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Volumetric interactions between major ruptures and fault zones illuminated by small earthquake properties

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Volumetric interactions between major ruptures and fault zones illuminated by small earthquake properties

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Volumetric interactions between major ruptures and fault zones
illuminated by small earthquake properties

by

YIFANG CHENG

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Geological Sciences)

August 2021

Copyright 2021 Yifang Cheng
ii
Dedication

To my family and everyone who has helped me
iii
Acknowledgements
Over the past five-year time as a PhD student, my life has changed tremendously. I had
my first time living alone for three years. I married. I received my first job offer. I met COVID
time and my first-time burnout. I got my PhD degree. My PhD journey involves both happiness
and frustration, many confusing moments and some eureka moments, good days and bad days.
But when I recollect all the memories, I simply cherish the perseverance and inspiration I have
had, all lessons I have learned, and most importantly, the love and support I got from everyone
around me along this adventure.
First and foremost, I would like to express my highest gratitude to my advisor Prof.
Yehuda Ben-Zion. He is patient, caring, and always energetic and excited about various
scientific problems. Every time when I got frustrated, he always tries his best to support me via
his encouragement and constructive guidance. Every time when I got any achievement, he is
even happier than me. He always respects my decisions and kindly provides his suggestions. I
have learned how to be a good scientist and a good advisor from him through his passionate
vision of science and life, his diligence and persistence, and his selfless help and respect to his
students.
I also would like to express great gratefulness to my committee members for their
mentorships and guidance. Prof. John Vidale taught me about deep structure. He showed me how
to be a careful, open-minded scientist and how to be a humorous, energetic, and helpful person.
He always shares his insights generously and promotes me with great efforts. Great thanks to
Prof. Stephan Haas, He is always willing to help, responds to my emails quickly, and is very
supportive on the progress of my PhD program. His constructive suggestions during committee
meetings also helped me improve my research. I was also very fortunate to have Prof. Charlie
iv
Sammis and Prof. William Frank on my qualifying exam committee, their knowledge on
earthquake physics and seismology helped me a lot in data analysis and interpretations.
I would like to thank all my co-authors and collaborators, without whom I cannot conduct
many of my projects. I thank Zachary Ross, Egill Hauksson, Ilya Zaliapin, Lupei Zhu, Florent
Brenguier, Zefeng Li, Pieter-Ewald Share, Aurélien Mordret, Pierre Boué, Frank Vernon, Xin
Wang, Zhongwen Zhan, Dun Wang, and Fangyu Li. Zach has taught me a lot in coding and
writing and mentored me through the years with great patience. Egill is always supportive and
provides me all data and codes I need. Ilya and Lupei have provided me programs to analyze
earthquake clusters and moment tensors. Zefeng and Fangyu are always patient and helps me in
designing techniques and methodologies for better observations. Dun provided me a precious
opportunity to work with students in his group on an interesting earthquake sequence in Japan. It
has been great teaming with Florent, Aurélien, Pierre, Pieter and Frank on the Cahuilla array
project.
I am also grateful to all members of Yehuda’s group, including Haoran Meng, Hongrui
Qiu, Lei Qin, Niloufar Abolfathian, Pieter-Edward Share, Malcolm White, Bruce Zhou, Jing Hu,
Christopher Johnson, Lu Yang, Shiqing Xu, Xin Liu, and Zachary Ross. I enjoyed every moment
we shared in our group meetings, TA classes, SCEC office, field work, and many annual
academic meetings. I thank all friends I met during my days at USC, including Xin Song, Wei
Ma, Xueyao Shen, Gen Li, Christine Wu, Qiang Qiu, Lifeng Wang, Alan Juarez, Mark Peaple,
Jun Shao, Shiying Nie, Wei Wang, Sijia Dong, Luis Vazquez, Xiaopeng Bian, Hengdi Liang,
Feng Zhu, Guang-sin Lu. I would also like to thank my other geophysicist friends out of USC,
Zhichao Shen, Zhe jia, Nan Wang, Minyan Zhong, Shujuan Mao. In particular, I want to thank
Ailin Zhang for always being with me. We share every interesting and frustrating moments in
v
our lives, double our happiness and halve our sadness. We enjoyed many colorful journeys to
many places in the past several years. I thank scientists who encouraged me these years, Roland
Bürgmann, Daniel Trugman, Peter Shearer, Wenyuan Fan, Xiaowei Chen, Fenglin Niu. Roland
is always active and provide all kinds of warm help and comments to my research during the
meeting, paper review and my postdoc application. Daniel shared with me many of his
experiences, thoughts about both his work and life. Peter is always a good listener and would like
to share many of his ideas. Wenyuan is always available whenever I need some suggestions for
my career. Xiaowei is my advisor for my master’s degree. She is positive to everything and
keeps encouraging me for years. Fenglin shared many of his life and research experiences with
me that motivates me to move forward. I also would like to thank all extremely helpful staff
members in our department, John McRaney, John Yu, Cynthia Waite, Karen Young, Vardui Ter-
Simonian, Tran Huynh, Deborah Gormley, Barbara Grubb, and Miguel Rincon. I cannot have
such an enjoyable and smooth PhD life without any of you.
Finally, I would like to express my endless appreciation to my family. My parents always
give me all kind of support they can provide and encourage me to pursue a better future. My
parents-in-law encourage me to be a better me, treat me as their own daughter, and cheer me up
with their endless positive energy. Last but not least, I am so lucky for having my husband,
Gaoyuan Zhang, who accepts me as who I am, accommodates my life, and never asks me to
change. We have totally opposite habits and characters, and he is always the best teacher telling
me the truth of life. I cannot wait for the new journey we will share together in the future.

vi
Table of Contents

Dedication ...................................................................................................................................... ii

Acknowledgements ...................................................................................................................... iii

List of Tables ................................................................................................................................ ix

List of Figures ................................................................................................................................ x

Abstract ....................................................................................................................................... xvi

Introduction ................................................................................................................................... 1

1. Diverse Volumetric Faulting Patterns in the San Jacinto Fault Zone (Cheng et al.,
2018) ............................................................................................................................................... 7
1.0 Summary ............................................................................................................................................ 7
1.1 Introduction ....................................................................................................................................... 8
1.2 Data .................................................................................................................................................. 12
1.3 Results .............................................................................................................................................. 14
1.3.1 Overview of Seismicity ............................................................................................................. 14
1.3.2 Lateral Variation of Focal Depths ............................................................................................. 15
1.3.3 Variations of Focal Mechanisms ............................................................................................... 16
1.3.4 Spatial Patterns of Aftershocks ................................................................................................. 19
1.4 Discussion and Conclusions ........................................................................................................... 28
1.5 Acknowledgments ........................................................................................................................... 32

2. Transient Brittle‐Ductile Transition Depth Induced by Moderate‐Large Earthquakes
in Southern and Baja California (Cheng & Ben-Zion, 2019) ................................................. 33
2.0 Abstract ............................................................................................................................................ 33
2.1 Introduction ..................................................................................................................................... 33
2.2 Data .................................................................................................................................................. 36
2.3 Method ............................................................................................................................................. 36
2.3.1 Clusters and Background Events Identification ....................................................................... 37
2.3.2 Depth Estimations of Groups of Events ..................................................................................... 39
2.4 Results .............................................................................................................................................. 40
2.4.1 Variations of the Brittle-Ductile Transition Depth .................................................................... 40
2.4.2 Temporal Evolution of the Brittle-Ductile Transition Depth .................................................... 42
2.5 Discussion and Conclusions ........................................................................................................... 43
vii
2.6 Acknowledgements ......................................................................................................................... 47

3. Variations of Earthquake Properties Before, During, and After the 2019 M7.1
Ridgecrest, CA, Earthquake (Cheng & Ben-Zion, 2020) ........................................................ 48
3.0 Abstract ............................................................................................................................................ 48
3.1 Introduction ..................................................................................................................................... 48
3.2 Data .................................................................................................................................................. 51
3.3 Results .............................................................................................................................................. 51
3.3.1 Transient Deepening of Seismicity ........................................................................................... 51
3.3.2. Variations of Potency Distribution ........................................................................................... 52
3.3.3 Spatiotemporal Variations of Focal Mechanisms ...................................................................... 54
3.4 Discussion and Conclusions ........................................................................................................... 59
3.5 Data Availability Statement ........................................................................................................... 62
3.6 Acknowledgments ........................................................................................................................... 63

4. Isotropic source components of events in the 2019 Ridgecrest, California, earthquake
sequence (Cheng et al., 2021) ..................................................................................................... 64
4.0 Abstract ............................................................................................................................................ 64
4.1 Introduction ..................................................................................................................................... 64
4.2 Data .................................................................................................................................................. 68
4.3 Method ............................................................................................................................................. 69
4.3.1 Source decomposition ............................................................................................................... 69
4.3.2 Automated moment tensor inversion ......................................................................................... 70
4.4 Results .............................................................................................................................................. 71
4.4.1 Robustness analysis of non-DC component .............................................................................. 72
4.4.1.1 Misfit Reduction ................................................................................................................. 72
4.4.1.2 The Trade-off between CLVD and ISO components ........................................................ 73
4.4.1.3 The effect of near-fault data on the resolved isotropic components .................................. 76
4.4.2 Spatiotemporal variations of non-DC components ................................................................... 77
4.5 Discussion ........................................................................................................................................ 78
4.7 Acknowledgments ........................................................................................................................... 80

5. An Automated Method for Developing a Catalog of Small Earthquakes Using Data of
a Dense Seismic Array and Nearby Stations (Cheng et al., 2020) .......................................... 81
5.0 Abstract ............................................................................................................................................ 81
5.1 Introduction ..................................................................................................................................... 82
5.2 Method and Representative Examples .......................................................................................... 85
5.2.1 Signal detection and discrimination with dense array data ....................................................... 86
5.2.1.1 Method ............................................................................................................................... 86
5.2.1.2 Representative example ..................................................................................................... 89
5.2.1.3 Application to 1-day dataset ............................................................................................... 91
5.2.2 Earthquake location ................................................................................................................... 93
viii
5.2.2.1 Method ............................................................................................................................... 93
5.2.2.2 Representative example and application to 1-day dataset .................................................. 94
5.2.3 Magnitude estimation ................................................................................................................ 95
5.3 Discussion and conclusions ............................................................................................................ 97
5.4 Data and Resources ....................................................................................................................... 101
5.5 Acknowledgements ....................................................................................................................... 101

6. Discussion .......................................................................................................................... 102
6.1 Summary ........................................................................................................................................ 102
6.2 Future research directions ........................................................................................................... 104
6.2.1 Crustal stress evolution ............................................................................................................ 105
6.2.2 Precursory phenomena ............................................................................................................ 105
6.2.3 Real-time ground motion prediction ....................................................................................... 106

Appendix1. Chapter 1 supplementary materials ................................................................... 107

Appendix2. Chapter 2 supplementary materials ................................................................... 117

Appendix3. Chapter 3 supplementary materials ................................................................... 122
A3.1 Data and method for computing focal mechanisms using HASH algorithm and deep
learning algorithms ............................................................................................................................. 122
A3.1.1 Data ....................................................................................................................................... 122
A3.1.2 Method .................................................................................................................................. 122
A3.1.2.1 Phase arrival identification ............................................................................................ 122
A3.1.2.2 S/P amplitude ratio calculation ..................................................................................... 122
A3.1.2.3 Polarity recognition ....................................................................................................... 123
A3.1.2.4 Focal mechanism calculation ........................................................................................ 123
A3.1.3 Quality classification ............................................................................................................ 123
A3.2 Aftershock-mainshock potency ratio ....................................................................................... 124

Appendix4. Chapter 4 supplementary materials ................................................................... 131
A4.1 Introduction ................................................................................................................................ 131
A4.2 Moment tensor results using 1D velocity model ...................................................................... 131

Appendix5. Chapter 5 supplementary materials ................................................................... 134

References .................................................................................................................................. 143

ix
List of Tables

Table 1.1 Details of the M ≥ 4.5 Earthquakes Shown in Figure 1.1 ............................................ 12
Table 1.2 Horizontal Location Errors of Chosen Aftershock Sequences, Estimated Mainshock-
Aftershock Epicentral Distance Errors, and the Percentage of Aftershocks With Epicentral
Distance > 1 km ............................................................................................................................ 25
Table 2.1. Event Numbers of Four M ≥ 6.7 Mainshock‐Aftershock Sequences and the Other
Clusters Within Different Depth Ranges ...................................................................................... 41
Table A1.1 Velocity model used for GrowClust relocations. The velocity model assumes a
layered structure with Vp/Vs ratio as 1.732. (Hutton et al., 2010) ............................................. 116
Table A1.2 Location errors of the M > 4.5 earthquakes shown in Fig. A1.1 (from Southern
California Seismic Network (SCSN) standard catalog). ............................................................. 116
Table A3.1 Data format of the focal mechanism catalog in the Ridgecrest area (Dataset S1) .. 130

x
List of Figures

Figure 1.1 Map view of 2000–2016 seismicity (dots and stars) and main faults (thin solid lines)
in the trifurcation area of the San Jacinto fault zone. The dashed lines indicate cross sections
used in Figure 1.2. The inset shows the location of the study area (red box) in southern California
along with the entire San Jacinto fault zone (SJFZ), San Andreas Fault (SAF), and Elsinore Fault
(EF). .............................................................................................................................................. 10
Figure 1.2 Depth profile of seismicity along (a) A‐A′ and (b) B‐B′ in Figure 1.1. Dashed lines
indicate the estimated geodetic locking depth from Fialko (2006). .............................................. 11
Figure 1.3 Temporal variation of seismicity in the trifurcation area (events in Figure 1.1). (a)
Earthquake magnitude versus time. Red line shows the estimated magnitude of completeness
within a 4‐year sliding window. (b) Number of events (M ≥ 1.5) per month within the study area.
There are five time periods with a high seismicity rate correspond to M ≥ 4.5 aftershock
sequences (Table 1.1). (c) Normalized cumulative density function (CDF) of seismicity for
various minimum magnitude thresholds. ...................................................................................... 13
Figure 1.4 (a) D05 and (b) D95 distribution over a 0.005° × 0.005° (0.465 × 0.556 km) grid.
M ≥ 3.5 events are denoted by their focal mechanisms and scaled by magnitude. White ellipses
highlight the deep seismogenic zone between the Buck Ridge and Clark faults. ......................... 16
Figure 1.5 Map view of seismicity colored by the relative distance from the main faults. Red
dots denote events within 1‐km distance from the main faults (near‐fault area). Blue dots are
events outside of the fault zone with distance more than 1 km from the main faults (off‐fault
area). Green dots show events between main faults with distance more than 1 km from the
mapped main faults (intra‐fault area). M ≥ 3.5 events are denoted by white stars and scaled by
size. ............................................................................................................................................... 17
Figure 1.6 Distribution of focal mechanisms for each depth interval within the near‐fault (a), off‐
fault (b), and intrafault (c) areas. Dashed lines indicate the estimated geodetic locking depth from
Fialko (2006). ................................................................................................................................ 18
Figure 1.7 (a) Distribution of nearest‐neighbor statistics for all available events in the
trifurcation area of the San Jacinto fault zone (2000–2016) with magnitude cutoff Mmin = 0. The
white line shows the nearest‐neighbor distance threshold used for clustering (based on the
method in Zaliapin & Ben‐Zion, 2016). (b) Histogram of nearest‐neighbor distance η of all used
events. Red line denotes the nearest‐neighbor distance threshold used for clustering. ................ 20
Figure 1.8 (a–e) Magnitude‐time plots of five chosen M > 4.5 aftershock sequences. Most events
within 15 days of a mainshock (blue stars) are classified as aftershocks (blue dots) and only a
few of them are background events (red dots). ............................................................................. 22
Figure 1.9 (a–f) Map views of seismicity for the five main sequences. Large magnitude events
(M ≥ 3.5) are shown as focal mechanisms. Note the lack of aftershocks within 1 km of each
mainshock (solid circles; dashed circles have radiuses of 1 km plus the estimated mainshock‐
aftershock distance errors, respectively). ...................................................................................... 25
Figure 2.1 (a) Temporal variation of seismicity in southern California from the relocated catalog
(Hauksson et al., 2012). The red line denotes the estimated magnitude of completeness within a
5‐year sliding window. (b) Map view of 1981–2017 seismicity (M ≥ 1.5; dots), four M ≥ 6.7
major earthquakes (white stars), and major faults (thin solid line) in southern California. ......... 35
xi
Figure 2.2 (a) Distribution of nearest-neighbor statistics in southern California (1981–2017)
using events with magnitude M ≥ 1.5. (b) Histogram of nearest-neighbor distance η of all events.
The bimodal distribution is clearly seen in (a) and (b). The line log10(η) = −4.59 separating the
two modes is shown in white and red in (a) and (b), respectively. (c) Scatterplot of cluster size
versus mainshock magnitude. Clusters within red box are selected for further analysis. (d)
Epicenters of events within selected clusters as a function of time and latitude. Events in the
same cluster share the same color. ................................................................................................ 38
Figure 2.3 Map view of all well‐located events within the selected clusters (dots in Fig. 2.2d)
colored by (a) event occurrence time, (b) D95b, and (d) depth differences between D95c and
D95b. Events with depth 3 km below D95b are extracted and shown in (c). Four M ≥ 6.7
mainshock‐aftershocks sequences show significantly deeper D95c than D95b with more than 15
events that are at least 3 km deeper than D95b. Embedded plots in (c) show the histograms of
epicentral distances from deep events to their mainshock ruptures planes obtained from finite
fault models (Wald & Heaton, 1994; Wald et al., 1996; Ji et al., 2002; and Wei et al., 2011; white
lines). The source models of the Joshua Tree M6.1 foreshock and the Big Bear M6.5 aftershock
to 1992 Landers mainshock are also shown in white lines. .......................................................... 40
Figure 2.4 Depth‐time plots of well‐located events within (a) box A, (c) box B, (e) box C, and
(g) box D in Figure 2.3. Events belonging to 1992 M7.3, 1994 M6.7, 1999 M7.1, and 2010 M7.2
mainshock‐aftershock sequences and within corresponding boxes are denoted as red dots in (a),
(c), (e), and (g). The CDFs (cumulative density function) of occurrence time of the events in (a),
(c), (e), and (g) with different depth ranges are shown in (b), (d), (f), and (h), respectively. The
deepest event in each cluster is more than 5 km deeper than D95b. ............................................ 43
Figure 3.1. (a) Depth-time plots of earthquakes from 1981 to 2019 and (b) from 5 days before to
50 days after the 2019 Mw7.1 Ridgecrest earthquake. (c) A map view of events from 1981 to the
2019 Mw6.4 earthquake (black dots), between the Mw6.4 and Mw7.1 events (green dots) and
within 50 days after the Mw7.1 mainshock (red dots: depth >14 km, blue dots: depth <14 km).
Red curves denote the D95 of 500 events with a 99% overlapping moving time window. ......... 49
Figure 3.2. Potency distributions of events in the Ridgecrest sequence. (a) Potency of the Mw6.4
event along AA′. (b) Potencies of events between the Mw6.4 and Mw7.1 earthquakes along AA′.
(c) Potency of the Mw7.1 mainshock along AA′. (d) Potencies of aftershocks within 50 days after
the Mw7.1 event along AA′. The vertical solid lines and white stars in (a)–(d) denote the
projection of the boundaries and hypocenters of the Mw7.1 (gray) and Mw6.4 (black) slips along
AA′, respectively. (e) A map view of events that occurred between the Mw6.4 to Mw7.1 events
(green dots) and within 50 days after the Mw7.1 mainshock (red dots: depth >14 km, blue dots:
depth <14 km). Potency amplitude histograms of ML0–5 events along the fault normal direction
within boxes BB′ (f), CC′ (g), DD′ (h), EE′ (i), and FF′ ( j). Yellow stars denote the potency
values of ML5–6 events. ................................................................................................................ 53
Figure 3.3. Distributions of epicenters of earthquakes with Quality A–C focal mechanisms (a)
from 1981 to 2019, (b) from 5 days before to 5 days after the Mw7.1 event, and (c) from 5 days to
50 days after the mainshock as a function of time and distance along the AA′ in Fig. 3.2e.
Corresponding temporal variations of the percentages of normal faulting, reverse faulting, and
strike-slip focal mechanisms (d), (e), and (f), respectively. Corresponding temporal variations
of rNORM (g), (h), and (i), respectively. .......................................................................................... 56
xii
Figure 3.4. Map views of P wave velocity at 6 km depth (Zhang & Lin, 2014) and P axis
distributions of source mechanisms of events that occurred (a) from 1995 to 2010, (b) from 2010
to the 2019 Mw6.4 event, (c) between the Mw6.4 and Mw7.1 events, and (d) within 0–50 days
after the Mw7.1 event. The P axes are centered at the events' hypocenters and colored by their
azimuths. Cyan solid lines in (c) represent the fault geometry for the Mw6.4 slip model (Liu et
al., 2019). ...................................................................................................................................... 57
Figure 3.5. Same as Fig. 3.4, but P axes are colored by their faulting types. .............................. 58
Figure 4.1. Map view of moment tensors of 224 M ³ 3.0 events in the 2019 M7.1 Ridgecrest
earthquake sequence colored by the percentage of (a) CLVD component and (b) ISO component.
(c) Distribution of epicenters of the analyzed events as a function of time and distance along AA’
colored by the percentage of ISO components. ............................................................................ 67
Figure 4.2. Full moment tensor inversion results for the 2019/07/05 12:38 Mw4.1 event. (a) Map
view of the earthquake location (yellow star) and seismic stations (squares) used in the study.
Stations are colored by the averaged CC. (b) The number of waveforms that can be fitted (with
the CC larger than 70%), the averaged waveform CC, and the waveform misfit as a function of
focal depth and moment tensor solution, indicate a well-constrained focal depth of ~9.5 km. (c)
Distribution of misfit in the moment tensor lune-diagram. (d) Waveform fitting at different
stations. The black, red, and blue colors indicate data, synthetics, and the waveforms discarded in
the automatic data selection, respectively. .................................................................................... 68
Figure 4.3. The percentage of relative misfit changes of moment tensor inversions using (a) pure
deviatoric (DC + CLVD) sources compared with pure double-couple sources (DC), (b) full
tensor sources (DC + CLVD + ISO) compared with pure deviatoric (DC + CLVD) sources, (c)
DC + ISO sources compared with pure DC sources, and (d) full tensor sources (DC + CLVD +
ISO) compared with pure deviatoric (DC + CLVD) sources. Comparisons of (e) the percentages
of CLVD component obtained with and without ISO component and (f) the percentages of ISO
component obtained with and without CLVD component. .......................................................... 75
Figure 4.4. Variations of the percentage of isotropic (red symbols) and CLVD (blue symbols)
components as a function of minimum station distance cutoff for (a) three events with significant
ISO component and (b) three events without significant ISO component. The beachballs on the
upper side show the best-fitting double-couple solutions for different station cutoffs. ................ 77
Figure 5.1. (a) Map view of Cahuilla dense array (magenta square) and the 24 regional stations
(blue triangles) within 50 km of the dense array. Magenta box outlines the candidate epicentral
locations for dense array detection. (b) Spatial distribution of the vertical geophones of the dense
array colored by elevation. Inset shows the fault map of southern California. Red box denotes the
area of (a). EF, Elsinore fault; SAF, San Andreas fault; SJF, San Jacinto fault. .......................... 84
Figure 5.2. Schematic diagrams of the dense array earthquake detection workflow. For all
combinations of (a) candidate source epicentral location d (within 0.2°×0.2°box around the
array) and (b) apparent horizontal slowness ss (⁠0–15s/km⁠), (c) waveforms are shifted based on
the estimated travel time t and (d) correlated with neighboring stations’ waveforms. (e) The time
windows with averaged neighboring station similarity above the chosen threshold are selected as
positive detections. S&D corresponds to apparent horizontal slowness and horizontal distance. 85
Figure 5.3. (a) One min waveforms (15–25 Hz) of the dense array from 21 July 2018 T00:26:30
to 21 July 2018 T00:27:30. (b) Spectrogram of station index 70 in (a). (c) Temporal variation of
xiii
the maximum averaged neighboring station similarity (CC) versus apparent horizontal slowness.
(d–f) Spatial distribution of the maximum CC at the best-fitting times of the detected events in
(c). Vertical red lines and white stars highlight the best-fitting times, slowness values, and
locations of the detected events. ................................................................................................... 90
Figure 5.4. (a) Histogram of detected events from 21 July 2018 T00:00:00 to 22 July 2018
T00:00:00 with respect to the slowness and time. Spatial density of detections with slowness
(b) below and (c) above 0.4 s/km⁠. ................................................................................................. 92
Figure 5.5. Diagrams of the earthquake phase association and location. (a) For each possible
source location, we calculate its P-wave travel time to the dense array as well as P- and S-wave
travel times to the regional stations. (b) The location (Loc) with the maximum number of phase
arrivals within the estimated arrival-time window is selected as the earthquake location. (c–
e) Spatial distribution of the number of arrivals within 0.75 s from the predicted arrival times for
event 3 in Figure 3. White star denotes the best-fitting location. ................................................. 94
Figure 5.6. (a) Temporal variation and (b) spatial distribution of the catalog events (yellow
dots) and additional detected events (blue dots) from 21 July 2018 T00:00:00 to 22 July 2018
T00:00:00 scaled by event magnitude. ......................................................................................... 97
Figure A1.1 Map view of M ≥ 5 earthquakes in San Jacinto Fault Zone (SJFZ) from 1932 to
2016. Black box shows the study area in Fig. 1.1. ...................................................................... 107
Figure A1.2 Stations used for detection and relocation. AZ, CI and PB network stations are
colored blue, red and green, respectively. Black box shows the study area in Fig. 1.1. ............. 108
Figure A1.3 Temporal evolution of M4 earthquakes in the trifurcation area (area in Fig. 1.1)
from 1932 to 2016. ...................................................................................................................... 109
Figure A1.4 Map view of seismicity colored by the relative distance from the main faults using
different fault zone widths. ......................................................................................................... 110
Figure A1.5 Distribution of focal mechanisms for each depth interval within the near-fault, off-
fault, and intra-fault areas using different fault zone widths. Dashed line indicates the estimated
geodetic locking depth from Fialko (2006). ............................................................................... 111
Figure A1.6 Depth histograms of seismicity for different fault zone widths. ........................... 112
Figure A1.7 (left) Distribution of nearest-neighbor statistics for all available events in the
trifurcation area of San Jacinto Fault zone (2000-2016) with different magnitude cutoff values.
The white line shows the nearest-neighbor distance threshold used for clustering (based on
Zaliapin & Ben-Zion, 2016). (right) Histogram of nearest-neighbor distance 𝜂. Red vertical lines
denote the nearest-neighbor distance threshold used for clustering. .......................................... 113
Figure A1.8 Estimated location errors for the 2001 M5.2, 2005 M5.0, 2010 M5.4 and 2013 M4.7
aftershock sequences. “For the 2016 Borrego Springs sequence, 95% of the relative errors are
less than 150 m (horizontal) and 162 m (vertical).” (Ross et al., 2017a) ................................... 114
Figure A1.9 Map view of seismicity for the 2005 M5.0, 2010 M5.4 and 2013 M4.7 aftershock
sequences relocated using differential time data from all available stations (left) and only stations
in Fig. A1.1a (right). The characteristics of the relocated events are similar when using different
station datasets for relocation. ..................................................................................................... 115
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Figure A2.1 Map view of events within selected clusters (dots in Fig. 2.2d). Each event is
colored by the number of surrounding (within 3km epicentral distance) well-located (a)
background events and (b) events in the same cluster, respectively. .......................................... 117
Figure A2.2 Map view of well-located events with depth at least (a) 1 km and (b) 2 km below
D95b within the selected clusters (dots in Fig. 2.2d) colored by event occurrence time. .......... 117
Figure A2.3 Map view of (a) events with depth 3km below D95b and (b) all well-located events
within the selected clusters (dots in Fig. 2.2d) colored by depth differences between D95c and
D95b. Embedded plots in (a) show the histograms of epicentral distances from deep events to
their mainshock ruptures planes obtained from finite fault models. D95b and D95c are estimated
using events within 3km radius and 20 cut-off event number. ................................................... 118
Figure A2.4 Map view of (a) events with depth 3km below D95b and (b) all well-located events
within the selected clusters (dots in Fig. 2.2d) colored by depth differences between D95c and
D95b. Embedded plots in (a) show the histograms of epicentral distances from deep events to
their mainshock ruptures planes obtained from finite fault models. D95b and D95c are estimated
using events within 10km radius and 80 cut-off event number. ................................................. 118
Figure A2.5 The cumulative density function (CDF) of epicentral distance to mainshock fault
planes for events in (a) box A, (b) box B, (c) box C, and (d) box D with difference depth ranges.
..................................................................................................................................................... 119
Figure A2.6 (a) Map view of all well-located events within the selected clusters (dots in Fig.
2.2d) colored by local D95 estimated using all catalog events (D95all). D95all is estimated using
events within 5km radius and 30 cut-off event number. Events with depth 3km below D95all are
extracted and shown in (b). White lines denote M 3 6.7 mainshock ruptures planes obtained from
finite fault models (Wald & Heaton, 1994; Wald et al., 1996; Ji et al., 2002; and Wei et al.,
2011). The source models of the Joshua Tree M6.1 foreshock and the Big Bear M6.5 aftershock
to 1992 Landers mainshock are also shown in white lines. ........................................................ 120
Figure A2.7 Depth-time plots of well-located events within (a) box A, (c) box B, (e) box C, and
(g) box D in Fig. 2.3. Events belonging to 1992 M7.3, 1994 M6.7, 1999 M7.1, and 2010 M7.2
mainshock-aftershock sequences and within corresponding boxes are denoted as red dots in Fig.
(a), (b), (c), and (d). The pink curves denote the temporal D95 in each box for an overlapping
window (80% overlap) and a constant number (1000) of events. .............................................. 121
Figure A3.1 Map view of events from 1981 to the 2019 M6.4 event (black dots), from the M6.4
to the M7.1 event (green dots) and those within 50 days after the M7.1 event (red dots:
depth>14km; blue dots: depth<14km). ....................................................................................... 125
Figure A3.2 Distributions of epicenters of earthquakes with quality A-C focal mechanisms (a)
from 1981 to 2019, (b) from 5 days before to 5 days after the Mw7.1 event, (c) and from 5 days to
50 days after the mainshock as a function of time and distance along the HH’ in Fig. 3.2e.
Corresponding temporal variations of the percentages of normal faulting (red curves), reverse
faulting (green curves), and strike-slip (blue curves) focal mechanisms (d), (e), (f), respectively.
Corresponding temporal variations of rNORM (g), (h), (i), respectively. ...................................... 126
Figure A3.3 Cross-section views of P-wave velocity along AA’ (Zhang & Lin, 2014) and P-axis
distributions of events that occurred (a) from 1995 to 2010, (b) from 2010 to the 2019 Mw6.4
xv
event, (c) between the Mw6.4 and Mw7.1 events, and (d) within 0-50 days after the Mw7.1 event.
The P-axes are centered at the events’ hypocenters and colored by fault style. ......................... 127
Figure A3.4 Cross-section view of P-wave velocity (Zhang & Lin, 2014) along AA’. Magenta
Lines denote the slip boundary of the Mw6.4 event. Magenta stars denote the hypocenters of the
Mw6.4 and Mw7.1 earthquakes. ................................................................................................... 128
Figure A3.5 Map view of all events in relocated catalog (Hauksson et al., 2012) from 1981 to
2019 colored by event depth. White stars show the location of five M>=6.7 earthquakes. Black
boxes denote the chosen area for aftershock selection. .............................................................. 128
Figure A3.6 Aftershock-mainshock potency ratio of five M>=6.7 earthquakes in southern and
Baja California. ........................................................................................................................... 129
Figure A4.1. Comparisons of the percentages of the (a) isotropic components and (b) CLVD
components obtained using 1D and 3D velocity models. ........................................................... 132
Figure A4.2. Variations of the percentage of (upper) ISO components and (lower) CLVD
components in relation to events’ (left) depth and (right) magnitude. ....................................... 133
Figure A5.1. Four-second waveforms (15-25 Hz) of the dense array from 2018-07-21T00:27:17
to 2018-07-21T00:27:21, corresponding to 47-51 s in Fig. 5.3a. Red solid line denotes the
detected arrival time. Red dashed line denotes the hand-pick P-wave arrival. ........................... 134
Figure A5.2. Histogram of average neighboring station similarity of the one-day waveform
dataset from 07/21/2018T00:00:00 to 07/22/2018T00:00:00. The vertical line shows the
𝐶𝐶𝑡ℎ𝑟𝑒𝑠 (12 times of the MAD above the median value). ........................................................ 135
Figure A5.3. (a) Temporal variation and (b) spatial distribution of the catalog events (Hauksson
et al., 2012) from 07/21/2018T00:00:00 to 07/22/2018T00:00:00 scaled by event magnitude. Red
box shows the region plotted in Fig. 5.1 and Fig. 5.6. (c) The catalog events’ CC values obtained
using 2-15 Hz (blue dots) and 15-25 Hz (red dots) waveforms and their relationship to the
epicentral distance to the Cahuilla array. .................................................................................... 136
Figure A5.4. Histograms of the estimated uncertainties of the detected events’ (from
07/21/2018T00:00:00 to 07/22/2018T00:00:00) (a) latitudes, (b) longitudes, (c) depths and (d)
magnitudes. ................................................................................................................................. 137
Figure A5.5. Map view of the maximum azimuthal gap of the station coverage. ..................... 138
Figure A5.6. The comparisons between the catalog events’ (from 07/21/2018T00:00:00 to
07/22/2018T00:00:00) locations and magnitudes estimated in this study and those in the catalog
(Hauksson et al., 2012). .............................................................................................................. 139
Figure A5.7. The temporal variation of the threshold of average neighboring station similarity
𝑎𝑣𝑔𝐶𝐶𝑡ℎ𝑟𝑒𝑠 used for detection (12 times of the MAD above the median value). .................... 140
Figure A5.8. (a) Temporal variation and (b) spatial distribution of the detected events from
07/20/2018T03:00:00 to 08/12/2018T00:00:00 scaled by event magnitude. ............................. 141
Figure A5.9. (a) Waveform and (b) spectrogram of station index 70 in Fig. 5.3a. (c) Average
STA/LTA (0.5 short time window and 5s long time window) of all 99 stations without time shift.
(d) Maximum average STA/LTA of all slowness-location combinations. ................................. 142

