University of Southern California Dissertations and Theses

High-resolution imaging and monitoring of fault zones and shallow structures: case studies in southern California and on Mars

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High-resolution imaging and monitoring of fault zones and shallow structures: case studies in southern California and on Mars

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High-resolution imaging and monitoring of fault zones and shallow
structures:

Case studies in southern California and on Mars

by

Lei Qin

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

May 2021

Copyright 2021 Lei Qin
ii

Dedication

To my father, in loving memory
iii
Acknowledgements
I want to thank my parents for giving me tremendous love and support during my adventures
in life. I’m also blessed to be with My fiancé, Hongrui Qiu, who was also a Ph.D. student during
2013-2019 working with Yehuda. We’ve gone through all the happiness and difficulties together
in the past 10 years. Without my family’s support, I would not be able to finish my Ph.D.
successfully.
I also would like to express my special appreciation to my Ph.D. advisor, Professor Yehuda
Ben-Zion, who is a great mentor to my research and life. Throughout my Ph.D. study, he always
spares time for me and helps me to focus on my research while keeping the big picture in mind.
He also teaches me valuable skills about scientific writing and presentation that is critical for my
career. I would also like to thank, Professor Charles Sammis, Professor Frank Corsetti, Professor
Richard Leahy, and Professor David Okaya, for serving on my qualifying exam and thesis
defense committees and providing useful comments on my research.
I’d like to thank all my collaborators during my Ph.D. study for their support and feedback
that greatly improve my research. The ones that most directly involved in my work are: Yehuda
Ben-Zion, Hongrui Qiu, Pieter-Edward Share, Frank L. Vernon, Luis Fabian Bonilla, Zachary
Ross, Christopher W. Johnson, Jamison H. Steidl, Sunyoung Park, Amir A. Allam, Nori Nakata,
and Alan Levander. I’m also grateful to all my friends, Yifang Cheng, Niloufar Abolfathian, Gen
Li, Christian Wu, Xueyao Shen etc., and all the Earth Science department staff, John McRaney,
John Yu, Cynthia Waite, Karen Young, Vardui Ter-Simonian, Tran Huynh, Deborah Gormley,
Barbara Grubb, and Miguel Rincon, for all your help and care during Ph.D. study.
iv
Table of Contents
Dedication ...................................................................................................................................... ii
Acknowledgements ...................................................................................................................... iii
List of Tables ................................................................................................................................ vi
List of Figures .............................................................................................................................. vii
Abstract ..................................................................................................................................... xviii
Introduction ................................................................................................................................... 1
1. Internal structure of the San Jacinto fault zone in the trifurcation area southeast of
Anza, California, from data of dense seismic arrays ................................................................. 5
1.0 Summary ........................................................................................................................................... 5
1.1 Background ....................................................................................................................................... 6
1.2 Data .................................................................................................................................................... 8
1.3 Analysis ............................................................................................................................................ 11
1.3.1 Waveform changes .................................................................................................................... 11
1.3.2 Delay time analysis of teleseismic arrivals ................................................................................... 14
1.3.4 Fault Zone Trapped Waves ....................................................................................................... 19
1.4. Discussion and Conclusions .......................................................................................................... 28
1.5 Acknowledgments ........................................................................................................................... 31
2. Internal structure of the San Jacinto fault zone at the Ramona Reservation, north of
Anza, California, from dense array seismic data ..................................................................... 32
2.0 Summary ......................................................................................................................................... 32
2.1 Background ..................................................................................................................................... 33
2.2 Data and preprocessing .................................................................................................................. 36
2.3 Analyses ........................................................................................................................................... 38
2.3.1 Waveform changes .................................................................................................................... 38
2.3.2 Delay time analysis ................................................................................................................... 40
2.3.3 Fault zone head waves ............................................................................................................... 43
2.3.4 Fault zone trapped waves .......................................................................................................... 53
2.4 Discussion and Conclusions ........................................................................................................... 56
2.5 Acknowledgements ......................................................................................................................... 60
3. Imaging and monitoring temporal changes of shallow seismic velocities at the Garner
Valley near Anza, California, following the M7.2 2010 El Mayor-Cucapah earthquake .... 61
3.0 Summary ......................................................................................................................................... 61
3.1 Background ..................................................................................................................................... 62
3.2 Data .................................................................................................................................................. 64
3.3 Analysis and results ........................................................................................................................ 67
3.3.1 Analysis of direct P- and S-wave .............................................................................................. 67
3.3.2 Temporal changes of seismic velocities after the EMC earthquake ......................................... 70
3.4 Discussion and Conclusions ........................................................................................................... 80
3.5 Acknowledgements ......................................................................................................................... 86
v
4. Daily changes of seismic velocities in shallow materials on Mars .................................. 87
4.0 Summary ......................................................................................................................................... 87
4.1 Background ..................................................................................................................................... 87
4.2 Data and Methods ........................................................................................................................... 90
4.2.1 Data properties and preprocessing ............................................................................................ 90
4.2.2 Properties of ACF ...................................................................................................................... 92
4.2.3 Variations of travel time and resonance frequencies ................................................................. 93
4.2.4 Influence of source variations ................................................................................................... 95
4.3 Results .............................................................................................................................................. 96
4.3.1 / measurements ................................................................................................................... 96
4.3.2 / measurements .................................................................................................................. 99
4.4 Discussion ...................................................................................................................................... 101
4.4.1 Variation of the lander ............................................................................................................. 101
4.4.2 Thermoelastic strain ................................................................................................................ 103
4.5 Conclusions .................................................................................................................................... 108
4.6 Acknowledgements ....................................................................................................................... 108
5. Spectral characteristics of daily to seasonal ground motion at the Piñon Flats
Observatory from coherence of seismic data ......................................................................... 110
5.0 Summary ....................................................................................................................................... 110
5.1 Background ................................................................................................................................... 111
5.2 Data and methods ......................................................................................................................... 114
5.2.1 Data ......................................................................................................................................... 114
5.2.2 Methods ................................................................................................................................... 115
5.3 Analysis and results ...................................................................................................................... 117
5.3.1 Basic data features from cross-station seismic coherences ..................................................... 117
5.3.2 Local atmospheric effects ........................................................................................................ 125
5.3.3 Seasonal variations in cross-station seismic coherences ......................................................... 132
5.3.4 Cross-station seismic coherence anomalies ............................................................................ 136
5.4 Discussion and conclusions .......................................................................................................... 138
5.5 Data and resources ....................................................................................................................... 142
5.6 Acknowledgements ....................................................................................................................... 143
6. Discussion .......................................................................................................................... 144
Appendices ................................................................................................................................. 147
Appendix A: Chapter 1 supplementary materials ........................................................................... 147
Appendix B: Chapter 2 supplementary materials ........................................................................... 150
Appendix C: Chapter 3 supplementary materials ........................................................................... 153
Appendix D: Chapter 4 supplementary materials ........................................................................... 161
Appendix E: Chapter 5 supplementary materials ........................................................................... 170
References .................................................................................................................................. 178

vi
List of Tables
Table 1.1. Selected teleseismic events ........................................................................................... 9
Table 3.1. Average velocities and velocity reductions between stations ..................................... 70
Table 3.2. Average velocity changes from surface to borehole depths ........................................ 75
Table 5.1. Summary of main features ........................................................................................ 142

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List of Figures
Figure 1.1. (a) Location map of the SJFZ and the ∼20,000 local events used in the study. Fault
traces are shown with black lines. The green triangle marks the SGB site, and the four white
triangles are four other linear arrays straddling the Clark Fault (BB, RA, DW and JF from north
to south). SAF and EF denote the San Andreas and Elsinore faults. Yellow and red circles
represent events recorded by the linear SGB and dense rectangular arrays, respectively. The long
blue line (AA’) indicates the geological strike direction of the Clark fault. The blue (200 km ×
50 km) and cyan (60 km × 20 km) boxes, centered at the SGB site, include events used for the
FZTW and delay time analysis, respectively. The lower panel is the depth profile projected to the
cross-section AA’. The two cyan lines correspond to boundaries of the cyan box in the top panel
and the five triangles correspond to the five linear arrays. (b) Locations of nine teleseismic
events with high-quality first arrivals. Color represents depth and circle size represents
magnitude. TS1 is the example event in Fig. 1.6(a). See Table 1.1 for additional information. (c)
Sensors of the linear SGB array (white balloons with labels) and dense rectangular array (dots).
Orange lines indicate fault surface traces including the main Clark fault (MCF). The row and
column numbers of the dense array start from the SW corner and increase toward the NW and
NE (cyan arrows), respectively. Row 13 of the dense array, closest to the linear SGB array, is
labeled. Data of rows 12–18 (green sensors) are stacked to identify S-type FZTW. Some sensors
are colored yellow for identification of row and column numbers. ................................................ 8
Figure 1.2. Average P-wave velocity over the depth range 1–10 km based on the tomography
results of Allam & Ben-Zion (2012). The town of Anza and several linear arrays are shown by a
square and triangles, respectively. Black lines represent fault surface traces. The SJFZ branches
into three faults (Buck Ridge, Clark and Coyote Creek) near the SGB site. ................................ 10
Figure 1.3. Location map of events (black dots) used to analyze waveform changes across the
array. The long blue line (AA’) is the same as in Fig. 1.1(a) and the short blue line perpendicular
to AA’ is centered at the SGB site. The two lines separate the area into four quadrants with
events colored by orange, yellow, purple and cyan showing clear waveform changes in row 13 of
the dense array. The stars mark the four example events (EQ1∼4) from the four quadrants. The
lower panel is the depth profile projected to AA’. ........................................................................ 12
Figure 1.4. Waveforms (0.5–20 Hz) of four example events (stars in Fig. 1.3) recorded by row
13. Horizontal axis is the time relative to the origin time (all future plots use the same convention
unless otherwise stated). The red dashed line, corresponding to column 32, indicates the location
with clear waveform changes. The light orange lines mark phases that only exist on one side of
the fault. ........................................................................................................................................ 13
Figure 1.5. Waveforms (0.5–20 Hz) of event EQ3 recorded by (a) row 01, (b) row 10 and (c)
row 19. The red dashed lines indicate locations of clear waveform changes. .............................. 13
Figure 1.6. Delay time analysis results from teleseismic events. (a) Waveforms (0.1–1.0 Hz) of
TS1 (Fig. 1.1b) recorded by row 13. The red dashed lines indicate the 5.5 s time window for the
cross-correlation. (b) Results from event TS1: observed delay time (ODT, red triangles) obtained
by cross-correlation and relative delay time (RDT, blue triangles) after event-station geometry
and station elevation corrections. (c) Average observed delay time (AODT, red triangles) and
average relative delay time (ARDT, blue triangles) from all the nine teleseismic events. The error
bar is one standard deviation. (d) Station elevation profile of row 13. ......................................... 16
Figure 1.7. Delay time analysis results of data from the dense (a)–(c) and linear SGB (d)–(e)
arrays. (a) Waveforms (0.5–20 Hz) of an event recorded by row 13 of the dense array. The red
viii
triangles represent automatic P picks. The location (column 32) of waveform change is indicated
by a red dashed line. Potential P-type FZTW (see Section 1.3.4 for details) is marked by the
orange box. (b). Along-path average slowness calculated from the data in (a). (c) Statistical result
on relative slowness from data recorded by the dense array. The dots represent the mean value of
relative slowness and the error bar is one standard deviation. (d) Histogram of relative slowness
from data of station SGBS2 of the linear array with average relative slowness marked by the red
dashed line. (e) Average relative slowness obtained from events at different locations recorded
by the SGB array. The error bar is also one standard deviation. .................................................. 17
Figure 1.8. Location map of events (black circles) used for P-type FZTW analysis in the dense
array. The two perpendicular blue lines are the same as in Fig. 1.3. The orange, yellow, purple
and cyan circles mark events from the four quadrants that are confirmed to generate P-type
FZTW. The stars represent four example events (P-TW1 to P-TW4). The lower panel is the
depth profile projected on the cross-section AA’. ........................................................................ 22
Figure 1.9. Waveforms (0.5–20 Hz) of four example events (stars in Fig. 1.8) recorded by row
13 of the dense array. The red dashed lines represent locations of waveform changes. The blue
and orange boxes include the observed P-type FZTW. ................................................................ 23
Figure 1.10. Waveforms (0.5–20 Hz) of event P-TW3 (Fig. 1.8) recorded by rows 09, 11, 12, 16,
19 and 20 of the dense array. The red dashed lines indicate locations of waveform changes and
the orange boxes mark observed P-type FZTW. .......................................................................... 23
Figure 1.11. Histogram of automatic P-type FZTW detection results at different stations of row
13................................................................................................................................................... 24
Figure 1.12. Location map of events for S-type FZTW study. The large blue box and line AA’
are the same as in Fig. 1.1(a). Purple diamonds and black dots mark events used in data of dense
and linear SGB arrays, respectively. Orange diamonds and yellow circles represent events that
are confirmed to generate S-type FZTW in the dense and SGB arrays, respectively. Waveforms
from S-TW1 (red diamond) and S-TW2 (red circle) are shown and modeled in Figs 1.13&1.14,
respectively. Inversion results of S-TW3 and S-TW4 (red circles) are shown in Figs A1.2&A1.3
in Chapter APPENDIX 1. The lower panel is depth profile projected to the cross-section AA’
with red dashed line marking a depth of 15 km. ........................................................................... 26
Figure 1.13. Stacked waveforms at rows 12–18 generated by event S-TW1 (Fig. 1.12, red
diamond). Direct P and S waves are labeled by red dashed lines and orange boxes mark P- and S-
types FZTW. ................................................................................................................................. 27
Figure 1.14. Inversion results of waveforms generated by event S-TW2 (Fig. 1.12, red
diamond). (a) Comparison between observed (black) and synthetic (red) seismograms. (b)
Parameter-space results from last 10 inversion generations. Green dots represent the tested model
parameters and black circles mark the best-fitting parameters used to generate the synthetic
waveforms in (a). The black curves give probability density functions of the model parameters.
....................................................................................................................................................... 27
Figure 1.15. A simplified velocity model of the SGB site. Circles and balloons represent stations
of the dense and linear SGB arrays, respectively. The labeled rows and columns are the same as
in Fig. 1.1(a). Orange lines are fault surface traces. Yellow sensors mark the location of the main
seismogenic fault inferred from waveform changes. A low-velocity zone that generates P- and S-
types FZTW is beneath the stations in red. The main Clark fault (MCF) separates locally faster
material on the SW (cyan) from locally slower rocks on the NE (pink). The local velocity
contrast across the MCF is reversed with respect to the large-scale structure. ............................. 29
ix
Figure 2.1. (a). All local events recorded by the short RA and long RR arrays. Lower panel
shows the depth profile projected to AA’. The Ramona site is shown as a red triangle, and other
four linear arrays along the SJFZ (BB, SGB, DW, JF from NW to SE) are plotted with white
triangles. The blue, cyan, and red boxes define the areas where we search for FZTW and
waveform changes, FZHW, and perform delay time analysis of local earthquakes, respectively.
The four labeled events (evt 1-4; big yellow stars) are examples for waveform change study (Fig.
2.4), and TW1 (big green square) is the FZTW candidate event (Figs 2.12-2.13). (b). All
teleseismic events in 2012-2017 that are used in the short RA (circles) and long RR (stars) array
studies. Color represents event depth and circle size indicates event magnitude. The RA site
(black triangle) and example event Tele1 (Fig. 2.3) are outlined in white. .................................. 35
Figure 2.2. (a). Layout of the short RA (red balloons) and long RR (non-red balloons) arrays.
Several station numbers are labeled with the same color of the station symbol. The station
numbers increase from SW to NE, 01-12 for the RA and 01-65 (following the white dashed
lines) for the RR arrays. Green balloons are RR stations used for beamforming. The orange lines
represent the three fault surface traces of the Clark Fault that are related to previous M > 6
earthquakes, labeled as F1, F2, and F3. (b). Station elevation profiles for the RR (blue triangles)
and RA (red triangles) arrays. ....................................................................................................... 37
Figure 2.3. (a). 1 Hz lowpass filtered waveforms from event Tele1 (labeled in Fig. 2.1b). Zero
time indicates P arrival, and blue lines represent the 2.5 s time window for cross correlation.
Low SNR traces are removed. (b) and (c) are the median cross correlation coefficients of the RR
(b) and RA (c) arrays from all the teleseismic events. The locations of three fault surface traces
(F1, F2, F3) are plotted with black dashed lines. .......................................................................... 39
Figure 2.4. 1-20 Hz bandpass filtered waveforms from four local events (evt 1-4, labeled in Fig.
2.1a). Locations of the three fault surface traces (F1, F2, F3) are labeled. .................................. 40
Figure 2.5. Delay time analysis results from teleseismic events (a) and relative slowness analysis
from local events (b-d). (a). Teleseismic P wave delay time results from a single event Tele 1
(faded green line labeled as “Tele1"; event location is labeled in Fig. 2.1b and waveforms are
shown in Fig. 2.3a), median delay time from all events at the RR (black dashed line) and RA
(green dashed line) arrays, corrected median delay time using vref=4 km/s at the RR (blue dots)
and RA (red dots) arrays with error bar being one standard error. (b). Relative slowness from
local earthquakes at the RR (blue dots) and RA (red dots) arrays. Error bar is one standard error.
(c) and (d) show histograms and median values (red lines) of relative slowness at stations RA01
and RR15, respectively. ................................................................................................................ 43
Figure 2.6. Events that generate local (red squares) and regional (purple squares) FZHW. The
red star and circle represent the candidate and reference events for local FZHW (Fig. 2.7), and
purple star and circle for regional FZHW (Fig. 2.9). .................................................................... 44
Figure 2.7. 1-20 Hz bandpass filtered waveforms from a candidate event (a; red star in Fig. 2.6)
with and a reference event (b; red dot in Fig. 2.6) without local FZHW. Green and red dashed
lines show the FZHW and impulsive P arrivals, respectively. Waveforms from each event are
uniformly normalized by the array maximum, and zero time corresponds to event’s origin time.
....................................................................................................................................................... 45
Figure 2.8. Waveforms at stations RR47 (a) and RR50 (b) from all events (red squares in Fig.
2.6) that generate local FZHW. FZHW arrivals are labeled with green squares. Waveforms are
normalized by the array maximum for each event to preserve the amplitude information, and
aligned according to the first impulsive waves, i.e. direct P arrivals (zero time, red dashed lines).
....................................................................................................................................................... 47
x
Figure 2.9. 1-20 Hz bandpass filtered waveforms from a candidate event (a; purple star in Fig.
2.6) with and a reference event (b; purple dot in Fig. 2.6) without regional FZHW. The layout is
the same as in Fig. 2.7, but a longer time window is shown to highlight the original 1.5 s
reference beam trace for the central station RR34 (dark red) associated with the frequency
windowed beam stacks in Fig. 2.11(c). ......................................................................................... 48
Figure 2.10. Waveforms at stations RR47 (a) and RR50 (b) from all events (purple squares in
Fig. 2.6) that generate regional FZHW. The layout is the same as in Fig. 2.8. ............................ 49
Figure 2.11. Separation of FZHW and direct P wavefronts using beamforming. (a).
Beamforming results for the frequency band 4-6 Hz. The red cross represents a prominent
coherent phase within the FZHW spectrum. Radius of this beam to 50% of peak amplitude
corresponds to a slowness difference of ~0.05 s/km. (b). Beamforming results for the frequency
band 12-14 Hz. The black cross represents a prominent coherent phase within the direct P wave
spectrum. The beam radius here corresponds to a slowness difference of ~0.03 s/km. (c). Beam
traces and energy envelopes for the beamforming results in (a) (red) and (b) (black). (d).
Horizontal particle motions for the FZHW beam trace (red) and direct P beam trace (black)
compared to their respective azimuths determined in (a) (gray solid line) and (b) (gray dashed
line). .............................................................................................................................................. 51
Figure 2.12. Vertical (a) and fault parallel (b) component waveforms from the FZTW candidate
event TW1 (labeled in Fig. 2.1a). P- and S- type FZTW are labeled with red dashed boxes. ..... 54
Figure 2.13. S-type FZTW inversion results from event TW1. (a). Parameter space plot from the
last 2000 inversion models showing the fitness values (green dots), probability density functions
(black curves), and best fitting model (black dots). From top to bottom (left to right) shows the
shear wave velocity of host rocks, and shear wave velocity, Q value, width, SW edge and
propagation distance of FZTW inside the damage zone. (b). Observed (black) and synthetic (red)
waveforms from the best-fitting model (black dots in a). ............................................................. 55
Figure 2.14. A schematic local velocity model at the study site. ................................................. 56
Figure 3.1. (a). All the events that have passed the selection criteria in the travel time analysis of
direct arrivals. The star in the SW of GVDA shows the location of the example event (Fig. 3.4).
(b). All the events that are analyzed in the temporal change study. Black dots represent events
that are eliminated by the selection criteria. Yellow and green symbols represent events that
occurred before and after the EMC earthquake respectively. Squares and circles indicate events
that are used in the autocorrelation study and seismic interferometry study, respectively. .......... 65
Figure 3.2. (a). The conceptual cross-section placement and surface layout (lower right corner
inset) of the GVDA (available from http://nees.ucsb.edu/facilities/GVDA). Please note the plot is
not to scale vertically. Numbers on the top represent channel location codes and depths are
labeled beside the sensors. Different symbols in each layer represent different materials from top
to bottom: silty sand to sandy silt, sandy silt to clay, sand to sandy silt, sand to silty sand,
weathered granite and granite bedrock. Seismic stations (red dots) 00-05 and pore pressure
sensors (blue dots) 60-63 are used. (b). Velocity models of the GVDA site in the top 150 m from
Bonilla et al. (2002) (dashed lines) and Theodulidis et al. (1996) (solid lines). ........................... 66
Figure 3.3. The transverse (T), radial (R) and vertical (Z) accelerograms (in Gal) from the EMC
earthquake at the surface (a) and 150 m borehole (b) stations of the GVDA. Zero time
corresponds to the occurrence time of the EMC event. Please note the different y scales. .......... 67
Figure 3.4. Example results from one event (shown as a star in Fig. 3.1a). (a)-(c) are the 1-30 Hz
bandpass filtered vertical (P wave), transverse (SH wave), and radial (SV wave) component
waveforms from the six GVDA stations. Red triangles and solid lines represent the estimated
xi
direct arrivals, and blue dashed lines show the time windows used for cross-correlation. (d)-(f)
present the interpolated waveforms in the cross correlation time windows. Surface records are in
black, and borehole records are in blue. The red waveforms represent surface records shifted
based on the time delay obtained from cross-correlation. ............................................................ 68
Figure 3.5. Results from delay time analysis of direct phases. (a)-(c) are the travel time
histograms between the surface station (00) and five borehole stations (01-05) from vertical (a),
transverse (b), and radial (c) components, respectively. (d). Median (dots) and one stand
deviation (error bar) of P (green), SH (red), and SV (blue) wave travel times from boreholes to
the surface station. (e). The obtained velocities and VP/VS ratios assuming constant seismic
velocities between two adjacent stations. The P wave velocity in the top 15 m is plotted with
dotted line because of the limited data resolution. ........................................................................ 69
Figure 3.6. Transverse component waveforms showing free surface reflections before (a), during
(b), and after (c) the EMC earthquake. Blue and red dashed lines represent the up-going and
down-going waves centered at the surface station predicted by the reference travel time obtained
from Section 3.3.1. Blue and red triangles in (b) label the observed direct and reflected waves
from the EMC earthquake, which are delayed with respect to the reference travel time (blue and
red dashed lines). .......................................................................................................................... 73
Figure 3.7. (a). The 10-30 Hz autocorrelation functions (ACFs, color representing amplitudes)
normalized with zero lag amplitudes, reference travel time (black dashed lines), and ACF peaks
(black solid lines) corresponding to free surface reflections from the transverse component at the
22 m borehole station (03). The left, middle and right panels are the results before, during, and
after the EMC earthquake, respectively. Horizontal axes represent the time relative to the
occurrence time of the EMC earthquake, and vertical axes indicate the lag time for
autocorrelation. The 10-30 Hz waveforms from the EMC event are plotted in the middle panel.
(b). The corresponding velocity changes (black solid lines), velocity reduction oscillations (green
shaded areas), and PGAs (blue dashed lines with dots) inside the autocorrelation time windows.
Please note the irregular time axes, different time and PGA scales between the middle and
left/right panels. ............................................................................................................................ 74
Figure 3.8. (a). The 1-30 Hz impulse response functions (IRFs, color representing amplitudes)
normalized with the maximum amplitudes, reference travel time (black dashed lines), and IRF
peaks (solid black lines) from the transverse component between the surface station (00) and 22
m borehole station (03). The layout is similar to Fig. 3.7. The 1-30 Hz waveforms at the
shallower station (in this case, station 00) from the EMC earthquake is plotted inside the middle
panel. (b). The corresponding velocity changes (black solid lines), velocity reduction oscillations
(green shaded areas) and PGAs (blue lines with dots) inside the deconvolution time windows.
Please note the irregular time axes, different time and PGA scales between the middle and
left/right panels. ............................................................................................................................ 76
Figure 3.9. The 1-30 Hz IRFs (a) and corresponding velocity changes (b, c) from the transverse
component recorded by the 6 m (01) and 22 m (03) borehole stations. (b) is the average velocity
changes between stations 01 and 03, obtained from the IRF primary peak at ~0.06 s. (c)
represents the average velocity changes in the top 6 m, obtained from the IRF secondary peak at
~0.12 s, corresponding to waves traveling from station 03 to surface then reflected to station 01.
The blue horizontal axis ticks in (c) indicate Julian days in 2010. ............................................... 77
Figure 3.10. The 1-30 Hz IRFs (a) and corresponding velocity changes (b) from the transverse
component between the 22 m (03) and 150 m (05) borehole stations. The layout is the same as
Fig. 3.8. ......................................................................................................................................... 78
xii
Figure 3.11. Recovery time estimation of velocity changes. Black and red lines represent
observed dv/v curves and the best fitting linear functions. Each plot is labeled with the
station/station-pair numbers and the corresponding recovery time (T) in seconds. The top two
panels show results based on ACF analysis at stations 03 and 04, middle six subplots are IRF
analysis results from six station pairs, and bottom two panels show results based on the
secondary peaks of IRFs from 01-03 and 01-04, respectively. ..................................................... 80
Figure 3.12. The pore pressure recordings (black lines) from the GVDA at different depths and
transverse displacement (blue lines) at the surface station from the EMC earthquake high pass
filtered at 0.1 Hz. Mean values of each pore pressure trace are removed. ................................... 83
Figure 4.1. (a). Two days of air temperature (dashed black line), ground temperature (solid black
line), and wind data (dots) with color representing wind directions. (b). Two days of continuous
seismic recording of the EW component (gray curve). A bandpass filter between 1-5 Hz is
applied to the data. A smoothed envelope (red curve) is obtained using a 10-s-long moving
window, and the data after temporal balancing (Section 4.2.1) is shown in black. The purple
dashed lines indicate 8 am-12 pm local time. The waveform in black is magnified by a factor of
200 for illustration. (c). Spectrograms of the raw EW-component data. (d). An example
autocorrelation function (ACF; black curve) calculated at 1 pm on Sol 98 (hour 13), and the ACF
after source deconvolution (red curve; Section 4.2.2). (e). The spectra of the two ACFs in (d).
The approximate source spectrum used in the source deconvolution is illustrated in blue. ......... 91
Figure 4.2. (a). Two days of ACFs for the EW component data. (b). ACFs for the reference trace
(black dashed waveform), i.e., the stack of all ACFs in (a), and an example trace from 1 pm of
Sol 98 (black solid waveforms). The stacked envelope for all ACFs is shown in red with three
local maxima labeled by their lapse times. ................................................................................... 94
Figure 4.3. (a). Spectrogram of the ACFs calculated using the raw EW component recording.
Five resonance frequencies are clearly observed and tracked with black curves (at ~3.3, ~4.1,
~6.8, ~8.5 and ~9.8 Hz) as a function of recording time. (b). Maximum daily variation values of -
df/f for the five resonance frequencies shown in (a). .................................................................... 94
Figure 4.4. (a) Temporal patterns of travel time (dt/t; blue curve), frequency peak (-df/f; orange
curve) at ~4.1 Hz, linearly scaled ground temperature (black solid curves), and the best fitting
dt/t curve (black dashed curves) obtained by shifting the ground temperature by t0. The reference
frequency f0 and best fitting phase delay t0 are labeled. (b)-(e) Same as (a) but only for frequency
peaks at ~3.3, ~6.8, ~8.5, and ~9.8 Hz, respectively. ................................................................... 98
Figure 4.5. Amplitude of thermoelastic strain calculated at different depths y (0.1 m, 0.5 m, 1 m,
10 m, 20 m, and 200 m) relative to the bottom of the decoupled layer. The model consists of an
elastic half-space covered by a 0.1 m (yb = 0.1 m) decoupled layer with thermal diffusivity of
2×10
-8
m
2
/s. Results are computed for and of the elastic half-space in the ranges 2×10
-8
-10
-4

m
2
/s and 10
-5
-10
-3
°C
-1
, respectively. The wavelength of temperature field and Poisson’s ratio
are 15 km and 0.3, respectively. ................................................................................................. 106
Figure 5.1. (a). Large-scale map showing the locations of PY array (triangle), the 2016 Mw 5.2
Borrego Springs earthquake (BSE, star), and the buoy sensor 46086 (dot). (b). The PY array
layout with three eccentric circles (dashed circles). All stations are labeled with the station codes.
Squares and balloons represent the STS5 and Trillium 120PH sensors, respectively. Triangles
indicate the micro-barometers co-located with the seismometers, and the circle represents the
B084 borehole station at a depth of 148 m. ................................................................................ 113
Figure 5.2. HHE component results on Julian day 114, 2016 at stations 01 and 02 of the PY
array. (a). Detrended waveforms at 01 and 02. (b). One-day coherogram. (c) and (d) are the one-
xiii
day spectrograms from 01 (c) and 02 (d). The dashed boxes indicate the example tele (1) and
local (2) seismic arrivals, respectively. ....................................................................................... 118
Figure 5.3. HHZ component results on Julian day 114, 2016 at stations 01 and 02 of the PY
array. The layout is the same as Fig. 5.2. .................................................................................... 119
Figure 5.4. Three component median coherences (a) and spectra in counts
2
/Hz (b) at stations 01
and 02 on Julian day 114, 2016. ................................................................................................. 120
Figure 5.5. HHE component results on Julian day 114, 2016 (same day as in Figs 5.2-5.4) at
stations PY01 (surface) and B084 (148m-deep borehole). Instrument responses are removed. (a)
is the coherogram, and (b) and (c) show the spectrograms in (m/s)
2
/Hz from PY01 (b) and B084
(c). ............................................................................................................................................... 121
Figure 5.6. Three-year coherograms from HHE component at three STS5 (a, c, e) and thee
Trillium 120PH (b, d, f) station pairs. Each coherogram is labeled with the corresponding station
codes and interstation distances. The arrows indicate the beginnings of years 2015, 2016 and
2017 (same for all the following figures). The dashed circles in (e) and (f) point out the high-
coherence anomalies. .................................................................................................................. 122
Figure 5.7. Three-year median coherences from HHE (a), HHN (b) and HHZ (c) components at
three STS5 (01-02, 05-08, 10-11) and three Trillium120-PH (03-04, 06-07, 09-12) station pairs.
The interstation distances are 65 m, 330 m, and 780 m for 01-02/03-04, 05-08/06-07 and 10-
11/09-12 respectively. ................................................................................................................. 122
Figure 5.8. HHE component results from teleseismic events. (a). 1 Hz lowpass filtered HHE
waveforms from event 37381445 (labeled in Fig. E5.8a), at stations 01 (upper panel) and 02
(lower panel). The horizontal axis represents the time in seconds after the earthquake occurrence
time, and vertical dashed lines indicate the time window in which the coherences and spectra are
calculated. (b). Spectra (solid and dashed lines) and coherence (solid line with dots) calculated
from the data sets in (a). (c). HHE coherences (thin solid lines) from all teleseismic events (Fig.
E5.8a) and the corresponding median value (thick dashed line). ............................................... 125
Figure 5.9. 0.01-0.05 Hz bandpass filtered seismic (BH components) and barometric (BDO)
recordings at stations 01 (a) and 03 (b). ...................................................................................... 127
Figure 5.10. Seismic (BH components) and barometric (BDO) recordings at station 01, bandpass
filtered at 0.05-0.1 Hz (a) and 1-8 Hz (b). .................................................................................. 127
Figure 5.11. Cross-channel coherences at stations 01 (a, c, e) and 03 (b, d, f). All the
coherograms start from Oct 2015 when BDO recordings are available. .................................... 128
Figure 5.12. Coherences calculated with 8 hr moving windows and 95% overlaps. (a). Cross-
station (01-02) seismic coherogram (BHE component). (b). Cross-channel (BHE-BDO)
coherogram at station 01. (c). Cross-station (01-03) barometric coherogram (BDO component).
Station 03 is used here since there is no micro barometer at 02. All the coherograms start from
Oct 2015 when BDO recordings are available. .......................................................................... 131
Figure 5.13. High-coherence frequency bands of HHE component in five STS5 station pairs.
The vertical bars represent the frequency bands in which the coherences are larger than 0.95,
with solid lines indicating the upper and lower bounds. Each plot is labeled with the
corresponding station codes and interstation distances on the right. .......................................... 132
Figure 5.14. The lower bounds of high-coherence frequency bands (solid lines) and the best-
fitting boxcar function with modified amplitudes (dashed lines). The boxcar function is defined
with 0, = 92,160, and y0= 0.04, y1= 0.005 being the minimum and maximum of the lower
bounds from station pair 01-02. Each plot is labeled with the corresponding station codes and
interstation distances on the right. .............................................................................................. 133
xiv
Figure 5.15. Daily median temperature recordings (upper panel) at station 01 and significant
wave height recordings (lower panel) from the buoy sensor. Loosely dashed line in the upper
panel represents the best fitting temperature curve. Vertical dashed lines indicate the edges of the
best fitting boxcar function in Fig. 5.14. ..................................................................................... 135
Figure 5.16. Zoom ins of coherograms (HHE, HHN, HHZ) from station pair 06-12 during Julian
days 110-190, 2016. The 2016 Borrego Springs earthquake occurred on Julian day 162 (vertical
solid line). The dashed circles label the large coherence anomalies. .......................................... 137
Figure 5.17. HHE coherograms from station pair 06-12 on Julian days 135 (a) and 136 (b).
Horizontal axes represent the Pacific Time, and the high coherence anomalies observed on Julian
day 135 are labeled with a dashed box. ...................................................................................... 138

