experiment p5273. Here, we use a 0.1 s window to compute the acoustic variance. Acoustic variance remains at a steady-state value during sliding and decreases rapidly at the start of a hold. Upon re-shear, the variance increases, reaches a peak and decays back to the steady-state value. B. Acoustic variance and load-point displacement as a function of time. Note that acoustic variance tracks fault slip-rate. C. Acoustic variance and friction plotted as function of log time for a 10 s hold (see A). Both the acoustic variance and friction decay rapidly at the onset of the hold. However, the acoustic variance drops to a steady-state value whereas friction continues to decrease throughout the hold. ....................................................... 113

Figure 4-10: Shear stress and stress drop as a function of shear strain for experiments conducted with different median grain sizes. Note that stress drop increases during the initial part of each experiment and reaches a steady state for which larger grains produce bigger events. ................................................................................................. 114

Figure 4-11: Shear stress and acoustic variance versus shear strain for fault gouge composed of different median grain sizes. Plots are offset vertically for clarity. Fault zones composed of larger grains produce larger stress drops, have longer recurrence intervals and radiate more energy during co-seismic failure. ........................................ 115

Figure 4-12: A-C. Zoom of each experiment shown in Figure 4-11. Note the acoustic variance range is the same for each plot. The acoustic variance begins to increase later in the seismic cycle for fault zones composed of smaller grains. ........................... 116

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Figure 5-1: A. Double-direct shear (DDS) configuration, consisting of two layers of fault gouge sandwiched between three steel reinforcement blocks. A fault displacement transducer is mounted to the bottom of the center block and referenced to the base plate. Steel acoustic blocks embedded with piezoceramic transducers (orange squares) are placed 22 mm from the edge of the fault. Top inset shows AE channels. B. Shear stress and normal stress plotted versus time for two experiments. Each experiment starts off with a period of stable sliding, followed by the onset of slow stick-slip after ~ 10 mm of shear. C. Slip velocity and shear stress evolution for one seismic cycle. For each slip cycle, we compute the stress drop and peak slip rate. Stress drop is computed as the difference between the maximum and minimum shear stress (green circles). D. Stress drop as a function of peak slip velocity. Circles represent data from Experiment p5415 and triangles represent data from Experiment p5435; symbols are color coded according to normal stress. Black symbols represent averages at each normal stress and error bars represent 1 standard deviation. The transition between slow and fast stick-slip occurs ~ 1 mm/s (see Leeman et al., 2016). Stress drop scales systematically with peak slip rate. ......................................... 144

Figure 5-2: A. Slip velocity and shear stress for a slow slip event. Black dots denote the peak and minimum shear stress of the co-seismic slip phase. Slip DurationSS derived from the shear stress curve is estimated as the time difference between the minimum and peak shear stress. Slip durationSR is derived from the slip velocity curve. Blue symbols represent 20% of the peak slip rate. Slip durationSR is defined as the time difference between the two blue symbols. B-C Slip duration scales inversely with stress drop. Note, color coding and symbols are the same as Figure 5-1. We do not include the fastest events in C due to the limited resolution we have from at 100 Hz. Slip durations derived from the slip rate curve are smaller than the those derived from the shear stress curve. .......................................................................................... 145

Figure 5-3: A-E Shear stress and AE amplitude evolution during the co-seismic slip phase for a representative series of slow to fast laboratory earthquakes, with peak slip rates spanning between 98-5417 µm/s. Acoustic traces are 2s long and correspond to channel 1. F. Amplitude spectra from acoustic traces in A-E. Curves are color coded according to their respective trace. The spectra are essentially the same for the slow events between 7-11 MPa; fast events at 13 and 15 MPa show a modest increase in amplitude at low frequencies (<1000 Hz) and at high-frequencies (>= 10 kHz). Inset shows noise spectra from 2s long traces derived from the initial stages of the seismic cycle. G Signal to noise ratios derived from panel F. Slow events (7-11 MPa) have poor SNR across most of their bandwidth, with values slightly higher than 1 within the 100-500 kHz bandwidth. Fast events (13-15 MPa) have higher SNR for frequencies <10 kHz and between 80-500 kHz. ........................... 146

Figure 5-4: A. Zoom of slow slip events from 7-11 MPa. Note, acoustic traces correspond to the same data plotted in Figure 5-3. Acoustic traces are centered about their peak amplitude and offset vertically for clarity. The time-domain characteristics change slightly with normal stress and have a simplistic structure compared to the fast events in panel B. B. Zoom of time-domain signatures of fast slip events at 13 and 15 MPa (same events in Figure 5-3). Both events are larger and more impulsive compared to the slow events in panel A............................................... 147

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Figure 5-5: Top panel (A,C,E,G,I): Shear stress and raw acoustic amplitudes for slow (7-11 MPa) and fast (13-15 MPa) slip events. Bottom panel (B,D,F,H,J): Results from applying a high-pass filter at 10 kHz to time-domain signals in top panel. Both slow and fast slip events radiate high-frequency energy. The high-frequency pulse increases in size as events become progressively faster. Note, the scale difference for fast events.................................................................................................................... 148

Figure 5-6: A. Shear stress and AE time-series for fast event at 13 MPa. B. AE signal from A after high-pass filtering the signal at 10 kHz. Plotted in red is the acoustic energy (see Bolton et al., 2020). We parameterized the high-frequency pulse by estimating its peak amplitude, cumulative energy, and pulse duration. The cumulative energy is computed by integrating the red curve between the beginning and end of the pulse, denoted by the blue symbols. Pulse duration is estimated as time difference between the two blue symbols. C-E Peak amplitude, cumulative energy, and pulse duration as a function of stress drop, respectively. Peak amplitude and cumulative energy scale systematically with stress drop; pulse duration scales inversely with stress drop. ............................................................................................ 149

Figure 5-7: A-C. High-passed acoustic signals from slow slip events in Figures 5-3:5-5 at various cut-off frequencies. Note, the high-frequency pulse is band-limited and is most prominent within the 10-200 kHz bandwidth. D-E. Same as panels A-C, but for fast slip events in Figures 5-3:5-5. Unlike, the slow slip events the fast events have high-frequency energy >= 400 kHz and have a much broader band-width. ........... 150

Figure 5-8: A. Cumulative energy of high-frequency pulses as a function of cut-off frequency for slow and fast slip events (see Figure 5-6). We high-pass filter the same traces from Figures 5-3:5-5. Note, the cumulative energy can only be estimated for data that have high-frequency pulses above the noise level (see Figure 5-6B). Cumulative energy decreases with increasing cut-off frequency. B. Maximum frequency for which the cumulative energy can be computed in A as a function of normal stress. Maximum frequency increases with normal stress, suggesting that the highest frequencies radiated during failure scale with event size. .................................. 151

Figure 5-9: A. Shear stress and time versus load-point displacement for a stable sliding experiment. Loading-rate was increased from 0.44 µm/s to 435 µm/s. Grey circles represent the time stamps from which AE traces are derived in panel B. B. Amplitude spectra derived from the 2s long acoustic traces (see inset) for each load-point-velocity. The noise trace was collected during a hold at the beginning of the experiment (see panel A). C. Zoom of high-frequency components in B. The amplitudes and band-width of the high-frequency energy increase with loading-rate. D. Acoustic traces from B band-passed between 150-400 kHz. The size and number of AEs increases with loading rate. .............................................................................. 152

Figure A1: A-B Histogram of RDT and AE duration for several hundred AEs. .................. 164

Figure A2: A. Example of one AE at 3 µm/s. Superimposed on the acoustic time series data are 5 RDT curves. For this study, we use a 93 µs R.D.T to model all the AEs. B. Example of how the RDT parameter is implemented with a set of detected events

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(black symbols). Note, the event in question (candidate event) must have an amplitude that is larger than the RDT curves of the previous 5 events. In this case, the candidate event would be cataloged. ....................................................................... 165

Figure A3: Example of how AEs are detected and cataloged using our empirical thresholding procedure (see Chapter 2 for details). A. Raw continuous acoustic signal with 6 AEs (large spikes). B. Seismic signal and smoothed envelope (yellow). C. Seismic signal, smoothed envelope and detected AEs (black symbols). Note, the candidate events are detected after imposing a minimum amplitude (Amin) and time threshold (Tmin) (see Chapter for details). D. Same data as panel C. Events shown in green meet the RDT threshold (Figure S1) and are cataloged. The remaining events (black symbols) are discarded from the analysis. .......................................................... 166

Figure A4: A-B. Frequency-magnitude curves for a range of Tmin (A) and RDT (B) thresholds, respectively (see Chapter 2 for details). The number of smaller events detected increases as Tmin and RDT become smaller. C-D. Temporal evolution of b-value across one entire seismic cycle. Relative changes in b-value remain approximately the same for a wide range of Tmin and RDT values. ............................... 167

Figure A5: A-D. Cumulative number of AEs and shear stress plotted as a function of time for each shear velocity. The total number of AEs per seismic cycle scales with the recurrence interval and inversely with shear velocity. The total number of AEs used to compute b-value (see Chapter 2) corresponds to 10% of the cumulative number of AEs at a given shear velocity. ..................................................................... 168

Figure A6: A-C. Cumulative (solid line) and non-cumulative (histogram) frequency-magnitude plots at different locations within the seismic cycle. Note, the F/M curves correspond to the same data shown in Figure 3 of the main text. The peak of the non-cumulative distribution corresponds to the magnitude of completeness (Mc). Mc remains constant as a function of position within the seismic cycle for data at 0.3 µm/s. D-F. Cumulative and non-cumulative frequency-magnitude plots at different locations for the seismic cycle shown in Figure 2-3D. In contrast to the data at 0.3 µm/s, Mc shifts to higher values as failure approaches and the non-cumulative plots become more Gaussian-like and indicates that the catalog is deficient in lower magnitude events. ........................................................................................................ 169

Figure A7: AE rate as a function of normalized time for data shown in Figure 2-2 (see main text in Chapter 2). Note, the x-axis is scaled from the minimum shear stress to the peak shear stress for the slip cycles shown in Figure 2. AE rate is computed using the same windowing technique described in the main text, however here we only count events with the M >= 2.0. In general, the absolute value of event rates per unit shear displacement seems to be roughly independent of shear velocity for data <= 30 µm/s. Thus, the inverses relationship between event rate and shearing rate (Figure 2-2) could simply be due to a lack of smaller events at higher shearing velocities. .................................................................................................................... 170

Figure A8: B-value as a function of normalized slip velocity. The data plotted here correspond to the same data plotted in Figure 2-5. B-value scales inversely with both

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slip rate (low b-value at large slip velocities) and the far-field shearing rate (low b-value at large shearing rate). ........................................................................................ 171

Figure A9: A. Shear stress, AE amplitude and fault displacement plotted versus time for Experiment p5388. Initially, the fault was sheared under a constant loading rate boundary condition for ~ 10 mm. After shearing 10 mm at 21 µm/s, we reduced the shear stress on the fault to ~ 50% of the peak stress reached during the stick-slip cycles and placed a soft acrylic spring between the vertical ram and center block of the DDS to mitigate fault creep. Four series of shear stress oscillations (S1-S4) were performed at different amplitudes and frequencies that are representative of the stick-slip cycles in Experiment p5363. Amplitude and frequency of the oscillations are depicted in the left corner. The number and magnitude of AEs decreases from sequences S1 to S4. B. Non-cumulative frequency-magnitude data from S1 at different locations within the increasing shear stress limb. Symbols are averages across all channels and cycles in S1 at a specific location within the increasing shear stress limb and error bars represent one standard deviation. The magnitude of the AEs is approximately independent of location within the shear stress oscillation. ......... 172

Figure B1: Variance-Kurtosis feature space after computing the logarithm for each feature for a 1.36 s window with overlap sizes of (a): 0, (b): 50% and (c): 90%. The data values and underlying structure within the feature space do not change indicating that the window overlap does not have a significant effect on our results. Here, we use a constant bandwidth of .71 and analyze the same data of experiment p4677 between 2067-2337 s (see Figure 3-2). .............................................................. 179

Figure B2: Variance-kurtosis feature space after computing the logarithm for each feature with a window overlap of 90% and for window sizes of (a): .68 s and (b): 1.36 s. Here, we use a constant bandwidth of .71 and analyze the same section of data from experiment p4677 between 2067-2337 s (see Figure 3-2). The window size has a minimal impact on the data values and the clustering outcome in the feature space. ............................................................................................................... 180

Figure B3: Number of clusters as a function of bandwidth. Bandwidth scales inversely with the number of detected clusters. We optimize the bandwidth by computing a Silhouette Coefficient. Inset shows Silhouette Coefficient as a function of bandwidth. We select a bandwidth that results in the highest Silhouette Coefficient. For our data, this corresponds to bandwidth of .71. ...................................................... 181

Figure B4: Variance-kurtosis feature space without computing the logarithm of each feature. Clusters are identified primarily as a function of kurtosis, whose range varies between 0 and 20000. In order to prevent this bias, we compute the logarithm of each feature which decreases the range between the two features. ............................ 182

Figure B5: Variance-kurtosis feature space after using a smaller bandwidth, which results in four total clusters. The blue cluster is very arbitrary and does not occur throughout each slip cycle............................................................................................ 183

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Figure B6: Temporal evolution of clusters after using a smaller bandwidth relative to Figure 3-6a. (a). Cluster evolution over multiple slip cycles. Note, how the blue cluster only occurs in a few slip cycles. (b). Zoom of three cycles shown in A. Now, the ML algorithm differentiates the small and large stress drops with the cyan and green cluster respectively. ............................................................................................ 184

Figure B7: Clustering with respect to PC 1 and PC 2 using a larger bandwidth relative to Figure 6b. (a). Feature space for PC 1 and PC 2. (b). PC 1 and shear stress as a function of time. The inter-seismic period is classified by the yellow cluster and the co-seismic period is classified by the magenta cluster. ................................................. 185

Figure B8: Eigenvector coefficients for PC 1 and PC 2 plotted versus the number of features. Most of the features have similar coefficients and therefore are equally important in explaining the data variance. However, several of the amplitude based features (percentiles and amplitude counts) have higher coefficients relative to the other features. .............................................................................................................. 186

Figure B9: PC 2 and shear stress plotted as a function of time. The transition from yellow to purple occurs once the fault has reached its peak strength and therefore serves as a precursor to failure. .................................................................................... 187

Figure B10: (a). Temporal evolution of clusters in variance-kurtosis space as a function of variance plotted along with shear stress. (b). Zoom of A. Note the differences in slip cycles that contain small instabilities and those that do not. ................................... 188

Figure C1: Three methods to calculate acoustic signal variance for different shearing velocities, all plotted along with shear stress during stable sliding. A. Acoustic variance for a time window corresponding to a shear displacement of 5 µm; thus a factor of 30 longer window for 2 µm/s compared to 60 µm/s. Note that variance increases with shear velocity. B. Same as Panel A except the acoustic data are decimated such that the number of data points per window is the same for each velocity. Note that variance is identical to Panel A. C. Variance computed using a constant time window of .1s. The absolute values of variance are approximately the same as for A and B indicating that the amount of energy radiated is independent of slip displacement. ........................................................................................................ 191

Figure C2: A-B. Variance plotted as a function of time at two different shearing velocities from Experiment p5201 (see Chapter 4 for details). Variance is computed using two different window sizes (black and red). The data in black correspond to constant displacement window of 5 µm. The inter-seismic changes in variance are independent of window size, but the co-seismic peaks change systematically with window length. ............................................................................................................ 192

Figure C3: A. Variance versus friction for data corresponding to the onset of inelastic creep until peak shear stress (see Chapter 4 for details) from Experiment p5198. The data show that more energy is released prior to failure for lower normal stresses. B. Same as A, but data here correspond to Experiment p5201. Similar to A, more energy is released prior to failure for higher shear velocities. ....................................... 193

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Figure D1: A-B. Raw-acoustic traces (2s long) without (A) and with (B) the hydraulic power supply turned on. Note the significant increase in noise due to the hydraulic power supply. C. Average spectra of the traces shown in A and B. Here, we average the spectra for all channels in A and B, respectively. The hydraulic power supply contaminates the acoustic signals with noise for frequencies < 10 kHz. ........................ 195

Figure D2: A Time-domain signals from channel 6 during the co-seismic slip phase. AE signals are exclusively from Experiment p5435 (see Figure 2) and represent a different slip event compared to those plotted in Figure 2 of the main text. In general, the time-domain signals are similar to those plotted in Figure 2 of the main-text. B Spectra of events shown in A. The spectra have identical shapes to those in Figure 2. However, the fast events (13 and 15 MPa) have identical amplitudes at low-frequencies compared to the slow events. In contrast, the fast events in Figure 2 have slightly higher amplitudes at lower frequencies, relative to the slow events. These differences probably arise from the nature of the time-domain signals. Note, the differences between the 15 MPa events. Inset shows noise traces for data at each normal stress. .............................................................................................................. 196

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LIST OF TABLES

Table 2-1: List of experiments and boundary conditions for Chapter 2 ................................ 43

Table 4-1: List of experiments and boundary conditions for Chapter 4. ............................... 117

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ACKNOWLEDGEMENTS

This dissertation is a result of the collective support from family, friends, and colleagues.

I would like to first thank my wonderful and supportive wife and fur-child, Andrea and Skye

Bolton; thank you so much for the continuous support and love throughout these challenging and

interesting times. I’m also very grateful for the support and love from my parents and grandparents.

I am extremely thankful for the awesome, supportive, unique, and one-of-a-kind research

group-The Penn State Rock Mechanics Lab: Srisharan Shreedharan, Abby Kengisberg, Ben

Madara, Clay Wood (special thanks to Clay for always helping me debug Python code), Peter

Miller, Tim Witham, Zheng Lyu, Robert Valdez, John Leeman, Raphael Affinitio, and Kerry Ryan.

Special thanks to Steve Swavely for all your help and support in the lab. I will sincerely miss our

stimulating conversations and your wonderful attitude towards babysitting the lab. Perhaps more

importantly, I will miss our routine chats/complaining sessions, consisting of you chugging your

Diet Pepsi from a 2 liter bottle while I enjoy a freshly brewed espresso. I would also like to thank

my colleagues at Los Alamos National Laboratory for teaching me the intricacies of machine

learning: Bertrand Rouet-Leduc, Claudia Hulbert, and Ian McBrearty.

Last, but certainly not least, I would like to thank my dissertation committee: Chris Marone,

Charles Ammon, Don Fisher, Jacques Rivière , and Demian Saffer (former committee member) for

pushing my boundaries, making me work late nights, and always forcing me to think about the

broader implications of my research. I’m very grateful for my advisor, Chris Marone, for his

support, patience, encouragement, and guidance over the past 5 years. Your advising style provided

a well-rounded balance between oversight and freedom and allowed me to explore and become

interested in a variety of research topics; I am extremely grateful for these opportunities. Thank

you, Jacques, for all your support and wisdom as I struggled to survive during my initial years as

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PhD student. Lastly, I would like to thank my undergraduate advisor, Ashely Griffith, who helped

ignite my interest in rock mechanics/geomechanics.

1

Chapter 1

Introduction

1.1 Background and Motivation

Understanding the physical processes associated with earthquake nucleation is a key

problem in earthquake seismology (Ohnaka 1992, 1993, Abercrombie et al., 1995; McLaskey,

2019). However, earthquake nucleation properties are challenging to measure, observe, and

characterize. Nevertheless, elucidating these processes will help advance our understanding of

earthquake mechanics, earthquake early warning systems, and earthquake hazard assessment.

If the early stages of the earthquake initiation phase contains important information

regarding the nature of the impending earthquake, identifying a reliable and robust feature that

tracks this process—a so called precursor—would be a significant achievement in earthquake

science. Identifying precursory changes to earthquake-like failure has been a long sought-after

problem in seismology, but little progress has been made (Milne, 1899, Scholz, 1973, Rikitake,

1968; Bakun et al., 2005; Pritchard et al., 2020). The lack of success in this area is not too surprising

because without a-priori knowledge of when and where the next earthquake will occur it is

challenging to focus efforts on identifying small precursory signals embedded within seismic and

geodetic signals. Furthermore, it is not immediately clear what one should look for in terms of

identifying a “precursory” signature embedded within a geophysical signal. The general

characteristics and measurements (or lack thereof) of earthquakes adds additional complexities. In

particular, the earthquake source is typically uncontrolled (aside from repeating earthquakes),

there’s often a lack of instrumentation close to the fault zone, the recurrence intervals of earthquake

2

cycles are long and aperiodic, and there’s a dearth of knowledge about the boundary conditions

within the source region.

Most of these difficulties can be overcome by taking advantage of well-controlled, state-

of-the-art, and high resolution laboratory friction experiments. Laboratory experiments are

simplified analogs to tectonic faulting, but the similarities between the two are simply too strong

to overlook and ignore (Brace and Byerlee, 1966; Scholz, 1968; Scholz, 2015). Laboratory

experiments provide high-quality measurements of fault zone properties (i.e., stress, fault zone

thickness, slip displacement, shear strain) and can produce hundreds of laboratory earthquakes

within a single experiment. Furthermore, by integrating high-resolution acoustic emission (AEs)

measurements with lab experiments, a wealth of knowledge can be attained about the seismic

properties during the pre-, co-, and post- seismic stages of the seismic cycle. For example, AE

properties that nucleate prior to co-seismic failure are thought to be analogous to foreshock

sequences, and thus, a detailed understanding of their causal processes could provide key insights

into the physical processes associated with the preparatory stage of earthquakes (McLaskey and

Kilgore, 2013).

1.2 Key Questions

In this dissertation, I use machine learning and standard seismology methods to identify

and characterize seismic precursors to laboratory earthquakes. These seismic precursors are then

integrated with measured fault zone processes, in order to shed light on their physical origin. In

addition to pre-seismic activity, I also quantify the co-seismic properties of AEs for a range of

different stick-slip instabilities (slow and fast). I address the following questions in the chapters

below:

3

1. Chapter 2: What physical mechanisms are responsible for the temporal variations in

frequency-magnitude statistics for granular fault zones? What roles do shear stress,

shear velocity, and fault slip rate play in modulating AE characteristics?

2. Chapter 3: How does unsupervised machine learning characterize the continuous AE

signal throughout the laboratory seismic cycle? Can unsupervised machine learning

identify precursory signatures to laboratory earthquakes?

3. Chapter 4: Why are machine learning models able to estimate certain properties of

laboratory earthquakes? What controls the temporal evolution of acoustic energy

throughout the laboratory seismic cycle?

4. Chapter 5: What are the seismic signatures of slow and fast laboratory earthquakes?

Are the seismic characteristics of slow and fast laboratory earthquakes fundamentally

different and what do these observations tell us about slow tectonic earthquakes?

4

1.3 References

Abercrombie, R. E., Agnew, D. C., & Wyatt, F. K. (1995). Testing a model of earthquake

nucleation. Bulletin of the Seismological Society of America, 85(6), 1873-1878.

Bakun, W. H., Aagaard, B., Dost, B., Ellsworth, W. L., Hardebeck, J. L., Harris, R. A., ... &

Michael, A. J. (2005). Implications for prediction and hazard assessment from the 2004

Parkfield earthquake. Nature, 437(7061), 969-974.

Brace, W. F., & Byerlee, J. D. (1966). Stick-slip as a mechanism for earthquakes. Science, 153(3739), 990-992.

McLaskey, G. C., & Kilgore, B. D. (2013). Foreshocks during the nucleation of stick-slip

instability. Journal of Geophysical Research: Solid Earth, 118(6), 2982-2997.

McLaskey,G.C. Earthquake Initiation From Laboratory Observations and Implications for

Foreshocks, Journal of Geophysical Research: Solid Earth 124 (12) (2019) 12882–12904.

Milne, J. (1899). Earthquake Precursors. Nature, 59(1531), 414.

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. Journal of Physics of the Earth, 41(1), 45-56.

Pritchard, M. E., Allen, R. M., Becker, T. W., Behn, M. D., Brodsky, E. E., Bürgmann, R., ... &

Kaneko, Y. (2020). New Opportunities to Study Earthquake Precursors. Seismological

Research Letters.

Rikitake, T. (1968). Earthquake prediction. Earth-Science Reviews, 4, 245-282.

Scholz, C. H. (1968). The frequency-magnitude relation of microfracturing in rock and its

relation to earthquakes, Bulletin of the Seismological Society of America, 58(1), 399-415.

Scholz, C. H. (2015). On the stress dependence of the earthquake b value. Geophysical Research

Letters, 42(5), 1399-1402.

5

Scholz, C. H., Sykes, L. R., & Aggarwal, Y. P. (1973). Earthquake prediction: a physical basis.

Science, 181(4102), 803-810.

6

Chapter 2

Frequency-magnitude statistics of laboratory foreshocks vary with shear velocity, fault slip rate, and shear stress

2.1 Abstract

Understanding the temporal evolution of foreshocks and their relation to earthquake

nucleation has profound implications for earthquake early warning systems and earthquake hazard

assessment. Laboratory experiments on synthetic faults and intact rock samples have demonstrated

that the number and size of acoustic emission (AE) events increase and that the Gutenberg-Richter

b-value decreases prior to co-seismic failure. Pre-seismic AEs are analogous to seismic foreshocks

and for intact rock and rough fractures previous works have well established the reduction in b-

value prior to failure. However, for fault zones of finite width, where shear occurs within granular

gouge, the physical processes that dictate temporal variations in frequency-magnitude (F/M)

statistics of lab foreshocks are unclear. We report on a series of laboratory experiments using

granular fault gouge and illuminate the physical processes that govern temporal variations in b-

value. We record AE data continuously for hundreds of lab seismic cycles and report F/M statistics

for foreshocks derived from AE catalogs. Our data show that b-value decreases as the fault

approaches failure, consistent with previous works. We also find that b-value scales inversely with

fault slip velocity and the shearing velocity, suggesting that fault slip acceleration during

earthquake nucleation could impact foreshock F/M statistics. We propose that fault zone dilation,

porosity, and grain mobilization have a strong influence on foreshock magnitude. Higher shearing

rates increase fault zone porosity and promotes the failure of larger areas, which in turn, results in

larger foreshocks and smaller b-values. Our observations suggest that laboratory earthquakes are

7

preceded by a preparatory nucleation phase that is accompanied by systematic variations in acoustic

properties and measured fault zone properties.

2.2 Introduction

Earthquake forecasting has been a fundamental goal of seismology for over a century

(Milne, 1899; Scholz, 1973; Rikitake, 1976; Crampin et al., 1984; Bernard et al., 1997; Bakun et

al., 2005; Pritchard et al., 2020). The inability to accurately predict the location and timing of an

impending earthquake is, in part, due to a poor understanding of earthquake nucleation. In

particular, it is unclear how earthquake nucleation is linked to spatio-temporal changes in pre-

seismic activity (e.g., foreshocks). Foreshocks are often considered a manifestation of earthquake

nucleation and therefore identifying how foreshocks evolve in space and time could provide

important insight for the physics of earthquake nucleation (Ohnaka, 1992, 1993; Abercrombie et

al., 1995; Dodge et al., 1996; Chen and Shearer, 2013; Kato et al., 2016; Ellsworth and Bulut, 2018;

Yoon et al., 2019). Foreshock patterns in nature can be challenging to identify due to sparseness in

seismicity and/or a lack of network coverage (Bakun et al., 2005). However, there are well

documented examples of increased foreshock activity prior to the main-shock (Wyss and Lee,

1973; Papadopoulos et al. 2010; Nanjo et al. 2012; Bouchon et al., 2013; Kato et al., 2016; Brodsky

and Lay, 2014; Gulia et al., 2016; Ellsworth and Bulut, 2018; Gulia and Wiemer, 2019; Trugman

and Ross, 2019; Yoon et al., 2019; van den ende and Ampuero, 2020). In some cases, the

Gutenberg-Richter, b-value, decreases prior to the main-shock (Nanjo et al. 2012; Gulia et al.,

2016); implying that foreshock magnitude increases systematically as the fault approaches failure.

There are also cases where main-shocks are not preceded by any form of seismic precursor,

and these include examples with dense station coverage (Bakun et al., 2005). However, the absence

of foreshocks could simply be due to issues with the development of earthquake catalogs. Ideally,

8

earthquake catalogs should span several orders of magnitude and be complete down to low

magnitudes (e.g., Walter et al., 2015; McBrearty et al., 2019; Ross et al., 2019; Trugman and Ross,

2019). Earthquake catalogs often implement a thresholding scheme and/or some other constraint

where events below a certain magnitude are discarded. However, this can lead to misguided

conclusions about how foreshock patterns evolve in space and time. For instance, Trugman and

Ross (2019) implemented a template matching approach (Quake-Template-Matching or QTM) and

demonstrated that foreshock sequences maybe more common than previously thought (see also van

den ende and Ampuero, 2020). This observation was driven by the fact that the QTM catalog was

able to lower the magnitude of completeness well below that of standard catalogs. But the fact that

foreshocks are not observed universally raises a fundamental question: what are the physical

processes that control foreshock activity and why do some earthquakes appear to occur without a

progressive failure process that includes foreshocks?

Laboratory experiments coupled with acoustic monitoring provide high resolution

measurements of fault zone properties and acoustic activity throughout the lab seismic cycle.

Therefore, they provide a unique opportunity to study foreshock dynamics in tandem with

earthquake nucleation processes. Previous works have routinely documented precursory slip and

seismic precursors prior to lab earthquakes (Scholz, 1968a;1968b; Weeks et al., 1978; Ohnaka and

Mogi, 1982; Main et al. 1988; Sammonds et al., 1992; Thompson et al., 2009; McLaskey and

Kilgore, 2013; Goebel et al., 2013; Kaproth and Marone, 2013; McLaskey et al, 2014; McLaskey

and Lockner, 2014; Goebel et al., 2015; Scuderi et al., 2016; Tinti et al., 2016; Renard et al., 2017,

2018; Passelegue et al. 2017; Jiang et al, 2017; Rivière et al. 2018; Acosta et al., 2019; Shreedharan

et al., 2020; Bolton et al., 2019, 2020). Many of these studies demonstrate that the event rate

(number of events per unit time or slip) and magnitude increase as failure approaches. However,

despite the robustness of this observation, it is not universally clear what physical processes allow

AEs to become bigger as failure approaches.

9

In the laboratory and in the field, foreshock sequences are often studied in terms of the

Gutenberg-Richter, b-value, (Gutenberg and Richter, 1944):

𝑙𝑜𝑔$%(𝑁) = 𝑎 − 𝑏𝑀 (2.1)

where N is the number of events greater than or equal to magnitude M, ‘a’ is a measure of

seismic activity and ‘b’, referred to as the b-value, describes the F/M distribution. It has long been

known that b-value decreases prior to failure of intact rock specimens (Scholz, 1968a) and prior to

lab earthquakes (Weeks at al., 1978; Main et al., 1989; Goebel et al., 2013). Rock fracture

experiments indicate that seismic events become bigger as time to failure decreases because stress

increases and micro-fractures coalesce (Scholz, 1968a). Numerous studies have documented and

validated the claim that b-value and stress state are inversely related (Mori and Abercrombie, 1997;

Wiemer and Wyss, 1997; Schorlemmer et al., 2005; Goebel et al. 2013; Spada et al., 2013; Scholz,

2015; Rivière et al. 2018; Nanjo et al., 2019; Gulia and Wiemer, 2019). However, it is not clear if

shear stress alone is responsible for the temporal changes in b-value that occur throughout the

seismic cycle. Other possibilities include spatio-temporal variations in fault slip rate, fault zone

dilation, stressing rate, and fault roughness (Sammonds et al., 1992; McLaskey and Kilgore, 2013;

Goebel et al., 2017). Furthermore, several laboratory studies have demonstrated that AEs become

more frequent and larger under boundary conditions that are well below the failure strength (Jiang

et al., 2017; Rouet-Leduc et al., 2017; Rivière et al. 2018; Hulbert et al., 2019; Bolton et al., 2020).

Hence, it is possible that micro-fracturing plays a minor role in these experiments and that

foreshock activity is dictated by other grain scale processes, such as the rupturing (i.e. sliding) of

contact junctions. In this case, the size, strength and number of contact junctions breaking per unit

slip could play a fundamental role in regulating spatio-temporal properties of AE activity (e.g.,

Yabe, 2002; Yabe et al., 2003; Mair et al., 2007; Bolton et al., 2020).

It is also important to note that the decrease in b-value observed in many laboratory studies

occurs during inelastic loading where shear stress and fault slip rate are highly coupled (e.g., Dresen

10

et al., 2020). Hence, without isolating these variables it is not immediately clear which variable

drives AE activity in lab experiments. Isolating the effects of shear stress and fault slip rate can be

achieved experimentally by conducting shear stress oscillation experiments (e.g., Shreedharan et

al., 2021) at stresses below the shear strength. Note that in these experiments the fault does not

undergo periodic stick-slip failure; instead the shear stress is systematically modulated about a

mean value that is just below the fault strength. Thus, the fault slip rate is zero and only the shear

stress on the fault changes throughout the course of the oscillation. Hence, combining both types

of experiments can isolate the effects of shear stress on F/M statistics of AEs, allowing for a more

robust understanding of the causal processes that drive AE activity.

Here, we use laboratory friction experiments to document high-resolution temporal

characteristics of F/M statistics prior to stick-slip failure. Experiments were conducted on simulated

fault gouge over a wide range of conditions (Table 2-1). F/M statistics of AEs were derived from

event catalogs and we performed an extensive set of sensitivity analysis on our event detection

procedure. We record continuous AE data and we corroborate results from the earthquake catalogs

by analyzing the continuous acoustic data. Our results are consistent with previous studies showing

that b-value decreases prior to failure. We show that the reduction in b-value is most significant

when the shear stress is >= 60% of the failure stress. In addition, we show that b-value and AE

magnitude scale inversely with the fault slip velocity and shearing velocity.

2.3 Methods

2.3.1 Friction Experiments and Acoustic Emission Monitoring

We report on laboratory shear experiments conducted on soda-lime glass beads and quartz

powder (Min-U-Sil) in a servo-hydraulic testing machine using the double-direct shear (DDS)

11

configuration (Figure 2-1 inset). Glass beads are commonly used as synthetic fault gouge because

their frictional and seismic properties are highly reproducible and include both the time- and slip

rate- dependent friction effects observed for geologic materials (Mair et al., 2002, Anthony and

Marone, 2005; Marone et al., 2008; Scuderi et al., 2014; Scuderi et al., 2015; Jiang et al., 2017;

Rivière et al. 2018). We shear two fault zones between three roughened steel forcing blocks. The

surfaces of the forcing blocks are rough (triangular grooves that are 0.8 mm deep and 1 mm in

width) to eliminate slip at the fault zone boundary. We studied shear velocities from 0.3-100 µm/s,

and a range of grain sizes and fault zone thicknesses (Table 2-1). All experiments were run at

constant fault normal stress of 5 MPa. Fault stresses and displacements were measured

continuously at 1 kHz using strain-gauge load cells and direct-current displacement transformers

(DCDT). The loading velocity was prescribed at the central block of the DDS configuration (Figure

2-1). We also measured the true fault slip velocity with a DCDT mounted on the central shearing

block and referenced to the base of the vertical load frame (Figure 2-1). Throughout the text we

refer to the load point velocity as the shearing velocity and refer to the slip rate of center block as

the fault slip rate. To ensure reproducibility among experiments all experiments were conducted

at room temperature and 100% relative humidity (RH). Prior to each experiment gouge layers were

placed inside a plastic bag for 12-15 hours with a 1:2 ratio of sodium carbonate to water solution.