xvi
Abstract
The interactions between major ruptures and faults have significant impact on their
individual properties. Many standard mechanical concepts and models assume that a major
rupture is a stick-slip along a single surface in a homogeneous continuum solid. While these
simplified models provide important insights to the earthquake and fault mechanics, they
contradict to the observed complex earthquake features and may obscure important processes
associated with the major ruptures. In this thesis, I investigate how the earthquake rupture
processes deviate from the simplified models using small earthquake properties and understand
the implications from the observed deviations.
To determine the validity of the single-fault-surface assumption, I investigate the
differences of earthquake properties in near-fault and off-fault regions and the complexities of
five M>4.5 earthquake sequences in the San Jacinto Fault Zone. The results show highly diverse
volumetric faulting patterns of the fault networks, suggesting the necessity to investigate the
rupture processes from a volumetric perspective. Therefore, I implement the volumetric
framework to examine the transient changes of seismic depth following four moderate-large
earthquakes in southern and Baja California. Two mechanisms are considered for the changes of
seismic depth: seismic-aseismic transition and brittle-ductile transition. The results show wide-
spread deeper-than-usual early aftershocks around the main faults, suggesting brittle-ductile
transition as the mechanism governing the base of the seismogenic zone. In addition to the depth
variations of seismicity, I monitor the temporal variations of earthquake properties before,
during, and after the 2019 M7.1 Ridgecrest sequence. The variations suggest a long-term
increase of shear stress in 20 years prior to the sequence, the termination of the M6.4 and M7.1
earthquakes near fault zone barriers, and the caused diverse volumetric damage in the
xvii
surrounding upper and lower crust. The complex failure pattern of the Ridgecrest sequence
suggests that earthquake ruptures may generate damage-related radiations. Therefore, I study the
spatiotemporal variation of isotropic components in the 2019 Ridgecrest sequence. Most events
with significant isotropic components occurred at the beginning of the sequence and are located
around rupture ends, intersections, which likely reflect damage rock fracturing.
To further enhance the monitoring resolution of fault zone evolutions and major ruptures,
it is important to improve the ability of earthquake detection. On this front, I propose a new
automated method to detect and locate earthquakes using a dense array and its nearby regional
stations. The method achieves automated detection with high spatiotemporal resolution without
using any prior information about seismic-waveform features or local velocity model.
1
Introduction
The interactions between major ruptures and faults have significant impact on their
individual properties. The fault zone properties around major ruptures can significantly affect
their preparation, initiation and termination (e.g. Zaliapin & Ben-Zion, 2020; Aki, 1979; King,
1986), change the amplification of seismic waves (Kurzon et al., 2014), and affect the aftershock
distribution and rupture area (McNamara et al, 2014; Schorlemmer and Wiemer, 2005). On the
other hand, the ruptures can change the properties of the fault zone as well, create a broad
damage zone (Qiu et al., 2017; Share et al., 2017), and further affect the long-term tectonics
(Jamveit et al., 2018). Therefore, monitoring and investigating the spatiotemporal evolution of
major ruptures and fault zone properties is critical for earthquake forecasting, hazard assessment,
and understanding tectonic motions. In the following chapters, I characterize the interactions of
major ruptures and fault zones using the properties of small earthquakes.
Many standard mechanical concepts and models for earthquake and fault mechanics
assume that a major rupture is a stick-slip along a single surface in a homogeneous continuum
solid (Anderson, 1951; Rice, 1980; Scholz, 2019; Aki & Richards, 2002, Ben-Zion & Sammis,
2003). This assumption has been widely used in theoretical research and observational analyses
(e,g,, Hillers et al., 2006; Thomas et al., 2017). However, in contrast to a homogeneous
continuum solid, the geological maps (Jennings, 1977), tomographical imaging (Fang et al.,
2016, Lee et al., 2014), and stress inversion results (Yang & Hauksson, 2013) in southern
California show that the shallow crust consists of a network of faults and varying material
properties with highly complex deformations and stress loadings (e.g. the San Jacinto Fault zone,
the Eastern California Shear zone). Many recent major ruptures (1992 M7.3 Landers, 1999 M7.1
Hector Mine, 2019 M7.1 Ridgecrest) have occurred in the Eastern California Shear zone, where
2
there are no clear pre-existing localized faults. Major earthquakes also cause distributed, off-fault
deformations on the earth’s surface (Milliner et al., 2016), in the seismogenic zone (Hauksson et
al., 1993; Ross et al., 2017), and even in the lower crust (Jamtveit et al., 2018). Therefore,
describing a major rupture as a single fault surface may obscure important aspects of the rupture
dynamics. To determine the validity of the single-fault-surface assumption, it is essential to
characterize the evolutionary processes of major ruptures from a volumetric perspective and
unravel the different processes that occur in the surrounding regions.
The volumetric framework may also provide additional insights into the mechanisms that
govern the depth extent of the seismogenic zone. Seismic depth is essential for understanding
crustal rheology and dynamics (Sibson, 1986, Scholz, 2019), estimating the maximum possible
rupture area and magnitude, investigating the possible existence of deep creeping faults
(Wdowinski, 2009; Meng & Peng, 2016), and exploring the long-term dynamics of the lower
crust (Austrheim & Boundy, 1994; Jamtveit et al., 2018). Previous studies have shown that the
spatial distribution of the base of seismogenic zone in southern California is mainly controlled by
temperature and lithology (Magistrale, 2002, Hauksson & Meier, 2019). However, there may be
a transient deepening of seismicity after major ruptures as demonstrated by numerical
simulations (Ben-Zion & Lyakhovsky, 2006), geological observations (e.g. Hawemann et al.,
2018; Menegon et al., 2017; Sibson, 1980), and seismological observations (Schaff et al., 2002;
Rolandone et al., 2004). There are two possible general mechanisms: a transition from seismic to
aseismic slip along a fault plane and a transition from brittle to ductile deformation in the rock
volume. Understanding which mechanism is dominant requires a systematic volumetric analysis
of multiple mainshock-aftershock sequences.
3
Mainshock-aftershock sequences can also help to understand many other processes
associated with major ruptures that may have a volumetric nature and cannot be simply
explained by a slip along a localized fault surface. For example, the 2019 Ridgecrest earthquake
sequence contained the largest earthquake in southern California since the 1999 M7.1 Hector
Mine earthquake and activated a complex fault network with many previously unmapped faults
(DuRoss et al., 2020). It started with the M6.4 earthquake with both NW-SE and NE-SW
oriented faults followed by a ~50km NW-SE oriented M7.1 mainshock 34 hours later. The
sequence included plenty of aftershocks with orthogonal lines of seismicity in a broad crustal
region (Shelly et al., 2020; Lomax, 2020; Ross et al., 2019b). The large number of unmapped
faults, the occurrences of two major ruptures in a short time period, and the broad complex
aftershock zone illuminate volumetric processes associated with the preparation, initiation and
arrest of the major ruptures, as well as the interaction of the mainshock with the surrounding
crust. These processes can be quantified using the temporal evolutions of earthquake properties
and further help to monitor the volumetric crustal deformation during inter-seismic, co-seismic
and post-seismic periods.
Furthermore, the volumetric rupture processes of the Ridgecrest sequence may involve
isotropic radiation in the source area, which has important implications for many topics, such as
the heat flow paradox (Brune et al., 1993; Ben-Zion, 2001), the crack versus slip mode of
earthquake ruptures, and the identification of small explosions from shear ruptures (Stroujkova,
2018). However, solving the small isotropic components of tectonic earthquakes is a challenging
task because isotropic radiation has small wavelength and decays fast with wave propagation
distance. Therefore, reliably solving isotropic components requires nearfield stations, high
frequency records, accurate earthquake locations and material properties. In the Ridgecrest area,
4
the large number of M>3.5 earthquakes, dense instrumentation, and high-resolution 3D velocity
models (Lee et al., 2014; Zhang & Lin, 2014) offer an unprecedented opportunity to perform a
comprehensive characterization of isotropic components and to investigate detailed local
processes and governing physics.
To further enhance the monitoring resolution of fault zone evolutions and major ruptures,
it is important to improve the ability of earthquake detection. Many recent successful detection
methods like template-matching method (Peng & Zhao, 2009; Shelly et al., 2016) and
surpervised deep-learning algorithms (e.g., Ross et al., 2018; Zhu & Beroza, 2018) can detect
several times more events than the standard detection workflow. However, these methods use
known earthquakes’ signals to detect new earthquakes and cannot detect earthquakes that are
highly different from the known earthquakes. One possible way to detect unknown seismic
signals is using the recent increasing number of dense arrays (e.g., Ben-Zion, et al., 2015; Inbal
et al., 2016; Li et al., 2018; Meng & Ben-Zion, 2018a; Gradon et al., 2019; Johnson et al., 2020).
However, dense array detection is highly sensitive to local velocity model and has limited
location resolution due to the small aperture (< 3km). Therefore, combining the small spacing of
the array and the large aperture of the regional stations has a great potential to achieve better
earthquake detection with high sensitivity in time and high resolution in space.
Chapters 1 to 5 of this thesis were originally written for individual publication. A brief
overview of these chapters is provided below.
Chapter 1 is a reformatted version of a publication in Journal of Geophysical Research:
Cheng, Y., Ross, Z., Ben-Zion, Y. (2018), Diverse Volumetric Faulting Patterns in the San
Jacinto Fault Zone. Journal of Geophysical Research: Solid Earth, 123(6), 5068-5081, doi:
10.1029/2017JB015408. I was the primary investigator and author of this paper, which describes
5
how we detect and locate five M4.5 aftershocks sequences in San Jacinto fault zone and analyze
the systematic differences and interactions between near-fault and off-fault events. The abundant
complex off-fault aftershocks and five non-overlapping aftershock sequences highlights the
volumetric failure patterns in this area.
Chapter 2 is a reformatted version of a publication in Geophysical Research Letters:
Cheng, Y., Ben-Zion, Y. (2019), Transient brittle-ductile transition depth induced by moderate-
large earthquakes in southern and Baja California. Geophysical Research Letters, 46(20), 11109-
11117, doi: 10.1029/2019GL084315. I was the primary investigator and author of this paper,
which describes how we analyze the temporal variation of brittle-ductile transition depth,
observe abrupt deepening and gradual recovery of the maximum event depth following four
M>=6.7 mainshocks. The wide-spread deeper-than-usual early aftershocks suggest classical
brittle-ductile transition as the mechanism governing the base of the seismogenic zone.
Chapter 3 is a reformatted version of a publication in Geophysical Research Letters:
Cheng, Y., Ben-Zion, Y. (2020), Variations of Earthquake Properties Before, During, and After
the 2019 M7. 1 Ridgecrest, CA, Earthquake. Geophysical Research Letters, 47(18), doi:
10.1029/2020GL089650. I was the primary investigator and author of this paper, which
describes how we analyze the spatiotemporal variations of earthquake properties before, during
and after the 2019 M7.1 Ridgecrest earthquake. The variations of earthquake properties suggest a
long-term increase of shear stress in 20 years prior to the sequence, the termination of the M6.4
and M7.1 earthquakes near fault zone barriers, and the caused diverse volumetric damage in the
surrounding upper and lower crust.
Chapter 4 is being prepared for publication: Isotropic source components of events in the
2019 Ridgecrest earthquake sequence. In this chapter, we study the spatiotemporal variation of
6
isotropic components in the 2019 Ridgecrest sequence using nearfield data. Most events with
significant isotropic components are located around rupture ends and intersections and occurred
at the beginning of the sequence, which likely reflect damage rock fracturing.
Chapter 5 is a reformatted version of a publication in Seismological Research Letters:
Cheng, Y., Ben-Zion, Y., Brenguier, F., Johnson, C., Li, Z., Share, P.E., Mordret, A., Boué, P.
and Vernon, F. (2020), An Automated Method for Developing a Catalog of Small Earthquakes
Using Data of a Dense Seismic Array and Nearby Stations. Seismological Society of
America, 91(5), 2862-2871, doi: 10.1785/0220200134. I was the primary investigator and author
of this paper, in which we proposed a new automated method to detect and locate earthquakes
using a dense array and its nearby regional stations. The method achieves automated detection
with high spatiotemporal resolution without using any prior information about seismic-waveform
features or local velocity model.
In Chapter 6, I summarize the main results and discuss future research plans.

7
1. Diverse Volumetric Faulting Patterns in the San Jacinto Fault
Zone (Cheng et al., 2018)
1.0 Summary
We examine locations, magnitudes, and faulting types of post-2000 earthquakes in the
trifurcation area of San Jacinto fault zone to clarify basic aspects of failure processes in the area.
Most M ≥ 3.5 events have strike-slip mechanisms, occur within 1 km of the main faults (Clark,
Buck Ridge, and Coyote Creek), and have hypocenter depths of 10–13 km. In contrast, many
smaller events have normal source mechanisms and hypocenters in intrafault areas deeper than
13 km. Additional small events with hypocenter depth <13 km occur in off-fault regions and
have complex geometries including lineations normal to the main faults. Five moderate
earthquakes with M 4.7–5.4 have high aftershock rates (~150 M ≥ 1.5 events within 1 day from
the mainshock). To obtain more details on aftershock sequences of these earthquakes, we detect
and locate additional events with the matched filter method. There are almost no aftershocks
within 1 km from the mainshocks, consistent with large mainshock stress drops and low residual
stress. The five aftershock sequences have almost no spatial overlap. While the mainshocks are
on the main faults, most aftershocks are located in intrafault and off-fault regions. Their locations
and spatial distribution reflect the mainshock rupture directions, and many also follow structures
normal to the main faults. The significant diversity of observed features highlights the essential
volumetric character of failure patterns in the area. The increasing rate of moderate events,
productive aftershock sequences, and large inferred stress drops may reflect processes near the
end of a large earthquake cycle.
8
1.1 Introduction
The standard model for earthquake and fault mechanics assumes that moderate and large
earthquakes can be described to first order in terms of slip along a single (potentially
heterogeneous) surface in a continuum solid (e.g., Ben‐Zion & Sammis, 2003; Tse &
Rice, 1986). This model is used widely in theoretical research and analyses of seismic and
geodetic data (e.g., Hillers et al., 2006; Thomas et al., 2017), although some studies adopt
granular mechanics, damage rheology, and other frameworks that emphasize the simultaneous
failure of, and interactions between, networks of slipping regions (e.g., Ben‐Zion, 2008, and
references therein). Inspections of rupture properties of well‐recorded large earthquake such as
(among many) the 1992 Mw7.3 Landers (e.g., Hauksson et al., 1993), 2010 MW 7.2 El Mayor‐
Cucapah (e.g., Wei et al., 2011), 2012 Mw 8.6 Indian Ocean (e.g., Yue et al., 2012), 2016 Mw 7.0
Kumamoto (e.g., Asano & Iwata, 2016; Shirahama et al., 2016), and 2016 Mw 7.8 Kaikoura (e.g.,
Clark et al., 2017; W. Xu et al., 2018a) earthquakes, and seismicity patterns in well‐instrumented
areas (e.g., California, Taiwan, Japan), indicate that complex volumetric failure patterns of fault
networks are common rather than the exception. This suggests that efforts to collapse the
dynamics of moderate and large earthquakes to single surfaces may miss important aspects of the
physics governing earthquake behavior. In the present paper, we analyze detailed seismicity
patterns associated with several moderate earthquakes in the San Jacinto fault zone (SJFZ) in
southern California in an effort to clarify basic characteristics of earthquake dynamics. The SJFZ
provides a good natural laboratory for detailed studies of earthquake dynamics because it is
highly active and well instrumented. The observed results are likely to be relevant to earthquake
processes in other areas. We note that various processes such as rock fracturing and deviations
from planarity can produce isotropic source terms (e.g., Ben‐Zion & Ampuero, 2009; Julian et
9
al., 1998; Ross et al., 2015) that can be important for the local physics. However, here we focus
on larger‐scale phenomena involving the occurrence of earthquakes in geometrically complex
crustal volumes that cannot be approximated by surfaces or narrow tabular zones.
The SJFZ is the most seismically active fault zone in southern California (Hauksson et
al., 2012) and accommodates a large portion of the plate motion in the region (e.g., Fay &
Humphreys, 2005; Lindsey & Fialko, 2013). Since 1890, the SJFZ produced 11 MW > 6
earthquakes (Wdowinski, 2009), and paleoseismic records indicate that it is capable of larger
events (e.g., Onderdonk et al., 2013; Petersen & Wesnousky, 1994; Rockwell et al., 2015) that
pose significant seismic hazard to large urban areas in southern California. The Anza seismicity
gap in the central SJFZ is notable due to a lack of microseismicity and moderate to large
earthquakes in the previous century (Sanders & Kanamori, 1984). In the trifurcation area located
to the southeast of the Anza gap, the SJFZ branches into the Coyote Creek, Clark, and Buck
Ridge faults (Fig. 1.1). In contrast to the seismic quiescence in the Anza gap, since 2000 more
than 10% of all detected earthquakes in Southern California have occurred in the trifurcation
area. Since 1 January 2000, four earthquakes with ML ≥ 5 occurred in the trifurcation area
(Fig. A1.1). For comparison, only three ML ≥ 5 events occurred from 1932 to 1999 along the
entire 100‐km‐long Clark fault in the SJFZ (in 1937, 1963, and 1980, respectively). The recent
frequent moderate earthquakes and high rate of ongoing seismicity in the trifurcation area
suggest increasing potential for the occurrence of large earthquake on the SJFZ (e.g., Zöller &
Ben‐Zion, 2014). The analysis done in this study helps to probe processes associated with the
possible approach of a large earthquake in the region.

10

Figure 1.1 Map view of 2000–2016 seismicity (dots and stars) and main faults (thin solid lines) in the
trifurcation area of the San Jacinto fault zone. The dashed lines indicate cross sections used in Figure 1.2.
The inset shows the location of the study area (red box) in southern California along with the entire San
Jacinto fault zone (SJFZ), San Andreas Fault (SAF), and Elsinore Fault (EF).

The depth extent of seismogenic faults is essential for estimating the possible rupture
area, magnitude and seismic hazard associated with large events. Wdowinski (2009) noted a
significant discrepancy between the geodetically inferred locking depth in the trifurcation area
and maximum depth of seismicity, and suggested that the deeper events reflect a deep creeping
zone below the SJFZ. Meng & Peng (2016) analyzed seismicity associated with 10 M > 4
earthquakes after 2000 and found that mainshocks with hypocenters depth below 11 km have
11
significantly larger aftershock zones than shallower events with comparable magnitudes.
However, these studies assumed implicitly that all examined events (moderate mainshocks and
microseismicity) essentially occur on the main fault plane. Ross, Hauksson, & Ben‐Zion (2017)
analyzed aftershocks of the 2016 Mw 5.2 Borrego Springs earthquake and observed complex
volumetric patterns with distinctly different spatial and frequency‐size event properties within
1 km of the main faults and those in the surrounding region. While the moderate earthquakes are
located on the main faults, much of the lower magnitude events including many deep events are
in a broad damage zone around the main faults (Figs. 1.1 and 1.2). Projecting all events to a
single surface as done in many analyses may lead to erroneous inferences.

Figure 1.2 Depth profile of seismicity along (a) A‐A′ and (b) B‐B′ in Figure 1.1. Dashed lines indicate
the estimated geodetic locking depth from Fialko (2006).