Figure A1.1. (a). Left: waveforms (0.5-20 Hz) of an event recorded by row 13. The red dashed
lines indicate the 3.0 s time window in which DMN is calculated. The orange box includes the P
type FZTW. Right: Corresponding DMN values represented by color. The white dashed line is
the median of automatic P picks in row 13. The orange box indicates the location where the P
type FZTW are detected. (b). Same as (a) for an event without P type FZTW. ......................... 147
Figure A1.2. FZTW inversion results of waveforms generated by event S-TW3 (location marked
in Fig. 1.12). The layout is the same as Fig. 1.14. ...................................................................... 148
Figure A1.3. FZTW inversion results of waveforms generated by event S-TW4 (location marked
in Fig. 1.12). The layout is the same as Fig. 1.14. ...................................................................... 149

Figure B2.1. Teleseismic P wave delay times corrected with two extreme reference velocities: 1
km/s (purple dotted line) and 6 km/s (purple dash dotted line). Other symbols are the same as in
Fig. 2.5(a). ................................................................................................................................... 150
Figure B2.2. Array transfer functions for the array geometry employed in beamforming analysis
(green balloons in Fig. 2.2) and frequency ranges 4-6 Hz (a) and 12-14 Hz (b). The average radii
of the respective beams (measured out to 50% of the beam peak amplitude) are 0.1 s/km (a) and
0.04 s/km (b). .............................................................................................................................. 151
Figure B2.3. S-type FZTW inversion results from an example event. The layout is the same as in
Fig. 2.13. ..................................................................................................................................... 151
Figure B2.4. Regional P-wave velocity model (Allam & Ben-Zion, 2012) averaged over the
depth range 1-10 km, surrounded by qualitative comparisons between the regions and
dimensions of internal San Jacinto fault zone structures at the different BB/BS (Share et al.,
2017, 2019b), RA/RR (Chapter 2), SGB (Chapter 1) and JF (Qiu et al., 2017) sites. ................ 152

Figure C3.1. (a). The 10-30 Hz autocorrelation functions (ACFs, color representing amplitudes)
normalized with zero lag amplitudes, reference travel time (black dashed lines), and ACF peaks
(black solid lines) corresponding to free surface reflections from the radial component at the 22
m borehole station (03). The left, middle and right panels are the results before, during, and after
the EMC earthquake, respectively. Horizontal axes represent the time relative to the occurrence
time of the EMC earthquake, and vertical axes indicate the lag time for autocorrelation. The 10-
30 Hz waveforms from the EMC event are plotted in the middle panel. (b). The corresponding
velocity changes (black solid lines), velocity reduction oscillations (green shaded areas), and
PGAs (blue dashed lines with dots) inside the autocorrelation time windows. Please note the
irregular time axes, different time and PGA scales between the middle and left/right panels. .. 153
xv
Figure C3.2. The 10-30 Hz ACFs (a) and corresponding velocity changes (b) from the
transverse component at the 50 m borehole station (04). The layout is the same as Fig. C3.1. . 154
Figure C3.3. The 10-30 Hz ACFs (a) and corresponding velocity change (b) from the radial
component at the 50 m borehole station (04). The layout is the same as Fig. C3.1. .................. 154
Figure C3.4. (a). The 1-30 Hz impulse response functions (IRFs, color representing amplitudes)
normalized with the maximum amplitudes, reference travel time (black dashed lines), and IRF
peaks (solid black lines) from the transverse component between the surface station (00) and 15
m borehole station (02). The layout is similar to Fig. C3.1. The 1-30 Hz waveforms at the
shallower station (in this case, station 00) from the EMC earthquake is plotted inside the middle
panel. (b). The corresponding velocity changes (black solid lines), velocity reduction oscillations
(green shaded areas) and PGAs (blue lines with dots) inside the deconvolution time windows.
Please note the irregular time axes, different time and PGA scales between the middle and
left/right panels. .......................................................................................................................... 155
Figure C3.5. The 1-30 Hz IRFs (a) and corresponding velocity changes (b) from the transverse
component between the surface (00) and 50 m borehole (04) stations. The layout is the same as
Fig. C3.4. .................................................................................................................................... 156
Figure C3.6. The 1-30 Hz IRFs (a) and corresponding velocity changes (b) from the transverse
component between the surface (00) and 150 m borehole (05) stations. The layout is the same as
Fig. C3.4. .................................................................................................................................... 156
Figure C3.7. The 1-30 Hz IRFs (a) and corresponding velocity changes (b, c) from the
transverse component recorded by the 6 m (01) and 50 m (04) borehole stations. (b) is the
average velocity change between stations 01 and 04 obtained from the IRF primary peak at ~0.11
s. (c) represents the average velocity change in the top 6 m calculated from the IRF secondary
peak at ~0.175 s, corresponding to waves traveling from station 04 to surface then reflected to
station 01. The blue horizontal axis ticks in (c) indicate Julian days in 2010. ........................... 157
Figure C3.8. The 1-30 Hz impulse response functions (IRFs, color representing amplitudes)
normalized with the maximum amplitudes (a) and corresponding velocity changes (b, c) from the
radial component recorded by the 6 m (01) and 22 m (03) borehole stations. The layout is the
same as Fig. C3.7. ....................................................................................................................... 158
Figure C3.9. The 10-20 Hz ACFs (a), velocity changes (b) and 15-30 Hz ACFs (c), velocity
changes (d) from the transverse component at the 22 m borehole station (03). The layout is the
same as the middle panel of Fig. C3.1. ....................................................................................... 159
Figure C3.10. The 10-30 Hz IRFs (a) and corresponding velocity changes (b, c) from the
transverse component recorded by the 6 m (01) and 22 m (03) borehole stations. The layout is
the same as Fig. C3.8. ................................................................................................................. 160

Figure D4.1. Synthetic test using Ricker wavelets: (a). Two time series with dominant
frequencies of 4.5 Hz (D0; black) and 3 Hz (D1; red), containing reflection phases at 1.3 s and
1.365 s, respectively. (b). The normalized autocorrelation functions of D0 (black) and D1 (red).
The blue vertical lines indicate the time window used for cross-correlation. (c) The cross-
correlation of the D0 and D1 autocorrelation functions at 0.5-2 s, which peaks at -0.06 s, implying
the reflection phase in D1 is delayed by 0.06 s with respect to that in D0. .................................. 162
Figure D4.2. Two days of continuous seismic recording (gray curve) of the NS (top panel) and
vertical (bottom panel) components. A bandpass filter between 1-5 Hz is applied to the data. A
smoothed envelope (red curves) is obtained using a 10-s-long moving window, and the data after
xvi
temporal balancing (Section 4.2.1) is shown in black. The waveform in black is magnified by
200 times for demonstration purpose. ......................................................................................... 163
Figure D4.3. Two-day ACFs from NS (a, b) and vertical (c, d) components. The layout is similar
to Fig. 4.2. ................................................................................................................................... 164
Figure D4.4. Spectrograms of two-day ACF from NS (a, b) and vertical (c, d) components. The
layout is similar to Fig. 4.3. ........................................................................................................ 165
Figure D4.5. Travel time variation (blue curves), peak frequency variation (orange curves),
linearly scaled ground temperature (black solid curves) and best fitting dt/t curves (black dashed
curves) from NS and vertical components. The layout is similar to Fig. 4.4. ............................ 166
Figure D4.6. Amplitude of thermoelastic strain calculated at different depths y, 0.1 m (a, b, c)
and 200 m (d, e, f) relative to the bottom of the decoupled layer and with different wavelengths
0.5 km (a, d), 3 km (b, e) and 15 (c, f) of temperature field. Here we assume the decoupled
surface layer is 0.1 m thick (yb) with thermal diffusivity of 2 × 10
-8
m
2
/s. The Poisson’s ratio
in half-space is set to 0.3. Results are computed for the elastic half-space with and ranging
from 2 × 10
-8
- 10
-8
m
2
/s and 10
-5
- 10
-3
°C
-1
, respectively. ........................................................ 168
Figure D4.7. Amplitude of thermoelastic strain calculated at different depths y, 0.1 m (a, b, c)
and 200 m (d, e, f) relative to the bottom of the decoupled layer and with different Poisson’s ratio
0.1 (a, d), 0.3 (b, e) and 0.5 (c, f). Here we assume the decoupled surface layer is 0.1 m thick
(yb= 0.1 m) with thermal diffusivity of 2×10
-8
m
2
/s. The wavelength of temperature field is set
to 15 km. Results are computed for the elastic half-space with and ranging from 2 × 10
-8
-
10
-8
m
2
/s and 10
-5
- 10
-3
°C
-1
, respectively. ................................................................................. 169

Figure E5.1. Normalized instrument responses of STS5 (solid/dotted, HH/BH), Trillium120-PH
(densely dashed/loosely dashed, HH/BH) and HS-1-LT (dashdotted, i.e. B084) sensors, with the
vertical lines indicating the corresponding frequencies of sensitivity (STS5, 0.5 Hz for HH, 0.2
Hz for BH; Trillium120-PH, 0.6 Hz for HH, 0.2 Hz for BH; HS-1-LT, 20 Hz). The responses of
HH and BH components overlap with each other below the 20 Hz Nyquist frequency of the BH
components. ................................................................................................................................ 170
Figure E5.2. HHN component results (a. waveforms; b. coherogram; c-d. spectrograms of PY01
and PY02) on Julian day 114, 2016 at stations 01 and 02 of the PY array. The layout is the same
as Fig. 5.2. ................................................................................................................................... 171
Figure E5.3. (a) HHN and (b) HHZ coherograms (top panel) and spectrograms in (m/s)2/Hz
(bottom two panel) at stations PY01 and B084 on Julian day 114, 2016. The layouts of (a) and
(b) are the same as Fig. 5.5. ........................................................................................................ 172
Figure E5.4. Three-year HHN coherograms from three (a, c, e) STS5 and three (b, d, f) Trillium
120PH station pairs. The layout is the same as Fig. 5.6. ............................................................ 172
Figure E5.5. Three-year HHZ coherograms from three (a, c, e) STS5 and three (b, d, f) Trillium
120PH station pairs. The layout is the same as Fig. 5.6. ............................................................ 173
Figure E5.6. Three-year HHE coherograms from three station pairs (a. 01-04; b. 05-06; c. 09-
10) with one STS5 sensor and one Trillium 120PH sensor. Each plot is labeled with the
corresponding station codes and interstation distances. ............................................................. 174
Figure E5.7. Three-year (a) HHE, (b) HHN and (c) HHZ median coherences from six station
pairs with different sensor types (one STS5 and one Trillium 120PH). Interstation distances are
65 m for 01-04/02-03, 340 m for 05-06, 360 for 07-08, 740 m for 09-10 and 760 m for 11-12. 174
Figure E5.8. (a). All the teleseismic events in 2015-2017 with magnitude larger than 7. The
triangle shows the PY array location. (b) and (c) are HHN and HHZ coherences from all
xvii
teleseismic events, calculated with the same parameter settings as Fig. 5.8(c). Only two events
exhibit minimum HHN coherence values below 0.95. ............................................................... 175
Figure E5.9. (a, c) cross-station (01-02) seismic coherograms from (a) BHN and (c) BHZ
components. (b, d) cross-channel (BHN-BDO; BHZ-BDO) coherograms at station 01. All the
coherograms are calculated with the same parameter settings as Fig. 5.12. ............................... 176
Figure E5.10. High-coherence frequency bands of (a) HHN and (b) HHZ component in five
STS5 station pairs (same stations as in Fig. 5.13). The vertical bars represent the frequency bands
where the coherences are larger than 0.95, with solid lines indicating the upper and lower
bounds. The station codes and interstation distances are labeled on the right. ........................... 176
Figure E5.11. Results from five STS5 stations pairs (same stations as in Fig. 5.14). From top to
bottom are the results for HHE, HHN and HHZ components, respectively. (a) displays the misfit
functions with y0=0.01 and y1=0.005 fixed at the best-fitting model. The crosses indicate the
minimums of the misfit functions, located at ( 0,) equaling to (92,160) for HHE, (96,150) for
HHN, and (0,19) for HHZ. (b) shows the corresponding absolute gradients (solid lines) with the
best fitting boxcar functions (thick dashed lines) from the three components. .......................... 177
Figure E5.12. The lower bounds of the high-coherence frequency bands (solid lines) and the
best-fitting boxcar functions (thick dashed lines) with modified amplitudes for (a) HHN and (b)
HHZ components in five STS5 station pairs (similar to Fig. 5.14). Station codes and interstation
distances are labeled on the right. ............................................................................................... 177

xviii
Abstract
I developed several seismologically-based tools for imaging and monitoring fault zones,
especially the shallow materials (top hundred meters) with high spatial-temporal resolutions.
This thesis includes analyses of fault zone phases (e.g. P- and S- waves, fault zone head waves,
and fault zone trapped waves) for internal structures of the San Jacinto Fault Zone (SJFZ) in
southern California (SoCal) at two sites (Sage Brush and Ramona Reservation), monitoring
materials in the top hundred meters using seismic interferometry at the Garner Valley in SoCal,
and at the site of NASA’s Interior Exploration using Seismic Investigations, Geodesy and Heat
Transport (InSight) mission on Mars. I also investigate wavefield characteristics with coherence
at Piñon Flats in SoCal to study the dynamics of shallow materials.
With seismic recordings from the linear dense arrays crossing the SJFZ at Sage Brush and
Ramona Reservation, I image the fault internal structures at the two sites with resolution
comparable to the station spacing (10-30 m) which cannot be achieved with traditional regional-
scale imaging techniques. Waveform changes are analyzed to identify the location of the main
seismogenic fault. Delay times of P-waves from local and teleseismic events are used to estimate
variations of seismic velocities across the fault zone structure. Fault zone head waves that
propagate exclusively along a bimaterial interface (i.e. the interface which separates two crustal
blocks with distinctive seismic velocities) are identified to image the properties (e.g. location,
depth extent) of fault-related bimaterial interfaces. P- and S- type fault zone trapped waves are
indicative of constructively interfering seismic energy within fault damage zones resulted from
the asymmetric rock damages related to earthquake ruptures with preferred propagation
direction. Analyses of these signals at the two sites provide detailed imaging of internal fault
structures and suggest consistent preferred propagation of earthquake ruptures to the NW.
xix
Along with imaging the subsurface structures, I monitor temporal variations and resolve
susceptibility of the shallow materials to various loadings (e.g. strong ground motions from
earthquakes, thermal elastic strains). At the Garner Valley Downhole Array in SoCal, the direct
P- and S- wave travel times between surface and borehole stations are used to study the velocity
structures in the top 150 m. Temporal changes at different depth ranges of seismic velocities
after the 2010 M7.2 El Mayor-Cucapah earthquake are estimated using autocorrelations of data
in moving time windows and seismic interferometry between multiple station pairs.
Autocorrelations of single-station seismic data on Mars also reveal daily variations of seismic
velocities on Mars, especially in the top ~20 m, in response to thermoelastic strains. The results
suggest up to 10% temporal variation of seismic velocities in response to a dynamic strain level
of 10
-7
in the top ~20 m weak sediment materials.
An innovative way to study the behavior of shallow material is to investigate the coherence,
a value ranging from 0 to 1, that evaluates the similarity between two recordings and depends on
frequency and interstation distance, and is sensitive to minute discrepancies between seismic
recordings. Analysis of coherence in different frequency bands at the Piñon Flats Observatory
array and a collocated 148 m deep borehole station reveals influence on seismic recordings from
atmospheric loadings, anthropogenic activities, thermoelastic strains, and potential near-surface
failures.

1
Introduction
Complex hierarchical structures of fault zones and shallow materials significantly modify
surface seismic recordings and mask information from deeper structures and processes, while
they are only understood in general terms. Incorporating temporal monitoring with imaging of
the fault zones and top few hundred meters of the crust is essential for a better understanding of
material dynamics and seismic hazard estimation. As one of the most intensively studied areas,
the San Andreas Fault system, located in the densely populated southern California (SoCal), is
close to the end of its interseismic phase of large (Mw>7) earthquake cycle. On the other hand, an
increasingly large volume of high-quality seismic data is collected at various sites in SoCal. Thus
there’s an urgent need for new methods for high-resolution imaging and monitoring the shallow
crust and near-fault zones, especially in the top hundred meters, for improved understanding of
earthquake processes and prediction of strong ground motions from future earthquakes.
The San Jacinto fault zone (SJFZ) is one of the most seismically active and complicated
components in SoCal with diverse fault structures and failure patterns (Cheng et al., 2018;
Hauksson et al., 2012; Ross et al., 2017). Tomography imaging results of the SJFZ (Qiu et al.,
2017; Share et al., 2017, 2019b; Yang et al., 2014) indicate complex structures with broad
damage zones and various large-scale velocity contrasts across the fault, but only with a
resolution of ~1-2 km. Finer scale imaging, usually with resolution comparable to the station
spacing (e.g. ~10-100 m), can be achieved with dense array techniques (e.g., Ben-Zion et al.,
2015; Bowden et al., 2015). Five linear dense arrays with 10–30 m station spacing were
deployed across main traces of the SJFZ in the Blackburn Saddle (BB; Share et al., 2017,
2019b), Ramona Reservation (RA), Sage Brush Flat (SGB), Dry Wash (DW) and Jackass Flat
(JF; Qiu et al., 2017) sites. Regional imaging results at these sites reveal fault interfaces that
2
separate a crustal block with higher seismic velocity to the NE from that to the SW (Allam et al.,
2014b; Allam & Ben-Zion, 2012; Zigone et al., 2015). Ruptures on a right-lateral fault associated
with the observed large-scale velocity contrast tend to propagate to the NW (Andrews & Ben-
Zion, 1997; Brietzke et al., 2009; Shi & Ben-Zion, 2006). Asymmetric rock damage with more
concentrating in shallow materials (e.g., top ~2-5 km) on the faster side (i.e. NE side along the
SJFZ) is expected from repeating occurrence of such bimaterial ruptures. Thus high-resolution
fault zone imaging at these sites shed light on important fault properties related to local
earthquake ruptures and long-term evolution processes.
In addition to imaging, it is also critical to monitor temporal variations and resolve
susceptibility of the shallow materials to various loadings (e.g. strong ground motions from
earthquakes, thermoelastic strains), for better physics-based seismic hazard evaluations. Though
linear material behavior is assumed for various studies, nonlinear site responses (e.g. decrease of
seismic velocities, increase of damping) are reported at an increasing rate due to more high-
quality data sets and better monitoring methods (e.g., Beresnev & Wen, 1996; Karabulut &
Bouchon, 2007; Sawazaki et al., 2006; Wu et al., 2010). Three methods are widely adopted in
current in-situ monitoring: spectral ratio, cross-correlation of ambient noise and repeating
earthquakes. However, three major issues regarding seismic monitoring remain to be addressed.
First, under what circumstances will the nonlinear effects be significant enough and need to be
considered? The threshold of dynamic strain for triggering nonlinear behavior is still under
debate (e.g., Wu et al., 2010). Laboratory experiments imply geomaterials (e.g. sandstones) start
to behave nonlinearly when the strain is on the order of 10
-7
(Pasqualini et al., 2007; TenCate et
al., 2004), while in-situ observation seldomly resolves velocity change for such a low level of
strain (e.g., Rubinstein, 2011). This could probably result from the rough time and spatial
3
resolution of in-situ monitoring because much of the material recovers rapidly after the change
occurs (with logarithmic time scale; e.g., Dieterich & Kilgore, 1996), and much of the velocity
reduction concentrates in weak materials, e.g., the shallow structure (top hundred meters; e.g.,
Chandra et al., 2015; Rubinstein & Beroza, 2005) and fault damage zones (hundred meters wide
and ~2-5 km deep).
This leads to the second issue, i.e. how to improve the temporal and spatial resolution (to the
level of, e.g., meters-seconds) of seismic monitoring. Continuous monitoring can be achieved
with the noise cross-correlation method, but the stacking of waveforms is required to enhance the
signal-to-noise ratio, resulting in time resolution of hours to days. Repeating earthquakes also do
not appear at a considerable high rate or in wide areas. While the spectral ratio method could
potentially reach a higher spatial-temporal resolution, it requires a reference station, assuming
there are no temporal changes at the reference station. This is not necessarily a valid assumption
and prevents similar analyses from being widely applied.
Thus the third question is, how to effectively monitor a wide range of areas using currently
available data sets? With a high temporal (5.12 s) resolution by using autocorrelation of surface
seismic data, Bonilla et al. (2019) obtained up to 60% velocity change that was not observed by
previous studies. This single-station monitoring technique with high temporal resolution could
play a critical role to retrieve information on the dynamics of shallow materials. As an example,
there is one seismic station on Mars, deployed by NASA’s InSight (Interior Exploration using
Seismic Investigations, Geodesy and Heat Transport) mission, which is a great adventure in
science that enables exploration of other planets in the universe. Taking advantage of this single
seismic station on Mars, seismic monitoring could provide information on the near-surface
processes that have shaped the land on Mars, and serve as guidance for seismic monitoring on
4
Earth and future planetary missions (e.g., site selection, deployment of seismometers on other
planets).
This dissertation is composed of five chapters: four are published in peer-reviewed journals,
and one is currently under review. In Chapters 1 and 2, I present fault zone imaging results at the
SGB and RA sites using seismic data from local dense arrays. Chapter 3 includes studies of
temporal variations of sediment materials saturated with water at the Garner Valley site in
response to the large (Mw=7.2), long-distance (~200 km away) El Mayor-Cucapah earthquake.
In Chapter 4 I discuss temporal variations of shallow materials on Mars using the single-station
seismic data from NASA’s InSight mission. Chapter 5 develops a method using coherence to
study the characteristics of seismic waveforms in different frequency bands and along various
distance ranges. Then I summarize all the results in Chapter 6.
5
1. Internal structure of the San Jacinto fault zone in the trifurcation
area southeast of Anza, California, from data of dense seismic
arrays
(Qin, L., Ben-Zion, Y., Qiu, H., Share, P.-E., Ross, Z. E. & Vernon, F. L., 2018. Internal
structure of the San Jacinto fault zone in the trifurcation area southeast of Anza, California, from
data of dense seismic arrays, Geophysical Journal International, 213(1), 98–114,
https://doi.org/10.1093/gji/ggx540.)

1.0 Summary
We image the internal structure of the San Jacinto fault zone (SJFZ) in the trifurcation area
southeast of Anza, California, with seismic records from dense linear and rectangular arrays. The
examined data include recordings from more than 20,000 local earthquakes and nine teleseismic
events. Automatic detection algorithms and visual inspection are used to identify P and S body
waves, along with P- and S-types fault zone trapped waves (FZTW). The location at depth of the
main branch of the SJFZ, the Clark fault, is identified from systematic waveform changes across
lines of sensors within the dense rectangular array. Delay times of P arrivals from teleseismic
and local events indicate damage asymmetry across the fault, with higher damage to the NE,
producing a local reversal of the velocity contrast in the shallow crust with respect to the large-
scale structure. A portion of the damage zone between the main fault and a second mapped
surface trace to the NE generates P- and S-types FZTW. Inversions of high-quality S-type FZTW
indicate that the most likely parameters of the trapping structure are width of ~70 m, S-wave
velocity reduction of 60 percent, Q value of 60 and depth of 2 km. The local reversal of the
shallow velocity contrast across the fault with respect to large-scale structure is consistent with
preferred propagation of earthquake ruptures in the area to the NW.
6

1.1 Background
Large fault zone (FZ) structures separate different crustal blocks and have hierarchical
damage zones resulting from long-term evolution and recurring earthquake ruptures (e.g., Ben-
Zion & Sammis, 2003). High-resolution imaging of FZ structures can provide important
information on a wide range of topics including likely properties of earthquake ruptures, stress
and strength of the crust, development of improved seismic catalogues and crustal hydrology. In
particular, asymmetric rock damage across the main fault can reflect statistically preferred
propagation direction of earthquake ruptures in the area (Ben-Zion & Shi, 2005; Dor et al., 2006;
Lewis et al., 2005). This may result from ruptures that are localized along a deep bimaterial
interface in the FZ structure (e.g., Andrews & Ben-Zion, 1997; Ben-Zion, 2001; Brietzke & Ben-
Zion, 2006). Rock damage is expected to be pronounced in the top few kilometers of the crust,
and to exist primarily on the side with faster seismic velocity at depth (Ben-Zion & Shi, 2005;
Xu & Ben-Zion, 2017). Such rock damage asymmetry may generate a local reversal of the
velocity contrast across the fault in the shallow crust compared with the large-scale contrast.
The 230 km long SJFZ is the most seismically active component of the plate boundary
system in Southern California over the last several decades (Hauksson et al., 2012), and is
subparallel to the southern San Andreas fault to the NE and the Elsinore fault to the SW (Fig.
1.1a). In the last few years, data recorded by the regional seismic networks and local arrays
crossing the SJFZ at several locations were used to obtain earthquake- and noise-based
tomographic images for the region with nominal resolution of 1–2 km (Allam et al., 2014b;
Allam & Ben-Zion, 2012; Zigone et al., 2015). These studies were accompanied by finer scale
imaging of fault bimaterial interfaces and damage zones (order 100 m wide) at several locations
7
(Qiu et al., 2017; Share et al., 2017, 2019b; Yang et al., 2014), along with anisotropy analysis
within and around the fault (e.g., Li et al., 2015). In this chapter, we provide detailed information
on the internal structure of the SJFZ at the Sage Brush (SGB) site SE of Anza, California, using
seismic data recorded by linear and dense rectangular arrays (Fig. 1.1c). Our main goals are to
find the seismogenic location of the main branch of the SJFZ in the region, the Clark fault, and to
analyze the symmetry properties of the FZ damage with respect to the Clark fault. The imaged
SGB site is in the complex trifurcation area of the SJFZ, which is highly active seismically with
ongoing small and moderate events (Cheng et al., 2018; Kurzon et al., 2014; Ross et al., 2017).
The detailed seismic imaging at this site complements similar studies done with linear arrays
across the SJFZ at other locations marked in Fig. 1.2.
In Section 1.2, we describe the seismic data used in this work. In Section 1.3, we first
examine data recorded by the dense rectangular array for systematic waveform changes to
identify the location of the main seismogenic fault. Then, we analyze delay times of P waves
generated by teleseismic and local events to estimate variations of slowness across the FZ
structure. In addition, we use automatic detection algorithms to find P- and S-types fault zone
trapped wave (FZTW), and invert high-quality S-type trapped waves for parameters of the FZ
trapping structure. The results show systematic rock damage asymmetry across the fault,
producing locally lower velocities in the shallow structure on the crustal block with faster
seismic velocity at depth. The results are summarized and discussed in Section 1.4.

8
1.2 Data

Figure 1.1. (a) Location map of the SJFZ and the ∼20,000 local events used in the study. Fault traces are
shown with black lines. The green triangle marks the SGB site, and the four white triangles are four other
linear arrays straddling the Clark Fault (BB, RA, DW and JF from north to south). SAF and EF denote the
San Andreas and Elsinore faults. Yellow and red circles represent events recorded by the linear SGB and
dense rectangular arrays, respectively. The long blue line (AA’) indicates the geological strike direction
of the Clark fault. The blue (200 km × 50 km) and cyan (60 km × 20 km) boxes, centered at the SGB
site, include events used for the FZTW and delay time analysis, respectively. The lower panel is the depth
profile projected to the cross-section AA’. The two cyan lines correspond to boundaries of the cyan box in
the top panel and the five triangles correspond to the five linear arrays. (b) Locations of nine teleseismic
events with high-quality first arrivals. Color represents depth and circle size represents magnitude. TS1 is
the example event in Fig. 1.6(a). See Table 1.1 for additional information. (c) Sensors of the linear SGB
array (white balloons with labels) and dense rectangular array (dots). Orange lines indicate fault surface
traces including the main Clark fault (MCF). The row and column numbers of the dense array start from
the SW corner and increase toward the NW and NE (cyan arrows), respectively. Row 13 of the dense
array, closest to the linear SGB array, is labeled. Data of rows 12–18 (green sensors) are stacked to
identify S-type FZTW. Some sensors are colored yellow for identification of row and column numbers.
The analyzed data are recorded by two seismic arrays at the Sage Brush site: a linear SGB
array and a dense rectangular array (Fig. 1.1c). Both arrays straddle the Clark branch of the
SJFZ southeast of Anza, California, and the linear array overlaps with columns 26–40 of row 13
9
of the dense rectangular array. The linear SGB array has six 3-component accelerometers
recording at 200 Hz with instrument spacing of about 25 m, and is part of a larger PASSCAL
deployment within and around the SJFZ that started in 2010 (Vernon & Ben-Zion, 2010). The
rectangular array consists of 1108 vertical 10 Hz ZLand geophones and it operated with a
sampling rate of 500 Hz between 2014 May 7 and June 13 (Ben-Zion et al., 2015). This array
covers an area of ~650 m × 650 m with ~55 columns in the fault-normal direction (SW-NE)
with instrument spacing of 10 m, and 20 rows in the fault-parallel direction (SE-NW) with 30 m
instrument spacing.
Table 1.1. Selected teleseismic events
Event ID Origin time
Latitude (degree), Longitude
(degree), Depth (km)
Magnitude
Great circle
distance (m)
37199173
2014/05/09,
10:32:18.700
-18.9, -175.6, 153 5.8 8553
37199493
2014/05/10,
07:36:01.400
17.2, -100.8, 23 6 2408
37199653
2014/05/10,
14:16:09.000
60, -152.1, 91 5.6 3904
37200141 (TS1)
2014/05/13,
06:35:24.300
7.2, -82.3, 10 6.5 4581
37201893
2014/05/16,
11:01:42.900
17.1, -60.4, 25 6 5864
37202405
2014/05/21,
10:06:14.900
17.2, -94.9, 127 5.6 2829
37202789
2014/05/24,
08:24:47.500
16.5, -98.2, 12 5.6 2644
37202885
2014/05/28,
21:15:04.900
18.1, -68.4, 91 5.8 5073
37203109
2014/05/31,
11:53:48.100
18.9, -107.4, 10 6.2 1874

For the SGB array, we use local seismic data recorded over a three-year period (2012–
2014), during which >20,000 local events were detected by the ANZA network (Fig. 1.1a). For
the dense rectangular array, local and teleseismic data are used together during the one-month
10
deployment period. We analyze nine teleseismic events with magnitude M > 5.5 (Table 1.1)
from the Southern California Earthquake Data Center (SCEDC 2013), and 1000 local events
from a local catalogue detected by Ben-Zion et al. (2015). Fig. 1.1 shows the study area, seismic
stations and event information. The large blue box in Fig. 1.1(a) (200 km in the along strike and
50 km in the fault-normal directions) marks the area used to search for events generating FZTW.
The small cyan box includes events used for delay time analysis of P waves. The nine
teleseismic events in Fig. 1.1(b) are selected because they generate clear first P arrivals and are
also used for delay time analysis.

Figure 1.2. Average P-wave velocity over the depth range 1–10 km based on the tomography results of
Allam & Ben-Zion (2012). The town of Anza and several linear arrays are shown by a square and
triangles, respectively. Black lines represent fault surface traces. The SJFZ branches into three faults
(Buck Ridge, Clark and Coyote Creek) near the SGB site.