During the runs, samples were isolated with a plastic membrane to maintain 100% RH conditions.

Changes in RH conditions are known to greatly affect frictional properties of granular media (Frye

and Marone, 2002; Scuderi et al., 2014), hence keeping it constant helps ensure reproducibility

across experiments.

Acoustic emission data were recorded throughout the experiment using a 15-bit Verasonics

data acquisition system. AE data were recorded continuously at 4 MHz using broadband (~.0001-

2 MHz) piezoceramic sensors (6.35 mm diameter and 4 mm thick). The sensors are located 22 mm

from the edge of the fault zone at the base of blind holes in steel loading platens (Figure 2-1 inset,

12

Rivière et al., 2018; Bolton et al., 2019). We recorded data from a total of six sensors located on

both sides of the DDS configuration. Here, we report data from three sensors located on the left

side of the DDS assembly (Figure 2-1 inset).

2.3.2 Acoustic Emission Catalog Development and b-value calculation

We derive frequency-magnitude statistics of AEs using a thresholding procedure to scan

through the continuous AE signal and catalog events according to their peak amplitude. Our method

derives from that of Rivière et al. (2018) with extensive modifications and sensitivity analysis to

evaluate the effect of the thresholding parameters on event detection (see Supplement for additional

details). Our detection algorithm uses four thresholding parameters. First, we compute the envelope

of the continuous AE signal and smooth the envelope using a moving average, AEnv. We then scan

through the continuous data and detect a set of candidate AEs based on a minimum inter-event time

threshold, Tmin, and minimum amplitude threshold, Amin. Tmin ensures that two adjacent AEs are

separated in time by a minimum value and Amin is set right above the noise level. In theory, there

is no reason why two adjacent AEs must be separated in time by Tmin; however, imposing this

constraint helps ensure that the same event is not picked repeatedly. To determine Tmin, we manually

compute the duration of several hundred AEs and use the median of this distribution as Tmin (Figure

A1). In addition, we impose a ring-down-time (RDT) threshold, TRDT, to avoid picking the same

event repeatedly immediately after the peak amplitude and to account for sensor resonance. The

objective of TRDT is to ensure that AEs are not detected within the coda of a former event. TRDT is

imposed after the algorithm has identified a set of candidate events based on Aenv, Amin, and Tmin.

Once the algorithm has identified a set of candidate events, we apply TRDT through the following

procedure. For a candidate event Aj, we apply TRDT to the previous 5 events. If the amplitude of Aj

lies above the ring-down time curves of the previous 5 events, then we catalog the peak amplitude

13

and time of event Aj (Figure A2). More specifically, we catalog event Aj if it meets the following

criteria:

𝐴/ > 𝐴/23 ∗ 𝑒𝑥𝑝 8−9:;2:;<=>?@AB

Cwhere𝑖 = [1, 2, … , 5] (2.2)

where 𝑡/ and 𝑡/23 are the time stamps associated with the candidate event and the previous

5 events, respectively. We determine TRDT by computing the ring-down times of ~100 randomly

picked AEs. We then compute the median value of this distribution and set this equal to TRDT

(Figure A1). Therefore, we use one RDT to model all the AEs detected. We recognize that this

approach may not optimally model all the events (Figure A2) because the RDT of an event can

change depending upon the source mechanism associated with that particular event. A more robust

approach would involve using a multi-valued RDT to model different “families of AEs.” However,

this is beyond the scope of the current study and we use other techniques to verify our results, as

described below.

Once the event criteria are set by the four thresholding parameters we scan the continuous

data for each channel and catalog the peak AE amplitudes and times (see Figure A3). Note, the

event detection procedure treats each channel independently. For Experiment p5363, we used the

following thresholding parameters: AEnv: 5 data points, Amin: 20 (bits), Tmin: 131 µs, RDT: 93 µs.

We show results from an extensive sensitivity analysis for each thresholding parameter and its

impact on b-value in the Supplement. Our analysis indicates that the thresholding parameters do

not have a significant impact on the temporal changes in b-value (Figure A4).

We use a moving window on the catalogued events to compute the Gutenberg-Richter b-

value. B-values were estimated using a maximum-likelihood approach (Aki, 1965):

𝑏 = MNOPQ(R)(ST2SU) (2.3)

14

Where Mc is the magnitude of completeness and 𝑀T is the average magnitude above Mc.

Similar to previous field and laboratory studies, we compute b-values using a constant number of

events to ensure that each b-value is statistically similar (Ojala et al., 2004; Nanjo et al., 2004;

Tormann et al., 2013; Goebel et al. 2013; Goebel et al. 2015; Rivière et al. 2018; Herrmann et al.,

2019; Nanjo et al., 2020; Gulia et al., 2020). To determine the number of events for each b-value

calculation (NAE), we first compute the cumulative number of events across multiple seismic cycles

and for every channel (Figure A5). We focus here on the inter-seismic period and thus consider

events from the interval defined by the minimum shear stress and the peak stress of a given seismic

cycle. To compute NAE, we average the cumulative number of events across multiple slip cycles

for each channel and take NAE as 10% of this value. Because the recurrence interval scales inversely

with shear velocity, the cumulative number of events per seismic cycle, and thus NAE, is larger at

lower shearing rates (Figure A5). Increasing or decreasing NAE has a trivial effect on the results;

decreasing this number simply increases the number of b-value calculations per seismic cycle, and

therefore the temporal resolution.

It is important to acknowledge that our F/M distributions do not strictly follow an

exponential relation. However, we stick with convention and refer to the slope of the F/M curves

as the b-value. Accurate estimations of Mc are essential for reliable b-value calculations. In this

study, we determine Mc from the peak of the non-cumulative distribution (e.g., Woessner &

Wiemer, 2005). We acknowledge that this method may not be suitable for all of our F/M curves,

particularly those that contain some degree of curvature (e.g., 100 µm/s; Figure A6). In such cases,

the peaks of the non-cumulative distribution may not accurately represent the best Mc value.

However, other standard approaches for estimating Mc (e.g., goodness-to-fit) for data at 100 µm/s

place Mc at a slightly higher value (M > 2.0) which results in estimating b-values based on the tails

of F/M distributions, where few events exist. All in all, the main complexity here is not in the

15

methods used to compute Mc, but rather the fact that not all of the F/M curves exhibit a power-law

scaling.

We plot the non-cumulative and cumulative distribution of AEs for a single moving

window at different locations in the seismic cycle for data at 0.3 µm/s and 100 µm/s in Figure A6.

At 0.3 µm/s Mc is ~1.35 and does not change as a function of position within the seismic cycle. In

contrast, at 100 µm/s Mc is higher and increases as the fault approaches failure. Because we use a

moving window approach to compute b-values, we could let Mc vary for each moving window and

for each shearing velocity. However, we argue that this approach would result in an inconsistent

comparison of b-values as a function of shearing velocity and position within the seismic cycle

because of the different magnitude ranges (Figure A6). To circumvent this issue and to ensure a

more reliable comparison of b-value as a function of shearing velocity, we select a ‘global Mc’ to

compute b-values. That is, we use a single Mc value to compute b-values across the entire seismic

cycle and for each shearing velocity. Our data show that the highest shear velocity (100 µm/s)

produces the highest Mc. Therefore, we select our ‘global’ Mc such that it is >= Mc at 100 µm/s.

To determine our ‘global Mc’, we use focus on data at 100 µm/s and compute Mc (peak of the non-

cumulative distribution) at multiple locations within the stick-slip cycle for each channel. For a

given channel, we then average the Mc values across the multiple locations and set this average

value equal to the ‘global Mc.’ This procedure results in a Mc of 2.15, 2.16, and 2.02 for channels

4-6, respectively. We then estimate b-values for each channel using its corresponding Mc value.

Here, M is defined as logarithm of the peak amplitude.

2.4 Results

Experiment p5363 began with a run-in shear displacement of 5 mm after which the shear

velocity was decreased to 0.3 µm/s and then subsequently increased in steps to 100 µm/s (Figure

16

2-1). The size of the slip events and the recurrence interval of the seismic cycles decrease with

increasing shear velocity (Figure 2-1). AE amplitude also increases with shearing velocity,

consistent with previous works (Yabe, 2003; Ojala et al., 2004; Jiang et al., 2017). Our system

records acoustic data continuously, so the AE amplitudes plotted in Figure 2-1A are derived from

the continuous AE data (e.g. Figure 2-1B and Figure 2-1C). The spikes in the continuous AE

records correspond to discrete AEs that are detected using our cataloging procedure described

above.

We analyze AE event rates across the inter-seismic period using a moving window. The

width of each window corresponds to 10% of the recurrence interval of the seismic cycle and each

window overlaps the previous window by 99%. In addition, windows are normalized by the load-

point displacement, to account for the expectation that more AEs could occur if the fault shears

more (e.g., Mair et al., 2007). After a lab mainshock, the AE event rate decreases, reaches a

minimum and then increases continuously until the next event (Figure 2-2). The post-seismic

reduction in event rates appear to scale with the size of the previous event. The absolute value in

AE event rates decreases modestly with increasing shear velocity for low shearing rates (0.3-3.0

µm/s), and is more pronounced for shearing rates >= 30 µm/s (Figure 2-2). The evolution of event

rate over the seismic cycle also varies with loading velocity. The AE event rate increases

significantly prior to failure for slower shearing rates. In contrast, at higher shearing rates the event

rate appears to saturate prior to failure (Figure 2-2).

We document temporal changes in b-value as a function of position in the seismic cycle

and as a function of shearing velocity (Figures 2-3:2-7). F/M curves vary systematically with shear

velocity and position within the seismic cycle (Figure 2-3). The data demonstrate that the b-value

(black dotted line) decreases as the fault approaches failure. This can be seen by noting how the

F/M curves become vertically offset at larger magnitudes as failure approaches (Figure 2-3). The

changes in b-value are subtle during the early stages of the seismic cycle. The b-value only begins

17

to decrease significantly once the fault has surpassed ~ >= 60% of its peak stress. In addition to the

stress dependence of b-value, we also find that b-value depends on the shearing velocity (and fault

slip rate). This can be seen clearly by noting how the F/M curves become more offset as the fault

transitions from 60-90% of the peak stress for different shearing velocities (Figure 2-3). At 0.3

µm/s the F/M curves are nearly identically at 60% and 90% of the peak stress (implying that the b-

values are similar). In contrast, at 100 µm/s the offset between the F/M curves at 60% and 90%

peak stress is more significant (Figure 2-3).

Our data show that b-value varies with shear stress and fault slip velocity (Figure 2-4). To

characterize uncertainty in our b-value measurements, we plot the average b-value for three

channels (see Figure 2-1); error bars represent one standard deviation among the channels. To

compute the temporal changes in b-value, we use a moving window on the cataloged AEs (Figure

2-1). The size of each window contains a constant number of events (see methods) and each

window overlaps the previous window by 90%. Fault slip velocity is derived from the on-board

DCDT (Figure 2-1A). Generally, the fault unlocks early on in the seismic cycle and the fault slip

rate increases continuously until co-seismic failure. B-value decreases slightly during the early

stages of the seismic cycle and more significantly once the fault is closer to failure, consistent with

previous works (Scholz, 1968a; 1968b; Weeks et al., 1978; Sammonds et al., 1992; Goebel et al.,

2013; 2015; Rivière et al. 2018; Figure 2-4). To assess the shear stress and shear velocity

dependence of b-value more clearly, we plot data from Figure 2-4 as a function of location within

the seismic cycle and shear velocity (Figure 2-5). Consistent with the data from Figures 2-3:2-4, b-

value decreases significantly once the fault reaches 60-80% of its peak stress and scales inversely

with the shearing velocity. Also, note the strong correlation between b-value with fault slip velocity

in Figure 2-5B. To investigate the far-field shear velocity dependence of b-value further, we stack

multiple F/M curves located at 90% of the peak stress and estimate their b-values for different shear

18

velocities (Figures 2-5C and 2-5D). The data clearly indicate that higher shearing rates produce a

net increase in larger AEs relative to smaller AEs.

The data of Figures 2-3:2-5 demonstrate that b-value is lower near failure and scales

inversely with fault slip velocity and shearing velocity. However, these results are based on a

catalog of AEs and it is possible that the detection algorithm (see Section 2.1) misses some of the

smaller AEs. In particular, it is possible that we miss lower magnitude events as the fault approaches

failure because the events occur quasi-simultaneously and larger amplitude events mask smaller

events.

To assess the possibility of missed events, we also analyzed the raw, continuous acoustic

data. Figure 2-6 shows the mean acoustic signal amplitude as a function of normalized shear stress

for multiple seismic cycles. Here, we use a 1 µm window to compute mean amplitudes across

multiple locations in the seismic cycle from the stick-slip cycles shown in Figure 2-4. These data

show that AE amplitude increases as failure approaches and that it scales inversely with the

shearing velocity. Therefore, the results confirm those of our AE event catalogs and suggest that

the trends we observe in Figures 2-3:2-5 are not an artifact of the cataloging procedure.

In addition to verifying the trends observed in Figures 2-3:2-5, we also verified the velocity

dependence of AE size by analyzing F/M statistics of AEs generated during a stable sliding

experiment (p5348; Figure 2-7A). We then compared these data to F/M statistics derived from

Experiment p5363 (Figures 2-1:2-6). In Experiment p5348, we sheared quartz powder (Min-U-Sil)

under a constant normal load of 9 MPa and swept through a range of shearing velocities from 2-60

µm/s. The boundary conditions of Experiment p5348 permitted stable frictional sliding (i.e., no

stick-slips). The velocity dependence of AE size is clear (Figure 2-7A); higher shearing rates

produce bigger AEs. We further verify these results by using a 5 µm window to compute non-

cumulative F/M distributions of AEs at each shearing velocity (Figure 2-7B). F/M distributions

19

indicate that higher shearing rates are deficient in smaller magnitude AEs and result in a net increase

in larger magnitude events (Figure 2-7B).

Experiment p5363 (stick-slip experiment; Figure 2-1) shows similar event distributions

compared to the stable sliding experiment (Figure 2-7C). Here, we plot results after stacking

multiple seismic cycles at 85% of the peak stress for each shear velocity. Again, higher shearing

rates show a systematic increase in larger magnitude events and are deficient in smaller magnitude

events (Figure 2-7C). Note, that the shape of the F/M curves is similar for both the stable sliding

experiment and stick-slip experiment. That is, at low shear rates the non-cumulative event

distributions scale ~ linearly with magnitude. Whereas at higher shearing rates, the F/M curves

approach a Gaussian-like shape.

2.5 Discussion

Connecting temporal changes in foreshock sequences to the physical properties of fault

zones is a fundamental problem in earthquake seismology. The connection between seismic activity

and fault zone processes is key to understanding the physics of earthquake nucleation and

improving earthquake early warning systems and forecasting (Ohnaka, 1992,1993,2000;

Abercrombie et al., 1995; Ellsworth and Beroza, 1995; Dodge et al., 1996; Abercrombie and Mori,

1996; Chen and Shearer, 2013; Kato et al., 2016; McLaskey, 2019). A plethora of laboratory

studies, and several field studies, have demonstrated that the frequency and magnitude of

foreshocks increase prior to failure (Scholz,1968a;1968b; Sammonds et al., 1992; Papadopoulos et

al., 2010; Nanjo et al., 2012; Goebel et al., 2013; Bouchon et al., 2013; Chen and Shearer, 2013;

McLaskey and Lockner, 2014; Brodsky and Lay, 2014; Ruiz et al., 2014; Kato et al., 2016; Rivière

et al., 2018; Ellsworth and Bulut, 2018; Trugman et al., 2019; Guila and Wiemer, 2019). However,

the physical processes that cause earthquakes to become more frequent and larger as a mainshock

20

approaches is unclear. Scholz (1968a) demonstrated that the magnitude of AEs for failure of intact

rock is inversely related to the differential stress and he attributed this relationship to the formation

and coalescence of micro-fractures. However, it is unknown how well this interpretation

extrapolates to tectonic fault zones where failure may occur within breccia and fault gouge. Our

data show that shear stress plays an important role in modulating b-value, but we also see that b-

value scales inversely with fault slip velocity and shearing rate. Hence, there must be other

processes other than stress state that influence foreshock size.

2.5.1 Verification of F/M statistics using continuous acoustic records

In laboratory and field studies, the decrease in b-value prior to failure is often explained by

an increase in larger events due to some underlying physical process. However, it is possible that

b-value decreases prior to failure because the catalog is incomplete at low magnitudes. In fact, our

cataloged data show that Mc increases as time to failure decreases for data at 30 µm/s and 100 µm/s

(Figure 2-3 and Figure A6). In theory, if all events were detected, we would not expect Mc to shift

as a function of position in the seismic cycle. A potential culprit could be the thresholding

parameters used in catalog construction. If small events are systematically missed due to temporal

clustering of large events and/or sensor ring-down issues, as observed in field data (Herrmann et

al., 2019), Mc could vary as a function of position within the seismic cycle and with shearing

velocity. Therefore, the reduction in b-value prior to failure could simply be a catalog completeness

issue. To test this hypothesis and to circumvent common issues associated with cataloging, we

complement our catalog-based results by computing mean values of the continuous acoustic signal

(Figure 2-6). For this analysis, we directly utilize the continuous AE data.

We derive mean amplitudes from the continuous acoustic signal as a way to verify our

catalog results. The mean amplitudes of the continuous AE data are in some ways analogous to the

21

amplitudes we report from our catalogs. However, when working with the continuous data, the

mean amplitudes encode information based on the signal (AEs) and noise. This includes real –

electromagnetic – noise, as well as small amplitude events that get discarded in the cataloging

procedure. Nevertheless, the velocity dependence of AE size observed in Figures 2-3:2-5 should

be preserved in the continuous data; because the catalogs themselves are derived from the

continuous signal. AE amplitudes derived from the continuous data support the results from the

catalog (Figure 2-6). AE amplitude increases as the fault approaches failure and scales inversely

with shearing velocity. This implies that the temporal variations in b-value and the velocity

dependence of b-value are not an artifact of our event detection algorithm. In other words, our event

detection algorithm may indeed miss small AEs that occur in close proximity to bigger AEs, but

these missed events do not invalidate our results nor do they lead to misguided conclusions about

how b-value evolves throughout the seismic cycle.

2.5.2 Acoustic Emission Event Rates

Laboratory studies show that AE event rates increase systematically as failure approaches

and are consistent with the temporal evolution of foreshock sequences in tectonic fault zones (Mogi,

1963; Scholz, 1968a;1968b; Weeks et al., 1978; Sammonds et al., 1992; Amitrano, 2003; Ojala et

al., 2004; McLaskey and Lockner, 2014; Goebel et al., 2015; Acosta et al., 2019). However, few

studies have documented the velocity dependence of this process. Our data show that the event rate

of lab foreshocks per unit fault slip scales inversely with shear velocity (Figure 2-2). However, the

changes are largest at our highest loading rates (30 µm/s and 100 µm/s) and the increase in Mc with

velocity could partially bias the AE rate evolution if more small events are missed at larger shearing

velocities (Figure A7).

22

On the other hand, low event rates at higher velocities could arise from a true lack of

smaller events at these shearing rates. For example, it is possible that pre-seismic fault zone dilation

plays an important role in controlling the event rates (Figure 2-8). Our data indicate that pre-seismic

fault dilation scales inversely with the far-field shearing velocity, thus higher dilation at lower

shearing rates could lead to more inter-particle slip and rolling among grains, and as a result an

increase in acoustic activity.

The temporal evolution in event rates across the seismic cycle is also worth mentioning.

In particular, the post-seismic reduction in event rate seems to scale with the stress drop of the

previous slip event (Figure 2-2). This post-seismic reduction in event rate could be a proxy for

aftershock activity. It should be made clear that the reduction in event rate is not due to an artifact

of the windowing procedure. The moving windows start at the beginning of the seismic cycle and

do not include temporal information from the previous slip cycle. Furthermore, this reduction in

AE activity is actually captured in other higher-order statistics of the AE signal, such as the

acoustic energy (i.e., variance). The acoustic energy decreases following a slip event and shows a

similar temporal evolution to the AE event rates (Hulbert et al., 2019; Bolton et al., 2020).

Although it is not mentioned in these studies, the reduction in AE energy following the slip event

could also be evidence of aftershock activity. In addition, these observations are consistent with

3D discrete element models (DEM) that show elevated levels of kinetic energy and micro-slips

following stick-slip events (Ferdowsi et al., 2013).

2.5.3 Shear Stress, fault slip rate, and shearing velocity dependence of F/M Statistics

Our data show that b-value decreases prior to failure for a wide range of shearing velocities

(Figures 2-4 and 2-5). When plotted as a function of stress state, b-value decreases significantly

once the fault surpasses 60-85% of the peak stress (Figure 2-5). This can also be seen in Figure 2-

23

3 where the F/M curves become more vertically offset as the fault transitions from 60-90% of its

peak stress. This observation is consistent with previous studies on uniaxial and triaxial

compression texts on intact rock samples, which showed accelerated AE activity and lower b-

values after the rock specimens reached ~50-60% of the failure stress (Scholz, 1968a).

For a given shear velocity, the data from Figure 2-5A are strongly correlated with the true

fault slip velocity (Figure 2-5B). To assess the shear velocity dependence on b-value, we normalize

the true fault slip velocity by the shearing velocity and re-plot the data from Figure 2-5B (Figure

A8). The data show that b-value scales inversely with normalized fault slip rate. Interestingly, the

b-values are still offset with respect to shearing velocity. Because the data do not collapse onto a

single curve, this suggests that b-value is modulated by both the shearing velocity and fault slip

rate. The shear velocity only affects the absolute values of b-value and does not seem to have a

significant effect on the temporal changes; if indeed the shearing velocity did have an effect on the

temporal reduction in b, then we should expect to see a higher-order effect superimposed on the

data in Figure A8. Hence, these observations suggest that the reduction in b-value prior to co-

seismic failure is ultimately tied to the simultaneous and continuous increase in fault slip rate and

shear stress.

In most laboratory stick-slip experiments, shear stress and fault slip rate are highly coupled

and increase continuously throughout the laboratory seismic cycle (Figure 2-4). In our experiments,

this coupling could be due to the intrinsic, mechanical properties of glass beads and/or the fact that

our experiments are conducted at low normal stresses (5 MPa). Thus, we decoupled the effects of

fault slip rate from shear stress by conducting shear stress oscillation experiments under boundary

conditions that resulted in zero fault slip (Figure A9). Prior to shear stress oscillations, faults were

sheared for 10 mm at 21 µm/s, producing lab earthquakes as in Figure 2-1. Then the shear stress

was reduced to ~ 50% of the peak stress. This limits the amount of fault creep and helps ensure that

the fault slip rate was ~ 0 during the shear stress oscillations. However, because the shear stress

24

was reduced to 50% of the peak stress these experiments are only compatible with the early stages

(e.g., <= 50% of the peak stress) of our stick-slip experiments. Nevertheless, for stresses below

50% of the peak stress, our data demonstrate that changes in shear stress on the fault alone do not

induce changes in the F/M statistics of AEs (Figure A9). These results are consistent with those in

Figure 2-5A, which show that b-value changes are subtle in the early stages of the seismic cycle

(<= 60% of the peak stress). The data of Figure A9 show that the shear stress does not affect F/M

statistics early in the seismic cycle. At stresses above 50% of the peak stress both shear stress and

changes in fault slip rate impact F/M statistics of lab foreshocks.

2.5.4 A micromechanical model for the velocity dependence of AE size and b-value

Our data demonstrate that F/M statistics of lab foreshocks, AE events that occur during the

inter-seismic period prior to lab mainshocks, scale inversely with fault slip velocity and shearing

rate (Figures 2-5:2-6). At first glance these observations may seem counter-intuitive with respect

to frictional healing processes. Basic concepts of time-dependent frictional healing would predict

stronger contacts and elevated friction at lowering shearing rates. Our data indeed show that stress

drop decreases with increasing shear velocity, consistent with expectations for frictional aging and

previous lab results (e.g., Karner and Marone, 2000). Moreover, our previous work establishes: 1)

that stress drop varies systematically with peak fault slip velocity of laboratory earthquakes, with

slow events having smaller stress drop and 2) that co-seismic acoustic energy release scales directly

with stress drop (Bolton et al., 2020). Thus, the expectation that laboratory earthquakes with larger

stress drop have larger co-seismic acoustic amplitude is consistent with our data. However, we

find that larger laboratory foreshocks nucleate at higher slip rates, so the underlying mechanism

seems to derive from something other than contact junction age and frictional healing.

25

At a simplistic level the generation of AEs in granular fault gouge must arise from a

combination of grain fracturing, grain sliding/rolling, and the breaking of force chains. Because our

experiments were conducted at low normal stress (5 MPa) grain crushing and comminution are

insignificant (Mair and Marone, 2002; Scuderi et al., 2015). Thus, AE generation in our

experiments is driven by nondestructive grain scale processes, such as grain sliding and rolling,

and shear of partially-welded contact junctions. The duration of our AE events suggests that a single

AE represents failure of multiple grain contact junctions, rather than a single contact junction,

which is consistent with previous works (e.g., Kato et al., 1994; Yabe et al., 2003; Anthony and

Marone, 2005). Thus, we suggest a micromechanical model that connects the velocity dependence

of AE event size with fault zone porosity and granular packing.

2.5.5 Pre-seismic Fault Zone Dilation and AE Size

At higher loading velocity, the co-seismic stress drop is smaller and the

dilation/compaction that occurs within a seismic cycle is smaller. We quantified this relation for

our suite of experiments and found that pre-seismic fault zone dilation is proportional to stress drop

(Figure 2-8). During steady-state shearing (Figure 2-1, Figure 2-4) when stress drop is roughly

constant from one event to the next, the co-seismic compaction is equal to the pre-seismic fault

zone dilation and the net fault zone porosity is constant (Figure 2-8A). Note, we do not explicitly

measure fault zone porosity; instead we use changes in layer thickness as a proxy for porosity

(Figure 2-8A). Under these conditions, the dilation that occurs during the pre-seismic stage

represents an increase in fault zone porosity (reduction in granular density). The dilation is localized

within shear bands, rather than a bulk effect, which is why dilation scales with stick-slip stress drop

and decreases with net shear strain as shear localization intensifies.

26

An increase in fault zone dilation is accompanied by the rolling/sliding of granular particles

(Ferdowsi et al., 2013). Higher amounts of dilation cause fault zone porosity to increase and makes

it easier for particles slide/roll past each other. This process could permit the failure of larger areas,

which would nucleate larger and more energetic foreshocks. However, our data show that smaller

foreshocks (higher b-values) are correlated with larger amounts pre-seismic dilation (Figure 2-5

and Figure 2-8). Therefore, pre-seismic fault zone dilation cannot fully explain the shear velocity

dependence of AE size observed in Figure 2-5. However, we cannot fully rule out the effect of pre-

seismic fault zone dilation on AE size because the rate dependence of the bulk fault zone thickness

at steady-state (DHSS) could be masking this effect (see section 2.5.6).

It is also possible that the slip rate between two adjacent contacts is the driving factor

behind AE size and b-values. In other words, the inter-particle slip rate, which is coupled to the

fault slip rate, controls AE size and b-values. Furthermore, because the far-field elastic

displacements of seismic waves/acoustic waves are proportional to the moment rate/slip rate, then

it is reasonable that AE amplitudes are directly proportional to the slip rate of the fault.

2.5.6 Enhanced porosity and grain mobilization as a mechanism for the shear velocity dependence of AE size and b-value in granular fault zones

It is well established that shear within granular fault zones localizes along shear bands and

that changes in fault zone dilation can be used to approximate (qualitatively) the width of the shear

bands (Marone et al., 1990; Marone & Kilgore, 1993). Previous works show that shear band width

decreases progressively with shear strain and that such shear localization tends to drive fault zones

toward velocity weakening behavior (Marone, 1998). Our experiments are consistent with this

view. Upon a step increase in slip velocity the net fault zone thickness increases and undergoes a

semi-permanent net dilation, consistent with previous work (Marone et al., 1990). The increase in

27

bulk fault zone thickness (DHSS), increases the porosity of the fault zone (decrease granular

density), and allows for greater particle motion and the possibility for larger regions to slip in a

given AE event. Thus, we propose that the shear velocity dependence of AE size seen in Figure 5

is modulated by the bulk fault zone density/porosity (Figure 2-9). This view is consistent with

previous studies on bare-rock surfaces, which have suggested that fault zone morphology (shear

localization) regulates AE size and b-values (Goebel et al., 2017; Dresen et al., 2020).

To further assess this hypothesis we conducted experiments with different particle sizes

and fault zone thicknesses (Table 2-1). We varied particle size and fault thickness so as to vary the

average number of grains across the Layer (GAL), or potential force chain length (Figure 2-10).

Granular density increases (decrease in fault zone porosity) with force chain length because longer

chains involve more particles with greater potential for smaller particles to occupy a void. Our data

show that the tails of the non-cumulative AE distributions (i.e., histograms) are systematically

higher for ~ M >= 3.0 for thinner fault zones (Figure 2-10). Hence, foreshock magnitude scales

inversely with fault zone thickness. The data of Figure 2-10 confirm the idea that larger AE events

are expected for lower density shear bands, such as occur in our experiments at higher shearing

velocity.

Our model for the relationship between AE event size and granular density suggests that

larger AE events should have longer duration, given that multiple particles must move or multiple

microshear surfaces must coalesce to produce large events. We measured AE event duration for

several events and found a strong positive relationship between event duration and AE energy

(Figure 2-11). The acoustic energy release is larger for longer duration AEs and this relationship

extends over next two orders of magnitude. These data are consistent with results from photoelastic

granular shear experiments, which show that bigger and more energetic stick-slip events rupture

larger areas (Daniels and Hayman, 2008). Furthermore, our data are consistent with seismic

28

observations which show that larger earthquakes have longer durations and rupture larger areas

(Aki, 1967; Kanamori and Anderson, 1975).

2.5.7 The reduction in b-value prior to co-seismic failure for granular fault zones

The data on event duration integrate well with the hypotheses proposed above, connecting

fault zone porosity and grain mobilization to AE size. Higher shearing rates enhance grain

mobilization, which in turn, allows bigger areas (fault patches) to fail. Furthermore, the correlation

between AE size, AE duration, and the size of the fault patch could explain the reduction in b-value

prior to failure in granular fault zones. That is, AEs that nucleate prior to co-seismic failure in

granular fault zones are a manifestation of the failure of small “fault patches”. Because AE duration

scales with AE size, then this implies that bigger fault patches are breaking/rupturing closer to co-

seismic failure. Bigger areas are likely to rupture closer to failure because the fault slip rate and

fault zone dilation act in parallel to increase the fault zone porosity as failure approaches, which

enhances grain mobilization and promotes the destruction of grain contact junctions. Ultimately,

all of these processes act in concert to allow bigger patches to rupture, which in turn, allows AE

event sizes to grow and b-values to reduce prior to co-seismic failure.

To conclude, we propose that the porosity of the fault zone controls the degree of

grain mobilization, which in turn, controls the size of AEs. In other words, if the fault zone porosity

is low, grain motion is restricted, frictional healing processes dominate, and only small fault patches

are allowed to rupture pre-seismically. These conditions nucleate small AEs and result in high b-

values. In contrast, if the fault zone porosity is high, grain motion is enhanced, the destruction of

contact junctions dominate, and bigger fault patches are allowed to fail. Such conditions produce

bigger AEs and lower b-values pre-seismically.

29

2.5.8 The relationship between AE size and frictional healing processes

Basic concepts of time-dependent healing predicts bigger and stronger contacts at lower

shearing velocities, which at first glance might seem counter-intuitive to the inverse relationship

between AE size, shear velocity, and fault slip rate. However, we suggest that these two concepts

are in fact connected. That is, fault zone porosity acts in parallel with frictional healing processes.

At higher shearing/fault slip rates, fault zone porosity is high and contact junctions are younger,

smaller, and weaker (Dieterich, 1972; 1978; Marone, 1998). These conditions promote pre-seismic

grain motion, allow bigger areas to rupture, and results in bigger AEs (lower b-values). In contrast,

at low shearing/fault slip rates, fault zone porosity is low and contact junctions are older, larger,

and stronger. These conditions inhibit pre-seismic grain motion and result in smaller AEs (higher

b-values).

2.5.9 Scaling up laboratory AEs to foreshock sequences of seismogenic fault zones

Previous works show that laboratory earthquakes and F/M characteristics of AE events can

improve understanding of the physics of foreshock sequences and nucleation processes for tectonic

earthquake. Laboratory foreshocks are the result of micromechanical processes acting along grain

contacts with length scales on the order of microns to mm. In contrast, foreshocks in nature

represent the rupture of much larger fault patches with length scales on the order of meters-

kilometers, and likely involve grain crushing and comminution, which is absent in our experiments.

Furthermore, laboratory experiments involve high-resolution measurements of fault zone and

acoustic properties throughout multiple seismic cycles; such high-resolution measurements of

seismic and mechanical attributes are often not unavailable at the field-scale. Therefore, it is not

immediately clear if and how characteristics of laboratory seismicity scale up to tectonic fault

30

zones. At this stage we can simply state that our laboratory experiments indicate that shearing

velocity, fault slip rate, and fault zone porosity play key roles in regulating F/M statistics of lab

foreshocks. Interpreting our results in light of what has been observed from previous field studies,

suggests that a lack of foreshock activity preceding some earthquakes could simply indicate that

the fault stays locked and the fault slip rate (and preslip) is low (or non-existent). Furthermore, it is

also possible that thermal and/or chemical processes act to lithify the fault zone, thereby reducing

its porosity and inhibiting any type of movement that would otherwise radiate seismic energy. This

is a simplistic view that does not account for the role of secondary faults or damage zones and

neglects the role of pore-fluids (e.g., Chiarabba et al., 2020; Paola et al., 2020). Future work should

focus on these aspects of foreshock dynamics. Regardless, our work highlights the importance of

fault-slip rate and fault zone porosity in regulating the size of foreshocks in laboratory experiments

and should be carefully considered when analyzing foreshock sequences in the field.

2.6 Conclusion

We conducted shear experiments on granular fault gouge and found systematic variations

in acoustic emissions as a function of time within the lab seismic cycle. We focused on AE prior

to lab earthquakes and thus these events represent foreshocks to the main stick slip events (lab

mainshocks). We analyzed F/M statistics of lab foreshocks using a standard cataloging approach

and supplemented these observations with an analysis of raw acoustic data. Statistics from the

continuous acoustic records are consistent with those produced by cataloging. Our data are

consistent with previous works and demonstrate that b-value decreases as co-seismic failure

approaches. In addition to the importance of shear stress, we demonstrate that b-value scales

inversely with the shearing velocity and fault slip rate for AE data during the inter-seismic period.

We propose that the velocity dependence of AE size and b-value arises from variations in fault

31

zone porosity and grain mobilization processes. Higher shearing rates increase fault zone porosity

and grain mobilization, which in turn, promotes the failure of bigger fault patches and results in

bigger AEs. Our data highlights the importance of fault slip rate and fault zone porosity in

unraveling the dynamics of foreshock sequences.