To analyze characteristics associated with additional moderate events in the trifurcation
area and unravel key aspects of the evolving earthquake failure processes in relation to the main
12
faults, we investigate in detail lateral and depth variations of seismicity and focal mechanisms in
the region. We examine both the overall earthquake population based on the regional seismic
catalog from 2000 to 2016 (Figs. 1.1 and 1.2) and detailed features associated with five M > 4.5
events (Table 1.1) and their aftershock sequences. In the next section, we describe the data used
in the study. In section 1.3 we present results on spatiotemporal‐magnitude‐mechanism patterns
in different crustal volumes in the trifurcation area of the SJFZ. The results highlight the
essential volumetric character and diversity of failure processes in the area. The aftershock
sequences of the M > 4.5 events have very little overlap and occur collectively in a broad
damage zone. The depth of seismicity is near the geodetic locking depth close to the main faults
and is significantly deeper in the outer regions. These and other aspects of the results are
discussed in the final section 1.4.
Table 1.1 Details of the M ≥ 4.5 Earthquakes Shown in Figure 1.1

Date Time Longitude Latitude Depth
(km)
M Template
events
no.
No. of
differential
times used
in
relocation
Event no.
after
detection
and
relocation
10/31/2001 07:56:16 -116.514 33.508 13.7 5.0 484 2,294,006 6211
06/12/2005 15:41:46 -116.567 33.532 13.1 5.2 897 690,004 6031
07/07/2010 23:53:33 -116.475 33.417 12.3 5.4 1506 3,352,111 10328
03/11/2013 16:56:06 -116.458 33.501 10.9 4.7 1331 9,181,498 9288
06/10/2016 08:04:39 -116.443 33.431 12.3 5.2 1619 28,000,000 12,487

1.2 Data
The study is based on several different data sets. We use 25 M ≥3.5 earthquakes from
Southern California Seismic Network (SCSN) standard catalog (nonrelocated). An additional
data set with 44,153 M < 3.5 events (2000–2016; Figs. 1.1-1.3) is based on the relocated
southern California catalog (Hauksson et al., 2012) and its most recent update
(http://scedc.caltech.edu). The locations of larger magnitude (M ≥ 3.5) events are taken from the
standard (rather than relocated) catalog, since the largest events do not correlate well with small
13
ones. We also use 20,802 focal mechanism solutions (2000–2016) from the catalog of Yang et al.
(2012) and its most recent update.

Figure 1.3 Temporal variation of seismicity in the trifurcation area (events in Figure 1.1). (a) Earthquake
magnitude versus time. Red line shows the estimated magnitude of completeness within a 4‐year sliding
window. (b) Number of events (M ≥ 1.5) per month within the study area. There are five time periods
with a high seismicity rate correspond to M ≥ 4.5 aftershock sequences (Table 1.1). (c) Normalized
cumulative density function (CDF) of seismicity for various minimum magnitude thresholds.

The continuous waveform data at 28 stations are used to detect additional earthquakes
during five highly active seismic sequences (Fig. A1.2) listed in Table 1.1. Of these stations,
there are 15 broadband sensors from the AZ network (Fletcher et al., 1987), 6 borehole
seismometers from the Plate Boundary Observatory network (since 2006), and 7 broadband
14
stations from the CI network (Hutton et al., 2010). Aftershock sequences in 2001 and 2005 are
recorded only by the AZ network, while sequences in 2010, 2013, and 2016 are recorded by the
AZ, CI, and PB networks (Fig. A1.2). For each sequence, we use all available continuous
waveform data from the Southern California Earthquake Data Center starting 1 day before to
15 days after the mainshock. Template events are selected from the same time period (1 day
before mainshocks to 15 days after mainshocks) in the standard SCSN catalog. The number of
template events for each aftershock sequence is listed in Table 1.1. For each template event, we
extract template waveforms from all available stations based on the phase data produced by
SCSN. For the 2016 sequence we use the refined catalog produced by Ross, Hauksson, & Ben‐
Zion (2017).
1.3 Results
1.3.1 Overview of Seismicity
As mentioned, the trifurcation area of the SJFZ has produced many moderate magnitude
earthquakes since 2000. There are 38 M ≥ 4 earthquakes within the trifurcation area in the SCSN
catalog (Fig. A1.3) from 1932 to 2016 (85 years), with 10 occurring from 2000 to 2016
(17 years). Moreover, 4 out of 6 ML ≥ 5 earthquakes in the trifurcation area from 1932 to 2016
occurred after 2000 (Figs. A1.1 and A1.3). Figs. 1.1 and 1.2 provide a map view and projection
on vertical cross sections (A‐A′ and B‐B′) of the 2000–2016 seismicity from the Hauksson et al.
(2012) catalog. Most M > 4.5 earthquakes are located near the main faults with depth between 10
to 14 km, while most M < 4.5 events are broadly distributed and occasionally form localized
structures with various trends and depths. Most events shallower than 11 km are located on the
northeast and southwest sides of the Buck Ridge and Coyote Creek faults, respectively, and are
aligned normal to the main faults. In contrast, events deeper than 11 km are located between the
15
Buck Ridge and Coyote Creek faults and delineate the depth variation of the bottom of the
seismogenic zone (Fig. 1.2b).
The temporal evolution of seismicity within the region also shows multiple interesting
patterns (Fig. 1.3). Due to temporal variations of the seismic network stations in Southern
California, we use a 4‐year moving time window to estimate the magnitude of completeness
based on the maximum curvature method (Woessner & Wiemer, 2005). For consistency, we
select MC = 1.5 to perform further temporal analysis over the examined time range. It is
interesting to note that the five events with M ≥ 4.5 are quasi‐periodic in time (Figs. 1.3b
and 1.3c), while the small events with M ≥ 1.5 approximately follow a constant seismicity rate
(red line in Fig. 1.3c).
In the following sections, we examine in more detail relations between different aspects
of the SJFZ in the trifurcation area and spatiotemporal aspects of seismicity in different
magnitude ranges.
1.3.2 Lateral Variation of Focal Depths
Fig. 1.4 shows the 5th percentile (D05) and 95th percentile (D95) of focal depths of
events in the relocated regional catalog on a 0.005° × 0.005° (0.465 × 0.556 km) grid in the
trifurcation area. The focal depths exhibit strong lateral variation across the trifurcation area. The
D05 distribution is very shallow (~5 km) around the Buck Ridge fault, but parts of the area
between the Buck Ridge and Clarks faults have D05 deeper than 11 km (white circle in
Figs. 1.4a and 1.4b). The D95 distribution is a proxy for the bottom of seismogenic zone and
may be compared to the geodetically inferred locking depth (~11 km; Fialko, 2006; Wdowinski
et al., 2007). We note that regions close to the main faults tend to have D95 values that are less
than the locking depth, while regions between the main faults tend to have D95 values that are
16
deeper than the locking depth. Clear examples of this are the strong changes in D95 across the
Buck Ridge and Coyote Creek faults. Additionally, most large (M ≥ 4.5) events are along the
main faults with strike‐slip focal mechanisms. In contrast, some of the mechanisms of the
smaller events are normal faulting and they occur between the main faults (Figs. 1.4a and 1.4b).

Figure 1.4 (a) D05 and (b) D95 distribution over a 0.005° × 0.005° (0.465 × 0.556 km) grid. M ≥ 3.5
events are denoted by their focal mechanisms and scaled by magnitude. White ellipses highlight the deep
seismogenic zone between the Buck Ridge and Clark faults.

1.3.3 Variations of Focal Mechanisms
Bailey et al. (2010) showed that the SJFZ is associated with high diversity of focal
mechanisms. To examine focal mechanisms in relation to the main faults in the trifurcation area,
we divide the earthquakes into three groups based on their distance to the main faults: (1) events
with distance <1 km to the three primary faults (near‐fault area, red dots in Fig. 1.5), (2) events
outside of the Buck Ridge and Coyote Creek faults with distance >1 km to the nearest main
faults (off‐fault area, blue dots in Fig. 1.5), and (3) events between the Buck Ridge and Coyote
Creek faults with distance >1 km from the main faults (intrafault area, green dots in Fig. 1.5).
The events in these categories have different focal depths, faulting types, and magnitudes.
Because of the large number and diversity of focal mechanism solutions, it is hard to use scatter
17
plots to compare results between these categories. We therefore first normalize the observed rake
angles and express the mechanisms on a continuous scale from −1 to 1, with normal faulting
having a value of −1, strike‐slip denoted by 0 and thrust faulting denoted by 1 (Shearer et
al., 2006).

Figure 1.5 Map view of seismicity colored by the relative distance from the main faults. Red dots denote
events within 1‐km distance from the main faults (near‐fault area). Blue dots are events outside of the
fault zone with distance more than 1 km from the main faults (off‐fault area). Green dots show events
between main faults with distance more than 1 km from the mapped main faults (intra‐fault area). M ≥ 3.5
events are denoted by white stars and scaled by size.

Fig. 1.6 displays depth‐faulting‐type 2‐D histograms. The focal mechanisms are
subdivided into depth and faulting type bins of width 1 km and 0.1 units, respectively, with the
estimated geodetic locking depth indicated by a dashed line. The results show clear differences
among the three groups. The events in the near‐fault region are widely distributed in depth
(Fig. 1.6a). Because the seismogenic depth changes abruptly across the main faults, the depth
18
distribution of seismicity on the main faults is hard to define using small magnitude events in the
near‐fault region. However, as shown by Ross, Hauksson, & Ben‐Zion (2017), near‐fault
M ≥ 3.5 magnitude events are more likely to occur on the main faults. Most M ≥ 3.5 near‐fault
events (white stars in Fig. 1.6a) are around the estimated geodetic locking depth between 11 to
13 km depth (dash lines in Fig. 1.6a), and the focal mechanisms of M ≥ 3.5 near‐fault events are
aligned with the direction of mapped main faults (focal mechanisms in Fig. 1.4).

Figure 1.6 Distribution of focal mechanisms for each depth interval within the near‐fault (a), off‐fault (b),
and intrafault (c) areas. Dashed lines indicate the estimated geodetic locking depth from Fialko (2006).

While all M ≥ 4.5 earthquakes in the near‐fault region are deeper than 11 km (Fig. 1.6a),
most off‐fault events are above 11 km (Fig. 1.6b). Moreover, events in the off‐fault region show
19
structures normal to the primary faults (Fig. 1.5). The depth discrepancy between large near‐fault
events and the near‐normal off‐fault seismicity suggests that these off‐fault events may not be
related to the large events along the main faults. The intrafault events are generally concentrated
below 11 km depth and are even deeper than in the near‐fault region. There are few intrafault
events in the top 11 km (Fig. 1.6c). Below 13 km depth, there are many normal faulting events,
as well as two M ≥ 4.5 oblique reverse strike‐slip events (Fig. 1.6c). Most of these deep events
are located at the northwest part of the trifurcation area near the Anza gap (white circle in
Figs. 1.4a and 1.4b). The focal mechanism heterogeneity and deeper focal depths indicate a
deformation environment that is distinct from that of the three main faults.
The results in this section are determined using assumed fault zone width of 1 km. To test
the sensitivity of the results to other values, we perform corresponding analyses using different
fault zone widths (0.5, 1, and 1.5 km). As the assumed fault zone width increases, more events
are included in the near‐fault group and fewer are included in the intrafault and off‐fault groups.
However, the observed patterns are generally similar (Figs. A1.4–A1.6). In particular, the depth‐
faulting‐type distribution of each group is generally insensitive to the employed fault zone width.
1.3.4 Spatial Patterns of Aftershocks
The previous observations demonstrate that off‐fault and intrafault events have
significantly different spatial and focal mechanism patterns from near‐fault events. We can
further analyze volumetric faulting characteristics by exploring the interaction between large
strike‐slip events and their aftershocks in the surrounding area. To separate aftershocks from
background events, we use the cluster detection approach of Zaliapin & Ben‐Zion (2013) based
on nearest‐neighbor distances in a combined space‐time‐magnitude domain. For each event
pair i and j, we calculate,
20
𝜂
!"
= -
𝑡
!"
.𝑟
!"
/
#
10
$%&
!
, 𝑡
!"
> 0;
∞, 𝑡
!"
≤ 0,
(1)
where 𝑡
!"
= 𝑡
"
−𝑡
!
is the interevent time, 𝑟
!"
is the interevent distance, 𝑑 is the fractal
dimension of hypocenters, 𝑏 is the parameter of Gutenberg‐Richter distribution, and 𝑚
!
is the
magnitude of event 𝑖. The nearest neighbor of event 𝑗 is the previous event 𝑖 with the smallest
distance based on equation 1. 𝜂
!"
can be represented in terms of space and time components
normalized by the magnitude of the earlier event i:
𝑇
!"
= 𝑡
!"
10
$'%&
!
,𝑅
!"
= 𝑟
!"
#
10
$()$')%&
!
,0 < 𝑞 < 1. (2)
In this paper, we compute 1 using 𝑏 = 1, 𝑑𝑓 = 1.6, and 𝑞 = 0.5. The distribution of
nearest‐neighbor distances is bimodal (Figs. 1.7 and A1.7), with the largest mode corresponding
to background events and the smaller mode corresponding to clustered events (Zaliapin & Ben‐
Zion, 2013). We separate the two modes by fitting a Gaussian mixture model and choosing the
midpoint between the two modes as the threshold for clustering (Zaliapin & Ben‐Zion, 2016).

Figure 1.7 (a) Distribution of nearest‐neighbor statistics for all available events in the trifurcation area of
the San Jacinto fault zone (2000–2016) with magnitude cutoff Mmin = 0. The white line shows the nearest‐
neighbor distance threshold used for clustering (based on the method in Zaliapin & Ben‐Zion, 2016). (b)
Histogram of nearest‐neighbor distance η of all used events. Red line denotes the nearest‐neighbor
distance threshold used for clustering.

21
We use catalogs with multiple cutoff magnitudes (0.0, 0.5, 1.0, 1.5) to examine the
variation of the distribution of nearest‐neighbor distances (Fig. A1.7). The results show that the
threshold of nearest‐neighbor distances is stable with respect to the magnitude cutoff. As
representative analysis we use the threshold 𝜂
+, -./
= 10
$0.22
to detect earthquake clusters. Each
event is linked to their nearest neighbor (parent) if 𝜂
!"
is smaller than the chosen
threshold 𝜂
+, -./
. The five largest event clusters are found to be associated with the M > 4.5
aftershock sequences (Fig. 1.8). For each mainshock, most events within 1 day before to 15 days
after the mainshock are in the same cluster as the mainshock. We therefore use events from the
same time window for each mainshock (1 day before to 15 days after mainshock) and regard
them as an earthquake sequence to analyze (Table 1.1).
22

Figure 1.8 (a–e) Magnitude‐time plots of five chosen M > 4.5 aftershock sequences. Most events within
15 days of a mainshock (blue stars) are classified as aftershocks (blue dots) and only a few of them are
background events (red dots).

For each earthquake sequence, we apply a matched filter method to detect previously
unidentified earthquakes in the continuous data following Ross, Hauksson, & Ben‐Zion (2017).
First, waveforms are downsampled to 50 Hz and band‐pass filtered from 2 Hz to 15 Hz. Then,
template waveforms are prepared using a 2.5 s time window for the P wave and a 4.0 s window
for the S wave, starting 0.2 s before the analyst's pick. Templates are formed from all channel
and phase combinations. Cross correlations between the template waveforms and continuous
data are computed in 24‐hr segments, using only matching channels. All cross‐correlation
23
functions are shifted back in time by the observed travel time of the template and summed up for
detection. The detection threshold is either 9 times the median absolute deviation for the
respective day or 0.4 if greater. We further require that at least four of the individual phase
correlation functions have a peak absolute value of at least 8 times the median absolute deviation
to ensure that the stacked correlation function is not dominated by a small number of phases.
Detections separated by less than 2 s apart are linked, and the template with the largest stacked
cross‐correlation coefficient is selected as the reference for single detection. Magnitudes are
estimated from the median peak amplitude ratio between detected phase and template phase
under the assumption that 1 unit magnitude difference corresponds to a factor of 10 in amplitude
ratio.
For each detected event, we first set its initial location to that of the best matching
template event. Then we calculate cross correlation coefficients between detected events with
their 200 nearest template events (in spatial distance) on all three components using 1.0 s time
windows for P waves and 1.5 s for S waves (e.g., Hauksson et al., 2012). For each station, the
largest positive cross‐correlation coefficient of each phase is saved. If there are more than 5
differential times with cross‐correlation coefficients larger than 0.6 for a given event pair, we use
the differential times of this event pair for relocation process. To ensure consistency among the
mainshocks and their aftershocks, we use nonrelocated locations from the standard SCSN
catalog as the initial locations and the SCSN 1‐D velocity model (Table A1.1) for relocation
(Hutton et al., 2010).
The relocation employs the GrowClust algorithm (Trugman & Shearer, 2017a) with a
minimum correlation coefficient of 0.6 and a minimum of 6 differential times as input
parameters. Newly detected events that are not relocated by GrowClust are removed from further
24
consideration. The total number of events for each sequence before and after detection and
relocation is listed in Table 1.1. The obtained catalogs contain at least 7 times more earthquakes
than the SCSN catalog in the same space‐time window (Table 1.1). The location errors of each
sequence were estimated by the nonparametric bootstrapped error estimation procedure in
GrowClust (Fig. A1.8). In addition to uncertainty introduced from the velocity model and the
relocation procedure, variations in the station distribution for each sequence (Fig. A1.2) can also
lead to inconsistencies between the resulting seismicity patterns. To check the influence of
station distribution on earthquake relocation, we use a fixed set of stations (Fig. A1.2a) to
conduct the relocation of all sequences. Fig. A1.9 compares the relocation results derived with
all available stations to those obtained using the stations in Fig. A1.2a. The results demonstrate
that the overall characteristics of the obtained sequences discussed in the paper are not sensitive
to the station distribution. This is probably due to the fact that most nearby stations have been
available from 2001 to 2016.
The aftershock sequences in the updated catalogs exhibit a variety of noteworthy patterns
(Fig. 1.9). One striking observation is that for each M ≥ 5 aftershock sequence, more than 98%
of the events are at least 1 km epicentral distance from the mainshock (solid‐line circles in
Figs. 1.9a to 1.9e). There also is no obvious fault plane structure among the seismicity for any
mainshock. If we take the horizontal location errors of aftershocks 𝜀
345
(Fig. A1.8) and
mainshocks 𝜀
65
(Table 1.2) into consideration, the errors 𝜀
#!/+
between each mainshock's
horizontal location 𝑋
65
and its aftershocks' horizontal locations 𝑋
345
can be roughly estimated
using
𝜀
#!/+
= 𝜀.𝑋
⃑
65
−𝑋
⃑
345
/≤ 𝜀(𝑋
65
−𝑋
345
) = I𝜀
345
7
+𝜀
65
7
"
. (3)
25

Figure 1.9 (a–f) Map views of seismicity for the five main sequences. Large magnitude events (M ≥ 3.5)
are shown as focal mechanisms. Note the lack of aftershocks within 1 km of each mainshock (solid
circles; dashed circles have radiuses of 1 km plus the estimated mainshock‐aftershock distance errors,
respectively).

Table 1.2 Horizontal Location Errors of Chosen Aftershock Sequences, Estimated Mainshock-Aftershock
Epicentral Distance Errors, and the Percentage of Aftershocks With Epicentral Distance > 1 km
Event Mainshock
horizontal
errors (km)
90
th

percentile
aftershocks
horizontal
errors (km)
Epicentral
distance error
(km)
Percentage of
aftershocks
with
epicentral
distances > 1
km (without
consideration
of location
errors)
Percentage of
aftershocks
with
epicentral
distances > 1
km (with
consideration
of location
errors)
26
2001 M5.2 0.26 0.41 0.48 97.3% 72.9%
2005 M5.0 0.16 0.42 0.45 98.7% 95.6%
2010 M5.4 0.17 0.27 0.32 99.9% 99.5%
2013 M4.7 0.14 0.14 0.20 77.8% 61.5%
2016 M5.2 0.13 0.15 0.20 99.9% 99.8%

The calculated epicentral distance errors of aftershock sequences are shown in Table 1.2.
At least 70% of the events are more than 1‐km epicentral distance from their respective
mainshock (dashed‐line circles in Figs. 1.9a–1.9c and 1.7e). The 2013 M4.7 event has about 60%
of the aftershocks more than 1‐km distance away (Table 1.2). Ross, Kanamori, & Hauksson
(2017) noted this feature for the 2016 sequence and showed that this gap was coincident with the
coseismic slip distribution of the mainshock. They further argued that the lack of aftershocks
within the slip zone and large stress drop (~80 MPa) suggests that the residual stress on the fault
is low. Besides the 2016 sequence, Trugman & Shearer (2017b) observed that the stress drops of
these mainshocks are quite large, which is consistent with the generally large mainshock‐
aftershock distances of all examined aftershock sequences (Fig. 1.9). Similar observations for
global megathrust earthquakes were analyzed by Wetzler et al. (2018).
The newly detected aftershocks also delineate numerous structures with various
orientations. Interestingly, none of these aftershock sequences share a similar spatial pattern. The
aftershocks of the 2001 M5.0 event are clustered together without any clear lineations
(Fig. 1.9a). The 2005 and 2010 sequences are distributed sparsely in space and show some linear
structures at an oblique angle to the main faults (Figs. 1.9b and 1.9c). In contrast, the 2013 and
2016 sequences are highly clustered with abundant small scale lineations that are almost
orthogonal to the main faults (Figs. 1.9d and 1.9e). Despite the broad distribution of aftershocks
and diverse seismicity patterns, only a few aftershocks are located near the main faults and a
limited number of the lineations are oriented parallel to the main faults (Figs. 1.9a–1.9e).
27
Additionally, while each aftershock distribution covers a broad area, they only have limited
overlap in space (Fig. 1.9f). The lack of overlap and the fact that the sequences occur only a few
years apart suggest that each aftershock zone has a different stress distribution. This is most
prominent when comparing the 2010 and 2016 sequences, where the 2010 aftershock distribution
“bends” around the eventual site of the 2016 aftershock distribution. These diverse patterns
provide clear evidence for the complex volumetric interactions of earthquakes in the region.
Although all mainshock hypocenters have depths between 11 km to 14 km, the depth
ranges of their aftershock sequences are much broader. Most aftershocks of the 2001 M5.0 and
2005 M5.2 aftershock sequences in the intrafault area at the northwest between the Buck Ridge
and Coyote Creek faults are between 13 and 17 km (Figs. 1.9a and 1.9b). The 2013 M4.7 event
along the Buck Ridge fault triggered many off‐fault aftershocks on the northeast side with depth
shallower than 11 km (Fig. 1.9d). The 2010 M5.4 and 2016 M5.2 events produced a large
number of intermediate‐depth (10–15 km) aftershocks (Figs. 1.9e and 1.9f). These results are
consistent with the observation from the entire relocated catalog that off‐fault aftershocks are
shallower than 11 km, while the intrafault region has aftershocks deeper than 11 km.
Horizontally, the aftershock patterns exhibit a strong correlation with the focal mechanisms of
their mainshocks. The 2001 M5.0 and 2005 M5.2 events are oblique reverse‐strike‐slip events
followed by many aftershocks deeper than 13 km on the east side of their mainshocks (Figs. 1.9a
and 1.9b). The 2010 M5.4, 2013 M4.7, and 2016 M5.2 events share similar focal mechanisms
and produce aftershocks on the northwest of mainshocks, despite their different locations,
magnitudes, and depths (Figs. 1.9c–1.9e).
28
1.4 Discussion and Conclusions
We perform several types of analyses to clarify basic aspects of earthquake and fault
mechanics in the trifurcation area of the SJFZ using relocated seismicity, focal mechanisms, and
detection of additional aftershocks for five M > 4.5 earthquakes. Both the historical seismicity
and focused analyses of moderate aftershock sequences illustrate the complexity and essential
volumetric characteristics of tectonic deformation in the region. Spatiotemporal variations of
seismicity, magnitudes, and source mechanisms highlight the importance of distinguishing
between failure processes associated with the main faults and those occurring in the surrounding
crustal volumes.
There are various general reasons for complex volumetric behavior of earthquakes of the
type documented in this paper (Fig. 1.9). On an elementary level, tendencies of dynamic ruptures
to branch from a fault during propagation (e.g., Sharon et al., 1995; Yoffe, 1951) and to generate
high‐angle off‐fault fractures near barriers (e.g., S. Xu & Ben‐Zion, 2013) can produce off‐fault
complexity even in a homogenous solid under single‐mode loading. More importantly,
preexisting structural heterogeneities and mixed‐mode loadings, which are common in the crust,
can prevent localization of deformation and produce seismic responses over a network of faults
and fracture zones (e.g., Finzi et al., 2009; Lyakhovsky & Ben‐Zion, 2008). Aftershocks
generally occupy volumes around mainshock ruptures and produce distributed rock damage that
can delocalize the earthquake deformation zone. Aftershocks in the lower crust due to transient
deepening of the brittle‐ductile transition after large mainshocks (e.g., Ben‐Zion &
Lyakhovsky, 2006; McNamara et al., 2017; Rolandone et al., 2004), and related changes of rock
type and dynamics of the lower crust (e.g., Jamtveit et al., 2018), can also broaden the seismic
deformation zone. In the trifurcation area of the SJFZ, likely major contributing factors to the
29
observed volumetric failure patterns are the complex geometry of the fault system with three
main faults (Buck Ridge, Clark, and Coyote Creek) and many subsidiary structures including
some orthogonal to the main faults (Fig. 1.1), shear loading of the plate‐boundary combined with
opening in the Gulf of California (e.g., Axen & Fletcher, 1998) and possible additional transient
loadings from ductile shear zones off the main faults.
A number of recent studies showed that the three main faults in the trifurcation area have
strong velocity contrasts and asymmetric damage zones concentrated on the northeast sides of
the faults (Allam et al., 2014; Qin et al., 2018; Qiu et al., 2017). The large available surface areas
along the main faults allow for the occurrence of relatively large events. Almost all near‐fault M
≥3.5 earthquakes are right‐lateral strike‐slip events with strike direction consistent with the plate‐
boundary shear deformation (focal mechanisms in Fig. 1.4). Most large ruptures are concentrated
between 11 km to 13 km depth near the bottom of the near‐fault seismicity and the geodetic
locking depth (Fig. 1.6a). Some of these near‐fault mainshocks (Figs. 1.9–1.9e) triggered a large
number of aftershocks on the northeast sides of their rupture zones. Some historical moderate
events in trifurcation area like the 1937 Buck Ridge earthquake and 1980 Whitewash earthquake
also have right‐lateral focal mechanisms with abundant aftershocks to the northeast of the main
faults (Sanders et al., 1986; Sanders & Kanamori, 1984).
The intrafault and off‐fault areas have complex smaller‐size faults and fractures with
distributed seismicity at different depth sections and various focal mechanisms (Fig. 1.6). Bailey
et al. (2010) analyzed focal mechanism heterogeneity in the SJFZ and suggested that it is
controlled primarily by fault zone structure rather than time or magnitude. The distributed
cracking in the intrafault and off‐fault regions produce collectively damage zones manifested by
reduced seismic velocities and anomalous Vp/Vs ratios (Allam et al., 2014; Zigone et al., 2015).
30
The intrafault mainshocks have some different characteristics from the near‐fault mainshocks.
The 2001 M5.0 and 2005 M5.2 events have hypocenters below 13 km and oblique reverse‐strike‐
slip mechanisms. The spatial distributions of these aftershock sequences do not exhibit along‐
strike asymmetry with respect to the mainshock as seen for the moderate five mainshocks and
other events on main fault sections (Zaliapin & Ben‐Zion, 2011). These two aftershock
sequences are located at the northwest of the trifurcation area and are deeper than other
aftershock sequences on the main faults. The different depths may be related to the fact that the
seismogenic zone is becoming overall shallower to the southwest likely because of regional
variations of heat flow (Doser & Kanamori, 1986; Sibson, 1984). In addition, these two events
may occur along large thrust faults around the restraining bend formed by left stepping of the
Buck Ridge fault that may cause a deepening of the seismogenic zone (Sibson, 1984). The
abundant normal faulting events in the intrafault area (Fig. 1.6c) and numerous near‐orthogonal
structures delineated by the aftershock sequences (Figs. 1.9a–1.9e) demonstrate the broad
damage zone between the main fault segments. Events with purely extensional normal faulting
mechanisms indicate small‐scale pull‐apart structures between parallel fault segments. For events
deeper than 13 km, there are increasing numbers of normal mechanisms and decreasing numbers
of strike‐slip events.
The five recent M > 4.5 mainshocks have aftershock sequences with only a little spatial
overlap, and four M ≥ 5 mainshocks have more than 70% of the aftershocks at least 1‐km
epicentral distance from their mainshock hypocenters (Fig. 1.9). The lack of aftershocks near the
mainshock hypocenters is consistent with the large stress drops in the range 80–150 MPa found
for the mainshocks (Ross & Ben‐Zion, 2016; Trugman & Shearer, 2017b; Ross, Kanamori, &
Hauksson, 2017), while the occurrence of distinct sequences with little spatial overlap point to
31
significant regional heterogeneities. As shown by Ross, Hauksson, and Ben‐Zion (2017), most of
the background seismicity in the area occurs within off‐fault damage zones, implying that the
main faults are locked. These broad damage zones extend down to 15 km and coincide with
Vp/Vs anomalies (Allam et al., 2014). The discrepancy between the locking depth of the main
faults and maximum depth of seismicity is largely a consequence of projecting all the events to
the main fault surfaces. As shown in Fig. 1.4b, the depth of seismicity in the near‐fault region is
consistent with the geodetically inferred locking depth. This eliminates the need for a deep
creeping zone to reconcile the difference between locking depth and maximum depth of
seismicity. However, a deep creeping zone may still exist as suggested by the long duration and
along‐strike spatial extent of aftershock zones of some of the M > 4.5 events (Wdowinski, 2009;
Meng & Peng, 2016; Ross, Hauksson, & Ben‐Zion, 2017) and possible slow slip events triggered
by the 2010 Mw 7.2 El Mayor‐Cucapah earthquake and recent M > 5 mainshocks in the area
(Inbal et al., 2017).
The observations examined in this study reflect processes that occur in different crustal
volumes. The majority of events within the damage zone differ from the larger events on the
main faults in many aspects including focal mechanisms, stress drops, and geometric complexity.
The diverse seismicity structures, large aftershock zones with little spatial overlap, long‐duration
sequences, and significant distance between mainshocks and aftershocks point to complex
interactions between the main faults and the surrounding damage zones. The low level of low
magnitude seismicity on the primary faults and large seismicity gaps around the M > 4.5
mainshocks suggests that the main fault structures in the area are locked in agreement with
geodesy. The increasing rate of moderate strike‐slip events between 10 to 13 km depth near the
main faults, productive aftershock sequences and large lapse time since the last major San
32
Jacinto fault zone earthquake, suggests that the region may be approaching the next major
earthquake. At the same time, the barely overlapping aftershock sequences of the analyzed
M > 4.5 events point to the significant heterogeneity and complex dynamics of earthquakes in
the most seismically active fault zone in southern California. Describing deformation in the SJFZ
(and other large fault zones) as occurring on a single fault surface can obscure essential aspects
of the dynamics. Improving the understanding of evolutionary processes leading to major
earthquakes requires volumetric frameworks that account for different processes occurring on
main faults and their surrounding regions.
1.5 Acknowledgments
The study was supported by the National Science Foundation (grants EAR‐1551411 and
EAR‐1722561). The paper benefitted from comments by Shimon Wdowinski, an anonymous
referee, and the Associate Editor. The waveform data and initial seismicity catalogs used are
publicly available via the Southern California Earthquake Data Center (2013)
(scedc.caltech.edu). The seismicity catalogs produced in this study are available in
the supporting information, with the exception of the 2016 sequence which is available in the
open‐access supporting information of Ross, Hauksson, & Ben‐Zion (2017).