11
1.3 Analysis
The regional P-wave velocity model (Allam & Ben-Zion, 2012) shows that within the study
area, the mapped surface trace of the Clark fault separates faster material in the northeast from
slower rocks to the southwest (Fig. 1.2). However, the location of the seismogenic fault at depth
and other details of the internal FZ structure are unresolved by the regional tomographic images.
To clarify the location of the main seismogenic fault and properties of the damage FZ structure,
we apply several types of analysis at different scales. These include searching the waveforms for
systematic changes at given instrument locations, analysis of delay times of P waves generated
by teleseismic and local events and analysis of S- and P-types FZTW.
1.3.1 Waveform changes
Ben-Zion (1989, 1998) and Ben-Zion & Aki (1990) showed with model calculations that
lateral variations of seismic properties across and within FZ affect the travel time, wave
amplitude, spectral content and motion polarities. Because of the FZ heterogeneity in the study
area, substantial variations in waveform character and phases are expected within the arrays.
These features are analyzed below in detail to resolve the location of the main fault separating
different crustal blocks at the SGB site. We apply a 0.5–20 Hz bandpass filter to all waveforms
and examine the data visually for row 13 to find clear waveform changes in the fault-normal
direction generated by many events. Then, we check the waveforms from all other rows inside
the dense rectangular array, and track the location of the waveform changes within each row to
find the primary fault location.
Fig. 1.3 shows the locations of events generating clear and consistent waveform changes
along row 13 of the dense rectangular array, identified from visual examination. The area is
separated into four quadrants by the fault-parallel and fault-normal directions of the Clark fault at
12
SGB. Fig. 1.4 displays waveforms of four representative events from the different quadrants
recorded by row 13. The waveform shapes generated by the four examples, and other
earthquakes in the different quadrants, have some differences related to event locations and other
factors such as focal mechanisms. Nevertheless, we observe a clear transition in the character of
the waveforms at column 32 marked by the dashed red line. To see if this is persistent along
strike, we examine data recorded by other rows of the dense rectangular array. The results
indicate clear waveform changes at columns 28–32 of the dense rectangular array (this zone is
marked in the final Fig. 1.15). As an example, Fig. 1.5 shows waveforms of EQ3 recorded by
three other rows, with clear similar waveform changes at columns 29, 30 and 32 for rows 01, 10
and 19, respectively. We conclude that the seismogenic fault at depth is beneath columns 28–32
of the dense array.

Figure 1.3. Location map of events (black dots) used to analyze waveform changes across the array. The
long blue line (AA’) is the same as in Fig. 1.1(a) and the short blue line perpendicular to AA’ is centered
at the SGB site. The two lines separate the area into four quadrants with events colored by orange, yellow,
purple and cyan showing clear waveform changes in row 13 of the dense array. The stars mark the four
example events (EQ1∼4) from the four quadrants. The lower panel is the depth profile projected to AA’.
13

Figure 1.4. Waveforms (0.5–20 Hz) of four example events (stars in Fig. 1.3) recorded by row 13.
Horizontal axis is the time relative to the origin time (all future plots use the same convention unless
otherwise stated). The red dashed line, corresponding to column 32, indicates the location with clear
waveform changes. The light orange lines mark phases that only exist on one side of the fault.

Figure 1.5. Waveforms (0.5–20 Hz) of event EQ3 recorded by (a) row 01, (b) row 10 and (c) row 19. The
red dashed lines indicate locations of clear waveform changes.
14
1.3.2 Delay time analysis of teleseismic arrivals
Teleseismic arrivals sample the structure underneath the array with a nearly vertical incident
angle and lower frequency content than the local seismic waves. Ozakin et al. (2012) analyzed
teleseismic arrival time differences at stations across the North Anatolian fault; Qiu et al. (2017)
and Share et al. (2017) applied similar analyses, respectively, to the JF and BB arrays (Fig. 1.2).
The clear direct P waves from teleseismic events recorded by the long across-fault lines of the
dense array can be used to analyze the local velocity structure. This is done here with a similar
analysis as Qiu et al. (2017), with the main difference that we use the southwestern-most station
in a row as the reference. First, the observed delay time (tij,obs) from event i at station j in a given
row is obtained using cross-correlation between the jth trace and the template trace, i.e. the
record from the reference station. Then, we use the TauP toolkit (Crotwell et al., 1999) and
iasp91 velocity model to calculate the predicted travel time. Since this does not account for the
local velocity structure, the travel time difference from the reference station due to the station-
event geometry (tij,geo) is equal to the predicted travel time difference between each station and the
reference station. In addition, the travel time difference caused by the station topography (tj,elv) is
calculated by (dj-dref)/vref, where dj and dref are the elevations of the analyzed and reference stations,
and vref is the average velocity of the surface layer. The relative delay time (tij) from event i at
station j with respect to the reference station, resulting from the local lateral variations across the
fault, can be written as tij = tij,obs - tij,geo - tj,elv. Considering the small aperture of the array relative to
the event-station distance, the ray path difference between different stations stems primarily from
the local structure. Thus the observed delay time corrected by the geometry and elevation
difference contains information of the local structure beneath the array. In a final analysis step,
we average the observed and relative delay time from all the teleseismic events.
15
We apply a 0.1-1.0 Hz bandpass filter to waveforms of teleseismic events with M > 5.5 that
occurred during the dense rectangular array deployment and discard events without clear first P
phases. We end up with 9 teleseismic events with high-quality waveforms (Fig. 1.1b and Table
1.1). We analyze data recorded by row 13 of the dense array, choose the SW-most station as the
reference, and cross-correlate waveforms of each station with those of the reference station in a
5.5 s time window around the first arrival. This gives observed delay times, which are then
corrected by the event-station geometry and station elevation difference to get the relative delay
times. For average velocity of the surface layer, we use vref = 2.0 km/s, which is similar to the
value used by Qiu et al. (2017).
Fig. 1.6a provides example waveforms from event TS1 (Fig. 1.1b) that change from SW to
NE; the changes are smoother compared to those produced by the local events (Figs 1.4 and 1.5)
because of the lower frequency content. The observed delay times obtained from cross-
correlation (Fig. 1.6b, red triangles) suggest that locally, the NE side of the fault is slower than
the SW side. The relative delay times (Fig. 1.6b, blue triangles) obtained after event-station
geometry and station elevation correction with a reference velocity of 2.0 km/s show a similar
pattern. These results point to a local reversal of the velocity structure from that associated with
(Fig. 1.2) the regional tomography of Allam & Ben-Zion (2012). The average delay times (Fig.
1.6c) follow a similar pattern as that from a single event (Fig. 1.6b). The small error bars imply
that the delay time patterns are independent of the event locations, and therefore represent the
local velocity structure. The relative delay times correlate with the station elevations (Fig. 1.6d);
the elevation difference can produce travel time difference as large as ~0.02 s while the
maximum observed delay time is ~0.04 s. This does not affect the general conclusion on the
local reversal of the velocity structure in the region with little topography.
16

Figure 1.6. Delay time analysis results from teleseismic events. (a) Waveforms (0.1–1.0 Hz) of TS1 (Fig.
1.1b) recorded by row 13. The red dashed lines indicate the 5.5 s time window for the cross-correlation.
(b) Results from event TS1: observed delay time (ODT, red triangles) obtained by cross-correlation and
relative delay time (RDT, blue triangles) after event-station geometry and station elevation corrections.
(c) Average observed delay time (AODT, red triangles) and average relative delay time (ARDT, blue
triangles) from all the nine teleseismic events. The error bar is one standard deviation. (d) Station
elevation profile of row 13.
1.3.3 Delay time analysis of local direct P waves
For the analysis of local direct P-waves, we follow the procedure of Qiu et al. (2017) and
Share et al. (2017). The first step is to pick P-wave arrival times with an automatic algorithm
(Ross et al., 2016; Ross & Ben-Zion, 2014). Then we calculate the theoretical P wave travel time
and along-path distance using an average 1D velocity model based on the 3D tomographic
results of Allam & Ben-Zion (2012). The slowness is equal to the ratio between the observed P-
wave travel time and the along-path distance (the slowness from deeper events is generally
smaller since it includes more information from the deeper structure). To obtain the relative
slowness we normalize the slowness at each site by the average slowness across the array. The
17
normalization procedure is designed to mitigate effects of 3D structure outside the FZ, and to
minimize the effect of event depth.

Figure 1.7. Delay time analysis results of data from the dense (a)–(c) and linear SGB (d)–(e) arrays. (a)
Waveforms (0.5–20 Hz) of an event recorded by row 13 of the dense array. The red triangles represent
automatic P picks. The location (column 32) of waveform change is indicated by a red dashed line.
Potential P-type FZTW (see Section 1.3.4 for details) is marked by the orange box. (b). Along-path
average slowness calculated from the data in (a). (c) Statistical result on relative slowness from data
recorded by the dense array. The dots represent the mean value of relative slowness and the error bar is
one standard deviation. (d) Histogram of relative slowness from data of station SGBS2 of the linear array
with average relative slowness marked by the red dashed line. (e) Average relative slowness obtained
from events at different locations recorded by the SGB array. The error bar is also one standard deviation.
18
To obtain reliable slowness values, we develop several criteria. First we ignore automatic P
picks that have more than 1.0 s difference from the estimated P-wave travel time. Second the
signal-to-noise ratio, defined by the ratio between the energy observed in a 1.0 s time window
after and before the automatic P pick, is required to be larger than 10. Finally, the obtained
along-path average slowness values should be in a reasonable range, i.e., between 0.125 s/km
and 0.25 s/km, corresponding to an average P-wave velocity between 4 km/s and 8 km/s.
The analysis is constrained to events that are close to the stations since the calculated
slowness represents the along-path average. Specifically, we use events within the cyan box in
Fig. 1.1a centered on the SGB site, extending 20 km in the fault-normal and 60 km in the along-
strike directions. With this we have ~600 and ~8,000 local events for the statistical delay time
analysis for data of the dense rectangular and SGB arrays, respectively. To address possible
effects of event locations on the results, we also analyze separately data of the SGB array
generated by events on the SW and NE side of the Clark fault. The large number of events
allows us to discard records with relatively low signal to noise ratio, bad automatic P picks, or
other problems. We exclude ~16% and ~80% of the lower quality records at the dense and SGB
arrays, respectively, and perform delay time analyses using data of ~500 and ~1500 high-quality
events at the dense and SGB arrays, respectively.
Fig. 1.7a shows waveforms for an example event recorded along row 13 of the dense
rectangular array, displaying a clear change around column 32 consistent with the inferred
seismogenic fault location in Section 1.3.1. The automatic picking algorithm gives high-quality
P picks (Fig. 1.7a, red triangles), enabling the entire data set to be processed efficiently. The
large amplitude wave package following the direct P-wave in the records of columns 36-40
(highlighted by orange box in Fig. 1.7a) is the potential P-type FZTW, which is discussed in
19
more detail in Section 1.3.4. The along-path average slowness (Fig. 1.7b) calculated from the
example event is around 0.15 s/km and increases gradually from SW to NE. The results from all
events recorded by row 13 of the dense rectangular array (Fig. 1.7c) also indicate that the NE
side of the fault is locally slower than the SW. The distribution of relative slowness values from
station SGBS2 (Fig. 1.7d) has well-defined mean and standard deviation values, demonstrating
the reliability of the procedures and results. The relative slowness values obtained from data at
the SGB array (Fig. 1.7e) imply again a locally slower NE side. The smaller error bar compared
with results for the dense rectangular array is due to having a larger number of events. The
separate analyses of events on the NE and SW sides of the fault generate similar results (Fig.
1.7e), leading us to conclude that the observed trends are not biased by the event locations. The
delay time analyses from local events recorded at both the dense rectangular (Fig. 1.7c) and SGB
(Fig. 1.7e) arrays imply a local reversal of the velocity contrast across the fault with respect to
the large-scale contrast (Fig. 1.2), in agreement with the previous results from teleseismic events.
1.3.4 Fault Zone Trapped Waves
FZTW are associated with constructive interference of critically reflected phases propagating
within low velocity FZ layers that are sufficiently coherent to act as seismic waveguides (e.g.,
Ben-Zion & Aki, 1990; Jahnke et al., 2002). For the SH case they are analogous to surface Love
waves in a horizontally layered structure. These waves follow the S body wave with relatively
high amplitude and low frequencies, are somewhat dispersive, and exist predominantly in the
vertical and fault parallel components of ground motion (e.g., Lewis & Ben-Zion, 2010; Peng et
al., 2003). For the P-SV phases, FZTW have properties similar to Rayleigh type resonance or
leaky modes (e.g., Gulley et al., 2017; Malin et al., 2006). The latter appear between the P and S
body waves with appreciable amplitudes on the radial and vertical components (Ellsworth &
20
Malin, 2011). The data of the dense rectangular and SGB arrays contain clear candidate trapped
waves following the S and P body waves, referred to below as S- type and P- type FZTW,
respectively. In the following we first present an automatic algorithm for detection of P-type
FZTW and summarize the detection results. Then we present observations and modeling of S-
type FZTW.
1.3.4.1 P-type FZTW
To identify P-type FZTW objectively in large data sets, as done in recent analyses of S-type
FZTW (Qiu et al., 2017; Ross & Ben-Zion, 2015), we develop an automatic detection algorithm
for these phases. We apply a 0.5-20 Hz bandpass filter to the waveforms, compute the energy
around every data point and cross-correlate waveforms of neighboring stations. We first choose a
3.0 s time window starting 0.5 s before the median value of the automatic P picks. The median P
arrival across the array is used for choosing the time window to avoid possible incorrect
individual P picks. For each sample inside the time window, we use a 0.1 s sliding window
centered at the sample and calculate the maximum cross-correlation coefficient (CC) between all
pairs of nearby stations and the energy (E) according to
[,] =
!
:∑
",$
[]∙
"%&,$
[+]
'
( ) *'
@ (1.1)
[,] = ∑
",$
+
[]
'
( ) &
(1.2)
where d represents the data, j is station index, k is sample index and N denotes the number of
samples inside the sliding window. Large-amplitude trapped waves make the energy and cross-
correlation coefficients stand out. A detection matrix (DM) for P-type trapped waves is obtained
by multiplying the cross-correlation coefficient and energy matrices point by point. A
normalized detection matrix (DMN) is defined by

'
[,] = ([,]−())/ (1.3a)
21
where MAD is the median-absolute-deviation defined as
= (|−()|) (1.3b)
The matrix DM suppresses possible anomalies only in the CC or E, while DMN helps to find
outliers in the matrix that provide a strong indication of P-type FZTW. Fig. A1.1 shows an
example of automatic detection of P-type trapped waves, and illustrates the waveforms and DMN
of one event with (Fig. A1.1a) and one event without (Fig. A1.1b) P-type FZTW. The
waveforms in Fig. A1.1a contain clear P-type FZTW in columns 36-40, and the corresponding
DMN exhibits clear peak value (~9000) at these locations. On the other hand, the waveforms in
Fig. A1.1b do not contain clear P-type FZTW, and the maximum DMN value (~1200) is much
smaller than that in Fig. A1.1a. Testing different thresholds for the maximum value of DMN
indicates that 4000 provides a good balance between detecting many generating events and
reducing the number of false detections. In the subsequent analysis, events with a maximum DMN
value above 4000 are flagged as potential candidates. Sensors that have DMN values larger than
40% of the peak DMN, and with separation between potential P-type FZTW and median P arrival
by at least 0.1 s, are identified as recording P-type trapped waves.
We run the automatic detection algorithm for all the events in Fig. 1.8 and visually check the
flagged events to eliminate false detections. The remaining events are spread in all four
quadrants around the SGB site (Fig. 1.8) over the approximate depth range 10-20 km. Fig. 1.9
presents examples of seismograms from four events (one in each quadrant) marked as stars in
Fig. 1.8 that generate P-type FZTW in columns 36-40 of row 13 of the dense array. The
repeating occurrence of these wave packets at similar sensor locations, independent of the event
locations, implies that they are resonance modes associated with the FZ structure. The generation
of FZTW from events at considerable distances from the fault implies a relatively shallow
22
trapping structure (Ben-Zion et al., 2003; Fohrmann et al., 2004). This is because a deep low
velocity FZ layer would reflect most of the energy from off-fault events, and generate trapped
waves only from events very close to the fault (Ben-Zion, 1998; Jahnke et al., 2002).

Figure 1.8. Location map of events (black circles) used for P-type FZTW analysis in the dense array. The
two perpendicular blue lines are the same as in Fig. 1.3. The orange, yellow, purple and cyan circles mark
events from the four quadrants that are confirmed to generate P-type FZTW. The stars represent four
example events (P-TW1 to P-TW4). The lower panel is the depth profile projected on the cross-section
AA’.
To clarify the along-strike extent of the trapping structure, we plot the waveforms generated
by event P-TW3 recorded by several other rows (Fig. 1.10). The results from this and other
examples show P-type FZTW in columns 36-40 of rows 12 and 19, while in other rows there are
no such waves after the direct P arrival. Ben-Zion et al. (2015) presented similar observations on
the spatial extent of the trapping structure based on Betsy gunshot data recorded by the dense
rectangular array. Fig. 1.11 summarizes the automatic detection of P-type FZTW from all
examined events. The detections at columns 36-40 stand out and the corresponding waveforms
23
are consistent with the results shown in Fig. 1.9. The false detections near columns 10-25 and
45-55 are associated with amplified motions in other local low velocity zones in the area (Ben-
Zion et al., 2015; Hillers et al., 2016; Roux et al., 2016).

Figure 1.9. Waveforms (0.5–20 Hz) of four example events (stars in Fig. 1.8) recorded by row 13 of the
dense array. The red dashed lines represent locations of waveform changes. The blue and orange boxes
include the observed P-type FZTW.

Figure 1.10. Waveforms (0.5–20 Hz) of event P-TW3 (Fig. 1.8) recorded by rows 09, 11, 12, 16, 19 and
20 of the dense array. The red dashed lines indicate locations of waveform changes and the orange boxes
mark observed P-type FZTW.
24

Figure 1.11. Histogram of automatic P-type FZTW detection results at different stations of row 13.
1.3.4.2 S-type FZTW
To study S-type trapped waves we apply different methods to data recorded by the dense and
SGB arrays. For the dense array, which only has vertical component data, we stack the
waveforms from events deeper than 15 km recorded by multiple rows that have similar elevation
(i.e. rows 12-18, green dots in Fig. 1.1c). This reduces small-scale local variations due to
uncorrelated noise and scattering, and enhances common resonance modes associated with
FZTW with relatively large amplitude and small time offset. For the SGB array, we first rotate
the recordings to the fault-parallel component to maximize the signal strength. Next, we run the
automatic S-type FZTW detector (Ross & Ben-Zion, 2015) and check the detected events
visually to eliminate incorrect detections. Detected high-quality S-type trapped waves are
inverted for properties of the FZ waveguide using a genetic inversion algorithm with a forward
kernel based on the 2D analytic solution (Ben-Zion, 1998; Ben-Zion & Aki, 1990). We assume a
simple model with a low velocity FZ layer in a half space (e.g., Qiu et al., 2017), and invert for
the following six parameters: shear wave velocity, Q value and width of the FZ layer, shear wave
25
velocity of the host rock, distance of the SW edge of the FZ layer from sensor SGBS3, and
propagation distance inside the FZ. The inversion algorithm explores systematically the trade-
offs among these six parameters (Ben-Zion, 1998) and finds the best model that explains the
observed trapped waves. The best model should be close to the most likely model associated
with peaks of the probability density distributions of the parameter space explored by the
inversion algorithm (Ben-Zion et al., 2003).
Fig. 1.12 shows the events examined for S-type FZTW and detection results for the dense
and SGB arrays. For data recorded by the dense array, we search over all events deeper than 15
km (purple diamonds in Fig. 1.12) during the dense array deployment and stack the waveforms
of rows 12-18 (green symbols in Fig. 1.1c). As with the P-type FZTW, the detections are spread
in a broad region around the fault implying a relatively shallow waveguide. Fig. 1.13 presents
stacked waveforms for example event S-TW1. The stacked data show clear S-type FZTW along
with P-type FZTW at the previously inferred core damage zone (columns 36-40). For the SGB
array, detected S-type FZTW by the automatic algorithm are observed at sensors SGBF0-SGBN2
that overlap with columns 36-40 of row 13 of the dense array. This consistently suggests a
trapping structure beneath SGBF0-SGBN2. Fig. 1.14 presents inversion results of S-type FZTW
generated by example event S-TW2. The synthetic waveforms in Fig. 1.14a (red lines) are
generated by model parameters producing the highest fitness values (Fig. 1.14b, solid circles) in
10,000 inversion iterations. The fitness is defined as (1+C)/2 where C is the cross-correlation
coefficient between observed and synthetic waveforms. Summing the fitness values of the final
2,000 inversion iterations (green dots in Fig. 1.14b) and normalizing the results to have unit sums
give probability density functions for the various model parameters (curves in Fig. 1.14b). The
most likely parameters of the trapping structure (peaks of curves in Fig. 1.14b) are width of ~70
26
m, S-wave velocity reduction of ~60%, and Q value of ~60. The most likely propagation distance
within the trapping structure is ~2 km, confirming the presence of a shallow trapping structure at
the study site (Section 1.3.4). Modeling additional high-quality S-type FZTW recorded by the
SGB array lead to similar results (Figs A1.2&A1.3).

Figure 1.12. Location map of events for S-type FZTW study. The large blue box and line AA’ are the
same as in Fig. 1.1(a). Purple diamonds and black dots mark events used in data of dense and linear SGB
arrays, respectively. Orange diamonds and yellow circles represent events that are confirmed to generate
S-type FZTW in the dense and SGB arrays, respectively. Waveforms from S-TW1 (red diamond) and S-
TW2 (red circle) are shown and modeled in Figs 1.13&1.14, respectively. Inversion results of S-TW3 and
S-TW4 (red circles) are shown in Figs A1.2&A1.3 in Chapter APPENDIX 1. The lower panel is depth
profile projected to the cross-section AA’ with red dashed line marking a depth of 15 km.
27

Figure 1.13. Stacked waveforms at rows 12–18 generated by event S-TW1 (Fig. 1.12, red diamond).
Direct P and S waves are labeled by red dashed lines and orange boxes mark P- and S-types FZTW.

Figure 1.14. Inversion results of waveforms generated by event S-TW2 (Fig. 1.12, red diamond). (a)
Comparison between observed (black) and synthetic (red) seismograms. (b) Parameter-space results from
last 10 inversion generations. Green dots represent the tested model parameters and black circles mark the
best-fitting parameters used to generate the synthetic waveforms in (a). The black curves give probability
density functions of the model parameters.

Z
28
1.4. Discussion and Conclusions
We image the internal structure of the SJFZ at the Sage Brush site in the trifurcation area,
using data recorded by a dense rectangular array with 1108 vertical-component sensors around
the Clark branch of the SJFZ and a linear array of six 3-component sensors. The two arrays
provide complementary recordings that allow us to extract important information on key
mechanical components of the FZ structure. The fine-gridded areal coverage of the dense array
compensates for the shorter recording duration of one month and vertical-component data, while
the shorter aperture linear array provides 3 years of three-component data. The data are
examined for clear localized changes of waveforms that indicate a transition between different
crustal blocks, delay times of P waves that provide information on variations of slowness in the
study area, and P- and S- types FZTW that propagate within a seismic waveguide in a portion of
the damage structure.
Fig. 1.15 summarizes the local velocity structure inferred from the performed analyses. The
location of the main Clark fault at depth is inferred to be below the sensors marked by yellow.
This location is found by examining waveform changes in the fault-normal and fault-parallel
directions and observing systematically (Figs 1.4&1.5) different phases across the marked zone.
The delay time analysis of teleseismic and local earthquakes (Figs 1.6&1.7) indicate higher
slowness to the NE of the main Clark fault. Examination of recorded seismograms with
automatic detection algorithms and visual inspection show regular occurrence of P- and S- types
FZTW in a zone on the NE side of the main Clark fault denoted by red sensors. This region is
associated with columns 36-40 of the dense array along with stations SGBF0-SGBN2 of the
linear array, and is approximately bounded to the NE with another mapped surface trace of the
fault. These results are consistent with observations of FZTW generated by Betsy gunshots (Ben-
29
Zion et al., 2015) and detailed noise-based imaging of a significant low velocity zone on the NE
side of the main Clark fault (Hillers et al., 2016; Roux et al., 2016).

Figure 1.15. A simplified velocity model of the SGB site. Circles and balloons represent stations of the
dense and linear SGB arrays, respectively. The labeled rows and columns are the same as in Fig. 1.1(a).
Orange lines are fault surface traces. Yellow sensors mark the location of the main seismogenic fault
inferred from waveform changes. A low-velocity zone that generates P- and S-types FZTW is beneath the
stations in red. The main Clark fault (MCF) separates locally faster material on the SW (cyan) from
locally slower rocks on the NE (pink). The local velocity contrast across the MCF is reversed with respect
to the large-scale structure.
Earthquake- and noise-based tomographic models show that the SJFZ in the study area
separates a crustal block with higher seismic velocity to the NE from a block with lower velocity
to the SW (Allam et al., 2014b; Allam & Ben-Zion, 2012; Zigone et al., 2015). Theoretical
studies indicate that bimaterial ruptures on a right-lateral fault associated with the imaged large-
scale velocity contrast would tend to propagate to the NW (Andrews & Ben-Zion, 1997; Brietzke
et al., 2009; Shi & Ben-Zion, 2006). Repeating occurrence of large bimaterial ruptures to the
30
NW is expected to generate significantly more shallow damage on the NE side with faster
velocity at depth (Ben-Zion & Shi, 2005; Xu et al., 2012b), leading to a local reversal of the
shallow velocity contrast in the immediate vicinity of the Clark fault as summarized in Fig. 1.15.
Geological mapping shows slivers of gneisses in the area predominantly NE of the fault
(Gutierrez et al., 2010; Sharp, 1967; Wade et al., 2017). These rocks have lower than average
velocities in the region (Allam & Ben-Zion, 2012; Share et al., 2017) and may contribute to the
local reversal in the velocity contrast. However, comparison of the surface geology with the
seismic imaging results of Roux et al. (2016) suggests that these rocks may exist only near the
surface and have small effect on the asymmetric damage structure that extends to a depth of
about 2 km (Section 1.3.4). Similar damage-related local reversals of the shallow velocity
contrast across the Clark fault were documented at sites JF and BB (Qiu et al., 2017; Share et al.,
2017) several tens of km to the SE and NW from the SGB site, respectively (Fig. 1.2). The
discussed observational and theoretical results suggest consistently preferred propagation of
earthquake ruptures in the central SJFZ to the NW. This is in agreement with observed
directivity of small to moderate events (Kurzon et al., 2014; Ross & Ben-Zion, 2016), along-
strike asymmetry of aftershocks (Zaliapin & Ben-Zion, 2011) and locations of reversed-polarity
secondary deformation structures in the region (Ben-Zion et al., 2012).
Paleoseismic and historic records indicate that the SJFZ is capable of large (MW > 7.0)
earthquakes (Petersen & Wesnousky, 1994; Rockwell et al., 2015), and has the potential to
rupture along nearly the entire length of the fault zone in a single event (e.g., Onderdonk et al.,
2013; Salisbury et al., 2012). The last through-going event probably occurred in 1800 (Salisbury
et al., 2012) and the average recurrence time for such events is estimated at 257±79 years
(Rockwell et al., 2015). The SJFZ poses a significant current seismic hazard to large urban areas
31
in southern California. Propagation direction of a large SJFZ earthquake to the NW, consistent
with the statistical tendencies implied by the discussed results, would amplify the seismic
shaking in Riverside and other communities in that direction.

1.5 Acknowledgments
We are grateful to Bud Wellman for allowing us to deploy the instruments on his property.
The study was supported by the National Science Foundation (grant EAR-1620601) and the
Department of Energy (awards DE-SC0016520 and DE-SC0016527). The seismic instruments of
the dense rectangular array were provided by Nodal Seismic with help from Dan Hollis and
Mitchell Barklage. The seismic instruments of the linear array were provided by the Incorporated
Research Institutions for Seismology (IRIS) through the PASSCAL Instrument Center at New
Mexico Tech. The facilities of the IRIS Consortium are supported by the National Science
Foundation under Cooperative Agreement EAR-1261681 and the DOE National Nuclear
Security Administration. The work benefitted from comments of two anonymous referees.

32
2. Internal structure of the San Jacinto fault zone at the Ramona
Reservation, north of Anza, California, from dense array seismic
data
(Qin, L., Share, P.-E., Qiu, H., Allam, A. A., Vernon, F. L. & Ben-Zion, Y., 2020. Internal
structure of the San Jacinto fault zone at the Ramona Reservation, north of Anza, California,
from data of dense seismic arrays. Geophysical Journal International, 224(2), 1225-1241,
https://doi.org/10.1093/gji/ggaa482)

2.0 Summary
We image the internal structure of the San Jacinto fault zone (SJFZ) near Anza, California,
with seismic data recorded by two dense arrays (RA and RR) from ~42,000 local and ~180
teleseismic events occurring between 2012-2017. The RA linear array has short aperture (~470
m long with 12 strong motion sensors) and recorded for the entire analyzed time window,
whereas the RR is a large three-component nodal array (97 geophones across a ~2.4 km x 1.4 km
area) that operated for about a month in September-October 2016. The SJFZ at the site contains
three near-parallel surface traces F1, F2, and F3 from SW to NE that have accommodated several
Mw>6 earthquakes in the past 15,000 years. Waveform changes in the fault normal direction
indicate structural discontinuities that are consistent with the three fault surface traces. Relative
slowness from local events and delay time analysis of teleseismic arrivals in the fault normal
direction suggest a slower SW side than the NE with a core damage zone between F1 and F2.
This core damage zone causes ~0.05 second delay at stations RR26-31 in the teleseismic P
arrivals compared with the SW-most station, and generates both P- and S- type fault zone
trapped waves. Inversion of S trapped waves indicates the core damaged structure is ~100 m
wide, ~4 km deep with a Q value of ~20 and 40% S-wave velocity reduction compared with
33
bounding rocks. Fault zone head waves observed at stations SW of F3 indicate a local bimaterial
interface that separates the locally faster NE block from the broad damage zone in the SW at
shallow depth and merges with a deep interface that separates the regionally faster NE block
from rocks to the SW with slower velocities at greater depth. The multi-scale structural
components observed at the site are related to the geological and earthquake rupture history at
the site, and provide important information on the preferred NW propagation of earthquake
ruptures on the San Jacinto fault.

2.1 Background
Large fault zones often have large-scale bimaterial interfaces that separate two crustal blocks
with different seismic velocities and hierarchical damage zones having reduction of elastic
properties with respect to the bounding rocks (Ben-Zion & Sammis, 2003, and references therin).
A large-scale bimaterial fault interface may induce preferential rupture propagation direction
related to the velocity contrast and sense of loading (e.g., Andrews & Ben-Zion, 1997; Ben-Zion,
2001; Shlomai & Fineberg, 2016; Weertman, 1980). Numerous such ruptures on a given fault
section are expected to generate asymmetric rock damage with the regionally faster block
sustaining most of the damage (Ben-Zion & Shi, 2005; Xu et al., 2012b). The asymmetric fault
damage zone may include pulverized rocks that provide important information on the generating
dynamic strain field (Dor et al., 2006; Mitchell et al., 2011; Xu & Ben-Zion, 2017) and is
typically concentrated in the top few kilometers of the crust (Lewis et al., 2005; Peng et al.,
2003). Information on bimaterial fault interfaces, damage zones and other fault properties can be
obtained through high-density deployments of seismic instruments within and around the fault
zone (Ben-Zion et al., 2015; Harjes & Henger, 1973; Rost & Thomas, 2002).
34
Located in the highly populated Southern California area, the San Jacinto fault zone (SJFZ)
is one of the most seismically active fault zones along the boundary between the American and
Pacific plates in the region (e.g. Hauksson et al., 2012; Ross et al., 2017) and accommodates a
comparable potion of the plate motion to that of the southern San Andreas fault (e.g., Becker et
al., 2005; Fay & Humphreys, 2005; Lindsey & Fialko, 2013). Historical records indicate that the
SJFZ hosted numerous Mw > 7 earthquakes (Petersen & Wesnousky, 1994; Rockwell et al.,
2015), some rupturing most of the length of the SJFZ in a single event (Onderdonk et al., 2013;
Salisbury et al., 2012), thus posing significant seismic hazard to the area. Tomography imaging
results of the SJFZ (Qiu et al., 2017; Share et al., 2017; Share et al., 2019b; Yang et al., 2014)
with nominal resolution of 1-2 km indicate complex structures with broad damage zones and
various large-scale velocity contrasts across the fault.
To obtain high-resolution information on internal fault structures, five linear dense arrays
with 10-30 m station spacing were deployed across main traces of the SJFZ in the Blackburn
Saddle (BB), Ramona Reservation (RA), Sage Brush Flat (SGB), Dry Wash (DW) and Jackass
Flat (JF) sites (white and red triangles from NW to SE in Fig. 2.1a). Analyses of direct arrivals,
fault zone head waves that propagate along bimaterial interfaces, and fault zone trapped waves
generated by interference of internal reflections within core fault damage zones reveal high-
resolution local velocity variations, extent and velocity contrasts of bimaterial interfaces, and
seismic and geometrical properties of damage zones at these sites (Qin et al., 2018; Qiu et al.,
2017; Share et al., 2017, 2019b). In addition, Zigone et al. (2019) used 2-35 Hz high-frequency
noise data from these linear dense arrays to obtain shear wave velocities (0.3-0.9 km/s) in the top
~100 m.
35
To complement these studies, we image in the present study the internal fault zone structures
at the Ramona Reservation using local and tele seismic data (Fig. 2.1) from the two dense arrays
RA and RR (Fig. 2.2). The main aim of this work is to resolve bimaterial interfaces, velocity
variations within the fault zone, and properties of the fault damage structures in the study area.
The rest is organized as follows. In the next section we describe the data used for the imaging
analyses. The employed techniques and derived results are presented in Section 2.3 and
discussed in Section 2.4.