32

Figure 2-1: A Shear stress and AE amplitude plotted as a function of time. Open symbols represent AE amplitudes and are color coded according to the sensor they were detected on. Top left inset shows double-direct shear configuration with acoustic blocks. Top right inset shows 2D schematic of acoustic block and the locations of the three sensors used in this study. Acoustic amplitude increases throughout the seismic cycle and larger AEs nucleate during the inter-seismic period for higher shear velocities. B-C. Shear stress and continuous AE data plotted as a function of time for one entire seismic cycle at 3 µm/s and 100 µm/s. Spikes in the continuous acoustic data are AEs that are cataloged according to their peak amplitude and plotted in panel A.

33

Figure 2-2: A-D Shear stress and AE rate (per unit displacement) as a function of time for different shear velocities explored in this study (see Figure 2-1). AE rate is calculated using a time window whose width corresponds to 10% of the recurrence interval of the seismic cycle. For each window we count how many events were detected and normalize each time window by the amount of slip displacement covered. Event rates are high after a failure event, decrease to a minimum, and subsequently increase until co-seismic failure.

34

Figure 2-3: A-D Frequency-magnitude plots are shown for each shear velocity at different locations in the seismic cycle. F/M plots represent AE statistics derived from our cataloging approach from Experiment p5363. Curves are color coded according to their location within the seismic cycle and the black dashed line represents the magnitude range used to compute b-values. Note, each inset shows the specific seismic cycle from which the F/M curves are derived from. The color coded squares in the inset corresponds to the time window associated with each F/M curve. F/M curves are plotted using a constant number of events, and thus, windows vary in time at each location within the seismic cycle and become smaller as time to failure approaches zero due to higher event rates (see Figure 2-2). B-value decreases as failure approaches and scales inversely with shear velocity.

35

Figure 2-4: A-D Shear stress, fault slip velocity, and b-value as a function of time for different shear velocities. B-values are averaged across three channels and the error bars represent one standard-deviation among the channels. The pre-seismic changes in fault slip rate show that the fault unlocks very early on in the seismic cycle and increases continuously until co-seismic failure. B-value decreases systematically throughout the seismic cycle for each shearing velocity.

36

Figure 2-5: A. B-value plotted as a function of shear stress. Note, b-values correspond to the same data plotted in Figure 4. B-value scales inversely with shear stress once the fault surpasses ~ 60% of its peak stress and is inversely correlated with shear velocity. B. B-value versus true fault slip velocity. Note, the strong correlation between b-value and slip rate for a given shearing velocity. C. F/M statistics derived from stacking multiple F/M curves at 90% of the peak stress, resulting in a total of ~ 7,400 AEs for each F/M curve. D. B-value scales inversely with shear velocity for data at 90% of the peak stress. Note, b-values are estimated from F/M curves in C.

37

Figure 2-6: Mean acoustic amplitude derived from the continuous AE data. Amplitudes are averaged across all the slip cycles shown in Figure 4 for a given shear velocity and location within the seismic cycle. 1 µm windows are used to compute mean values. AE amplitude increases as the fault approaches failure and scales inversely with the shear velocity.

20 40 60 80 100Percent of Peak Stress

20

40

60

80

100A

mpl

itude

(bits

)

100 µm/s

30 µm/s

3 µm/s

.3 µm/s

38

Figure 2-7: A. AE amplitude and shear stress plotted as a function of time for a stable-sliding friction experiment. AE amplitude increases with shearing velocity. B. Histogram of AE amplitudes for 500 µm windows. Higher shearing velocities produce fewer small events (M < 1.4) and show a net increase in larger events relative to lower shearing rates. C. Histogram of AE amplitudes derived from stacking multiple seismic cycles at 85%, resulting in ~ 7,400 AEs for each shear velocity. F/M data show an increase in bigger events relative to smaller events at higher shearing rates.

1.0 1.5 2.0 2.5 3.0 3.5 4.0M = log10 (Amplitude (bits))

100

101

102

103

# of

Eve

nts

.3 m/s3 m/s30 m/s100 m/s

p5363

C

A

p5348

3800 4000 4200Time (s)

4600 4800 50004400

6.0 Shea

r Stre

ss (M

Pa)

6.1

6.2

6.3

AE

Am

plitu

de (b

its)

101

102

103

104

B

1.2 1.4 1.6 1.8 2.0M = log10 (Amplitude (bits))

101

103

105

# of

Eve

nts

2 m/s5 m/s10 m/s20 m/s40 m/s60 m/s

p5348

39

Figure 2-8: A. Layer-thickness and shear stress plotted for one seismic cycle. Pre-seismic dilation is computed as the change in layer-thickness across the inter-seismic period. B. Dilation plotted as a function of stress drop for each shearing velocity explored in Experiment p5363. Dilation scales systematically with stress drop and inversely with shearing velocity.

18.40 18.42 18.44 18.46 18.48

Load-Point Displacement (mm)

H (

µm

)

Shear S

tress (

MP

a)

1 µm

.2 MPa

Pre-seismic Dilation Co-seismic

Compaction

A

0.4 0.6 0.8 1 1.2

Stress Drop (MPa)

0

2

4

6

8

Pre-seis

mic

Dil

ati

on

(µ

m)

.3 m/s

3 m/s

30 m/s

100 m/s

B

40

Figure 2-9: A 2D schematic of a micro-mechanical model describing the velocity dependence of AE size and b-value in granular fault zones. This simplistic view suggests that sub-parallel structures (shear bands/force chains) support the bulk of the stress and strain throughout the inter-seismic period. Highly stressed regions (depicted by darker particles) are separated by spectator regions (light shaded particles) that accommodate very little strain throughout the seismic cycle. Upon step increase in loading velocity, the fault zone width increases by ∆H. The increase in fault zone width, increases fault zone porosity (decreases density), and permits the nucleation of large AEs and lower b-values.

Increasing Shear Velocity

At low shear velocities the width of the fault zone (H) is

narrower and fault zone porosity is low. These characteristics

inhibit grain mobilization and promote frictional healing via

elasto-plastic deformation of grain contact junctions.

Inter-seismically the fault is able to store more elastic-strain

energy, resulting in a dearth of large AEs and higher

b-values. The increase in stored energy during the

inter-seismic period allows bigger stress drops and radiates

more acoustic energetic during the co-seismic slip phase

(Bolton et al., 2020).

∆H

At higher shear velocities the width of the fault zone (H) is

wider and fault zone porosity is higher. These characteristics

promote grain mobilization and allow less frictional healing

to take place. This enhances grain mobilization and allows

bigger areas to fail pre-seismically, which result in bigger

AEs and lower b-values. As a result, the system is able to

store less energy (pre-seismically), resulting in smaller stress

drops and less energetic AEs during the co-seismic period.

(Shear zone thickness)

H

41

Figure 2-10: Histogram of AE amplitudes located at 85% of the peak stress for 10,000 AEs from 20 seismic cycles. The average number grains across each gouge layer (GAL) was systematically modified by varying the fault zone thickness and/or particle size (see Table 2-1). F/M curves show an inverse relationship between AE size and the number of grains across each gouge layer.

1 1.5 2 2.5 3 3.5 4M = log10 (Amplitude (bits))

22.3 GAL;p53496.4 GAL; p53642.5 GAL; p5365

47 GAL; p5357

102

100

101

103

# of

Eve

nts

42

Figure 2-11: Acoustic energy of AEs as a function of AE duration. Larger AEs radiate more energy and contain longer time-domain signals.

10-2 10-1 100

AE Duration (ms)

103

105

107

Aco

ustic

Ene

rgy

(bits

2 )

43

Table 2-1: List of experiments and boundary conditions for Chapter 2

Experiment Normal Stress (MPa) Shear Velocity (µm/s) Mean Grain Size (µm)

p5363 5

5

5

5

5

0.3-100

21

21

21

21

126.5

126.5

126.5

450

1100

List of Experiments and Boundary Conditions

2-60 10.5p5348 9

Layer Thickness (mm)

3.0

3.0p5349

p5357

p5364

p5365

3.0

3.0

3.0

6.0

44

2.7 References

Abercrombie, R. E., Agnew, D. C., & Wyatt, F. K. (1995). Testing a model of earthquake

nucleation. Bulletin of the Seismological Society of America, 85(6), 1873-1878.

Abercrombie, R. E., & Mori, J. (1996). Occurrence patterns of foreshocks to large earthquakes in

the western United States. Nature, 381(6580), 303-307.

Acosta, M., Passelègue, F. X., Schubnel, A., Madariaga, R., & Violay, M. (2019). Can precursory

moment release scale with earthquake magnitude? A view from the laboratory. Geophysical

Research Letters, 46(22), 12927-12937.

Aki, K. (1967). Scaling law of seismic spectrum. Journal of geophysical research, 72(4), 1217-

1231.

Amitrano, D. (2003). Brittle-ductile transition and associated seismicity: Experimental and

numerical studies and relationship with the b value. Journal of Geophysical Research: Solid

Earth, 108(B1).

Anthony, J. L., & Marone, C. (2005). Influence of particle characteristics on granular

friction. Journal of Geophysical Research: Solid Earth, 110(B8).

Baccheschi, P., De Gori, P., Villani, F., Trippetta, F., & Chiarabba, C. (2020). The preparatory

phase of the Mw 6.1 2009 L’Aquila (Italy) normal faulting earthquake traced by foreshock

time-lapse tomography. Geology, 48(1), 49-55.

Bakun, W. H., Aagaard, B., Dost, B., Ellsworth, W. L., Hardebeck, J. L., Harris, R. A., ... &

Michael, A. J. (2005). Implications for prediction and hazard assessment from the 2004

Parkfield earthquake. Nature, 437(7061), 969-974.

Bernard, P., Pinettes, P., Hatzidimitriou, P. M., Scordilis, E. M., Veis, G., & Milas, P. (1997).

From precursors to prediction: a few recent cases from Greece. Geophysical Journal

International, 131(3), 467-477.

45

Bolton, D. C., Shokouhi, P., Rouet-Leduc, B., Hulbert, C., Rivière, J., Marone, C., & Johnson, P.

A. (2019). Characterizing acoustic signals and searching for precursors during the laboratory

seismic cycle using unsupervised machine learning. Seismological Research Letters, 90(3),

1088-1098.

Bolton, D. C., Shreedharan, S., Rivière, J., & Marone, C. (2020). Acoustic energy release during

the laboratory seismic cycle: Insights on laboratory earthquake precursors and

prediction. Journal of Geophysical Research: Solid Earth, 125,

e2019JB018975. https://doi.org/10.1029/2019JB018975

Bouchon, M., Durand, V., Marsan, D., Karabulut, H., & Schmittbuhl, J. (2013). The long

precursory phase of most large interplate earthquakes. Nature geoscience, 6(4), 299-302.

Brodsky, E. E., & Lay, T. (2014). Recognizing foreshocks from the 1 April 2014 Chile

earthquake. Science, 344(6185), 700-702.

Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from

earthquakes. Journal of geophysical research, 75(26), 4997-5009.

Chen, X., & Shearer, P. M. (2013). California foreshock sequences suggest aseismic triggering

process. Geophysical Research Letters, 40(11), 2602-2607.

Chiarabba, C., Buttinelli, M., Cattaneo, M., & De Gori, P. (2020). Large earthquakes driven by

fluid overpressure: The Apennines normal faulting system case. Tectonics, 39(4),

e2019TC006014.

Crampin, S., Evans, R., & Atkinson, B. K. (1984). Earthquake prediction: a new physical basis.

Geophysical Journal International, 76(1), 147-156.

Daniels, K. E., & Hayman, N. W. (2008). Force chains in seismogenic faults visualized with

photoelastic granular shear experiments. Journal of Geophysical Research: Solid

Earth, 113(B11).

46

Dieterich, J. H. (1972). Time-dependent friction in rocks. Journal of Geophysical Research,

77(20), 3690-3697.

Dieterich, J. H. (1978). Time-dependent friction and the mechanics of stick-slip. In Rock Friction

and Earthquake Prediction (pp. 790-806). Birkhäuser, Basel.

Dodge, D. A., Beroza, G. C., & Ellsworth, W. L. (1996). Detailed observations of California

foreshock sequences: Implications for the earthquake initiation process. Journal of

Geophysical Research: Solid Earth, 101(B10), 22371-22392.

Dresen, G., Kwiatek, G., Goebel, T., & Ben-Zion, Y. (2020). Seismic and Aseismic Preparatory

Processes Before Large Stick–Slip Failure. Pure and Applied Geophysics, 177(12), 5741-

5760.

Ellsworth, W. L., & Beroza, G. C. (1995). Seismic evidence for an earthquake nucleation

phase. Science, 268(5212), 851-855.

Ellsworth, W. L., & Bulut, F. (2018). Nucleation of the 1999 Izmit earthquake by a triggered

cascade of foreshocks. Nature Geoscience, 11(7), 531-535.

Ferdowsi, B., Griffa, M., Guyer, R. A., Johnson, P. A., Marone, C., & Carmeliet, J. (2013).

Microslips as precursors of large slip events in the stick-slip dynamics of sheared granular

layers: A discrete element model analysis. Geophysical Research Letters, 40(16), 4194-4198.

Frye, K. M., & Marone, C. (2002). Effect of humidity on granular friction at room temperature.

Journal of Geophysical Research: Solid Earth, 107(B11), ETG-11. Geophysical Research,

78(29), 6936-6942.

Goebel, T. H. W., Sammis, C. G., Becker, T. W., Dresen, G., & Schorlemmer, D. (2015). A

comparison of seismicity characteristics and fault structure between stick–slip experiments

and nature. Pure and Applied Geophysics, 172(8), 2247-2264.

47

Goebel, T. H. W., Schorlemmer, D., Becker, T. W., Dresen, G., & Sammis, C. G. (2013).

Acoustic emissions document stress changes over many seismic cycles in stick-slip

experiments. Geophysical Research Letters, 40(10), 2049-2054, doi:10.1029/2010/GL043066

Goebel, T. H., Kwiatek, G., Becker, T. W., Brodsky, E. E., & Dresen, G. (2017). What allows

seismic events to grow big?: Insights from b-value and fault roughness analysis in laboratory

stick-slip experiments. Geology, 45(9), 815-818.

Gulia, L., & Wiemer, S. (2019). Real-time discrimination of earthquake foreshocks and

aftershocks. Nature, 574(7777), 193-199.

Gulia, L., Tormann, T., Wiemer, S., Herrmann, M., & Seif, S. (2016). Short-term probabilistic

earthquake risk assessment considering time-dependent b values. Geophysical Research

Letters, 43(3), 1100-1108.

Gulia, L., Wiemer, S., & Vannucci, G. (2020). Pseudoprospective Evaluation of the Foreshock

Traffic-Light System in Ridgecrest and Implications for Aftershock Hazard Assessment.

Seismological Research Letters. https://doi.org/10.1785/0220190307

Gupta, I. N. (1973). Seismic velocities in rock subjected to axial loading up to shear fracture.

Journal of

Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the

Seismological Society of America, 34(4), 185-188.

Herrmann, M., Kraft, T., Tormann, T., Scarabello, L., & Wiemer, S. (2019). A consistent high-

resolution catalogof induced seismicity in Basel based on matched filter detection and

tailored post-processing. Journal of Geophysical Research: Solid Earth, 124, 8449–8477.

https://doi.org/10.1029/ 2019JB017468

48

Hulbert, C., Rouet-Leduc, B., Johnson, P. A., Ren, C. X., Rivière, J., Bolton, D. C., & Marone, C.

(2019). Similarity of fast and slow earthquakes illuminated by machine learning. Nature

Geoscience, 12(1), 69-74.

Jiang, Y., Wang, G., & Kamai, T. (2017). Acoustic emission signature of mechanical failure:

Insights from ring-shear friction experiments on granular materials. Geophysical Research

Letters, 44(6), 2782-2791.

Kanamori, H., & Anderson, D. L. (1975). Theoretical basis of some empirical relations in

seismology. Bulletin of the seismological society of America, 65(5), 1073-1095.

Kaproth, B. M., & Marone, C. (2013). Slow earthquakes, preseismic velocity changes, and the

origin of slow frictional stick-slip. Science, 341(6151), 1229-1232.

Kato, A., Fukuda, J. I., Kumazawa, T., & Nakagawa, S. (2016). Accelerated nucleation of the

2014 Iquique, Chile Mw 8.2 earthquake. Scientific reports, 6, 24792.

Leeman, J. R., Saffer, D. M., Scuderi, M. M., & Marone, C. (2016). Laboratory observations of

slow earthquakes and the spectrum of tectonic fault slip modes. Nature communications, 7(1),

1-6.

Lockner, D. A., Walsh, J. B., & Byerlee, J. D. (1977). Changes in seismic velocity and

attenuation during deformation of granite. Journal of Geophysical Research, 82(33), 5374-

5378.

Lockner, D., Byerlee, J. D., Kuksenko, V., Ponomarev, A., & Sidorin, A. (1991). Quasi-static

fault growth and shear fracture energy in granite. Nature, 350(6313), 39.

Lubbers, N., Bolton, D. C., Mohd-Yusof, J., Marone, C., Barros, K., & Johnson, P. A. (2018).

Earthquake Catalog-Based Machine Learning Identification of Laboratory Fault States and the

Effects of Magnitude of Completeness. Geophysical Research Letters, 45(24), 13-269.

Main, I. G., Meredith, P. G., & Jones, C. (1989). A reinterpretation of the precursory seismic b-

value anomaly from fracture mechanics. Geophysical Journal International, 96(1), 131-138.

49

Mair, K., Frye, K. M., & Marone, C. (2002). Influence of grain characteristics on the friction of

granular shear zones. Journal of Geophysical Research: Solid Earth, 107(B10), ECV-4.

Mair, K., & Marone, C. (1999). Friction of simulated fault gouge for a wide range of velocities

and normal stresses. Journal of Geophysical Research: Solid Earth, 104(B12), 28899-28914.

Marone, C., Raleigh, C. B., & Scholz, C. H. (1990). Frictional behavior and constitutive

modeling of simulated fault gouge. Journal of Geophysical Research: Solid Earth, 95(B5),

7007-7025.

Marone, C., & Kilgore, B. (1993). Scaling of the critical slip distance for seismic faulting with

shear strain in fault zones. Nature, 362(6421), 618-621.

Marone, C., Carpenter, B. M., & Schiffer, P. (2008). Transition from rolling to jamming in thin

granular layers. Physical review letters, 101(24), 248001.

McBrearty, I. W., Gomberg, J., Delorey, A. A., & Johnson, P. A. (2019). Earthquake Arrival

Association with Backprojection and Graph Theory. Bulletin of the Seismological Society of

America, 109(6), 2510-2531.

McLaskey, G. C., & Kilgore, B. D. (2013). Foreshocks during the nucleation of stick-slip

instability. Journal of Geophysical Research: Solid Earth, 118(6), 2982-2997.

McLaskey, G. C., & Lockner, D. A. (2014). Preslip and cascade processes initiating laboratory

stick slip. Journal of Geophysical Research: Solid Earth, 119(8), 6323-6336.

McLaskey,G.C. Earthquake Initiation From Laboratory Observations and Implications for

Foreshocks, Journal of Geophysical Research: Solid Earth 124 (12) (2019) 12882–12904.

Mignan, A. (2014). The debate on the prognostic value of earthquake foreshocks: A meta-

analysis. Scientific reports, 4, 4099.

Milne, J. (1899). Earthquake Precursors. Nature, 59(1531), 414.

Mogi, K., Study of the elastic shocks caused by the fracture of heterogeneous materials and its

relation to earthquake phenomena, Bull. Earthquake Res.Inst.Tokyo Univ., 40, 125,1962

50

Mori, J., & Abercrombie, R. E. (1997). Depth dependence of earthquake frequency-magnitude

distributions in California: Implications for rupture initiation. Journal of Geophysical

Research: Solid Earth, 102(B7), 15081-15090.

Nanjo, K. Z., Hirata, N., Obara, K., & Kasahara, K. (2012). Decade-scale decrease in b value

prior to the M9-class 2011 Tohoku and 2004 Sumatra quakes. Geophysical Research

Letters, 39(20).

Nanjo, K. Z. "Were changes in stress state responsible for the 2019 Ridgecrest, California,

earthquakes?" Nature communications 11, no. 1 (2020): 3082-3082.

Niu, F., Silver, P. G., Daley, T. M., Cheng, X., & Majer, E. L. (2008). Preseismic velocity

changes observed from active source monitoring at the Parkfield SAFOD drill site. Nature,

454(7201), 204.

Ohnaka, M., & Mogi, K. (1982). Frequency characteristics of acoustic emission in rocks under

uniaxial compression and its relation to the fracturing process to failure. Journal of

geophysical research: Solid Earth, 87(B5), 3873-3884.

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. Journal of Physics of the Earth, 41(1), 45-56.

Ohnaka, M. (2000). A physical scaling relation between the size of an earthquake and its

nucleation zone size. Pure and Applied Geophysics, 157(11-12), 2259-2282.

Ojala, I. O., Main, I. G., & Ngwenya, B. T. (2004). Strain rate and temperature dependence of

Omori law scaling constants of AE data: Implications for earthquake foreshock-aftershock

sequences. Geophysical research letters, 31(24).

51

Papadopoulos, G. A., Charalampakis, M., Fokaefs, A., & Minadakis, G. (2010). Strong foreshock

signal preceding the L'Aquila (Italy) earthquake (Mw 6.3) of 6 April 2009. Natural Hazards

and Earth System Sciences, 10(1), 19.

Passelègue, F. X., Latour, S., Schubnel, A., Nielsen, S., Bhat, H. S., & Madariaga, R. (2017).

Influence of fault strength on precursory processes during laboratory earthquakes. Fault Zone

Dynamic Processes, 229-242.

Pritchard, M. E., Allen, R. M., Becker, T. W., Behn, M. D., Brodsky, E. E., Bürgmann, R., ... &

Kaneko, Y. (2020). New Opportunities to Study Earthquake Precursors. Seismological

Research Letters.

Renard, F., Cordonnier, B., Kobchenko, M., Kandula, N., Weiss, J., & Zhu, W. (2017).

Microscale characterization of rupture nucleation unravels precursors to faulting in rocks.

Earth and Planetary Science Letters, 476, 69-78.

Renard, F., Weiss, J., Mathiesen, J., Ben-Zion, Y., Kandula, N., & Cordonnier, B. (2018). Critical

Evolution of Damage Toward System-Size Failure in Crystalline Rock. Journal of

Geophysical Research: Solid Earth, 123(2), 1969-1986.

Rikitake, T. (1968). Earthquake prediction. Earth-Science Reviews, 4, 245-282.

Rivière, J., Lv, Z., Johnson, P. A., & Marone, C. (2018). Evolution of b-value during the seismic

cycle: Insights from laboratory experiments on simulated faults. Earth and Planetary Science

Letters, 482, 407-413

Ross, Z. E., Trugman, D. T., Hauksson, E., & Shearer, P. M. (2019). Searching for hidden

earthquakes in Southern California. Science, 364(6442), 767-771.

Rouet-Leduc, B., Hulbert, C., Bolton, D. C., Ren, C. X., Riviere, J., Marone, C., ... & Johnson, P.

A. (2018). Estimating fault friction from seismic signals in the laboratory. Geophysical

Research Letters, 45(3), 1321-1329.

52

Ruiz, S., Metois, M., Fuenzalida, A., Ruiz, J., Leyton, F., Grandin, R., ... & Campos, J. (2014).

Intense foreshocks and a slow slip event preceded the 2014 Iquique Mw 8.1

earthquake. Science, 345(6201), 1165-1169.

Sammonds, P. R., Meredith, P. G., & Main, I. G. (1992). Role of pore fluids in the generation of

seismic precursors to shear fracture. Nature, 359(6392), 228-230.

Savage, J. C. (1972). Relation of corner frequency to fault dimensions. Journal of geophysical

research, 77(20), 3788-3795.

Scuderi, M. M., Carpenter, B. M., & Marone, C. (2014). Physicochemical processes of frictional

healing: Effects of water on stick-slip stress drop and friction of granular fault gouge. Journal

of Geophysical Research: Solid Earth, 119(5), 4090-4105.

Scuderi, M. M., Carpenter, B. M., Johnson, P. A., & Marone, C. (2015). Poromechanics of stick-

slip frictional sliding and strength recovery on tectonic faults. Journal of Geophysical

Research: Solid Earth, 120(10), 6895-6912.

Scuderi, M. M., Marone, C., Tinti, E., Di Stefano, G., & Collettini, C. (2016). Precursory changes

in seismic velocity for the spectrum of earthquake failure modes. Nature geoscience, 9(9),

695-700.

Scholz, C. H. (1968a). The frequency-magnitude relation of microfracturing in rock and its

relation to earthquakes, Bulletin of the Seismological Society of America, 58(1), 399-415.

Scholz, C. H. (1968b). Microfracturing and the inelastic deformation of rock in

compression. Journal of Geophysical Research, 73(4), 1417-1432.

Scholz, C. H. (2015). On the stress dependence of the earthquake b value. Geophysical Research

Letters, 42(5), 1399-1402.

Scholz, C. H., Sykes, L. R., & Aggarwal, Y. P. (1973). Earthquake prediction: a physical basis.

Science, 181(4102), 803-810.

53

Schorlemmer, D., Wiemer, S., & Wyss, M. (2005). Variations in earthquake-size distribution

across different stress regimes. Nature, 437(7058), 539-542.

Shreedharan, S., Rivière, J., Bhattacharya, P., & Marone, C. (2019). Frictional State Evolution

During Normal Stress Perturbations Probed With Ultrasonic Waves. Journal of Geophysical

Research: Solid Earth, 124(6), 5469-5491.

Shreedharan, S., Bolton, D. C., Rivière, J., & Marone, C. (2020). Preseismic fault creep and

elastic wave amplitude precursors scale with lab earthquake magnitude for the continuum of

tectonic failure modes. Geophysical Research Letters, 46.

https://doi.org/10.1029/2020GL086986

Spada, M., Tormann, T., Wiemer, S., & Enescu, B. (2013). Generic dependence of the frequency-

size distribution of earthquakes on depth and its relation to the strength profile of the

crust. Geophysical research letters, 40(4), 709-714.

Thompson, B. D., Young, R. P., & Lockner, D. A. (2009). Premonitory acoustic emissions and

stick-slip in natural and smooth-faulted Westerly granite. Journal of Geophysical Research:

Solid Earth, 114(B2).

Tinti, E., Scuderi, M. M., Scognamiglio, L., Di Stefano, G., Marone, C., & Collettini, C. (2016).

On the evolution of elastic properties during laboratory stick-slip experiments spanning the

transition from slow slip to dynamic rupture. Journal of Geophysical Research: Solid Earth,

121(12), 8569-8594.

Tormann, T., Wiemer, S., Metzger, S., Michael, A., & Hardebeck, J. L. (2013). Size distribution

of Parkfield's microearthquakes reflects changes in surface creep rate. Geophysical Journal

International, 193(3), 1474-1478.

Trugman, D. T., & Ross, Z. E. (2019). Pervasive foreshock activity across southern California.

Geophysical Research Letters.

54

van den Ende, M. P., & Ampuero, J. P. (2020). On the statistical significance of foreshock

sequences in Southern California. Geophysical Research Letters, 47(3), e2019GL086224.

Walter, J. I., Meng, X., Peng, Z., Schwartz, S. Y., Newman, A. V., & Protti, M. (2015). Far-field

triggering of foreshocks near the nucleation zone of the 5 September 2012 (MW 7.6) Nicoya

Peninsula, Costa Rica earthquake. Earth and Planetary Science Letters, 431, 75-86.

Weeks, J., Lockner, D., & Byerlee, J. (1978). Change in b-values during movement on cut

surfaces in Granite. Bulletin of the Seismological Society of America, 68(2), 333-341.

Whitcomb, J. H., Garmany, J. D., & Anderson, D. L. (1973). Earthquake prediction: Variation of

seismic velocities before the San Francisco earthquake. Science, 180(4086), 632-635.

Wiemer, S., & Wyss, M. (1997). Mapping the frequency-magnitude distribution in asperities: An

improved technique to calculate recurrence times?. Journal of Geophysical Research: Solid

Earth, 102(B7), 15115-15128.

Wiemer, S., & Wyss, M. (2000). Minimum magnitude of completeness in earthquake catalogs:

Examples from Alaska, the western United States, and Japan. Bulletin of the Seismological

Society of America, 90(4), 859-869.

Wyss, M., & Lee, W. H. K. (1973). Time variations of the average earthquake magnitude in

central California. In Proceedings of the conference on tectonic problems of the San Andreas

fault system (pp. 24-42). Stanford University Geol. Sci..

Yabe, Y., Kato, N., Yamamoto, K., & Hirasawa, T. (2003). Effect of sliding rate on the activity

of acoustic emission during stable sliding. pure and applied geophysics, 160(7), 1163-1189.

Yabe, Y. (2002). Rate dependence of AE activity during frictional sliding. Geophysical research

letters, 29(10), 26-1.

Yoon, C. E., Yoshimitsu, N., Ellsworth, W. L., & Beroza, G. C. (2019). Foreshocks and

Mainshock Nucleation of the 1999 M w 7.1 Hector Mine, California, Earthquake. Journal of

Geophysical Research: Solid Earth, 124(2), 1569-1582.

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Chapter 3

Characterizing acoustic signals and searching for precursors during the laboratory seismic cycle using unsupervised machine learning

Reprinted with permission from Seismological Research Letters and may be cited as “Bolton, D. C., Shokouhi, P., Rouet-Leduc, B., Hulbert, C., Rivière, J., Marone, C., & Johnson, P. A. (2019). Characterizing acoustic signals and searching for precursors during the laboratory seismic cycle using unsupervised machine learning. Seismological Research Letters, 90(3), 1088-1098.

3.1 Abstract

Recent work shows that machine learning (ML) can predict failure time and other aspects

of laboratory earthquakes using the acoustic signal emanating from the fault zone. These

approaches use supervised ML to construct a mapping between features of the acoustic signal and

fault properties, such as the instantaneous frictional state and time to failure. We build on this work

by investigating the potential for unsupervised ML to identify patterns in the acoustic signal during

the laboratory seismic cycle and precursors to labquakes. We use data from friction experiments

showing repetitive stick-slip failure (the lab equivalent of earthquakes) conducted at constant

normal stress (2.0 MPa) and constant shearing velocity (10 µm/s). Acoustic emission signals are

recorded continuously throughout the experiment at 4 MHz using broad-band pizeoceramic

sensors. Statistical features of the acoustic signal are used with unsupervised ML clustering

algorithms to identify patterns (clusters) within the data. We find consistent trends and systematic

transitions in the ML clusters throughout the seismic cycle, including some evidence for precursors

to lab earthquakes. Further work is needed to connect the ML clustering patterns to physical

mechanisms of failure and estimates of the time to failure.

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3.2 Introduction

3.2.1 Precursors to Earthquakes

Earthquake forecasting is an important problem for mitigating seismic hazard and it can

help illuminate the physics of earthquake nucleation. Forecasts could be based on physical models

of the nucleation process and/or changes in fault zone properties (so called precursors) prior to

failure. However, with current monitoring techniques and models of earthquake nucleation we are

far from forecasting earthquakes or even identifying reliable precursors; despite long-standing

interests in the problem (Milne, 1899; Marzocchi, 2018) and a broad range of related and direct

observations ranging from landslides (Poli, 2017), to glacial motion (e.g., Faillettaz et al., 2015,

2016), geochemical signals (Cui et al., 2017; Martinelli and Dadomo, 2017), geodesy (Chen et al.,

2010; Xie et al., 2016; Moro et al., 2017), and seismology (Antonioli et al., 2005; Niu et al., 2008;

Rivet et al., 2011; Bouchon et al., 2013). The situation is somewhat better for laboratory

earthquakes. Laboratory friction experiments coupled with ultrasonic measurements have been

used to document the approach to failure (Scholz, 1968; Weeks et al., 1978; Chen et al., 1993),

with important recent advances in documenting precursors, based on spatio-temporal changes in

rock properties prior to failure (Pyrak-Nolte, 2006; Mair et al., 2007; Goebel et al., 2013; Johnson

et al., 2013; Kaproth and Marone, 2013; Hedayat et al., 2014; McLaskey and Lockner, 2014;

Goebel et al., 2015; Scuderi et al., 2016; Rouet-Leduc et al., 2017,2018; Jiang et al., 2017; Renard

et al., 2018; Rouet-Leduc et al., 2017,2018; Rivière et al., 2018; Hulbert et al., 2018).

Lab observations of precursors prior to earthquake-like failure encompass a variety of

measurements including high-resolution images that illuminate the failure nucleation process.

These include passive measurements of AEs (e.g., McLaskey and Lockner, 2014; Goebel et al.

2015), active measurements of fault zone elastic properties (e.g., Scuderi et al., 2016; Tinti et al.,

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2016), and direct observations, using x-ray microtomography (micro-CT), of damage evolution in

the failure zone (Renard et al., 2017). The micro-CT work reveals micro-fracture patterns and the

interplay between shear deformation and local volume strain (Renard et al., 2017; Renard et al.,

2018). The AE studies show that the Gutenberg Richter b-value decreases systematically during

the laboratory seismic cycle (Goebel et al., 2013; Rivière et al., 2018). In addition, active source

measurements of elastic wave speed and travel time show systematic changes throughout the

laboratory seismic cycle and distinct precursors to failure for the complete spectrum of failure

modes from slow to fast elastodynamic events (Kaproth and Marone, 2013; Scuderi et al., 2016;

Tinti et al., 2016). These studies include measurements for dozens of repetitive stick-slip failure

events showing that elastic wave speed and transmitted amplitude increase during the linear-elastic

loading stage and decrease during inelastic loading.

3.2.2 Machine learning and acoustic signals prior to failure

Recent developments in the application of machine learning (ML) to seismic data suggest

a number of possible benefits for seismic hazard analysis and earthquake prediction. One approach

shows systematic changes in event occurrence patterns and seismic spectra that could illuminate

the earthquake nucleation process (e.g., Holtzman et al., 2018; Wu et al., 2018). Another approach,

using lab data similar to those that we focus on in this paper, has shown that supervised ML can

predict stick-slip frictional failure events –the lab equivalent to earthquakes (Rouet-Leduc et al.,

2017). These works show that the timing of failure events can be predicted with fidelity using

continuous records of the acoustic emissions generated within the fault zone (Rouet-Leduc et al.,

2017; Rouet-Leduc et al., 2018; Hulbert et al., 2018). Stick-slip failure events are preceded by a

cascade of micro-failure events that radiate elastic energy in a manner that foretells catastrophic

failure. Remarkably, this signal predicts the time of failure, the slip duration, and for some events

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the magnitude of slip. However, successful implementation of a supervised ML algorithm demands

access to a large labeled training dataset. Unsupervised ML offers an alternative approach that can

be applied when labeled data are not available.

The purpose of this paper is to explore the application of unsupervised ML to characterize

acoustic emissions during the laboratory seismic cycle and search for precursors to failure. This

approach differs significantly from previous work using supervised ML in which statistical features

are used to build a function that maps an input (statistics of the acoustic signal) to an output (e.g.,

time to failure). Supervised ML involves a training stage followed by a stage in which the algorithm

is tested against new observations. In unsupervised ML, the task at hand is quite different. In our

case, the goal is to find structure (clusters) within the seismic signal and track its evolution

throughout the seismic cycle. Clusters are characterized and identified within a n-dimensional

feature space via a ML clustering algorithm. We employ a mean-shift ML clustering algorithm

(Cheng, 1995; Comaniciu and Meer, 2002) to assess statistical features of the acoustic signal and

compare our results to those obtained using the commonly used k-means clustering algorithm (Tan

et al., 2006). We apply both clustering algorithms to 43 statistical features after conducting a

principal component analysis (PCA). For comparison to our previous work, we perform a second

analysis using only the variance and kurtosis of the acoustic signal identified as the most significant

features in the supervised ML analysis (Rouet-Leduc et al., 2017; Rouet-Leduc et al., 2018; Hulbert

et al., 2018). That is, they improved the accuracy of the ML regression analysis the most out of ~

100 statistical features. Our goal is to assess how robust these features are when attempting to

identify precursors to failure via unsupervised ML. We acknowledge that using results from a

supervised ML study as inputs to an unsupervised ML analysis may violate the truly unsupervised

nature of the analysis. However, we argue that this approach is well warranted as it can help connect

unsupervised and supervised ML approaches. Our work has the potential to improve the

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understanding of laboratory precursors and ultimately to improve methods for seismic hazard

analysis.