33
2. Transient Brittle‐Ductile Transition Depth Induced by Moderate‐
Large Earthquakes in Southern and Baja California (Cheng &
Ben-Zion, 2019)
2.0 Abstract
We analyze space-time variations in the depth distribution of seismicity in Southern and
Baja California, focusing on transients following four M ≥ 6.7 mainshocks. The regular brittle-
ductile transition depth is estimated at different locations as the local bottom of 99,636
background events and is compared with the bottom of events within earthquake clusters. The
four M ≥ 6.7 mainshock-aftershock sequences exhibit early aftershocks with depths up to 5 km
below the regular brittle-ductile transition depth and epicentral distances up to 15 km from the
mainshock ruptures. The maximum aftershock depth increases abruptly following the
mainshocks and recovers to the background level after several years. The wide-spread deeper-
than-usual early aftershocks favor classical brittle-ductile transition over change from unstable to
stable frictional response as the mechanism governing the base of the seismogenic zone.
Episodic transient deepening of the brittle-ductile transition following major earthquakes can
have important long-term effects on the lower crust.
2.1 Introduction
The depth distribution of seismicity has significant effects on a wide range of topics
including crustal rheology and dynamics (e.g., Scholz, 2019; Sibson, 1986), maximum expected
rupture depth and event size (e.g., Hillers & Wesnousky, 2008), possible existence of deep
creeping fault patches (e.g., Cooke & Beyer, 2018; Wdowinski, 2009), and reduction of elastic
moduli and seismic velocities by earthquakes (e.g., Ben‐Zion & Zaliapin, 2019; Lyakhovsky et
34
al., 1997). The brittle upper crust sustains localized failures associated with fracturing, friction
and granulation processes (e.g., Ben‐Zion, 2008). The typical response to loading of the hotter
deeper material in the lower crust involves distributed dislocation‐based ductile deformation
(e.g., Bürgmann & Dresen, 2008). Episodic brittle failures below the regular seismogenic zone
can have significant long‐term effects on metamorphic reactions and long‐term dynamics of the
lower crust (Austrheim & Boundy, 1994; Jamtveit et al., 2018).
The brittle‐ductile transition depth depends strongly on temperature, pressure, lithology,
fluid content, and strain rate (e.g., Kohlstedt et al., 1995; Meissner & Strehlau, 1982;
Sibson, 1982; Sibson, 1984). Previous studies found that the spatial distribution of the brittle‐
ductile transition depth in southern California is primarily controlled by temperature and
lithology (e.g., Hauksson & Meier, 2019; Magistrale, 2002). Numerical simulations in a 3‐D
model with a brittle upper crust over a viscoelastic lower crust with power‐law viscosity
demonstrate that high strain rates generated by large ruptures below the regular seismogenic
zone can induce a transient deepening of the brittle‐ductile transition depth manifested by deep
early aftershocks (Ben‐Zion & Lyakhovsky, 2006). This is consistent with wide‐spread
geological observations of numerous localized ruptures in lower crust rocks (e.g., Austrheim &
Andersen, 2004; Hawemann et al., 2018; Menegon et al., 2017; Sibson, 1980).
Schaff et al. (2002) and Rolandone et al. (2004) observed transient deepening in the depth
of aftershocks following the 1984 M6.2 Morgan Hill earthquake on the Calaveras fault and the
1992 M7.3 Landers earthquake in the Eastern California Shear Zone (ECSZ). In the present
paper, we reexamine the transient deepening of seismicity following the 1992 M7.3 Landers
earthquake and three additional moderate to large events in Southern and Baja California: the
1994 M6.7 Northridge, 1999 M7.2 Hector Mine and 2010 M7.2 El Mayor‐Cucapah earthquakes
35
(Fig. 2.1). The analysis uses the high‐quality relocated catalog of Hauksson et al. (2012,
extended to later years) and the systematic clustering detection method of Zaliapin & Ben‐Zion
(2013). The clusters‐based results are more stable and robust than those associated with
individual events.

Figure 2.1 (a) Temporal variation of seismicity in southern California from the relocated catalog
(Hauksson et al., 2012). The red line denotes the estimated magnitude of completeness within a 5‐year
sliding window. (b) Map view of 1981–2017 seismicity (M ≥ 1.5; dots), four M ≥ 6.7 major earthquakes
(white stars), and major faults (thin solid line) in southern California.

36
In the section 2.2, we describe the data used in the study. In section 2.3, we discuss the
methods used for identification of seismicity clusters and background events and estimation of
the brittle‐ductile transition depth. The results, presented in section 2.4, show that the four
examined M ≥ 6.7 mainshock‐aftershock sequences have deeper‐than‐usual early aftershocks,
distributed around their mainshocks, and that the maximum event depths decrease back to the
regular seismic zone with increasing time from the mainshocks. The observations imply abrupt
deepening and gradual recovery of the brittle‐ductile transition depth around the mainshock
rupture zones. The implications of the results to crustal dynamics are discussed in section 2.5.
2.2 Data
We use the relocated southern California earthquake catalog of Hauksson et al. (2012,
extended to later years) for the period 1 January 1981 to 31 December 2017 with 615,113 events.
The magnitude of completeness of the catalog, estimated using a 5‐year moving time window
with the maximum curvature method (Woessner & Wiemer, 2005), is typically around 1.5 with
higher values around 2 during a few years (Fig. 2.1a). The performed analysis relies largely on
earthquake clusters. Zaliapin & Ben‐Zion (2013) showed that the detection and internal structure
of earthquake clusters are not very sensitive to the catalog completeness. We therefore select a
low cutoff magnitude Mc = 1.5 and consider 274,392 events with M ≥ 1.5 (Fig. 2.1b).
2.3 Method
Space‐time variations of the seismogenic zone in southern California are tracked using
depth differences between events in earthquake clusters and background events. The analysis
involves two steps that are described in the following sections 2.3.1 and 2.3.2.
37
2.3.1 Clusters and Background Events Identification
The regular base of the seismogenic zone at different locations is estimated using
background events generated by the ongoing tectonic loading without significant stress
perturbations from moderate to large events. To extract background events from the catalog, we
identify seismicity clusters using the approach of Zaliapin & Ben‐Zion (2013) outlined below
and produce a declustered catalog with background events. The distances between each pair of
events i and j in a combined space‐time‐magnitude domain are calculated using
𝜂
!"
= -
𝑡
!"
.𝑟
!"
/
#
10
$%&
!
, 𝑡
!"
> 0;
∞, 𝑡
!"
≤ 0,
(1)
where 𝑡
!"
= 𝑡
"
−𝑡
!
is the interevent time, 𝑟
!"
is the interevent distance, 𝑑 is the fractal
dimension of hypocenters, 𝑏 is the parameter of Gutenberg‐Richter distribution, and 𝑚
!
is the
magnitude of event 𝑖. The nearest neighbor of event 𝑗 is the earlier event 𝑖 with the smallest
𝜂
!"
. The distance 𝜂
!"
can be represented using rescaled space and time components
𝑇
!"
= 𝑡
!"
10
$'%&
!
, (2)
𝑅
!"
= 𝑟
!"
#
10
$()$')%&
!
,0 < 𝑞 < 1 (3)
As in Zaliapin & Ben‐Zion (2013), the distances 𝜂
!"
are computed using 𝑏 = 1, 𝑑 = 1.6,
and 𝑞 = 0.5. The results exhibit a clear bimodal distribution (Figs. 2.2a and 2.2b); the larger
mode associated with shorter distance η corresponds to clustered events and the smaller mode
involving larger distance η corresponds to background events. The two modes are separated by
fitting a Gaussian mixture model and choosing the midpoint between the two modes as the
threshold for clustering (Zaliapin & Ben‐Zion, 2016). The obtained threshold value is 𝜂
+, -./
=
10
$8.09
. Each event 𝑗 is linked to its nearest neighbor 𝑖 (parent) if 𝜂
!"
is smaller than the
threshold 𝜂
+, -./
and is otherwise unlinked. This procedure produces 99,636 clusters, including
38
clusters having a single event (cluster size 1 in Fig. 2.2c). The largest event in each cluster is
referred to as a mainshock, and the set of mainshocks comprises the background events. For
further analysis we use 155 clusters with cluster size ≥50 and mainshock magnitude larger than
3.5 (red circles in Fig. 2.2c). The space‐time distributions of the events in these clusters are
shown in Fig. 2.2d.

Figure 2.2 (a) Distribution of nearest-neighbor statistics in southern California (1981–2017) using events
with magnitude M ≥ 1.5. (b) Histogram of nearest-neighbor distance η of all events. The bimodal
distribution is clearly seen in (a) and (b). The line log10(η) = −4.59 separating the two modes is shown in
white and red in (a) and (b), respectively. (c) Scatterplot of cluster size versus mainshock magnitude.
Clusters within red box are selected for further analysis. (d) Epicenters of events within selected clusters
as a function of time and latitude. Events in the same cluster share the same color.

39
2.3.2 Depth Estimations of Groups of Events
The 95th percentile of event depths, D95, is widely used to estimate the bottom of the
seismogenic zone (e.g., Rolandone et al., 2004). To image the spatial variation of D95 in
southern California, we estimate the local D95 for each event in the selected clusters. For the
D95 estimation, we only use events with both absolute depth error and relative depth error
smaller than 2 km (well‐located events). In total, about 68% of M ≥ 1.5 events in the relocated
catalog satisfy these criteria. For each event in selected clusters (target event), we use its
surrounding well‐located background events within 5‐km epicentral distance to estimate the local
background D95 (D95b). We also calculate the local cluster D95 (D95c) using well‐located
events in the same cluster as the target event and within 5‐km epicentral distance from the target
event. We require at least 30 events for D95 estimation. Fig. A2.1 in the Section A2 shows all
events in the selected clusters colored by the number of surrounding well‐located events
available for D95b and D95c estimations. If the event does not have enough nearby well‐located
events for D95b and D95c estimations (blue dots in Fig. A2.1), it is not used in the following
analysis. Fig. 2.3 shows the events in the selected clusters having both D95c and D95b estimated.
The events are colored by their occurrence time (Figs. 2.3a and 2.3c), the estimated
D95b (Fig. 2.3b), and the depth difference between D95c and D95b (Fig. 2.3d). We tried multiple
sets of cutoff epicentral distance and event number (Figs. A2.3 and A2.4). The main results are
generally not sensitive to these parameters.

40

Figure 2.3 Map view of all well‐located events within the selected clusters (dots in Fig. 2.2d) colored by
(a) event occurrence time, (b) D95b, and (d) depth differences between D95c and D95b. Events with
depth 3 km below D95b are extracted and shown in (c). Four M ≥ 6.7 mainshock‐aftershocks sequences
show significantly deeper D95c than D95b with more than 15 events that are at least 3 km deeper than
D95b. Embedded plots in (c) show the histograms of epicentral distances from deep events to their
mainshock ruptures planes obtained from finite fault models (Wald & Heaton, 1994; Wald et al., 1996; Ji
et al., 2002; and Wei et al., 2011; white lines). The source models of the Joshua Tree M6.1 foreshock and
the Big Bear M6.5 aftershock to 1992 Landers mainshock are also shown in white lines.

2.4 Results
2.4.1 Variations of the Brittle-Ductile Transition Depth
To find clusters with possible transient deepening of the seismogenic zone, we examine
all events in the analyzed clusters that are 3km deeper than their local D95b (Fig. 2.3b). Four
41
prominent M ≥ 6.7 mainshock‐aftershock sequences have more than 15 well‐located events
considerably below D95b (Figs. 2.3c and A2.2 and Table 2.1). Although the M ≥ 6.7 earthquakes
trigger many aftershocks that are widely distributed in space (Fig. 2.3a), most deep events are
located relatively close to their mainshock ruptures (Figs. 2.3c and A2.2). We calculate the
epicentral distances from deep aftershocks to their mainshock rupture planes, extracted from the
finite source models (Ji et al., 2002; Wald et al., 1996; Wald & Heaton, 1994; Wei et al., 2011)
and marked by white lines in Fig. 2.3c. Many deep aftershocks are located within about 5 km
from their mainshock rupture planes, and some deep aftershocks of the M7.3 Landers and M7.2
El Mayor events are located more than 10 km from their mainshock ruptures (histograms in
Fig. 2.3c).
Table 2.1. Event Numbers of Four M ≥ 6.7 Mainshock‐Aftershock Sequences and the Other Clusters
Within Different Depth Ranges
Mainshock No. of events in
cluster with depth >
D95b + 1km

No. of events in
cluster with depth >
D95b + 2km

No. of events in
cluster with depth >
D95b + 3km

1992 M7.3 560 239 28
1994 M6.7 139 44 17
1999 M7.1 151 54 22
2010 M7.2 124 76 54
The other clusters <120 <40 <15

To check how significant the deepening of the brittle‐ductile transition depth is, we
compare the difference between the estimated D95b and D95c. Most locations have deeper
D95b than D95c (blue dots in Fig. 2.3d), indicating that most events in the clusters are above the
regular base of the seismogenic zone. Most events with significantly deeper D95c than D95b (red
dots in Fig. 2.3d) are located within 20‐km epicentral distance from the four M ≥ 6.7 mainshocks
(green stars in Fig. 2.3d). Comparing the lateral spatial distributions of all events in the clusters
(Fig. 2.3a), events located 3‐km deeper than the local D95b (Fig. 2.3c), and events with deeper
42
local D95c than local D95b (Fig. 2.3d), the four M ≥ 6.7 mainshock‐aftershock sequences show
significant transient deepening of the brittle‐ductile transition depth, with many deep aftershocks
and significantly deeper D95c. Moreover, the smaller the epicentral distance to the mainshocks is,
the more significant the transient deepening is (Figs. 2.3 and A2.5).
2.4.2 Temporal Evolution of the Brittle-Ductile Transition Depth
In addition to spatial correlation with M ≥ 6.7 mainshocks, the depth distributions of
events in M ≥ 6.7 mainshock‐aftershock sequences have systematic temporal variations
(Fig. 2.4). We extract all well‐located events in each selected box (black boxes in Figs. 2.3a
and 2.3d) and find that the maximum event depth increases abruptly after the M ≥ 6.7
mainshocks and then decreases gradually with time (Figs. 2.4a, 2.4c, 2.4e, and 2.4g). The
maximum depth of the aftershocks extends more than 5 km below the estimated D95b and is
restored to the background level and becomes stable several years after the mainshocks
(Fig. 2.4). Following the method discussed in section 2.3.2, we estimate D95b of all events in
four selected boxes (black boxes in Figs. 2.3a and 2.3b). The cumulative density functions of
events within different depth ranges are shown in Figs. 2.4b, 2.4d, 2.4f, and 2.4h with time in
logarithm scale. Compared with events above D95b (Blue lines in Figs. 2.4b, 2.4d, 2.4f,
and 2.4h), most events with depths below D95b occur at the early stage of the mainshock‐
aftershock sequences. The duration of seismicity deepening is roughly estimated by manually
picking the time when the slope of cumulative density function of events deeper than
D95b changes significantly (dashed black lines in Figs. 4b, 4d, 4f, and 4h). The abrupt deepening
and gradual recovery of the maximum seismicity depth following the four mainshocks, as well as
the spatial concentration of deep seismicity, imply clear perturbations to the brittle‐ductile
transition depth by the four M ≥ 6.7 events.
43

Figure 2.4 Depth‐time plots of well‐located events within (a) box A, (c) box B, (e) box C, and (g) box D
in Figure 2.3. Events belonging to 1992 M7.3, 1994 M6.7, 1999 M7.1, and 2010 M7.2 mainshock‐
aftershock sequences and within corresponding boxes are denoted as red dots in (a), (c), (e), and (g). The
CDFs (cumulative density function) of occurrence time of the events in (a), (c), (e), and (g) with different
depth ranges are shown in (b), (d), (f), and (h), respectively. The deepest event in each cluster is more
than 5 km deeper than D95b.

2.5 Discussion and Conclusions
We examine transient changes in the depth of seismicity in southern California following
the occurrence of four M ≥ 6.7 earthquakes using clusters of M ≥ 1.5 events with relatively high
signal‐to‐noise ratio that are recorded by many stations. The events used for the D95 estimates
44
have both relative and absolute depth errors smaller than 2 km. The vertical location errors of
these events should be less than those associated with the whole catalog, which is less than
1.5 km for >90% of the events (Hauksson et al., 2012). The transient deepening of seismicity is
estimated conservatively using clusters of such high‐quality data. The cluster‐based estimation
provides more robust results than those associated with individual events, although transient
deepening associated with individual events may be more pronounced. Moreover, our estimated
D95b may be somewhat deeper than the regular base of the seismogenic zone since the D95b is
estimated using all background events in the catalog from 1981 to 2017, which might include
some lower crust earthquakes. Under such conservative estimation, many events following
the M ≥ 6.7 mainshocks exhibit focal depth (Figs. 2.3c and A2.2) deeper by about 5 km than the
local D95b and/or local D95c (Fig. 2.3d) deeper by about 2 km than the local D95b. Many of the
transient deep events belong to aftershock sequences and are close to their mainshocks in both
space (Fig. 2.3) and time (Fig. 2.4). These space‐time associations imply that they are causally
related to the mainshock ruptures rather than associated with location errors and/or analysis
artifacts.
There are two general mechanical explanations for the base of the seismogenic zone: a
transition at some depth from localized brittle failure to distributed ductile deformation (e.g.,
Kohlstedt et al., 1995) and a transition from unstable rate‐state friction to stable sliding (e.g.,
Blanpied et al., 1991). The rapid fault displacements of major earthquakes increase the strain
rates around and below the bottom of the rupture zone by many orders of magnitude (Ben‐Zion
et al., 1993; Bouchon et al., 1998; Ellis & Stöckhert, 2004). The elevated post mainshock strain
rates below the regular seismogenic zone can produce a transition in that region from ductile
45
behavior under typical low tectonic strain rate to brittle response and deep early aftershocks
(Ben‐Zion & Lyakhovsky, 2006).
The effect of elevated strain rates on the stability of rate‐state friction is less clear. Some
laboratory experiments found that increasing loading rate produces increasing stability (e.g.,
Baumberger et al., 1994; Beeler et al., 2001; Wong & Zhao, 1990), while others reported more
unstable response (Kato et al., 1992, McLaskey & Yamashita, 2017; Xu et al., 2018b). In
addition, a dynamic deepening of the unstable regime of rate‐state friction might be expected to
produce deeper seismicity in narrow localized zones (e.g., Hillers et al., 2006; Jiang &
Lapusta, 2017), whereas the observed deeper transient events occupy volumes around the
mainshock ruptures (white lines in Fig. 2.3c) extending up to 15 km from the mainshocks
(histograms in Fig. 2.3c). The transient deepening of seismicity and, hence, the mechanism
governing the base of the seismogenic zone appear to be more consistent with the classical
brittle‐ductile transition framework. However, both frameworks likely apply to some extent, with
rate‐state friction being one of the micromechanisms that govern locally the behavior at depth.
The widely distributed deep transient aftershocks might also reflect complex rupture geometries
in the brittle crust, which may produce high strain rate over relatively wide area in the lower
crust.
The gradual shallowing of the deepest aftershocks is consistent with the decay of
aftershocks in the upper crust (Fig. 2.4). The timescale of the shallowing process is comparable
with that of postseismic relaxation observed in geodetic data (e.g., Freed & Burgmann, 2004;
Nishimura & Thatcher, 2003). The relaxation timescale depends mainly on the mainshock
magnitude and various properties (e.g., thermal gradient, fluid content, and grain size) that
govern the effective viscosity of the rocks (Ben‐Zion & Lyakhovsky, 2006; Rolandone et
46
al., 2004). The duration of observed transient deepening of seismicity can thus provide useful
information on the effective viscosity of the deforming region. For example, the shorter duration
of the observed seismicity deepening after the 2010 M7.2 mainshock in Baja California
compared to that associated with the 1992 and 1999 M > 7 mainshocks in the ECSZ may be
attributed to lower effective viscosity. This is consistent with the general increase of heat flow
(Blackwell & Richards, 2004) as well as the estimated low viscosity (Dickinson‐Lovell et
al., 2017) to the south of the ECSZ. The shorter duration of the observed seismicity deepening
after the 1994 M6.7 mainshock compared to the other sequences has a simple explanation in
terms of lower mainshock magnitude.
The widely distributed deep aftershocks (Fig. 2.3c) indicate that large earthquakes may
produce a considerable damage volume in the surrounding crust also below the nominal
seismogenic zone. The observed transient deepening produced by the examined M ≤ 7.3
mainshocks is limited to about 5 km, but larger mainshocks that are bound to occur over longer
timescale than that covered by the used catalog can produce more wide‐spread and deeper early
aftershocks. The extent of deep early aftershocks can also be more pronounced, as mentioned, in
regions that have lower effective viscosity (Ben‐Zion & Lyakhovsky, 2006). This may be
relevant, for example, to observations in the India‐Tibet collision zone of aftershocks that
penetrate several tens of kilometer below the Moho depth (Copley et al., 2011; Monsalve et
al., 2006). The cumulative occurrence of deep early aftershocks can generate large volumes of
fractures in the lower crust, which create abundant pathways for fluid migration that facilitate
metamorphic reactions, leading to significant long‐term effects on the properties and dynamics
of the lower crust (Jamtveit et al., 2018).
47
2.6 Acknowledgements
We thank Ilia Zaliapin and John Vidale for their useful discussions. The Hauksson et al.
(2012, extended to later years) catalog used in the paper is available
at http://scedc.caltech.edu/research‐tools/downloads.html. The declustered version of the catalog
employed in the analysis is given in the supporting information. The manuscript benefitted from
constructive comments by Shiqing Xu, Roland Bürgmann, two anonymous referees, and Editor
Gavin Hayes. The research was supported by the National Science Foundation (grant and EAR‐
1722561) and the Southern California Earthquake Center (based on NSF Cooperative Agreement
EAR‐1600087 and USGS Cooperative Agreement G17AC00047).