Figure 2.1. (a). All local events recorded by the short RA and long RR arrays. Lower panel shows the
depth profile projected to AA’. The Ramona site is shown as a red triangle, and other four linear arrays
along the SJFZ (BB, SGB, DW, JF from NW to SE) are plotted with white triangles. The blue, cyan, and
red boxes define the areas where we search for FZTW and waveform changes, FZHW, and perform delay
time analysis of local earthquakes, respectively. The four labeled events (evt 1-4; big yellow stars) are
examples for waveform change study (Fig. 2.4), and TW1 (big green square) is the FZTW candidate
event (Figs 2.12-2.13). (b). All teleseismic events in 2012-2017 that are used in the short RA (circles)
and long RR (stars) array studies. Color represents event depth and circle size indicates event magnitude.
The RA site (black triangle) and example event Tele1 (Fig. 2.3) are outlined in white.

36
2.2 Data and preprocessing
Regional tomography results (Allam et al., 2014b; Allam & Ben-Zion, 2012; Share et al.,
2019a) suggest the main strand of the SJFZ in the Ramona Reservation, the Clark fault, separates
overall faster velocity rocks to the NE from the SW at depth. At this site, two dense arrays (RA
and RR in Fig. 2.2) were installed across three fault surface traces (F1, F2, F3 in Fig. 2.2)
associated with Mw>6 earthquakes in the past 15,000 years (Rockwell et al., 2015). The short
linear RA array (red balloons in Fig. 2.2) has 12 three-component strong motion sensors (01 to
12 from SW to NE) over an aperture of ~470 m crossing F2, and started recording in 2012 at 200
samples per second (sps). The RR array contains 65 stations installed along a line with an
aperture of ~2.4 km in the fault normal direction (01 to 65 from SW to NE in Fig. 2.2) and 32
stations distributed around the SW-NE line (Fig. 2.2) expanding for ~1.4 km in the along fault
direction. The RR array has three-component geophones sampling at 500 sps and recorded from
Sep 1st to Oct 2nd in 2016. RR stations 28-41 cover a similar area as the RA array. The fault
surface traces, F1, F2 and F3, are located between stations RR20-21, RR31-32/RA04-05 and
RR42-43, respectively.
We investigate data from 2012-2017 associated with ~180 M>5 teleseismic events (Fig.
2.1b) with clear P arrivals, and ~42,000 local events within an area (blue box in Fig. 2.1a) of 200
km in the fault-parallel and 60 km in the fault-normal directions centered on the study site. Of
these, ~1700 local and ~11 teleseismic events occurred during the deployment of the RR array.
Local P and S wave arrivals are automatically detected (Ross et al., 2016; Ross & Ben-Zion,
2014), and teleseismic P wave arrivals are estimated using the TauP toolkit (Crotwell et al.,
1999) and IASP91 velocity model. Seismic recordings are discarded if the signal-to-noise ratio is
37
smaller than 3, defined as the ratio of root-mean-square values between the signal window (e.g.
P/S arrivals) and the preceding noise window of the same length.

Figure 2.2. (a). Layout of the short RA (red balloons) and long RR (non-red balloons) arrays. Several
station numbers are labeled with the same color of the station symbol. The station numbers increase from
SW to NE, 01-12 for the RA and 01-65 (following the white dashed lines) for the RR arrays. Green
balloons are RR stations used for beamforming. The orange lines represent the three fault surface traces
of the Clark Fault that are related to previous M > 6 earthquakes, labeled as F1, F2, and F3. (b). Station
elevation profiles for the RR (blue triangles) and RA (red triangles) arrays.
We first analyze spatial changes of waveforms in the fault normal direction (Section 2.3.1) to
identify structural discontinuities. Next, P-wave delay time from teleseismic events, and P-wave
relative slowness from local earthquakes within a 60 km × 20 km box centered on the site (red
box in Fig. 2.1a), are analyzed to investigate local velocity variations (Section 2.3.2). Using the
RR array, fault zone head waves (FZHW, Section 2.3.3) from events located <10 km normal to
the fault (cyan box in Fig. 2.1a) are analyzed to constrain bimaterial interface properties (location
38
and velocity contrast). Fault zone trapped waves (FZTW, Section 2.3.4) are investigated to
constrain parameters of the core damage zone.

2.3 Analyses
2.3.1 Waveform changes
Theoretical results (e.g., Ben-Zion, 1998; Ben-Zion & Aki, 1990; Igel et al., 1997; Jahnke et
al., 2002) and in-situ observations (e.g., Catchings et al., 2016; Cormier & Spudich, 1984;
Korneev et al., 2003; Qin et al., 2018; Rovelli et al., 2002) show that lateral variations in fault
zone structures can affect waveform characteristics, e.g., amplitude, travel time, particle motion
and spectral content. We investigate changes in these properties across the RR array using cross-
correlation analysis and visual inspection applied to tele and local seismic data. In general, while
waveforms change to some extent because of factors such as focal mechanism and event
location, there are persistent transitions of waveform characteristics across the three fault surface
traces at the study site.
Fig. 2.3(a) presents 1 Hz lowpass filtered P waves from a teleseismic event (Tele1, labeled in
Fig. 2.1b). We calculate the matrix of cross-correlation coefficients (CC) of the array data in a
2.5 s time window (blue lines in Fig. 2.3a) starting 0.5 s before the P arrival. The short time
window is chosen to suppress the influence of later arrivals. The median CC from all events at
RR and RA arrays are presented in Fig. 2.3(b)&(c). Waveforms at RR stations NE of F3 are
highly correlated with each other with CC values close to 1, and less correlated with those from
stations to the SW (CC=<0.8). The same pattern emerges for stations between F1 and F3, where
the waveforms show high correlation with each other but not with stations outside. There is,
however, only a slight decrease in CC values for stations between F2 to F3 compared to those
39
between F1 to F2 (Fig. 2.3b). This is more clearly seen in the CC results of the short RA array
based on more events (Fig. 2.3c). Fig. 2.4 displays 1-20 Hz bandpass filtered waveforms of four
local events (labeled in Fig. 2.1a) from four quadrants separated by the local fault-parallel and
fault-normal directions. Despite differences in focal mechanisms and locations, we consistently
observe changes in phase, amplitude and frequency across stations near the surface traces F1, F2
and F3 (blue, green and red dashed lines in Fig. 2.4). Events with similar waveform change
patterns are shown in Fig. 2.1(a) with yellow stars. The CC patterns and local waveform changes
across the arrays imply structural blocks separated by the three fault traces with different
material properties that may be related to the fault zone evolution and previous rupture activities.

Figure 2.3. (a). 1 Hz lowpass filtered waveforms from event Tele1 (labeled in Fig. 2.1b). Zero time
indicates P arrival, and blue lines represent the 2.5 s time window for cross correlation. Low SNR traces
are removed. (b) and (c) are the median cross correlation coefficients of the RR (b) and RA (c) arrays
from all the teleseismic events. The locations of three fault surface traces (F1, F2, F3) are plotted with
black dashed lines.
40

Figure 2.4. 1-20 Hz bandpass filtered waveforms from four local events (evt 1-4, labeled in Fig. 2.1a).
Locations of the three fault surface traces (F1, F2, F3) are labeled.
2.3.2 Delay time analysis
Following previous studies (e.g. Qiu et al., 2017; Share et al., 2017), we analyze the arrival
time patterns of tele and local seismic P waves to obtain the velocity variations inside the fault
zone. Teleseismic waves are lowpass filtered at 1 Hz, and then the delay time for each station
relative to the reference station (the SW-most station) in each array is calculated via cross
correlation in a 2.5 s time window starting 0.5 s before the P arrival (same time window as in
Section 2.3.1). Since the delay times in the two arrays are calculated with respect to different
reference stations (RR01 for RR array and RA01 for RA array), only delay time trends in the two
arrays are comparable, not the absolute values. Fig. 2.5(a) presents the delay time from a
teleseismic event (location labeled in Fig. 2.1b, waveforms and time windows shown in Fig.
2.3a) and the median delay time from all events at RR array. The results indicate a faster NE
Figure 4. 1-20 Hz bandpass filtered waveforms from four local events (evt 1-4, labeled in Fig. 1a).
Locations of the three fault surface traces (F1, F2, F3) are labeled. (d). evt4 (c). evt3 (b). evt2 (a). evt1
F1
F2
F3
Page of 4 14
41
block relative to the SW, with a broad damage zone that includes areas near the three fault traces.
The RA delay time (green dashed line in Fig. 2.5a) shows consistent results with RR stations
over the similar area.
Considering the significant topographic change at the study site (Fig. 2.2b), we correct the
influence of station-event geometry and local topography following Qin et al. (2018). The time
difference caused by station-event geometry is approximated by the travel time difference
predicted from the TauP toolkit (Crotwell et al., 1999) and the IASP91 velocity model. Local
topography induced delay time is calculated via = (
,
−
-./
)/
-./
where
,
and
-./
are
the elevations of station and the reference station, and
-./
is the reference velocity of the
surface layer. We use a reference P-wave velocity here of 4 km/s for the elevation correction.
Since station elevation increases from SW to NE, the choice of reference velocity will not affect
the general trend that the NE is faster than the SW side; any reasonable velocity used during
topography correction will only further decrease the delay on the NE side (Fig. 2.5) and will not
change the major trend of the delay time (see Fig. B2.1 for results using different reference
velocities).
The corrected delay times are shown in Fig. 2.5(a) as blue (RR array) and red (RA array)
dots with error bars representing one standard error. Stations to the NE of F3 are located on a
generally faster block compared to the SW side, consistent with the large-scale velocity
structure. Stations between RR01 and RR47 have positive relative delay times, indicating an
underlying broad damage zone. The maximum delay time is ~0.05 s and occurs at stations
RR26-31 between F1 and F2, indicating the core of the fault damage zone, which is further
elaborated by FZTW analysis in Section 2.3.4. A bimaterial interface with the most significant
velocity contrast at the site marks the transition between the broad damage zone and the
42
regionally faster NE block. This interface is imaged in Section 2.3.3 using local FZHW. For
local P wave analysis, we use events that are close to the site (red box in Fig. 2.1a), and exclude
P picks that are more than 1 s away from predicted values using 1D velocity model averaged
from the 3D tomographic results of Allam & Ben-Zion (2012). Then we calculate the along-path
average slowness using the P-wave travel time divided by the along-path distance, and reject
slowness values that are larger than 0.25 s/km or smaller than 0.125 s/km. The relative slowness
is obtained as slowness values normalized by the array median value. This procedure was
applied at other sites along the SJFZ (Qin et al., 2018; Qiu et al., 2017; Share et al., 2017; Share
et al., 2019b) and produced stable and reliable relative slowness values within the fault zones
irrespective of regional 3D velocity variations.
Figs. 2.5(b)-(d) show relative slowness inside the two arrays and relative slowness
histograms from two stations RA01 and RR15. The well-defined median and standard deviation
values at each station support the reliability of the obtained relative slowness. The RR results
show similar patterns as the teleseismic analysis with the NE side faster than the SW, while the
short aperture RA stations show a slightly uniform relative slowness. The RR results exhibit
larger variations than those from the RA array because of the limited data available for the RR
array. The broad damage zone is less pronounced in Fig. 2.5(b) as the higher frequency local P
arrivals have higher resolution and highlight shallower small-scale variations within the broader
damage zone, including very low velocity structures around F2 and stations RR23-27. Ambient
noise tomography shows similar variation in shallow S-wave velocity structures contained within
a broader low velocity damage zone (Wang et al., 2019). More details about the fault damage
zone are presented in Section 2.3.4.
43

Figure 2.5. Delay time analysis results from teleseismic events (a) and relative slowness analysis from
local events (b-d). (a). Teleseismic P wave delay time results from a single event Tele 1 (faded green line
labeled as “Tele1"; event location is labeled in Fig. 2.1b and waveforms are shown in Fig. 2.3a), median
delay time from all events at the RR (black dashed line) and RA (green dashed line) arrays, corrected
median delay time using v ref=4 km/s at the RR (blue dots) and RA (red dots) arrays with error bar being
one standard error. (b). Relative slowness from local earthquakes at the RR (blue dots) and RA (red dots)
arrays. Error bar is one standard error. (c) and (d) show histograms and median values (red lines) of
relative slowness at stations RA01 and RR15, respectively.
2.3.3 Fault zone head waves
Fault zone head waves (FZHW) are emergent phases that propagate most of their path along
a bimaterial interface with the velocity of the faster block and radiate from the interface to the
slower side (e.g. Ben-Zion, 1990). Synthetic and observed seismograms show that the emergent
FZHW have significantly different amplitudes and frequency contents than the impulsive direct
P waves (Ben-Zion & Malin, 1991; McGuire & Ben-Zion, 2005). FZHW can be used to analyze
Figure 5. Delay time analysis results from teleseismic events (a) and relative slowness analysis from
local events (b-d). (a). Teleseismic P wave delay time results from a single event Tele 1 (faded green
line labeled as “Tele1"; event location is labeled in Fig. 1b and waveforms are shown in Fig. 3a),
median delay time from all events at the RR (black dashed line) and RA (green dashed line) arrays,
corrected median delay time using vref=4 km/s at the RR (blue dots) and RA (red dots) arrays with error
bar being one standard error. (b). Relative slowness from local earthquakes at the RR (blue dots) and
RA (red dots) arrays. Error bar is one standard error. (c) and (d) show histograms and median values
(red lines) of relative slowness at stations RA01 and RR15, respectively. Tele1
(a) (b) (c)
RA01
RR15
(d)
F1
F2
F3
Page of 5 14
44
properties of bimaterial interfaces such as continuity and degree of velocity contrast. The
emergent FZHW arrive before the direct impulsive P waves at stations on the slower side closer
to the fault than a critical distance
0
defined as
0
= ∙(
+
+
/
&
+
−1)
!
"
, where ,
+
,
&
are the
propagation distance along bimaterial interface, P-wave velocity on the fast and slow sides,
respectively. The separation time (∆) between the FZHW and P-wave arrivals decreases when
the propagation distance () of FZHW along bimaterial interface decreases or the fault normal
distance of the station and/or event increases (Share & Ben-Zion, 2018), and can be estimated
with ∆ = ∙∆/
+
with ∆ and representing, respectively, the differential and average P-
wave velocities of the bimaterial interface.

Figure 2.6. Events that generate local (red squares) and regional (purple squares) FZHW. The red star
and circle represent the candidate and reference events for local FZHW (Fig. 2.7), and purple star and
circle for regional FZHW (Fig. 2.9).
45
A small critical distance, or fast decay of P-wave and FZHW differential arrival time in the
fault normal direction, imply a small velocity contrast or/and short propagation distance of
FZHW along bimaterial interface. Different waveform characteristics like motion polarity (e.g.
Ben-Zion & Malin, 1991; Bulut et al., 2012), frequency content (Share et al., 2019b), and arrival
time moveout patterns related to the different azimuths of the direct P and FZHW wavefronts are
critical to identifying FZHW. Inside the RR array, we observe two types of FZHW: (1) local
FZHW (red squares in Fig. 2.6) related to a local interface between the broad low-velocity
damage zone and regionally faster rocks to the NE; (2) regional FZHW (purple squares in Fig.
2.6) propagating along a deep large scale interface that is connected to the local bimaterial
interface.

Figure 2.7. 1-20 Hz bandpass filtered waveforms from a candidate event (a; red star in Fig. 2.6) with and
a reference event (b; red dot in Fig. 2.6) without local FZHW. Green and red dashed lines show the
FZHW and impulsive P arrivals, respectively. Waveforms from each event are uniformly normalized by
the array maximum, and zero time corresponds to event’s origin time.
(a). Candidate event (b). Reference event
46
Fig. 2.7 presents waveforms from a candidate event (red star in Fig. 2.6) that generate local
FZHW and a reference event nearby (red dot in Fig. 2.6) that does not. The reference event is
likely located too far NE (regional faster side of the SJFZ) at depth to produce critically refracted
local FZHW. For stations RR47-26, the first arrivals from the candidate event are emergent with
smaller amplitudes compared with those at other stations. From stations RR47 to RR26, the
separation time between the first arrivals (i.e. FZHW, green line in Fig. 2.7a) and direct P waves
(red dashed line in Fig. 2.7a) decreases dramatically from ~0.1 to 0 s. In contrast, the reference
event generates impulsive P waves as first arrivals at all stations. In Fig. 2.7a, the lack of
observed FZHW at stations SW of RR26 implies a short propagation distance of FZHW along a
bimaterial interface.
To confirm this, we present in Fig. 2.8 the waveforms from all candidate events (red squares
in Fig. 2.6) at stations RR47 with and RR50 without FZHW. Waveforms in Fig. 2.8 are aligned
with the first impulsive P wave arrivals, and plotted with respect to the along-fault-distances of
events to the Ramona site. Although the two stations are only ~120 m apart, they are located on
different sides of a bimaterial interface, resulting in significantly different first arrivals (i.e.
emergent FZHW vs. impulsive P waves). The separation time of FZHW and P waves is 0.1 s,
and does not change with event distance along the fault, indicating that all these FZHW
propagate the same distance along a similar bimaterial patch. Therefore, this type of FZHW is
related to a relatively shallow and local bimaterial interface, with structure on the SW of station
RR47 being slower than to the NE of that station. Combined with the analysis in Sections 2.3.1-
2.3.2, this local bimaterial interface corresponds to the interface between the broad damage zone
and regionally faster block to the NE. A near surface S-wave velocity contrast in a similar
47
location and with the same velocity contrast polarity is observed using ambient noise
tomography (Wang et al., 2019).

Figure 2.8. Waveforms at stations RR47 (a) and RR50 (b) from all events (red squares in Fig. 2.6) that
generate local FZHW. FZHW arrivals are labeled with green squares. Waveforms are normalized by the
array maximum for each event to preserve the amplitude information, and aligned according to the first
impulsive waves, i.e. direct P arrivals (zero time, red dashed lines).
There is also evidence for a deep bimaterial interface that continuously extends from the edge
of the broad damage zone down to seismogenic depths. Fig. 2.9 shows waveforms from a
candidate event (purple star in Fig. 2.6) with FZHW propagating along a deep interface and a
reference event nearby (purple dot in Fig. 2.6). Despite locating also on the regionally slow side
of the SJFZ at depth (Allam & Ben-Zion, 2012; Share et al., 2019a), the reference event is likely
too far SW of the deep bimaterial interface and too close to the Ramona site to generate first
arriving FZHW (Share & Ben-Zion, 2018). The first arrivals from the candidate event at stations
RR47-1 are emergent FZHW (green line in Fig. 2.9a), while the first arrivals from the reference
event are impulsive direct P waves. Fig. 2.10 shows waveforms from all candidate events (purple
squares in Fig. 2.6 in the trifurcation area) at stations RR47 with and RR50 without FZHW. The
48
P waves are delayed by ~0.25 s with respect to the FZHW arrivals. This delay is approximately
equal for these events given their similar hypocenters.

Figure 2.9. 1-20 Hz bandpass filtered waveforms from a candidate event (a; purple star in Fig. 2.6) with
and a reference event (b; purple dot in Fig. 2.6) without regional FZHW. The layout is the same as in Fig.
2.7, but a longer time window is shown to highlight the original 1.5 s reference beam trace for the central
station RR34 (dark red) associated with the frequency windowed beam stacks in Fig. 2.11(c).
Compared with Figs 2.7-2.8, the differential arrival times between P waves and FZHW in
Figs 2.9-2.10 are generally larger and all stations SW of RR47 record first arriving FZHW
(increased critical distance, e.g., Share & Ben-Zion, 2018). Especially on the SW of station
RR26 where there is no FZHW in Figs 2.7-2.8, the P-wave and FZHW differential travel time
decreases with a significantly small rate. These observations imply a longer propagation distance
of FZHW in Figs 2.9-2.10 along a deep bimaterial interface, which connects to the local interface
between damage zone and faster NE fault block at the study site. Unfortunately, no other clear
FZHW generating events with significantly different hypocentral distances occurred during the
49
month-long RR array deployment. Thus, we are unable to accurately constrain the extent of and
velocity contrast across this deep interface. Nevertheless, a deep bimaterial fault that extends
continuously from the Clark fault surface trace to seismogenic depth in the trifurcation area is
consistent with analysis of FZHW recorded at the Blackburn Saddle site (Fig. 2.1a, Share et al.,
2017, 2019b) and regional scale seismic tomography showing generally faster velocities on the
NE side of the Clark fault (Allam et al., 2014b).

Figure 2.10. Waveforms at stations RR47 (a) and RR50 (b) from all events (purple squares in Fig. 2.6)
that generate regional FZHW. The layout is the same as in Fig. 2.8.
Despite the poor constraints on P velocity properties of the regional bimaterial interface at
depth, we are able to use the azimuthal and frequency differences between the FZHW and direct
P waves to constrain the properties of the bimaterial interface near the surface. This is done
using beamforming (e.g. Rost & Thomas, 2002) over azimuth, horizontal slowness and
frequency space to separate coherent FZHW (lower frequency) from coherent direct P waves
(higher frequency). For beamforming, we only use stations SW of the bimaterial interface (SW
of RR47), inside the broader damage zone (e.g., Fig. 2.5a) and only a selection of stations along
50
the main across-fault profile. Stations for beamforming analysis are plotted with green balloons
in Fig. 2.2(a). This allows the best beamforming results using stations that (1) all record FZHW,
(2) all locate within similar velocity structure (even though the velocity is lowest), (3) are more
homogeneously spaced and (4) have comparable elevations relative to the array aperture (all
selected stations are within 40 m elevation of the central station – RR34).
We systematically search slowness space from 0.03 to 0.43 s/km in increments of 0.01 s/km,
azimuth space from 0 to 360 in 1 degree increments and frequency space from 2 to 19 Hz in
steps of 1 Hz with a bandwidth of +/- 1 Hz at each step. For each combination of slowness,
azimuth and frequency, beamforming is done on 2 s P waveforms (starting 0.5 s before first
arrival) using a 4-th root slant slack (Rost & Thomas, 2002) to capture as best as possible the
weak FZHW signals. The beamforming results applied to the candidate event in Fig. 2.9(a) are
shown in Fig. 2.11. Similar results are obtained for the other candidate events in Fig. 2.8(a) (not
shown). The centers of the two most pronounced beams, and therefore coherent plane
wavefronts, are associated with parameters s=0.14 km/s, azimuth=100 degrees and central
frequency=5 Hz (Fig. 2.11a), and s=0.17 km/s, azimuth=152 degrees and central frequency=13
Hz (Fig. 2.11b). These represent respectively the FZHW wavefront propagating from the fault
(lower dominant frequency) and the direct P wavefront originating from the event epicenter
(higher dominant frequency). Due to the irregular geometry of the array stations employed in
beamforming, some quantification of uncertainty in these estimates is required. Array transfer
function for the 4-6 Hz and 12-14 Hz frequency ranges (Fig. B2.2) show faint artefacts are
present in the across-fault (azimuth=40°) and along-fault (azimuth=130°) directions, because of
the two main array profile azimuths. The average radii of the central beams in these plots are 0.1
s/km (4-6 Hz) and 0.04 s/km (12-14 Hz) (Fig. B2.2). However, neither the obtained FZHW nor
51
direct P beams are close to the 40°, 130° azimuths so we consider them well constrained to
within a slowness error of 0.04-0.1 s/km.

Figure 2.11. Separation of FZHW and direct P wavefronts using beamforming. (a). Beamforming results
for the frequency band 4-6 Hz. The red cross represents a prominent coherent phase within the FZHW
spectrum. Radius of this beam to 50% of peak amplitude corresponds to a slowness difference of ~0.05
s/km. (b). Beamforming results for the frequency band 12-14 Hz. The black cross represents a prominent
coherent phase within the direct P wave spectrum. The beam radius here corresponds to a slowness
difference of ~0.03 s/km. (c). Beam traces and energy envelopes for the beamforming results in (a) (red)
and (b) (black). (d). Horizontal particle motions for the FZHW beam trace (red) and direct P beam trace
(black) compared to their respective azimuths determined in (a) (gray solid line) and (b) (gray dashed
line).
52
Using the obtained FZHW and direct P parameters, we slant stack the respective traces (4-th
root modulation not applied), cross correlate the resultant beam trace with each individual trace
allowing only a time shift equal to the dominant period for that phase (1/5 s = FZHW and 1/13 s
= direct P), and then stack the highest correlating traces again. This allows the best quality
coherent beam trace in the presence of complex fault zone structures and an uneven surface. The
final stacked beam traces at the location of station RR34 shows the earlier arrival of the FZHW
wavefront (red) compared to the direct P wavefront (black) (Fig. 2.11c). The time difference
between FZHW and direct P waves is reduced compared to station RR47 (Fig. 2.8a) as RR34 is
farther from the bimaterial interface. The horizontal particle motions of the beam traces (Fig.
2.11d) highlight again the FZHW radiating from the fault (red particles) and direct P waves
pointing to the event epicenter (black particles). The deviation in azimuth obtained from
beamforming and horizontal particle motions for the high frequency direct P waves (Fig. 2.11d)
probably relates to the interactions of the respective wavefronts with the free surface, and may
also indicate anisotropic velocity structure within the broad damage zone (Bear et al., 1999; Li et
al., 2015). Using the more robust estimate of FZHW azimuth from beamforming (Fig. 2.11a), we
estimate an apparent velocity contrast across the interface around RR47. Given the surface fault
strike of 130 degrees (FZHW propagate along fault surface on fast side) and a FZHW azimuth of
100 degrees in the SW, using Snell’s Law the apparent velocity contrast relative to the NE block
is 13.4%. This is an apparent estimate because it doesn’t consider potential dipping fault
geometry and the incident angles of the respective P phases.

53
2.3.4 Fault zone trapped waves
Fault zone trapped waves (FZTW) are critically reflected phases that constructively interfere
inside a low-velocity zone such as fault related core damage zone (e.g., Ben-Zion, 1998; Ben-
Zion & Aki, 1990). The most common type of FZTW, Love-type SH signals following the direct
S arrival, have been observed in many places (e.g., Ben-Zion et al., 2003; Cochran et al., 2009;
Haberland et al., 2003; Lewis & Ben-Zion, 2010; Li et al., 1990, 1994, 1997; Mamada et al.,
2004; Mizuno & Nishigami, 2006). A less common type of trapped waves involving leaky
modes between the P and S body waves is also generated in some cases (Gulley et al., 2017;
Malin et al., 2006). Both types of FZTW have been observed in previous studies along the SJFZ
(e.g., Qin et al., 2018; Qiu et al., 2017). Events that generate FZTW inside the RR array are
shown as green squares in Fig. 2.1(a). These events are selected using the automatic picking
algorithm (Ross & Ben-Zion, 2015) and confirmed based on visual inspection. Fig. 2.12 presents
the vertical and fault parallel waveforms from a candidate event (TW1, labeled in Fig. 2.1a)
containing large amplitude wave packages related to P- and S- type FZTW (red dashed boxes in
Fig. 2.12). The locations of stations recording FZTW (RR26-31) are consistent with the lowest
velocity zone (maximum delay) obtained from delay time analysis (Section 2.3.2, Fig. 2.5).
We next model the observed Love-type FZTW using the 2D analytic solution of Ben-Zion &
Aki (1990), and invert for properties of the core damage zone with a genetic inversion algorithm
(e.g. Ben-Zion et al., 2003; Qiu et al., 2017; Share et al., 2017). We use a three-layer fault zone
model with a low velocity zone sandwiched between two half spaces, and describe the model
with six parameters: shear wave velocities of the half space and damage zone, and, Q value,
width, depth, and location of the SW edge of the damage zone. Though the study site has quite
complex structures based on the analyses in Sections 2.3.1-2.3.3, adding more parameters will
54
greatly increase the null space of the inversion and the possibility of ending up with local
minima. Therefore, this simplified three-layer six parameter model provides a useful approach
because it encompasses the key average properties affecting FZTW in the core damage zone,
while accounting analytically for the significant trade-offs between model parameters (Ben-Zion,
1998).

Figure 2.12. Vertical (a) and fault parallel (b) component waveforms from the FZTW candidate event
TW1 (labeled in Fig. 2.1a). P- and S- type FZTW are labeled with red dashed boxes.
Fig. 2.13 shows the fitness values (green dots in Fig. 2.13a) for the six model parameters and
waveform fit for the candidate event in Fig. 2.12. The black curves in Fig. 2.13(a) represent the
probability density functions obtained by summing the fitness values for the final 2000 models
during inversion. The black dots in Fig. 2.13(a) shows the best-fitting model that generates the
synthetic waveforms in Fig. 2.13(b), which are close to the probability density distribution peaks,
i.e. the most likely model. Both the phase and amplitude of FZTW from the best fitting model
55
are similar to the observed FZTW (Fig. 2.13b). The large fitness values (>0.7) and narrow peaks
of the probability density functions, and, the good fit between the best-fitting and most likely
models imply robust inversion results. Combined with the modeling results from another event
(Fig. B2.3), the obtained core damage zone is ~100 m wide and ~4 km deep, with Q value of ~20
and 40% S-wave velocity reduction compared with the host rock with S-wave velocity of ~3.2
km/s, consistent with the analyses in Sections 2.3.1-2.3.3. The FZTW results pinpoint the
location, depth extent and other parameters of a core damage zone that lies within the flower-
shaped broader damage zone at the site (Wang et al., 2019).

Figure 2.13. S-type FZTW inversion results from event TW1. (a). Parameter space plot from the last
2000 inversion models showing the fitness values (green dots), probability density functions (black
curves), and best fitting model (black dots). From top to bottom (left to right) shows the shear wave
velocity of host rocks, and shear wave velocity, Q value, width, SW edge and propagation distance of
FZTW inside the damage zone. (b). Observed (black) and synthetic (red) waveforms from the best-fitting
model (black dots in a).
56

Figure 2.14. A schematic local velocity model at the study site.

2.4 Discussion and Conclusions
This study uses various fault zone phases and analysis techniques to provide collectively
high-resolution images for the SJFZ at the Ramona Reservation, north of Anza, California. Fig.
2.14 presents a schematic local velocity model based on the study. Delay times (Section 2.3.2)
from tele and local seismic data indicate a faster NE side than the SW, with the major velocity
contrast close to station RR47 separating the regionally NE faster block from a broad low
velocity damage zone. This velocity contrast is also the interface from which local and regional
FZHW (Section 2.3.3) refract before being recorded at SW stations, and, is consistent with the
waveform changes (Section 2.3.1) across the local fault surface trace F3. The core damage zone
beneath stations RR26-31 (i.e. between the local fault surface traces F1 and F2 related to the
observed waveform changes in Section 2.3.1) causes the most significant P-wave delays (0.05 s;
Fig. 2.5a) inside the array and generates P- and S- type FZTW (Section 2.3.4). Modeling of S-
57
type FZTW indicates that the core damage zone is ~100 m wide ~4 km deep and has Q value of
20 and 40% S-wave velocity reduction compared with the host rock with S-wave velocity of 3.2
km/s. Assuming that the local bimaterial interface around RR47 also extends to ~4 km depth and
the local FZHW propagate near-vertically along most of that length, the ~0.1 s differential time
between FZHW and direct P waves observed at RR47 (Fig. 2.8a) corresponds to a velocity
contrast of ~12% for a NE-side P-wave velocity of 5.6 km/s (1.75x3.2 km/s). This is consistent
with the apparent contrast of 13.4% in Section 2.3.3 and lie within the 11-23% P velocity
contrast range for the deep bimaterial SJFZ ~10 km to the NW (Share et al., 2019b).
The analyses of different data sets (e.g. teleseismic and local seismic data, travel time and
azimuth) also resolve structures at different scales. The teleseismic waves have almost identical
paths before arriving at the stations, thus the delay time patterns are indicative of the shallow
structure beneath the array with NE side faster than the SW and a core damage zone beneath
stations RR26-31. The observed fault damage zone is compatible with waveform modeling
results based on FZTW. Relative slowness analysis of local seismic data uses along-path average
slowness and can be affected by both regional (e.g. bimaterial interface) and local (e.g. local
damage zones) structures. Previous large-scale imaging results suggest that the velocity contrast
at the Ramona Reservation is as large as 20% and very well confined (Allam & Ben-Zion, 2012),
therefore the large-scale velocity structure plays a major role in affecting the along-path average
slowness. The relative slowness study shows a velocity contrast with NE of station RR47 faster
than the SW, consistent with the bimaterial interface properties from FZHW analyses. However,
it does not resolve the local fault damage zone, because the core damage zone is highly confined
(~100 m wide in Section 2.3.4) and the broad damage zone concentrates in the shallow structure.
All the obtained results consistently imply faster velocity on the NE side with a core damage
58
structure between F1 and F2 embedded within a broader flower-shape damage zone at the study
site. Accounting for the imaged bimaterial interfaces and local damage zones can improve the
accuracy of earthquake locations with respect to the fault, focal mechanisms, receiver function
results and local body wave tomography models (e.g., Ben-Zion & Malin, 1991; Bennington et
al., 2013; McNally & McEvilly, 1977; Schulte-Pelkum & Ben-Zion, 2012).
Large-scale imaging of the region around the central SJFZ (e.g., Allam & Ben-Zion, 2012;
Zigone et al., 2015) show that the NE block in the study area is faster than the SW. Detailed
linear array studies along the SJFZ (Qin et al., 2018; Qiu et al., 2017; Share et al., 2017; Share et
al., 2019b) consistently indicate such a regional bimaterial interface polarity (Fig. B2.4). For
right-lateral loading, this velocity contrast can produce a statistically preferred rupture
propagation direction to the NW (Andrews & Ben-Zion, 1997; Brietzke et al., 2009; Shi & Ben-
Zion, 2006). This theoretical expectation is supported by observational studies of directivity of
small earthquakes in the region (Kurzon et al., 2014; Meng et al., 2020; Ross & Ben-Zion, 2016).
Repeated rupture with preferred propagation direction will generate damaged material on the
faster side of the fault (Ben-Zion & Shi, 2005; Xu et al., 2012a). Such damage zones are
observed at various sites (BB, SGB, JF) on the NE side of the SJFZ based on analysis of FZTW.
Modeling of FZTW at BB, SGB and JF sites along the SJFZ suggests narrow (~70-200 m wide)
core damage zones with significant 30-60% S-wave velocity reductions and Q values of 20-60 in
the top 2-5 km. Severely damaged structures at the SGB site cause local reversals of the large-
scale velocity contrast, complicating the internal fault structures. Local FZHW further validate
the existence of bimaterial interfaces and damage zones, observed at the JF and BB sites on the
SW of the interface between local damage zones and the faster NE fault block (Fig. B2.4).