3.3 Methods

3.3.1 Friction Stick-Slip Experiments

We use data from frictional experiments conducted in a biaxial deformation apparatus

(Figure 3-1a) using the double-direct shear configuration (DDS) (e.g., Rathbun and Marone, 2010).

Two layers of simulated fault gouge are sheared simultaneously within three forcing blocks that

contain grooves perpendicular to the shear direction to prevent shear at the layer boundary. The

grooves are 0.8 mm deep and spaced every 1.0 mm. The initial gouge layer thickness is ~ 5 mm

and the nominal contact area is 100 x 100 mm2. The center forcing block (15 cm) is longer than the

side blocks (10 cm) so that the friction area remains constant during shear. Our experiment used

glass beads with particle diameters in the range of 104-149 µm to simulate granular fault gouge

(Anthony and Marone, 2005). The gouge layers are bounded by cellophane tape around the edges

and a thin rubber jacket is placed around the bottom half of the sample to help prevent material loss

during shear. In addition, two steel side plates are mounted over the front/back of the layers to

prevent material loss from the sides (Figure 3-1a).

Prior to shearing, the sample assembly is placed in the apparatus and a constant normal

stress boundary condition is applied perpendicular to the gouge layers. Fault normal stress is

maintained constant during shear using using a load-feedback servo-control. After the sample has

compacted, the central forcing block is driven down at a constant velocity to impose fault zone

shear (Figure 3-1a). Displacements parallel and perpendicular to the fault are measured using

direct-current displacement transformers (DCDT), which are coupled directly to the vertical and

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horizontal pistons. Similarly, forces parallel and perpendicular to the fault are measured with load

cells and are mounted in series with vertical and horizontal pistons. Stresses and displacements are

recorded continuously throughout the experiment at 1 kHz with a 24-bit, ±10V data acquisition

system.

We measure elastic waves generated within the fault zones using an array of 36 P-polarized

piezoceramic transducers (Figure 3-1). The sensors (6.35 mm in diameter and 4-mm thick) are

epoxied in the bottom of blind holes within steel blocks that flank the side forcing blocks (Figure

1b). The blind holes (18-mm deep and 8 mm in diameter) are filled with epoxy to hold the sensors

and their respective cables in place (Rivière et al., 2018). The sensor array is located approximately

22 mm from the edge of the gouge layers (Figure 3-1b). Acoustic emission data are sampled

continuously at 4 MHz using a 14-bit Verasonics data acquisition system (Rivière et al., 2018).

Here, we show results from one of the 36 channels, which was chosen as representative based on

calibrations and analysis of all channels.

Our database for these experiments includes over 50 experiments. We focus here on a few

select runs, conducted at constant normal stress of 2.0 MPa and a constant shearing velocity of 10

µm/s. These experiments include many stick-slip cycles. After ~ 10 mm of shear (see upper x-axis

label in Figure 3-2a) slip events include periodic and aperiodic behavior (Figure 3-2a and 3-2b).

We analyze a section of ~ 25 stick-slip cycles of the experiment where the recurrence interval

between failure events is aperiodic (Figure 3-2). These data are representative of our complete data

set. Each stick-slip cycle is characterized by a linear-elastic loading stage followed by inelastic

loading. The departure from linear-elastic loading denotes the onset of fault creep (Anthony and

Marone, 2005; Johnson et al., 2008). We observe a range of failure events including creep, small

stick-slip events and larger events that define the overall lab seismic cycle (Figure 3-2c). Acoustic

data for a representative lab seismic cycle are shown along with a zoom during the linear-elastic

loading stage (Figure 3-3). On average, we detect several thousand AEs including small (Figure 3-

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3c) and large AEs (Figure 3-3d) as defined by their amplitude and duration. We observe a non-

linear increase in the amplitude and number of acoustic events as the fault approaches failure

(Figure 3-3), with AE amplitude increasing by three orders of magnitude (e.g. Rivière et al., 2018).

3.3.2 Unsupervised Machine Learning Analysis of Acoustic Signal

We implement two clustering algorithms to find systematic trends in the continuous

acoustic signal emanating from the fault zone throughout the laboratory seismic cycle. Clustering

is an unsupervised ML analysis used to identify structures within a dataset and partition the data

into distinct groups called clusters based on prescribed similarity measures (Jain et al., 1999). We

focus on statistics of the continuous acoustic signal (features) and use a cluster analysis to find

groups of similar data (clusters). The clusters and their member data points are in general, functions

of all n statistical features that define the feature space as well as the similarity measure.

Our dataset consists of statistical features that quantity both the amplitude and frequency

content of the acoustic emission time series. Following Rouet-Leduc et al., 2017, we compute a

total of 43 statistical features of the acoustic signal using a moving window approach (see Appendix

B for details). Our acoustic data are recorded at 4 MHz and we calculate statistics in a time window

1.36 s in length. Windows overlap by 90% and we use a backward looking approach to time stamp

the data for comparison with our mechanical data (e.g., stress, displacement) recorded at 1 kHz.

The ML analysis is conducted using data between 2067-2337 s; this results in a 1979 by 43 data

matrix. Details of the statistical features along with a sensitivity analysis of window size and

overlap are given in Appendix B.

A range of clustering algorithms are available, many of which make predefined

assumptions about the data that can induce bias (Tan et al., 2006). Specifically, many algorithms

require the number of clusters to be known a priori and assume each cluster is characterized by a

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specific shape (such as an ellipse). To avoid making these assumptions, we implemented the mean-

shift clustering algorithm from scikit-learn, which seeks to identify the modes of the dataset

(Comaniciu and Meer, 2002). In addition to mean-shift, we use the scikit-learn implementation of

a k-means clustering algorithm for comparison.

In mean-shift, modes are found through an iterative process of computing a mean-shift

vector over a spatial region defined by a bandwidth parameter within a n-dimensional feature space.

Since the bandwidth has to be known a priori, we optimize the bandwidth by selecting the value

that yields the highest Silhouette Coefficient (Rousseeuw,1987; Tan et al., 2006; see Appendix B).

In the following we give a brief summary of how this algorithm works in a 2D feature space. For a

more thorough mathematical explanation of the algorithm, we refer readers to Cheng, (1995) and

Comaniciu and Meer (2002). The algorithm commences by computing the mean of data points

within a window of feature space. In this context, window refers to a bounded region in the feature

space. The size of this bounded region is set beforehand via the bandwidth parameter (Cheng, 1995;

Comaniciu and Meer, 2002). The bandwidth sets the size over which the mean is computed within

n-space, and thus, controls the total number of clusters as well as the number of data points mapped

to each cluster (see Appendix B). The mean of the data points within this confined window

corresponds to the densest region in the window. A vector is then defined from the center of the

window to the calculated mean, which is called the mean-shift vector. In the next iteration, the

window is shifted such that the mean of the previous distribution of data points is now the center

of the current window. As a result of this shift, some data points move out of the window while

others move in. Again, the mean of the data points is computed within the window and the mean-

shift vector is calculated. This iterative process continues until the mean-shift vector approaches

zero i.e., the center of the window coincides with the densest region in the feature space. The

process of computing the mean-shift vector over a predefined space is repeated for every data point

within the feature space (i.e., it is initialized for every data point). After this process is completed,

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each data point will be assigned to a specific region (a mode) in the feature space that it converged

to. One way of thinking about this process is that all data points have a trajectory in feature space

that they follow and their final location represents the densest region in feature space based upon

that path. In other words, the total number of modes found after this step will equal the number of

data points. As a final step, the algorithm filters out modes that lie within a bandwidth of one

another. Specifically, the modes which have the least number of data points within them are

removed. The result of this process is a unique set of modes that model the underlying feature

space.

Our analysis consists of clustering all 43 features after performing a PCA. In addition, we

perform a second analysis where we focus on variance and kurtosis, the two most important feature

for predicting instantaneous friction and time to failure of lab earthquakes through supervised ML

(Rouet-Leduc et al., 2017). In fact, the variance alone can accurately predict the instantaneous

frictional state along with the magnitude of slip events (Rouet-Leduc et al. 2018; Hulbert et al.,

2018) as illustrated in Figure 3-4. In our analysis, we use the logarithms of the variance and kurtosis

as a way to normalize their values, given that kurtosis ranges up to >104 while variance is typically

an order of magnitude smaller. If clustering is performed without normalization, the results would

be biased towards kurtosis (see Appendix B). The purpose of this second study is to compare the

supervised and unsupervised ML approaches. It is established that a supervised ML technique can

predict lab earthquakes, and hence that the acoustic signal contains information about impending

failure during all times of the seismic cycle. In this work, we seek to determine if unsupervised ML

can identify patterns and precursors to failure. To our knowledge, using unsupervised ML to

identify precursors to stick-slip failure is a new approach that has yet to be explored. Moreover, an

unsupervised ML approach could be more applicable to field data, where labeled data (i.e shear

stress, time to failure, etc.) are typically unavailable.

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3.3.3 Clustering in Principal Component Space

To test the full set of 43 statistical features, we perform a principal component analysis

(PCA). PCA offers several incentives for our analysis. First, it identifies the most important features

for explaining the data variance. Second, it enables us to reduce the dimensionality of our problem

while still exploiting all 43 features. Lastly, it identifies correlated features. After performing the

PCA, we can project our dataset into a lower dimension principal component space and perform

the clustering analysis in this space. Specifically, PCA is an eigenvalue decomposition of the

covariance matrix. Before calculating the covariance matrix, the original 1479 by 43 data matrix is

normalized by subtracting the mean and dividing by the standard deviation. The decomposition of

this covariance matrix gives a set of eigenvalues and eigenvectors (principal components), both of

which can be used to describe the structure of the data. In particular, each principal component

(PC) is a linear combination of the original features, scaled by an eigenvector coefficient (see

Supplement). In addition, the PCs are ordered such that by selecting the first few PCs we can

capture most of the data variance (see Figure 3-5c) while reducing the dimensionality of the

problem.

Our PCA results show that the first two PCs account for about 85% of the total data

variance (Figure 3-5c). This implies that we can represent our original 43-D space in a 2-D PC

space (Figure 3-5). When projected into the 2-D PC space, the acoustic data appear in groups of

different shape and density. For example, a subset of data points form distinct streaks that extend

from the top left to the bottom right of this space. A careful examination of the temporal trends of

PC 1 and PC 2 shown in Figure 3-5b reveal that these data points correspond to the inter-seismic

period. The remaining data points in Figure 3-5d represent data from the co-seismic slip phase.

These data have a different structure compared to the inter-seismic period and plot in a different

region within the feature space (i.e on the left-hand side of Figure 3-5d). Note that all data from

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Figure 3-2b are plotted in Figure 3-5d, and thus, it is clear that these trends are remarkably

systematic across multiple lab earthquake cycles. We use clustering to identify such patterns in the

acoustic data statistics and study them in relation to the seismic cycle.

3.4 Results

In Figure 3-6, we demonstrate how mean-shift and k-means partition both feature spaces

explored in this study. The mean-shift algorithm identifies two clusters (defined by the red and

cyan symbols) with respect to variance and kurtosis (Figure 3-6a). The red cluster is defined by

areas of low-variance and kurtosis values and the cyan cluster defines areas of high-variance and

kurtosis. When using k-means the number of clusters the algorithm finds must be set a-priori (Tan

et al., 2006). Therefore, we use the Silhouette Coefficient to find the optimal number of clusters.

That is, we select the number of clusters that results in the highest Silhouette Coefficient. In

variance-kurtosis space (Figure 3-6c), k-means also partitions the data into two clusters. More

interestingly, the two sets of clusters found by the two algorithms in variance-kurtosis space are

identical (Figure 3-6c). Figure 3-6b and 3-6d show how both algorithms partition the data in PC

space. The mean-shift identifies a total of four clusters (denoted by yellow-magenta-green-blue

symbols).

Although the boundaries between clusters may seem arbitrary in this space, when plotted

as a function of time or shear stress, it becomes clear that these boundaries mark specific transitions

with respect to the stress state (Figure 3-7 and Figure 3-8). We cluster the same data using the k-

means algorithm with the number of clusters set to three. Again, we determine the number of

clusters based on the maximum Silhouette Coefficient. Despite the differences in the number of

identified clusters, the results from the two algorithms are effectively the same; the only differences

lie in how the algorithms partition the data associated with the co-seismic slip phase (i.e green-blue

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data points). For mean-shift the co-seismic data are partitioned into two clusters (blue-green),

whereas with k-means these data are partitioned into only one cluster (green). Since we are

primarily interested in identifying precursors to failure, the data associated with the co-seismic

phase are of less importance. Furthermore, we have conducted the same analysis using a spectral

clustering algorithm and achieved similar results. Therefore, we argue that our analysis does not

depend on the choice of the clustering algorithms. From here forward, we present all results with

respect to mean-shift.

As previously stated, the mean-shift analysis identifies four clusters in PC space (Figure 3-

6b). To observe how clusters evolve temporally over the course of the lab seismic cycle, we plot

data from Figure 3-6b as a function of time together with shear stress (Figure 3-7). The yellow and

magenta clusters coincide with the linear-elastic loading and creep stages while the green and blue

clusters coincide with the main slip events (Figure 3-7). Clustering in PC space also reveals

precursory changes in the acoustic signal as the fault approaches failure, and as result we observe

that the inter-seismic period of each slip cycle is characterized by two clusters (Figures 3-7 and 3-

8). When performing the same analysis with respect to variance and kurtosis we did not observe

such systematic change in clusters (Figure B10). Specifically, when clustering data in variance-

kurtosis space, we observe two clusters prior to the main slip event only when there are small

instabilities during aseismic creep. In contrast, the systematic transitions of clusters in PC space are

observed for every slip cycle analyzed. In addition, both PC 1 and PC 2 show similar precursory

trends (see Appendix B for PC 2 results plotted with time).

Figures 3-7 and 3-8 suggest that the partitioning of the acoustic data into four clusters is

purely a function of position within the stick-slip cycle. Specifically, the yellow and magenta

cluster correspond to the linear and non-linear loading stages of the stick-slip cycle, while the

green and blue clusters mark the slip event (Figure 3-7). The transition from yellow to magenta

clusters occurs once the fault has reached peak strength and the shear stress is no longer

67

increasing. This is an interesting discovery given that the clustering algorithm has no input on the

stress state of the fault, yet the results clearly show when the fault has reached its peak strength

(Figure 3-8). Finally, the division between the green and blue clusters occurs during the co-

seismic stage, as the fault evolves from a large (green cluster) to a small (blue cluster) shear

stress.

3.5 Discussion

We show that an unsupervised ML approach based on a clustering analysis of acoustic data

define distinct clusters that evolve systematically during the lab seismic cycle. Clustering in PC

space partitions the dataset into four clusters, including two distinct clusters for the inter-seismic

period (Figure 3-7a, 3-7b, and Figure 3-8). The temporal evolution of these clusters shows that

within each seismic cycle there is a cluster transition once the fault begins to creep at a shear stress

near its maximum value, followed by separate transitions during the main failure event (Figure 3-

7 and Figure 3-8). The cluster transitions for PC 1 and PC 2 provide information about what stage

the fault is in within its seismic cycle, and thus, could be identified as potential precursors to failure.

Specifically, the yellow cluster is associated with shear loading, and thus, indicates that the fault is

in its earliest stage of the seismic cycle (Figure 3-8). While the magenta cluster is associated with

the latter stages of the seismic cycle and denotes that the fault is creeping and is close to failure

(Figure 3-8).

In a previous study, we found that out of ~100 statistical features, the variance and kurtosis

are the most important features when building the ML regression model. However, this study

demonstrates that the clustering of data based on these two features is unable to identify precursors

(Figure B10). Despite the fact that the resulting clusters define a systematic pattern during the

seismic cycle, the transition between clusters occurs after failure, and thus, provides no precursory

68

information to failure (Figure B10). The majority of the laboratory seismic cycle is mapped into

one cluster, while small segments associated with slip events are assigned to another cluster. This

implies that even though signal variance and kurtosis are evolving throughout the course of a stick-

slip cycle these parameters do not change enough to result in separate clusters.

We show that the differences between clustering in PC space and clustering in variance-

kurtosis space are from the features themselves and not the number of clusters (see Appendix B for

details). The data suggest that while it is possible to identify four clusters when clustering in

variance-kurtosis space, the clusters themselves are not systematic across multiple slip cycles. In

particular, one of the clusters is associated with only 5 slip cycles. Moreover, none of the four

identified clusters in the variance-kurtosis space are correlated to fault strength. Therefore, we

hypothesize that the differences found in the PCA result from differences in the features themselves

and not the number of clusters found.

One potential drawback of clustering in PC space is the loss of a physical meaning behind

the clusters; because each principal component is a linear combination of 43 features scaled by an

eigenvector coefficient. Our data show that the coefficients for the first two PCs are similar for

most features, implying that they are equally important in explaining the data variance (see

Appendix B). However, several of the amplitude-based features in PC 1 and PC 2 have large

coefficients relative to other features, indicating that they are more important relative the other

features in explaining the data variance.

Our ML approach compares well with the traditional approach of monitoring failure in the

laboratory using the b-value of AE events (Goebel et al., 2013; Rivière et al., 2018). However, our

approach extends to both quasi-periodic failure events and aperiodic failure events with significant

fault creep and minor events associated with small stress drops (Figure 3-8). A key problem with

application of b-value to failure prediction is that it often shows a continuous decrease as failure

approaches (Goebel et al., 2013; Rivière et al., 2018), without any clear connection to the time to

69

failure. The clustering in variance-kurtosis space shows a similar limitation, but results in PC space

suggest that with additional features the cluster transitions could be related quantitatively to the

time to failure.

A comparison of the methods explored in this study suggests that clustering in PC space

offers a more systematic and reliable precursory trends to failure. The clusters defined by the PCs

show systematic changes as failure approaches. These changes occur for every slip cycle analyzed

and they occur at the same points during the lab seismic cycle (Figure 3-8). However, further work

is needed to provide better temporal resolution and to document precursory trends for a wider range

of conditions. One possibility is that additional information could be found using another ML

algorithm, different statistical features, or with a more direct connection between an unsupervised

ML approach and supervised ML. These are useful directions for further study.

3.6 Conclusions

We explore the use of unsupervised machine learning for characterizing acoustic signals

during the laboratory seismic cycle. We apply an unsupervised ML technique to a known data set,

for which supervised machine learning can predict the time to failure for repetitive failure events.

Overall, the unsupervised approach is less informative of the physical state of the fault than its

supervised counterpart. However, the unsupervised ML cluster analysis is successful in identifying

patterns in the statistics of acoustic signals throughout the seismic cycle when using all 43 statistical

features. Clusters formed from the two most important features identified by supervised ML

analysis, variance and kurtosis, define transitions but these do not provide reliable, new information

on impending failure. However, the ML cluster analysis using the two primary eigenvectors

defined by a principal component analysis of all 43 statistical features of the continuous acoustic

70

signal, reveals clear precursors to failure. The precursors are identified in all slip cycles analyzed

and occur once the fault has reached its peak strength.

Both of our cluster analyses are consistent with temporal trends observed in the seismic b-

value over the complete cycle of shear loading to failure (Rivière et al., 2018). We find that while

it is possible to infer the stress state of a laboratory fault during the laboratory seismic cycle with

supervised ML, such detailed information cannot be found when feeding the same statistics into an

unsupervised machine learning algorithm. Nonetheless, the simplicity of unsupervised ML

compared to supervised approaches and the fact that it does not require large labeled training

datasets is likely to make it a valuable, complementary tool when tackling large-scale data. Our

work shows that unsupervised ML algorithms hold promise for identifying precursors to seismic

failure; however, further work is necessary to develop this approach into a reliable tool that could

have an impact in seismic hazard analysis.

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Figure 3-1: (a). Biaxial shear apparatus with the double-direct shear configuration. Normal and shear forces on the fault are measured with strain-gauge load cells mounted in series with the horizontal and vertical pistons. Displacements parallel and perpendicular to the fault are measured with direct-current displacement transformers (DCDT) coupled to the vertical and horizontal pistons respectively. (b). Sample configuration with two gouge layers placed between three steel loading platens. Piezoceramic sensors (PZT) are embedded within steel blocks that transmit the fault normal stress.

Horizontal DCDT

Multi-channel PZT Blocks

Vertical DCDT

(a)

(b)

72

Figure 3-2: (a). Shear stress evolution for one entire experiment. Slip events transition from periodic to aperiodic to stable sliding as a function of load-point displacement. We focus on the section of aperiodic lab earthquakes shown in panel (b). Note that inter-event times vary and that large events are often preceded by small foreshocks. (c). Zoom of three seismic cycles with aseismic creep and foreshocks prior to the main event.

(c)

p4677(a)

(b)

5 s

73

Figure 3-3: (a). Shear stress and acoustic amplitude plotted for one slip cycle within the aperiodic section of the experiment (see Figure 2.). Grey box shows a 1.36-s moving window used to compute statistical features of the acoustic signal. (b). Zoom of the window. Note that the signal is dominated by spikes that look like noise at this scale. (c). Small AEs occur frequently throughout all stages of the seismic cycle. (d). Large AEs occur during all stages of the laboratory seismic cycle; however, they are more commonly associated with the inelastic loading stage just prior to failure (see Figure 3-2).

Figure 3-4: Shear stress as a function of time (red dashed line) plotted with the machine learning prediction (blue line) for experiment p4679. Here, a supervised ML algorithm (gradient boosted tree algorithm) is used to estimate the instantaneous shear stress based on similar statistical features used in this study (see Supplement). The tight correlation between measurements and the ML prediction shows that the acoustic signal contains important information regarding the physical state of the fault during all stages of the lab seismic cycle. (After Hulbert et al., 2018)

5.1

5.0

4.9

4.84400 4450 4500

Time (s)

Stre

ss (M

Pa)

p4679

ML modelExperimental Data

75

Figure 3-5: (a) Shear stress evolution and acoustic amplitude for one stick-slip cycle in experiment p4677. Grey box shows a moving window that slides through the continuous time series (4 MHz sampling rate) and is used to compute statistical features of the acoustic signal. We use the end time of each window for the time stamp associated with the window. (b) Temporal evolution of PC 1 (black) and PC 2 (red) throughout one stick-slip cycle shown in (a). Grey box with circles shows the time stamp derived from the moving window in (a). (c) Cumulative eigenvalue percentage plotted versus number of principal components. The first two principal components account for about 85% of the data variance. (d) Data for all slip cycles between 2067-2337 s (Figure 3-2b) in PC 1-PC 2 space (black symbols). Highlighted in red are data for the slip cycle shown in panel a.

76

Figure 3-6: a-b. Data for all stick-slip cycles analyzed in this study (see Figure 3-2b) after clustering with a mean-shift algorithm. (a) Results for acoustic variance and kurtosis. The red cluster encompasses all data that are not associated with a lab earthquake, while the cyan cluster classifies the acoustic data associated with both foreshocks and mainshocks. (see Figure 3-2c). (b) Results for PC 1 and PC 2 after clustering in principal component space. Each point represents a linear combination of the 43 statistical features and each color corresponds to a single cluster. The yellow and purple cluster classify the acoustic signal associated with the linear-elastic and inelastic loading stages of each seismic cycle, while the green and blue clusters classify the acoustic data associated with the co-seismic phase. c-d. Results after clustering with a k-means algorithm. In each case, we determine the number of clusters by optimizing the Silhouette Coefficient as a function of the number of clusters (see Supplement). Note, that the results are identical for k-means and mean-shift when clustering in variance-kurtosis space. When clustering in PC space the acoustic data associated with the inter-seismic period (i.e yellow and purple clusters) are independent of the choice of clustering algorithm. However, the co-seismic data are partitioned differently by the two clustering algorithms (i.e green and blue cluster).

77

Figure 3-7: (a) Temporal evolution of clusters with respect to PC 1 (see supplement for results for PC 2). Shear stress curves are color coded corresponding to their respective cluster color defined by PC 1 and PC 2. The clusters reveal a distinct and systematic temporal trend as failure approaches. (b) Zoom showing details of how the clusters evolve as failure approaches. The early stages of the inter-seismic period are mapped to the yellow cluster, while the latter stages are mapped to the magenta cluster. The co-seismic phase is further divided into the green and blue clusters.

(b)

(a)

78

Figure 3-8: Comparison of PC 1 and PC 2 as a function of shear stress. In both panels, we plot data for all seismic cycles analyzed in this study (Figure 3-2b), color coded by cluster. Note that the partitioning of data into clusters by the ML algorithm is reproducible across multiple lab seismic cycles and labquakes. Plotting the acoustic data as a function of shear stress illuminates the relationship between cluster transitions (e.g yellow to purple) and it becomes clear that the transition from yellow to magenta occurs once the fault has reached its peak strength. Acoustic data associated with the co-seismic phase are mapped to the green and blue clusters.

(a)

(b)

79

3.7 References

Anthony, J. L., & Marone, C. (2005). Influence of particle characteristics on granular friction. Journal of

Geophysical Research: Solid Earth, 110(B8).

Antonioli, A., Piccinini, D., Chiaraluce, L., & Cocco, M. (2005). Fluid flow and seismicity pattern:

Evidence from the 1997 Umbria-Marche (central Italy) seismic sequence. Geophysical Research

Letters, 32(10), L10311. https://doi.org/10.1029/2004GL022256

Bouchon, M., Durand, V., Marsan, D., Karabulut, H., & Schmittbuhl, J. (2013). The long precursory

phase of most large interplate earthquakes. Nature geoscience, 6(4), 299.

Chen, J. H., Froment, B., Liu, Q. Y., & Campillo, M. (2010). Distribution of seismic wave speed changes

associated with the 12 May 2008 Mw 7.9 Wenchuan earthquake: wave speed changed by the

Wenchuan earthquake. Geophysical Research Letters, 37(18), L18302.

https://doi.org/10.1029/2010GL044582

Chen, W. Y., Lovell, C. W., Haley, G. M., & Pyrak-Nolte, L. J. (1993). Variation of shear-wave

amplitude during frictional sliding. In International journal of rock mechanics and mining sciences &

geomechanics abstracts (Vol. 30, No. 7, pp. 779-784).

Cheng, Y., (1995) Mean shift, mode seeking, and clustering, IEEE Transactions on Pattern Analysis and

Machine Intelligence, vol 17, No 8.

Comaniciu, D., Ramesh, V., & Meer, P. (2001). The variable bandwidth mean shift and data-driven scale

selection. In Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference

on (Vol. 1, pp. 438-445). IEEE.

Comaniciu, D., & Meer, P. (2002). Mean shift: A robust approach toward feature space analysis. IEEE

Transactions on pattern analysis and machine intelligence, 24(5), 603-619.

80

Cui, Y., Ouzounov, D., Hatzopoulos, N., Sun, K., Zou, Z., & Du, J. (2017). Satellite observation of CH4

and CO anomalies associated with the Wenchuan MS 8.0 and Lushan MS 7.0 earthquakes in China.

Chemical Geology, 469, 185–191. https://doi.org/10.1016/j.chemgeo.2017.06.028

Faillettaz, J., Funk, M., & Vincent, C. (2015). Avalanching glacier instabilities: Review on processes and

early warning perspectives. Reviews of geophysics, 53(2), 203-224.

Faillettaz, J., Or, D., & Reiweger, I. (2016). Codetection of acoustic emissions during failure of

heterogeneous media: New perspectives for natural hazard early warning. Geophysical Research

Letters, 43(3), 1075-1083.

Goebel, T. H. W., Sammis, C. G., Becker, T. W., Dresen, G., & Schorlemmer, D. (2015). A comparison

of seismicity characteristics and fault structure between stick–slip experiments and nature. Pure and

Applied Geophysics, 172(8), 2247-2264.

Goebel, T. H. W., Schorlemmer, D., Becker, T. W., Dresen, G., & Sammis, C. G. (2013). Acoustic

emissions document stress changes over many seismic cycles in stick-slip experiments. Geophysical

Research Letters, 40(10), 2049-2054, doi:10.1029/2010/GL043066.

Gutenberg, B., & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of the

Seismological Society of America, 34(4), 185-188.

Hedayat, A., Pyrak-Nolte, L. J., & Bobet, A. (2014). Precursors to the shear failure of rock

discontinuities. Geophysical Research Letters, 41(15), 5467-5475.

Holtzman, B. K., Paté, A., Paisley, J., Waldhauser, F., & Repetto, D. (2018). Machine learning reveals

cyclic changes in seismic source spectra in Geysers geothermal field. Science advances, 4(5),

eaao2929.

81

Hulbert, C., Rouet-Leduc, B., Johnson, P. A., Ren, C. X., Rivière, J., Bolton, D. C., & Marone, C. (2019).

Similarity of fast and slow earthquakes illuminated by machine learning. Nature Geoscience, 12(1),

69.

Jain, A. K., Murty, M. N., & Flynn, P. J. (1999). Data clustering: a review. ACM computing surveys

(CSUR), 31(3), 264-323.

Jiang, Y., Wang, G., & Kamai, T. (2017). Acoustic emission signature of mechanical failure: Insights

from ring-shear friction experiments on granular materials. Geophysical Research Letters, 44(6),

2782-2791.

Johnson, P. A., Savage, H., Knuth, M., Gomberg, J., & Marone, C. (2008). Effects of acoustic waves on

stick–slip in granular media and implications for earthquakes. Nature, 451(7174), 57.

Johnson, P.A., Ferdowsi, B., Kaproth, B.M., Scuderi, M.M., Griffa, M., Carmeliet, J., Guyer, R.A., Le

Bas, P-Y., Trugman, D.T., & Marone, C. (2013). Acoustic emission and microslip precursors to stick-

slip failure in sheared granular material. Geophysical Research Letters, 40(21), 5627-5631, doi:

10.1002/2013GL057848.

Jolliffe, I. (2011). Principal component analysis. In International encyclopedia of statistical science (pp.

1094-1096). Springer, Berlin, Heidelberg.

Kaproth, B. M., & Marone, C. (2013). Slow earthquakes, preseismic velocity changes, and the origin of

slow frictional stick-slip. Science, 341(6151), 1229-1232.

Mair, K., Marone, C., & Young, R. P. (2007). Rate dependence of acoustic emissions generated during

shear of simulated fault gouge. Bulletin of the seismological Society of America, 97(6), 1841-1849,

doi:10.1785/0120060242.

Martinelli, G., & Dadomo, A. (2017). Factors constraining the geographic distribution of earthquake

geochemical and fluid-related precursors. Chemical Geology, 469, 176-184.

82

Marzocchi, W. Predictive Seismology. Seismological Research Letters.

McLaskey, G. C., & Lockner, D. A. (2014). Preslip and cascade processes initiating laboratory stick

slip. Journal of Geophysical Research: Solid Earth, 119(8), 6323-6336.

Milne, J. (1899). Earthquake Precursors. Nature, 59(1531), 414.

Moro, M., Saroli, M., Stramondo, S., Bignami, C., Albano, M., Falcucci, E., ... & Macerola, L. (2017).

New insights into earthquake precursors from InSAR. Scientific Reports, 7(1), 12035.

Niu, F., Silver, P. G., Daley, T. M., Cheng, X., & Majer, E. L. (2008). Preseismic velocity changes

observed from active source monitoring at the Parkfield SAFOD drill site. Nature, 454(7201), 204.

Poli, P. (2017). Creep and slip: Seismic precursors to the Nuugaatsiaq landslide (Greenland). Geophysical

Research Letters, 44(17), 8832-8836.

Pyrak-Nolte, L. (2006, January). Monitoring a Propagating Front: Exploiting Fresnel Precursors from

Fractures. In Golden Rocks 2006, The 41st US Symposium on Rock Mechanics (USRMS). American

Rock Mechanics Association.

Rathbun, A. P., & Marone, C. (2010). Effect of strain localization on frictional behavior of sheared

granular materials. Journal of Geophysical Research: Solid Earth, 115(B1)

Renard, F., Cordonnier, B., Kobchenko, M., Kandula, N., Weiss, J., & Zhu, W. (2017). Microscale

characterization of rupture nucleation unravels precursors to faulting in rocks. Earth and Planetary

Science Letters, 476, 69-78.

Renard, F., Weiss, J., Mathiesen, J., Ben-Zion, Y., Kandula, N., & Cordonnier, B. (2018). Critical

Evolution of Damage Toward System-Size Failure in Crystalline Rock. Journal of Geophysical

Research: Solid Earth, 123(2), 1969-1986.

83

Rivet, D., Campillo, M., Shapiro, N. M., Cruz-Atienza, V., Radiguet, M., Cotte, N., & Kostoglodov, V.

(2011). Seismic evidence of nonlinear crustal deformation during a large slow slip event in

Mexico. Geophysical Research Letters, 38(8).

Rivière, J., Lv, Z., Johnson, P. A., & Marone, C. (2018). Evolution of b-value during the seismic cycle:

Insights from laboratory experiments on simulated faults. Earth and Planetary Science Letters, 482,

407-413.

Rouet-Leduc, B., Hulbert, C., Bolton, D. C., Ren, C. X., Riviere, J., Marone, C., ... & Johnson, P. A.

(2018). Estimating Fault Friction From Seismic Signals in the Laboratory. Geophysical Research

Letters, 45(3), 1321-1329.

Rouet-Leduc, B., Hulbert, C., Lubbers, N., Barros, K., Humphreys, C. J., & Johnson, P. A. (2017).

Machine learning predicts laboratory earthquakes. Geophysical Research Letters, 44(18), 9276-9282.

Rousseeuw, P. J. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster

analysis. Journal of computational and applied mathematics, 20, 53-65.

Scholz, C. H. (1968). The frequency-magnitude relation of microfracturing in rock and its relation to

earthquakes, Bulletin of the Seismological Society of America, 58(1), 399-415.

Scholz, C. H. (2015). On the stress dependence of the earthquake b value. Geophysical Research

Letters, 42(5), 1399-1402.

Scuderi, M.M., Marone, C., Tinti, E., Stefano, G. Di., & Collettini, C. (2016). Seismic velocity changes

reveal precursors for the spectrum of earthquake failure modes. Nature geoscience, 9(9), 695,

doi:10.1038/NGEO02775.

Singh, M. K., & Ahuja, N. (2003, October). Regression based Bandwidth Selection for Segmentation

using Parzen Windows. In ICCV (pp. 2-9).

Tan, P. N., Steinbach, M., & Kumar, V. (2006). Introduction to Data Mining.

84

Tinti, E., Scuderi, M. M., Scognamiglio, L., Di Stefano, G., Marone, C., & Collettini, C. (2016). On the

evolution of elastic properties during laboratory stick-slip experiments spanning the transition from

slow slip to dynamic rupture. Journal of Geophysical Research: Solid Earth, 121(12), 8569-8594.