48
3. Variations of Earthquake Properties Before, During, and After
the 2019 M7.1 Ridgecrest, CA, Earthquake (Cheng & Ben-Zion,
2020)
3.0 Abstract
We attempt to clarify processes associated with the 2019 Ridgecrest earthquake sequence
by analyzing space‐time variations of seismicity, potency values, and focal mechanisms of
earthquakes leading to and during the sequence. Over the 20 years before the M
w
7.1 mainshock,
the percentage of normal faulting events decreased gradually from 25% to below 10%, indicating
a long‐term increase of shear stress. The M
w
6.4 and M
w
7.1 ruptures terminated at areas with
strong changes of seismic velocity or intersections with other faults producing arresting barriers.
The aftershocks are characterized by highly diverse focal mechanisms and produced volumetric
brittle deformation concentrated in a 5–10 km wide zone around the main ruptures. Early
aftershocks of the M
w
7.1 event extended over a wide area below typical seismogenic depth,
consistent with a transient deepening of the brittle‐ductile transition. The Ridgecrest earthquake
sequence produced considerable rock damage in the surrounding crust including below the
nominal seismogenic zone.
3.1 Introduction
The 2019 Ridgecrest earthquake sequence included the largest earthquake in Southern
California since 1999 and activated a complex fault network with numerous previously
unmapped faults (DuRoss et al., 2020) in the Eastern California Shear Zone (Fig. 3.1). Located
near the southern end of the Walker Lane Shear Zone, the sequence started with the 4 July M
w
6.4
Searles Valley event (plus foreshocks) that ruptured two ortho- gonal faults—a SE‐NW oriented
49
right‐lateral fault and a SW‐NE orientated left‐lateral fault (Barnhart et al., 2019; Liu et al.,
2019). About 34 hr later, the M
w
7.1 Ridgecrest earthquake reruptured the right‐lateral fault and
significantly extended it toward the Garlock Fault (GF) in the south and the Cotton Wood Fault
(CWF) to the north (Chen et al., 2020; Fielding et al., 2020; Ross et al., 2019b). The M
w
6.4 and
M
w
7.1 earth- quakes were followed in the next 50 days by over 24,000 M
L
> 0.5 aftershocks,
occurring mostly in the top 10 km of a broad crustal region (Hauksson & Jones, 2020).

Figure 3.1. (a) Depth-time plots of earthquakes from 1981 to 2019 and (b) from 5 days before to 50 days
after the 2019 Mw7.1 Ridgecrest earthquake. (c) A map view of events from 1981 to the 2019 Mw6.4
earthquake (black dots), between the Mw6.4 and Mw7.1 events (green dots) and within 50 days after
the Mw7.1 mainshock (red dots: depth >14 km, blue dots: depth <14 km). Red curves denote the D95 of
500 events with a 99% overlapping moving time window.

50

The complex ruptures of the Searles Valley and Ridgecrest events, abundant aftershocks
with orthogonal lines of seismicity extending to the bottom of the seismogenic zone (Lomax,
2020; Ross et al., 2019b; Shelly, 2020) and other observations demonstrated again (along with
many other examples) the complex volumetric nature of crustal earthquakes (e.g., Ben‐Zion,
2008; Cheng et al., 2018, and references therein). In the present paper we attempt to clarify
processes associated with the Ridgecrest sequence using the rich seismic data set recorded in the
region. In particular, we examine the effective width of the zone sustaining brittle deformation
during the Ridgecrest sequence, processes associated with the preparation, initiation, and arrest
of the M
w
6.4 and M
w
7.1 earthquakes, and interaction of the M
w
7.1 rupture with the substrate
below the nominal seismogenic zone. The study employs catalogs of earthquakes and focal
mechanisms and compares the derived results with seismic velocity model for the area and slip
distributions for the M
w
6.4 and M
w
7.1 earthquakes.
In the next section, we briefly describe the data used in the study. Section 3.3 presents the
results associated with spatiotemporal distribution of the seismicity, scalar seismic potencies of
the events, and focal mechan- isms. The observations show deep early aftershocks in a wide off‐
fault region consistent with transient deepening of the brittle‐ductile transition depth, highly
heterogeneous aftershock focal mechanisms, and appreci- able potency release by aftershocks in
a 5–10 km wide zone. The results also suggest a gradual increase of shear stress in the region
over 20 years before the Ridgecrest sequence, and correlations of the M
w
6.4 and M
w
7.1
terminations with fault junctions and contrasts of seismic veloci- ties. The implications of these
results are discussed in Section 3.4.
51
3.2 Data
The research employs several data sets. We use the relocated Southern California
earthquake catalog (Hauksson et al., 2012, extended to later years) from 1981 to 50 days after the
M
w
7.1 Ridgecrest earthquake, with 68,658 events in the area of Fig. 3.1 around the Ridgecrest
sequence. Focal mechanisms of 17,646 events with Qualities A–C (Section A3) are derived with
deep learning algorithms (Cheng et al., 2019; Section A3.1) and are used to characterize the
earthquake source properties in the area. We also analyze the association among the slip
distributions of the M
w
6.4 and M
w
7.1 earthquakes obtained by Liu et al. (2019), the derived
source characteristics of other events in the Ridgecrest sequence, and 3‐D velocity model in the
area (Zhang & Lin, 2014).
3.3 Results
3.3.1 Transient Deepening of Seismicity
Several previous studies observed transient deepening of aftershocks following major
earthquakes (Rolandone et al., 2004; Schaff et al., 2002). Cheng & Ben‐Zion (2019) examined
this phenomenon follow- ing four M
w
≥ 6.7 mainshocks from 1981 to 2018 in Southern and Baja
California. All examined mainshocks had early aftershocks with depths up to 5 km below the
regular seismic depth and epicentral distances up to 15 km from the mainshock ruptures. The
results likely reflect transient deepening of the brittle‐ductile tran- sition induced by high strain
rates generated by large ruptures below the regular seismogenic zone (e.g., Ben‐ Zion &
Lyakhovsky, 2006). The 2019 Ridgecrest sequence, with a large number of previous seismicity
and aftershocks, provides a valuable opportunity to further investigate seismicity deepening in
relation to major earthquakes.
52
Examination of seismicity depths shows that almost all hypocenters from 2005 to the
2019 M
w
7.1 earthquake were above 14 km (black and green dots in Fig. 3.1) After the M
w
7.1
mainshock, many events had depth below 14 km (red dots in Fig. 3.1). The 95th percentile depth
(D95) of 500 events with 99% overlapping moving time window increases from under 10.5 km
before the M
w
7.1 event to over 11.5 km after (red curve in Fig. 3.1). The D95 and maximum
aftershock depth decrease gradually with time (Figs. 3.1a and 3.1b). Rather than being localized
below the rupture zone, the deep aftershocks are widely distributed around the Ridgecrest rupture
area, as for other large earthquakes examined by Cheng & Ben‐Zion (2019). The data analyses in
the first few days after the M
w
6.4 event may suffer from artifacts related to the high seismicity
rate. However, the deeper‐than‐usual events persist tens of days after the Ridgecrest mainshock
and are in clear contrast with the seismicity depth over the previous few years obtained with
essentially the same seismic network.
3.3.2. Variations of Potency Distribution
To compare source properties of events in the Ridgecrest sequence with the large
earthquakes, we first quantify their sizes using the scalar seismic potency associated with the
integral of slip over the failure area (e.g., Ben‐Zion, 2008). The spatial distribution of potency
densities of the M
w
6.4 and M
w
7.1 events are cal- culated based on the slip models of Liu et al.
(2019). The potency values of all other events, from the M
w
6.4 earthquake to 50 days after the
M
w
7.1 mainshock, with epicentral distances less than 10 km from line AA' (Fig. 3.2e), are
calculated using the quadratic potency‐magnitude scaling relations of Ben‐Zion & Zhu (2002).
Figs. 3.2a and 3.2c show the spatial distribution of potency densities of the M
w
6.4 and M
w
7.1
events, respectively, projected on the vertical plane AA′. Figs. 3.2b and 3.2d display
53
corresponding projec- tions of the potency values of the events between the M
w
6.4 and M
w
7.1
earthquakes and the events within 0–50 days after the M
w
7.1 mainshock, respectively.

Figure 3.2. Potency distributions of events in the Ridgecrest sequence. (a) Potency of the Mw6.4 event
along AA′. (b) Potencies of events between the Mw6.4 and Mw7.1 earthquakes along AA′. (c) Potency of
the Mw7.1 mainshock along AA′. (d) Potencies of aftershocks within 50 days after the Mw7.1 event along
AA′. The vertical solid lines and white stars in (a)–(d) denote the projection of the boundaries and
hypocenters of the Mw7.1 (gray) and Mw6.4 (black) slips along AA′, respectively. (e) A map view of events
that occurred between the Mw6.4 to Mw7.1 events (green dots) and within 50 days after the Mw7.1
mainshock (red dots: depth >14 km, blue dots: depth <14 km). Potency amplitude histograms of ML0–5
events along the fault normal direction within boxes BB′ (f), CC′ (g), DD′ (h), EE′ (i), and FF′ ( j). Yellow
stars denote the potency values of ML5–6 events.

The M
w
6.4 event had orthogonal ruptures (Fig. 3.1c) with potency projection along AA′
between 25–40 km (Fig. 3.2a). Most potency of the events between the M
w
6.4 and M
w
7.1
earthquakes is distributed NW of the M
w
6.4 earthquake. This bridges the slip gap between the
M
w
6.4 slip and the M
w
7.1 hypocenter, with some scattered extension of potency further to the
NW (Fig. 3.2b). The potency of the M
w
7.1 mainshock includes large patches along AA′ to the
NW of its epicenter and around the M
w
6.4 epicenter (Fig. 3.2c). Published slip models of the
54
M
w
7.1 event exhibit large variability but agree that the potency is concentrated NW to the M
w
6.4
epicenter between 10 and 35 km along AA′ (Wang et al., 2020). The potency of events following
the mainshock covers most of the rupture area with a concentration to the NW around 0–10 km
along AA′ (Fig 3.2d). The results in Figs. 3.2a–3.2d show that the center of the seismic potency
distribution of the entire sequence moved with time from the southeast to the northwest.
To further investigate the relationship of aftershocks to the main faults, we separate the
box AA′ in Fig. 3.2e into five subregions based on the seismicity and mapped fault traces. In
each subregion, we obtain the dis- tribution of potency values along the direction normal to line
AA′ (Figs. 3.2f–3.2j). The potency values in all subregions are widely distributed within about 5
km from AA′, and there is no clear decay with distance from the main rupture. Moreover, the
aftershock potency distribution is asymmetric with respect to the main faults, with most potency
located NE of the mainshock rupture in box BB′ (Fig. 3.2f) and SW of it in boxes DD′, EE′, and
FF′ (Figs. 3.2h–3.2j).
3.3.3 Spatiotemporal Variations of Focal Mechanisms
Focal mechanisms contain valuable information about fault geometry and stress state in
the crust. Faulting styles can be classified as normal, reverse, or strike‐slip based on rake angles:
normal faulting is between −45° and −135°, reverse is from 45° to 135°, and others are strike‐slip
(Yang et al., 2012). We quantify properties of a set of focal mechanisms with the percentages of
different faulting styles and the degree of their heterogeneity. The latter is estimated as in Bailey
et al. (2010). To focus on the source geometry instead of size, we use a normalized potency
tensor 𝑃
N
!"
with O𝑃
N
!"
𝑃
N
!"
= 1, which gives the orientation of the coseismic strain drop of the
double couple seismic source. For a population of N normalized tensors, we calculate their
summed source mechanism tensor:
55
𝐸
!"
= ∑ 𝑃
N
!"
(:)
;
:
. (1)
If 𝑃
N
!"
(:)
is the same for all events, the summed source mechanism tensor is 𝐸
!"
= (
;
√7
)𝑃
N
!"
and its
Euclidean norm is
I
𝐸
!"
𝐸
!"
= 𝑁. If the normalized potency tensors are highly different and
cancel each other, the norm of 𝐸
!"
approaches zero. Therefore, we quantify the degree of
heterogeneity for a population of N mechanisms using:
𝑟
;=>6
= 1−
?
@
!#
@
!#
;
, (2)
where 0 ≤ 𝑟
;=>6
≤ 1 (Bailey et al., 2010).
To estimate the temporal variations of these source properties in the study area (Fig.
3.1c), we use Quality A–C focal mechanisms from 1981 to 2019 and sort them chronologically
(Figs. 3.3a–3.3c). We calculate the percentages of different faulting styles and r
NORM
of 300 focal
mechanisms with a moving window having 299 overlapping events and assign the values to the
time of the last event in the group (Figs. 3.3d–3.3i). The percentage of reverse faulting events
stays below 10% for the whole period, while the percentage of normal faulting events decreases
gradually from over 20% before 2000 to below 10% after 2013 (Fig. 3.3d). The percentages of
strike‐slip events stay around 90% for the 2019 Ridgecrest sequence (Figs. 3.3d–3.3f). The r
NORM
increases dramatically from less than 0.5 before the M7.1 earthquake (Fig. 3.3g) to over 0.5
afterward (Fig. 3.3h) and stays above 0.5 for over 50 days (Fig. 3.3i).
56

Figure 3.3. Distributions of epicenters of earthquakes with Quality A–C focal mechanisms (a) from 1981
to 2019, (b) from 5 days before to 5 days after the Mw7.1 event, and (c) from 5 days to 50 days after the
mainshock as a function of time and distance along the AA′ in Fig. 3.2e. Corresponding temporal
variations of the percentages of normal faulting, reverse faulting, and strike-slip focal mechanisms (d),
(e), and (f), respectively. Corresponding temporal variations of rNORM (g), (h), and (i), respectively.

The spatial variations of focal mechanisms are analyzed further in four separate time
periods: from 1995 to 2010, from 2010 to the M
w
6.4 event, between the M
w
6.4 and M
w
7.1
earthquakes, and within 0–50 days after- the M
w
7.1 mainshock. For each focal mechanism, we
obtain its faulting style and maximum pressure axis (P axis). Figs. 3.4a–3.4d show, respectively,
the P axes of focal mechanisms in the four time periods colored by P axis azimuth on the
background of P wave velocity at 6 km depth (Zhang & Lin, 2014). Corresponding map views of
the P axes colored by faulting style are shown in Fig. 3.5. Most events before the M
w
6.4 earth-
quake are located NW of the M
w
7.1 epicenter and have mainly N‐S and NE‐SW oriented P axes.
57
After 2010, most events remain located in the same region, with similar horizontal P axis
orientations (Figs. 3.4a and 3.4b), but there is a considerable reduction of normal faulting events
(Figs. 3.3 and 3.5). Events between the M
w
6.4 and M
w
7.1 earthquakes are located SE to the
M
w
7.1 epicenter in low P wave velocity zone. Most of these events are strike‐slip (Fig. 3.5c) with
NNW‐SSE oriented P axes (Fig. 3.4c).

Figure 3.4. Map views of P wave velocity at 6 km depth (Zhang & Lin, 2014) and P axis distributions of
source mechanisms of events that occurred (a) from 1995 to 2010, (b) from 2010 to the 2019 Mw6.4
event, (c) between the Mw6.4 and Mw7.1 events, and (d) within 0–50 days after the Mw7.1 event.
The P axes are centered at the events' hypocenters and colored by their azimuths. Cyan solid lines in (c)
represent the fault geometry for the Mw6.4 slip model (Liu et al., 2019).

58

Figure 3.5. Same as Fig. 3.4, but P axes are colored by their faulting types.

The aftershocks of the M
w
7.1 mainshock are distributed in a wide area with significant
spatial variations of focal mechanisms. Most aftershocks near the northwestern end of the rupture
are strike‐slip with P axes orientations showing a clear clockwise rotation from N‐S in the west
to NE‐SW in the east. This is consistent with the observed horsetail fractures (Ross et al., 2019b;
Wang & Zhan, 2020b) and the orientation of nearby CWF. The events located 0–10 km NW to
59
the M
w
7.1 hypocenter, in high P wave velocity zone, exhibit a higher degree of focal mechanism
heterogeneity (Fig. 3.4d) with more diverse fault orientations than the other regions (Fig. 3.5d).
The events between the M
w
7.1 and M
w
6.4 epicenters have similar focal mechanism patterns
before (Figs. 3.4c and 3.5c) and after (Figs. 3.4d and 3.5d) the M
w
7.1 mainshock. In the area SW
to the M
w
6.4 epicenter, a large portion of events are strike‐slip with N‐S oriented P axes (Fig.
3.4d), whereas other events have diverse P axis orientations (Fig. 3.5d). The southeastern end of
the aftershock zone near the GF has many strike‐slip events with NE‐SW oriented P axes.
3.4 Discussion and Conclusions
The Ridgecrest earthquake sequence occurred along a previously not well‐recognized
fault zone and had high geometrical complexity with multiscale near‐orthogonal and subparallel
ruptures and lines of seismicity (Lomax, 2020; Ross et al., 2019b; Shelly, 2020). We attempt to
quantify the geometrical complexity with basic measures of earthquake properties and clarify
several important issues. These include the preparation process that allowed the M
w
6.4 and M
w
7.1
ruptures to propagate along such a disordered fault zone, the barrier that separates the NW end of
the M6.4 event and epicenter of the 7.1 earthquake 34 hr later, and inter- actions of the
Ridgecrest sequence with the surrounding volume.
The long‐term decreasing percentage of normal faulting events before the M
w
7.1
earthquake implies changes of stress orientations or activation of faults with different
orientations. To eliminate the latter, we select the nearby Coso area with highly fractured rocks
and diverse focal mechanisms (Fig. A3.1) and apply the same temporal focal mechanism
analysis as in section 3.3.3 (Fig. A3.2). The results show a similar long‐ term decreasing
percentage of normal faulting events with time (Figs. 3.3 and A3.2d). These observations suggest
that the faulting style changes are primarily controlled by regional stress field variations. Since
60
the P axis azimuths did not vary much before and after 2010 (Figs. 3.4a and 3.4b), the decreasing
percentage of normal faulting events are not caused by changes of horizontal stress orientation
but likely reflect an increase of horizontal stress.
Sheng & Meng (2020) found that the maximum compressive stress axis had little
variations of azimuth but changed from varying plunges with large uncertainties before the
M
w
6.4 to near‐horizontal afterward. Inversions of focal mechanisms to spatiotemporal variations
of stress field using separately background events and aftershocks can provide additional useful
information (e.g., Abolfathian et al., 2020; Martínez‐ Garzón et al., 2016). Such analysis is
deferred to future work. The preparation process leading to the Ridgecrest sequence may also
have been manifested by earthquake‐induced rock damage around the even- tual rupture zone in
the past decades, and localization of seismicity in the area 2–3 years before the 2019 Ridgecrest
mainshock (Ben‐Zion & Zaliapin, 2020). The gradual increase of horizontal shear stress and gen-
eration of rock damage probably co‐evolved and produced together conditions that allow failure
to cascade over the large‐scale associated with Ridgecrest mainshock.
Both the M
w
7.1 and M
w
6.4 earthquakes terminated at regions with abrupt changes of
seismic velocities and fault geometries. The northwestern end of the M
w
6.4 rupture terminated
(near the M
w
7.1 hypocenter) at an area with high seismic velocity (Figs. 3.4c and 3.5c). The focal
mechanism pattern also changes abruptly across this boundary from dominant NNW‐SSE P axis
and strike‐slip faulting to the SE to highly heteroge- neous fault orientations to the NW. The
strong changes of velocity and focal mechanisms at depth suggest a barrier (Aki, 1979), which
terminated the M
w
6.4 earthquake with large stress concentration at the end region. Many
immediate aftershocks of the M
w
6.4 event in the stress concentration area produced distributed
potency (Fig. 3.2) that bridged the gap between the M
w
6.4 slip and M
w
7.1 hypocenter 34 hr later
61
(Huang et al., 2019; Ross et al., 2019b). The M
w
7.1 hypocenter had shallow depth (Lomax, 2020)
in an area with strong velocity change and a few foreshocks (Figs. 3.2, A3.3, and A3.4). The
M
w
7.1 slip terminated near intersections with the GF to the SE and the CWF to the NW (Fig.
3.4d) with abrupt changes of focal mechanism P axis azimuths coinciding with the orientations
of the nearby intersected faults. Overall, the seismic potency release during the 2019 Ridgecrest
sequence moved from the southeast to the northwest (Figs. 3.2f–3.2j) with
multiple stops correlated with strong velocity changes and fault junctions acting as barriers (Aki,
1979).
Following the M
w
7.1 rupture, the aftershocks were widely distributed producing
volumetric potency release in a damaged structure with strong geometrical complexities (Figs.
3.1, 3.2, and 3.4). The surface fractures included horsetail fractures in the NW aftershock zone
and subparallel faults in the SE aftershock zone (Xu et al., 2020). The aftershock focal
mechanisms exhibit abrupt changes of P axis azimuths at the north- western and southeastern
ends near the intersections with the GF and CWF. The aftershocks delineate multiscale
orthogonal faults and other volumetric patterns in a zone that is 5–10 km wide. The high‐angle
faults and fractures at the ends of and within the main ruptures may have been generated by
several mechanisms including reactivation of preexisting faults, high‐angle branching produced
by abrupt rupture deceleration when encountering strong barriers (Xu & Ben‐Zion, 2013), and
reduction of normal stress on high‐angle faults by slip on the main rupture (Hudnut et al., 1989).
The horsetail fractures in the NW aftershock zone might form when slip decrease gradually
toward the fault tip (Kim et al., 2004).
The low‐average rupture velocities and radiated energy of the M
w
6.4 and M
w
7.1
earthquakes (Liu et al., 2019), highly complex aftershock properties in the 5–10 km wide zone,
62
and segmented surface fractures are all indi- cative of failure processes associated with
volumetric damage zone rather than highly localized one or a few fault surfaces (Klinger et al.,
2018). Similarly, the deeper‐than‐usual early aftershocks following the M
w
7.1 earthquake are
also widely distributed across the aftershock zone. The pattern of deep early aftershocks is
consistent with a transient deepening of the brittle‐ductile transition due to the coseismic high
strain rate in the nominal ductile substrate, rather than a transition from stable to unstable
frictional behavior on a deep localized fault surface (Ben‐Zion & Lyakhovsky, 2006; Cheng &
Ben‐Zion, 2019).
Strong heterogeneities of velocity structure and fault geometry may act as barriers that
arrest earthquake ruptures (e.g., Aki, 1979; Hubbard et al., 2016; King, 1986; Wesnousky, 2006).
On the other hand, ongoing seismicity can generate elevated rock damage around such barriers
and create conditions that allow large ruptures to propagate through barriers (Ben‐Zion &
Zaliapin, 2019, 2020). The connections between evol- ving regional stress field and fault zone
damage with possible occurrence of major earthquakes motivate monitoring the evolving
localization of shear strain and stress, rock damage, and seismicity using geodetic data and
catalogs of earthquakes and focal mechanisms (Ben‐Zion & Zaliapin, 2020; Zeng et al., 2018).
Additional useful properties to monitor include evolving percentage of events with different
faulting styles (Figs. 3.3 and A3.2), changes of b values of seismicity (e.g., Nanjo, 2020; Wyss et
al., 2004) and changes of seis- mic velocities at depth (e.g., Baccheschi et al., 2020; Brenguier et
al., 2019; Niu et al., 2008).
3.5 Data Availability Statement
The employed earthquake catalog of Hauksson et al. (2012, extended to later years) is
available online (at http://scedc.caltech.edu/research‐tools/downloads.html). The used focal
63
mechanisms are available through the Mendeley Data
(https://dx.doi.org/10.17632/h6rbr6d6n2.1) (Cheng & Ben‐Zion, 2020).
3.6 Acknowledgments
We thank Fenglin Niu for useful discussions. The manuscript benefited from constructive
comments by Roland Bürgmann, an anonymous referee and Editor Germán Prieto. The used
focal mechanisms are provided in the supporting information (Data Set S1). The research was
supported by the National Science Foundation (Grants EAR‐1945781 and EAR‐1722561) and
the Southern California Earthquake Center (based on NSF Cooperative Agreement EAR‐
1600087 and USGS Cooperative Agreement G17AC00047).

64
4. Isotropic source components of events in the 2019 Ridgecrest,
California, earthquake sequence (Cheng et al., 2021)
4.0 Abstract
We investigate non-double-couple components of 224 M ³ 3 earthquakes in the 2019
Mw7.1 Ridgecrest sequence, which occurred on a complex fault system in the Eastern California
Shear Zone. Full moment tensors are derived using waveform data from near-fault and regional
stations with a generalized cut-and-paste inversion and a 3D velocity model. The results show
limited Compensated Linear Vector Dipole components but considerable explosive isotropic
components (5-15% of the total moments) for approximately 50 earthquakes. Most of these events
occur in the first two days after the Mw7.1 mainshocks and are mainly distributed around the
rupture ends and fault intersections. The percentage of isotropic components is reduced when data
recorded by near-fault stations are not included in the inversions, highlighting the importance of
near-fault data. The results suggest that high-frequency damage-related radiation and other local
dilatational processes are responsible for the observed isotropic source terms.
4.1 Introduction
Earthquakes are typically assumed to have pure deviatoric sources (Zhu & Helmberger,
1996; Clinton et al., 2006) because the isotropic components are usually very small (Miller et al.,
1998; Ma et al., 2012, Ross et al., 2015). However, even small isotropic components in rupture
zones can have fundamental implications for many aspects of earthquake physics including the
partitioning between dissipation and seismic radiation, crack vs. pulse mode of rupture and
amplitude ratio of the generated P and S waves (e.g., Brune et al., 1993; Ben-Zion et al., 2001;
Kurzon et al., 2019). The P/S amplitude ratio of seismic radiation is also important for a
65
discrimination of explosions from earthquakes (e.g., Bukchin et al., 2001; Patton and Taylor, 2011;
Stroujkova, 2018).
Transient volumetric changes in earthquake source volumes can be caused by a wide
variety of processes. It is well known that brittle fracturing is accompanied by dilatational effects
(e.g., Brace et al., 1966; Lockner et al., 1991; Renard et al. 2019). Dynamic reduction of elastic
moduli in earthquake rupture zones reduces the capacity of the affected local volume to sustain the
elastic strain energy and produces damage-related radiation with a large isotropic component (Ben-
Zion & Ampuero, 2009; Ben-Zion and Lyakhovsky 2019). This and other dynamic dilatational
effects around a propagating rupture front are associated with short wavelengths that decay rapidly
with distance from the fault (Lyakhovsky and Ben-Zion, 2020). Additional mechanisms that can
generate high frequency isotropic source terms include fracture opening/closing caused by fluid
pressure variations (e.g. Miller et al., 1998, Dreger et al., 2000; Martínez‐Garzón et al., 2017),
ruptures on rough or nonplanar surfaces (e.g. Castro, 1991; Julian et al., 1998), elastic collisions
along sliding surfaces (Lomnitz-Adler, 1991; Tsai and Hirth, 2020), and near-source anisotropy
(Vavryčuk, 2005).
Resolving reliably small isotropic source terms of crustal earthquakes is a challenging task
because they are associated with rapidly decaying high frequency waves and require dense station
coverage, high frequency records, and accurate earthquake locations. Due to these challenges,
other parameters have been used to infer the possible existence of isotropic source components.
Examples include large P/S amplitude ratios (Castro et al., 1991; Castro & Ben-Zion, 2013),
reduced directivity effects of high frequency waves (Spudich & Chiou, 2008), and strong transient
rotation of double-couple (DC) focal mechanisms (Ross & Ben-Zion, 2013). The recent increase
of high-quality near-fault seismic data improved the ability to derive reliable source mechanisms
66
of earthquakes, some of which include considerable explosive isotropic components (Stierle et al.,
2014; Ross et al., 2015; Hayashida et al., 2020). Nevertheless, the number of studies resolving
isotropic source terms of regular crustal earthquakes remains rather limited.
The 2019 Ridgecrest, California, earthquake sequence in southern California, which
included the Mw6.4 event on July 4, the Mw7.1 mainshock on July 6, and over 200 of M ³ 3.0
earthquakes within the first month after the Mw6.4 event, provides important opportunities to
analyze earthquake source processes. The Mw6.4 and Mw7.1 earthquakes exhibited lower-than-
average rupture speeds (Liu et al., 2019). The earthquake sequence had abundant aftershocks (Ross
et al., 2019; Shelly, 2020) that occurred on broad zones with complex geometries and rock damage
(Chen et al., 2020; Xu et al., 2020, Jia et al., 2020). The Ridgecrest sequence occupied a complex
fault network with many previously unmapped faults, suggesting that many events in the sequence
may generate damage-related radiation. The area was well monitored by a regional network of
broadband seismic stations, and it has a good regional 3D seismic velocity model (Lee et al., 2014).
In the following, we perform a comprehensive analysis of isotropic source terms of earthquakes in
the Ridgecrest sequence in an effort to explore the governing earthquake physics.