59
Similar bimaterial interfaces and damage structures illuminated by various fault zone phases
were observed at other large fault systems. FZHW were used to image deep velocity contrasts
along the Hayward fault (Allam et al., 2014a), the North Anatolian fault (Bulut et al., 2012) and
various sections of the San Andreas fault (Lewis et al., 2007; McGuire & Ben-Zion, 2005; Zhao
et al., 2010). FZTW were observed along the North Anatolian fault (Ben-Zion et al., 2003), the
San Andreas fault (e.g. Lewis & Ben-Zion, 2010; Li et al., 1990), Japan (Mamada et al., 2004;
Mizuno & Nishigami, 2006), Italy (e.g., Rovelli et al., 2002), Israel (Haberland et al., 2003) and
other locations. The observed core damage structures are usually 100-200 m wide and
concentrate in the top 2-4 km with 20-40% S-wave velocity reductions. The resulting high-
resolution images of the internal fault zone features provide important information for
understanding persistent properties of local earthquake ruptures, and improve the accuracy of
derived earthquake locations, focal mechanisms and more.
The Ramona Reservation site is characterized by three fault surface traces separating
different materials with a core damage zone surrounded by a broad shallow damage structure.
Multiple historic ruptures of moderate and large earthquakes in this area altered the local velocity
structure and produced rock damage asymmetry with more damage on the faster side of the main
fault (Dor et al., 2006). The most recent rupture in 1918 was located on a fault trace SW of F1
(Rockwell et al., 2015), and probably has contributed to the observed damage zone in this study
on the NE side of the ruptured trace. Studies at other sites along the SJFZ (Qin et al., 2018; Qiu
et al., 2017; Share et al., 2017; Share et al., 2019b) consistently resolve bimaterial interfaces
separating faster blocks to the NE and asymmetric damage zones in corroboration with the
preferred propagation direction of large earthquakes in the central section of the SJFZ to the NW.
This increases the seismic shaking hazard in the large communities to the NW of Anza, CA.
60

2.5 Acknowledgements
This work benefitted from useful comments by Christian Haberland, an anonymous referee
and Editor Ana Ferreira. The data used in this work can be obtained from Allam et al. (2016).
The study was supported by the U.S. Department of Energy (awards DE-SC0016520 and DE-
SC0016527).
61
3. Imaging and monitoring temporal changes of shallow seismic
velocities at the Garner Valley near Anza, California, following
the M7.2 2010 El Mayor-Cucapah earthquake
(Qin, L., Ben-Zion, Y., Bonilla, L. F., & Steidl, J. H., 2020. Imaging and Monitoring Temporal
Changes of Shallow Seismic Velocities at the Garner Valley Near Anza, California, Following
the M7.2 2010 El Mayor-Cucapah Earthquake. Journal of Geophysical Research: Solid Earth,
125(1), 1–17. https://doi.org/10.1029/2019JB018070.)

3.0 Summary
Seismograms from ~700 local earthquakes recorded at various depths (0 m, 6 m, 15 m, 22 m,
50 m, and 150 m) by sensors of the Garner Valley Downhole Array (GVDA) in southern
California are used to analyze the shallow velocity structure and temporal changes of seismic
velocities after the 2010 M7.2 El Mayor-Cucapah (EMC) earthquake. The direct P- and S-wave
travel times between surface and borehole stations reveal very low shear wave velocities (178-
259 m/s) and very high Vp/Vs ratios (6.2) in the top 22 m. Temporal changes of seismic
velocities after the EMC earthquake are estimated using autocorrelations of data in moving time
windows at two borehole stations (22 m and 50 m) and seismic interferometry between multiple
station pairs of the GVDA. The S-wave velocity in the top 6 m drops abruptly by 14.3±3.3%,
during the passage of surface waves from the EMC event with a peak ground acceleration of 39
Gal, and recovers in ~236 s. The average velocity reductions decrease with depth and are
10.9±3.1%, 8.5±2.1%, 6.3±2.1%, and 4.5±2.0% in the top 15 m, 22 m, 50 m, and 150 m,
respectively. Comparisons of seismic interferometry results between sensor pairs at 0-22 m and
22-150 m indicate that statistically significant velocity changes are limited at the site to the top
22 m. Pore pressure data are in phase with the surface displacement and reach maxima when the
62
highest velocity drop occurs, suggesting fluid effects contribute to the observed velocity
reductions.

3.1 Background
The properties and dynamics of the heavily damaged material in the top few hundred meters
of the crust are understood only in general terms, especially near fault zones, despite their great
importance to observed seismic motion, crustal hydrology, subsurface reservoirs, reliability of
underground facilities and numerous other applications. The low normal stress at shallow depth
renders the subsurface material highly susceptible to failure, masking details of deeper structures
and processes. The shear wave velocities in the top few hundred meters can be 200-400m/s or
lower (e.g., Bonilla et al., 2002; Theodulidis et al., 1996; Zigone et al., 2019) and the attenuation
coefficients can be as low as 1-20 (Aster & Shearer, 1991; Liu et al., 2015). Fault zone regions
have enhanced rock damage in the top 2-4 km with 30-60% reduced seismic velocities compared
to the surrounding rocks (e.g., Ben-Zion & Sammis, 2003, and references therein). Monitoring
how subsurface materials respond to the occurrence of earthquakes and other loadings can
provide important constraints for the rheology of shallow rocks, engineering seismology and
various other topics.
Non-linear site effects and temporal changes of seismic velocities of geomaterials have been
documented in laboratory experiments (Ostrovsky & Johnson, 2001; TenCate et al., 2004), and
in-situ investigations based on the spectral ratio method (Karabulut & Bouchon, 2007; Nakata &
Snieder, 2012; Sawazaki et al., 2006; Wu et al., 2010; Wu et al., 2009b; Wu et al., 2009a), cross-
correlations of the ambient noise (Brenguier et al., 2008b; Hillers et al., 2015; Hobiger et al.,
2012; Rivet et al., 2011), and repeating earthquakes (Peng & Ben-Zion, 2006; Poupinet et al.,
1984; Rubinstein & Beroza, 2004; Schaff & Beroza, 2004). Laboratory experiments show
63
reduction of seismic velocities under low confining pressure when dynamic strain is as small as
10
-7
, while in-situ observations imply minimum dynamic strains of 10
-6
-10
-5
, corresponding to
peak ground accelerations (PGAs) of ~30 Gal, are required to generate a velocity drop of less
than 5% (Rubinstein, 2011; Wu et al., 2010). Sediment soils, with loose particles and low shear
wave velocities, are more sensitive to strong motions than rocks and exhibit nonlinear and
hysteretic behaviors. Beresnev & Wen (1996) presented evidence for nonlinear soil behaviors
(e.g. resonance frequency shift and de-amplification) during large earthquakes with PGAs above
100 Gal. De-amplification by a factor of two was also observed at the Los Angeles basin related
to the 1994 Northridge earthquake compared with its aftershocks (Field et al., 1997). Bonilla et
al. (2005) found dilatant behavior of cohesionless soils that amplify surface motions from
occasional high-frequency spikes in a low-frequency carrier in accelerograms. Lawrence et al.
(2008) and Johnson et al. (2009) observed increasing reductions of shear wave velocity with
applied force load, especially in the top few meters. TenCate et al. (2016) showed that crack
orientation could have significant effects on nonlinear elasticity. Based on these observations, the
strain/PGA threshold for nonlinear behavior is highly site-dependent, and nonlinear site effects
may be more pervasive and prominent than usually thought.
The shallow crust has often relatively soft sediment in the top tens of meters consisting of
weathered and partially wet materials over relatively stiff bedrocks. Such shallow structures can
be best analyzed with borehole data for velocities (Gibbs, 1989; Gibbs et al., 1990, 2001; Nakata
& Snieder, 2012), attenuation (Aster & Shearer, 1991; Fletcher et al., 1990; Hauksson et al.,
1987), dispersion (Liu et al., 2005), and anisotropy (Coutant, 1996; Liu et al., 2004). The Garner
Valley Downhole Array (GVDA) was established in 1989 close to Lake Hemet, northeast of
Anza, California (Fig. 3.1, black triangle). The site has borehole seismic and pore pressure
64
sensors at various depths (Fig. 3.2), and provides valuable data sets to study shallow velocity
structures and local site responses to various loadings.
In the present study, we analyze the velocity structure in the top 150 m of the GVDA site,
and temporal changes of seismic velocities following the 2010 M7.2 El Mayor-Cucapah (EMC)
earthquake with an epicenter 206 km away in Baja California. The data used in the analyses are
described in Section 3.2. In Section 3.3, we first investigate the shallow velocity structure using
travel times of direct P and S waves recorded by GVDA stations, and then evaluate temporal
changes of seismic velocities by autocorrelation and seismic interferometry. The imaging results
indicate very low shear wave velocity (178-259 m/s) and very high Vp/Vs ratio (6.2) in the top 22
m. The analysis of velocity change indicates 14.3% S-wave velocity reduction in the top 6 m
after the EMC event, and that the velocity reduction concentrates in the top 22 m. Assuming
logarithmic recovery, the local velocity recovered approximately to the original state in ~236 s.
Correlations between pore pressure data and velocity changes suggest that fluid interactions with
shallow soft materials contributed to the observed temporal changes. The results are discussed
and summarized in the final Section 3.4.

3.2 Data
The GVDA (Fig. 3.1) was deployed in a narrow valley within the Peninsular Ranges
Batholith in southern California, about 7 km from the San Jacinto fault and 35 km from the San
Andreas fault, and started recording in the summer of 1989. The station layout of the GVDA is
shown in Fig. 3.2a. The site is characterized by alluvium in the top 18 m with a gradual transition
to decomposed granite from 18 m to 25 m, decomposed granite between 25 m and 87 m followed
by a transition zone from 87 m to 95 m, and granodiorite as bedrock deeper than 95 m (Bonilla et
65
al., 2002; Steller, 1996). The attenuation coefficients of P and S waves in the top 150 m are in
the ranges 15-50 and 10-30, respectively (Bonilla et al., 2002). Fig. 3.2(b) shows velocity models
at the site from earlier studies. Theodulidis et al. (1996) constructed a velocity profile with
results at different depths from previous studies, while Bonilla et al. (2002) obtained velocity
values by modeling accelerograms and using information from the velocity logs, core samples
and borehole suspension logging. Both models have a low shear wave velocity (<200 m/s) in the
top few meters, and the model of Bonilla et al. (2002) also includes a strong reflection interface
at 87 m that traps most of the reflected phases.

Figure 3.1. (a). All the events that have passed the selection criteria in the travel time analysis of direct
arrivals. The star in the SW of GVDA shows the location of the example event (Fig. 3.4). (b). All the
events that are analyzed in the temporal change study. Black dots represent events that are eliminated by
the selection criteria. Yellow and green symbols represent events that occurred before and after the EMC
earthquake respectively. Squares and circles indicate events that are used in the autocorrelation study and
seismic interferometry study, respectively.
We analyze seismic data from local earthquakes in 2010 (Fig. 3.1) recorded at the surface
(00) and five borehole (01-05) sensors at 6 m, 15 m, 22 m, 50 m, and 150 m depths (Fig. 3.2a).
66
Pore pressure recordings in the liquefiable layers at depths of 3.5 m, 6.2 m, 8.8 m, and 10.1 m are
also examined to investigate the influence of subsurface fluid on the local site response. The
seismic sensors and pressure transducers have a sampling rate of 200 Hz. We first remove the
seismic instrument responses, and rotate the east-west (HNE) and north-south (HNN) horizontal
seismic recordings to the radial (HNR) and transverse (HNT) directions. Then we inspect the
direct P- and S-wave travel times for additional results on the shallow velocity structure at the
site. Multiple stations are analyzed further to evaluate the temporal changes of seismic velocities
at various depth ranges following the EMC earthquake. The EMC earthquake recordings at the
surface and 150 m borehole stations are presented in Fig. 3.3, showing a PGA of about 39 Gal
when the surface waves arrive.

Figure 3.2. (a). The conceptual cross-section placement and surface layout (lower right corner inset) of
the GVDA (available from http://nees.ucsb.edu/facilities/GVDA). Please note the plot is not to scale
vertically. Numbers on the top represent channel location codes and depths are labeled beside the sensors.
Different symbols in each layer represent different materials from top to bottom: silty sand to sandy silt,
sandy silt to clay, sand to sandy silt, sand to silty sand, weathered granite and granite bedrock. Seismic
stations (red dots) 00-05 and pore pressure sensors (blue dots) 60-63 are used. (b). Velocity models of the
GVDA site in the top 150 m from Bonilla et al. (2002) (dashed lines) and Theodulidis et al. (1996) (solid
lines).
Figure 2. (a). The conceptual cross-section placement and surface layout (lower right corner inset) of the GVDA
(available from http://nees.ucsb.edu/facilities/GVDA). Please note the plot is not to scale vertically. Numbers on the top
represent channel location codes and depths are labeled beside the sensors. Different symbols in each layer represent
different materials from top to bottom: silty sand to sandy silt, sandy silt to clay, sand to sandy silt, sand to silty sand,
weathered granite and granite bedrock. Seismic stations (red dots) 00-05 and pore pressure sensors (blue dots) 60-63
are used. (b). Velocity models of the GVDA site in the top 150 m from Bonilla et al. (2002) (dashed lines) and
Theodulidis et al. (1996) (solid lines). (b) (a)
of 2 13
67

Figure 3.3. The transverse (T), radial (R) and vertical (Z) accelerograms (in Gal) from the EMC
earthquake at the surface (a) and 150 m borehole (b) stations of the GVDA. Zero time corresponds to the
occurrence time of the EMC event. Please note the different y scales.

3.3 Analysis and results
3.3.1 Analysis of direct P- and S-wave
To estimate the seismic velocities in the top 150 m, we calculate the P- and S-wave travel
times from stations at depth (6 m, 15 m, 22 m, 50 m and 150 m) to the surface by short time
window cross correlations. We first bandpass the waveforms at 1-30 Hz, and pick the direct P
and S arrivals at the surface and 150 m borehole stations by automatic picking algorithms (Ross
et al., 2016; Ross & Ben-Zion, 2014). The arrival times at other stations are estimated assuming
a constant velocity in the top 150 m. This preprocessing provides accurate reference times for
cross correlation, eliminating the possible bias caused by later arrivals. The waveforms are then
interpolated from 200 to 1000 samples per second to obtain subsample accuracy. The travel
times are obtained by cross-correlating the target waveforms (i.e. borehole traces) with reference
records at the surface in a short time window (0.15 s for P and 0.3 s for S), with 1/3 of the
window before the estimated arrivals. During the process, we discard the record if: (1) the event
is shallower than 5 km; (2) the average signal to noise ratio (SNR) is smaller than 2 in the 1-30
Hz band. The SNR is defined as the spectral ratio between the signal window (P/S waves for the
68
cross correlation) and the earlier noise window; (3) the cross correlation coefficient is smaller
than 0.5; (4) the travel time value has an absolute deviation from the median value outside the 80
percentile. Locations of about 450 events that pass the selection criteria are shown in Fig. 3.1a.

Figure 3.4. Example results from one event (shown as a star in Fig. 3.1a). (a)-(c) are the 1-30 Hz
bandpass filtered vertical (P wave), transverse (SH wave), and radial (SV wave) component waveforms
from the six GVDA stations. Red triangles and solid lines represent the estimated direct arrivals, and blue
dashed lines show the time windows used for cross-correlation. (d)-(f) present the interpolated waveforms
in the cross correlation time windows. Surface records are in black, and borehole records are in blue. The
red waveforms represent surface records shifted based on the time delay obtained from cross-correlation.
Fig. 3.4 illustrates results from an example event marked with a star in Fig. 3.1a. The shifted
surface record based on the delay time from cross correlation fits well with the waveforms at
depths, implying the reliability of the obtained travel time. The travel time histograms at the five
borehole stations are plotted in Fig. 3.5a-c. The distributions show small absolute deviations,
69
except that the P wave travel time at the 6 m borehole (i.e. station 01, blue symbols in Fig. 3.5a)
is less than 0.005 s, below the resolution of the data with a sampling rate of 200 Hz. Also the
obtained average P wave velocity in the top 15 m is over 2 km/s, implying a wavelength much
larger than the station distance. We therefore discard the corresponding P-wave velocity. The
median travel times, velocities and VP/VS ratios are summarized in Table 3.1 and Fig. 3.5,
assuming constant velocities between two successive stations.

Figure 3.5. Results from delay time analysis of direct phases. (a)-(c) are the travel time histograms
between the surface station (00) and five borehole stations (01-05) from vertical (a), transverse (b), and
radial (c) components, respectively. (d). Median (dots) and one stand deviation (error bar) of P (green),
SH (red), and SV (blue) wave travel times from boreholes to the surface station. (e). The obtained
velocities and VP/VS ratios assuming constant seismic velocities between two adjacent stations. The P
wave velocity in the top 15 m is plotted with dotted line because of the limited data resolution.
70
Table 3.1. Average velocities and velocity reductions between stations
Depth (m) 0-6 6-15 15-22 22-50 50-150
VP (m/s) 2283 2379 2804
VSH (m/s) 178 250 259 583 961
VP/VS ratio 6.2 2.8 2.1
dVSH/VSH (%) 14.3 7.7 3.4 2.0 2.0

The results from the radial and transverse components are similar, and the obtained P- and S-
wave velocities are consistent with previous studies (Fig. 3.2b). The top 22 m is characterized by
a low shear wave velocity (178-259 m/s) and large VP/VS ratio (6.2), corresponding to a
Poisson’s ratio of ~0.49, close to properties of saturated clay. This is compatible with the
geologic site conditions of soft soils and close-to-surface water table (Bonilla et al., 2002). The
S-wave velocities increase quickly with depth to 961 m/s between 50-150 m, and the VP/VS
ratios decrease to 2.1, corresponding to properties of the bedrock. The heterogeneous seismic
velocities within the top 150 m may significantly modify surface seismic recordings, making it
difficult to directly infer deep structural properties without deconvolving the response of the
shallow materials. The co-existence of water and soil in the top layer could increase the site
sensitivity to strong shakings during large earthquakes, providing a good opportunity to study
nonlinear site behavior with fluid interactions.
3.3.2 Temporal changes of seismic velocities after the EMC earthquake
The autocorrelation function (ACF) can retrieve the zero-offset reflection seismogram at a
station (Claerbout, 1968). The secondary peak in the ACF indicates the zero-offset reflection
from an interface, the location of which can be derived based on the travel time and local
velocity structure. Travel time variations of the zero-offset reflections reveal material changes
(e.g. change of seismic velocities or interface location) between the station and reflection
71
interface, and can be used to track the evolution of the subsurface materials in response to
various sources (e.g., strong ground motions from large earthquakes, seasonal loadings etc.). The
impulse response function (IRF) between two sites can be obtained by de-convolving the
waveform of a target site with that of a reference site (often at downhole or bedrock site).
Tracking the IRFs of surface-borehole station pairs is often used to monitor the surface layer,
where velocity reductions are the most pronounced in response to strong motions. Bonilla et al.
(2019) resolved a 30% S-wave velocity reduction from IRF analysis between a surface and
300m-deep borehole station in Japan, and a 50% reduction from ACF analysis at the surface
station, after the Mw 9 2011 Tohoku earthquake with a PGA of 585 Gal. Using these two
methods, we monitor temporal changes of seismic velocities at the GVDA site with a PGA of
about 39 Gal in response to the 2010 M7.2 EMC earthquake.
3.3.2.1 Autocorrelation
Fig. 3.6 shows SH waveforms before, during and after the EMC earthquake with clear free
surface reflections. Data of the 150 m sensor does not contain clear surface reflections because a
strong 87m-deep reflection interface traps most of the energy at shallower depth, and is therefore
not shown. The travel times are consistent with those predicted by the velocity model in Section
3.3.1 (blue and red dashed lines in Fig. 3.6), but during the EMC earthquake the SH waves (blue
and red triangles in Fig. 3.6b) are delayed with respect to the reference travel time. Since the
direct and free surface reflected waves are not well separated at the 6 m and 15 m borehole
stations, the ACFs are analyzed at the 22 m (03) and 50 m (04) borehole stations.
We first automatically pick the S-wave arrivals (Ross et al., 2016), and bandpass filter the
waveforms at 10-30 Hz. For all the earthquakes before and after the EMC event, the ACFs are
calculated in 5 s time windows starting 1 s before the S-wave arrivals. For the EMC earthquake
72
recordings, ACFs are obtained in 5 s moving time windows with 90% overlap. We then apply a
10-30 Hz bandpass filter to all the ACFs, normalize with the zero-lag amplitudes, interpolate
them from 200 to 1000 samples per second, and pick and track the secondary peaks’ locations,
i.e. the two-way travel times between the station and reflection interface (i.e. free surface). The
obtained two-way travel times () are smoothed with a 5-point median filter to eliminate outliers.
The reference two-way travel time
1
is defined as the median travel time from all the small
events with PGAs less than 5 Gal. The corresponding velocity change is
23
3
#
=
3*3
#
3
#
= −
4*4
#
4
#
(3.1)
with
1
and being the velocities before and after the strong motion respectively. Velocity
reduction oscillations caused by uncertainties of reference travel time are obtained as the velocity
reductions with respect to the travel times that are one standard deviation away from
1
for all
small events. The velocity reduction error is defined as the maximum background velocity
variation with respect to
1
from all the small events.
We filter out the signals below 10 Hz since the surface wave energy from the EMC
earthquake dominates the waveforms in this frequency band. The 5 s time window is chosen
because it generates a good balance between stabilizing the results and emphasizing the signal
strength of reflected phases. We also discard the event or time window from the EMC
earthquake if the average SNR is smaller than 2 at 10-30 Hz, or the ACF’s secondary peak value
is smaller than 0.2. Except for the EMC earthquake, events are discarded if they are shallower
than 5 km, or generate PGAs larger than 5 Gal at the GVDA site, or the absolute deviation of the
corresponding two-way travel time from
1
is outside the 80 percentile.
Fig. 3.7 shows the ACFs and velocity reductions from the transverse component (HNT) at
the 22 m station (03). ACFs from the radial component (HNR) show similar results and are given
73
in Fig. C3.1. The reference two-way travel time
1
(Fig. 3.7, black dashed lines) is 0.195 s,
corresponding to the S-wave two-way travel time between the station and free surface. The
average S-wave velocity in the top 22 m drops abruptly by 8.7±3.1% (with 3.1% indicating the
maximum background velocity variation) when the PGA reaches the maximum (~39 Gal) at the
surface wave arrival ~75 s after the EMC earthquake. This is consistent with the observation
from waveforms (Fig. 3.6) that the direct and free-surface-reflected S waves are delayed between
the surface and 22 m borehole stations relative to the reference. The recovery process only takes
~200 s. The recovery time scales are estimated in Section 3.3.2.3.

Figure 3.6. Transverse component waveforms showing free surface reflections before (a), during (b), and
after (c) the EMC earthquake. Blue and red dashed lines represent the up-going and down-going waves
centered at the surface station predicted by the reference travel time obtained from Section 3.3.1. Blue
and red triangles in (b) label the observed direct and reflected waves from the EMC earthquake, which are
delayed with respect to the reference travel time (blue and red dashed lines).
The transverse and radial component ACFs from the 50 m borehole station (04) are presented
in Figs A3.2-3.3. Compared with the results from station 03, the velocity variations show a
similar pattern with an abrupt drop followed by a gradual but quick recovery process after the
!
Figure 6. Transverse component waveforms showing free surface reflections before (a), during (b), and after (c) the
EMC earthquake. Blue and red dashed lines represent the up-going and down-going waves centered at the surface
station predicted by the reference travel time obtained from section 3.1. Blue and red triangles in (b) label the observed
direct and reflected waves from the EMC earthquake, which are delayed with respect to the reference travel time (blue
and red dashed lines). (a) (b) (c)
of 6 13
74
EMC event, with the reference two-way travel time (0.292 s) consistent with the local velocity
structure. The average S-wave velocity in the top 50 m decreases by 6.9±3.1% when the surface
waves arrive, and recovers in ~200 s. Table 3.2 summarizes the reference travel times and
velocity reductions from the analysis.

Figure 3.7. (a). The 10-30 Hz autocorrelation functions (ACFs, color representing amplitudes)
normalized with zero lag amplitudes, reference travel time (black dashed lines), and ACF peaks (black
solid lines) corresponding to free surface reflections from the transverse component at the 22 m borehole
station (03). The left, middle and right panels are the results before, during, and after the EMC
earthquake, respectively. Horizontal axes represent the time relative to the occurrence time of the EMC
earthquake, and vertical axes indicate the lag time for autocorrelation. The 10-30 Hz waveforms from the
EMC event are plotted in the middle panel. (b). The corresponding velocity changes (black solid lines),
velocity reduction oscillations (green shaded areas), and PGAs (blue dashed lines with dots) inside the
autocorrelation time windows. Please note the irregular time axes, different time and PGA scales between
the middle and left/right panels.
75
Table 3.2. Average velocity changes from surface to borehole depths
Depth (m) 0-6 0-15 0-22 0-50 0-150
Method IRF 01-03 IRF 01-04 IRF 00-02 IRF 00-03 ACF 03 IRF 00-04 ACF 04 IRF 00-05
Reference
travel time
(second)
0.0315 0.032 0.064 0.094 0.0985 0.142 0.146 0.245
Velocity
reduction ±
error (%)
14.3 ± 3.3 14.1 ± 1.8 10.9 ± 3.1 8.5 ± 2.1 8.7 ± 3.1 6.3 ± 2.1 6.9 ± 3.1 4.5 ± 2.0

3.3.2.2 Seismic interferometry
The evolution of the S-wave impulse response functions (IRFs) from different sensor pairs
are also analyzed for temporal changes of seismic velocities at various depth ranges. In the same
time windows defined in the ACF study (Section 3.3.2.1), we apply the multi-taper spectral
analysis method (Prieto et al., 2009; Thomson, 1982) with 5 tapers and 1% water level control to
calculate the spectral ratios, and then perform inverse FFT to obtain the IRFs. We bandpass filter
the waveforms and IRFs at 1-30 Hz, and interpolate the IRFs from 200 to 1000 samples per
second. The IRF peak locations correspond to the S-wave travel time between the two stations,
which is smoothed with a 5-point median filter to eliminate outliers. The reference travel time
1

is defined as the median value from all events with PGAs smaller than 5 Gal. Selection criteria
and result uncertainties are similar as in the ACF analysis, except that the SNR is defined in the
1-30 Hz band and an event is discarded if the IRF value at the picked peak is smaller than 0.8
after normalized by the maximum IRF amplitude. With the highest frequency of 30 Hz, IRFs are
stable and reliable between stations separated by at least one wavelength at 30 Hz, e.g. 00-05,
00-04, 00-03, 00-02, 01-03, and 03-05.
76

Figure 3.8. (a). The 1-30 Hz impulse response functions (IRFs, color representing amplitudes)
normalized with the maximum amplitudes, reference travel time (black dashed lines), and IRF peaks
(solid black lines) from the transverse component between the surface station (00) and 22 m borehole
station (03). The layout is similar to Fig. 3.7. The 1-30 Hz waveforms at the shallower station (in this
case, station 00) from the EMC earthquake is plotted inside the middle panel. (b). The corresponding
velocity changes (black solid lines), velocity reduction oscillations (green shaded areas) and PGAs (blue
lines with dots) inside the deconvolution time windows. Please note the irregular time axes, different time
and PGA scales between the middle and left/right panels.
Figs 3.8-3.10&A3.4-A3.7 illustrate the IRFs and velocity reductions from the transverse
components at 7 station pairs; Table 3.2 summarizes the results. Radial components show similar
results and Fig. C3.8 provide an example for station pair 01-03. The travel times between
stations are consistent with the local velocity structure obtained in Section 3.3.1. The velocity
variation patterns are similar to the observations from the ACF analysis, with an abrupt reduction
at the largest PGA followed by a gradual recovery in ~200 s. In Figs 3.8&A3.4-3.6, the
77
maximum velocity reductions are 10.9±3.1% (00-02), 8.5±2.1% (00-03), 6.3±2.1% (00-04), and
4.5±2.0% (00-05), averaged from the surface to 15 m, 22 m, 50 m, and 150 m, respectively.

Figure 3.9. The 1-30 Hz IRFs (a) and corresponding velocity changes (b, c) from the transverse
component recorded by the 6 m (01) and 22 m (03) borehole stations. (b) is the average velocity changes
between stations 01 and 03, obtained from the IRF primary peak at ~0.06 s. (c) represents the average
velocity changes in the top 6 m, obtained from the IRF secondary peak at ~0.12 s, corresponding to waves
traveling from station 03 to surface then reflected to station 01. The blue horizontal axis ticks in (c)
indicate Julian days in 2010.
The IRFs from station pairs 01-03 (6-22 m) and 01-04 (6-50 m) are shown in Figs 3.9&A3.7.
The primary peak (
(&)
) indicates direct waves traveling from 03/04 to 01, and the secondary
78
peak (
(+)
) corresponds to free-surface-reflected waves recorded by station 01 at 6 m depth. The
change of
(+)
−
(&)
represents the temporal changes of materials in the top 6 m, shown in Figs
3.9&A3.7. The average velocity changes between 6-22 m and 6-50 m calculated from the
primary peak are 8.3±3.3% (Fig. 3.9b) and 4.6±1.9% (Fig. C3.7b), respectively. The velocity
reductions in the top 6 m obtained from the two station pairs are consistent with each other with
values of 14.3±3.3% and 14.1±1.9%. In addition, travel times in the top 6 m show potential
seasonal variations, delayed in spring and summer. More data are required to confirm and
analyze the observations, which is not the main target of the current study and left for a future
work.