Weeks, J., Lockner, D., & Byerlee, J. (1978). Change in b-values during movement on cut surfaces in

Granite. Bulletin of the Seismological Society of America, 68(2), 333-341.

Wu, Y., Lin, Y., Zhou, Z., Bolton, D. C., Liu, J., & Johnson, P. (2018). DeepDetect: A Cascaded Region-

Based Densely Connected Network for Seismic Event Detection. IEEE Transactions on Geoscience

and Remote Sensing, (99), 1-14.

Xie, S., Dixon, T. H., Voytenko, D., Holland, D. M., Holland, D., & Zheng, T. (2016). Precursor motion

to iceberg calving at Jakobshavn Isbræ, Greenland, observed with terrestrial radar interferometry.

Journal of Glaciology, 62(236), 1134–1142. https://doi.org/10.1017/jog.2016.104

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Chapter 4

Acoustic Energy Release During the Laboratory Seismic Cycle: Insights on Laboratory Earthquake Precursors and Prediction

Reprinted with permission from Journal of Geophysical Research: Solid Earth and may be cited as Bolton, D. C., Shreedharan, S., Rivière, J., & Marone, C. (2020). Acoustic Energy Release During the Laboratory Seismic Cycle: Insights on Laboratory Earthquake Precursors and Prediction. Journal of Geophysical Research: Solid Earth, 125(8), e2019JB018975.

4.1 Abstract

Machine learning (ML) can predict the timing and magnitude of laboratory earthquakes using

statistics of acoustic emissions (AE). The evolution of acoustic energy is critical for lab earthquake

prediction, however, the connections between acoustic energy and fault zone processes leading to failure

are poorly understood. Here, we document in detail the temporal evolution of acoustic energy during the

laboratory seismic cycle. We report on friction experiments for a range of shearing velocities, normal

stresses and granular particle sizes. AE data are recorded continuously throughout shear using broadband

piezo-ceramic sensors. The co-seismic acoustic energy release scales directly with stress drop and is

consistent with concepts of frictional contact mechanics and time dependent fault healing. Experiments

conducted with larger grains (10.5 µm), show that the temporal evolution of acoustic energy scales directly

with fault slip rate. In particular, the acoustic energy is low when the fault is locked and increases to a

maximum during co-seismic failure. Data from traditional slide-hold-slide friction tests confirm that

acoustic energy release is closely linked to fault slip rate. Furthermore, variations in the true contact area

of fault zone particles play a key role in the generation of acoustic energy. Our data show that acoustic

radiation is related primarily to breaking/sliding of frictional contact junctions, which suggests that ML-

based laboratory earthquake prediction derives from frictional weakening processes that begin very early

in the seismic cycle and well before macroscopic failure.

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4.2 Introduction

A key goal of earthquake forecasting has been to identify temporal variations in the physical

properties within and around tectonic faults (so called seismic precursors). Yet, despite long-term interest

in this problem, there has been little progress in identifying systematic and reliable precursors to earthquake

failure (Milne, 1899; Rikitake, 1968; Scholz et al., 1973). Several studies have documented the complexity

of this problem and the lack of success in identifying robust earthquake precursors (e.g., Bakun et al., 2005).

Nevertheless, temporal changes in wave-speed and seismicity (eg. foreshocks, preseismic slip) have been

observed, in hindsight, prior to earthquake failure (Niu et al., 2008; Brenguier et al., 2008; Chen et al.,

2010; Papadopoulos et al., 2010; Nanjo et al., 2012; Gulia et al., 2016; Gulia and Wiemer, 2019).

Furthermore, recent studies based on machine learning (ML) show that the timing, instantaneous shear

stress and in some cases the magnitude of laboratory earthquakes can be predicted using statistics of the

continuous acoustic emission (AE) signal emanating from the fault zone (Rouet-Leduc et al., 2017, 2018;

Lubbers et al., 2018; Hulbert et al., 2019.) The lab based studies are simplified analogs to tectonic faulting,

but there are enough similarities between lab events and earthquakes (e.g., Brace and Byerlee, 1966; Scholz,

1968) to warrant further study.

Previous ML works demonstrate that the variance of the acoustic signal, which is a proxy for the

average acoustic energy per unit time, is a key parameter for successful lab earthquake prediction (Figure

4-1; Rouet-Leduc et al. 2018; Hulbert et al. 2019). Of the ~ 100 statistical features tested, AE signal

variance was found to be the most important predictor of shear stress and fault failure time (Rouet-Leduc

et al. 2017, 2018). Despite these observations, it is unclear how AE signal variance is connected to the

physical state of the fault. In particular, the mechanisms of AE radiation and their evolution during the

seismic cycle, which provides the physical basis for lab earthquake prediction, are unknown (Figure 4-1B

and 4-1C). Answers to such questions will help illuminate the mechanisms behind seismic precursors, and

thus, improve our physical understanding of ML-based predictions of laboratory earthquakes.

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There are strong parallels between ML-based lab earthquake prediction and previous laboratory

studies that have focused on the spatiotemporal evolution of seismic precursors to laboratory earthquakes

(Weeks et al., 1978; Rubinstein et al., 2007, 2009; Latour et al., 2011, 2013; Goebel et al. 2013; Johnson et

al., 2013, Kaproth and Marone, 2013, Goebel et al., 2015; Scuderi et al., 2016; Tinti et al., 2016; Renard et

al., 2017; Rivière et al., 2018; Bolton et al., 2019; Shreedharan et al., 2020). In particular, passive acoustic

measurements show that there are pervasive foreshocks that precede most laboratory earthquakes. Both the

frequency and magnitude of the foreshocks increase before the main slip event, and as a result, the

Gutenberg-Richter b-value decreases systematically before failure (Scholz 1968, Weeks et al., 1978;

Ohnaka and Mogi, 1982; Main et al. 1989; Lockner et al., 1991, Sammonds et al., 1992; Thompson et al.

2005; Thompson et al. 2009; Johnson et al., 2013; Goebel et al., 2013; McLaskey and Lockner, 2014; Lei

and Ma, 2014; Goebel et al., 2015; Jiang et al., 2017; Rivière et al., 2018). In addition, active source

measurements show clear precursory changes in fault zone properties, such as elastic wave speed prior to

failure (Gupta 1973; Whitcomb et al. 1973; Lockner et al. 1977; Crampin et al. 1984; Niu et al. 2008;

Kaproth and Marone, 2013; Scuderi et al., 2016; Tinti et al., 2016; Shreedharan et al., 2019; Shreedharan

et al., 2020). Previous studies have demonstrated that micro-factures nucleate and coalesce prior to rock

failure (Brace and Bombolakis, 1963; Tapponnier and Brace, 1978; Scholz 1998; Patterson and Wong,

2005). In addition, recent experiments have illuminated this process in higher detail using x-ray

microtomography (Renard et al., 2017,2018). Thus, numerous observations indicate that laboratory

earthquakes are preceded by a preparation phase that involves physical changes in the fault zone; however,

the underlying mechanisms and the physical processes that cause precursors and allow prediction are poorly

understood.

Here, we report on a suite of friction experiments to illuminate the physical mechanisms that control

the evolution and magnitude of acoustic energy released during frictional sliding. We study both stable

frictional sliding and unstable stick-slip sliding. Stick-slip experiments were conducted over a range of

boundary conditions to explore the physical properties that dictate the evolution of the acoustic energy. We

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augment data from frictional sliding experiments with slide-hold-slide frictional tests in order to show that

acoustic radiation during the lab seismic cycle may be primarily controlled by processes at frictional contact

junctions.

4.3 Methods

We report on a suite of friction experiments on quartz powder conducted in a double-direct shear

(DDS) configuration (Inset to Figure 4-1A). In this configuration, two layers of fault gouge are sheared at

constant fault normal stress between rough, steel forcing blocks (e.g., Frye and Marone, 2002). Our

experiments are conducted at constant shear velocity, which involves controlling the velocity of the fault

zone boundary (Figure 4-1A) with a fast-acting servo-controlled ram. We varied normal stresses from 6-11

MPa, shearing velocities from 2-60 µm/s and median grain sizes from 1.7-10.5 µm (Table 4-1). Forces and

displacements were measured continuously at 1 kHz with strain-gauge load cells and direct current

displacement transformers (DCDT). Fault slip was measured with a DCDT attached directly to the center

forcing block of the DDS assembly and referenced to the bottom of the load frame (Leeman et al. 2018;

Figure 4-1A). Fault slip velocity is computed using a moving window approach on the data recorded by the

DCDT mounted directly to the center block. To eliminate variation between experiments due to humidity

(e.g., Frye and Marone, 2002) all tests were conducted at 100% relative humidity. Prior to each experiment,

both layers were placed inside a plastic bag with a 1:2 sodium carbonate and water solution and allowed to

sit overnight for 12-15 hours. To ensure constant relative humidity throughout the experiment, humid air

was blown into a plastic chamber around the loading blocks.

Gouge layers were constructed using cellophane tape and a leveling jig (e.g., Karner and Marone,

1998; Anthony and Marone, 2005). In addition, side plates were mounted between the side blocks and

center block to limit extrusion of material along those edges. After the sample was humidified overnight,

the DDS assembly was placed inside the load frame and a normal force was applied perpendicular to the

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sample. The sample was then left to compact for 30-40 minutes until the layer thickness reached a steady-

state value. Once the sample reached a constant layer thickness, the center block was driven down to induce

a prescribed shear velocity at the layer boundary.

We observe a spectrum of slip behaviors from stable sliding to unstable stick-slip instabilities,

which are the lab equivalent of earthquakes. For stick-slip sliding, we observe a continuum of behaviors

ranging from slow slip to fast, dynamic slip events (Scholz et al. 1972; Leeman et al., 2015; Leeman et al.,

2016; Scuderi et al., 2016; Leeman et al., 2018). To produce a spectrum of slip behaviors, we modulate the

loading stiffness k, by placing an acrylic spring in series with the vertical ram, such that our effective loading

stiffness is equal to the critical frictional weakening rate, kc (Gu et al., 1984; Leeman et al., 2015; Leeman

et al., 2016).

We measured acoustic emissions continuously throughout the experiment using broad-band

(~.0001-2 MHz) lead-zirconate-titanate (PZT) piezoceramic sensors (Riviere et al., 2018). The

piezoceramic sensors (12.7 mm diameter; 4 mm thick) are embedded inside steel blocks and placed ~ 18

mm from the fault zone (Rivière et al., 2018; Bolton et al., 2019). Acoustic data were recorded continuously

throughout the experiment at 4 MHz using a 15-bit Verasonics data acquisition system. Our experiments

include data from two sensors. We conducted many calibration experiments and tests and found only minor

differences between the sensors (Rivière et al., 2018). Thus, we focus here on data from one sensor.

The acoustic variance, AV, (Eq. 4-1) is calculated as:

Av = $V∑ (𝑎3 − 𝑎X)YV

3Z$ (4-1)

where ai is the amplitude of the time series signal at index i, N is the number of data points

considered in a moving window and 𝑎X is the mean value in the window of size N (Rouet-Leduc et al., 2017,

2018; Hulbert et al., 2019). In this work, we use the terms variance and acoustic energy interchangeably

since variance is proportional to the acoustic energy release. We use a moving window on the acoustic

time series data to compute the acoustic variance. The size of the moving window is selected such that it is

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less than or equal to 10% of the recurrence interval. This approach ensures that the windows are small

relative to the recurrence interval of the seismic cycle. Each moving window overlaps the previous window

by 90% and we use a center-based time stamp for each window (i.e., it is therefore forward looking by a

half a window length).

4.4 Results

We conducted experiments over a range of boundary conditions (Table 4-1). All stick-slip

experiments start with a period of stable sliding followed by emergent quasi-periodic unstable slow slip

(Figure 4-1A). As shearing continued, the magnitude of the stick-slip events typically reached a steady-

state. We systematically modify the characteristics of the stick-slip events by changing the loading rate,

normal stress and grain size (Figure 4-2). For example, in Experiment p5198 we varied normal stress and

observed a spectrum of slip behaviors (Figures 4-2B and 4-2D). At a normal stress of 6 MPa, the slip events

contain very small stress drops, however after increasing the normal load to 7 MPa (not shown), the

magnitude of the stress drop increases and eventually reaches a steady state value (see data at 8-11MPa in

Figures 4-2B and 4-2D). For Experiment p5201, we systematically modulate the characteristics of the slip

cycles by changing the shear velocity from 2 to 60 µm/s (Figures 4-2A and 4-2C). At low shear velocities

slip events have long recurrence intervals and large stress drops while at high shear velocities the recurrence

intervals are shorter and stress drops are smaller (Figures 4-2A and 4-2C). The early stage of each loading

cycle is characterized by linear-elastic loading followed by the onset of inelastic creep (Figure 4-2E).

During inelastic loading, the fault slip velocity begins to increase and it reaches a peak during the co-seismic

slip phase.

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4.4.1 Acoustic Energy

In Figure 4-3, we show an example of the AE data for one of the hundreds of failure events

analyzed. Note that these data are from a portion of Experiment p5198 at 8 MPa and contain slow-slip

events. During the inter-seismic period, the acoustic time series signal is composed mainly of what looks

like noise with a few small discrete AEs (small spikes in the signal; Figure 4-3B). However, one can observe

that the number and size of the AEs increases as failure approaches. This is also observed in the temporal

trends of the acoustic energy (Figure 4-3). In addition to the inter-seismic trends, the acoustic data

associated with the co-seismic slip phase has a unique character. In particular, the envelope of the raw

acoustic signal has a broad-low amplitude signature during the co-seismic slip phase (Figure 4-3C). In

addition, there are many high frequency AEs, like the one shown in Figure 3B, that occur throughout the

co-seismic slip phase.

The radiated acoustic energy evolves systematically during the slip cycle (Figure 4-3). Here, a

window length of 0.636 s is used to compute the acoustic variance, which is time stamped to the center of

the window (Figure 4-3). After a failure event, the acoustic variance first decays and reaches a minimum

value. It then increases gradually and reaches a peak value during failure (Figure 4-1 and Figure 4-3). Note

that the increase in acoustic variance begins prior to co-seismic failure (Figure 4-3). To fully understand

the characteristics of the acoustic energy, we focus on the details of the temporal behavior of the acoustic

energy as well as other systematics such as the scaling relationship between the cumulative acoustic energy

radiated during co-seismic slip, stress drop and peak slip velocity.

4.4.2 The Influence of Normal Stress and Shear velocity on Acoustic Energy

Our results demonstrate that shear velocity has a significant influence on the temporal evolution

and magnitude of acoustically-radiated energy during the lab seismic cycle (Figure 4-4). For Experiment

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p5201, the normal load was held constant at 9 MPa, while the shear velocity was varied from 2-60 µm/s.

For each test, the initial shear velocity was 10 µm/s. After shearing ~14 mm the shear velocity was

decreased to 2 µm/s and subsequently increased from 2-60 µm/s after shearing between 1-8 mm at each

shear velocity. Shear stress and acoustic variance are plotted as functions of time and load-point

displacement (top) in Figure 4-4. For Experiment p5201, a constant time window of .1 s is used to compute

the acoustic variance. We plot shear stress and acoustic variance as functions of time for a representative

stick-slip cycle at 2 and 60 µm/s respectively in Figures 4-4B and 4-4C. Plotting the acoustic variance on

the same scale reveals distinct differences in the temporal variations in acoustic variance throughout the

stick-slip cycle. In particular, at 60 µm/s the acoustic variance first decreases, reaches a minimum, and then

begins to increase prior to failure. At 2 µm/s the acoustic variance decreases, reaches a minimum and

remains there throughout the inter-seismic period before it finally increases just before failure. In addition

to the temporal trends, we plot the cumulative acoustic energy (i.e variance) during co-seismic rupture and

stress drop as a function of shear velocity in Figure 4-4D. The cumulative acoustic energy is computed

from peak shear stress to minimum shear stress for the variance data shown in Figure 4-4A. We focus on

cumulative acoustic energy rather than the peak energy to avoid artifacts of different window lengths

(Figure S2). The data show that the cumulative acoustic energy radiated during co-seismic failure scales

inversely with shear velocity and linearly with stress drop (Figures 4-4A and 4-4D). In addition to the

temporal trends in acoustic variance, the minimum acoustic variance reached during the inter-seismic

period varies systematically with shear velocity. At 2 µm/s the minimum acoustic variance is slightly lower

(~ 10 bits2) compared to the minimum acoustic variance at 60 µm/s (~ 20 bits2).

It is important to note that we use a constant time window of .1 s to compute the acoustic variance

in Figure 4-4. The length of the moving window corresponds to 10% of the recurrence interval for data at

60 µm/s and since recurrence interval scales inversely with shear velocity this ensures that all moving

windows are less than or equal to 10% of the recurrence interval. Since windows are constant in time, the

amount of slip displacement covered by each moving window increases with shear velocity. We

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demonstrate that the acoustic variance is independent of slip displacement by using different windowing

techniques (see Supplement) and analyzing acoustic data during stable frictional sliding experiments

(Figure C1-C2). In particular, we compute acoustic variance using a moving window that is constant in slip

displacement (Figure C1A and Figure C2). Similar to Figure 4-4, the data show that more energy is released

at higher shear velocities (Figure C1A). However, since we use a constant displacement window in Figure

S1 and acoustic data are recorded at a constant sampling frequency in time, the number of data points (N)

considered in each moving window changes systematically with shear velocity. In other words, the window

size (N in Equation 4-1) decreases with increasing shear velocity. To circumvent this issue, we decimated

the acoustic data such that the number of data points is the same for each moving window. Again, the data

show an increase in energy release with increasing shear velocity and the absolute values of variance do

not change for the decimated case (Figure C1A and Figure C1B). Similarly, data from stick-slip

experiments (e.g p5201) demonstrate that the inter-seismic changes in energy are independent of window

length and slip displacement (Figure C2). However, acoustic data associated with the co-seismic slip phase

are affected by the window length (Figure C2). As mentioned above, we avoid the issue of window size

during the co-seismic slip phase by reporting on the cumulative energy released rather than peak energy. In

conclusion, the results shown in Figure 4-4 are independent of slip displacement and the inter-seismic trends

are independent of the window size (see Appendix C).

Our data show a robust relationship between the stress drop of the stick-slip event and the amount

of acoustic energy radiated from the fault (Figure 4-5). In Figure 4-5, we show results from two

experiments, p5198 (diamond symbols) and p5201 (circle symbols). For these experiments we

systematically change the stress drop of the slip events by changing the normal stress and shear velocity

respectively (see Figure 4-2). The relationship between stress drop and slip velocity as functions of normal

stress and shear velocity is consistent with previous works (Leeman et al., 2016; Scuderi et al., 2016;

Leeman et al., 2018). Data from experiment p5201 plot in the upper right corner of the Figure 4-5, while

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data from p5198 plot in the lower left corner of Figure 4-5. These data show that fast laboratory earthquakes

release greater amounts of acoustic energy during co-seismic failure compared to slow slip events.

To illuminate the mechanisms controlling the temporal evolution of acoustic energy throughout the

inter-seismic period, we plot the acoustic variance, shear stress and slip velocity for one seismic cycle in

Figure 4-6. After the failure event, the acoustic variance begins to decay and finally reaches a minimum at

around 6402.5 s. Interestingly, at this same time the slip velocity is also at a minimum. Following the

minimum, the acoustic variance begins to increase and reaches a peak during the co-seismic slip phase.

Again, at approximately the same time that the acoustic variance begins to increase the fault begins to

unlock and accelerate forward. Because the amount of inelastic creep varies systematically with normal

stress and shear velocity, we further probe the evolution of acoustic variance during the inter-seismic period

by showing the effects of normal stress and shear velocity on the inter-seismic changes in acoustic variance.

For fault zones composed of large grain sizes (10.5 µm), our data show that the acoustic variance

increases when the fault unlocks and begins to accelerate (Figure 4-6). Therefore, for each stick-slip cycle

we focus our analysis from the onset of inelastic creep until the fault has reached its peak slip velocity

during co-seismic failure. In Figures 4-7 and 4-8, we highlight these segments of the seismic cycle with

blue and green colors. Data in blue are from the onset of inelastic creep until peak shear stress, and those

in green are from the peak shear stress until the peak slip velocity (see Figure 4-6). We plot acoustic variance

as a function of slip velocity from multiple slip cycles (see Figure 4-2) at four different normal stresses in

Figure 4-7. The data show that the slip rate of the fault is higher at the onset of creep for lower normal

stresses. That is, the fault slip rate is less than 1 µm/s at the onset of creep for data at 10-11 MPa, but for

data at 8-9 MPa the slip rate is faster at the onset of creep (between 1-10 µm/s). The differences in minimum

slip rate as a function of normal stress has a direct consequence on whether or not the acoustic variance

begins to increase or remain at steady-state value. For data at 8-9 MPa, the acoustic variance begins to

increase once the fault unlocks. However, for data at 10-11 MPa the acoustic variance remains low even

when the fault begins to creep and only increases when the fault is near its peak shear stress (the transition

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from blue to green). In general, it seems that the fault slip rate must be ~10 µm/s before the acoustic energy

begins to increase. For data at 10-11 MPa, the fault only reaches this slip rate near the onset of peak shear

stress, while at 8-9 MPa the fault reaches this slip velocity earlier in its seismic cycle.

In Figure 4-8, we show how shear velocity influences the relationship between slip velocity and

acoustic variance. Similar to the data at high normal stresses, the acoustic variance at low shear velocities

(2-10 µm/s) does not increase prior to the peak shear stress (i.e., the transition from blue to green). However,

at higher shear velocities (> 10 µm/s) the acoustic variance begins to increase prior to reaching peak stress.

In addition, note that the acoustic variance does not begin to increase until the fault has reached a slip

velocity of ~10 µm/s. Furthermore, since the fault stays locked longer at low shear velocities it fails to reach

this slip velocity during the inter-seismic period. However, at higher shear velocities the fault reaches this

slip velocity early on in its seismic cycle and reaches a higher slip velocity upon peak shear stress as the

background loading rate increases. For example, the slip rate of the fault at the onset of creep is around 10

µm/s for data at 40 and 60 µm/s and the fault reaches a slip velocity of ~40-60 µm/s at peak shear stress. In

contrast, the slip rate of the fault at the onset of creep at 10 µm/s is ≤ 1 µm/s and the fault reaches a slip

velocity of only ~ 10 µm/s at peak shear stress.

4.4.3 Slide-Hold-Slide Tests

To further verify that the acoustic variance is linked to fault slip rate, we conducted conventional

slide-hold-slide (SHS) friction tests. These SHS tests were also conducted to help illuminate the relationship

between frictional restrengthening processes and the generation of acoustic energy. In conventional slide-

hold-slide tests, the fault is initially sheared at a constant displacement rate, followed by a pause in shearing,

and is finally resheared at the same displacement rate prior to the hold (Dieterich 1972, 1978; Marone,

1998). During a typical SHS test, friction first decays during the hold, and then reaches a maximum value

upon re-shear (Figure 4-9A). Our data show that the acoustic variance tracks the frictional evolution

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throughout the entire SHS test. Once the fault stops sliding, the acoustic variance decreases significantly,

followed by a gradual decay to a steady-state value (Figures 4-9B:4-9C). Upon reshear, the acoustic

variance begins to increase and reaches a maximum followed by a decay to a steady-state value. These data

corroborate our findings above and demonstrate that for fault zones composed of large particles the acoustic

variance tracks fault slip rate.

4.4.4 The Influence of grain size on acoustic energy

We varied fault zone grain size in order to study the impact of frictional contact junction size on

stick-slip dynamics and acoustic energy (Figures 4-10:4-12). For each experiment in Figure 4-10, we

change the median grain size of the fault gouge while maintaining a constant normal load, shear velocity

and initial layer thickness (Table 4-1). Furthermore, each material consists of monodispersed particles with

a similar, narrow, size range. We plot shear stress and stress drop as a function of shear strain in Figure 4-

10. We compute the instantaneous shear strain by integrating the load-point displacement data normalized

by the layer thickness (Scott et al., 1994). Despite the fact that our range of median grain sizes is less than

an order of magnitude, the character of the slip cycles varies significantly (Figure 4-10). Our data show

distinct differences in stick-slip properties as a function of median grain size. In particular, fault strength,

recurrence interval, and stress drop increase as a function of the median grain size (Figure 4-10).

Fault gouge grain size also has a significant impact on radiated acoustic energy (Figure 4-11:4-12).

Our data show that the peak acoustic variance scales systematically with grain size and stress drop (Figure

4-11). We show the temporal evolution of stress, slip velocity and acoustic variance for multiple seismic

cycles in Figures 4-12A-C. Fault zones composed of larger particles (median diameter of 10.5 µm) show a

decrease in acoustic variance following failure and then an increase prior to failure (Figure 4-12A). As

noted above, this temporal behavior tracks fault slip velocity. However, for grain sizes smaller than 10.5

µm, these temporal trends seem to diminish (Figure 4-12B-C). That is, for small particles (median sizes of

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1.67 and 4.67) the increase in acoustic variance prior to failure is significantly reduced. Moreover, for the

smallest grains the acoustic variance does not increase prior to failure, despite the fact that the fault slip rate

is rather high during the inter-seismic period (~ 10 µm/s). Rather, the acoustic variance seems to fluctuate

around a mean value before reaching its peak during co-seismic slip (Figure 4-12C).

4.5 Discussion

4.5.1 The effect of normal stress and shearing velocity on acoustic energy

Previous ML studies (eg. Rouet-Leduc et al., 2017) have found that the acoustic variance (energy)

is one of the main features that enable laboratory earthquake prediction. The temporal evolution in acoustic

energy is what ultimately enables certain aspects of laboratory earthquakes to be predicted. However, the

physics that control the release of acoustic energy prior to failure has been poorly understood. In this work,

by focusing on the physical parameters that control acoustic energy release throughout the seismic cycle,

we are able to offer a physical explanation behind the ML-based predications of laboratory earthquakes and

their associated precursors.

We carried out a suite of experiments to better understand the physical mechanisms that control the

magnitude and temporal evolution of acoustic energy release throughout the laboratory seismic cycle. We

find a robust relationship between the cumulative acoustic energy released during co-seismic slip and the

stress drop of the slip event (Figures 4-5). This relationship exists over a range of normal stresses, shear

velocities, grain sizes and over a spectrum of slip events ranging from slow to fast dynamic events. The

total amount of energy released during co-seismic rupture is a function of the experimental boundary

conditions. For each experiment, we directly control the amount of energy stored within the fault zone by

systematically changing the normal stress, shearing velocity and grain size. At high normal loads and low

shearing velocities, the fault stays locked longer during the inter-seismic period, which allows more

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frictional healing to take place. Similarly, for a constant normal load and shearing velocity more frictional

healing takes place during the inter-seismic period for fault zones composed of larger particle sizes. This

increase in frictional strength allows the fault zone to accumulate more elastic-strain energy during the

inter-seismic period. However, once the fault begins to unlock and creep a portion of this stored elastic-

strain energy is released through acoustic waves, while part of the remaining acoustic energy is released

during co-seismic failure. Our data show that the total acoustic energy released during co-seismic rupture

scales with the size of the stress drop (Figure 4-4 and Figure 4-5). Our data are consistent with field

observations that show a systematic relationship between energy, seismic moment, magnitude and duration

(Vassiliou & Kanamori, 1982; Kanamori et al., 1993; Ide et al., 2007). This suggests a simple

micromechanical model in which larger magnitude slip events experience more inter-seismic frictional

healing and as a result of this increase in strength they release more acoustic/seismic energy during co-

seismic failure when grain contacts are destroyed.

Our data show that the lowest level of acoustic energy release during the lab seismic scales

systematically with shear velocity (Figure 4-4). The minimum energy shown in Figure 4-4 occurs

approximately where the inelastic loading phase begins, and thus, represents the point at which grain contact

junctions begin to slip and break. However, it is important to point out that AEs do occur during the linear-

elastic loading phase (Figure 4-3). This suggest that grain contact junctions have already started to slide

and break during this phase. Previous works have demonstrated that there is a net increase in the number

of contacts and contact area during the linear-elastic loading phase (Shreedharan et al. 2019). However,

since both the slip velocity and acoustic energy are low during the linear-elastic loading phase, we

hypothesize that the total number of contact junctions breaking is low, and healing mechanisms dominate.

In contrast, once the fault begins to unlock and creep (i.e., slip velocity > 0) the total number of contact

junctions breaking increases significantly and results in a subsequent increase in energy radiation. This idea

is consistent with the data presented in Figure 4-4 and with physical models of frictional contact and contact

aging (e.g., Li et al., 2011; Shreedharan et al., 2019). That is, young grain contacts are smaller, weaker and

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have less time to heal at higher slip rates, which allows for more contacts to break prior to failure at faster

slip rates. The temporal trends in acoustic energy further verify this hypothesis (Figures 4-7:4-8). That is,

the temporal changes in acoustic energy release during the inter-seismic period is greater for higher shear

velocities (Figures 4-4B,4-4C, and Figures 4-7:4-8). More specifically, at high shear velocities/low normal

stresses the slip rate of the fault is much higher during the inter-seismic period, which enhances destruction

of grain contact junctions. If the acoustic energy is related to the slipping/breaking of contact junctions, we

should expect a higher rate of acoustic energy release to occur with higher slip rates. In contrast, at low

shear velocities/high normal stresses the fault stays locked longer and when it does unlock the fault slip rate

is much lower. This process results in more frictional healing and as a result less contacts are slipping and

breaking, which reduces the rate of acoustic energy released during the inter-seismic period. Therefore, our

data demonstrate that the magnitude and temporal changes in acoustic energy release are controlled by fault

slip velocity. Our results are consistent with previous laboratory works that have shown higher amounts of

AE activity with increasing strain rate/shearing velocity (Yabe, 2002; Ojala et al., 2004; McLaskey and

Lockner, 2014; Jiang et al., 2017). These findings could have important implications for micro-seismic

activity and precursors to frictional failure (e.g Ross et al., 2019; Trugman and Ross, 2019; Brodsky, 2019;

Gulia and Wiemer, 2019). Our data suggest that there could be an insignificant amount of seismic activity

released prior to larger earthquakes if the fault stays locked up and the minimum slip rate attained by the

fault is low. In contrast, if the fault does unlock and begins accelerating there could be a substantial increase

in seismic activity preceding failure. Furthermore, our data demonstrates that the acoustic energy radiating

from the fault zone is fundamentally linked to the fault slip rate. This is consistent with recent observations

of deep low-frequency earthquakes in Mexico where the maximum s-wave amplitude of low-frequency

earthquakes qualitatively tracks fault slip rate constrained by geodesy (see Figure 1 from Frank and

Brodsky, 2019). Therefore, our results could be particularly useful to help us understand the physics of

slow earthquakes.

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It is important to note that once the fault unlocks and the onset of inelastic loading occurs, both

shear stress and slip velocity begin to increase. Therefore, one could equally argue that acoustic energy

tracks shear stress during inelastic loading, which has been shown in previous works (Passelegue et al.,

2017). However, our data clearly show that slip velocity is the main parameter that controls acoustic energy

release and not shear stress. To demonstrate that shear stress is not the dominant parameter, we plot data

from the onset of inelastic creep until peak stress (i.e., blue data in Figures 4-7 and 4-8) in Figure C3. Data

from Experiment p5198 show that the amount of energy released prior to failure scales inversely with

friction. If acoustic energy tracked shear stress we should expect to see more energy released for higher

values of friction. However, our data show that more energy is released at lower values of friction, which

is inconsistent with the former hypothesis. As mentioned above, fault slip velocity is higher during the

inter-seismic period at lower normal stresses, and therefore more acoustic energy is released prior to failure

at lower normal stresses. Similarly, data from Experiment p5201 show that more elastic energy is released

prior to failure for higher shear velocities (Figure 4-4 and Figure C3). Again, if acoustic energy tracked

shear stress we should expect to see more energy released at lower shear velocities. However, our data show

that more energy released is at lower values of friction, which implies that slip velocity is the dominant

factor in controlling the energy released prior to failure. These observations further confirm the results from

our stable sliding data (Figure C1), and corroborate the idea that slip rate is the dominant effect on acoustic

energy release (not shear stress).

To develop a more physical understanding behind the source of acoustic energy and to further

verify that acoustic energy tracks slip velocity, we conducted conventional SHS tests and measured the

amount of acoustic energy radiated before, during and after the SHS (Figure 4-9A). Our data show that the

acoustic energy tracks shear stress during the entire SHS test. At the onset of the hold the acoustic energy

immediately decreases and remains at a minimum for the duration of the hold. Upon reshear, the acoustic

energy reaches a peak and then decays back to a steady-state value (Figures 4-9A:4-9C). Since this entire

process is analogous to the frictional behavior of the fault, we propose that the micro-mechanical processes

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that induce frictional healing are in fact the same processes that generate the release of acoustic energy. In

particular, we propose that generation of acoustic energy is fundamentally related to the micro-mechanics

of grain contact junctions. In terms of frictional healing, grain contacts are thought to increase in size and

number due to chemical activated processes during the hold (Rabinowicz, 1951; Frye and Marone, 2002).

As a result of this restrengthening process, the frictional strength increases upon reshear scales with duration

of the hold time. We hypothesize that when the fault is locked (e.g. during the hold or linear-elastic loading

stage) the acoustic energy remains low because grain contacts are quasi-stationary and growing in size and

number. When the fault unlocks (e.g. during reshear of a SHS or inelastic loading) the acoustic energy

begins to increase because grain contacts are being sheared and destroyed. This conceptual model is

supported by both our SHS tests as well as our stick-slip datasets.

4.5.2 The effect of grain size and contact junction size

Experiments conducted with different grain sizes demonstrate that grain size, and thus, contact

junction size play a significant role in the temporal evolution and magnitude of acoustic energy release.

Our data show that larger grain sizes produce more acoustic energy during the inter-seismic period and co-

seismic slip phase (Figures 4-11:4-12). For the largest grain size, the acoustic energy begins to increase

well before failure and correlates with slip velocity (Figure 4-12A). However, as the grain size is reduced

the acoustic energy begins to increase later during the seismic cycle (Figures 4-12B-C). As mentioned

above, slip velocity has a significant impact on the magnitude and temporal changes in elastic energy

release. However, fault slip velocity alone cannot explain the acoustic energy trends in Figures 4-12B-C.

That is, fault slip rate is highest during the inter-seismic period for fault zones composed of smaller grain

sizes. Therefore, if slip velocity is the main control on acoustic energy release we should expect to see an

increase in energy released prior to failure for the smallest grain size. However, data in Figure 4-12 do not

support this idea and therefore additional mechanisms must be considered.

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Data presented in Figures 4-10:4-12 are conducted with the same the initial layer thickness.

However, since the median particle size is different for each experiment the total number of grains across

the gouge layer increases as particle size decreases. In particular, there are more grain contact junctions

within a given volume (i.e., the particle coordination number) with decreasing grain size (Morgan and

Boettcher, 1999; Mair and Marone 2002; Gheibi and Hedayat, 2014). This implies that the true contact area

per unit volume is higher for fault zones composed of smaller grain sizes. Furthermore, since the applied

load is constant for each experiment the average contact force on each particle is smaller for smaller grain

sizes, due to a higher coordination number. Thus, if the average contact force decreases the shear strength

of the material, stress drop and radiated acoustic energy should all decrease. This explanation is in good

agreement with our data and is also consistent with previous works (Gheibi and Hedayat, 2014). This

implies that in addition to fault slip velocity the total number of contact junctions per unit volume (i.e., the

true contact area) plays a key role in the generation of acoustic energy.