67

Figure 4.1. Map view of moment tensors of 224 M ³ 3.0 events in the 2019 M7.1 Ridgecrest earthquake
sequence colored by the percentage of (a) CLVD component and (b) ISO component. (c) Distribution of
epicenters of the analyzed events as a function of time and distance along AA’ colored by the percentage
of ISO components.

68

Figure 4.2. Full moment tensor inversion results for the 2019/07/05 12:38 Mw4.1 event. (a) Map view of
the earthquake location (yellow star) and seismic stations (squares) used in the study. Stations are colored
by the averaged CC. (b) The number of waveforms that can be fitted (with the CC larger than 70%), the
averaged waveform CC, and the waveform misfit as a function of focal depth and moment tensor
solution, indicate a well-constrained focal depth of ~9.5 km. (c) Distribution of misfit in the moment
tensor lune-diagram. (d) Waveform fitting at different stations. The black, red, and blue colors indicate
data, synthetics, and the waveforms discarded in the automatic data selection, respectively.

4.2 Data
We derive full moment tensor solutions for 224 M ³ 3 earthquakes in the 2019
Ridgecrest sequence using locations from the refined local earthquake catalog of Ross et al.
(2019). For each event, we utilize waveform data recorded by 39 SCSN stations within 100 km
from the epicenters (Fig. 4.2a), and the 3-D SCEC Community Velocity Model (CVM) (Lee et
al., 2014) for the moment tensor inversions. The waveform data are obtained from the Southern
69
California Earthquake Data Center (http://scedc.caltech.edu). The usage of near-fault stations
and 3D velocity model can help to better constrain the moment tensor solutions, and is especially
useful for analysis of isotropic source terms.
4.3 Method
4.3.1 Source decomposition
We implement the source decomposition of Zhu and Ben-Zion (2013) to quantify the full
tensorial components of each event. The seismic potency tensor 𝑃
!"
is first decomposed into
isotropic (ISO) and deviatoric components:
𝑃
!"
=
A
$
√7
S
B
√C
𝛿
!"
+I1−𝜁
7
𝐷
!"
W, (1a)
where 𝑃
2
is the scalar potency, 𝛿
!"
is the Kronecker delta, 𝜁 quantifies the strength of the
isotropic term, and 𝐷
!"
is a normalized deviatoric tensor. The dimensionless parameter 𝜁 is given
by:
𝜁 =O
7
C
+-(A)
A
$
, (1b)
and it varies from -1 (implosion) to 1 (explosion). The normalized deviatoric tensor 𝐷
!"
is
decomposed into DC and Compensated Linear Vector Dipole (CLVD) components:
𝐷
!"
=I1−𝜒
7
𝐷
!"
DE
+𝜒𝐷
!"
EFGD
, (1c)
where 𝜒 represents the strength of the CLVD component with a range from -0.5 to 0.5. The
relative strength of the individual components is quantified by the square ratio of the scalar
moment of each component relative to the total scalar potency:
Λ
HIJ
= 𝑠𝑔𝑛(𝜁)𝜁
7
, (2a)
Λ
KL
= (1−𝜁
7
)(1−𝜒
7
), (2b)
Λ
LMNK
= 𝑠𝑔𝑛(𝜒)(1−𝜁
7
)𝜒
7
. (2c)
70
The sum of the absolute values of relative strengths is:
|Λ
HIJ
|+Λ
KL
+|Λ
LMNK
| = 1. (2d)
Note that the maximum CLVD and ISO strengths are 25% and 100%, respectively. This
decomposition can be used efficiently for full moment tensor inversion with a grid search over
the possible DC, ISO, and CLVD components within the allowable ranges.
4.3.2 Automated moment tensor inversion
We employ an automated moment tensor inversion algorithm (Wang and Zhan, 2020a)
that fits the observed body and surface waves at stations with epicentral distance less than 100
km using the 3-D SCEC CVM. We first calculate 3-D Green’s functions for all events and
stations, using the 3D velocity model through a 3D finite difference method and source-receiver
reciprocity approach. We then invert the waveforms for source terms using the gCAP3D method
(Zhu and Zhou, 2016). The source parameters include strike, dip, rake, Mw, hypocentral depth,
ISO term 𝜁, and CLVD term 𝜒. For each combination of parameters, we calculate synthetic
waveforms using 3D Green’s functions, window the synthetic waveforms into Pnl and S/surface
waves, and estimate the fit between the synthetic and observed waveforms. The lengths of
waveform segments and frequency bands (approximately between 0.03 to 0.3 Hz) are
automatically chosen based on the magnitude of the earthquake as in (Wang and Zhan, 2020a).
To accommodate inaccuracies in the assumed velocity model and earthquake locations, we allow
time shifts between the observations and synthetics to maximize their cross-correlation
coefficients. The time shifts provide information on the relative accuracy of the earthquake
locations and used velocity model. We also automatically control the data quality and optimize
the inversion by iteratively rejecting or reducing the weight of waveform segments that are too
complicated to be fitted with synthetic waveforms (Wang and Zhan, 2020a). The horizontal
71
locations of events are fixed to those in Ross et al., (2019) during the waveform inversion, but
we search over different depths to find the best fitting focal depths associated with the minimum
misfit and maximum number of waveform segments. The uncertainties of the final moment
tensor solutions are estimated using a bootstrapping method (Zhan et al., 2012; Ross et al., 2015;
Wang and Zhan, 2020a).
The method is illustrated in Fig. 4.2 with inversion results for an Mw4.1 event, which
occurred on 05 July 2019 12:38 near the Mw7.1 epicenter. The solved best-fitting depth is at 9.5
km, with average waveform cross-correlation above 85% (Fig. 4.2b), and most waveforms are
well-fitted with the synthetic waveforms. Fig. 4.2c shows the relative misfit in the moment
tensor lune-diagram (Tape and Tape, 2012). The best solution has positive isotropic component
with considerably smaller misfit compared with other solutions. Well-constrained full moment
tensors based on high-quality waveforms, 3D velocity model and automated algorithm, allow us
to systematically investigate the solutions and possible causes of the non-double-couple (non-
DC) components.
4.4 Results
We derive full moment tensor solutions for 224 aftershocks of the 2019 Mw7.1
Ridgecrest earthquake, and about 50 of these have considerably large non-DC components (5%-
15%). The derived non-DC components can have several causes including uncertainties in the
inversion procedure, heterogeneous and anisotropic velocity structure, and genuine non-DC
earthquake processes. To evaluate the influence of different velocity models, Wang and Zhan
(2020a) compared moment tensors solved using 1D and 3D velocity models and found that the
incorporation of a 3D velocity model can dramatically decrease the percentage of non-DC
components. A similar result is documented in the Supplementary Material (Text S1 and Fig.
72
A4.1), highlighting the importance of using a 3D velocity model for moment tensor inversions.
However, there are about 50 events have considerably large non-DC components, which cannot
be explained by the error of 3D velocity model, given the relatively long-period waveforms used
in inversion. In addition to velocity structure effects, we test the robustness of the non-DC
components by performing 3D moment tensor inversions using different source constraints
(Section 4.4.1.1, 4.4.1.2) and minimum station distance cutoffs (Section 4.4.1.3). The
spatiotemporal variations of the non-DC components are analyzed in Section 4.4.2.
4.4.1 Robustness analysis of non-DC component
4.4.1.1 Misfit Reduction
It is well-known that adding model parameters can reduce the data misfit of an inversion.
However, if the incorporation of additional parameters does not significantly reduce the misfit,
the added parameters may not be meaningful and the solved parameters may not be reliable. To
evaluate the significance of the solved non-DC components, we perform a series of inversions
using different source constraints, including pure DC sources, pure deviatoric (CLVD + DC)
sources, cases with only DC and isotropic terms (ISO + DC), and full moment tensor sources
(CLVD + ISO + DC). We compare the relative misfit change 𝑅𝑀𝐶
!"
of the results using source
constraint 𝑖 relative to the results using source constraint 𝑗 by:
𝑅𝑀𝐶
!;"
=
6!/P!+
!
$6!/P!+
#
6!/P!+
#
×100%, (3)
where 𝑀𝑖𝑠𝑓𝑖𝑡
!
is the total waveform misfit between the observations and synthetic waveforms
using source constrain 𝑖.
Figs. 4.3a and 4.3b show the variations of 𝑅𝑀𝐶
DEQEFGD;DE
and 𝑅𝑀𝐶
DEQEFGDQR5=;DEQEFGD

versus the CLVD strengths (𝜒). Almost all events show reduced misfits with the incorporation of
a CLVD component, with a misfit reduction that is overall proportional to the absolute CLVD
73
strength. Some events with large CLVD strength have more than 5% misfit reduction. Figs. 4.3c
and 4.3d show corresponding results that compare the relative misfit changes for inversions
incorporating isotropic components with cases assuming CLVD+DC and DC sources versus the
solved ISO strengths (𝜁). The misfit reduction shows again a close correlation with the absolute
value of ISO strength. When |𝜁| is smaller than 0.2 (|Λ
HIJ
| < 4%), most misfit reductions are less
than 1%. However, there are considerable numbers of earthquakes having |𝜁| larger than 0.2
(|Λ
HIJ
| > 4%) and misfit reduction larger than 2%. Note that most events with misfit reduction
larger than 2% have explosive ISO terms (Figs. 4.3c, 4.3d). The large misfit reductions after the
incorporation of CLVD and ISO components in the inversions suggest that the earthquakes are
not pure double-couples, and that the resolved non-DC components provide useful information
about physical processes associated with these earthquakes.
4.4.1.2 The Trade-off between CLVD and ISO components
A number of studies showed that there are trade-offs between isotropic and vertically-
oriented CLVD components for deep earthquakes recorded by distant stations, with station
coverage primarily around the edge of the focal sphere (Kawakatsu 1991, 1996; Hara et al.,
1996). However, shallow crustal earthquakes have much better coverage above and around the
events. Ross et al. (2015) examined trade-offs between the CLVD and isotropic components for
shallow crustal earthquakes in the San Jacinto fault zone, using synthetic tests based on a 1D
velocity model and a station configuration with epicentral distances between 40 to 300 km. Their
results indicated insignificant trade-offs between the CLVD and isotropic components in such
cases.
To examine further trade-offs between ISO and CLVD terms, we use the 3D SCEC
velocity model and stations within 100 km epicentral distance. We compare the solved CLVD
74
strength with and without isotropic components (DC + CLVD vs. DC + CLVD + ISO) (Fig.
4.3e), and the solved isotropic strength with and without CLVD components (DC+ISO vs. DC +
CLVD + ISO) (Fig. 4.3f). The different assumed cases have insignificant impact on the solved
CLVD and isotropic strengths (Figs. 4.3e-f), suggesting that limited trade-offs exist between
these components. Furthermore, based on the comparisons in Figs. 4.3a and 4.3b, most events
with substantial misfit reductions show negative CLVD strength. However, only positive CLVD
components cause trade-offs with the explosive isotropic components for strike-slip mechanisms
(Ross et al., 2015). We therefore conclude that the observed explosive isotropic components are
unlikely to have significant trade-offs with CLVD components.
75

Figure 4.3. The percentage of relative misfit changes of moment tensor inversions using (a) pure
deviatoric (DC + CLVD) sources compared with pure double-couple sources (DC), (b) full tensor sources
(DC + CLVD + ISO) compared with pure deviatoric (DC + CLVD) sources, (c) DC + ISO sources
compared with pure DC sources, and (d) full tensor sources (DC + CLVD + ISO) compared with pure
deviatoric (DC + CLVD) sources. Comparisons of (e) the percentages of CLVD component obtained with
and without ISO component and (f) the percentages of ISO component obtained with and without CLVD
component.

76
4.4.1.3 The effect of near-fault data on the resolved isotropic components
In addition to trade-offs, different station coverages can impact the solved non-DC
components through the signals they are able to record above the noise level (e.g., Kwiatek &
Ben‐Zion, 2016). This is especially important for high-frequency waves that may reflect key
aspects of the local governing physics and decay strongly with propagation distance. To analyze
the impact of near-fault data on the resolved isotropic components, we use three events with the
largest ISO components and three with the smallest for comparison (Fig. 4.4). We first invert
their moment tensors using all available stations within 100 km epicentral distance (Leftmost
solution in each subfigure). We then iteratively invert the moment tensors by gradually removing
the near-fault data until only three stations remain (at least three stations were used to ensure the
reliability of moment tensor inversion). Fig. 4.4 shows the variations of |Λ
HIJ
| and |Λ
LMNK
| with
the minimum epicentral station distance used in the inversions. When gradually removing near-
fault data for the events with the largest ISO components, the |Λ
HIJ
| decreases from over 15% to
around 5% while the |Λ
LMNK
| does not show significant changes (Figs. 4.4a, 4.4c, 4.4e). The
incorporation of more near-fault data also helps to suppress solution uncertainties, which further
demonstrates the robustness of the solved non-DC components using near-fault data. In contrast,
for events with the smallest ISO components, the solved non-DC components do not show strong
changes with the minimum station distance (Figs. 4.4b, 4.4d, 4.4f).
77

Figure 4.4. Variations of the percentage of isotropic (red symbols) and CLVD (blue symbols)
components as a function of minimum station distance cutoff for (a) three events with significant ISO
component and (b) three events without significant ISO component. The beachballs on the upper side
show the best-fitting double-couple solutions for different station cutoffs.

4.4.2 Spatiotemporal variations of non-DC components
Fig. 4.1 shows spatiotemporal variations of the derived non-DC components. Most events
do not show large CLVD components (Fig. 4.1a). In contrast, over 50 events have 5%-15%
isotropic components. Approximately 20 of them occurred before the Mw7.1 mainshock and are
located between the Mw6.4 and the Mw7.1 epicenters. After the Mw7.1 mainshock, most of the
events with large ISO components occurred within 1 day. They are mainly located around fault
intersections that are either NW to the Mw7.1 hypocenter or SE to the Mw6.4 hypocenter.
0
5
10
15
20
25
ISO (%)
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
ISO (%)
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
20
25
ISO (%)
0 10 20 30 40 50 60 70 80 90 100
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
CLVD (%)
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
CLVD (%)
0 10 20 30 40 50 60 70 80 90 100
0
5
10
15
CLVD (%)
Events with large ISO components Events with small ISO components
Event ID: 38599327
Magnitude: 3.8
Event ID: 38461775
Magnitude: 3.4
Event ID: 38449719
Magnitude: 3.6
Event ID: 38448295
Magnitude: 3.6
Event ID: 38458375
Magnitude: 4.3
Event ID: 38475431
Magnitude: 4.2
min Station Distance (km) min Station Distance (km)
min Station Distance (km) min Station Distance (km)
min Station Distance (km) min Station Distance (km)
78
Additional events with large ISO components are located around the NW and SE ends of the
rupture zone. On the other hand, in the NW aftershock zone with splay faults and subvertical
antithetic faults or the SE aftershock zone with subparallel faults, there are just a few events with
large ISO components. The maximum value of the isotropic components decays with time after
the occurrence of the Mw7.1 earthquake. Most of the events with large non-DC components
have magnitude ranging from 3 to 4 (Figs. A4.2b, A4.2d) and the values of non-DC components
do not show a clear depth dependency (Figs. A4.2a, A4.2c).
4.5 Discussion
Isotropic source terms of earthquakes can have important implications for various topics
including the energy partitioning between P and S waves (Kwiatek & Ben-Zion, 2013),
discrimination between earthquakes and explosions (Patton & Taylor, 2011; Stroujkova, 2018),
generated frictional heat (Brune et al., 1993) and other aspects of earthquake ruptures (Ben-Zion,
2001). However, resolving isotropic components of regular crustal earthquakes is very
challenging due to the dominance of shear deformation, limited seismic data, uncertainties in the
inversion procedures and low-resolution velocity models (Russakoff et al., 1997; Lyakhovsky &
Ben-Zion, 2020). These difficulties may produce improperly constrained isotropic components
and lead to misinterpretation of source processes (Vavryčuk et al., 2008). The analysis done in
this work includes near-fault data, is accompanied by examination of trade-off effects, and is
based on a version of the “cut and paste” inversion algorithm not very sensitive to modest errors
in the velocity model (e.g. Zhu & Helmberger, 1996; Ross et al., 2015).
Several features of our results suggest that the resolved isotropic components are robust.
The incorporation of isotropic components is shown to reduce over 1% of the data misfits of
some events (Figs. 4.3b, 4.3c). There are limited trade-offs between the isotropic and CLVD
79
components of the analyzed events (Fig. 4.3d). Many adjacent earthquakes with similar ray paths
have very different isotropic components, indicating that the resolved isotropic components are
not caused by errors in the velocity model (or instruments). In addition, there are clear
correlations between the events with significant isotropic components, fault geometry and
mainshock time (Fig. 4.1), suggesting that they are likely caused by local physical processes.
Mechanisms that can produce isotropic source terms include fault-normal motion generated by
ruptures on non-planar faults (Castro et al., 1991; Lomnitz-Adler, 1991; Julian et al., 1998),
tensile faulting in an extensional stress regime with involvement of fluids (Sibson, 1994,
Vavryčuk 2002, Stierle et al., 2014), and damage-related radiation generated by dynamic
reduction of elastic moduli in rupture zones (Ben-Zion & Ampuero, 2009; Ben-Zion &
Lyakhovsky, 2019; Lyakhovsky & Ben-Zion, 2020).
The relatively large number of the derived full moment tensor solutions for M ³ 3
earthquakes (Fig. 4.1) allow us to assess the likely physical processes responsible for the
observed isotropic components. A tensile stress regime is not consistent with the dominant
strike-slip regime indicated by the focal mechanisms of events between the Mw6.4 and Mw7.1
earthquakes (Cheng & Ben-Zion, 2020; Sheng & Meng, 2020). There is also no clear reason why
fluid effects would concentrate in the locations of the events that have significant isotropic
components. Moreover, non-planar fault geometries or fluid-related tensile faulting do not
explain why the strength of the isotropic components decayed so fast (~1 days) after the
mainshock. However, rock damage in earthquake source volumes is likely to be more
pronounced for events near fault intersections and ends of the rupture zone, and for early
aftershocks since later events may occur in already faulted materials. This is consistent with the
80
pattern observed in Fig. 4.1, suggesting that damage-related radiation may be a dominant source
of the observed isotropic components.
As illustrated in Fig. 4.4 and Fig. A4.2, most events with significant isotropic
components have magnitude less than four and the ability to resolve isotropic source terms
depends strongly on the availability of near-fault data. This is because volumetric source terms
are associated with short wavelengths proportional to the rupture zone width that decay rapidly
with distance from the fault, in contrast to the deviatoric terms that have wavelengths
proportional to the rupture length (Lyakhovsky & Ben-Zion, 2020). Earthquakes may commonly
generate a small amount of isotropic radiation, because of one or several of the discussed
mechanisms, which is not resolved in typical far-field data. Additional deployments of near-fault
stations will provide improved data for detailed investigations of earthquake source processes
(e.g. Hayashida et al., 2020).
4.6 Data Availability Statement
The employed earthquake catalog of Ross et al., (2019) is available online (at
https://scedc.caltech.edu/data/qtm-ridgecrest.html). The used earthquake waveform data is
available from the Southern California Earthquake Data Center (http://scedc.caltech.edu).
4.7 Acknowledgments
The research was supported by the Southern California Earthquake Center (based on NSF
Cooperative Agreement EAR-1600087 and USGS Cooperative Agreement G17AC00047).

81
5. An Automated Method for Developing a Catalog of Small
Earthquakes Using Data of a Dense Seismic Array and Nearby
Stations (Cheng et al., 2020)
5.0 Abstract
We propose a new automated procedure for using continuous seismic waveforms
recorded by a dense array and its nearby regional stations for P-wave arrival identification,
location, and magnitude estimation of small earthquakes. The method is illustrated with a one-
day waveform dataset recorded by a dense array with 99 sensors near Anza, California, and 24
surrounding regional stations within 50 km of the dense array. We search a wide range of
epicentral locations and apparent horizontal slowness values ( ⁠0–15 s/km ⁠) in the 15–25 Hz range
and time shift the dense array waveforms accordingly. For each location–slowness combination,
the average neighboring station waveform similarity (avgCC) of station pairs <150 m apart is
calculated for each nonoverlapping 0.5 s time window. Applying the local maximum detection
algorithm gives 966 detections. Each detection has a best-fitting location–slowness combination
with the largest avgCC. Of 331 detections with slowness <0.4 s/km ⁠, 324 (about six times the
catalog events and 98% accuracy) are found to be earthquake P-wave arrivals. By associating the
dense array P-wave arrivals and the P- and S-wave arrivals from the surrounding stations using a
1D velocity model, 197 detections ( ⁠∼4 times of the catalog events) have well-estimated locations
and magnitudes. Combining the small spacing of the array and the large aperture of the regional
stations, the method achieves automated earthquake detection and location with high sensitivity
in time and high resolution in space. Because no preknowledge of seismic-waveform features or
82
local velocity model is required for the dense array, this automated algorithm can be robustly
implemented in other locations.
5.1 Introduction
Improving the ability to detect small earthquakes can increase the resolution of
monitoring seismic processes at depth and imaging fault-zone structures and the crust.
Earthquake detection consists of identifying phase arrivals at the recording stations (phase
detection) and associating the arrivals from multiple stations to an individual event (phase
association). Modern earthquake catalogs usually use phase arrivals picked by data analysts or
traditional automated algorithms that use one or multiple waveform characteristics, such as
short-term average/long-term average (STA/LTA; Allen, 1982) or higher-order statistics (Ross,
White, et al., 2016). However, manual analysis varies from person to person, and traditional
automated algorithms are generally less precise than manual picking. With the increasing
number of seismic networks and large volume of data, more precise automated detection
algorithms are needed to detect smaller earthquakes. Separating small earthquakes from
nontectonic sources at and above the surface pose significant challenges (e.g., Inbal et al.,
2018; Meng & Ben-Zion, 2018a, b; Johnson et al., 2019).
One highly successful method that can enhance detection of small events using existing
earthquake waveforms is the template-matching algorithm (Peng & Zhao, 2009; Shelly et al.,
2016). This technique uses waveforms of catalog events as templates, searches over continuous
seismic records, and detects new events with waveforms highly similar to the templates. This
method is widely applied and often detects several times more events than the standard detection
workflow. However, event-similarity-based detection can only identify events that are very
similar (and inferred to be located very close) to the templates. Recently, supervised deep-
83
learning algorithms, which learn features from large amounts of labeled data to perform signal
recognition, can better differentiate earthquake signals from the other signals with higher
precision ( ⁠>90% ⁠) than traditional methods (e.g., Ross et al., 2018; Zhu & Beroza, 2018).
Because of the requirement of large amounts of manually labeled data in the study region and the
regional variations of earthquake waveform features, it would be difficult to apply algorithms
trained at one region to others without a training dataset. Because both the template-matching
method and supervised deep-learning algorithms are based on known earthquakes’ signals, they
are not able to detect earthquakes that have highly different rupture processes or hypocenters
compared with the known earthquakes. These missing small events are likely to provide (if
detected) additional important information on properties and dynamics of the crust.
One possible way to identify unknown seismic signals is to utilize waveform correlations
across closely spaced seismometers. Over the past decade, increasing number of dense array
deployments provide important opportunities to detect small earthquakes (e.g., Ben-Zion et al.,
2015; Inbal et al., 2016; Li et al., 2018). On the one hand, recorded waveforms from the same
signal exhibit high similarity across the whole or parts of the array and can be stacked to enhance
the signal-to-noise ratio. On the other hand, the relative time delays of the signals across the
array provide important information about wave propagation directions and velocities. One can
detect small earthquakes and other sources of seismic signals by stacking or backpropagating the
signals recorded at all stations based on the time delay from possible source locations to the
stations. However, separating subsurface from other events requires careful analyses (e.g., Meng
& Ben-Zion, 2018a; Gradon et al., 2019; Johnson et al., 2019). In addition, there are unsolved
methodological problems with dense array data such as the high sensitivity to the used velocity
model and limited location resolution caused by the small apertures of dense arrays ( ⁠<3 km ⁠).
84
In this study, we propose a high-precision automated method for detection and location of
earthquakes and apply it to a 23-day continuous waveforms data recorded (from 20 July to 11
August 2018) by a dense array and 24 regional stations located within 50 km of the dense array
(Fig. 5.1). The dense array is located at the Cahuilla Reservation close to the San Jacinto fault
zone in southern California, and it consists of 99 vertical-component geophones with 100 m
spacing, distributed in nine rows and 11 columns, and recording with 250 Hz sampling rate. The
method, a representative example of its implementation, and its application to a one-day
continuous waveforms are described in the section 5.2. The advantages of the method and its
potential applications are discussed in the section 5.3. The results from the entire 23-day dataset
are provided in the supplemental material available to this article.