Figure 3.10. The 1-30 Hz IRFs (a) and corresponding velocity changes (b) from the transverse
component between the 22 m (03) and 150 m (05) borehole stations. The layout is the same as Fig. 3.8.
79
Given the results, we consider the velocity drops to be 14.3%, 10.9%, 9.6%, 6.3%, and 4.5%
from the surface to 6 m, 15 m, 22 m, 50 m and 150 m. Combined with the corresponding travel
times (Table 3.2), the velocity reductions are calculated to be 7.7% between 6-15 m, 3.4%
between 15-22 m, 2.0% between 22-50 m and 2.0% between 50-150 m (Table 3.2). The
calculated velocity drops at 22-50 m and 50-150 m, 2.0%, are comparable to the background
velocity variations (≥2.0%) from small events, implying no statistically significant velocity
reduction below 22 m. This is consistent with IRF results from stations 03-05 (Fig. 3.10)
showing no clear velocity reduction between 22-150 m.
3.3.2.3 Recovery time estimation
We estimate the recovery times of the velocity changes by assuming a logarithmic recovery
function (e.g., Dieterich & Kilgore, 1996; Johnson & Sutin, 2005). Starting at time (
1
) when the
maximum velocity reduction occurs, the velocity change is written as
∆ () = R
∙
&1
(−
1
+1)+ ,
1
≤ ≤
1
+
0, ≥
1
+
, (3.2)
where and are constants and is the recovery time. In the logarithmic scale, we find the best
fitting function ∆() by tuning the parameter that minimizes the L2 norm between ∆() and
the observed /. Fig. 3.11 presents the observed and best fitting velocity change curves based
on all the analyses. The recovery times are similar at all stations with a median value of 236 s.
The somewhat larger recovery time from ACF analysis at stations 03 and 04 may be caused by
the large uncertainties in the estimation resulted from noise and modification of waves in the
surface layer.
80

Figure 3.11. Recovery time estimation of velocity changes. Black and red lines represent observed dv/v
curves and the best fitting linear functions. Each plot is labeled with the station/station-pair numbers and
the corresponding recovery time (T) in seconds. The top two panels show results based on ACF analysis
at stations 03 and 04, middle six subplots are IRF analysis results from six station pairs, and bottom two
panels show results based on the secondary peaks of IRFs from 01-03 and 01-04, respectively.
3.4 Discussion and Conclusions
We analyze inter-station velocities in the top 150 m at the GVDA site, using travel times of
direct phases recorded by the surface and borehole stations at different shallow depths, and track
the ACFs and IRFs for in-situ temporal changes of seismic velocities related to the 2010 M7.2
EMC earthquake with epicenter 206 km from the site. Tables 1-2 summarize the results. The
derived inter-station seismic velocities and VP/VS ratios (Fig. 3.5e) are consistent with those
from previous studies, and the S-wave velocity reductions between various station pairs using the
ACF and IRF techniques are compatible with each other. The Garner Valley site exhibits in top
81
22 m properties of saturated soils with very low shear wave velocity (178-259 m/s) and large
Vp/Vs ratio (6.2), followed by transitions to stiff soils and bedrocks between 22-150 m. During
the arrival of the surface waves from the EMC event with a PGA of ~39 Gal, the local S-wave
velocity does not have statistically significant changes below 22 m, but abruptly decreases by
3.4%, 7.7% and 14.3% at depths 15-22 m, 6-15 m and 0-6 m, and then recovers to the original
levels quickly in ~236 s.
The travel time estimations of direct phases based on cross correlating the surface recordings
with multiple borehole waveforms, especially the vertically propagating P waves, may be
affected by the free surface effect at this site. However, P waves at the surface station vanish
only when the incident angle is strictly zero at the free surface. This is usually not the case even
for vertically propagating P waves because of possible topography variations. This reduces the
free surface effect and enables clear observation of the vertically traveling P wave at station 00
(Fig. 3.4). Also the selection criteria require the cross correlation coefficient between surface and
borehole recordings to be larger than 0.5, which helps to exclude possible cases when the surface
recordings are significantly affected by the free surface effect.
Zhan et al. (2013) showed that velocity change measurements using the noise-based
stretching method could be biased by frequency content changes. However, the travel time
estimation from the ACFs and IRFs should not be significantly affected by frequency content
variations, considering the very short propagation time between stations and relatively narrow
frequency band in our analyses although the shallow Q values are small. We therefore use 1-30
Hz signals for estimating the local velocity structure and IRF analyses, and analyze the ACFs
using 10-30 Hz data since ACFs from the EMC recordings are significantly distorted by surface
waves below 10 Hz. Fig. C3.9 presents an example ACF analysis (transverse component at
82
station 03) in two narrower frequency bands (10-20 Hz and 15-30 Hz), and Fig. C3.10 shows
IRF results in 10-30 Hz at station pair 01-03 (transverse component). The ACFs at 10-20 Hz and
IRFs at 10-30 Hz are almost identical to those between 10-30 Hz and 1-30 Hz in Figs 3.7&3.9,
while the 15-30 Hz ACFs are less reliable because of the relatively low signal to noise ratios of
EMC waveforms in this frequency band. These comparisons show that the obtained results are
not affected significantly by attenuation and are independent of the used frequency bands given
enough signal to noise ratios. Another possible effect that may distort the ACF is local scattering
that may cause variations in the ACF side lobes (Fig. 3.7, 0.05-0.1 s). However, the travel time
variations do not correlate with the variations in the ACF side lobes. Since the free surface
reflection results are more coherent and stronger than local scattering, the measurement of travel
time (and velocity change) is not affected by scattering.
It is difficult to constrain the depth range of observed velocity changes without borehole data,
considering the very-high sensitivity of shallow materials to ground shaking compared to the
deeper materials. Chandra et al. (2015) showed that material in the top 15 m at the Garner Valley
site behaves nonlinearly already for strain ≥10
-6
, while below 50 m the response remains linear
for strain up to 10
-4
. This is consistent with our observations on velocity reductions in the top 22
m associated with weak ground motion. Rubinstein & Beroza (2005) showed that temporal
changes of S wave velocities caused by the 2004 Parkfield earthquake concentrate in the top 100
m. Modeling results from Yang et al. (2019) suggest that temporal changes of seismic velocities
in the top 1-3 km can produce observable changes in analyses using Rayleigh waves with periods
of 5-20 s. Therefore, resolving the depth range of temporal changes based on sensitivity kernels
of Rayleigh waves can be subjected to large uncertainties without information (e.g., from
borehole data) on changes in the shallow crust.
83

Figure 3.12. The pore pressure recordings (black lines) from the GVDA at different depths and transverse
displacement (blue lines) at the surface station from the EMC earthquake high pass filtered at 0.1 Hz.
Mean values of each pore pressure trace are removed.
Based on the results of this work and previous studies (Karabulut & Bouchon, 2007;
Sawazaki et al., 2006; Wu et al., 2009a), most of the velocity reductions recover in a short time
after the changes occur. This is consistent with the general log(t) healing of material properties
seen in laboratory experiments (Dieterich & Kilgore, 1996; Johnson & Sutin, 2005). The
resolved changes depend strongly, in addition to material properties and loading amplitudes, on
the time resolution of the analyses. Given the rapid early recovery and limited temporal
resolution, all measurements of temporal changes of seismic velocities should be considered as
lower limits. With cross-correlations of ambient noise, observed velocity reductions are typically
84
a fraction of 1% because of averaging over days to weeks across wide areas of several kilometers
(Brenguier et al., 2008a; Hobiger et al., 2012; Rivet et al., 2011). Analyses of repeating
earthquakes and cross correlations of earthquake waveforms with time steps of minutes resolve
velocity changes of 1-3% (Peng & Ben-Zion, 2006; Roux & Ben-Zion, 2014). Using the spectral
ratio method and 6 s time windows, Wu et al. (2010) resolved a velocity drop of less than 5% in
the top ~100 m generated by weak loadings of ~60 Gal. Bonilla et al. (2019) resolved with ACFs
and time steps of 1-2 s about 50% velocity drop in the upper ~100 m during the passage of
strong surface waves (~585 Gal). Our calculations of ACFs and IRFs in 5 s time windows with
90% overlap and applying a 5-point median filter have a time resolution of ~2.5 s, and resolve
about 14.3% changes in the top 6 m from loadings of ~40 Gal. Using borehole data at depths (6
m, 15 m, 22 m, 50 m, and 150 m) we achieve a high spatio-temporal resolution in monitoring the
behavior of shallow materials.
Detailed analysis of heterogeneous shallow structures remains highly challenging, especially
in the presence of fluids. Nonlinear mechanisms could be easily triggered in the presence of
water in porous media (Shapiro, 2003; Zinszner et al., 1997), particularly in the low saturation
range (Van Den Abeele et al., 2002). Earthquake-induced permeability changes were inferred in
source regions (Nur, 1972) and observed in the shallow crust (Rojstaczer et al., 1995; Wang et
al., 2004). Large excess pore pressures are also observed simultaneously with the significant
temporal change of seismic velocities at the Garner Valley site in response to ground motions
larger than 100 Gal (Steidl et al., 2014). Considering the high water table and large velocity
reduction (14.3%) in response to a relatively weak ground motion (~39 PGA), fluid interactions
with the sub-surface materials likely contribute to the observed results. Fig. 3.12 shows that pore
pressure variations at depth down to 10 m are in phase with the displacement data on the surface.
85
The largest velocity drop occurs ~75 s after the EMC event, when the absolute pore pressure
values increase with the surface wave arrivals. Deeper than 22 m with decomposed granite, the
pore pressure oscillates because the fluids flow in and out from essentially fixed cracks.
However, the soft sediments in the top 22 m likely fail partially and move with the fluids. It is
possible that the initial pulse of pore pressure weakens (loosens the bonds between soil grains)
the poorly consolidated near surface material, and the material remains in this weakened state
(with lower shear modulus and shear wave velocity) while the pore pressure oscillates. This may
contribute to the large coseismic velocity drops (14.3% in top 6 m) in response to a small PGA,
and the relatively rapid recovery (~236 s) when the material settles down and bonds between soil
grains reform strengthening the soil matrix. The precise details of the failure and recovery
mechanism should be modeled using additional information (e.g. soil grain size, permeability)
about the site.
Analyses of borehole data highlight the significance of shallow structures on observed
ground motion and temporal changes of properties, especially in the top 100 m. Despite intensive
theoretical research (Bentahar et al., 2006; Johnson & Rasolofosaon, 1996; Lyakhovsky et al.,
1997, 2009; Sens-Schönfelder et al., 2019; Sleep & Hagin, 2008; TenCate & Shankland, 1996),
the behavior of the shallow and heavily damaged crustal rocks is only understood in general
terms. Detailed in-situ spatio-temporal monitoring of shallow structures is critical to clarify the
properties and processes of subsurface materials. Such information is needed to estimate the
stability of the significant infrastructure that exists at the subsurface during ground motion
generated by future moderate and large earthquakes.

86
3.5 Acknowledgements
The study was supported by the U.S. Department of Energy (award DE-SC0016520). The
data used in this study are available on the Incorporated Research Institutions for Seismology
(IRIS) Data Management Center (https://doi.org/10.7914/SN/SB). The observations obtained at
the Garner Valley geotechnical array facility would not be possible without the cooperation and
decades-long partnership of the Lake Hemet Municipal Water District. The continuous
monitoring of geotechnical array data at UCSB is supported through an Inter-Governmental
Personnel Agreement with the U.S. Geological Survey, and by support from the Pacific Gas &
Electric Company. The work benefited from useful comments by Nori Nakata and an anonymous
referee.
87
4. Daily changes of seismic velocities in shallow materials on Mars
(Qin, L., Qiu, H., Deng, S., Levander, A., Ben-Zion, Y.. Daily changes of seismic velocities in
shallow materials on Mars. Earth and Planetary Science Letters, In review.)

4.0 Summary
We analyze seismic data on Mars using zero-offset reflection seismograms calculated by
autocorrelations to examine temporal changes of seismic velocities at the subsurface. Using the
lander vibration as an active continuous source, signals with ~1.3 s two-way travel time reflected
at an interface ~200 m deep show ~5% daily variations. The travel time variation shares a similar
shape to the ground temperature with an apparent phase delay time of ~40 min. Assuming the
travel time variation concentrates in the top ~18 composed of dominantly weak regolith
materials, the corresponding daily S-wave velocity variation is up to ~40%. Five peak
frequencies in autocorrelations at 3.3, 4.1, 6.8, 8.5 and 9.8 Hz also show similar daily variations
of 5%-25% and apparent phase delays of 45-25 mins compared with ground temperature. The
two peak frequencies at 3.3 and 4.1 Hz result from site-related resonance and yield similar
temporal pattern as the travel time of the reflected waves. The three high-frequency peaks likely
represent a combination of the lander vibration and site-related resonance modes, so their
variations likely also reflect at least partially changes at the subsurface. The dominant
mechanism for the observed temporal changes, based on the correlation (with phase delay) with
ground temperature and amplitude estimates, is thermoelastic strain.

4.1 Background
Seismic interferometry has been widely used to image (Lin et al., 2013; Phạm & Tkalčić,
2017; Romero & Schimmel, 2018; Shapiro & Campillo, 2004) and monitor buildings and
88
seismic structures on Earth (e.g. Bonilla et al., 2019; Brenguier et al., 2008; Mao et al., 2019;
Qin et al., 2020). Velocity variations associated with earthquakes (e.g. Karabulut & Bouchon,
2007; Peng & Ben-Zion, 2006) and periodic (e.g. daily, seasonal) environmental loadings such
as hydrological changes, thermoelastic strain and tides (Ben-Zion & Allam, 2013; Johnson et al.,
2017; Mao et al., 2019), shed light on in-situ structures and susceptibility of subsurface materials
to failure. These issues are of great importance to interpreting observed seismic motion,
reliability of underground facilities and other applications.
Recent developments enabled geophysical studies on Mars and other objects in the solar
system. Analysis of data from the Apollo Lunar Seismic Profiling Experiment (Nakamura et al.,
1982) resolved structures and thermal properties of the Moon (Kovach & Watkins, 1973;
Langseth et al., 1976; Larose et al., 2005; Tanimoto et al., 2008) and discovered moonquakes
triggered by diurnal temperature changes (Cooper & Kovach, 1975; Duennebier, 1976;
Duennebier & Sutton, 1974). The NASA’s Interior Exploration using Seismic Investigations,
Geodesy and Heat Transport (InSight) mission deployed a seismic station on Mars at the end of
2018 (Lognonné et al., 2019; Panning et al., 2017), providing the first direct geophysical
observations to investigate the internal structure of Mars.
Analysis of the seismic data on Mars indicates that the noise level is very low during Martian
night, and increases during the daytime due to atmospheric events and wind-generated lander
noise (Lognonné et al., 2020; Suemoto et al., 2020). Efforts to detect marsquakes yielded 174
events from February to September 2019 (Banerdt et al., 2020; Giardini et al., 2020).
Geophysical and geological studies (Golombek et al., 2020; Lognonné et al., 2020) at the landing
site suggest a relatively smooth terrain with a ~3-18m-thick layer of sand overlying coarse
breccia, with near-surface Young’s modulus of ~47 MPa, P-wave velocity of 118±34 m/s and
89
thermal inertia of 160-230 Jm
-2
K
-1
s
-1/2
in the top 1-2 m regolith layer. Using seismic
interferometry of ambient noise at low frequency (<1 Hz), Deng & Levander (2020) identified
prominent body-wave reflection phases in stacked vertical component autocorrelation data, and
associated them with reflections from deep interfaces (e.g. the Martian Moho and core-mantle
boundary). In a higher frequency band (5-7 Hz), Suemoto et al. (2020) showed that S-wave
reflected at a shallow interface with a two-way travel time of ~1.2 s can be extracted from the
autocorrelation of diffused ambient noise data.
Different from Earth, seismic recordings on Mars are more “quiet” without significant
transient sources (e.g., infrequent marsquakes, no anthropogenic activities) except for occasional
atmospheric events. Polarization study (Suemoto et al., 2020) suggests dominant seismic noise
source at >1 Hz is associated with the wind-generated lander vibration. Thus, instead of utilizing
the ambient noise, we use the lander vibration as a local active source and retrieve zero-offset
reflection seismograms via autocorrelation in short time windows to monitor temporal changes
of seismic velocities in subsurface structures. There is a ~2-hour time delay between the air
temperature recorded at ~1.4 m above the ground (dashed curve in Fig. 4.1a) and the ground
temperature (black curve in Fig. 4.1a) derived from the radiometer recording (Spohn et al.,
2018). We use the ground temperature to investigate possible temperature-induced changes to
seismic properties of subsurface materials. The analysis aims to provide high-resolution
information on the dynamics of shallow materials at the study area on Mars.

90
4.2 Data and Methods
4.2.1 Data properties and preprocessing
Fig. 4.1(b)-(c) show continuous seismic data sampled at 100 Hz and the spectrograms during
Sol days 98-99 (corresponding to UTC Julian days 66-67 on Earth). The large amplitude wave
packets, e.g., at 8 am to 12 pm local time (Fig. 4.1b), are associated with strong wind activities.
Multiple peak frequency lines (e.g., at ~4 Hz) with clear daily variations were observed in Fig.
4.1(c) and were previously attributed to resonance modes of the lander (Panning et al., 2020).
Numerical modeling of the wind-induced lander mechanical noise (hereinafter denoted as
“lander resonance mode”) implies that the resonance modes depend on ground stiffness and are
likely either below 1 Hz or above 10 Hz for the baseline parameters (Murdoch et al., 2017,
2018).
In this study, we take advantage of the lander vibration and use it as an active source. The
core of the analysis involves auto-correlating the 100 Hz seismic data on Mars in 20-s moving
time windows with 50% overlap. Since the signals from wind-generated lander vibration
dominate the seismic data at > 1 Hz, we bandpass filter the data between 1-5 Hz. Then we apply
temporal balancing to seismic recordings in the time domain, i.e., dividing the waveform by its
smoothed envelope function (Fig. 4.1b), to suppress the modulation of strong wind signals on
seismic data (e.g., 8 am-12 pm; Fig. 4.1b). Considering the autocorrelation functions (ACFs) are
calculated in 20-s time windows, a 10-s time window is used to smooth the envelope function in
temporal balancing (Fig. 4.1b). We then stack every consecutive 30 ACFs and normalize the
stacked trace by its maximum amplitude. We choose a window size of 30 considering the trade-
offs between time resolution and smoothness of the resulting travel time variation.
91

Figure 4.1. (a). Two days of air temperature (dashed black line), ground temperature (solid black line),
and wind data (dots) with color representing wind directions. (b). Two days of continuous seismic
recording of the EW component (gray curve). A bandpass filter between 1-5 Hz is applied to the data. A
smoothed envelope (red curve) is obtained using a 10-s-long moving window, and the data after temporal
balancing (Section 4.2.1) is shown in black. The purple dashed lines indicate 8 am-12 pm local time. The
waveform in black is magnified by a factor of 200 for illustration. (c). Spectrograms of the raw EW-
component data. (d). An example autocorrelation function (ACF; black curve) calculated at 1 pm on Sol
98 (hour 13), and the ACF after source deconvolution (red curve; Section 4.2.2). (e). The spectra of the
two ACFs in (d). The approximate source spectrum used in the source deconvolution is illustrated in blue.

92
4.2.2 Properties of ACF
The ACF amplitude spectrum is a multiplication of source (i.e., lander vibration) and site
terms in analysis using reflected signals. The seismic recording D(t) that includes a reflection
signal can be written as:
() = ()+∙(−Δ), (4.1a)
where S(t) is the direct wave generated by the source, δ is the reflection coefficient, and Δt is the
two-way travel time of the reflection. Equation (4.1a) can be written in the frequency domain as:

\
() =
]
()+∙
]
()
,784
=
]
()∙:1+∙
,784
@, (4.1b)
where
\
() and
]
() represent the Fourier transforms of the seismic recording and direct wave
at angular frequency ω, respectively. The ACF of D(t) in the frequency domain,
_
(), can be
written as

_
() =
\
()∙
\
∗
() = `
]
()`
+
∙:1+
+
+∙
,784
+∙
*,784
@ =
`
]
()`
+
∙[1+
+
+2∙cos(Δ)] = `
]
()`
+
∙
:
(,Δ), (4.2a)
The spectrum of ACF has zero phase at all frequencies and the amplitude spectrum is a
multiplication of the source term `
]
()`
+
related to the lander vibration and site term
:
(,Δ)
related to the reflection. Through inverse Fourier transform, the ACF in the time domain is given
by
() = (1+
+
)∙
;
()+∙
;
(−Δ)+∙
;
(+Δ), (4.2b)
where
;
() is the ACF of the direct wave that satisfies
;
() =
;
(−) and max(
;
) =
;
(0).
The Fourier transform of
;
() is given by `
]
()`
+
.
From Equation (4.2a), the site term,
:
(,Δ), oscillates in the frequency domain with
spectral peaks separated by Δf = 1/Δt, referred to below as “site-response-related resonance
93
frequencies”. The amplitude spectra of the seismic recording D(t) and its autocorrelation R(t)
peak at (N+0.5)/Δt for a negative reflection coefficient δ, where N is an integer. We do not
perform spectral whitening in the data preprocessing. This is because, following Equations (4.1b)
and (4.2a), spectral whitening of
\
() distorts the reflection signal in the time domain, as the
amplitude spectrum, `
\
()` = `
]
()`∙g1+
+
+2∙cos(Δ) contains information of the
reflection. Instead, we approximate the source term by the running average of the ACF spectrum
with a window size of Δf = 1/Δt. This assumes that the source spectrum varies smoothly in the
window with a size of Δf, and that there is only one major reflector (i.e., the amplitude of
reflection from the major reflector is much larger than those from other reflectors). Since the
source term only alters the shape of the arrivals in the time domain, we deconvolve the estimated
source term from the ACF, i.e., dividing the ACF spectrum by the approximate source spectrum.
4.2.3 Variations of travel time and resonance frequencies
The travel time change ( ) of the reflected signal with respect to a reference trace,
associated with the stack of all ACFs, is obtained through cross-correlation in a time window
where clear reflected phases are observed. The relative travel time change averaged over the
entire propagation path is calculated as /, with t being the lapse time for the center of the
cross-correlation time window. The cross-correlation time window is determined as follows: (i)
We stack the envelopes of all ACFs, and center the cross-correlation time window at the second
peak (i.e., the highest peak excluding the zero-lag) of the stacked envelope function (Fig. 4.2b).
(ii) Then we calculate the spectrum for each ACF and obtain the median dominant frequency
1

as ~4 Hz. The cross-correlation time window is defined as ±3 times the median dominant period

1
= 1/
1
from the center determined in step (i).
94

Figure 4.2. (a). Two days of ACFs for the EW component data. (b). ACFs for the reference trace (black
dashed waveform), i.e., the stack of all ACFs in (a), and an example trace from 1 pm of Sol 98 (black
solid waveforms). The stacked envelope for all ACFs is shown in red with three local maxima labeled by
their lapse times.

Figure 4.3. (a). Spectrogram of the ACFs calculated using the raw EW component recording. Five
resonance frequencies are clearly observed and tracked with black curves (at ~3.3, ~4.1, ~6.8, ~8.5 and
~9.8 Hz) as a function of recording time. (b). Maximum daily variation values of -df/f for the five
resonance frequencies shown in (a).
95
To suppress the potential effects of wavefield changes on the inferred delay times, we discard
the ACF if any of the following holds: (i) The peak value of envelope function in the cross-
correlation time window is smaller than 20% quantile of the peak envelope values from all
ACFs. (ii) The cross-correlation coefficient with the reference ACF trace is less than 0.5. (iii)
The retrieved deviates more than three times from the median absolute deviation from the
median.
We also document the daily changes of ACF peak frequencies between 1-10 Hz from ACFs
calculated without bandpass filtering and source deconvolution (Fig. 4.3a). This aims to examine
the features of the ACF spectral peaks and associate the results with the theoretical derivations in
Section 4.2.2 for information at different depth ranges. The variation of peak frequency is
measured via / =(−
1
)/
1
, where
1
is the median value during the nighttime.
4.2.4 Influence of source variations
Here we show with analytical results that variations in the lander vibration do not bias our
estimations of travel time changes derived from cross-correlation of ACFs. Let
41
() and

4&
() denote ACFs of two seismic recordings and
_
41
() and
_
4&
() be the corresponding
Fourier transforms. Based on Equation (4.2b) and Section 4.2.3, the cross-correlation cc(t) of
ACFs at the positive time lag, i.e., between ∙
;1
(−Δ
1
) and ∙
;&
(−Δ
&
) can be
expressed in the frequency domain as
j() = `
]
1
()`
+
∙`
]
&
()`
+
∙
+
∙
,7(84
#
*84
!
)
, (4.3a)
and thus, cc(t) is given by
() =
+
∙
00
:−(Δ
1
−Δ
&
)@, (4.3b)
where the Fourier transform of Acc(t) is `
]
1
()`
+
∙`
]
&
()`
+
. Since
00
() =
00
(−) and
max(
00
) =
00
(0), () reaches the maximum at Δ
1
−Δ
&
. This suggests that changes in the
96
source term `
]
()` only alter the shape of the correlation function but do not bias the estimation
of variations in the two-way travel time. A synthetic test (Fig. D4.1) demonstrates that the Δt
variation estimated via cross-correlation of ACFs is not affected although the peak frequency of
source spectrum decreases by > 30%.

4.3 Results
4.3.1 / measurements
We discuss here results based on the EW-component data. Results from the NS and vertical
components are similar and presented in Appendix 4 (Figs A4.2-A4.5). Fig. 4.1(d) shows the
ACF at 1 pm on Sol 98 before (black curve) and after (red curve) source deconvolution. The
source spectrum deconvolution is performed by dividing the raw ACF spectrum (black curve in
Fig. 4.1e) by the approximate source spectrum (blue curve in Fig. 4.1e), which is estimated as
the smoothed ACF spectrum with a window size of Δf=0.77 Hz given Δt~1.3 s (Fig. 4.1d). The
ACF after source deconvolution (red curve in Fig. 4.1d) shows clearer reflected signals, i.e.,
better separation between the wavelet at the zero-lag and reflected signals at ~1.3 s. Therefore we
perform source deconvolution to all ACFs using a window with Δf=0.77 Hz. The results are
almost identical using different Δf values between 0.67-1 Hz (i.e., Δt values between 1.5-1 s) for
source deconvolution.
Fig. 4.2 shows the obtained EW-component ACFs for the analyzed time period. The stacked
envelope function shows a reflection signal at ~1.3 s, and its multiples at ~2.4 and ~3.9 s, thus
the cross-correlation time window (blue lines in Fig. 4.2b; Section 4.2.3) is centered at ~1.38 s
and ~1.5 s long. The reference ACF trace (dashed curve in Fig. 4.2b), which is the stack of all
the ACFs over the entire analyzed period, does not contain clear signals at ~2.4 and ~3.9 s,
97
probably because the absolute travel time variations are larger in the multiples than in the
reflected wave at ~1.3 s. The arrival in the example ACF at 1 pm on Sol 98 (black solid curve in
Fig. 4.2b) is delayed compared with the reference ACF (black dashed curve in Fig. 4.2b),
yielding positive values via cross-correlation in the target time window.
We attribute the observed waves at ~1.3 s to reflected S-waves in the two horizontal
components since Suemoto et al. (2020) also found clear signals at ~0.6 s and ~1.2 s
corresponding to P- and S- waves, respectively, in autocorrelations of diffused noise at 5-7 Hz.
The first arriving reflected phase resolved in vertical-component ACFs also shows a two-way
travel time of ~1.3 s (Fig. D4.3). This is likely due to the leakage of S-wave energy onto the
vertical component (e.g. Deng & Levander, 2020; Gorbatov et al., 2013; Oren & Nowack, 2017;
Phạm & Tkalčić, 2017). Another possibility is that the first arriving phase in the vertical
component travels as P-waves in the top layer (~1-2 m thick; Lognonné et al., 2020), and
converts to S-waves at depth. We, therefore, attribute the / values measured from all three
components to temporal changes in S-wave travel times. The velocity model from Lognonné et
al. (2020) indicates the local S-wave velocity increases from 59.85 m/s to 95.82 m/s in the top 1
m, and remains 316.23 m/s between 1-10 m. Assuming the same S-wave velocity of 316.23 m/s
for structures below 10 m, the two-way travel time of ~1.3 s corresponds to a reflector at depth
of ~200 m.
The blue curve in Fig. 4.4(a) illustrates the / measurements from EW-component ACFs.
Gaps during the Martian nighttime result from the low-quality reflection signals in ACFs during
low wind period when the active source, i.e. lander vibration, is weak. The / curve, with a
maximum value of ~5% at ~2 pm, has a similar shape to the ground temperature recording with a
slight time delay. Different from the wind recordings with high-frequency fluctuations (colored
98
dots in Fig. 4.1a), both the / and ground temperature data show a relatively flat linear trend
during Martian night times (8:00 pm to 8:00 am) and significant variations during the daytime
(8:00 am to 8:00 pm). This is a strong evidence that the dominant mechanism driving the
temporal change is associated with temperature.

Figure 4.4. (a) Temporal patterns of travel time (dt/t; blue curve), frequency peak (-df/f; orange curve) at
~4.1 Hz, linearly scaled ground temperature (black solid curves), and the best fitting dt/t curve (black
dashed curves) obtained by shifting the ground temperature by t 0. The reference frequency f 0 and best
fitting phase delay t 0 are labeled. (b)-(e) Same as (a) but only for frequency peaks at ~3.3, ~6.8, ~8.5, and
~9.8 Hz, respectively.
We fit the / measurements with a linear transformation of the ground temperature
recording () given by (;,,
1
) = ∙(−
1
)+ , considering possible time shift
1

(a)
(b)
(c)
(d)
(e)
99
between the two data sets. The coefficients > 0 and are determined so that the maximum and
minimum values of the (;,,
1
) equal to, respectively, the median values of the upper 95
and lower 5 percentiles of the /. We note that the estimated time shift
1
is representative of
the wrapped phase delay and may be cycle skipped, i.e. the actual delay is
2
=
1
+
<
∙,
where M is an integer and
<
is one Martian day. We find the best fitting
1
by minimizing the
L2 norm of (;,,
1
)−/ for
1
ranging from -2 to 2 hrs. The best-fitting
1
is 43 mins
(Fig. 4.4), i.e., the travel time variation is apparently delayed by ~43 mins relative to the ground
temperature. The best-fitting curve fits well the observed /, especially during Martian night
times and at the turning point ~6 am. However, the observed / is slightly larger than the best
fitting curve when the ground temperature rapidly increases (e.g., at 8 am - 10 am) or decreases
(e.g., at 4 pm - 6 pm). This is likely caused by nonlinear processes induced by the large
temperature gradient during Martian daytime.
4.3.2 / measurements
Fig. 4.3 shows the spectra of ACFs without bandpass filtering and source deconvolution, and
the detected five frequency peaks (i.e. 3.3, 4.1, 6.8, 8.5, and 9.8 Hz) at 1-10 Hz. It is important to
point out that the spectra represent the convolution of source and site effects (Section 4.2.2). As
is discussed in Section 4.2.2, the site-response-related resonance frequencies are f = (N+0.5)/Δt,
where Δt is the two-way travel time of the reflected waves and N is an integer. For Δt = 1.3 s, the
observed peak frequencies at ~3.3 and ~4.1 Hz match well with the site-response-related
resonance frequencies predicted at N = 4 and 5, respectively. We note that, although each
reflection at Δt is expected to yield a series of resonance peaks at f=(N+0.5)/Δt, the clearly
observable ones are only those within the frequency range where the corresponding source is
strong. This might also explain why several other predicted frequency peaks (e.g. at 5.9 Hz for
100
Δt = 1.3 s and N=6) do not develop for the whole analyzed period. The three high-frequency
peaks (~6.8, ~8.5 and ~9.8 Hz) may also be site-response-related resonance, but they are difficult
to interpret without additional information on the subsurface structures (e.g. depths of reflection
interfaces). However, it is also possible that the five frequency peaks represent lander resonance
modes, dependent on properties of the lander (e.g., the shape of the lander, coupling with the
ground), even though the resonance frequencies of the lander vibration are likely to be either
above 10 Hz or below 1 Hz based on numerical modeling of the lander resonance mode
(Murdoch et al., 2017, 2018).
We present −/ in Fig. 4.4 for illustration purposes as the peak frequency decreases with
temperature and Δt. The −/ value measured at ~3.3 and ~4.1 Hz (orange curve in Fig.
4.4b&c) are almost identical to the / curve (blue curve in Fig. 4.4a). The maximum −/
values increase with frequency, ~5% at 3.3 and 4.1 Hz, ~12% at 6.8 Hz, ~19% at 8.5 Hz and
~23% at 9.8 Hz. Similar to the / data, the −/ curves have a similar shape to the ground
temperature recording, therefore we perform curve fitting following the same process described
in Section 4.3.1. The best-fitting wrapped phase delays of the five resonance frequencies are 42,
43, 45, 25 and 29 mins, respectively, comparable to that of the / curve (43 mins). The shifted
temperature curves match well with the observed −/ during Martian night times and at the
turning point ~6 am. However, the peak of the temperature curve from 8 am to 8 pm is slightly
narrower than that of the −/ curve, resulting in discrepancies between the observations and
best-fitting curves, especially at high frequencies. Besides, results at 3.3, 6.8, 8.5 and 9.8 Hz
show larger misfits at ~3-5 pm. These differences probably imply nonlinear processes induced
by the large temperature gradient at Martian daytime, especially during the cooling period.