To conclude, our data show that in order for acoustic energy to be radiated the total contact area

per unit volume needs to be small (e.g., large grain sizes) and the fault needs to unlock and accelerate prior

to failure. This finding could have important implications for the generation of micro-seismic activity and

precursors to laboratory earthquakes and natural earthquakes. In particular, for the smallest grains studied

we did not detect microseismic precursors for laboratory earthquakes. This could imply that generation of

foreshocks are controlled by fault zone maturity and/or fault zone comminution. However, additional work

is needed, including utilizing active source ultrasonics and pore fluid pressure, to verify the role of particle

coordination number and to explore implications of particle size for upscaling our results to mature faults

zones.

103

4.5.3 Machine Learning and Prediction of Failure

The systematic evolution of acoustic energy throughout the seismic cycle is what ultimately enables

accurate prediction of laboratory earthquakes. Here, we have begun to provide a physical basis for the ML-

based prediction using frictional contact mechanics. We find that the magnitude and the temporal evolution

of radiated acoustic energy can be explained by changes in fault slip rate and the true contact area per unit

volume within the fault zone. If our hypothesis is correct, then this implies that the ML-based predictions

of laboratory earthquakes are controlled by the breaking/sliding of contact junctions. Moreover, if the fault

slip rate is low enough or if the total number of contact junctions per unit volume is large (e.g., small grain

size) then there should be a lack of foreshocks and/or acoustic energy. A lack of AE activity would result

in a decrease in the performance of the ML-based predictions. This hypothesis is in part confirmed by

Lubbers et al., 2018, who showed that the ML based predictions are closely related to the magnitude and

frequency of foreshocks that occur before failure. However, more ML based studies are needed to verify if

this hypothesis is indeed correct.

4.6 Conclusion

We analyze acoustic data from friction experiments for a range of boundary conditions and

illuminate the physical processes that control the magnitude and temporal evolution of acoustic energy

throughout the seismic cycle. Our data show that the magnitude of the acoustic energy released during co-

seismic failure scales with the stress drop of the slip event. We show that fault slip rate plays a key role in

the generation of acoustic energy during the inter-seismic period. In addition, frictional contact area per

unit fault volume dictates the magnitude and evolution of elastic radiation. Fault zones composed of smaller

particles radiate less acoustic energy than fault zones composed of larger particles because the contact area

per unit volume is higher for smaller grain sizes, and thus, the average contact forces exerted on each

104

particle is smaller. We attribute the generation and evolution of acoustic energy to be fundamentally related

to the micro-physical processes acting at grain contact junctions. The magnitude of the acoustic energy is

related to the real area of contact between neighboring grains and the rupturing of grain contact junctions

is one of the main physical mechanisms that generates the acoustic energy throughout the laboratory seismic

cycle.

Our results have important implications for machine learning–based prediction of micro-seismic

activity and precursors to failure. Micro-seismic activity and precursors have a fundamental impact on the

ability to improve earthquake early warning systems and possibly earthquake forecasting. Ultimately, our

data suggest that generation of micro-seismic activity could be directly related to the fault slip rate and the

true contact area per unit volume of the fault gouge. In the context of ML, our data show that the machine

learning predictions are in some ways related to the slip rate of the fault. That is, the unlocking of the fault

is a key parameter that dictates the temporal evolution of the acoustic energy. Future ML based studies

should be devoted to understanding the effect of fault slip rate and grain contact size on the performance of

ML models. More specifically, it remains unknown whether ML models can still predict the time to failure

of impeding earthquakes if the fault remains locked and the generation of acoustic energy does not evolve

throughout the seismic cycle.

105

Figure 4-1: A. Data for one complete experiment (p5198) showing measured stresses as a function of load-point displacement. Inset in A shows double-direct shear configuration with acoustic sensors (orange squares) and on-board displacement transducer. Shear and normal forces are measured with strain gauge load cells mounted in series with the vertical and horizontal rams respectively. Horizontal and vertical displacements are measured with direct current displacement transformers (DCDT) and are referenced to the loading frame. B. Zoom of shear stress and acoustic energy during a series of lab earthquakes. Note the systematic evolution of acoustic variance throughout the seismic cycle. For the ML analysis (see Hulbert et al. 2019), we use the first 60% of the data for training and the remaining 40% for testing. C. Comparison of measured and predicted shear stress (r2 = .87) using ML.

106

Figure 4-2: A-B. Shear stress plotted as a function of time for data at different shear velocities and normal stresses (A 2-60 µm/s; B 6-11 MPa). Note that the lab seismic cycle changes systematically with shear velocity and normal stress. The stress drop during failure events decreases as fault normal stress decreases, and sliding becomes stable at the lowest normal stress. C. Shear stress normalized by the peak value prior to failure is plotted as a function of time for three different driving velocities. Note that stress drop scales inversely with shear velocity. D. Normalized shear stress during failure events at four normal stresses. Slip duration decreases and stress drop increases as normal load increases. E. Shear stress and slip velocity as a function of load-point displacement for one seismic cycle. Grey line shows elastic loading when the fault is locked. The onset of fault slip (inelastic creep) is marked with the red dot. Note that the onset of inelastic creep varies with normal stress and shear velocity. The fault reaches its peak slip velocity during co-seismic failure. Stress drop is calculated as the difference between the peak shear stress and the minimum shear stress.

Time (s)

Shea

r Stre

ss (M

Pa)

5 s

0.5MPa

60 µm/s

10

2

µm/s

µm/s

0 0.5 1 1.5 2 2.5 3Time (s)

0.94

0.95

0.96

0.97

0.98

0.99

1

Norm

alize

d She

ar Str

ess

2 m/s

60 m/s

10 m/s

C

27.66 27.67 27.68 27.69 27.7 27.71Load-Point Displacement (mm)

5

5.05

5.1

5.15

Shear

Str

ess (

MP

a)

0

20

40

Sli

p V

elo

cit

y (

m/s

)

Peak Slip Velocity

Onset of inelastic creep

N 8 MPa

Stre

ss D

rop

E

D

A

B

107

Figure 4-3: A. Shear Stress, acoustic amplitude, and acoustic variance plotted as a function of time for one seismic cycle. The dashed rectangle shows our moving window (0.636 s) used to compute the acoustic variance. At this scale acoustic data look like noise, however the signal is composed of individual AEs (some identifiable as small spikes) that grow in size and number as failure approaches (see B). The acoustic variance first decays following a failure event, reaches a minimum during the inter-seismic period and finally begins to increase prior to failure. B. Zoom of an AE that nucleated during the inter-seismic period. C. Zoom of the acoustic signal during co-seismic failure. Note the broad, low amplitude nature of the envelope with superimposed high-frequency AEs.

108

Figure 4-4: A. Shear stress and acoustic variance plotted as a function of time and load-point displacement for one complete experiment (p5201) with detail at (B) 2µm/s and (C) 60 µm/s. Note, the variance in A is a discrete time series signal computed at all times throughout the seismic cycle. When plotted on the same scale the acoustic variance time series shows distinct differences as a function of velocity. At low shear velocity the acoustic variance stays low for most of the seismic cycle and only begins to increase once the fault has reached its peak strength. In contrast, at high drive velocities the acoustic variance decays, reaches a minimum and begins to increase before the fault reaches its peak stress. D. Average cumulative acoustic energy and stress drop plotted as a function of shear velocity. The cumulative acoustic energy is computed from the variance time series data in Figure 4-4A. Variance is integrated from peak shear stress to minimum shear stress for each slip cycle shown in Figure 4-4A. Square symbols represent mean values and error bars represent one standard deviation. Cumulative acoustic energy scales directly with stress drop and inversely with shear velocity.

109

Figure 4-5: Normalized peak slip velocity during failure as a function of stress drop for all events in two experiments. Symbols are color coded according to the cumulative acoustic energy. Note the strong correlation between peak slip velocity, stress drop and cumulative acoustic variance radiated from the fault during failure.

107

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45Stress Drop (MPa)

5

10

15

20

25

Peak

Slip

Vel

ocity

/She

ar V

eloc

ity p5201; 2-60 µm/s; σN = 9 MPa

p5198; 10 µm/s; σN = 6-11 MPa

Cum

ulat

ive

Co-

seis

mic

Ene

rgy

x 10

4 (bi

ts2 )1

2

3

4

5

6

7

8

9

10

110

Figure 4-6: Shear stress, acoustic variance, and slip velocity as a function of time for one seismic cycle in experiment p5198 (8 MPa normal stress). Dashed rectangle shows the moving window used to compute the acoustic variance. Initially, the fault is locked, with near zero slip velocity. The fault begins to unlock about half way through the cycle, and the fault slip rate increases dramatically prior to failure. The acoustic variance mimics the slip velocity and reaches a peak during co-seismic failure. Acoustic variance is color coded based on the following: black to blue shows the onset of inelastic creep, blue to green coincides with the peak shear stress, and green to black corresponds to the peak slip velocity.

6401 6402 6403 6404 6405 6406 6407Time (s)

5

5.05

5.1

5.15

Shea

r Stre

ss (M

Pa)

0

10

20

30

40

50

60

70

Slip

Vel

ocity

(µm

/s)

7.24

10.86

14.49

18.11

21.73

25.36

28.98

32.60

36.23

Var

ianc

e (b

its2 )

p5198

111

Figure 4-7: Acoustic variance as a function of slip velocity plotted for four different normal stresses from Experiment p5198. Plots show data from multiple slip cycles at each load (see Figure 4-1). For each slip cycle, we plot data from the onset of inelastic creep until peak-slip velocity. Blue shows data from the onset of inelastic creep until peak shear stress. Green shows data from peak shear stress until peak slip velocity (see Figure 4-2E and Figure 4-6). A-B At low normal loads (8-9 MPa) the acoustic variance increases with slip velocity during the inter-seismic period (blue data). Also note that the acoustic variance increases only as the fault reaches a slip rate of ~ 10 µm/s. At higher normal loads (10-11 MPa) the fault slip rate is < 10 µm/s for most of the inter-seismic period and the acoustic variance only increases during the latter stages (green) of the seismic cycle.

Slip Velocity (µm/s)

Varia

nce

(bits

2 )

σN 8 MPa σN 9 MPa

σN 10 MPa σN 11 MPa

A B

DC

112

Figure 4-8: Acoustic variance as a function of slip velocity for data at six different shear velocities from Experiment p5201 (same color coding as Figure 4-7). At low shear velocities (2-5 µm/s) the acoustic variance does not increase during the inter-seismic period (e.g., blue data). In contrast, at high shear velocities (>= 20 µm/s), the acoustic variance increases systematically with slip velocity during the inter-seismic period.

Slip Velocity (µm/s)

Varia

nce

(bits

2 )

2 µm/s 5 µm/s 10 µm/s

20 µm/s 40 µm/s 60 µm/s

113

Figure 4-9: A. Friction and acoustic variance plotted as a function of time for a series of SHS tests for Experiment p5273. Here, we use a 0.1 s window to compute the acoustic variance. Acoustic variance remains at a steady-state value during sliding and decreases rapidly at the start of a hold. Upon re-shear, the variance increases, reaches a peak and decays back to the steady-state value. B. Acoustic variance and load-point displacement as a function of time. Note that acoustic variance tracks fault slip-rate. C. Acoustic variance and friction plotted as function of log time for a 10 s hold (see A). Both the acoustic variance and friction decay rapidly at the onset of the hold. However, the acoustic variance drops to a steady-state value whereas friction continues to decrease throughout the hold.

114

Figure 4-10: Shear stress and stress drop as a function of shear strain for experiments conducted with different median grain sizes. Note that stress drop increases during the initial part of each experiment and reaches a steady state for which larger grains produce bigger events.

p5263; 10.5 µmp5264; 4.67 µmp5293; 1.67 µm

Stre

ss D

rop

(MPa

)

115

Figure 4-11: Shear stress and acoustic variance versus shear strain for fault gouge composed of different median grain sizes. Plots are offset vertically for clarity. Fault zones composed of larger grains produce larger stress drops, have longer recurrence intervals and radiate more energy during co-seismic failure.

10.3 10.4 10.5 10.6 10.7 10.8 10.9 11

4.67 µm

11.1 11.2 11.3Shear Strain

10.5 µm

Shea

r Stre

ss (M

Pa)

Var

ianc

e (b

its2 )

1.67 µm.2 MPa 20 (bits2)

116

Figure 4-12: A-C. Zoom of each experiment shown in Figure 4-11. Note the acoustic variance range is the same for each plot. The acoustic variance begins to increase later in the seismic cycle for fault zones composed of smaller grains.

117

Table 4-1: List of experiments and boundary conditions for Chapter 4.

Experiment Normal Stress (MPa) Drive Velocity (µm/s) Median Grain Size (µm)

p5198

p5201

p5263

p5317

p5264

p5273

p5293

6-11

9

10

10

10

10

10

10

10

10

2-60

2-60

10.5

10.5

10.5

4.67

10.5

1.67

Table 1. List of Experiments and Boundary Conditions

9 2-60 10.5

p5348 9 2-60 10.5

118

4.7 References

Bakun, W. H., Aagaard, B., Dost, B., Ellsworth, W. L., Hardebeck, J. L., Harris, R. A., ... &

Michael, A. J. (2005). Implications for prediction and hazard assessment from the 2004

Parkfield earthquake. Nature, 437(7061), 969-974.

Bolton, D. C., Shokouhi, P., Rouet-Leduc, B., Hulbert, C., Rivière, J., Marone, C., & Johnson, P.

A. (2019). Characterizing Acoustic Signals and Searching for Precursors during the

Laboratory Seismic Cycle Using Unsupervised Machine Learning. Seismological Research

Letters, 90(3), 1088-1098.

Brace, W. F., & Bombolakis, E. G. (1963). A note on brittle crack growth in compression.

Journal of Geophysical Research, 68(12), 3709-3713.

Brace, W. F., & Byerlee, J. D. (1966). Stick-slip as a mechanism for

earthquakes. Science, 153(3739), 990-992.

Brodsky, E. E. (2019). The importance of studying small earthquakes. Science, 364(6442), 736-

737.

Brodsky, E. E., & van der Elst, N. J. (2014). The uses of dynamic earthquake triggering. Annual

Review of Earth and Planetary Sciences, 42, 317-339.

Chen, J. H., Froment, B., Liu, Q. Y., & Campillo, M. (2010). Distribution of seismic wave speed

changes associated with the 12 May 2008 Mw 7.9 Wenchuan earthquake. Geophysical

Research Letters, 37(18).

Crampin, S., Evans, R., & Atkinson, B. K. (1984). Earthquake prediction: a new physical basis.

Geophysical Journal International, 76(1), 147-156.

Dieterich, J. H. (1972). Time-dependent friction in rocks. Journal of Geophysical Research,

77(20), 3690-3697.

119

Dieterich, J. H. (1978). Time-dependent friction and the mechanics of stick-slip. In Rock Friction

and Earthquake Prediction (pp. 790-806). Birkhäuser, Basel.

Frank, W. B., & Brodsky, E. E. (2019). Daily measurement of slow slip from low-frequency

earthquakes is consistent with ordinary earthquake scaling. Science Advances, 5(10),

eaaw9386.

Frye, K. M., & Marone, C. (2002). Effect of humidity on granular friction at room temperature.

Journal of Geophysical Research: Solid Earth, 107(B11), ETG-11. Geophysical Research,

78(29), 6936-6942.

Gheibi, A., & Hedayat, A. (2018). Ultrasonic investigation of granular materials subjected to

compression and crushing. Ultrasonics, 87, 112-125.

Goebel, T. H. W., Sammis, C. G., Becker, T. W., Dresen, G., & Schorlemmer, D. (2015). A

comparison of seismicity characteristics and fault structure between stick–slip experiments

and nature. Pure and Applied Geophysics, 172(8), 2247-2264.

Goebel, T. H. W., Schorlemmer, D., Becker, T. W., Dresen, G., & Sammis, C. G. (2013).

Acoustic emissions document stress changes over many seismic cycles in stick-slip

experiments. Geophysical Research Letters, 40(10), 2049-2054, doi:10.1029/2010/GL043066.

Gu, J. C., Rice, J. R., Ruina, A. L., & Simon, T. T. (1984). Slip motion and stability of a single

degree of freedom elastic system with rate and state dependent friction. Journal of the

Mechanics and Physics of Solids, 32(3), 167-196.

Gulia, L., Tormann, T., Wiemer, S., Herrmann, M., & Seif, S. (2016). Short-term probabilistic

earthquake risk assessment considering time-dependent b values. Geophysical Research

Letters, 43(3), 1100-1108.

Gulia, L., & Wiemer, S. (2019). Real-time discrimination of earthquake foreshocks and

aftershocks. Nature, 574(7777), 193-199.

120

Gupta, I. N. (1973). Seismic velocities in rock subjected to axial loading up to shear fracture.

Journal of

Hulbert, C., Rouet-Leduc, B., Johnson, P. A., Ren, C. X., Rivière, J., Bolton, D. C., and C.

Marone, (2018). Machine learning predictions illuminate similarity of fast and slow laboratory

earthquakes, Nat. Geosc.

Ide, S., Beroza, G. C., Shelly, D. R., & Uchide, T. (2007). A scaling law for slow earthquakes.

Nature, 447(7140), 76.

Jiang, Y., Wang, G., & Kamai, T. (2017). Acoustic emission signature of mechanical failure:

Insights from ring-shear friction experiments on granular materials. Geophysical Research

Letters, 44(6), 2782-2791.

Johnson, P.A., Ferdowsi, B., Kaproth, B.M., Scuderi, M.M., Griffa, M., Carmeliet, J., Guyer,

R.A., Le Bas, P-Y., Trugman, D.T., & Marone, C. (2013). Acoustic emission and microslip

precursors to stick-slip failure in sheared granular material. Geophysical Research Letters,

40(21), 5627-5631, doi: 10.1002/2013GL057848.

Kanamori, H., Mori, J., Hauksson, E., Heaton, T. H., Hutton, L. K., & Jones, L. M. (1993).

Determination of earthquake energy release and ML using TERRAscope. Bulletin of the

Seismological Society of America, 83(2), 330-346.

Kaproth, B. M., & Marone, C. (2013). Slow earthquakes, preseismic velocity changes, and the

origin of slow frictional stick-slip. Science, 341(6151), 1229-1232.

Karner, S. L., & Marone, C. (1998). The effect of shear load on frictional healing in simulated

fault gouge. Geophysical research letters, 25(24), 4561-4564.

Karner, S. L., & Marone, C. (2001). Fractional restrengthening in simulated fault gouge: Effect of

shear load perturbations. Journal of Geophysical Research: Solid Earth, 106(B9), 19319-

19337.

121

Latour, S., Schubnel, A., Nielsen, S., Madariaga, R., & Vinciguerra, S. (2013). Characterization

of nucleation during laboratory earthquakes. Geophysical Research Letters, 40(19), 5064-

5069.

Latour, S., Voisin, C., Renard, F., Larose, E., Catheline, S., & Campillo, M. (2013). Effect of

fault heterogeneity on rupture dynamics: An experimental approach using ultrafast ultrasonic

imaging. Journal of Geophysical Research: Solid Earth, 118(11), 5888-5902.

Leeman, J. R., Marone, C., & Saffer, D. M. (2018). Frictional mechanics of slow earthquakes.

Journal of Geophysical Research: Solid Earth, 123(9), 7931-7949.

Leeman, J. R., Saffer, D. M., Scuderi, M. M., & Marone, C. (2016). Laboratory observations of

slow earthquakes and the spectrum of tectonic fault slip modes. Nature communications, 7,

11104.

Leeman, J., Scuderi, M. M., Marone, C., & Saffer, D. (2015). Stiffness evolution of granular

layers and the origin of repetitive, slow, stick-slip frictional sliding. Granular Matter, 17(4),

447-457.

Lei, X., & Ma, S. (2014). Laboratory acoustic emission study for earthquake generation process.

Earthquake Science, 27(6), 627-646.

Li, Q., Tullis, T. E., Goldsby, D., & Carpick, R. W. (2011). Frictional ageing from interfacial

bonding and the origins of rate and state friction. Nature, 480(7376), 233.

Lockner, D. A., Walsh, J. B., & Byerlee, J. D. (1977). Changes in seismic velocity and

attenuation during deformation of granite. Journal of Geophysical Research, 82(33), 5374-

5378.

Lockner, D., Byerlee, J. D., Kuksenko, V., Ponomarev, A., & Sidorin, A. (1991). Quasi-static

fault growth and shear fracture energy in granite. Nature, 350(6313), 39.

122

Lubbers, N., Bolton, D. C., Mohd-Yusof, J., Marone, C., Barros, K., & Johnson, P. A. (2018).

Earthquake Catalog-Based Machine Learning Identification of Laboratory Fault States and the

Effects of Magnitude of Completeness. Geophysical Research Letters, 45(24), 13-269.

Main, I. G., Meredith, P. G., & Jones, C. (1989). A reinterpretation of the precursory seismic b-

value anomaly from fracture mechanics. Geophysical Journal International, 96(1), 131-138.

Mair, K., Marone, C., & Young, R. P. (2007). Rate dependence of acoustic emissions generated

during shear of simulated fault gouge. Bulletin of the seismological Society of America, 97(6),

1841-1849, doi:10.1785/0120060242.

Marone, C. (1998). Laboratory-derived friction laws and their application to seismic faulting.

Annual Review of Earth and Planetary Sciences, 26(1), 643-696.

Marone, C., & Scholz, C. H. (1989). Particle-size distribution and microstructures within

simulated fault gouge. Journal of Structural Geology, 11(7), 799-814.

McLaskey, G. C., & Lockner, D. A. (2014). Preslip and cascade processes initiating laboratory

stick slip. Journal of Geophysical Research: Solid Earth, 119(8), 6323-6336.

Milne, J. (1899). Earthquake Precursors. Nature, 59(1531), 414.

Nanjo, K. Z., Hirata, N., Obara, K., & Kasahara, K. (2012). Decade-scale decrease in b value

prior to the M9-class 2011 Tohoku and 2004 Sumatra quakes. Geophysical Research

Letters, 39(20).

Niu, F., Silver, P. G., Daley, T. M., Cheng, X., & Majer, E. L. (2008). Preseismic velocity

changes observed from active source monitoring at the Parkfield SAFOD drill site. Nature,

454(7201), 204.

Ohnaka, M., & Mogi, K. (1982). Frequency characteristics of acoustic emission in rocks under

uniaxial compression and its relation to the fracturing process to failure. Journal of

geophysical research: Solid Earth, 87(B5), 3873-3884.

123

Paterson, M. S., & Wong, T. F. (2005). Experimental rock deformation-the brittle field. Springer

Science & Business Media.

Papadopoulos, G. A., Charalampakis, M., Fokaefs, A., & Minadakis, G. (2010). Strong foreshock

signal preceding the L'Aquila (Italy) earthquake (Mw 6.3) of 6 April 2009. Natural Hazards

and Earth System Sciences, 10(1), 19.

Rabinowicz, E. (1951). The nature of the static and kinetic coefficients of friction. Journal of

applied physics, 22(11), 1373-1379.

Renard, F., Cordonnier, B., Kobchenko, M., Kandula, N., Weiss, J., & Zhu, W. (2017).

Microscale characterization of rupture nucleation unravels precursors to faulting in rocks.

Earth and Planetary Science Letters, 476, 69-78.

Renard, F., Weiss, J., Mathiesen, J., Ben-Zion, Y., Kandula, N., & Cordonnier, B. (2018). Critical

Evolution of Damage Toward System-Size Failure in Crystalline Rock. Journal of

Geophysical Research: Solid Earth, 123(2), 1969-1986.

Rikitake, T. (1968). Earthquake prediction. Earth-Science Reviews, 4, 245-282.

Rivière, J., Lv, Z., Johnson, P. A., & Marone, C. (2018). Evolution of b-value during the seismic

cycle: Insights from laboratory experiments on simulated faults. Earth and Planetary Science

Letters, 482, 407-413.

Ross, Z. E., Trugman, D. T., Hauksson, E., & Shearer, P. M. (2019). Searching for hidden

earthquakes in Southern California. Science, 364(6442), 767-771.

Rouet-Leduc, B., Hulbert, C., Bolton, D. C., Ren, C. X., Riviere, J., Marone, C., ... & Johnson, P.

A. (2018). Estimating Fault Friction From Seismic Signals in the Laboratory. Geophysical

Research Letters, 45(3), 1321-1329.

Rouet-Leduc, B., Hulbert, C., Lubbers, N., Barros, K., Humphreys, C. J., & Johnson, P. A.

(2017). Machine learning predicts laboratory earthquakes. Geophysical Research Letters,

44(18), 9276-9282.

124

Rubinstein, S. M., Cohen, G., & Fineberg, J. (2007). Dynamics of precursors to frictional

sliding. Physical review letters, 98(22), 226103.

Rubinstein, S. M., Cohen, G., & Fineberg, J. (2009). Visualizing stick–slip: experimental

observations of processes governing the nucleation of frictional sliding. Journal of Physics D:

Applied Physics, 42(21), 214016.

Sammonds, P. R., Meredith, P. G., & Main, I. G. (1992). Role of pore fluids in the generation of

seismic precursors to shear fracture. Nature, 359(6392), 228-230.

Scholz, C. H. (1968). The frequency-magnitude relation of microfracturing in rock and its

relation to earthquakes, Bulletin of the Seismological Society of America, 58(1), 399-415.

Scholz, C. H. (2015). On the stress dependence of the earthquake b value. Geophysical Research

Letters, 42(5), 1399-1402.

Scholz, C. H., Sykes, L. R., & Aggarwal, Y. P. (1973). Earthquake prediction: a physical basis.

Science, 181(4102), 803-810.

Scholz, C., Molnar, P., & Johnson, T. (1972). Detailed studies of frictional sliding of granite and

implications for the earthquake mechanism. Journal of geophysical research, 77(32), 6392-

6406.

Scott, D. R., Marone, C. J., & Sammis, C. G. (1994). The apparent friction of granular fault

gouge in sheared layers. Journal of Geophysical Research: Solid Earth, 99(B4), 7231-7246.

Scuderi, M. M., Carpenter, B. M., Johnson, P. A., & Marone, C. (2015). Poromechanics of stick-

slip frictional sliding and strength recovery on tectonic faults. Journal of Geophysical

Research: Solid Earth, 120(10), 6895-6912.

Scuderi, M.M., Marone, C., Tinti, E., Stefano, G. Di., & Collettini, C. (2016). Seismic velocity

changes reveal precursors for the spectrum of earthquake failure modes. Nature geoscience,

9(9), 695, doi:10.1038/NGEO02775.

125

Shreedharan, S., Rivière, J., Bhattacharya, P., & Marone, C. (2019). Frictional State Evolution

during Normal Stress Perturbations Probed with Ultrasonic Waves. Journal of Geophysical

Research: Solid Earth.

Shreedharan, S., Bolton, D. C., Rivière, J., & Marone, C. (2020). Preseismic fault creep and

elastic wave amplitude precursors scale with lab earthquake magnitude for the continuum of

tectonic failure modes. Geophysical Research Letters,

46.https://doi.org/10.1029/2020GL086986

Tapponnier, P., & Brace, W. F. (1976, April). Development of stress-induced microcracks in

Westerly granite. In International Journal of Rock Mechanics and Mining Sciences &

Geomechanics Abstracts (Vol. 13, No. 4, pp. 103-112). Pergamon.

Thompson, B. D., Young, R. P., & Lockner, D. A. (2005). Observations of premonitory acoustic

emission and slip nucleation during a stick slip experiment in smooth faulted Westerly granite.

Geophysical research letters, 32(10).

Thompson, B. D., Young, R. P., & Lockner, D. A. (2009). Premonitory acoustic emissions and

stick-slip in natural and smooth-faulted Westerly granite. Journal of Geophysical Research:

Solid Earth, 114(B2).

Tinti, E., Scuderi, M. M., Scognamiglio, L., Di Stefano, G., Marone, C., & Collettini, C. (2016).

On the evolution of elastic properties during laboratory stick-slip experiments spanning the

transition from slow slip to dynamic rupture. Journal of Geophysical Research: Solid Earth,

121(12), 8569-8594.

Trugman, D. T., & Ross, Z. E. (2019). Pervasive foreshock activity across southern California.

Geophysical Research Letters.

Vassiliou, M. S., & Kanamori, H. (1982). The energy release in earthquakes. Bulletin of the

Seismological Society of America, 72(2), 371-387.

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Weeks, J., Lockner, D., & Byerlee, J. (1978). Change in b-values during movement on cut

surfaces in Granite. Bulletin of the Seismological Society of America, 68(2), 333-341.

Whitcomb, J. H., Garmany, J. D., & Anderson, D. L. (1973). Earthquake prediction: Variation of

seismic velocities before the San Francisco earthquake. Science, 180(4086), 632-635.

Yabe, Y. (2002). Rate dependence of AE activity during frictional sliding. Geophysical research

letters, 29(10), 26-1.

Yabe, Y., Kato, N., Yamamoto, K., & Hirasawa, T. (2003). Effect of sliding rate on the activity

of acoustic emission during stable sliding. pure and applied geophysics, 160(7), 1163-1189.

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Chapter 5

The high-frequency signature of slow and fast laboratory earthquakes

5.1 Abstract

Tectonic faults fail through a spectrum of slip modes, ranging from aseismic creep to fast

ordinary earthquakes. Understanding the seismic radiation patterns emitted during these slip modes

is key for advancing earthquake science and earthquake hazard assessment. However, the

connection between seismic radiation and the mode of faulting is difficult to establish without

isolating a single fault patch that is capable of hosting a full continuum of slip modes. In addition,

the lack of high-resolution measurements near the fault zone impede the ability to make key

inferences about seismic properties of slow and fast ruptures. In this work, we use high-resolution

laboratory friction experiments, instrumented with ultrasonic sensors to document the seismic

radiation properties of slow and fast laboratory earthquakes. Experiments were conducted on

granular fault gouge at a constant loading rate of 10 µm/s and we swept through a range of normal

stresses from 7-15 MPa. Following previous studies we produced a full spectrum of rupture modes

by modulating the loading stiffness in tandem with the fault zone normal stress. Acoustic emission

(AE) data were recorded continuously at 5 MHz from a network of sensors. We high-pass filter

the acoustic data at 10 kHz and document distinct differences and similarities between slow and

fast slip events. Interestingly, our data show that both slow and fast laboratory earthquakes radiate

high frequency energy (> 100 kHz). This includes slow events with peak fault slip rates < 100 µm/s

and stress drops of ~ 100 kPa. On the other hand, the cumulative energy and amplitude of the high-

frequency time-domain signals scale systematically with stress drop and thus are systematically

smaller for slow vs. fast lab earthquakes. Stable-sliding experiments demonstrate that the origin of

the high-frequency energy is fundamentally linked to changes in fault slip rate and breaking of

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contact junctions. The high-frequency signature of our slow and fast events suggests that these slip

modes maybe more similar than previously thought and that documented differences in their

seismic properties could arise from both source characteristics and variations in crustal properties

and/or observational constraints.

5.2 Introduction

Over the past 20+ years, high-resolution seismometers and continuous global positioning

system (GPS) networks have helped illuminate a continuum of fault slip behaviors (Beroza

and Ide, 2011). These observations show that tectonic faults store and release elastic-strain

energy through a spectrum of slip behaviors, ranging from slow slip to fast dynamic

earthquakes. Slow earthquakes encompass a range of slip behaviors including aseismic

creep, very-low frequency earthquakes (VLFE), low-frequency earthquakes (LFE), non-

volcanic tremor (NVT), and episodic tremor and slip (ETS) (Obara, 2002; Rogers and

Dragert, 2003; Shelly et al., 2007). Since the discovery of slow earthquakes, a fundamental

goal in earthquake seismology has been to elucidate the connection between slow and

regular earthquakes (Obara and Kato, 2016). If the underlying physics associated with slow

earthquakes is similar to ordinary earthquakes then we can use slow earthquakes, which

occur more frequently, to strengthen our understanding of larger earthquakes. Furthermore,

it is thought that slow earthquakes can trigger larger megathrust earthquakes, and thus,

tracking the spatio-temporal properties of slow events could help advance seismic hazard

analysis, earthquake early warning systems, and statistical forecasting (Kato et al., 2012;

Obara and Kato, 2016).

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Seismic radiation properties of earthquakes encode key information about

earthquake source processes, which in turn, can be used to help illuminate the connection

between slow and fast earthquakes. Recall, that the recorded ground motion from a seismic

sensor is a convolution of the source, propagation effects, and sensor/recording response.

Hence, the earthquake source properties can be disentangled from the seismogram via

spectral deconvolution (Aki, 1967; Brune 1970). In an ideal source spectrum, the

amplitudes are roughly constant for frequencies smaller than the corner frequency (fc) and

subsequently fall off at higher frequencies (Aki, 1967). The flat portion of the spectrum at

low-frequencies is approximately equal to the seismic moment and fc is inversely

proportional to the rise time, which represents the amount of time it takes the fault to reach

its maximum slip at a particular location on the fault (Udias et al., 2014). Furthermore, the

corner frequency is often used to infer the size of the source region and the stress drop of

the earthquake (Brune, 1970; Savage, 1972). Hence, basic properties of the recorded

ground motion are fundamentally linked to the source properties of earthquakes and the

analysis of these properties can provide important insights into the similarities and

differences between slow and fast earthquakes.

Unlike ordinary earthquakes the measured ground motion from slow tectonic

earthquakes is depleted in high-frequency energy (> 10 Hz) (Obara, 2002; Shelly et al.,

2007; Ito et al., 2007). The amplitude spectra of tremor, LFEs, and VLFEs show that these

events have small corner frequencies and are enriched in low-frequency energy between

.005-10 Hz (Shelly et al., 2007; Kao et al., 2005; Rubinstein, 2007). The depletion in high-

frequency energy can also be seen in the raw time-domain signals (Shelly et al., 2007; Kao

et al., 2005). Because slow earthquakes typically occur in regions that bound the locked

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seismogenic zone, it is possible that variations in path-effects, such as a low-velocity zone

within the source region could have a significant effect on the spectra of slow earthquakes

(Gomberg et al, 2012; Bostock et al, 2017). Alternatively, the lack of high-frequency

energy in slow earthquakes could be linked to their source properties (Bostock et al., 2015;

Thomas et al., 2016). For example, Thomas et al. 2016 pointed out that the depletion of

high-frequency energy in LFEs can be explained by the slow slip rates, low stress drops,

and slow rupture velocities.

Ultimately, the spectral properties of slow and fast events have significant

implications for earthquake scaling laws, earthquake nucleation, and earthquake rupture.

If the source properties of slow earthquakes are fundamentally different, then they should

obey different scaling laws and their underlying physics could be different than regular

earthquakes (Ide et al. 2007). However, the relationship between slow and fast ruptures is

not well understood and it is clear that more work is needed to help establish the connection

between slow and fast earthquakes (Michel et al., 2019; Frank and Brodsky, 2019)

In this work, we highlight elastic radiation properties of slow and fast laboratory

earthquakes. We use laboratory stick-slip experiments instrumented with an array of

ultrasonic transducers and elucidate the acoustic signatures of slow and fast ruptures. We

high-pass filter the acoustic signals and show that even our slowest laboratory earthquakes

generate high frequency energy. The remnants of this high-frequency pulse scale

systematically with event size and are modulated by fault slip rate. This high-frequency

signature suggests that slow and fast ruptures maybe more similar than previously thought

and the connections between the two can easily be overlooked without high-resolution

measurements.