Figure 5.1. (a) Map view of Cahuilla dense array (magenta square) and the 24 regional stations (blue
triangles) within 50 km of the dense array. Magenta box outlines the candidate epicentral locations for
dense array detection. (b) Spatial distribution of the vertical geophones of the dense array colored by
elevation. Inset shows the fault map of southern California. Red box denotes the area of (a). EF, Elsinore
fault; SAF, San Andreas fault; SJF, San Jacinto fault.
85
5.2 Method and Representative Examples
In this section, we explain the method and describe the obtained results step by step. We
first automatically detect coherent signals from dense array data and discriminate P-wave
arrivals from detected signals without using any local velocity models (Section 5.2.1).
Earthquakes are located (Section 5.2.2) by associating the detected P-wave arrivals at the array
sensors with arrivals from the surrounding regional stations using an average 1D velocity model
for southern California (Fang et al., 2016). The magnitude estimation of the detected events is
presented in Section 5.2.3.

Figure 5.2. Schematic diagrams of the dense array earthquake detection workflow. For all combinations
of (a) candidate source epicentral location d (within 0.2°×0.2°box around the array) and (b) apparent
horizontal slowness ss (⁠0–15s/km⁠), (c) waveforms are shifted based on the estimated travel time t and
(d) correlated with neighboring stations’ waveforms. (e) The time windows with averaged neighboring
station similarity above the chosen threshold are selected as positive detections. S&D corresponds to
apparent horizontal slowness and horizontal distance.

86
5.2.1 Signal detection and discrimination with dense array data
5.2.1.1 Method
Interstation waveform similarity can be used to identify coherent signals from continuous
waveform. When the source–station distance is much larger than the interstation distance, the
signals from common sources are expected to share highly similar travel paths and hence similar
waveforms, whereas signals from random noise or very local sources are expected to be
different.
Signals from a common source arrive at different stations at different times, and it is thus
useful to correlate the waveforms based on their relative arrival‐time differences, which requires
a good velocity model. However, the seismic velocities can vary considerably around fault
zones, are generally not well known in the uppermost ∼100–500 m of the crust, and are strongly
frequency dependent (e.g., Allam et al., 2014; Hillers et al., 2016; Mordret et al., 2019).
Therefore, instead of using a velocity model, we assume a given constant apparent horizontal
slowness and grid search a range of values (Fig. 5.2b). To determine the incoming direction of
the signals, we search all candidate epicentral locations around the array (Fig. 5.2a). For
slowness 𝑠
!
⁠, the estimated travel time 𝑡
:;!"
from source location 𝑗 to station 𝑘 is

𝑡
:;!"
= 𝑑
:;"
×𝑠
!
, (1)

In which 𝑑
:;"
is the distance from location 𝑗 to station 𝑘. Similarly, the travel time from location
𝑗 to the center of the array 𝑐 can be written as
𝑡
S;!"
= 𝑑
S;"
×𝑠
!
. (2)
87
We use the time that the signal arrives at the array center as the reference time and shift the
recorded waveforms at each station accordingly. If a coherent signal propagates across the array
at time 𝑡, the waveforms recorded at multiple station pairs are expected to be similar with
waveform similarity exceeding a threshold value 𝑐𝑐
+, -./
. The waveform similarity 𝑐𝑐
&T;!"
(𝑡)
between station 𝑚 and 𝑛 for possible source location 𝑗 and slowness 𝑠
!
at time 𝑡 can be written
as:
𝑐𝑐
&T;!"
(𝑡) =
U∑ W
%
(+Q+
%;!#
$+
';!#
QXY)W
(
(+Q+
(;!#
$+
';!#
QXY)
)
*+,)
U
Z∑ W
%
"
(+Q+
%;!#
$+
';!#
QXY)W
(
"
(+Q+
(;!#
$+
';!#
QXY)
)
*+,)
, if 𝑐𝑐
&T;!"
(𝑡) > 𝑐𝑐
+, -./
, (3)
𝑐𝑐
&T;!"
(𝑡) = 0, if 𝑐𝑐
&T;!"
(𝑡) ≤ 𝑐𝑐
+, -./
, (4)
in which 𝛿 is the sampling rate and (2𝐿+1)𝛿 is the sliding window length. We obtain the
average neighboring station similarity, 𝑎𝑣𝑔𝐶𝐶
!"
(𝑡) for the mean correlation value 𝐶𝐶
&T
!"

observed at station pairs with inter-station distance 𝑑𝑖𝑠𝑡(𝑚,𝑛) smaller than 𝑑𝑖𝑠𝑡
&!T
(Fig. 5.2c,
5.2d):
𝑎𝑣𝑔𝐶𝐶
!"
(𝑡)= 𝑎𝑣𝑔
(&,T)
(𝐶𝐶
&T;!"
),∀ 𝑑𝑖𝑠𝑡(𝑚,𝑛)< 𝑑𝑖𝑠𝑡
&!T
. (5)
The source location 𝑗 and apparent horizontal slowness 𝑠
!
with the largest 𝑎𝑣𝑔𝐶𝐶
!"
(𝑡) are
selected as the best-fitting solution for time 𝑡 (Fig. 5.2e). The source incoming azimuth can be
determined using the best-fitting source location, and the source depth can be estimated from the
best-fitting apparent horizontal slowness. If the source is very shallow, most of its travel paths to
the dense array are either along the near-surface layer with high apparent horizontal slowness or
diving into the medium with different paths and hence different waveforms. If the source is
located deep beneath the array, stations in the dense array will receive its signals almost at the
same time with low apparent horizontal slowness. Therefore, the best-fitting apparent horizontal
slowness can be used to differentiate earthquake signals and near-surface signals.
88
For the Cahuilla array, 338 stations pairs have inter-station distance smaller than 150 m
and are chosen for calculating waveform correlation (of these, 212 station pairs were active
through the entire 23-day period). We search possible apparent horizontal slowness from 0 to 15
s/km, with 0.025 s/km spacing from 0 to 1 s/km, 0.05 bin from 1 to 5 s/km, and 0.2 s/km spacing
from 5 to 15 s/km, considering all possible signals propagating in the crust and along the surface.
The pattern of recorded signals is strongly related to epicentral locations. If the distance from the
source to the array is much larger than the array aperture, the signals recorded by the array are
approximately plane waves with similar waveforms and are not sensitive to source location
variation. If the source is close to the array, a small location change may strongly affect the
relative time delays and waveform similarity. Therefore, we search epicentral locations within a
0.20×0.20 degree box around the array with increasing spacing from 0.002 degree at the array
center to 0.02 degree at the edge of the box (magenta box in Fig. 5.1a). Considering local noise
and the different travel paths from a common source to the station pair, we use 𝑐𝑐
+, -./
= 0.7 to
differentiate signals from noise.
An appropriate frequency band selection is also essential for detection accuracy. Ideally,
the selected frequency band only has earthquake signals, related to used phase and event size and
proximity, or it is easy to separate earthquake signals from other signals in this frequency band.
Here we aim at detecting near-field P-waves from small local earthquakes that have more high
frequency component (> 15 Hz) compared to teleseismic signals and S-waves. In addition,
surface wave slowness is comparable with that of earthquake signals in the low frequency band
(< 10 Hz) but is much higher in the high frequency band (> 15 Hz). We perform the detection
using 15-25 Hz frequency band, which can sufficiently suppress other low frequency signals and
easily distinguish earthquake P-wave arrivals from surface sources. Since P-wave velocity below
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300 m or so is usually larger than 2.5 km/s (e.g., Mordret et al., 2019), we use 0.4 s/km as the
threshold to discriminate P-wave arrivals from other signals. In order to detect P-wave arrivals
from the continuous stacked neighboring station similarity 𝑎𝑣𝑔𝐶𝐶
!"
(𝑡), we first extract the
largest 𝑎𝑣𝑔𝐶𝐶
!"
(𝑡) value at each time window 𝑎𝑣𝑔𝐶𝐶
&\]
(𝑡) and then search local maximum
𝑎𝑣𝑔𝐶𝐶
&\]
(𝑡) above the chosen threshold 𝑎𝑣𝑔𝐶𝐶
+, -./
. In the analysis below, we apply the
median value plus 12 times the median absolute deviation (MAD) of 𝑎𝑣𝑔𝐶𝐶
&\]
(𝑡) as the
threshold 𝑎𝑣𝑔𝐶𝐶
+, -./
for event detection. This threshold is based on a visual examination of
waveforms from 07/21/2018T00:00:00 to 07/22/2018T00:00:00, and the thresholds used in the
other waveform-similarity-based detection methods (Ross et al., 2019a; Li et al., 2018; Shelly et
al., 2007).
5.2.1.2 Representative example
Fig. 5.3a displays one-minute waveforms (15-25 Hz) of the dense array from 2018-07-
21T00:26:30 to 2018-07-21T00:27:30. There are three coherent signals recorded in this time
window with different apparent horizontal slowness. Fig. 5.3b shows the spectrogram of data at
one of the dense array stations. Events 1 and 2 are near-surface signals with high slowness values
(~ 4 s/km), narrow-frequency-band (at ~18 Hz) and long duration (>5s). Event 3 is an earthquake
with two peaks in the spectrogram (corresponding to P- and S-wave arrivals), low slowness (~
0.1 s/km), wider frequency band (0-60 Hz), and short duration (~3s).
For each 0.5s waveform, we calculate the averaged neighboring station similarity
𝑎𝑣𝑔𝐶𝐶(𝑡) for all slowness-location combinations and show the variation of the maximum
𝑎𝑣𝑔𝐶𝐶(𝑡) with respect to slowness (Fig. 5.3c). If the temporal maximum of 𝑎𝑣𝑔𝐶𝐶
&\]
(𝑡)
(magenta line) is above the calculated threshold 𝑎𝑣𝑔𝐶𝐶
+, -./
in a certain period, we retain the
local maximum 𝑎𝑣𝑔𝐶𝐶
&\]
(𝑡) with best-fitting time, slowness, location and regard it as a
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detection. Event 1 and Event 2 (near-surface signals) in this time window show high 𝑎𝑣𝑔𝐶𝐶(𝑡)
at high slowness region while Event 3 (earthquake) has peak 𝑎𝑣𝑔𝐶𝐶(𝑡) at very low slowness
region. From the spatial distribution of the 𝑎𝑣𝑔𝐶𝐶(𝑡) at the best-fitting time of the detections
(Fig. 5.3d, 5.3e, 5.3f), we observe that Events 1 and 2 propagate from southwest to northeast
while Event 3 comes from south of the array. The detection time of Event 3 is very close to the
manually picked P-wave arrival with only 0.025s time difference (Fig. A5.1).

Figure 5.3. (a) One min waveforms (15–25 Hz) of the dense array from 21 July 2018 T00:26:30 to 21
July 2018 T00:27:30. (b) Spectrogram of station index 70 in (a). (c) Temporal variation of the maximum
averaged neighboring station similarity (CC) versus apparent horizontal slowness. (d–f) Spatial
distribution of the maximum CC at the best-fitting times of the detected events in (c). Vertical red lines
and white stars highlight the best-fitting times, slowness values, and locations of the detected events.
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5.2.1.3 Application to 1-day dataset
We apply the detection method to a one-day waveform dataset from
07/21/2018T00:00:00 to 07/22/2018T00:00:00 and obtain 966 detections with 𝑎𝑣𝑔𝐶𝐶
&\]
(𝑡)
above the calculated threshold 𝑎𝑣𝑔𝐶𝐶
+, -./
(Fig. A5.2, available in the supplemental material to
this article). For each detection, we keep the best-fitting location and apparent horizontal
slowness with the maximum 𝑎𝑣𝑔𝐶𝐶(𝑡). Based on the slowness value, detections in the test day
are separated into 635 high-slowness detections (slowness ≥ 0.4 s/km) and 331 low-slowness
detections (slowness < 0.4 s/km). Most high-slowness detections occur around 6:00:00 UTC
time while most low-slowness detections occur around 12:00:00 UTC time (Fig. 5.4a). Spatially,
most low-slowness detections are located southwest to the array (Fig. 5.4b), corresponding
generally to the long-duration Cahuilla swarm (Hauksson et al., 2019). High-slowness detections
corresponding to near-surface signals exhibit a more uniform distribution (Fig. 5.4c). These
high-slowness signals may originate from multiple local sources such as possible small failures
at the subsurface (Ben-Zion et al., 2015; Qin et al., 2019), air and surface traffic (Meng & Ben-
Zion, 2018b; Inbal et al., 2018), wind shaking surface objects (Johnson et al., 2019) and other
sources of cultural noise.
We check all 67 M > 0 catalog events in our study period (Hauksson et al., 2012,
extended to later years) and find that 46 out of 47 events located within 90 km from the array are
detected with slowness < 0.4s/km and 16 events located at least 120km away from the array are
not detected due to high attenuation of high frequency signals from distant sources to the
stations. We manually check the waveforms of 333 low-slowness detections to ensure that
almost all stations record clear P- and S-wave arrivals; both P- and S-wave signals have wide
frequency band; the P-wave arrivals show higher frequency component and smaller apparent
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horizontal slowness compared with S-wave arrivals, and the median P-wave arrival time is
within a 0.5s time window around the detection. Out of 331 detections, 324 satisfy these criteria
and are considered as earthquake P-wave arrivals (~98% accuracy). We also manually pick P-
wave arrivals from the continuous waveform data in the entire day 07/21/2018 based on the
above-mentioned criteria. Only 28 manually picked P-wave arrivals are not detected (~92%
recall). This method detects six times more earthquake P-wave arrivals compared with the
relocated earthquake catalog (Hauksson et al., 2012, extended to later years), including 46 out of
47 catalog events within 90 km epicentral distance from the array.

Figure 5.4. (a) Histogram of detected events from 21 July 2018 T00:00:00 to 22 July 2018 T00:00:00
with respect to the slowness and time. Spatial density of detections with slowness (b) below and
(c) above 0.4 s/km⁠.

93

5.2.2 Earthquake location
Most earthquake detections are located outside of the array (Fig. 5.4b), where the dense
array data cannot provide good location solutions. As a result, we combine the results with
detected arrivals from the surrounding regional stations to perform earthquake location analysis.
5.2.2.1 Method
Traditional earthquake location methods search all possible earthquake locations and
origin times, calculate theoretical arrival times, and try to find the location-time combination that
matches most of the picked arrival times. Since dense array detection provides high accuracy P-
wave arrivals, we can use the dense array P-wave arrivals to predict earthquake origin times and
perform phase association. For each dense array P-wave detection 𝑡
^;S
, if we assume the source
is at location 𝑖, the P-wave arrival time to the dense array 𝑡
^;S
can be regarded as the summation
of event origin time 𝑡
_-!`;!
and the P-wave travel time 𝑇𝑇
^;!S
:
𝑡
^;S
= 𝑡
_-!`;!
+𝑇𝑇
^;!S
. (6)
Similarly, the theoretical P- and S-wave arrival times 𝑡
^;!"
, 𝑡
/;!"
at the regional station j can be
written as:
𝑡
^;!"
= 𝑡
_-!`;!
+𝑇𝑇
^;!"
= 𝑡
^;S
−𝑇𝑇
^;!S
+𝑇𝑇
^;!"
, (7)
𝑡
/;!"
= 𝑡
_-!`;!
+𝑇𝑇
/;!"
= 𝑡
/;S
−𝑇𝑇
/;!S
+𝑇𝑇
/;!"
, (8)
where 𝑇𝑇
^;!"
, 𝑇𝑇
/;!"
are P- and S travel times from location 𝑖 to the regional station 𝑗 (Fig. 5.5a).
Therefore, we first estimate the theoretical arrival times using 1D velocity model for the region.
We search all possible source locations and consider the one that minimizes the misfit between
the theoretical and observed arrival times of detected P- and S-wave arrivals as the earthquake
location (Fig. 5.5b).
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Figure 5.5. Diagrams of the earthquake phase association and location. (a) For each possible source
location, we calculate its P-wave travel time to the dense array as well as P- and S-wave travel times to
the regional stations. (b) The location (Loc) with the maximum number of phase arrivals within the
estimated arrival-time window is selected as the earthquake location. (c–e) Spatial distribution of the
number of arrivals within 0.75 s from the predicted arrival times for event 3 in Figure 3. White star
denotes the best-fitting location.

5.2.2.2 Representative example and application to 1-day dataset
In order to detect the arrivals from the surrounding stations and combine them with the
dense array arrivals, we first apply the convolutional neural network (CNN) phase picker (Ross
et al., 2018) to all 24 stations located within 50 km of the dense array to detect P- and S-wave
arrivals. All phase arrivals within ±40 s from the dense array P-wave detection are selected for
phase association. Since most of the detected catalog events are located within 90km from the
array in the red square in Fig. 5.1a (Fig. A5.3), we search all source locations within this area
using 1 km spacing, estimate their corresponding theoretical arrival times at all 24 stations using
an average 1D velocity model for southern California (Fang et al., 2016), and obtain the total
95
number of P- and S-wave arrivals within ±0.75 s from the theoretical arrival times (equations 7,
8) for each location. The location with the maximum number of P- and S-wave arrivals is
selected as the event location (white star in Fig. 5.5c, 5.5d, 5.5e). We obtain all source locations
with more than 80% of the maximum number of P- and S- arrivals (green circles in Fig. 5.5c,
5.5d, 5.5e) and calculate the standard deviation of their latitudes, longitudes and depths as the
location uncertainties of the located event. The source location of Event 3 is close to the dense
array, which is consistent with the small P- and S-wave arrival time differences (Fig. 5.3a, 5.3b).
The entire phase detection, association, and location process is applied to all candidate
detections in Section 5.2.1.3. There are 242 well-located detections with at least four P- and S-
wave arrivals in total from the surrounding regional stations, which is about 4 times of the
catalog events. The median uncertainties of events’ latitudes, longitudes, and depths are 0.024°
(~2.7 km), 0.027° (~2.5 km), and 3.6km, respectively (Fig. A5.4). Note that events with larger
than 50km epicentral distances from the array may have relatively larger location uncertainties
due to limited station azimuthal coverage (Fig. A5.5). Compared with catalog events (Hauksson
et al., 2012, extended to later years), over 80% of the common events have time differences
within 0.4s, horizontal location differences within 2.2km, and depth differences within 3.2km
(Fig. 5.6, A5.6).
5.2.3 Magnitude estimation
We utilize the nearby catalog events to estimate the magnitude of the detected events by
assuming that near-by events share similar path and site effects when the station-event distance is
much larger than the inter-event distances. For each well-located detection, we first find the
reference catalog events (Hauksson et al., 2012, extended to later years) within a 5 km
hypocentral distance from the detected event. If a station 𝑖 has P-wave arrivals from both the
96
reference event 𝑗 and the detected event 𝑘, we obtain a magnitude estimation by measuring the
peak amplitude ratio between event 𝑗 and 𝑘 under the assumption that a one-unit magnitude
difference corresponds to a factor of 10 in amplitude ratio. The magnitude of the detected event
𝑘 is estimated to be the median value of magnitude estimations from all available reference-
event-station combinations
𝑀
:
= 𝑚𝑒𝑑𝑖𝑎𝑛
!"
h𝑙𝑜𝑔
)2
h
3
-
!
3
#
!
k+𝑀
"
k. (9)
We apply the magnitude estimation to all well-located events and obtain 191 well-estimated
event magnitudes with more than 10 individual magnitude estimations and standard deviation of
the estimations smaller than 1 unit. The magnitude-time distribution of our results is consistent
with that of the catalog events with over 80% of the common events having magnitude
differences below 0.13 unit (Fig. 5.6, A5.6d). Many newly detected events have magnitudes as
low as -1 (Fig. 5.6a). There are 82 events that are not detected by template matching method
(Ross et al., 2019a) but are detected using our new method.
97

Figure 5.6. (a) Temporal variation and (b) spatial distribution of the catalog events (yellow dots) and
additional detected events (blue dots) from 21 July 2018 T00:00:00 to 22 July 2018 T00:00:00 scaled by
event magnitude.

5.3 Discussion and conclusions
Similar to the other dense array detection methods (Inbal et al., 2016; Li et al., 2018;
Meng et al., 2018a; Gradon et al., 2019), we time-shift and stack the characteristic functions of
waveforms based on the estimated travel time delay to extract correlated signals hidden in noise.
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However, our method has several improvements that allow detecting earthquake P-waves with
high accuracy and temporal resolution. Instead of shifting and stacking amplitude or phase
information (Meng et al., 2018a; Gradon et al., 2019), we utilize waveform similarity of
neighboring stations as the characteristic functions, which does not require significantly high
amplitude or waveform coherency across the whole array and is more sensitive to weak signals.
The method does not require narrowband frequency with bandwidth less than 3 Hz (like phase-
based detection methods) and can be applied to a wide frequency range. Instead of using
traditional earthquake detection frequency band (2-15 Hz), we use a higher frequency band (15-
25 Hz), which helps us to focus on P waves of local small events, avoid low-frequency S and
teleseismic waves, separate P-waves from surface waves in slowness domain, and finally achieve
high detection precision. For relative time delay estimation, we assume a circular wave at the
surface with constant slowness and search over a wide range of slowness considering not only
the small relative time delay for earthquake P-wave (< 0.4s across the whole array) but also wide
range of slowness values for surface wave. The assumption approximates actual wave
propagation and is expected to be better than assuming plane wave or spherical wave
propagation in a fixed layered velocity model. Moreover, we apply the shift-and-stack process to
all non-overlapping 0.5s time windows in the study period without time window pre-selection,
which allows us to obtain more detections with high temporal resolution. To sum up, our
detection method does not require pre-knowledge about velocity models, earthquake waveform
features, or time window pre-selection, and can successfully detect earthquake P-wave arrivals
with high precision (> 95%) and temporal resolution (~ 0.5s). This method is transferable to
other regions, totally automated, highly accurate and can potentially be applied in real time.
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The combination of dense array and regional stations can significantly improve the
earthquake catalog and outperform detections using dense arrays or regional stations separately.
Benefitting from inter-station waveform similarity of the dense array, many more earthquake P-
wave arrivals can be detected with high precision. On the other hand, the regional station
networks have large aperture important for high spatial resolution. After associating the dense
array arrivals with regional station arrivals, many traditional earthquake detection methods and
magnitude estimation methods can be applied and combined with the dense array detections. In
this study, we use a CNN phase picker (Ross et al., 2018) to detect earthquakes at regional
stations, and relative amplitude ratio to estimate local magnitudes. We can also use traditional
detection methods like STA/LTA (Allen, 1982) and high order statistics (Ross et al., 2016a) to
pick P- and S-wave arrivals. Similarly, many other magnitude estimation methods, like absolute
peak amplitude for local magnitude estimation (Richter, 1935) and amplitude spectrum for
potency magnitude estimation (Ross et al., 2016b), can be applied as well. The association
between dense array P-wave arrivals and regional station phase arrivals successfully merges the
dense array detection method within the traditional earthquake detection workflow, and allows to
estimate the locations and magnitudes of the large number of additional detections from the
dense array. A future network configuration combining multiple dense arrays with different
inter-sensor spacing and surrounding regional stations can significantly enhance the detectability
of small events.
In spite of the above advantages, the performance of our detection method strongly
depends on the shallow medium properties and array spacing. The inter-station waveform
similarity is strongly affected by travel path differences, seismic wavelength, and attenuation
effects. Only when interstation distances are close enough compared with the source-array
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distance (e.g., less than 1/5) can the recorded array signals from the same source be similar. The
wavelength is required to be larger than the interstation distance to ensure the alignment of
waveforms and avoid cycle skipping. Moreover, the source energy for given magnitude and
propagation distance should be larger than the background noise level for possible detection (e.g.
Kwiatek & Ben-Zion, 2016). If the signal frequency of an event is so high or ray paths of station
pairs are so different that even adjacent stations cannot record similar waveforms, the presented
detection method will not be useful and amplitude-based methods may work better. Furthermore,
our method may not be suitable to areas with strong contrasts of seismic properties due to high
scattering attenuation and violation of the constant slowness assumption. Even for areas with
relatively simple and homogeneous structure, our method can separate surface wave signals from
earthquake P-wave arrivals only when the surface wave slowness for the selected frequency band
(15-25 Hz in this study) is much larger than that of the subsurface signals (0.4 s/km).
The proposed procedure can be augmented in multiple ways. The detected earthquake P-
wave arrivals can be used for template matching detection and training deep learning algorithms,
which can further improve the earthquake catalog and help to perform more detailed analyses.
Besides earthquake signals, the detected surface signals can also help to identify the surface
sources and estimate the near-surface medium properties. We can apply the detection algorithm
to multiple frequency bands selected to detect surface signals (e.g., Gradon et al., 2019). The
spatiotemporal patterns as well as the waveform features of the detected surface signals can be
used to explore the signal sources. If there are repeating surface events occurring at the same
location and covering long time periods, we can investigate their waveform variation across the
whole array to estimate temporal changes of the near-surface seismic properties. The
combination of the presented detection algorithm with other new techniques for signal
101
characterization, detection and location of events, and utilizing detected phases for tomography
can improve considerably the understanding of properties and dynamics of the crust.
5.4 Data and Resources
The Cahuilla dense array data are available upon request to F. Brenguier. The relocated
earthquake catalog is from Hauksson et al. (2012, extended to later years)
(https://scedc.caltech.edu/research-tools/altcatalogs.html; last accessed 2019/11/01). The
continuous waveforms of the stations around the dense array are available at Southern California
Earthquake Data Center (SCEDC; doi:10.7909/C3WD3xH1). The used average 1D velocity
model is from Fang et al., (2016). The CNN phase picker is from Ross et al., (2018). Figures
were prepared using Matplotlib (Hunter, 2007) and Cartopy (https://scitools.org.uk/cartopy).
Supplemental material for this article includes various figures showing the strategy for choosing
the detection threshold, the temporal variation of detection threshold, spatiotemporal variation of
all detected events in the study period, the uncertainties of the obtained detections, the
comparisons between the detected events and their corresponding catalog events, and the
detection results using different characteristic functions like waveform similarity in 2-15Hz and
STA/LTA.
5.5 Acknowledgements
We thank the Cahuilla Band of Mission Indians Reservation for graciously allowing us to
deploy instruments on tribal land. The study was supported by the U.S. Department of Energy
(awards DE-SC0016520 and DE-SC0016527) and the European Research Council under Grant
817803, FAULTSCAN.