101
4.4 Discussion
The observed / and −/ curves correlate well with the ground temperature (Fig. 4.4),
implying the dominant mechanism for the variations of travel time and frequency peaks are
driven by temperature changes. The two most plausible temperature-related mechanisms that
could contribute to the observations are: (1) variations of the lander vibration; (2) changes of
seismic velocities in the subsurface due to thermoelastic strain. These mechanisms are discussed
further below.
4.4.1 Variation of the lander
The wind on Mars produces vibrations of the lander at certain resonance frequencies
(Murdoch et al., 2017, 2018; Panning et al., 2020) that depend on the shape of the lander (e.g.,
the solar panel) and the ground properties (e.g. ground stiffness and damping). When the
temperature increases, the resonance frequency decreases due to expansion of the lander and
reduced ground stiffness, consistent with the observed correlation between the −/ curves
and ground temperature. However, as discussed in Section 4.2.2, the peak frequencies observed
in amplitude spectra of the ACFs of reflected waves are associated (Equation 4.2a) with the
source term (lander vibration) convolved with the site term.
The reflected S-wave with a two-way travel time of ~1.3 s is observed in ACFs using the
lander vibration as the active source at 1-5 Hz (Figs 4.1d&4.2). It is possible to explain the
wavelet at ~1.3 s and its multiples with the beating effect between the two frequency peaks at
~3.3 and ~4.1 Hz, assuming both peaks result from the lander resonance modes. However, this
possibility can be ruled out for the following reasons. First, Suemoto et al. (2020) also observed
reflected S-wave with a similar two-way travel time through interferometry of ambient noise
filtered between 5-7 Hz, where the lander resonance modes are weak. Also, since the lander is
102
made of metal, the lander material is expected to respond rapidly to changes in the incoming
solar intensity. Because the lander and the ground are heated by the solar radiation essentially
simultaneously, temporal changes of the lander material should be in phase with or only slightly
delayed (e.g., a few minutes) relative to the ground temperature. However, −/ curves at ~3.3
and ~4.1 Hz yield a wrapped delay time of more than 40 mins relative to the ground temperature
(Fig. 4.4). It is therefore unlikely that the observed daily variations in peak frequencies at ~3.3
and ~4.1 Hz are due to material changes in the lander structure. The frequency peaks at ~3.3 and
~4.1 Hz more likely correspond to the site-response-related resonance modes, f = (N+0.5)/Δt
(Section 4.2.2), for N = 4 and 5, respectively, with Δt = 1.3 s.
In Section 4.2.4, we demonstrated that changes in the source spectrum do not bias /
measured from ACFs. The observed / values imply 5% daily material variations averaged
from surface to the depth of the reflection interface (~200 m). In turn, such material variations
will induce changes of the site-response-related resonance frequencies, e.g., at ~3.3 and ~4.1 Hz.
Indeed, the amplitude (5%) and phase delay (~40 mins) of the two resonance frequency
variations are almost identical to that of the / curve. This is consistent with the derivation in
Section 4.2.2, f = (N+0.5)/Δt, that indicates / = −/ at ~3.3 Hz for N = 4 and at ~4.1 Hz
for N = 5 with Δt = 1.3 s. The observed variations of travel time, and probably also resonance
frequencies at ~3.3 and ~4.1 Hz, are therefore likely associated with changes of seismic
properties of subsurface materials rather than variations of the lander vibrations.
Unlike the observation at low frequencies (~3.3 and ~4.1 Hz), we do not observe clear
reflected S-wave in the time domain from ACFs computed in a higher frequency band (e.g., > 5
Hz), likely due to poor signal to noise ratio. Therefore, the high-frequency peaks at ~6.8, ~8.5
and ~9.8 Hz are interpreted as the convolution of the source (lander resonance modes) and site
103
effects. If the lander resonance is the dominating mechanism for these vibrations, the observed
−/ values are less likely caused by material changes in the lander structure since
considerable delay times (25-45 mins) are seen in the three −/ curves relative to the ground
temperature (Fig. 4.4). Instead, they may imply changes in the coupling between the lander and
Mars surface because of thermal-induced variations in ground stiffness of the near-surface
material. Murdoch et al. (2018) estimated that the lander resonance modes decrease
logarithmically (slope=1/2) with decreasing ground stiffness. Since the origin of these high-
frequency peaks is unclear, we do not quantify the corresponding value or location of material
variation in this study. If the site-response-related resonance is the dominating mechanism, the
wave reflected from a shallower interface (< 200 m) may dominate the ACFs at higher
frequencies, considering the stronger attenuation of higher frequency waves. The larger daily
variations at higher frequency (Fig. 4.3b) may indicate larger material changes in shallow
materials (e.g., top tens of meters).
4.4.2 Thermoelastic strain
As discussed in Sections 4.2.4 and 4.4.1, the observed daily variations in the / curve (Fig.
4.4) are not generated by changes of resonance frequency and are therefore associated with
changes of material properties in the subsurface. Since the temporal pattern of / correlates
well with the ground temperature recording with an apparent delay time of ~40 min, we conclude
the most plausible mechanism is thermoelastic strain at the subsurface. Appendix 4 provides the
equations of thermoelastic strain in an elastic half-space induced by a traveling or stationary
temperature wavefield at the surface (Ben-Zion & Leary, 1986; Berger, 1975). The thermoelastic
strain at a given depth is a superposition of two terms: (i) ‘body force’ term associated with the
(attenuated and delayed) temperature variation at that depth and (ii) a ‘surface traction’ term
104
involving transmission of thermoelastic strains generated at shallower depth that are elastically
coupled to that depth. The ‘body force’ term decreases rapidly with depth, while the ‘surface
traction’ can penetrate to a depth that is on the order of the surface temperature wavelength. If
the half-space is covered by unconsolidated material in a (decoupled) surface layer, the
thermoelastic strain at the underlying half-space is generated by the temperature variations at the
bottom of the surface layer (Ben-Zion & Leary, 1986). The phase delay of thermoelastic strain in
an elastic half-space relative to the temperature field increases with depth, and has a value of /8
below the thermal boundary layer (usually less than ~1 m for diurnal variations; Berger, 1975;
Tsai, 2011) where is the dominant period of the temperature field. A decoupled surface layer
introduced an additional phase delay that equals to the time the temperature field travels through
the unconsolidated layer (Ben-Zion & Leary, 1986; Ben-Zion & Allam, 2013).
The delay of the thermoelastic strain at depth with respect to the surface temperature is
expected to produce delay of temporal variations in the / curve, as observed in our analysis
results (Fig. 4.4). The precise value of the phase delay represents the cumulative effects of time
delays within the considered structure, and it depends strongly on material properties (e.g., depth
of unconsolidated layer and thermal diffusivities in the layer and underlying elastic structure)
that are not well constrained. We therefore do not analyze further quantitatively the observed
delay time (~40 min plus possible Martian daily cycle skipping). The amplitude of the
thermoelastic strain depends on various properties such as coefficient of linear thermal expansion
, thermal diffusivity , Poisson’s ratio , the thickness of decoupled surface layer
=
, and the
wavelength of the temperature field . These parameters are also poorly constrained and may
vary by orders of magnitude on Mars. Nevertheless, we show that reasonable ranges of
parameter values generate thermoelastic strain at depth with amplitudes that can affect the
105
seismic velocities at the subsurface and produce the observed changes in the / curve (blue
curve in Fig. 4.4a).
A geological study at the landing site (Golombek et al., 2020) indicates a microns thick
surficial dust layer above ~1-cm-thick unconsolidated sand, overlying on a layer of 5-10 cm
duricrust with poorly sorted sand and rocks beneath. We therefore use a model of elastic half-
space overlain by a 10 cm thick decoupled layer to provide estimates of plausible daily
thermoelastic strains (Equations A4.1a and A4.1b in Appendix 4). Estimations from Morgan et
al. (2018) suggest that the thermal diffusivity coefficient of the unconsolidated layer on Mars
is in the range 2-6×10
-8
m
2
/s, close to that of the atmosphere on Mars. We assume that the
coefficient of linear thermal expansion in the surface layer is on the order of 10
-3
°C
-1
. Typical
values of and for crystalline rocks are ~10
-6
m
2
/s and ~10
-5
°C
-1
, respectively.
Fig. 4.5 presents amplitudes of volumetric thermoelastic strain in an elastic half-space
covered by a 10cm-thick decoupled layer at depths in the range 0.1-200m for different thermal-
physical parameters. The volumetric strain is given by the sum of horizontal and vertical strains
assuming isotropic deformation in the two horizontal directions, and the wavelength of the
temperature field and Poisson’s ratio are set to be = 15 km and = 0.3. Additional results in
Appendix 4 show that the amplitude of thermoelastic strain at shallow depth is not sensitive to
when > 500 (Fig. D4.6) or to the value of Poisson’s ratio in the range of 0.1-0.5 (Fig.
D4.7). The results indicate that the amplitude of thermoelastic strain decreases rapidly in the top
20 m, and remains approximately constant (~10
-8
for = 10
*>

+
/ and = 10
*?
℃
*&
) in the
depth range 20-200 m. The average volumetric strain in the top 20 m with and values typical
for soil and rocks in the ranges of 10
-7
-10
-6
m
2
/s and 10
-5
-10
-4
°C (Robertson, 1988) is in the range
of 10
-7.5
-10
-5.5
.
106

Figure 4.5. Amplitude of thermoelastic strain calculated at different depths y (0.1 m, 0.5 m, 1 m, 10 m, 20
m, and 200 m) relative to the bottom of the decoupled layer. The model consists of an elastic half-space
covered by a 0.1 m (y b = 0.1 m) decoupled layer with thermal diffusivity of 2×10
-8
m
2
/s. Results are
computed for and of the elastic half-space in the ranges 2× 10
-8
-10
-4
m
2
/s and 10
-5
-10
-3
°C
-1
,
respectively. The wavelength of temperature field and Poisson’s ratio are 15 km and 0.3, respectively.
107
Laboratory studies (Nur & Simmons, 1969) indicate that strain levels in the range 10
-7
-10
-6

(associated with stress levels 10
1
-10
2
Pa assuming rigidity of 10
8
Pa, a value between that for
typical crystalline rocks, 10
9
Pa, and near-surface material on Mars, 10
7
Pa) can generate velocity
changes without causing any material damage under low confining pressure. Moreover,
experiments also show that sandstone and other rocks begin to suffer material damage under
strain levels of about 10
-7
(Pasqualini et al., 2007; TenCate et al., 2004). In-situ observations on
earth (e.g. Qin et al., 2020) indicate up to 10% average velocity reduction in the top 15 m for
dynamic strain level of 10
-7
-10
-6
. Therefore, the daily variations of thermoelastic strain in the
subsurface can explain the observed amplitude of the derived / results and phase delay
relative to the ground temperature (Fig. 4.4).
The estimated 5% daily velocity variations are a cumulative value associated with variations
in the top ~200 m. Since the material strength increases with increasing confining pressure (e.g.,
Nur & Simmons, 1969; Pasqualini et al., 2007; TenCate et al., 2004) and the amplitude of the
thermoelastic strain decreases with depth (Figs 4.5, A4.6, A4.7), the estimated 5% daily velocity
variations are likely to concentrate in the very shallow materials. Indeed, analysis of borehole
data on Earth shows that temporal changes tend to concentrate in the top few tens of meters (e.g.
Bonilla et al., 2019; Qin et al., 2020; Rubinstein, 2011). Assuming no changes below the 18 m
regolith layer (Golombek et al., 2020) and using the velocity model from Lognonné et al. (2020),
the daily fluctuation in S-wave velocity in the top 18 m is up to ~40% to account for the 5%
travel time variation (i.e. ~0.03 s). The velocity perturbation in response to surface temperature
variations on Mars is significantly larger than those resolved on Earth, and may result from the
combined effects of large temperature variation of ~101ºC (Fig. 4.1a), low barometric pressure
108
of ~700 Pa and the local structure with extremely low S-wave velocities of <100 m/s in the top
few meters.

4.5 Conclusions
We use the lander vibration on Mars as an active source and track the variations of S-wave
travel time and the resonance modes in ACFs. Reflection phases are observed at ~1.3, ~2.4, ~3.9
s in autocorrelations of the InSight seismic data. The daily variations of S-wave travel time and
the resonance modes at 3.3 and 4.1 Hz suggest ~5% material changes averaged in the top ~200
m. The changes likely concentrate in the top tens of meters below the surface, and may be up to
40% if they are limited to the top ~18 m regolith layer. The three high-frequency modes at 6.8,
8.5 and 9.8 Hz likely reflect a combination of the source (lander vibration) and site effects. The
variations of high-frequency modes imply ground stiffness change at the foot of the lander if the
source term dominates, or material variations at different depth ranges assuming the site effect
dominates. The variations of travel time and resonance frequencies are similar to the ground
temperature recording with apparent phase delays of 25-45 min. This correlation combined with
amplitude estimate for reasonable ranges of parameter values implies that the most likely
dominant mechanism is thermoelastic strain at the subsurface. The results highlight the
importance of seismic monitoring in planetary missions for better understanding of properties
and dynamics of sub-surface materials.

4.6 Acknowledgements
We acknowledge NASA, CNES, their partner agencies and Institutions (UKSA, SSO, DLR,
JPL, IPGP-CNRS, ETHZ, IC, MPS-MPG) and the flight operations team at JPL, SISMOC,
109
MSDS, IRIS-DMC and PDS for providing SEED SEIS data (InSight Mars SEIS Data Service,
2019) and ground temperature data (https://pds-geosciences.wustl.edu/insight/urn-nasa-pds-
insight_rad/data_derived/). The wind and air temperature data are downloaded from
https://atmos.nmsu.edu/data_and_services/atmospheres_data/INSIGHT/insight.html#Selecting_
Data. The study was supported by the U.S. Department of Energy (award DE-SC0016520).
110
5. Spectral characteristics of daily to seasonal ground motion at the
Piñon Flats Observatory from coherence of seismic data
(Qin, L., Vernon, F. L., Johnson, C. W. & Ben-Zion, Y., 2019. Spectral characteristics of daily to
seasonal ground motion at the Piñon Flats Observatory from coherence of seismic data, Bulletin
of the Seismological Society of America, 109, 1948–1967, https://doi.org/10.1785/0120190070)

5.0 Summary
We investigate coherences of seismic data recorded during three years (2015-2017) at the
Piñon Flats Observatory (PY) array and a co-located 148m-deep borehole station B084, along
with oceanic data from a buoy SW of the PY array. Seismic and barometric recordings at PY
stations are analyzed with a multitaper spectral technique. The coherence of signals from seismic
sources is >0.6 at 0.05-8 Hz between closely spaced (<65 m) surface stations, and decreases to
~0.2 in frequency bands where the wavelengths are smaller than interstation distances. There are
several local coherence increases at 1-8 Hz between nearby (<65 m) surface stations, whereas
large coherence values between a surface and 148m-deep borehole stations are only present at
the secondary microseism (~0.14 Hz). This points to significant modification of seismic
recordings in the top crust, and that continual near surface failures might produce shallow rapidly
attenuating signals at surface stations. Incoherent local atmospheric effects induce incoherent
seismic signals in low and high frequency ranges through different coupling mechanisms.
Between 0.003-0.05 Hz, atmospheric loadings generate ground tilts that contaminate the two
horizontal seismic recordings and decrease their coherence, while the vertical component is less
affected. At 1-8 Hz, coupling of atmospheric pressure with surface structures transmits
incoherent signals into the ground, degrading the seismic coherence in all three components. The
two horizontal coherences show seasonal variations with extended coherent frequency bands in
111
winter and spring, likely to be produced by seasonal variations in microseisms and local ground
tilts. The coherences also contain high anomalies between ~2-4 Hz resulting from anthropogenic
activities. The results provide useful information on instrument characteristics and variations in
the shallow crustal response to earthquakes, seasonal and ambient sources of seismic energy,
along with atmospheric pressure-temperature changes and anthropogenic activities.

5.1 Background
Describing spatio-temporal variations in seismic recordings on multiple scales helps to assess
the performance of sensors and network detection ability, while providing insights on crustal
properties and response to multiple natural and anthropogenic processes. Joint analyses of high-
quality data sets collected from temporary and permanent seismic arrays with meteorological and
oceanic data (e.g. pressure, temperature, wind, rain) can clarify properties of the ambient seismic
noise and monitor small variations in seismic properties, especially in the top hundred meters.
Wind, pressure and temperature fluctuations can induce variations in the ground motion and
properties of shallow layers through direct loading and coupling with surface obstacles, which
produce related signals in low and high frequency ranges, respectively. De Angelis & Bodin
(2012) measured surface tilt up to several tenths of a rad, likely generated by atmosphere
pressure changes, causing 25 dB power spectral density differences between horizontal and
vertical seismic recordings at periods >30 s. Edwards et al. (2007) estimated the energy
admittance of acoustic-seismic coupling to be 2.13±0.15% in the infrasonic range observed from
reentry of NASA’s Stardust sample return capsule. Hillers & Ben-Zion (2011) analyzed
meteorological data in southern California and concluded that variations of surface temperature
and wind are the two main sources for observed noise amplitude variations at 2-18 Hz. Seismic
112
recordings at the Sage Brush Flats site on the San Jacinto fault zone southeast of Anza are also
considerably affected by wind-related signals propagating at the surface and in the shallow crust
(Johnson et al., 2019b).
Ambient noise data from continuous seismic records are now often used to derive Green’s
functions from cross correlations between stations pairs, based on the assumption that the two
stations contain coherent noise (e.g., Campillo & Paul, 2003; Wapenaar, 2004). The noise-based
Green’s functions can be used to image and monitor subsurface structures (Lin et al., 2008; Sens-
Schönfelder & Wegler, 2006; Shapiro et al., 2005), and are commonly analyzed in the 0.05-1 Hz
band where the strongest seismic noise signals are detected. This frequency range includes the
microseisms at ~0.07 Hz and ~0.14 Hz associated with ocean-continent interactions (Hillers et
al., 2012; Longuet-Higgins, 1950). With recent dense array recordings at high sampling rates,
ambient noise tomography can be performed at 4-5 Hz (Lin et al., 2013; Mordret et al., 2019),
with some studies using up to 50 Hz (Ben-Zion et al., 2015; Zigone et al., 2019). In these high
frequency bands from 2-50 Hz, signals in the noise are also associated with changes in the
temperature and wind (Hillers & Ben-Zion, 2011; Johnson et al., 2019a), anthropogenic activities
such as car and air traffic events (Meng & Ben-Zion, 2018), and microearthquakes (Inbal et al.,
2015). In longer periods between 100-500 s, the lowest noise amplitudes are attributed to the
very weak Earth’s hum (Kurrle & Widmer-Schnidrig, 2008; Rhie & Romanowics, 2004) and
ground tilts induced by changes in atmosphere pressure (De Angelis & Bodin, 2012; Beauduin et
al., 1996). In the very low frequencies, e.g. ~970 mHz, solar modes coupling to the Earth
through magnetic fields are observed (Thomson & Vernon, 2015, 2016).
The coherency of earthquake waveforms has been widely applied to assessing the spatial
variations in ground motion (Ancheta et al., 2011; Zerva & Zervas, 2002) in the frequency bands
113
(e.g. ~1-15 Hz) of interest to earthquake engineers. Empirical coherency models have also been
developed to help evaluate the response of lifelines to strong ground motions (Abrahamson et al.,
1991). However, the ambient noise field, which constitutes most of the seismic recordings (e.g.,
Meng & Ben-Zion, 2018), was not used in most coherency studies. In this study we analyze the
coherence of continuous seismic data at the Piñon Flats Observatory (PY) array, and describe the
seismic noise properties from different sensor channels and station pairs for a wide frequency
band between 0.0003-100 Hz in relation to meteorological and ocean buoy records. The
remainder of the chapter is organized as follows. We first describe the data and methods used in
this work, followed by discussion about basic aspects of the data, atmosphere induced ground
motions, seasonal variations in high-coherence frequency bands compared with local
temperature recordings and ocean swell heights, and observed anomalously large coherences in
the 2-4 Hz band generated by anthropogenic activities. Then the observed coherence features are
summarized and discussed.

Figure 5.1. (a). Large-scale map showing the locations of PY array (triangle), the 2016 M w 5.2 Borrego
Springs earthquake (BSE, star), and the buoy sensor 46086 (dot). (b). The PY array layout with three
eccentric circles (dashed circles). All stations are labeled with the station codes. Squares and balloons
represent the STS5 and Trillium 120PH sensors, respectively. Triangles indicate the micro-barometers co-
located with the seismometers, and the circle represents the B084 borehole station at a depth of 148 m.
114
5.2 Data and methods
5.2.1 Data
The PY seismic array (Fig. 5.1) is located at the Piñon Flats in the San Jacinto Mountains of
southern California, ~12 km northeast of the San Jacinto Fault zone. Piñon Flats is characterized
by granodiorite bedrock covered by 25 m of unconsolidated materials with little topographic
variations (Wyatt, 1982). The local P wave velocity increases from 400 m/s in the shallowest
surface layer to 2700 m/s at 15 m, and to ~5400 m/s at the bedrock below 65m (Vernon et al.,
1998). At the site there are 13 broadband seismometers (Fig. 5.1b, 01 to 13) deployed with
posthole installations at depths of 2.2-2.6 m in Nov 2014. Twelve of them are on three eccentric
circles with nearest station distances of 65 m (inner ring, 01 to 04), 330 m (middle ring, 05 to 08)
and 780 m (outer ring, 09 to 12). Station 13 is located halfway between 09 and 12. Stations 01,
02, 05, 08, 10, 11, 13 use STS5 sensors (Fig. 5.1b, squares) and 03, 04, 06, 07, 09, 12 use
Trillium 120PH sensors (Fig. 5.1b, balloons). Each station records seismic velocities at 200
samples per second (sps) (HH), 40 sps (BH), and 1 sps (LH). The BH and HH recordings have
essentially identical responses (Fig. E5.1) below the 20 Hz Nyquist frequency of the BH
components and are used interchangeably in that frequency band in this study. Stations 01, 03,
05, 06, 07, 09, 10, 11, 12 also have Setra 278 micro-barometers (Fig. 5.1b, triangles) measuring
atmosphere pressure at 40 sps (BDO). All the micro-barometers began recording in Oct 2015
except 06 and 07 that started in Jan 2016. In addition, located 90 m NW of PY01 is the Plate
Boundary Observatory borehole station B084 with a HS-1-LT sensor at a depth of 148 m that
began recording in 2012. The response functions for all the seismometers are shown in Fig. E5.1.
In the present study three years of continuous data from 2015-2017 are analyzed from the surface
and borehole seismometers and the co-located micro-barometers. To better inform the results, we
115
also use the ocean wave data recorded by the buoy sensor 46086 (labeled in Fig. 5.1a) from the
National Oceanic and Atmospheric Administration located SW of the PY array ~80 km off the
coast.
5.2.2 Methods
The coherency
@A
(,) between two recordings x(t) and y(t) is defined (e.g., Ancheta et al.,
2011) as the cross spectral density
@A
(,) normalized by the square root of power spectral
density product
@@
()
AA
():

@A
(,) =
B
$%
(/,C)
DB
$$
(/)B
%%
(/)
= `
@A
(,)`
*,E
$%
(/,C)
(5.1)
where f and represent the frequency and distance between the two stations that record x(t) and
y(t). The cross spectral density is defined as
@A
(,) = lim
F→H
&
F
{
∗
()
C
()~ with () and

C
() representing the Fourier transforms of () and () , respectively, and {∙} is the
expectation operator. Similarly
@@
() = lim
F→H
&
F
{
∗
()()} . The function
@A
(,) has
complex values with `
@A
(,)` and
@A
(,) being the amplitude and phase, respectively. The
phase can be expressed by
@A
(,) = 2∙/
IJJ
+(,). The first term represents a non-
dispersive wave propagating with a constant apparent velocity (
IJJ
) in the medium between the
two stations, and the second term indicates a random phase component (,) accounting for
scattering effects. The amplitude `
@A
(,)` is referred to as coherence with a value from 0 to 1
representing the relative intensity of coherent and incoherent signals in the two recordings at
discrete frequencies. Coherent signals correspond to those that can be related via an invertible
linear time-invariant system. The coherence evaluates the linear predictability between the two
recordings, i.e. `
@A
(,)` = 1 indicates that x(t) and y(t) are related through an invertible linear
116
time-invariant system, while incoherent signals in x(t) or y(t) will decrease the value of
`
@A
(,)`.
Random scattering effects at the PY array dominate the phase of noise coherency; therefore,
we investigate the properties of weak ground motions by analyzing the amplitude of coherency,
i.e. the coherence, in the background seismic noise. The multitaper method with adaptive
weights (Prieto et al., 2009; Thomson, 1982) is applied to obtain reliable and high-resolution
coherences and spectra. Unless otherwise stated, the continuous time series for each day is
partitioned into 144 independent non-overlapping time windows that are 600-s long each. Ten
Slepian tapers with a time-bandwidth product of 6 are applied to each time window for the
coherence and spectrum calculations. The 144 coherences for each 1-day data constitute the 1-
day coherogram, the median of which is the 1-day median coherence. Similarly, the 1-year
coherogram is composed of the daily median coherences in 1 year, and the 1-year median
coherence is the median value of the 1-year coherogram. The 600-s time window leads to a
frequency resolution of 1/600 Hz, and with a time-bandwidth product of 6 in the multitaper
method the final frequency resolution is 0.01 Hz (6*1/600 Hz). This is ideal to get smooth and
reliable coherences with reasonable computational loads for the frequency band of 0.01-100 Hz.
We attribute the recorded signals in the examined frequency range to two general sources: (1)
seismic sources, e.g. earthquakes, microseisms and Earth hum; (2) local effects caused by
atmosphere pressure and temperature changes. In the following we analyze three different types
of coherences: (1) cross-station seismic coherence, i.e. the coherence between the seismic
recordings from two stations; (2) cross-station barometric coherence, i.e. the coherence between
the barometric recordings from two micro-barometers; (3) cross-channel coherence, i.e. the
coherence between the seismic and barometric recordings at the same station.
117
5.3 Analysis and results
5.3.1 Basic data features from cross-station seismic coherences
Basic features of the cross-station seismic coherences are presented in Figs 5.2-5.4 using the
HH components on Julian day 114, 2016 at stations 01 and 02 separated by 65 m. In the 0.01-
0.05 Hz band, the HHE component has a low coherence value around 0.2 (Fig. 5.2b), resulting
from the large amplitude incoherent signals at 0.01-0.05 Hz (Fig. 5.2c) exhibiting different daily
variation patterns at stations 01 and 02. From UTC hours 0-14, the large amplitude incoherent
noise at 0.05-0.1 Hz (Fig. 5.2c&d) overwhelms the coherent signal, i.e. the primary microseism,
resulting in small HHE coherence values around 0.2, while at hours 14-24 the coherence
increases to ~0.6 because of the decreased amplitude of incoherent signals. A teleseismic arrival
(Fig. 5.2, dashed box 1) increases the coherence from 0.03-0.1 Hz at about 02 hour. Between
0.1-1 Hz, the coherence is close to 1 associated with the strong secondary microseism. The 1-8
Hz coherence shows similar patterns as in the 0.05-0.1 Hz band. The simultaneous coherence
decays in these two frequency bands suggest incoherent signals from the same source that affect
the data in different frequency bands (discussed in detail in the next section, Local atmospheric
effects). Above 8 Hz, the HHE coherence is close to 0.2, with local earthquake signals (Fig. 5.2,
dashed box 2) causing spikes in coherence up to 50 Hz. Compared with the results from Vernon
et al. (1991, 1998), the observed coherent frequency bands for local earthquakes are much wider,
which probably results from the high data quality. The details of these observations are discussed
further in the following two sections.
The HHN results are almost identical to the HHE and shown in Fig. E5.2, while the HHZ
results are different and presented in Fig. 5.3. The median coherences and spectra from the three
components on Julian day 114, 2016, are summarized in Fig. 5.4. The vertical coherence is
118
smaller than the horizontal coherences at 1-8 Hz, while the reverse holds in frequencies lower
than the primary microseism. The vertical spectra do not contain high-amplitude low frequency
signals at 0.01-0.05 Hz and are ~20 dB smaller than the horizontal spectra (Fig. 5.4b). The
different behaviors of the horizontal and vertical coherences at 1-8 Hz and 0.01-0.05 Hz are
discussed in more details in the next section, Local atmospheric effects.

Figure 5.2. HHE component results on Julian day 114, 2016 at stations 01 and 02 of the PY array. (a).
Detrended waveforms at 01 and 02. (b). One-day coherogram. (c) and (d) are the one-day spectrograms
from 01 (c) and 02 (d). The dashed boxes indicate the example tele (1) and local (2) seismic arrivals,
respectively.
119

Figure 5.3. HHZ component results on Julian day 114, 2016 at stations 01 and 02 of the PY array. The
layout is the same as Fig. 5.2.
120

Figure 5.4. Three component median coherences (a) and spectra in counts
2
/Hz (b) at stations 01 and 02
on Julian day 114, 2016.
Next, we describe the seismic coherences between the 148m-deep borehole station B084 and
the closest surface station PY01, with a surface interstation distance of 90 m. We first remove the
instrument responses (Fig. E5.1), and rotate the two horizontal components of B084, which are
65º and 155º clockwise from the North, to EW and NS directions. Fig. 5.5 shows the HHE
results at Julian day 114, 2016. Corresponding HHN and HHZ results are given in Fig. E5.3. The
instrument response of B084 (Fig. E5.1) decreases by more than two orders below 0.07 Hz,
while the level of instrument noise remains approximately the same in all frequencies.
Consequently, the signal to noise ratio is reduced significantly below 0.07 Hz, making the
spectral values after instrument correction dominated by large instrument noise (Fig. 5.5). We
therefore only study the signals above 0.07 Hz. The HHE component exhibits large coherence
values at the secondary microseism ~0.14 Hz and is ~0.2 for all other frequency ranges except
during local earthquakes. The HHN results are similar to the HHE, while the vertical component
does not show high coherence in the full frequency band, probably resulting from the weak
secondary microseism in the vertical component at the borehole station. Compared with the
121
results from PY01-PY02 (Figs 5.2-5.4), the coherences from PY01-B084 above 0.14 Hz are
much smaller except during local earthquakes, indicating that without strong seismic signals like
microseisms and earthquakes, high frequency seismic noise recordings are significantly modified
in the top hundred meters of the crust.

Figure 5.5. HHE component results on Julian day 114, 2016 (same day as in Figs 5.2-5.4) at stations
PY01 (surface) and B084 (148m-deep borehole). Instrument responses are removed. (a) is the
coherogram, and (b) and (c) show the spectrograms in (m/s)
2
/Hz from PY01 (b) and B084 (c).
122

Figure 5.6. Three-year coherograms from HHE component at three STS5 (a, c, e) and thee Trillium
120PH (b, d, f) station pairs. Each coherogram is labeled with the corresponding station codes and
interstation distances. The arrows indicate the beginnings of years 2015, 2016 and 2017 (same for all the
following figures). The dashed circles in (e) and (f) point out the high-coherence anomalies.

Figure 5.7. Three-year median coherences from HHE (a), HHN (b) and HHZ (c) components at three
STS5 (01-02, 05-08, 10-11) and three Trillium120-PH (03-04, 06-07, 09-12) station pairs. The
interstation distances are 65 m, 330 m, and 780 m for 01-02/03-04, 05-08/06-07 and 10-11/09-12
respectively.
123
Fig. 5.6 displays three-year coherograms of the HHE component comparing pairs of STS-5
sensors and Trillium 120PH sensors. Corresponding HHN and HHZ coherograms are shown in
Figs A5.4&5.5. The three-year median coherences from the three components are summarized in
Fig. 5.7. The HHN coherograms are similar to the HHE, and the major differences between the
vertical and horizontal coherences are similar to those observed from one-day data (Figs 5.2-5.4).
As the interstation distances increase, the coherences decrease significantly for frequencies >1
Hz and remain almost unchanged at and below the secondary microseism. Considering the
interstation distance as one wavelength and the shallow P wave velocity of ~400 m/s at Piñon
Flats, the corresponding wave frequencies are 6.2 Hz, 1.2 Hz, and 0.5 Hz for station pairs 01-
02/03-04, 06-07/05-08, and 10-11/09-12. These values are consistent with the frequencies where
the coherences start to decrease dramatically (Fig. 5.7). In these frequency bands, signals from
seismic sources dominate the recordings, whereas in the low frequency range, e.g. 0.01-0.05 Hz,
incoherent signals from local atmospheric effects (see details in the next section) overwhelm the
coherent signals from seismic sources and degrade the corresponding cross-station seismic
coherence. In addition, the coherences from 01-02/03-04 (Fig. 5.7) with interstation distances of
~65 m contain several local increases at 1-8 Hz (e.g. at ~3 Hz, ~5 Hz, ~7 Hz), exhibiting larger
values in the horizontal components than in the vertical. However, with a larger interstation
distance the coherences decrease almost monotonically in this frequency band without local
increases. Stations PY01 and B084 also do not have coherent signals in the 1-8 Hz band (Fig.
5.5). This implies rapidly attenuating 1-8 Hz coherent signals at the shallow structure that can
only be simultaneously recorded by nearby surface stations (e.g. <65 m). The coherograms from
STS5 (Fig. 5.6, left column) and Trillium 120PH (Fig. 5.6, right column) stations are similar to
each other, indicating equivalent performance for the two types of broadband seismometers. In
124
Figs A5.6&5.7, we present the HHE coherograms and three-year median coherences between
two stations with different sensor types (i.e. STS5 vs. Trillium 120PH). The major coherence
characteristics (e.g. discrepancies between horizontal and vertical components, high coherence in
0.1-1 Hz, and coherence decrease above 1 Hz) are similar to those from station pairs with the
same sensor type. From the perspective of spectral levels and coherence observations, the STS5
and the Trillium 120PH sensors provide nearly identical results.
The results of Figs 5.2-5.7 show that the horizontal coherences are as low as 0.2 at 0.01-0.05
Hz, while the vertical component behaves differently with coherence values larger than 0.7. To
investigate whether this is from possible sensor problems, we study the coherences of teleseismic
waves that dominate the low-frequency seismograms. We first apply a 1 Hz lowpass filter to the
data from all the teleseismic events with magnitudes larger than 7 from 2015-2017 (Fig. E5.8a)
and down sample the data to 2 Hz to reduce the computational load. We use the TauP toolkit
(Crotwell et al., 1999) and the IASP91 velocity model to predict the P and S wave arrival times.
The coherences are obtained in a time window 10 s before the P wave and 4000 s after the S
wave arrivals. Fig. 5.8 shows the results from an example event and all the HHE component
results at stations 01 and 02. The HHN and HHZ components are similar to the HHE (Fig.
E5.8b-c). The spectra at 0.01-0.1 Hz from event 37381445 (labeled in Fig. E5.8a) is ~10
6

counts
2
/Hz, and more than 10 times larger than the noise spectra (Fig. 5.4b). The corresponding
coherence value remains close to one from 10
0
-10
-4
Hz. The HHE coherences from all
teleseismic events (Fig. E5.8c) are very high with median values larger than 0.95, and only three
events exhibit coherences below 0.95. This indicates the low coherence of seismic noise at 0.01-
0.05 Hz results from incoherent signals in this frequency band, and not a problem with the sensor.
125

Figure 5.8. HHE component results from teleseismic events. (a). 1 Hz lowpass filtered HHE waveforms
from event 37381445 (labeled in Fig. E5.8a), at stations 01 (upper panel) and 02 (lower panel). The
horizontal axis represents the time in seconds after the earthquake occurrence time, and vertical dashed
lines indicate the time window in which the coherences and spectra are calculated. (b). Spectra (solid and
dashed lines) and coherence (solid line with dots) calculated from the data sets in (a). (c). HHE
coherences (thin solid lines) from all teleseismic events (Fig. E5.8a) and the corresponding median value
(thick dashed line).
5.3.2 Local atmospheric effects
The low horizontal coherences in long periods, differing behaviors of horizontal and vertical
coherences, and the complex daily coherence variations (Figs 5.2-5.3) from cross-station seismic
data indicate the influence of local incoherent signals in agreement with previously observed
126
atmosphere-induced effects in long periods (De Angelis & Bodin, 2012; Beauduin et al., 1996).
The major effects on the sensor mass related to atmospheric pressure/temperature variations are
(Zürn & Wielandt, 2007): (1) gravity variations because of density changes in the deformed crust,
i.e. the free air effect; (2) Newtonian attraction between the air and sensor mass; (3) inertial force
caused by the ground acceleration from the free air effect. In the vertical direction, the downward
free air effect and inertial force cancel with the upward Newtonian attraction, therefore the
atmospheric effects are not significant. However, in the horizontal directions, the three forces are
in the same direction and combine to affect the sensor mass and horizontal seismic recordings.
The atmospheric effects in long period (>20 s) are often referred as ‘ground tilts’, depending on
the local temperature/pressure field, the compliance of the near surface structures, and the
deployment of seismic stations. Small ground tilts of 10
-6
rad can induce apparent horizontal
ground accelerations as large as 10
-3
cm/s
2
, comparable to signals from regional earthquakes
(Graizer, 2009).
Fig. 5.9 shows the 0.01-0.05 Hz bandpass filtered seismograms and micro-barometer
recordings on Julian day 114, 2016 (i.e. same day as in Figs 5.2-5.5) from stations 01 (STS5) and
03 (Trillium 120PH) separated by 90 m. At both stations, the horizontal seismograms record
clear barometric signals, e.g. at UTC hours 0-4 and 10-14, while the vertical component contains
far less contamination. The seismic and pressure recordings differ somewhat at the two stations.
This implies that the ground tilts induced by atmospheric pressure changes generate incoherent
signals at 0.01-0.05 Hz at different stations that are most prominent in the horizontal components.
Therefore the horizontal cross-station seismic coherences are as small as 0.2 while the vertical
coherence is larger than 0.6 (Figs 5.2-5.3). Examining the results from other stations suggests
that there are no systematic differences between STS5 and Trillium 120PH sensors.
127

Figure 5.9. 0.01-0.05 Hz bandpass filtered seismic (BH components) and barometric (BDO) recordings at
stations 01 (a) and 03 (b).