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5.3 Slow and Fast Laboratory Earthquakes and Acoustic Emission Monitoring

We performed stick-slip experiments using a servo-controlled biaxial deformation

apparatus in a double-direct shear (DDS) configuration (Figure 5-1A). We sheared 3 mm layers of

quartz powder (median particle size 10.5 µm) under a constant loading rate of 10 µm/s and swept

through a range of normal stresses from 7-15 MPa. Fault displacements, normal and parallel to the

direction of shear, were measured by direct current displacement transformers (DCDT). Shear and

normal loads were measured with stain gauge load cells mounted in series with the load axes. We

measured the true fault slip by placing a small DCDT at the bottom of center forcing block of the

DDS referenced to the base plate (Figure 5-1A). Fault displacements and stresses were measured

continuously throughout the experiment at 100 Hz. Experiments were conducted at 100% relative

humidity by enclosing the DDS inside a plastic membrane and blowing humid air around the

sample throughout the experiment (see Bolton et al., 2020).

We document a continuum of slip behaviors from stable sliding to fast stick-slip events

(i.e., laboratory earthquakes) with peak slip rates ~ 5 mm/s (Figure 5-1). We modulate the loading

stiffness loading stiffness k, such that k/kc ~ 1, and systematically change the fault normal stress to

produce both slow and fast laboratory earthquakes (e.g., Leeman et al., 2016; Scuderi et al.,2016;

2017; Figure 5-1).

AE data are measured continuously throughout the experiment using broadband (~ 0.0001-

2 MHz) piezoceramic sensors (6.25 mm diameter; 4 mm thick). The sensors are epoxied inside

steel blocks and positioned ~ 22 mm from the edge of the fault zone. Acoustic data are sampled

continuously at 25 MHz and decimated to 5 MHz using a 16-bit National Instruments PXIe-5171

data acquisition system. In order to avoid clipping the co-seismic AEs, AE data are digitized

between 200 mV-1400 mV. It should also be noted that the acoustic signals are not pre-

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amplified/filtered during the data acquisition process. AE data are recorded from a total of 6

channels oriented parallel to the direction of shear (see Figure 5-1 inset).

5.4 Results

5.4.1 Geodetic source properties of Slow and Fast Laboratory Earthquakes

Each stick-slip experiment started out with a period of stable of sliding, followed

by the onset of slow (silent) laboratory earthquakes and transitioned into fast (audible)

stick-slip events as the normal stress was systematically increased from 7-15 MPa (Figure

5-1B). We quantified the size of the stick-slip event by estimating the stress drop and the

peak fault slip rate (Figure 5-1C). Stress drop is estimated geodetically as the difference

between the peak shear stress and minimum shear stress of the co-seismic slip phase

(Figure 5-1B). The peak fault slip rate is estimated from the time derivative of the fault

displacement transducer (see Figure 5-1A). Note, it’s temporal evolution represents the

average fault motion and is fundamentally different than the far-field loading rate. Stress

drop and peak slip rate of lab earthquakes scale systematically with fault normal stress and

is consistent with previous studies (Figure 5-1D; Leeman et al., 2016; Shreedharan et al.,

2020; Wu and McLaskey, 2019). Slip events are bifurcated into a slow or fast category

depending upon their peak slip velocities. Specifically, slip events with peak slip velocities

< 1 mm/s are defined as slow and slip events with peak slip rates >= 1 mm/s are defined as

fast. This threshold marks the transition from silent to audible stick-slip and is consistent

with previous studies (e.g., Leeman et al., 2016; Shreedharan et al., 2020).

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We estimate the slip duration of the stick-slip events using two different methods

(Figure 5-2A). Consistent with previous studies we estimate the slip duration as the time

difference between the minimum shear stress and peak shear stress (Leeman et al., 2016;

Figure 5-2B). We also use the slip velocity to estimate the slip duration (Figure 5-2A). In

particular, we identify when the slip velocity reaches 20% of its peak during the

acceleration and deceleration phase and take the difference between these two time stamps

as the slip duration (Figure 5-2A and Figure 5-2C). Both methods demonstrate that slip

duration scales inversely with stress drop, consistent with previous laboratory studies

(Leeman et al, 2016; 2018; Scuderi et al., 2016; McLaskey and Yamashita, 2017;

Shreedharan et al., 2020). However, slip durations derived from the slip velocity are much

lower than those derived from the shear stress curve. This discrepancy exists because of

the slow nucleation phases (i.e., slow decreases in shear stress) that precedes the rapid fault

acceleration.

As mentioned above fc ~ 1/T, where T is the duration of sliding. We use the slip

duration derived from the slip velocity to approximate fc because its definition is directly

associated with the rapid fault acceleration/deceleration. From here forward we refer to

low-frequency signals as f <= fc and high-frequency signals as f > fc.

5.4.2 Spectral characteristics of slow and fast laboratory earthquakes

The raw continuous AE signals we report on are not high-passed filtered, and thus, are

contaminated with low-frequency electrical noise and mechanical noise. We do not filter the signals

during the data acquisition process because we are interested in preserving the full bandwidth of

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the seismic signals. Unfortunately, our hydraulic power-supply (HPS) adds a significant amount

of noise to the acoustic signals at low-frequencies (Figure 5-3 and Figure D1). The effect of the

HPS can be seen clearly by comparing the time-series and spectra of recorded AE signals with and

without the HPS turned on (Figure D1). The HPS radiates energy between ~ 0-10000 Hz and has

significant impact on frequencies < 1000 Hz, where it adds ~ 2-orders of magnitude in noise. It’s

also important to note that the HPS noise is in the same bandwidth as the slip events (see Figure 5-

3), thus the HPS noise cannot be removed with standard filtering approaches. The HPS noise

hinders our ability to comment on the spectral characteristics in Figure 5-2 because the signal-to-

noise-ratios (SNR) are so low. If we follow the convention of previous laboratory studies (Wu and

McLaskey, 2019), then a SNR >= 20 dB is needed to confidently assess the data in Figure 5-2.

Because this is not feasible we have focused most of our analysis on the time-domain

characteristics.

AE time-series and shear stress evolution for a representative set of slow and fast events

are illustrated in Figures 5-3A:E. Acoustic traces are 2s long and centered about their peak AE

amplitude reached during the co-seismic slip phase. The amplitude spectra of these traces are

plotted in Figures 5-3F:G. Prior to computing the spectra we remove the mean and taper the

acoustic traces with a Kaiser window. We also compute the spectra of 2s long noise traces derived

from the initial stages of the seismic cycle (Figure 5-3F inset). The initial stages of the seismic

cycle is associated with low levels of AE activity, and thus, represents an ideal location to quantify

the noise (see Bolton et al., 2020). Furthermore, because the acoustic signals are not pre-amplified,

only the co-seismic slip events are detected (i.e., we do not observe pre-seismic AEs). Following

Wu and McLasky, 2018, we perform an averaging scheme in the frequency domain after computing

the discrete Fourier transform (DFT). This averaging procedure ensures that the frequency bins are

equally spaced on a log scale (~ 20 bins per decade in frequency) and requires at least 3 samples

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of the DFT for each frequency bin. As a result of our 2s long time windows and the averaging

scheme, our amplitude spectra plots span from ~ 11 Hz-2.5 MHz.

The amplitude spectra in Figure 5-3 are characterized by a roughly flat low-frequency

component, followed by a sharp fall-off between ~400-10000 Hz, and a subtle decay between .01-

2.5 MHz. We observe a high-frequency band between ~ 80-500 kHz that lights up, irrespective of

the size of the slip event (Figure 5-3F and 5-3G). The center frequency of the acoustic sensors is

between ~ 200-500 kHz, so it’s likely that this high-frequency ban is related to the sensitivity of

the sensors. Although the sensors are most efficient at high-frequencies, they are still able to record

low frequency signals < 1000 Hz (see also Wu and Mclaskey 2018;2019).

The spectral content of our slow laboratory earthquakes (i.e., 7-11 MPa) are practically

indistinguishable from one another for frequencies smaller than 1000 Hz and are modestly different

within the 100-400 kHz bandwidth, with faster events radiating more high-frequency energy

(Figure 5-3F:5-3G). However, the SNR is ~ 1 for frequencies <= 100 kHz for the slow events, and

thus, the spectra are primarily noise and do not necessarily reflect the low-frequency characteristics

of the source (Figure 5-3G). The corner frequency for the slow events is < 10 Hz, and thus, lies

within the bandwidth where the SNR is too low to comment on. As a result, we can only comment

on the high-frequency characteristics, where the SNR is slightly higher than 1. Note, that the slow

events still radiate high-frequency energy between ~ 100-500 kHz, despite having peak slip rates

<= 500 µm/s. The shape of the spectra for the slow events are remarkably similar between 100-500

kHz (Figure 5-3G). The spectral amplitudes increase from ~ 100 kHz and reach a peak between

200-300 kHz (Figure 5-3G). Note, the data reported in Figure 5-3 are derived from one channel

and one stick-slip event from each normal stress. However, the characteristics in Figure 5-3 are

generally representative of other channels/stick-slip events (Figure D2).

In contrast, our fast laboratory earthquakes (13-15 MPa) have slightly higher SNR across

most of their bandwidth. We are unable to calculate the slip duration and corner frequency for the

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fastest event at 15 MPa due to the limited resolution we have at 100 Hz. However, we expect that

the true corner frequency is ~ 1000 Hz based on the data in Figure 5-3G. The fastest event at 15

MPa contains a significant amount of energy < 10 kHz and between 100-500 kHz and the shape of

its spectrum is different than the slow events (Figures 5-3G). In particular, the spectral amplitudes

increase abruptly from 80-100 kHz and have two dominant peaks around 100 and 300 kHz. The

fast event at 13 MPa has a SNR ~ 2 for frequencies < 100 Hz and the shape of its spectrum between

100-500 kHz is similar to the event at 15 MPa (Figure 5-3G).

5.4.3 Time-domain and High-Frequency Characteristics

To distinguish the similarities and differences between our slow and fast events, we plot

zooms of the main AE signals associated with the co-seismic stress drops from Figure 5-3 (Figure

5-4). Peak slip rates for these events range between 98-5417 µm/s, and thus, are representative

analogs of the full continuum of tectonic failure modes. The seismic characteristics of our slow and

fast slip events are similar to those reported in previous studies (e.g., Wu and McLaskey, 2019). In

particular, our slow laboratory events have broad-time domain signals with low amplitudes that are

slightly above the noise level (Figure 5-4A). The character of the main slip event (approximately

in the center of the traces) is very simplistic and resembles an ideal source-time function of a natural

earthquake. On the other hand, the fast events (e.g., 15 MPa) have impulsive time-domain signals,

large amplitudes, and contain a significant degree of coda energy following the first arrival (Figure

5-4B). The overall signature of these events is in many ways similar to the time-domain signatures

of natural earthquakes (Peng and Gomberg, 2010).

To illuminate the similarities and differences between slow and fast laboratory

earthquakes, we analyze the high-frequency content of their time-domain signals. In particular, we

high-pass filter the acoustic traces in Figure 5-3 at 10 kHz (Figure 5-5). We use a 10 kHz cutoff

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frequency because frequencies below this are contaminated by the HPS noise (see section 5.3.2 and

Figure D1). Interestingly, all of the slip events analyzed in Figure 5-5 contain remnants of high-

frequency energy (> 10 kHz) and is consistent with the spectra in Figure 5-3. Note, this high-

frequency energy exists in the slowest events that have peak slip rates < 100 µm/s and stress drops

~ 100 kPa (e.g., Figure 5-5A). This observation is contrary to previous laboratory and field studies

that have demonstrated that slow earthquakes (i.e., NVT, LFEs, VLFEs) are deficient in high-

frequency energy (Kato et al., 2005; Shelly et al., 2007; Rubinstein 2007; Thomas et al., 2016; Wu

and McLaskey, 2019;). To further assess the robustness of this observation, we parameterized the

high-frequency time-domain pulse by computing its duration, cumulative energy, and peak

amplitude for all of the stick-slip events for which AE data were recorded (Figure 5-6).

Remarkably, our data show that the characteristics depicted in Figure 5-5 are common features

among all of our stick-slip events. The radiated energy and peak amplitude of the high-frequency

pulse scale systematically with stress drop, while the pulse duration scales inversely with stress

drop (Figures 5-6C:E).

We quantify the band-width of the high-frequency energy by filtering the acoustic traces

at various cutoff frequencies (Figures 5-7:5-8). This filtering approach reveals that the high-

frequency character of slow and fast laboratory earthquakes is in fact band-limited. In particular,

the slowest events only radiate high-frequency energy between 100-500 kHz, while the fastest

events contain high-frequency energy between 80-800 kHz (Figure 5-8). This procedure reveals

that the slowest events are indeed deficient in high frequency energy > 500 kHz. Furthermore, the

maximum frequency radiated during co-seismic failure scales systematically with increasing

normal stress (Figure 5-8B).

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5.5 Discussion

Seismic waves are enriched in information regarding earthquake source properties and are

key for establishing scaling laws of earthquake rupture (Aki, 1967; Brune, 1970; Ide and Beroza,

2001). If the physical processes that govern earthquake rupture are invariant to earthquake size,

then earthquakes of all sizes should follow similar scaling laws (Aki, 1967; Prieto et al., 2004).

However, slow earthquakes represent a conundrum in earthquake science because they are depleted

in high-frequency energy ( > 10 Hz), have small corner frequencies, low slip rates, small stress

drops, low rupture velocities, when compared to regular earthquakes. These properties often give

rise to different scaling laws (e.g., moment-duration), which in turn could reflect differences in

earthquake source processes and violate arguments for self-similarity of earthquake rupture (Ide et

al., 2007; Bostock et al., 2015; Thomas et al., 2016).

However, recent work suggests that slow earthquakes may follow similar scaling

relationships to regular earthquakes (Brodsky and Frank, 2019; Michel et al., 2019). In addition,

laboratory studies show that both slow and fast earthquakes can originate along the same fault by

simply modulating the effective stiffness and frictional properties of the fault interface (Kaproth

and Marone, 2013; Leeman et al., 2016; 2018; Scuderi et al., 2016;2017;2020; Tinti et al., 2016;

McLaskey and Yamashita, 2017; Wu and McLaskey, 2019; Hulbert et al., 2019; Shreedharan et al.

2020; Bolton et al., 2020). Despite these recent advances, the connection between slow and fast

ruptures is still not well understood. Here, we use well-controlled laboratory experiments

instrumented with ultrasonic transducers to illuminate the seismic radiation properties of slow and

fast laboratory earthquakes.

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5.5.1 The high-frequency signature of slow and fast laboratory earthquakes

We document systematic differences in the time-domain signatures of slow and fast

laboratory earthquakes. We high-pass filter the time-domain signals at 10 kHz and demonstrate that

both slow and fast laboratory earthquakes emanate high-frequency energy (Figures 5-5:5-6). Slow

laboratory earthquakes radiate high-frequency energy over a smaller bandwidth compared to faster

events and is consistent with the band-limited nature of slow tectonic earthquakes (Figures 5-7:5-

8). Our data are in good agreement with previous laboratory studies, which show that fast laboratory

earthquakes radiate high-frequency energy (McLaskey and Glaser, 2011; McLaskey et al., 2012;

Wu and McLaskey, 2019; Marty et al., 2020). In addition, we show that cumulative energy and

peak amplitude of the high-frequency pulses scale systematically with stress drop, with faster

ruptures radiating more energy. This is consistent with seismic observations that show that tectonic

earthquakes with large stress drops radiate more high-frequency energy (Hanks and McGuire,

1981). Furthermore, we show that the maximum frequency (Fmax) radiated during co-seismic slip

scales systematically with event size (Figure 5-8B). We follow the interpretation of previous works

and propose that earthquakes with bigger stress drops radiate more high-frequency energy due to a

systematic increase in frictional healing during the inter-seismic period (McLaskey et al., 2012).

In contrast to previous laboratory studies, our data show that slow laboratory earthquakes

with peak slip rates <100 µm/s and stress drops < 200 kPa radiate high-frequency energy (> 10

kHz) (Figure 5-5; McLaskey and Yamashita, 2017; Wu and McLaskey, 2019). This observation is

also in contrast to field observations which show that NVT,LFEs, and VLFEs are depleted in high-

frequency energy (Kao et al., 2005; Shelly et al., 2007; Rubinstein et al., 2007; Ide et al., 2007; Ito

et al., 2007; Bostock et al., 2015; Thomas et al., 2016). In particular, LFEs have small corner

frequencies, low stress drops, slow rupture velocities, and slow slip rates, which are thought to act

in concert to suppress the high-frequency energy (Thomas et al., 2016). These studies suggest that

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the deficiency in high-frequency energy of slow tectonic earthquakes is fundamentally linked to

their source properties. However, our slow laboratory earthquakes share most, if not all, of the same

source properties of LFEs. That is, relative to our fast events, our slow events have low stress drops,

long slip durations, and small slip rates (Figures 5-1:5-2). Nevertheless, our slow slip events still

contain a high-frequency signature. Why then are tectonic slow slip events (e.g., LFEs) depleted in

high-frequency energy, but slow laboratory earthquakes are not?

We propose that attenuation plays a key role in the ability to measure high-frequency

radiation during slow and fast ruptures. The geometry of our setup along with our high-resolution

measurements allow us to measure small amounts of high-frequency energy generated during slow

slip (Figure 5-1A). More specifically, our acoustic sensors are placed ~ 22 mm from the edge of

the fault and the acoustic waves that are radiated during co-seismic failure spend most of their time

propagating through the steel loading blocks (Figure 5-1A). Aside from the thin gouge layer where

the events nucleate, the acoustic waves do not propagate through a highly attenuating medium, such

as a low-velocity zone, where the loss of high-frequency seismic waves is more likely to occur. It

has been suggested that the depletion of high-frequency energy in LFEs could be driven by near-

source attenuation associated with a low-velocity zone (Gomberg et al., 2012 and Bostock et al.,

2017). Therefore, the dichotomy in seismic radiation patterns between slow and fast ruptures could

simply be explained by variations in crustal properties and/or inadequate measurements near the

fault zone. Furthermore, in our laboratory experiments the entire 100 x 100 mm2 fault patch ruptures

during co-seismic failure and our sensors are only 22 mm away from the source. Hence, we are

most likely to be considered in the near-field, which in turn, would be favorable for observing high-

frequency characteristics. In fact, this could explain why previous laboratory studies were unable

to measure high-frequency energy in slow laboratory earthquakes. For example, the slowest events

reported in Wu and Mclaskey, 2019 have peak slip rates of 500 µm/s (5x faster than our slowest

events), but lack a high-frequency signature. However, their sensors are located ~ 200 mm from

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edge of the fault and the radiated waves propagate through a thick block of granite (opposed to the

steel loading blocks in our case). It’s possible that the slow events reported in Wu and McLaskey,

2019 do indeed radiate high-frequency energy. However, the high-frequency waves could be

significantly attenuated before reaching the sensors. In fact, this could also explain why previous

investigators have been unable to measure a high-frequency signature associated with slow tectonic

earthquakes.

The fact that slow and fast laboratory earthquakes radiate high-frequency energy provides

additional evidence that these two slip modes maybe more common than previously thought.

Furthermore, our work implies that the source-sensor geometry and the medium surrounding the

fault zone could have a significant effect on high-frequency characteristics. Because we are so close

to the fault zone and the acoustic waves propagate mainly through steel loading blocks we are able

measure high-frequency energy during slow slip. Our work highlights the importance of having

near-field measurements and suggests that attenuation plays a key role in regulating seismic

properties (e.g., Abercrombie et al., 2021).

5.5.2 The origin of high-frequency energy in laboratory earthquakes

The data presented in Figures 5-5:5-8 suggest that slow laboratory earthquakes contain a

high-frequency signature and the bandwidth over which this high-frequency energy exists scales

with event size. Given that both slow and fast laboratory earthquakes radiate high-frequency

energy, the physical mechanism and the control variable(s) responsible for the high-frequency

energy must be common to both of styles of rupture. The systematic scaling in Figures 5-6C:E,

suggests that the high-frequency energy is regulated by event size. Furthermore, based on previous

works we know that AE properties are strongly affected by changes in fault slip rate (McLaskey et

al., 2014; Dresen et al., 2020; Bolton et al., 2020; 2021). Thus, we propose that the origin of high-

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frequency energy in our stick-slip experiments is connected to fault slip rate and the

breaking/sliding of grain contact junctions (e.g., McLaskey and Glaser, 2011).

To test this idea, we conducted a stable-sliding experiment at a constant normal load of 9

MPa and swept through 4-orders of magnitude in sliding velocity (Figure 5-9). We compute the

amplitude spectra of 2s long time traces for each shearing velocity (Figure 5-9B). Similar to the

stick-slip events the data show a distinct high-frequency band between 80-500 kHz. Both the band-

width and amplitude of this frequency band increases with shearing rate/fault slip rate (Figures 5-

9B-C). Interestingly, the shape of the spectra for the stable sliding data and the stick-slip data are

remarkably similar. In particular, the spectra of the slow stick slip events are similar to the stable

sliding data at 4.0 and 43 µm/s. They both show a gradual increase in amplitude between 100-300

kHz and have a single peak at 300 kHz. The data at 435 µm/s is identical to the fast stick slip event

at 15 MPa in Figure 5-3G. Both spectra have a similar shape and are characterized by two peaks

near ~ 100 and 300 kHz. For the slowest shearing rate (0.44 µm/s) the amplitudes remain flat across

this entire band-width and approximate that of the noise. This integrates well with the stick-slip

data, given that the slowest events have peak slip rates ~ 100 µm/s. The fact that our sensors are

unable to record high-frequency energy at 0.44 µm/s could simply be related to the

resolution/source-sensor geometry.

Fracture mechanics models and laboratory data suggest that high-frequency ground motion

is localized behind the rupture front and is caused by abrupt changes in rupture velocity (Madariaga,

1977; 1984; Marty et al., 2020). It’s also possible that the high-frequency energy radiated during

laboratory earthquakes originates from the breaking/sliding of contact junctions (e.g., Tsai and

Hirth, 2020). In particular, the elastic impact model proposed by Tsai and Hirth, 2020, implies that

high-frequency energy can radiate at any time during the rupture process. This view is consistent

with our stable sliding data, which shows that high-frequency energy is radiated at all times during

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frictional sliding. Taken together our data indicate that the high-frequency energy radiated during

slow and fast lab earthquakes is modulated by fault slip rate and originates from the breaking and

sliding of grain contact junctions (Glaser and McLaskey, 2011; Bolton et al., 2020; Tsai and Hirth,

2020). Larger and faster laboratory earthquakes experience more frictional healing during the inter-

seismic period and as a result radiate more high-frequency energy during the co-seismic slip phase.

Our observations are also in good agreement with previous lab and field studies that have suggested

that fault slip rate plays a key role in regulating seismic and acoustic properties (McLaskey et al.,

2014; Wech and Bartlow, 2014; Thomas et al., 2016; Dresen et al., 2020; Bolton et al., 2020; 2021;

Bletery and Nocquet, 2020).

5.6 Conclusion

We analyze AE data associated with a full continuum of slip behaviors, ranging from

stable-sliding to fast-dynamic stick-slip. For stick-slip experiments, we focus our analysis on AE

characteristics of the co-seismic slip events and document systematic differences and similarities

in seismic radiation properties. We demonstrate that both slow and fast lab earthquakes radiate

high-frequency energy between 80-800 kHz. We high-pass filter the AE signals and show that the

cumulative energy and amplitude of the high-frequency pulses scale systematically with stress

drop. We augment our stick-slip experiments with data from a stable sliding experiment and

demonstrate that high-frequency energy in our experiments is modulated by fault slip rate and

originates from the breaking and sliding of grain contact junctions. Taken together our results

suggest that slow and fast laboratory earthquakes have overlapping seismic properties and reported

differences between these slip modes could originate from variations in crustal properties and/or a

lack of high-resolution measurements near the fault zone.

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Figure 5-1: A. Double-direct shear (DDS) configuration, consisting of two layers of fault gouge sandwiched between three steel reinforcement blocks. A fault displacement transducer is mounted to the bottom of the center block and referenced to the base plate. Steel acoustic blocks embedded with piezoceramic transducers (orange squares) are placed 22 mm from the edge of the fault. Top inset shows AE channels. B. Shear stress and normal stress plotted versus time for two experiments. Each experiment starts off with a period of stable sliding, followed by the onset of slow stick-slip after ~ 10 mm of shear. C. Slip velocity and shear stress evolution for one seismic cycle. For each slip cycle, we compute the stress drop and peak slip rate. Stress drop is computed as the difference between the maximum and minimum shear stress (green circles). D. Stress drop as a function of peak slip velocity. Circles represent data from Experiment p5415 and triangles represent data from Experiment p5435; symbols are color coded according to normal stress. Black symbols represent averages at each normal stress and error bars represent 1 standard deviation. The transition between slow and fast stick-slip occurs ~ 1 mm/s (see Leeman et al., 2016). Stress drop scales systematically with peak slip rate.

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Figure 5-2: A. Slip velocity and shear stress for a slow slip event. Black dots denote the peak and minimum shear stress of the co-seismic slip phase. Slip DurationSS derived from the shear stress curve is estimated as the time difference between the minimum and peak shear stress. Slip durationSR is derived from the slip velocity curve. Blue symbols represent 20% of the peak slip rate. Slip durationSR is defined as the time difference between the two blue symbols. B-C Slip duration

scales inversely with stress drop. Note, color coding and symbols are the same as Figure 5-1. We do not include the fastest events in C due to the limited resolution we have from at 100 Hz. Slip durations derived from the slip rate curve are smaller than the those derived from the shear stress curve.

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Figure 5-3: A-E Shear stress and AE amplitude evolution during the co-seismic slip phase for a representative series of slow to fast laboratory earthquakes, with peak slip rates spanning between 98-5417 µm/s. Acoustic traces are 2s long and correspond to channel 1. F. Amplitude spectra from acoustic traces in A-E. Curves are color coded according to their respective trace. The spectra are essentially the same for the slow events between 7-11 MPa; fast events at 13 and 15 MPa show a modest increase in amplitude at low frequencies (<1000 Hz) and at high-frequencies (>= 10 kHz). Inset shows noise spectra from 2s long traces derived from the initial stages of the seismic cycle. G Signal to noise ratios derived from panel F. Slow events (7-11 MPa) have poor SNR across most of their bandwidth, with values slightly higher than 1 within the 100-500 kHz bandwidth. Fast events (13-15 MPa) have higher SNR for frequencies <10 kHz and between 80-500 kHz.

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Figure 5-4: A. Zoom of slow slip events from 7-11 MPa. Note, acoustic traces correspond to the same data plotted in Figure 5-3. Acoustic traces are centered about their peak amplitude and offset vertically for clarity. The time-domain characteristics change slightly with normal stress and have a simplistic structure compared to the fast events in panel B. B. Zoom of time-domain signatures of fast slip events at 13 and 15 MPa (same events in Figure 5-3). Both events are larger and more impulsive compared to the slow events in panel A

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Figure 5-5: Top panel (A,C,E,G,I): Shear stress and raw acoustic amplitudes for slow (7-11 MPa) and fast (13-15 MPa) slip events. Bottom panel (B,D,F,H,J): Results from applying a high-pass filter at 10 kHz to time-domain signals in top panel. Both slow and fast slip events radiate high-frequency energy. The high-frequency pulse increases in size as events become progressively faster. Note, the scale difference for fast events.

149

Figure 5-6: A. Shear stress and AE time-series for fast event at 13 MPa. B. AE signal from A after high-pass filtering the signal at 10 kHz. Plotted in red is the acoustic energy (see Bolton et al., 2020). We parameterized the high-frequency pulse by estimating its peak amplitude, cumulative energy, and pulse duration. The cumulative energy is computed by integrating the red curve between the beginning and end of the pulse, denoted by the blue symbols. Pulse duration is estimated as time difference between the two blue symbols. C-E Peak amplitude, cumulative energy, and pulse duration as a function of stress drop, respectively. Peak amplitude and cumulative energy scale systematically with stress drop; pulse duration scales inversely with stress drop.

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Figure 5-7: A-C. High-passed acoustic signals from slow slip events in Figures 5-3:5-5 at various cut-off frequencies. Note, the high-frequency pulse is band-limited and is most prominent within the 10-200 kHz bandwidth. D-E. Same as panels A-C, but for fast slip events in Figures 5-3:5-5. Unlike, the slow slip events the fast events have high-frequency energy >= 400 kHz and have a much broader band-width.

151

Figure 5-8: A. Cumulative energy of high-frequency pulses as a function of cut-off frequency for slow and fast slip events (see Figure 5-6). We high-pass filter the same traces from Figures 5-3:5-5. Note, the cumulative energy can only be estimated for data that have high-frequency pulses above the noise level (see Figure 5-6B). Cumulative energy decreases with increasing cut-off frequency. B. Maximum frequency for which the cumulative energy can be computed in A as a function of normal stress. Maximum frequency increases with normal stress, suggesting that the highest frequencies radiated during failure scale with event size.

152

Figure 5-9: A. Shear stress and time versus load-point displacement for a stable sliding experiment. Loading-rate was increased from 0.44 µm/s to 435 µm/s. Grey circles represent the time stamps from which AE traces are derived in panel B. B. Amplitude spectra derived from the 2s long acoustic traces (see inset) for each load-point-velocity. The noise trace was collected during a hold at the beginning of the experiment (see panel A). C. Zoom of high-frequency components in B. The amplitudes and band-width of the high-frequency energy increase with loading-rate. D. Acoustic traces from B band-passed between 150-400 kHz. The size and number of AEs increases with loading rate.

153

5.7 References

Abercrombie, R., Trugman, D., Shearer, P., Chen, X., Zhang, J., Pennington, C., Hardebeck, J.,

Goebel, T., and Ruhl, C. (2021). Does earthquake stress drop increase with Depth in the crust?

htttps:/doi.org/10.1002/essoar.10506989.1

Aki, K. (1967). Scaling law of seismic spectrum. Journal of geophysical research, 72(4), 1217-

1231.

Bletery, Q., & Nocquet, J. M. (2020). Slip bursts during coalescence of slow slip events in

Cascadia. Nature communications, 11(1), 1-6.

Bolton, D. C., Shreedharan, S., Rivière, J., & Marone, C. (2020). Acoustic energy release during

the laboratory seismic cycle: Insights on laboratory earthquake precursors and

prediction. Journal of Geophysical Research: Solid Earth, 125,

e2019JB018975. https://doi.org/10.1029/2019JB018975

Bostock, M. G., Thomas, A. M., Savard, G., Chuang, L., & Rubin, A. M. (2015). Magnitudes and

moment-duration scaling of low-frequency earthquakes beneath southern Vancouver

Island. Journal of Geophysical Research: Solid Earth, 120(9), 6329-6350.

Bostock, M. G., Thomas, A. M., Rubin, A. M., & Christensen, N. I. (2017). On corner

frequencies, attenuation, and low-frequency earthquakes. Journal of Geophysical Research:

Solid Earth, 122(1), 543-557.

154

Brune, J. N. (1970). Tectonic stress and the spectra of seismic shear waves from

earthquakes. Journal of geophysical research, 75(26), 4997-5009.

Dresen, G., Kwiatek, G., Goebel, T., & Ben-Zion, Y. (2020). Seismic and Aseismic Preparatory

Processes Before Large Stick–Slip Failure. Pure and Applied Geophysics, 177(12), 5741-

5760.

Frank, W. B., & Brodsky, E. E. (2019). Daily measurement of slow slip from low-frequency

earthquakes is consistent with ordinary earthquake scaling. Science advances, 5(10),

eaaw9386.

Gomberg, J., Creager, K., Sweet, J., Vidale, J., Ghosh, A., & Hotovec, A. (2012). Earthquake

spectra and near-source attenuation in the Cascadia subduction zone. Journal of Geophysical

Research: Solid Earth, 117(B5).

Hanks, T. C., & McGuire, R. K. (1981). The character of high-frequency strong ground

motion. Bulletin of the Seismological Society of America, 71(6), 2071-2095.

Hulbert, C., Rouet-Leduc, B., Johnson, P. A., Ren, C. X., Rivière, J., Bolton, D. C., & Marone, C.

(2019). Similarity of fast and slow earthquakes illuminated by machine learning. Nature

Geoscience, 12(1), 69-74.

Ide, S., & Beroza, G. C. (2001). Does apparent stress vary with earthquake size?. Geophysical

Research Letters, 28(17), 3349-3352.

Ide, S., Beroza, G. C., Shelly, D. R., & Uchide, T. (2007). A scaling law for slow

earthquakes. Nature, 447(7140), 76-79.

Ito, Y., Obara, K., Shiomi, K., Sekine, S., & Hirose, H. (2007). Slow earthquakes coincident with

episodic tremors and slow slip events. Science, 315(5811), 503-506.

Kanamori, H., & Anderson, D. L. (1975). Theoretical basis of some empirical relations in

seismology. Bulletin of the seismological society of America, 65(5), 1073-1095.

155

Kao, H., Shan, S. J., Dragert, H., Rogers, G., Cassidy, J. F., & Ramachandran, K. (2005). A wide

depth distribution of seismic tremors along the northern Cascadia margin. Nature, 436(7052),

841-844.

Kaproth, B. M., & Marone, C. (2013). Slow earthquakes, preseismic velocity changes, and the

origin of slow frictional stick-slip. Science, 341(6151), 1229-1232.

Kato, A., Obara, K., Igarashi, T., Tsuruoka, H., Nakagawa, S., & Hirata, N. (2012). Propagation

of slow slip leading up to the 2011 Mw 9.0 Tohoku-Oki earthquake. Science, 335(6069), 705-

708.

Leeman, J. R., Saffer, D. M., Scuderi, M. M., & Marone, C. (2016). Laboratory observations of

slow earthquakes and the spectrum of tectonic fault slip modes. Nature communications, 7(1),

1-6.

Leeman, J. R., Marone, C., & Saffer, D. M. (2018). Frictional mechanics of slow

earthquakes. Journal of Geophysical Research: Solid Earth, 123(9), 7931-7949.

Madariaga, R. (1977). High-frequency radiation from crack (stress drop) models of earthquake

faulting. Geophysical Journal International, 51(3), 625-651.

Madariaga, R. (1983). High frequency radiation from dynamic earthquake. Ann. Geophys., 1, 17.

Mair, K., Frye, K. M., & Marone, C. (2002). Influence of grain characteristics on the friction of

granular shear zones. Journal of Geophysical Research: Solid Earth, 107(B10), ECV-4.

Marty, S., Passelègue, F. X., Aubry, J., Bhat, H. S., Schubnel, A., & Madariaga, R. (2019). Origin

of high-frequency radiation during laboratory earthquakes. Geophysical Research

Letters, 46(7), 3755-3763.

McLaskey, G. C., & Glaser, S. D. (2011). Micromechanics of asperity rupture during laboratory

stick slip experiments. Geophysical Research Letters, 38(12).

156

McLaskey, G. C., Thomas, A. M., Glaser, S. D., & Nadeau, R. M. (2012). Fault healing promotes

high-frequency earthquakes in laboratory experiments and on natural

faults. Nature, 491(7422), 101-104.

McLaskey, G. C., & Lockner, D. A. (2014). Preslip and cascade processes initiating laboratory

stick slip. Journal of Geophysical Research: Solid Earth, 119(8), 6323-6336.