102
6. Discussion
6.1 Summary
Characterizing the evolution of earthquakes and faults is essential for understanding
earthquake and faulting mechanics, providing important constraints for mitigating earthquake
hazards, and revealing the related tectonic processes. Frequently occurring small earthquakes
provide rich information of the spatiotemporal evolution of major ruptures and the surrounding
crustal volume.
Using a large number of small earthquakes can illuminate the fault zone properties major
ruptures with fewer assumptions about major fault geometry and can better capture their nature.
Therefore, we analyzed the earthquake properties in the San Jacinto fault zone and observed
highly different seismicity patterns in the near-fault, intrafault and off-fault areas (Cheng et al.,
2018). Five moderate earthquakes were followed by abundant off-fault aftershocks and none of
these aftershock sequences overlaps. Both the historical seismicity and moderate aftershock
sequences consistently indicate that the major ruptures involved different failure processes along
the main faults and in the surrounding crustal volumes, suggesting the importance of
incorporating a volumetric framework for analyzing major ruptures instead of using a single fault
plane. For example, when all events are projected on the main fault surfaces, the discrepancy
between the geodetic locking depth and the maximum depth of seismicity in the San Jacinto
Fault zone was thought to be caused by a deep creeping zone (Wdowinski, 2007; Meng & Peng,
2016). Using a volumetric perspective reveals that the near-fault seismic depth is comparable to
the geodetic locking depth and most deep earthquakes are off-fault, which provides a different
explanation for the observed discrepancy between geodetic and seismic locking depth.
Therefore, analyzing the depth extent of seismicity in a volumetric framework may
provide a fundamental rethinking of the governing mechanics and the dynamics of the lower
103
crust. In Chapter 2, we systematically investigated the temporal evolution of seismic depth in
southern California following the occurrence of five M>=6.7 earthquakes (Cheng & Ben-Zion,
2019; Cheng & Ben-Zion, 2020). We observed that the maximum aftershock depth increases
abruptly following the mainshocks and gradually recovers after several years. The deeper-than-
usual early aftershocks are widely distributed around the major ruptures, suggesting that the
elevated post-mainshock strain rates cause the deepening of brittle-ductile transition depth in the
large volumes around major ruptures. The cumulative occurrence of deep early aftershocks may
produce considerable damage volume in the lower crust, create abundant pathways for the
interactions between fluid and rocks, facilitate metamorphic reactions, and lead to long-term
effects on the properties and dynamics of the lower crust (Jamtveit et al., 2018).
While major ruptures often have a considerable effect on their surrounding fault zone
properties, the fault zone properties also affect the rupture behaviors. 2019 M7.1 Ridgecrest
sequence occurred along a previously not well-recognized fault zone with complex fault
geometry, which provides us to a great opportunity to investigate the evolution of the major
ruptures and their surrounding fault zone. So, we analyzed the earthquake properties before,
during, and after the M7.1 Ridgecrest earthquake. We find a long-term increase of the regional
shear stress over the 20 years before the M7.1 mainshock, the terminations of the M6.4 and M7.1
events around the areas with strong velocity contrast or fault intersections, as well as a 5-10 km
wide zone with considerable rock damage in the surrounding upper and lower crust. The results
highlight the heterogeneous volumetric nature of crustal deformation, which motivates us to use
high-resolution geodetic and seismic data to monitor the evolving stress field and fault zone
damage.
104
One possible way to identify and monitor the local rock damage during earthquake
rupture processes is to resolve the isotropic components of earthquakes. However, the isotropic
radiations are hard to resolve due to their short wavelength and fast decay. Benefitting from the
nearfield data in the Ridgecrest area, we resolved the source mechanisms of the Ridgecrest
sequence and observed significant isotropic components. The significant isotropic components
near rupture tips and intersections indicate rock fracturing involved in the brittle deformation,
which can cause considerable brittle damage, generate new faults, and change the fault zone
properties. The solved isotropic components decrease dramatically without nearfield data,
suggesting the necessity of using nearfield data for imaging detailed rupture processes.
For more detailed nearfield observations, many dense arrays have been deployed and
widely used for high-resolution fault imaging and earthquake characterizations. However, there
is few ways to combine dense array data with the data from the surrounding stations for
earthquake detection. Therefore, we combined the small spacing of the array and the large
aperture of the regional stations and developed an automated earthquake detection and location
method. The method exhibits high accuracy in time (98% accuracy) and high resolution in space
(~ 1km) without using any local velocity models or seismic-waveform features. The method can
be applied to detecting earthquake and surface signals, exploring the signal sources, and
providing phases for tomography, which is potential to improve our understanding of crustal
properties and dynamics.
6.2 Future research directions
The findings presented in this study have important implications for earthquake and
faulting mechanics. They also offer a number of future research directions that will help to
monitor earthquakes and faults from a volumetric perspective.
105
6.2.1 Crustal stress evolution
Earthquakes occur when stress accumulated in the crust exceeds its strength. Therefore,
identification of areas with stress concentrations would help us to monitor earthquake
preparation processes. However, current spatiotemporal resolution of stress field is still very low
due to large uncertainties (>20 degree) of input earthquake focal mechanisms and the limited
knowledge of fault plane orientations. I plan to develop new methods to further improve focal
mechanism calculations using relative radiation patterns of co-located earthquakes, determine
fault plane orientations from earthquake rupture directivities, and delineate more detailed
evolution of fault geometry and crustal stress. The spatiotemporal variations of crustal stress
field have significant implications to plate motions (e.g., subduction zones, mid-ocean ridges,
continental collision zones), climate changes (e.g., rain, hurricane), tides (e.g., earth tides, ocean
tides), and human induced perturbations (e.g., wastewater disposal, hydraulic fracturing, mining
activities). Moreover, the stress released by seismic deformations can be compared with aseismic
deformations by quantifying the correlations of stress evolutions with earthquake activities and
surface displacements. The quantification of the strong interactions among stress evolutions, near
surface processes, and crustal deformations would significantly advance our ability to quantify
the interactions of different crustal deformations, estimate the influence of stress perturbations on
earthquake properties, and provide deterministic forecasts of future major ruptures.
6.2.2 Precursory phenomena
Possible precursors preceding major earthquakes have been reported in numerous studies,
including foreshocks, tremors, low-frequency earthquakes, and aseismic slip events. However,
not all of these are followed by major earthquakes. To determine how indicative of impeding
ruptures such precursory candidates are, it is necessary to systematically detect and document
106
these signals. This can only be done with automated algorithms that use intensive computations.
Equipped with the detection method and other tools I developed, I plan to document various
kinds of seismic signals, evaluate whether they foreshadow or perhaps trigger large earthquakes,
and if so, estimate their contributions to major rupture initiations. I also intend to characterize the
variations of different slips, which is critical to understanding the physics of various slip
behaviors and deciphering the dominant earthquake types and their triggering mechanisms in
different tectonic environments, such as geothermal areas, volcanic areas, subduction zones, and
ice sheets.
6.2.3 Real-time ground motion prediction
Earthquake early warning systems utilize differential arrival times of different seismic
phases to characterize earthquakes in real time and send out automated alerts for areas that may
experience intense ground motions. The predicted ground motion intensities still have large
uncertainties due to the uncertainties in the source estimates. Therefore, continuously updating
the source estimates would improve the robustness of real-time early warnings. On this front, I
plan to apply source property estimation methods to large earthquake datasets to obtain real-time
source parameter estimations, and I hope to incorporate the data products into early warning
systems. For example, such operations may help better ground motion prediction in the greater
Los Angeles region and the San Francisco Bay area.

107
Appendix1. Chapter 1 supplementary materials
This supporting information includes additional details regarding the data used and
sensitivity tests of the results. Fig. A1.1 shows the spatial distribution of M ≥ 5 events in the San
Jacinto Fault Zone. Fig. A1.2 shows the stations used for detection and relocation of each
aftershock sequence. Fig. A1.3 shows the temporal variation of seismicity in the trifurcation area
since 1937. Figs. A1.4 to A1.6 show depth-faulting-type distributions calculated using different
fault zone widths. Fig. A1.7 shows the nearest-neighbor distance distribution with different
cutoff magnitudes. Fig. A1.8 and TableA1.2 show the location uncertainties of all relocated
aftershocks and mainshocks, respectively. Fig. A1.9 compares relocation results using different
station distributions. Table A1.1 is the 1D velocity model used for relocation, which was used for
location of SCSN catalog.

Figure A1.1 Map view of M ≥ 5 earthquakes in San Jacinto Fault Zone (SJFZ) from 1932 to 2016. Black
box shows the study area in Fig. 1.1.

108

Figure A1.2 Stations used for detection and relocation. AZ, CI and PB network stations are colored blue,
red and green, respectively. Black box shows the study area in Fig. 1.1.
109

Figure A1.3 Temporal evolution of M4 earthquakes in the trifurcation area (area in Fig. 1.1) from 1932 to
2016.
110

Figure A1.4 Map view of seismicity colored by the relative distance from the main faults using different
fault zone widths.
111

Figure A1.5 Distribution of focal mechanisms for each depth interval within the near-fault, off-fault, and
intra-fault areas using different fault zone widths. Dashed line indicates the estimated geodetic locking
depth from Fialko (2006).

112

Figure A1.6 Depth histograms of seismicity for different fault zone widths.

113

Figure A1.7 (left) Distribution of nearest-neighbor statistics for all available events in the trifurcation
area of San Jacinto Fault zone (2000-2016) with different magnitude cutoff values. The white line shows
the nearest-neighbor distance threshold used for clustering (based on Zaliapin & Ben-Zion, 2016). (right)
Histogram of nearest-neighbor distance 𝜂. Red vertical lines denote the nearest-neighbor distance
threshold used for clustering.

114

Figure A1.8 Estimated location errors for the 2001 M5.2, 2005 M5.0, 2010 M5.4 and 2013 M4.7
aftershock sequences. “For the 2016 Borrego Springs sequence, 95% of the relative errors are less than
150 m (horizontal) and 162 m (vertical).” (Ross et al., 2017a)

115

Figure A1.9 Map view of seismicity for the 2005 M5.0, 2010 M5.4 and 2013 M4.7 aftershock sequences
relocated using differential time data from all available stations (left) and only stations in Fig. A1.1a
(right). The characteristics of the relocated events are similar when using different station datasets for
relocation.

116
Table A1.1 Velocity model used for GrowClust relocations. The velocity model assumes a layered
structure with Vp/Vs ratio as 1.732. (Hutton et al., 2010)
Depth (km) Vp (km/s)
0.0 – 5.5 5.5
5.5 – 16.0 6.3
16.0 – 32.0 6.7
32.0 – 99.0 7.8

Table A1.2 Location errors of the M > 4.5 earthquakes shown in Fig. A1.1 (from Southern California
Seismic Network (SCSN) standard catalog).
Event Horizontal error (km) Depth error (km)
2001 M5.2 0.26 0.34
2005 M5.0 0.16 0.35
2010 M5.4 0.17 0.26
2013 M4.7 0.14 0.32
2016 M5.2 0.13 0.34

117
Appendix2. Chapter 2 supplementary materials

Figure A2.1 Map view of events within selected clusters (dots in Fig. 2.2d). Each event is colored by the
number of surrounding (within 3km epicentral distance) well-located (a) background events and (b)
events in the same cluster, respectively.

Figure A2.2 Map view of well-located events with depth at least (a) 1 km and (b) 2 km below D95b
within the selected clusters (dots in Fig. 2.2d) colored by event occurrence time.

118

Figure A2.3 Map view of (a) events with depth 3km below D95 b and (b) all well-located events within
the selected clusters (dots in Fig. 2.2d) colored by depth differences between D95 c and D95 b. Embedded
plots in (a) show the histograms of epicentral distances from deep events to their mainshock ruptures
planes obtained from finite fault models. D95 b and D95 c are estimated using events within 3km radius and
20 cut-off event number.

Figure A2.4 Map view of (a) events with depth 3km below D95 b and (b) all well-located events within
the selected clusters (dots in Fig. 2.2d) colored by depth differences between D95 c and D95 b. Embedded
plots in (a) show the histograms of epicentral distances from deep events to their mainshock ruptures
planes obtained from finite fault models. D95 b and D95 c are estimated using events within 10km radius
and 80 cut-off event number.

119

Figure A2.5 The cumulative density function (CDF) of epicentral distance to mainshock fault planes for
events in (a) box A, (b) box B, (c) box C, and (d) box D with difference depth ranges.

120

Figure A2.6 (a) Map view of all well-located events within the selected clusters (dots in Fig. 2.2d)
colored by local D95 estimated using all catalog events (D95 all). D95 all is estimated using events within
5km radius and 30 cut-off event number. Events with depth 3km below D95 all are extracted and shown in
(b). White lines denote M 3 6.7 mainshock ruptures planes obtained from finite fault models (Wald &
Heaton, 1994; Wald et al., 1996; Ji et al., 2002; and Wei et al., 2011). The source models of the Joshua
Tree M6.1 foreshock and the Big Bear M6.5 aftershock to 1992 Landers mainshock are also shown in
white lines.

121

Figure A2.7 Depth-time plots of well-located events within (a) box A, (c) box B, (e) box C, and (g) box
D in Fig. 2.3. Events belonging to 1992 M7.3, 1994 M6.7, 1999 M7.1, and 2010 M7.2 mainshock-
aftershock sequences and within corresponding boxes are denoted as red dots in Fig. (a), (b), (c), and (d).
The pink curves denote the temporal D95 in each box for an overlapping window (80% overlap) and a
constant number (1000) of events.

122
Appendix3. Chapter 3 supplementary materials
A3.1 Data and method for computing focal mechanisms using HASH algorithm and deep
learning algorithms
A3.1.1 Data
In this study, we used all earthquake waveforms for events in the study area (Fig. A3.1)
in the regional Southern California Seismic Network (SCSN) catalog for the period from 1981 to
50 days after 2019 M7.1 Ridgecrest earthquake (SCEDC, 2013). We used only EH, HH, BH
channels for the analysis. We also use phase picks and polarities that were manually reviewed by
the seismic analysts at the SCSN. All waveforms were resampled at 100 Hz. We use a 3-20 Hz
filter for phase picking and polarity recognition, and a 1-10 Hz frequency range for S/P
amplitude ratio estimation.
A3.1.2 Method
A3.1.2.1 Phase arrival identification
To pick additional phase arrivals, we apply the generalized phase detection (GPD)
algorithm (Ross et al., 2018b) to earthquake waveforms. For each station-event pair, we calculate
the theoretical arrival times using the event’s origin time and hypocenter as well as the 1D
velocity model in Hutton et al., (2010). Then we detect and pick P- and S-wave arrivals within 1s
from the theoretical arrival times using the GPD algorithms. If multiple picks are within this
window, the closest one is taken.
A3.1.2.2 S/P amplitude ratio calculation
We calculate P- and S-wave amplitudes from pre-processed waveforms recorded at three-
component stations. We use all available P and S arrivals to measure amplitudes. We choose 0.5s
before to 1.5s after P- and S-wave arrivals as the P- and S-wave signal windows and 2.5s to 0.5s
123
before P-wave arrivals as the noise windows. We obtain the vector summation over three-
component waveforms and take the difference between the maximum and the minimum
amplitude values in each time window to be the estimation of the signal or noise amplitudes. If
the time difference between P and S arrivals is larger than 2s and the P-wave SNR is larger than
3, we will calculate its S/P ratio and incorporate it into the focal mechanism calculation.
A3.1.2.3 Polarity recognition
We use a deep learning algorithm to pick first motion polarities from earthquake P-waves
(CNN polarity picker; Ross et al., 2018a). For each P-wave arrival time, we obtain the vertical
component of the waveform and select a 4s waveform segment centered at the phase arrival time
as the input to determine the P-wave first motion polarity using the CNN polarity picker.
A3.1.2.4 Focal mechanism calculation
We first identify additional P-wave phases from all broadband and short-period channels
(EH-) using the GPD algorithm. All available phases are used to select waveforms and compute
S/P amplitude ratios. We then apply the CNN polarity picker to M<2.8 events to obtain
additional P-wave polarities. The obtained S/P amplitude ratios, catalog polarities as well as the
additional CNN polarities are used to calculate the focal mechanism using the HASH program
(Hardebeck & Shearer, 2003). We use the same input parameters as those in Yang et al., (2012).
A3.1.3 Quality classification
We define the focal mechanisms with var_avg (root-mean-square angular difference of
the acceptable nodal planes from the preferred planes) below 25°, prob (fraction of acceptable
mechanisms within 45 degrees from the preferred solutions) larger than 0.8, mfrac (fraction of
polarity misfit) smaller or equal to 0.2, and STDR (distribution of observations relative to the
focal sphere) larger than 0.4 as quality A. From quality A to C, we gradually relax the
124
requirement. Quality B focal mechanisms have var_avg below 35°, prob larger than 0.6, mfrac
smaller or equal to 0.3, and STDR larger than 0.3. Quality C focal mechanisms have var_avg
below 45°, prob larger than 0.4, mfrac smaller or equal to 0.4, and STDR larger than 0.2.
A3.2 Aftershock-mainshock potency ratio
To compute the aftershock-mainshock potency ratio of major earthquake sequences, we
use the quadratic potency-magnitude scaling relations in Ben-Zion & Zhu (2002) to compute the
potency of mainshocks and their aftershocks.
For each M>=6.7 sequences in Southern and Baja California that occurred since 1981, we
compute the mainshock potency values and the aftershock potency values of events within one
day after the mainshock located near the mainshock in the selected boxes (Fig. A3.4), and obtain
the ratio between the summation of aftershock potency values and mainshock potency.
Fig. A3.5 shows the aftershock-mainshock potency ratios of selected major earthquakes. M7.3
Landers and M6.7 Northridge earthquakes have unusually higher aftershock-mainshock potency
ratios (>1%) compared with other earthquakes (<1%).
125

Figure A3.1 Map view of events from 1981 to the 2019 M6.4 event (black dots), from the M6.4 to the
M7.1 event (green dots) and those within 50 days after the M7.1 event (red dots: depth>14km; blue dots:
depth<14km).

126

Figure A3.2 Distributions of epicenters of earthquakes with quality A-C focal mechanisms (a) from 1981
to 2019, (b) from 5 days before to 5 days after the M w7.1 event, (c) and from 5 days to 50 days after the
mainshock as a function of time and distance along the HH’ in Fig. 3.2e. Corresponding temporal
variations of the percentages of normal faulting (red curves), reverse faulting (green curves), and strike-
slip (blue curves) focal mechanisms (d), (e), (f), respectively. Corresponding temporal variations of r NORM
(g), (h), (i), respectively.

127

Figure A3.3 Cross-section views of P-wave velocity along AA’ (Zhang & Lin, 2014) and P-axis
distributions of events that occurred (a) from 1995 to 2010, (b) from 2010 to the 2019 M w6.4 event, (c)
between the M w6.4 and M w7.1 events, and (d) within 0-50 days after the M w7.1 event. The P-axes are
centered at the events’ hypocenters and colored by fault style.

128

Figure A3.4 Cross-section view of P-wave velocity (Zhang & Lin, 2014) along AA’. Magenta Lines
denote the slip boundary of the Mw6.4 event. Magenta stars denote the hypocenters of the M w6.4 and
M w7.1 earthquakes.

Figure A3.5 Map view of all events in relocated catalog (Hauksson et al., 2012) from 1981 to 2019
colored by event depth. White stars show the location of five M>=6.7 earthquakes. Black boxes denote
the chosen area for aftershock selection.
129

Figure A3.6 Aftershock-mainshock potency ratio of five M>=6.7 earthquakes in southern and Baja
California.

130

Table A3.1 Data format of the focal mechanism catalog in the Ridgecrest area (Dataset S1)
Column Information
1 Year
2 Month
3 Day
4 Hour
5 Minute
6 Second
7 Event ID
8 Latitude
9 Longitude
10 Depth
11 Magnitude
12 Strike
13 Dip
14 Rake
15 1
st
nodal plane uncertainty
16 2
nd
nodal plane uncertainty
17 Number of polarities
18 Polarity misfit
19 Number of S/P amplitude ratios
20 Average log10(S/P) amplitude ratio misfit
21 Focal mechanism quality
22 Probability of solution close to real solution
23 Azimuth gap
24 Take-off angle gap
25 Station distribution ratio (STDR)

131
Appendix4. Chapter 4 supplementary materials
A4.1 Introduction
We calculate the moment tensors for events in the 2019 Ridgecrest sequence use a 1D
velocity model and a 3D velocity model in southern California. The comparisons of the results
using these two models are shown in Section A4.2 and Figure A4.1. The moment tensors solved
using 3D velocity model show much less non-double-couple (non-DC) components compared
with those using 1D velocity model, suggesting the importance of using high resolution 3D
velocity model for robust estimation of non-DC components. The relationships between the
percentages of non-DC components and the other event properties (depth, magnitude) are shown
in Figure A4.2.

A4.2 Moment tensor results using 1D velocity model

To evaluate the effect of different velocity models on non-DC components, we invert the
full moment tensors using 1D velocity model in southern California (Hadley & Kanamori, 1977),
and compare the results with those obtained using 3D velocity model (see Section 4).
We first choose all M>3.5 earthquakes in the Ridgecrest area (Fig. 4.1a) and manually
remove the bad waveforms with low signal-to-noise ratios. We keep the inversion parameters the
same as used for 3D moment tensor inversions for comparisons. We obtained moment tensors
for 52 M>3.5 earthquakes and compare the solved non-DC components with those obtained
using 3D velocity model (Fig. A4.1). Many events show strong non-DC components in
inversions using 1D velocity model and very limited non-DC components using the 3D velocity
model. The dramatic decrease of the percentage of non-DC components suggests that the large
non-DC components shown in 1D moment tensor inversion might be due to large misfit between
1D velocity model and the heterogeneous velocity structure. However, some events still have
132
large non-DC components using 3D moment tensor inversion. As shown in Fig. 4.1, co-located
events exhibit highly different percentages of non-DC components, suggesting that the large
non-DC components cannot be fully explained by the inaccuracies in the 3D velocity model and
are more related to the source rupture processes.

Figure A4.1. Comparisons of the percentages of the (a) isotropic components and (b) CLVD components
obtained using 1D and 3D velocity models.
133

Figure A4.2. Variations of the percentage of (upper) ISO components and (lower) CLVD components in
relation to events’ (left) depth and (right) magnitude.

134
Appendix5. Chapter 5 supplementary materials
This electronic supplement contains 9 figures showing an example of a detected events’
waveforms (Fig. A5.1), the strategy for choosing the detection threshold (Fig. A5.2) and the
temporal variation of detection threshold (Fig. A5.7). The spatiotemporal variation of catalog
events in 1-day test dataset is shown in Fig. A5.3 and that of all detected events in 23-day dataset
are shown in Fig. A3.8. For the detected events from 07/21/2018T00:00:00 to
07/22/2018T00:00:00, their location and magnitude uncertainties are shown in Fig. A5.4 and the
comparisons with their corresponding catalog events are shown in Fig. A5.6. The maximum
azimuthal gap of the station coverage is shown in Fig. A5.5. The detection result using average
STA/LTA is shown in Fig. A3.9 and can be compared with Fig. A5.3.

Figure A5.1. Four-second waveforms (15-25 Hz) of the dense array from 2018-07-21T00:27:17 to 2018-
07-21T00:27:21, corresponding to 47-51 s in Fig. 5.3a. Red solid line denotes the detected arrival time.
Red dashed line denotes the hand-pick P-wave arrival.
135

Figure A5.2. Histogram of average neighboring station similarity of the one-day waveform dataset from
07/21/2018T00:00:00 to 07/22/2018T00:00:00. The vertical line shows the 𝐶𝐶
!"#$%
(12 times of the MAD
above the median value).
136

Figure A5.3. (a) Temporal variation and (b) spatial distribution of the catalog events (Hauksson et al.,
2012) from 07/21/2018T00:00:00 to 07/22/2018T00:00:00 scaled by event magnitude. Red box shows the
region plotted in Fig. 5.1 and Fig. 5.6. (c) The catalog events’ CC values obtained using 2-15 Hz (blue
dots) and 15-25 Hz (red dots) waveforms and their relationship to the epicentral distance to the Cahuilla
array.
137

Figure A5.4. Histograms of the estimated uncertainties of the detected events’ (from
07/21/2018T00:00:00 to 07/22/2018T00:00:00) (a) latitudes, (b) longitudes, (c) depths and (d)
magnitudes.
138

Figure A5.5. Map view of the maximum azimuthal gap of the station coverage.
139

Figure A5.6. The comparisons between the catalog events’ (from 07/21/2018T00:00:00 to
07/22/2018T00:00:00) locations and magnitudes estimated in this study and those in the catalog
(Hauksson et al., 2012).

140

Figure A5.7. The temporal variation of the threshold of average neighboring station similarity
𝑎𝑣𝑔𝐶𝐶
!"#$%
used for detection (12 times of the MAD above the median value).
141

Figure A5.8. (a) Temporal variation and (b) spatial distribution of the detected events from
07/20/2018T03:00:00 to 08/12/2018T00:00:00 scaled by event magnitude.
142

Figure A5.9. (a) Waveform and (b) spectrogram of station index 70 in Fig. 5.3a. (c) Average STA/LTA
(0.5 short time window and 5s long time window) of all 99 stations without time shift. (d) Maximum
average STA/LTA of all slowness-location combinations.

143
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Abstract (if available)

Abstract The interactions between major ruptures and faults have significant impact on their individual properties. Many standard mechanical concepts and models assume that a major rupture is a stick-slip along a single surface in a homogeneous continuum solid. While these simplified models provide important insights to the earthquake and fault mechanics, they contradict to the observed complex earthquake features and may obscure important processes associated with the major ruptures. In this thesis, I investigate how the earthquake rupture processes deviate from the simplified models using small earthquake properties and understand the implications from the observed deviations. ? To determine the validity of the single-fault-surface assumption, I investigate the differences of earthquake properties in near-fault and off-fault regions and the complexities of five M>4.5 earthquake sequences in the San Jacinto Fault Zone. The results show highly diverse volumetric faulting patterns of the fault networks, suggesting the necessity to investigate the rupture processes from a volumetric perspective. Therefore, I implement the volumetric framework to examine the transient changes of seismic depth following four moderate-large earthquakes in southern and Baja California. Two mechanisms are considered for the changes of seismic depth: seismic-aseismic transition and brittle-ductile transition. The results show wide-spread deeper-than-usual early aftershocks around the main faults, suggesting brittle-ductile transition as the mechanism governing the base of the seismogenic zone. In addition to the depth variations of seismicity, I monitor the temporal variations of earthquake properties before, during, and after the 2019 M7.1 Ridgecrest sequence. The variations suggest a long-term increase of shear stress in 20 years prior to the sequence, the termination of the M6.4 and M7.1 earthquakes near fault zone barriers, and the caused diverse volumetric damage in the surrounding upper and lower crust. The complex failure pattern of the Ridgecrest sequence suggests that earthquake ruptures may generate damage-related radiations. Therefore, I study the spatiotemporal variation of isotropic components in the 2019 Ridgecrest sequence. Most events with significant isotropic components occurred at the beginning of the sequence and are located around rupture ends, intersections, which likely reflect damage rock fracturing. ? To further enhance the monitoring resolution of fault zone evolutions and major ruptures, it is important to improve the ability of earthquake detection. On this front, I propose a new automated method to detect and locate earthquakes using a dense array and its nearby regional stations. The method achieves automated detection with high spatiotemporal resolution without using any prior information about seismic-waveform features or local velocity model.

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Asset Metadata

Creator Cheng, Yifang (author)

Core Title Volumetric interactions between major ruptures and fault zones illuminated by small earthquake properties

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Geological Sciences

Degree Conferral Date 2021-08

Publication Date 07/26/2021

Defense Date 05/18/2021

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag fault zone,OAI-PMH Harvest,seismicity

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ben-Zion, Yehuda (committee chair), Haas, Stephan (committee member), Vidale, John (committee member)

Creator Email chengyif@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC15623324

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