Mclaskey, G. C., & Yamashita, F. (2017). Slow and fast ruptures on a laboratory fault controlled

by loading characteristics. Journal of Geophysical Research: Solid Earth, 122(5), 3719-3738.

Michel, S., Gualandi, A., & Avouac, J. P. (2019). Similar scaling laws for earthquakes and

Cascadia slow-slip events. Nature, 574(7779), 522-526.

Obara, Kazushige. "Nonvolcanic deep tremor associated with subduction in southwest

Japan." Science 296.5573 (2002): 1679-1681.

Obara, K., & Kato, A. (2016). Connecting slow earthquakes to huge

earthquakes. Science, 353(6296), 253-257.

Prieto, G. A., Shearer, P. M., Vernon, F. L., & Kilb, D. (2004). Earthquake source scaling and

self-similarity estimation from stacking P and S spectra. Journal of Geophysical Research:

Solid Earth, 109(B8).

Rubinstein, J. L., Vidale, J. E., Gomberg, J., Bodin, P., Creager, K. C., & Malone, S. D. (2007).

Non-volcanic tremor driven by large transient shear stresses. Nature, 448(7153), 579-582.

Savage, J. C. (1972). Relation of corner frequency to fault dimensions. Journal of geophysical

research, 77(20), 3788-3795.

Scuderi, M. M., Marone, C., Tinti, E., Di Stefano, G., & Collettini, C. (2016). Precursory changes

in seismic velocity for the spectrum of earthquake failure modes. Nature geoscience, 9(9),

695-700.

157

Scuderi, M. M., Collettini, C., Viti, C., Tinti, E., & Marone, C. (2017). Evolution of shear fabric

in granular fault gouge from stable sliding to stick slip and implications for fault slip

mode. Geology, 45(8), 731-734.

Scuderi, M. M., Tinti, E., Cocco, M., & Collettini, C. (2020). The Role of Shear Fabric in

Controlling Breakdown Processes During Laboratory Slow-Slip Events. Journal of

Geophysical Research: Solid Earth, 125(11), e2020JB020405.

Shelly, D. R., Beroza, G. C., & Ide, S. (2007). Non-volcanic tremor and low-frequency

earthquake swarms. Nature, 446(7133), 305-307.

Shreedharan, S., Bolton, D. C., Rivière, J., & Marone, C. (2020). Preseismic fault creep and

elastic wave amplitude precursors scale with lab earthquake magnitude for the continuum of

tectonic failure modes. Geophysical Research Letters, 46.

https://doi.org/10.1029/2020GL086986

Thomas, A. M., Beroza, G. C., & Shelly, D. R. (2016). Constraints on the source parameters of

low-frequency earthquakes on the San Andreas Fault. Geophysical Research Letters, 43(4),

1464-1471.

Tinti, E., Scuderi, M., Scognamiglio, L., Di Stefano, G., Marone, C., & Collettini, C. (2016). On

the evolution of elastic properties during laboratory stick-slip experiments spanning the

transition from slow slip to dynamic rupture. Journal of Geophysical Research: Solid

Earth, 121(12), 8569-8594.

Tsai, V. C., & Hirth, G. (2020). Elastic impact consequences for high-frequency earthquake

ground motion. Geophysical Research Letters, 47(5), e2019GL086302.

Udías, A., Vallina, A. U., Madariaga, R., & Buforn, E. (2014). Source mechanisms of

earthquakes: theory and practice. Cambridge University Press.

Wech, A. G., & Bartlow, N. M. (2014). Slip rate and tremor genesis in Cascadia. Geophysical

Research Letters, 41(2), 392-398.

158

Wu, B. S., & McLaskey, G. C. (2018). Broadband calibration of acoustic emission and ultrasonic

sensors from generalized ray theory and finite element models. Journal of Nondestructive

Evaluation, 37(1), 1-16.

Wu, B. S., & McLaskey, G. C. (2019). Contained laboratory earthquakes ranging from slow to

fast. Journal of Geophysical Research: Solid Earth, 124(10), 10270-10291.

159

Chapter 6

Concluding Remarks

6.1 Research Summary

Understanding the evolution of foreshocks and seismic signals throughout the seismic

cycle is key for improving earthquake early warning systems, earthquake hazard assessment, and

potentially earthquake forecasting. Furthermore, integrating fault zone measurements with

temporal properties of seismic signals can provide a more detailed understanding of fault zone

processes, which in turn, can help establish the casual processes driving seismic activity. In this

dissertation, I have documented how AE properties and laboratory experiments can be coupled

together to bolster our understanding of seismic signals, with a particular focus on seismic

precursors and the elastic radiation of slow and fast ruptures.

Chapter 2 focuses on understanding the temporal evolution of frequency-magnitude (F/M)

statistics/b-value throughout the laboratory seismic cycle. I derived F/M statistics using standard

cataloging approaches and supplemented these observations by analyzing statistics derived from

the continuous data. I provide new evidence documenting the velocity dependence of AE size and

b-value. B-value scales inversely with shear velocity and fault slip rate. I postulate that these

changes are driven by the velocity dependence of fault zone porosity. Enhanced fault zone porosity

promotes grain mobilization and allows bigger areas to rupture, which in turn, allows larger AEs

to nucleate and causes b-value to decrease prior to co-seismic failure.

In Chapter 3, I used a ML algorithm to characterize AE attributes throughout the seismic

cycle, with the hope of identifying precursory anomalies to stick-slip failure. In particular, I used

an unsupervised ML algorithm to classify acoustic signals into “clusters” based on common

160

statistical attributes. The ML algorithm partitioned the acoustic data into four clusters; two clusters

were associated with the inter-seismic period and the remaining two distinguished the co-seismic

slip phase. The transition in clusters during the inter-seismic period coincided with the fault

reaching its peak strength and could be used as a proxy for a precursor. However, more work is

needed to verify the robustness of this observation.

In Chapter 4 I provided a more physical explanation behind the ML based predictions of

laboratory earthquakes. In other words, the temporal evolution of the acoustic energy allows the

ML models to make accurate predictions, but the physical processes that control the evolution of

the acoustic energy are poorly understood. I showed that the temporal evolution of the acoustic

energy is closely linked to fault slip rate and the total contact area per unit volume. If the fault slip

rate is low and/or the total contact area per unit volume is high (e.g., small grain sizes), the acoustic

energy remains low throughout the entire inter-seismic period and only beings to increase during

the co-seismic slip phase. Under such conditions, ML performance would likely be insufficient in

making valid predictions when using only the acoustic energy as an input feature.

In Chapter 5, I characterized the AE radiation properties of slow and fast laboratory

earthquakes. The spectra characteristics of slow laboratory earthquakes are indistinguishable from

one another from ~0-2.5 MHz. Similarly, the fast lab events have identical frequency content, but

with slightly larger amplitudes at low (< 1000 Hz) and high frequencies (>= 10 kHz), relative to

the slow events. Interestingly, both slow and fast laboratory earthquakes radiate high-frequency

energy (>= 10 kHz). I high-pass filter the acoustic signals and show that even the slowest events

with peak slip rates <= 100 µm/s radiate high-frequency energy. This high-frequency energy pulse

scales systematically with stress drop and is closely connected to changes in fault slip rate.

Applying these results to tectonic faulting could suggest that reported differences between the

seismic properties of slow and fast earthquakes could simply be due to observational constraints.

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In conclusion, throughout this dissertation I have documented that laboratory earthquakes

are preceded by various forms of precursory anomalies under a variety of conditions. In most cases,

it seems that the AE properties are closely linked to variations in fault slip rate and fault zone

porosity. Finally, my work on slow and fast laboratory earthquakes provides additional evidence

that slow and fast earthquakes may be more common than previously thought.

6.2 Future research directions

Laboratory friction experiments instrumented with AE measurements can provide key

insights into the physical processes associated with the pre-,co-, and post-seismic stages of the

laboratory seismic cycle. AE monitoring of rock deformation has been around for 50+ years, with

most of the attention being centered around the failure of intact rock samples and stick-slip failure

on pre-cut fault surfaces. As a result, the effect of granular fault gouge on AE characteristics has

been poorly studied. In this dissertation, I have documented a few simple observations about how

granular fault gouge influences AE properties throughout the lab seismic cycle. However, the

experiments were conducted under simple boundary conditions at room temperature, using

synthetic fault gouge, and without the presences of pore-fluids. Future work should focus on

building off the observations and experiments presented above.

Future work should focus on locating AEs in space and tracking their spatio-temporal

evolution throughout the seismic cycle. This information would bolster our understanding of how

lab earthquakes initiate and could answer fundamental questions about the connection between pre-

seismic activity and the size of the impending earthquake. In particular, it is unknown if AEs follow

a systematic progression in space as co-seismic failure approaches and if/how the size of the

impending earthquake influences the spatio-temporal evolution of AEs. Furthermore, with high-

162

resolution AE locations it could be possible to image the evolution of shear zone structures

throughout the course of the seismic cycle.

Source location is a multi-step process that can be non-trivial given the structure and

amount of data at hand. For example, to solve the location problem one needs a robust and efficient

way to pick arrival times, associate phase arrivals, and to minimize travel-times across the network.

Several research groups have developed sophisticated and robust ML algorithms to solve most of

these problems (arrival time picking, phase association). These ML methods should be exploited

in future research focused on locating AEs in the laboratory, as they are far more efficient and

superior than the traditional methods (e.g., STA/LTA).

In addition to investing in the source location problem, understanding how poromechanical

processes influence AE statistics could be an fruitful avenue of future research. Little is known

about how AE properties such as frequency-magnitude statistics are affected by pore-fluid

processes. For example, it is unknown how pore-pressure, fluid flow, and permeability modulate

AE properties throughout the seismic cycle. This work would help in understanding how/if AE

properties can be scaled up to tectonic fault zones, where the role of pore-fluids is sure to play a

significant and complicated role in modulating seismicity.

Laboratory experiments instrumented with AE measurements can offer a wealth of

knowledge about laboratory seismicity. However, it’s not immediately clear if and how these

attributes scale to seismogenic fault zones. At the laboratory scale, AEs probably arise from micro-

scale processes with length scales on the order of microns to mm. In contrast, foreshocks and other

seismic signals emanating from tectonic fault zones represent the failure of much larger fault

patches with length scales on the order of km. Thus, future work should focus on learning how to

scale up laboratory observations of AE measurements to tectonic fault zones. Doing so would foster

inter-disciplinary research and would help guide future geophysics research in rock mechanics and

seismology.

Appendix A

Supplementary Information for Chapter 2

A.1 Overview

This supporting information contains figures that describe our cataloging procedure and

results from our event detection and b-value sensitivity analysis. We also show plots of the

cumulative number of AEs across multiple slip cycles and demonstrate how this scales with

recurrence interval and inversely with shear velocity. We show how AE event rates are

approximately independent of shear velocity when disregarding events with M <= Mc. Finally, we

plot F/M results from our shear stress oscillations experiments and demonstrate that F/M statistics

are independent of stress state for stresses <= 50% of the peak stress.

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Figure A1: A-B Histogram of RDT and AE duration for several hundred AEs.

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Figure A2: A. Example of one AE at 3 µm/s. Superimposed on the acoustic time series data are 5 RDT curves. For this study, we use a 93 µs R.D.T to model all the AEs. B. Example of how the RDT parameter is implemented with a set of detected events (black symbols). Note, the event in question (candidate event) must have an amplitude that is larger than the RDT curves of the previous 5 events. In this case, the candidate event would be cataloged.

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Figure A3: Example of how AEs are detected and cataloged using our empirical thresholding procedure (see Chapter 2 for details). A. Raw continuous acoustic signal with 6 AEs (large spikes). B. Seismic signal and smoothed envelope (yellow). C. Seismic signal, smoothed envelope and detected AEs (black symbols). Note, the candidate events are detected after imposing a minimum amplitude (Amin) and time threshold (Tmin) (see Chapter for details). D. Same data as panel C. Events shown in green meet the RDT threshold (Figure S1) and are cataloged. The remaining events (black symbols) are discarded from the analysis.

167

Figure A4: A-B. Frequency-magnitude curves for a range of Tmin (A) and RDT (B) thresholds, respectively (see Chapter 2 for details). The number of smaller events detected increases as Tmin and RDT become smaller. C-D. Temporal evolution of b-value across one entire seismic cycle. Relative changes in b-value remain approximately the same for a wide range of Tmin and RDT values.

1 1.5 2 2.5 3 3.5 4M = log10 (Amplitude)

0

0.5

1

1.5

2

2.5

# of

Eve

nts >

= M

30 100 200 300 b-value estimation

Aµs µs

µs µs

Tmin: 30-300µs

1 1.5 2 2.5 3 3.5 4M = log10 (Amplitude)

0

0.5

1

1.5

2

2.5

# o

f Eve

nts >

= M

500 µs

b-value estimation

B

RDT: 100-500 µs

250 µs 100 µs

6818.3 6818.5 6818.7 6818.9Time (s)

1.9

2.1

2.3

2.5

Shea

r Stre

ss (M

Pa)

0

0.5

1

1.5

2

2.5

b-va

lue

Shear Stress

30 µs

C

Tmin: 30-300µs

100 µs 200 µs 300 µs

6818.3 6818.5 6818.7 6818.9Time (s)

1.9

2.1

2.3

2.5

Shea

r Stre

ss (M

Pa)

0

0.5

1

1.5

2

2.5

b-va

lue

Shear Stress500 µs 250 µs 100 µs

D

RDT: 100-500 µs

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Figure A5: A-D. Cumulative number of AEs and shear stress plotted as a function of time for each shear velocity. The total number of AEs per seismic cycle scales with the recurrence interval and inversely with shear velocity. The total number of AEs used to compute b-value (see Chapter 2) corresponds to 10% of the cumulative number of AEs at a given shear velocity.

169

Figure A6: A-C. Cumulative (solid line) and non-cumulative (histogram) frequency-magnitude plots at different locations within the seismic cycle. Note, the F/M curves correspond to the same data shown in Figure 3 of the main text. The peak of the non-cumulative distribution corresponds to the magnitude of completeness (Mc). Mc remains constant as a function of position within the seismic cycle for data at 0.3 µm/s. D-F. Cumulative and non-cumulative frequency-magnitude plots at different locations for the seismic cycle shown in Figure 2-3D. In contrast to the data at 0.3 µm/s, Mc shifts to higher values as failure approaches and the non-cumulative plots become more Gaussian-like and indicates that the catalog is deficient in lower magnitude events.

A B C

D E F

100 µm/s20% of Peak Shear Stress

100 µm/s60% of Peak Shear Stress

100 µm/s90% of Peak Shear Stress

20% of Peak Shear Stress0.3 µm/s 0.3 µm/s

60% of Peak Shear Stress 90% of Peak Shear Stress0.3 µm/s

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Figure A7: AE rate as a function of normalized time for data shown in Figure 2-2 (see main text in Chapter 2). Note, the x-axis is scaled from the minimum shear stress to the peak shear stress for the slip cycles shown in Figure 2. AE rate is computed using the same windowing technique described in the main text, however here we only count events with the M >= 2.0. In general, the absolute value of event rates per unit shear displacement seems to be roughly independent of shear velocity for data <= 30 µm/s. Thus, the inverses relationship between event rate and shearing rate (Figure 2-2) could simply be due to a lack of smaller events at higher shearing velocities.

Normalized Time

AE

Rat

e µm

-1

0 0.2 0.4 0.6 0.8 1101

102

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Figure A8: B-value as a function of normalized slip velocity. The data plotted here correspond to the same data plotted in Figure 2-5. B-value scales inversely with both slip rate (low b-value at large slip velocities) and the far-field shearing rate (low b-value at large shearing rate).

0 0.2 0.4 0.6 0.8 1Slip Velocity/Shear Velocity

0.8

1

1.2

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Figure A9: A. Shear stress, AE amplitude and fault displacement plotted versus time for Experiment p5388. Initially, the fault was sheared under a constant loading rate boundary condition for ~ 10 mm. After shearing 10 mm at 21 µm/s, we reduced the shear stress on the fault to ~ 50% of the peak stress reached during the stick-slip cycles and placed a soft acrylic spring between the vertical ram and center block of the DDS to mitigate fault creep. Four series of shear stress oscillations (S1-S4) were performed at different amplitudes and frequencies that are representative of the stick-slip cycles in Experiment p5363. Amplitude and frequency of the oscillations are depicted in the left corner. The number and magnitude of AEs decreases from sequences S1 to S4. B. Non-cumulative frequency-magnitude data from S1 at different locations within the increasing shear stress limb. Symbols are averages across all channels and cycles in S1 at a specific location within the increasing shear stress limb and error bars represent one standard deviation. The magnitude of the AEs is approximately independent of location within the shear stress oscillation.

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Appendix B

Supplementary Information for Chapter 3

B.1 Statistical Features

Following Rouet-Leduc et al., 2017; Rouet-Leduc et al., 2018, we compute statistical

features that quantify both the amplitude and frequency content of the seismic signal. Note, that

each feature is calculated using a 1.36 s long moving window. The 43 computed statistical features

are: Frequency Content Features: To quantify the frequency content we compute the power of the

acoustic signal between 100-200 kHz, 200-300 kHz, 300-400 kHz and 400-500 kHz. These

specific frequency bands were selected based on the fact that our ultrasonic transducers have a

center frequency of 500 kHz. Amplitude Features: To quantify the amplitude of the acoustic signal

we calculate features based on thresholds, percentiles and higher-order moments. For thresholds,

we use five random amplitude thresholds at 500, 700, 900,1100 and 1300 (bits). For each threshold,

we calculate how much of the acoustic signal lies above and below the specific threshold. In

addition, we calculate the maximum and minimum amplitude of the seismic signal. For percentiles,

we calculate the 1st-9th, 90th-99th percentile and the interquartile range. Lastly, we calculate the

normalized and non-normalized mean, variance, kurtosis and skewness.

B.2 Sensitivity analysis of the moving window:

Prior to performing the cluster analysis, we compute a database of statistical features using

a moving window over the continuous acoustic signal. Each window is 1.36 s in length and adjacent

windows overlap by 90%. In this study, we present results using a window size similar to that

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presented in previous works (Rouet-Leduc et al., 2017; Rouet-Leduc et al., 2018). We investigated

the influence of window length and overlap by comparing the clustering outcome in variance-

kurtosis feature space as a function of these parameters. To allow for a straightforward comparison,

we use a constant mean-shift bandwidth parameter of .71 for all analyses (Figure B1 and Figure

B2). The sensitivity analyses suggest that the basic forms of these data in the feature space are

independent of window size and overlap. Thus, we conclude that neither the window size, nor the

window overlap have a significant influence on the structure of the feature space, and thus, the

results we present in this work.

B.3 Influence of the Bandwidth parameter

The mean-shift algorithm uses a bandwidth parameter that determines the area within

feature space over which the mean is computed (see Chapter 3 for details). The bandwidth scales

inversely with the number of clusters identified (Figure B3). A large bandwidth allows the

algorithm to be insensitive to subtle changes that might occur within the feature space. In contrast,

a small bandwidth enables the algorithm to finely partition the feature space into a large number of

non-systematic clusters. In other words, many clusters will be identified, but will have very few

data points mapped to them. Ultimately, finding the optimal bandwidth is a challenging problem

and is one of the main drawbacks of using mean-shift (Comaniciu et al., 2001; Singh et al., 2003).

We optimize this parameter using the Silhouette Coefficient, which quantifies how well each data

point is mapped to its own cluster, while at the same time measures how dissimilar the data points

are from nearby clusters (Rousseeuw,1987). We compute a silhouette coefficient based on the

scikit-learn implementation, which is defined as:

𝑆𝑖𝑙ℎ𝑜𝑢𝑒𝑡𝑡𝑒𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 = 𝑏 − 𝑎/max(𝑎, 𝑏) (B1)

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Here, b is the mean nearest-cluster distance and a is mean intra-cluster distance.

Specifically, a is a metric of how similar each data point is to other data points within the same

cluster. In contrast, b is a measure of how distinct a particular cluster is from its neighboring

clusters. The Silhouette coefficient ranges from -1 to +1. Values near zero imply that the clusters

are overlapping, while negative values indicate that the data point has been mapped to an incorrect

cluster (Tan et al. 2006). We compute the Silhouette coefficient for a range of bandwidth

parameters and select a bandwidth that results in the highest silhouette coefficient (Figure B3).

Optimizing the Silhouette Coefficient as a function of the number of clusters (or in our case

bandwidth) is a common approach for finding the correct number of clusters (Tan et al., 2006).

B.4 Scaling of Variance and Kurtosis

Before performing the clustering analysis in variance-kurtosis feature space, we compute

the logarithm of each feature. This computation is required due to the fact that the features span

several orders of magnitude. Without computing the logarithm, the algorithm will cluster data

points primarily as a function of the feature with the largest range (Figure B4). In our data set, this

corresponds to the kurtosis which ranges from 0-20000, whereas the variance ranges between 0-

3500 bits2. However, after computing the logarithm of each feature the data values range between

1 and 4.5. Furthermore, without this computation most of the clusters (green-blue-yellow-black)

identified are associated with subtle differences in the co-seismic stage between different slip

cycles. In this study, we are primarily interested in identifying precursory signals within the inter-

seismic stage, and therefore, differences associated with the slip event itself are beyond the scope

of this work.

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B.5 Clustering in Variance-Kurtosis Space vs PC Space

We address whether or not the differences between clustering in PC space versus clustering

in variance-kurtosis space are due to differences in features and not the number of clusters by

selecting a bandwidth that results in the same number of clusters (see Chapter 3 for details). More

specifically, we compare the results of the two methods when the number of clusters found is held

constant.

To obtain four clusters in the variance-kurtosis space, we decrease the bandwidth to .38

(Figure B5). The two new clusters are shown as the cyan and blue cluster. After overlaying the

clusters on top of the shear stress data it is clear that the blue cluster is not correlated to anything

physical, and is just an artifact of a small bandwidth (Figure B6). However, the cyan cluster is in

fact related to the small failure events that precede the larger failure events. These results indicate

that while it is possible to obtain four clusters in the variance-kurtosis space, the clusters are not as

systematic as the clusters found in PC space. Unlike the clusters in PC space, the clusters found in

the variance-kurtosis space are not correlated to fault strength. Therefore, we argue that only

features in PC 1 and PC 2 are able to track fault strength and not the variance or kurtosis. We

perform a similar analysis when clustering in PC space. To obtain two clusters, as is the case when

clustering with respect to variance-kurtosis, we must increase the bandwidth relative the previous

analysis in Figure 3-6b. By increasing the bandwidth, the inter-seismic period and co-seismic phase

are now classified by only one cluster (yellow and green). Comparing these results to those found

in Figure 3-6a, suggests that the differences in the statistical features are in fact what induce the

changes behind the temporal trends in clusters.

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B.6 Principal Component Analysis (PCA):

Principal component analysis is a way to decompose a high-dimensional data set, which

might have correlated features, into an uncorrelated lower dimension data set (Jolliffe, 2011). For

our case, this corresponds to reducing the dimensionality of our problem from 43 to 2. To do this,

we first compute an eigendecomposition of the covariance matrix for our N by 43 data matrix,

where N represents the number of samples (i.e the number of data points calculated using the

moving window approach). This decomposition gives us a set of eigenvectors (also called principal

components), which are ranked corresponding to their representative eigenvalue. That is, the first

eigenvector contains the largest eigenvalue, and explains most of the variance in our data set

(Jolliffe, 2011). Similarly, by adding up all of the eigenvectors we can explain 100% of the variance

in our data. However, to decrease the dimensionality of the problem we can use a small subset of

the eigenvectors to explain a significant percentage of the variance in our data. In our case, the first

two eigenvalues can explain 85% of the total variance (Figure 3-5C). Therefore, we can use the

first two eigenvectors to project our data into a new 2D space (Figure 3-5D). Each principal

component is linear combination of the original features scaled by a coefficient (Figure S8; Jolliffe,

2011).

B.7 Clustering results with respect to PC 2

PC 2 differs significantly as a function of time to failure compared to PC 1 (Figure 3-5 and

Figure B9). Specifically, PC 2 increases continuously until failure and then begins to decrease.

Note, this behavior is the exact opposite of how PC 1 evolves throughout the course of the seismic

cycle (Figure 3-5). The clusters transition systematically as function of PC 2 during the inter-

seismic and co-seismic periods. During the inter-seismic stage, the clusters evolve from yellow to

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magenta which correspond to when the fault has reached its peak strength. This differentiation

between clusters is seen clearly in Figure B9.

B.8 Variance and Kurtosis Clustering Results

We perform a clustering analysis with respect to variance-kurtosis in order to compare this

work with our previous supervised ML analysis. In our previous study, variance and kurtosis were

identified as the most significant features for the supervised regression analysis. However, when

clustering in a space consisting only of these two features, we observe no precursors to failure

(Figure B10). The feature space is partitioned by two clusters, which are depicted by red and cyan

symbols (Figure 3-6a). When plotting the clusters as a function of time along with shear stress it is

clear that the transition from red to cyan occurs after failure (B10). For slip cycles that contain a

small failure event prior to the main failure (for example between 2210-2015 s), we observe a

transition from red to cyan. However, this transition is similar to the one that occurs during the

main slip event. That is, the transition from red to cyan occurs after the failure event. We conclude,

that clustering with respect to variance and kurtosis does not reveal precursory information prior to

frictional failure.

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Figure B1: Variance-Kurtosis feature space after computing the logarithm for each feature for a 1.36 s window with overlap sizes of (a): 0, (b): 50% and (c): 90%. The data values and underlying structure within the feature space do not change indicating that the window overlap does not have a significant effect on our results. Here, we use a constant bandwidth of .71 and analyze the same data of experiment p4677 between 2067-2337 s (see Figure 3-2).

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Figure B2: Variance-kurtosis feature space after computing the logarithm for each feature with a window overlap of 90% and for window sizes of (a): .68 s and (b): 1.36 s. Here, we use a constant bandwidth of .71 and analyze the same section of data from experiment p4677 between 2067-2337 s (see Figure 3-2). The window size has a minimal impact on the data values and the clustering outcome in the feature space.

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Figure B3: Number of clusters as a function of bandwidth. Bandwidth scales inversely with the number of detected clusters. We optimize the bandwidth by computing a Silhouette Coefficient. Inset shows Silhouette Coefficient as a function of bandwidth. We select a bandwidth that results in the highest Silhouette Coefficient. For our data, this corresponds to bandwidth of .71.

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Figure B4: Variance-kurtosis feature space without computing the logarithm of each feature. Clusters are identified primarily as a function of kurtosis, whose range varies between 0 and 20000. In order to prevent this bias, we compute the logarithm of each feature which decreases the range between the two features.

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Figure B5: Variance-kurtosis feature space after using a smaller bandwidth, which results in four total clusters. The blue cluster is very arbitrary and does not occur throughout each slip cycle.

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Figure B6: Temporal evolution of clusters after using a smaller bandwidth relative to Figure 3-6a. (a). Cluster evolution over multiple slip cycles. Note, how the blue cluster only occurs in a few slip cycles. (b). Zoom of three cycles shown in A. Now, the ML algorithm differentiates the small and large stress drops with the cyan and green cluster respectively.

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Figure B7: Clustering with respect to PC 1 and PC 2 using a larger bandwidth relative to Figure 6b. (a). Feature space for PC 1 and PC 2. (b). PC 1 and shear stress as a function of time. The inter-seismic period is classified by the yellow cluster and the co-seismic period is classified by the magenta cluster.

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Figure B8: Eigenvector coefficients for PC 1 and PC 2 plotted versus the number of features. Most of the features have similar coefficients and therefore are equally important in explaining the data variance. However, several of the amplitude based features (percentiles and amplitude counts) have higher coefficients relative to the other features.

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Figure B9: PC 2 and shear stress plotted as a function of time. The transition from yellow to purple occurs once the fault has reached its peak strength and therefore serves as a precursor to failure.

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Figure B10: (a). Temporal evolution of clusters in variance-kurtosis space as a function of variance plotted along with shear stress. (b). Zoom of A. Note the differences in slip cycles that contain small instabilities and those that do not.

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Appendix C

Supplementary Information for Chapter 4

C.1 Overview

This supporting information contains figures that demonstrate the effect of computing the

acoustic variance (energy) using: (1) a constant time window, (2) a constant displacement window,

or (3) a constant displacement window applied to decimated acoustic data. In addition, we show

that acoustic energy is inversely related to shear stress.

In Figure C1, we plot acoustic variance and shear stress for data at different

shearing velocities from Experiment p5348. In this particular experiment, we do not use any acrylic

spring in series with the vertical ram, which promotes stable frictional sliding. Variance is

computed using a constant displacement window of 5 µm in C1A. Therefore, the length of each

moving window in time (N in Equation 4-1) changes systematically with shearing velocity. More

specifically, the window size becomes larger in time with decreasing shear velocity. The data show

that more energy is radiated at higher shear velocities. Since acoustic variance is normalized by N,

one could argue that the results in Figure C1A are simply due to the effect of N and a smaller

window size relative to the data at lower shear velocities. To verify that the results in Figure C1A

are independent of the window size (N), we compute variance using a 5 µm window for each shear

velocity and we decimate the acoustic data such that N is the same for each velocity (Figure C1B).

More specifically, N is smallest at 60 µm/s so the acoustic data corresponding shear velocities <60

µm/s are decimated such that each moving window of 5 µm contains the same number of data

points (N) as the 60 µm/s case. The values of variance are the exact same as those shown in Figure

C1A. Therefore, we can conclude that the size of the window (N) has no effect on energy radiation

during stable sliding. In addition, we verify that energy radiation is independent of slip

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displacement by computing variance using a constant time window of .1s in Figure C1C. Again,

the acoustic variance increases with shear velocity and the absolute values of variance are

approximately the same as the variance in Figure C1A. Since the absolute values of variance are

the same in Figures C1A and C1C, this implies that acoustic energy radiation is independent of slip

displacement. In Figure C2, we plot variance as a function of time for two different shear velocities

from Experiment p5201. The data demonstrate that the inter-seismic changes in variance are

independent of window length. However, the peak energy radiated during co-seismic slip changes

systematically with window length (Figure C2). Thus, using different window sizes can influence

the co-seismic trends, but does not affect the inter-seismic trends. This implies that a constant

window in time is the correct way to compute energy because N remains constant. Furthermore, to

avoid windowing effects associated with the energy release during co-seismic slip, we report all of

our co-seismic data in terms of the cumulative energy release instead of peak energy (see Chapter

4 for details). Lastly, we demonstrate that the energy released during the inelastic loading phase is

not correlated with friction (Figure C3). Our data clearly show that more energy is released at lower

values of friction during the inter-seismic period. This implies, that energy released during the

inelastic loading phase is more correlated with slip rate than stress.

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Figure C1: Three methods to calculate acoustic signal variance for different shearing velocities, all plotted along with shear stress during stable sliding. A. Acoustic variance for a time window corresponding to a shear displacement of 5 µm; thus a factor of 30 longer window for 2 µm/s compared to 60 µm/s. Note that variance increases with shear velocity. B. Same as Panel A except the acoustic data are decimated such that the number of data points per window is the same for each velocity. Note that variance is identical to Panel A. C. Variance computed using a constant time window of .1s. The absolute values of variance are approximately the same as for A and B indicating that the amount of energy radiated is independent of slip displacement.

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Figure C2: A-B. Variance plotted as a function of time at two different shearing velocities from Experiment p5201 (see Chapter 4 for details). Variance is computed using two different window sizes (black and red). The data in black correspond to constant displacement window of 5 µm. The inter-seismic changes in variance are independent of window size, but the co-seismic peaks change systematically with window length.

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Figure C3: A. Variance versus friction for data corresponding to the onset of inelastic creep until peak shear stress (see Chapter 4 for details) from Experiment p5198. The data show that more energy is released prior to failure for lower normal stresses. B. Same as A, but data here correspond to Experiment p5201. Similar to A, more energy is released prior to failure for higher shear velocities.

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Appendix D

Supplementary Information for Chapter 5

D.1 Overview

The supplementary information below documents the effect of the hydraulic power supply

(HPS) on the recorded acoustic signals. We show that HPS radiates a significant amount of

energy/noise at frequencies < 10 kHz. In addition, we also verify that the spectra results in the

main-text are consistent for different slip events and channels. Finally, we demonstrate that the

seismic moment and co-seismic slip change slightly with increasing normal stress. Thus, the

spectral content our our slow and fast events are remarkably similar at low-frequencies (< 1000

Hz).

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Figure D1: A-B. Raw-acoustic traces (2s long) without (A) and with (B) the hydraulic power supply turned on. Note the significant increase in noise due to the hydraulic power supply. C. Average spectra of the traces shown in A and B. Here, we average the spectra for all channels in A and B, respectively. The hydraulic power supply contaminates the acoustic signals with noise for frequencies < 10 kHz.

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Figure D2: A Time-domain signals from channel 6 during the co-seismic slip phase. AE signals are exclusively from Experiment p5435 (see Figure 2) and represent a different slip event compared to those plotted in Figure 2 of the main text. In general, the time-domain signals are similar to those plotted in Figure 2 of the main-text. B Spectra of events shown in A. The spectra have identical shapes to those in Figure 2. However, the fast events (13 and 15 MPa) have identical amplitudes at low-frequencies compared to the slow events. In contrast, the fast events in Figure 2 have slightly higher amplitudes at lower frequencies, relative to the slow events. These differences probably arise from the nature of the time-domain signals. Note, the differences between the 15 MPa events. Inset shows noise traces for data at each normal stress.

VITA

David Chas Bolton

Education The Pennsylvania State University, University Park, PA 2016-2021 Ph.D. Geoscience | GPA: 3.98/4.0 | Advisor-Chris Marone

University of Texas at Arlington, Arlington, TX 2010-2015 Bachelor of Science in Geology | GPA: 3.67/4.0 Minor in Chemistry Work Experience:

Research Assistant, Penn State Rock and Sediment Mechanics Lab, University Park, PA; 2016-2021

Graduate Intern, Non-linear Geophysics; Los Alamos National Laboratory; Summer 2017;2018

Undergraduate Research Assistant, Geomechanics Lab University of Texas at Arlington; Fall 2015

Selected Publications:

1. Bolton, D. C., Shreedharan, S., Rivière, J., & Marone, C. (2020). Acoustic Energy Release During the Laboratory Seismic Cycle: Insights on Laboratory Earthquake Precursors and Prediction. Journal of Geophysical Research: Solid Earth, 125, e2019JB018975. https://doi.org/10.1029/2019JB018975

2. Bolton, D. C., Shokouhi, P., Rouet-Leduc, B., Hulbert, C., Rivière, J., Marone, C., & Johnson, P. A. (2019). Characterizing acoustic signals and searching for precursors during the laboratory seismic cycle using unsupervised machine learning. Seismological Research Letters, 90(3), 1088-1098.

3. Shreedharan, S., Bolton, D. C., Rivière, J., & Marone, C. (2020). Preseismic fault creep and elastic wave amplitude precursors scale with lab earthquake magnitude for the continuum of tectonic failure modes. Geophysical Research Letters, 46. https://doi.org/10.1029/2020GL086986

Outreach:

Shake, Rattle, Rocks 2017-2019 • Taught basic principles of seismology and earthquake physics to a group of elementary

school students

Earth and Mineral Science Exposition 2017-2019 • Informed undergraduate students of the opportunities that are available in the Geosciences

Program at The Pennsylvania State University, and more specifically, the type of research conducted in the Geomechanics Lab