Figure 5.10. Seismic (BH components) and barometric (BDO) recordings at station 01, bandpass filtered
at 0.05-0.1 Hz (a) and 1-8 Hz (b).
The reduced coherences in the three components at 0.05-0.1 Hz and 1-8 Hz (Figs 5.2-5.3, e.g.
UTC hours 0-4, 10-14 on Julian day 114, 2016) correlate well with the atmospheric pressure
variations. Examples of the seismic and barometric data at 0.05-0.1 Hz and 1-8 Hz from station
01 are shown in Fig. 5.10. In the 0.05-0.1 Hz band the influence of atmospheric pressure is
comparable with the primary microseism in the waveforms; however, the corresponding
coherence decrease in Figs 5.2-5.3 implies atmospheric effects. At 1-8 Hz, the changes in
128
atmosphere pressures are clear in the seismograms (e.g. UTC hours 0-4 and 10-14) and can be
seen in all the three components, consistent with the coherence decreases in the three
components (Figs 5.2-5.3). The differing behavior of coherence at 0.01-0.05 Hz and 1-8 Hz
suggests the incoherent signals at 1-8 Hz may not be induced by local ground tilt, but a different
coupling mechanism between the local atmosphere conditions and the ground. This is further
supported by the cross-channel coherence behaviors, and is discussed further below. It is difficult
to infer the dominant coupling mechanism at 0.05-0.1 Hz since we cannot tell if the horizontal
components are more affected than the vertical in this frequency band.

Figure 5.11. Cross-channel coherences at stations 01 (a, c, e) and 03 (b, d, f). All the coherograms start
from Oct 2015 when BDO recordings are available.

129
Fig. 5.11 shows the coherences between atmospheric (BDO) and seismic (BH) recordings, i.e.
cross-channel coherences, at stations 01 and 03 from Oct 2015 to Jan 2018. Coherence results of
BHE and BDO components at stations 01 and 02 in the very low frequency range from 0.0003-1
Hz are shown in Fig. 5.12. The barometric recordings at 03 are used in Fig. 5.12 because there is
no micro-barometer at 02. The coherences in Fig. 5.12 are calculated in 8-hour moving time
windows with 95% overlap instead of the previous 600-s non-overlapping time windows and the
data are down sampled to 2 Hz. The frequency resolution is ~0.00021 and results are shown from
0.0003-1 Hz. The BHN and BHZ results (Fig. E5.9) are consistent with previous observations
that the BHN results are similar to BHE while the BHZ component is less affected by local
atmospheric effects below 0.05 Hz. The results from other station pairs are similar. We examine
collectively the results from Figs 5.11-5.12 to investigate the influence of local atmospheric
effects in the 0.0003-20 Hz band.
The cross-channel coherences (Figs 5.11&5.12b) show a maximum value of about 0.5 at
0.0003-0.05 Hz for the two horizontal components, implying a weak correlation between seismic
recordings and barometric pressures. At each station, signals from local atmospheric effects in
the horizontal seismic recordings correlate with the co-located barometric recordings, causing the
cross-channel coherence values (0.3-0.5) at 0.0003-0.05 Hz to stand out from the background
(~0.1). However, the seismic recordings contain signals that do not exist in the barometric
recordings, e.g., Earth hum, resulting in relatively small cross-channel coherence values.
We also observe different cross-station barometric coherences at 0.0003-0.003 Hz compared
to 0.003-0.05 Hz. In the lower frequency range 0.0003-0.003 Hz, the barometric recordings at
stations 01 and 03 are strongly correlated with barometric coherence values close to 1 (Fig.
5.12c), while it is the opposite at 0.003-0.05 Hz. This is true for all the cross-station barometric
130
coherences in the PY array with the interstation distances varying from 90 m to 680 m, though
the absolute value of barometric coherences decrease with the interstation distances. This implies
that large-scale atmosphere pressure variations dominate in the very low frequency band
(0.0003-0.003 Hz), and the barometric recordings are coherent for all the interstation distances in
the PY array. However at 0.003-0.05 Hz, localized fluctuations of atmosphere pressures and
temperatures that vary from station to station produce incoherence between two closely spaced
(~90 m) barometric recordings. This is also consistent with the observations in Fig. 5.9.
Considering the relatively homogeneous local structures and uniform posthole deployment of
stations at Piñon Flats, the coherent atmosphere pressures in the 0.0003-0.003 Hz band generate
relatively coherent local ground tilt at different stations; therefore, the corresponding seismic
recordings from two stations are coherent with a relatively large cross-station seismic coherence
value (>0.6; Fig. 5.12a). In the higher frequency band (0.003-0.05 Hz), however, the incoherent
atmosphere pressures between different stations contribute to the much smaller values (~0.2) of
the cross-station seismic coherences (Fig. 5.12a).
Local barometric pressure signals are also observed in the 1-8 Hz seismograms (Fig. 5.10),
and are expected to generate relatively large cross-channel coherence values at the same station;
however, our results show otherwise (Fig. 5.11). Compared to the observations at 0.0003-0.05
Hz, the local atmospheric effects cause a coherence decrease at 1-8 Hz in all three components
(Figs 5.2-5.3) and the cross-channel coherence values are close to 0.1. This implies different
coupling mechanisms at 0.0003-0.05 Hz and 1-8 Hz between the atmosphere pressure changes
and local ground motions. At 0.0003-0.05 Hz, the atmosphere pressures generate local ground
tilts contaminating the low frequency recordings, so the cross-channel coherences stand out and
the seismic recordings are more strongly influenced in the horizontal directions than in the
131
vertical. At 1-8 Hz, however, the atmosphere pressure variations (e.g. wind activities) can
transmit high-frequency signals into the ground through the shaking of objects above the surface
such as trees, antennas and buildings. This introduces incoherent signals to the three components
of seismic data and reduces the cross-station seismic coherences. The barometric data cannot be
related to the induced 1-8 Hz seismic motions via an invertible linear time-invariant system due
to the indirect and non-linear energy transfer process; therefore, the corresponding cross-channel
coherence values are close to zero.

Figure 5.12. Coherences calculated with 8 hr moving windows and 95% overlaps. (a). Cross-station (01-
02) seismic coherogram (BHE component). (b). Cross-channel (BHE-BDO) coherogram at station 01. (c).
Cross-station (01-03) barometric coherogram (BDO component). Station 03 is used here since there is no
micro barometer at 02. All the coherograms start from Oct 2015 when BDO recordings are available.
132
5.3.3 Seasonal variations in cross-station seismic coherences

Figure 5.13. High-coherence frequency bands of HHE component in five STS5 station pairs. The vertical
bars represent the frequency bands in which the coherences are larger than 0.95, with solid lines
indicating the upper and lower bounds. Each plot is labeled with the corresponding station codes and
interstation distances on the right.
Seasonal variations are investigated by analyzing the high-coherence frequency bands that
are defined as the widest continuous frequency bands where the daily median cross-station
seismic coherences are larger than 0.95. A large threshold is chosen to minimize the influence of
complexities above 1 Hz resulting from various local sources. The HHE results from five STS5
station pairs with varying station distances are presented in Figs 5.13-5.14. The variations in the
upper bounds of the high-coherence frequency bands decrease with interstation distances as the
133
signals from these frequencies are affected by localized coherent signals in the shallow structure
and incoherent signals from atmospheric effects. Conversely, the lower bounds of the high-
coherence frequency bands are similar in all station pairs and show more oscillations that extend
to lower frequencies in winter and spring than in summer and autumn (Fig. 5.14). The HHN
results are similar to the HHE, but the HHZ component does not show clear seasonal variations
(Fig. E5.10). Other station pairs show similar results.

Figure 5.14. The lower bounds of high-coherence frequency bands (solid lines) and the best-fitting
boxcar function with modified amplitudes (dashed lines). The boxcar function is defined with 0, =
92,160, and y0=0.04, y1=0.005 being the minimum and maximum of the lower bounds from station
pair 01-02. Each plot is labeled with the corresponding station codes and interstation distances on the
right.
134
To evaluate the observed periodicity in the low frequencies, the absolute gradients of the
lower bounds are modeled with an annual boxcar function by minimizing the L2 norm from all
investigated station pairs. The absolute gradient measures the oscillations in the lower bounds,
and the boxcar function is used to capture the abrupt transitions of the absolute gradient when the
lower bounds change from smooth in summer and autumn to varied in winter and spring. The
boxcar function is given by

=K@0I-
(;
1
,
&
,
1
,) = R

1
,0 ≤ ≤
1
,
1
++(−1)∗365 ≤ ≤
1
+∗365

&
,
1
+(−1)∗365 ≤ ≤
1
++(−1)∗365
(5.2)
where is an integer indicating the number of annual cycles. In each year,
=K@0I-
is equal to
&

in the days represented by , and
1
for the rest of the year. The value of
1
gives the time
period at the beginning of each year when
=K@0I-
is equal to
1
. The values of
1
and are the
two key parameters since we are more interested in the periodicity of the lower bounds. The
error is given by

,
(
1
,
&
,
1
,) = ∑
∫
=K@0I-
(;
1
,
&
,
1
,)−`
,"
()`
4
"
(5.3)
with
,"
() indicating the gradient of the lower bounds from a certain component i and station
pair j. Different components and different types of sensors, i.e. STS5 and Trillium 120PH, are
separately analyzed.
We apply a grid search on the four parameters
1
,
&
,
1
, in
=K@0I-
, with
1
and
&

varying from the minimum (0) to maximum (0.04) absolute gradient values with a step of 0.001,
and
1
and varying from 0 to 365 with a step of 1. Fig. E5.11 displays the error functions
from three components with
1
,
&
= 0.01,0.005 fixed at the best fitting model, and the
absolute gradients with the best fitting boxcar functions from five STS5 station pairs. The
minimum errors are at
1
, = 92,160 in the EW component and
1
, = 96,150 in the NS
135
component. There is no clear ‘best fitting’ in the vertical component (
1
, = 0, 19), indicating
there are no corresponding seasonal variations. The results suggest that in each year the lower
bounds show more oscillations in the first 92-96 days (
1
), i.e. spring, than in the next 150-160
days (), i.e. summer and early autumn, followed by more oscillations in late autumn and winter.
Fig. 5.14 shows the lower bounds from the EW component and the corresponding best fitting
boxcar function with modified amplitudes.

Figure 5.15. Daily median temperature recordings (upper panel) at station 01 and significant wave height
recordings (lower panel) from the buoy sensor. Loosely dashed line in the upper panel represents the best
fitting temperature curve. Vertical dashed lines indicate the edges of the best fitting boxcar function in
Fig. 5.14.
To explore effects of two possible mechanisms associated with thermoelastic strain and
ocean disturbance that might have induced the annual variations in Figs 5.13-5.14, we analyze
the temperature data in Piñon Flats and the significant wave height from the buoy sensor 46086
(labeled in Fig. 5.1). The air temperature recordings inside the sensor (i.e. VKI component) are
used since there is no complete atmospheric temperature recording during the studied time
136
period. Comparison of temperature data from inside and outside the sensor shows minor phase
shift between these two recordings, suggesting that the internal temperature has direct connection
to the outside. We model the temperature data using
4.(J
() = ∙cos()+∙sin()+
with fixed at 2 per year. The temperature data (Fig. 5.15, upper panel) reaches a peak at
Julian day ~202 of each year, preceding the oscillations in the lower bounds of the high-
coherence frequency bands (
1
+ ~252 ) by about 50 days, consistent with previously
observed delays of 1 to 2 months in thermoelastic strain signals (Ben-Zion & Leary, 1986;
Richter et al., 2014). The exact time delay between the atmosphere temperature and induced
thermoelastic strains depends on the depth of interest and properties of the shallow layer. The
significant ocean wave height, defined as the average of the highest one-third of the wave heights
during the 20-minute sampling period, increases in winter and spring due to oceanic storms,
correlating well with the variation patterns in the lower bounds of the high-coherence frequency
bands. The results suggest that stronger ocean waves generate stronger coherent microseisms and
modulate the lower bound of the frequencies showing varying coherence.

5.3.4 Cross-station seismic coherence anomalies
The cross-station seismic coherences show anomalous large values at ~2-4 Hz (Fig. 5.6,
labeled with dashed circles) in station pairs with large interstation distances (e.g. 10-11 and 09-
12), when the anomalies are large enough to stand out from the small background coherences.
Fig. 5.16 presents zoom-ins of the coherograms from the station pair 06-12 in 2016, showing the
anomalous increase of coherences (labeled with dashed circles in Fig. 5.16) at ~2-4 Hz starting at
Julian day ~132 in 2016 and lasting for ~30 days. Similar high coherence anomalies are observed
in the coherences of all components from multiple station pairs with relatively large interstation
137
distances (i.e. >500 m) in the PY array, e.g. T07-12, T07-09, T06-09, T09-12, S10-11, S10-13,
S11-13, T06-12 sorted by ascending interstation distances (S and T stand for STS5 and Trillium
120PH sensors, respectively). Based on these observations, we check all the daily coherograms
from Julian days 125-162, 2016. The coherence anomalies only occur at the daytimes in Julian
days 132-161 except for all Sundays and the Memorial Day (Julian day 151, May 30
th
, 2016).
This implies correlation with some anthropogenic activities. As an example, Fig. 5.17 shows the
coherograms of the station pair 06-12 from one day with (Julian day 135, Saturday) and without
(Julian day 136, Sunday) the high-coherence anomalies. The coherence anomalies (Fig. 5.17a)
exist at ~2-4 Hz from ~7 am to ~4 pm, consistent with anthropogenic activities. Interestingly, the
anomalies occur prior to the 2016 Borrego Springs earthquake (Julian day 162, 2016); however,
they do not represent precursory earthquake signals but rather cultural noise.

Figure 5.16. Zoom ins of coherograms (HHE, HHN, HHZ) from station pair 06-12 during Julian days
110-190, 2016. The 2016 Borrego Springs earthquake occurred on Julian day 162 (vertical solid line).
The dashed circles label the large coherence anomalies.
138

Figure 5.17. HHE coherograms from station pair 06-12 on Julian days 135 (a) and 136 (b). Horizontal
axes represent the Pacific Time, and the high coherence anomalies observed on Julian day 135 are labeled
with a dashed box.
5.4 Discussion and conclusions
Coherence evaluates signal similarity in the frequency domain and is sensitive to minute
discrepancies between recordings, providing a high-resolution tool for studying instruments and
ground motion characteristics. We investigate data features in seismic and meteorological data
from the PY array, an on-site borehole seismic station, and an oceanic buoy sensor (Fig. 5.1).
The seismic recordings are coherent when strong coherent signals are present including
microseisms at ~0.07 Hz and ~0.14 Hz (Figs 5.6-5.7), local earthquakes in high frequency range
(Figs 5.2-5.3), and teleseismic arrivals at 0.0001-1 Hz (Fig. 5.8). However, the coherences also
exhibit complicated variations in different frequency bands with main features summarized in
Table 5.1.
The 0.0003-0.05 Hz frequency band contains the lowest coherent seismic noise amplitude,
and the recordings are affected by local ground tilts generated by local atmospheric effects, e.g.
pressure and temperature changes. The atmospheric-induced forces constructively interfere in the
horizontal direction but cancel out for the vertical (Zürn & Wielandt, 2007). As a result, the
139
horizontal seismic coherences are more affected by variations of barometric pressure than the
vertical coherence as shown by our results. This has important implications for understanding the
seismic noise observations in this low frequency band, with horizontal components of seismic
noise spectra having significantly higher amplitudes than vertical components (Berger et al.,
2004). Our observations show the horizontal seismic data in this band is dominated by local
atmospheric effects, masking the ambient seismic noise generated by the solid earth and ocean.
The atmospheric effects also contaminate the seismic recordings at 1-8 Hz in all three
components via indirect nonlinear coupling with surface obstacles, e.g. trees and buildings.
Interactions of wind with local obstacles can generate earthquake- and tremor-like ground
motions in high frequencies and the signals may differ greatly at stations 30 m apart (Johnson et
al., 2019b). We observe similar atmosphere related energy bursts causing a decrease in seismic
coherence to ~0.2 for all three components at two closely spaced stations (65 m), suggesting that
multiple sources of atmospheric coupling are degrading the coherence in this frequency band.
Except for the atmospheric-induced coherence decreases at 1-8 Hz, the cross-station seismic
coherences in this frequency band are generally larger than 0.6 and contain several local maxima
at ~3 Hz, ~5 Hz, ~7 Hz when the interstation distance is small (e.g. 65 m), but decrease
significantly when the interstation distance is larger than the wavelength in the shallow layer.
Two mechanisms may produce these signals: local site amplification and possible existence of
localized sources in the shallow layer (which may be coupled with the site amplification). The
low coherence value from a surface-borehole station pair also indicates the possibility of local
site amplification and very shallow concentration of localized sources. The observations are
consistent with local site amplification exhibiting coherence increase at discrete frequencies (~3
Hz, ~5 Hz, ~7 Hz) and larger horizontal coherences than the vertical. The coherence dependence
140
on interstation distance implies variable site conditions and/or concentration of localized signal
sources at some locations.
Possible sources of coherent high-frequency noise in the shallow structure include
anthropogenic activities (Young et al., 1994), strong motion related bursts (Fischer et al., 2008a;
Fischer et al., 2008b), and ongoing failures at the subsurface (Ben-Zion et al., 2015; Hillers &
Ben-Zion, 2011). Anthropogenic activities exhibit clear daily and weekly variations (Bonnefoy-
Claudet et al., 2006), and our coherence results do not correlate with anthropogenic activity
except for the high coherence anomalies observed before the 2016 Borrego Springs earthquake.
The influence from strong motion is also excluded because the coherence results do not correlate
with large earthquakes in all frequency bands. Therefore the most likely sources of the observed
ongoing coherent signals at 1-8 Hz are near surface failures. Materials in the top few hundred
meters of the crust or so with very low (e.g., 1 MPa) confining pressure, very low (200-400m/s)
shear wave velocities (Bonilla et al., 2002; Theodulidis et al., 1996; Zigone et al., 2019) and very
low (Q~1-10) attenuation coefficients (Aster & Shearer, 1991; Liu et al., 2015) are highly
susceptible to failures (i.e., nonlinear behavior and instances of rapid inelastic strain).
Experimental results show that geomaterials can fail with dynamic strain levels of ~10
-7

(Pasqualini et al., 2007; TenCate et al., 2004). This suggests that thermoelastic strains at a level
of ~10
-6
, likely to exist in the top few hundred meters of the crust (Ben-Zion & Allam, 2013),
can be sufficient to induce continual occurrences of small local failures. This process can
generate coherent signals in closely spaced surface stations (e.g. 65 m) at 1-8 Hz that attenuate
rapidly with propagation distances, producing coherences that decrease significantly with
increasing interstation distances.
141
The observed seasonal variations in the lower bounds of the high-coherence frequency bands
are compatible with the thermoelastic strain mechanism, exhibiting a lag time of ~50 days with
respect to local temperature recordings. In summer and autumn when higher level of
thermoelastic strains are expected (e.g., Ben-Zion et al., 1990; Prawirodirdjo et al., 2006), local
ground tilts are more prominent, producing more low-frequency incoherent seismic signals,
especially in the horizontal components, and reducing the coherent frequency bands. This is
consistent with the observation that only the two horizontal components show clear seasonal
variations.
Variations in noise sources may also contribute to the seasonal patterns of coherences.
Previous studies (Bonnefoy-Claudet et al., 2006; Stehly et al., 2006) showed strong correlations
between the ocean swell heights and observed noise amplitudes. Our examination of oceanic data
shows increased significant wave heights in winter and spring; this implies stronger microseisms
in these seasons expected to increase coherent signal strength and produce wider high-coherence
frequency bands. The stronger microseisms in winter and spring, combined with reduced local
ground tilts due to reduced thermoelastic strains, likely generate the expanded high-coherence
frequency bands in these seasons, and the opposite in summer and autumn.
In addition to detecting variations in seismic recordings, the coherence analysis can also
reflect different coupling mechanisms between driving forces and generated ground motions.
The strong susceptibility of coherence to minute discrepancies in signals provides high-
resolution monitoring tool, while producing many complexities that require thorough
characterization of signal sources, propagation paths, and local site conditions. The results of this
study may be augmented by analyzing also the phase of coherency (Equation 5.1) and including
additional information on properties of the subsurface and other data sets such as water level
142
variations and other anthropogenic activities. Performing similar analyses with data recorded at
other locations will help clarify which aspects of the results are general and what features (e.g.,
local maxima in coherence) vary among different sites. Such studies can improve significantly
the understanding of properties and dynamics of the shallow crust and may be the subject of
follow up research.
Table 5.1. Summary of main features

5.5 Data and resources
The PY data are referenced under the FDSN DOI https://doi.org/10.7914/SN/PY, and the
B084 borehole data is provided by the Plate Boundary Observatory. Both are available on the
Incorporated Research Institutions for Seismology (IRIS) Data Management Center. The oceanic
data is obtained from the National Oceanic and Atmospheric Administration’s National Data
Buoy Center. The multitaper spectral analysis code is the python wrapper for the F90 library
(Prieto et al., 2009).
Frequency
band (Hz)
Cross-station seismic
coherence
Cross-station
barometric
coherence
Cross-
channel
coherence
Coherent
source
(example)
Incoherent source
(example)

Horizontal Vertical
0.0003-0.003 0.6-1 ~1 0.6-1 0.3-0.5
In general, ground tilts from
atmospheric effects are coherent,
mainly in horizontal components
0.003-0.05 0-0.2 0.6-1 0-0.3 0.2-0.3 Earth hum
Ground tilts from
atmospheric effects,
mainly in horizontal
components
0.05-0.1
0.6-1
(sometimes
0-0.2)
~1
(sometimes
~0.6)
0-0.1 0-0.1
Primary
microseism
Atmospheric effects
0.1-1 ~1 ~1 0-0.1 0
Secondary
microseism

1-8
0.6-1
(sometimes
0-0.2)
0.6-1
(sometimes
0-0.2)
0-0.1 0
Possible
continual near
surface
failures
Atmospheric effects
coupling with
surface structures,
in three components
143

5.6 Acknowledgements
The observations are based on work supported by the lncorporated Research Institutions for
Seismology under their Cooperative Agreement with the National Science Foundation. The high
quality instrumentation produced by Streckheisen, Nanometrics and Quanterra made the
observations possible. The analysis was supported by the Department of Energy (awards
DESC0016520 and DE-SC0016527). The work benefited from useful comments by three
anonymous referees.

144
6. Discussion
In the previous five chapters, I have introduced methods for imaging and monitoring fault
zones and shallow materials with high spatial and temporal resolutions. In Chapters 1 and 2,
using dense-array data we obtained detailed fault zone structures with a resolution comparable to
the station spacing (10-30 m), while the resolution of traditional large-scale tomography studies
is on the order of 1-2 km. These analyses consistently indicate preferred earthquake rupture
propagations to the NW, thus implying increased seismic hazard in the communities toward that
direction from the next large earthquake on the San Jacinto fault. The obtained fault zone
structure information in finer scales can be combined with regional tomography studies to better
resolve the earthquake process, rupture histories along large fault systems and predict the
motions from future large earthquakes.
Another important component for better seismic hazard prediction is the monitoring of the
fault zones and shallow materials. Compared with previous studies with a temporal resolution of
hours to days, I have achieved a higher resolution in time of a few seconds. In addition, the depth
extent of temporal change of seismic velocities at GVDA in response to the El Mayor-Cucapah
earthquake is confined to the top ~20 m by the available borehole data (Chapter 3), implying the
high susceptibility of shallow materials. Analysis of seismic data on Mars (Chapter 4) reveals
similar high sensitivity of the top ~20 m in response to thermoelastic strains. Both Chapters 3
and 4 resolved considerable temporal change of seismic velocities (~10%) in response to a strain
level of 10
-7
, which is widely observed in laboratory experiments but not in in-situ studies. These
results call for a fundamental rethinking of how near-surface materials evolve in response to
various loadings (e.g. large earthquakes, daily and seasonal forces) since nonlinear site effects
may be more pervasive and prominent than previously thought. For a better seismic hazard
145
estimation, the nonlinear response of shallow materials needs to be properly accommodated in
ground motion simulations.
Last but not least, a new approach using wavefield coherence provides additional information
on spatial and temporal variations of seismic data. Our study in Chapter 5 is based on the data
from the Piñon Flats Observatory, which is located on a relatively flat and quiet hard-rock site,
while the observed coherence values show variations in response to barometric pressure, human
activities and potential local near-surface failures. This implies the high sensitivity of coherence
value to minute discrepancies between two seismic recordings that are unresolvable with
traditional methods. Thus similar analysis can be systematically applied to various data sets to
track sensor performance, local structure variations and subsurface processes.
Given the increasingly large volume of collected dense-array seismic data at major fault
zones around the world, similar analysis of fault zone phases in Chapters 1 and 2 can be applied
for imaging at finer scales and information on long-term evolution and short-term rupture
activities of fault zones. This, with temporal and spatial monitoring (e.g. Chapters 3-5), as well
as combined analysis of seismic data with other data sets (e.g. meteorological data), is essential
for a better understanding of the earthquake process and seismic hazard estimation.
It’s also important to understand the limitation of these analyses, however. High-resolution
imaging and monitoring require high-density high-quality seismic data, especially from borehole
stations which are expensive to deploy. It’s critical to keep in mind the high spatial variability of
shallow materials and surface conditions, thus different sites may exhibit quite different
behaviors. Also, the high susceptibility of shallow structures may result in the convolution of
contributions from different loadings that needs to be carefully separated. These issues need to
be properly accommodated when the analysis is widely applied to larger datasets.
146
Based on this thesis, I have several ongoing research projects:
1) Detection of unconventional seismic sources at shallow depths (e.g. human activities,
local failures, and wind activities) based on wavefield coherence: Analysis of the 2D
dense array at the SGB site in the San Jacinto fault zone suggest abundant detections
likely associated with near-surface events that are only seen in highly dense sub-
arrays with apertures of ~200 m.
2) Long-term monitoring of shallow materials using borehole data: Analysis of 13-year
data from the GVDA indicates seasonal variations of seismic velocities in the top 6 m
likely caused by water level changes, consistent with results of cross-hole activate
source experiments.
3) Constraining shallow seismic properties based on the coherence between high-
frequency seismic and barometric data.
In conclusion, I plan to focus on applying similar analysis to other available seismic datasets
and developing new methods for multi-scale imaging and monitoring shallow structures. I also
aim to combine data and methods from seismology with those from other disciplines, e.g.
computer sciences and civil engineering, for the purpose to better understand shallow seismic
properties and mitigate seismic hazards from large earthquakes.

147
Appendices
Appendix A: Chapter 1 supplementary materials

Figure A1.1. (a). Left: waveforms (0.5-20 Hz) of an event recorded by row 13. The red dashed lines
indicate the 3.0 s time window in which DMN is calculated. The orange box includes the P type FZTW.
Right: Corresponding DMN values represented by color. The white dashed line is the median of automatic
P picks in row 13. The orange box indicates the location where the P type FZTW are detected. (b). Same
as (a) for an event without P type FZTW.
148

Figure A1.2. FZTW inversion results of waveforms generated by event S-TW3 (location marked in Fig.
1.12). The layout is the same as Fig. 1.14.
149

Figure A1.3. FZTW inversion results of waveforms generated by event S-TW4 (location marked in Fig.
1.12). The layout is the same as Fig. 1.14.

150
Appendix B: Chapter 2 supplementary materials

Figure B2.1. Teleseismic P wave delay times corrected with two extreme reference velocities: 1 km/s
(purple dotted line) and 6 km/s (purple dash dotted line). Other symbols are the same as in Fig. 2.5(a).
151

Figure B2.2. Array transfer functions for the array geometry employed in beamforming analysis (green
balloons in Fig. 2.2) and frequency ranges 4-6 Hz (a) and 12-14 Hz (b). The average radii of the
respective beams (measured out to 50% of the beam peak amplitude) are 0.1 s/km (a) and 0.04 s/km (b).

Figure B2.3. S-type FZTW inversion results from an example event. The layout is the same as in Fig.
2.13.
152

Figure B2.4. Regional P-wave velocity model (Allam & Ben-Zion, 2012) averaged over the depth range
1-10 km, surrounded by qualitative comparisons between the regions and dimensions of internal San
Jacinto fault zone structures at the different BB/BS (Share et al., 2017, 2019b), RA/RR (Chapter 2), SGB
(Chapter 1) and JF (Qiu et al., 2017) sites.

153
Appendix C: Chapter 3 supplementary materials

Figure C3.1. (a). The 10-30 Hz autocorrelation functions (ACFs, color representing amplitudes)
normalized with zero lag amplitudes, reference travel time (black dashed lines), and ACF peaks (black
solid lines) corresponding to free surface reflections from the radial component at the 22 m borehole
station (03). The left, middle and right panels are the results before, during, and after the EMC
earthquake, respectively. Horizontal axes represent the time relative to the occurrence time of the EMC
earthquake, and vertical axes indicate the lag time for autocorrelation. The 10-30 Hz waveforms from the
EMC event are plotted in the middle panel. (b). The corresponding velocity changes (black solid lines),
velocity reduction oscillations (green shaded areas), and PGAs (blue dashed lines with dots) inside the
autocorrelation time windows. Please note the irregular time axes, different time and PGA scales between
the middle and left/right panels.
154

Figure C3.2. The 10-30 Hz ACFs (a) and corresponding velocity changes (b) from the transverse
component at the 50 m borehole station (04). The layout is the same as Fig. C3.1.

Figure C3.3. The 10-30 Hz ACFs (a) and corresponding velocity change (b) from the radial component at
the 50 m borehole station (04). The layout is the same as Fig. C3.1.
155

Figure C3.4. (a). The 1-30 Hz impulse response functions (IRFs, color representing amplitudes)
normalized with the maximum amplitudes, reference travel time (black dashed lines), and IRF peaks
(solid black lines) from the transverse component between the surface station (00) and 15 m borehole
station (02). The layout is similar to Fig. C3.1. The 1-30 Hz waveforms at the shallower station (in this
case, station 00) from the EMC earthquake is plotted inside the middle panel. (b). The corresponding
velocity changes (black solid lines), velocity reduction oscillations (green shaded areas) and PGAs (blue
lines with dots) inside the deconvolution time windows. Please note the irregular time axes, different time
and PGA scales between the middle and left/right panels.
156

Figure C3.5. The 1-30 Hz IRFs (a) and corresponding velocity changes (b) from the transverse
component between the surface (00) and 50 m borehole (04) stations. The layout is the same as Fig. C3.4.

Figure C3.6. The 1-30 Hz IRFs (a) and corresponding velocity changes (b) from the transverse
component between the surface (00) and 150 m borehole (05) stations. The layout is the same as Fig.
C3.4.
157

Figure C3.7. The 1-30 Hz IRFs (a) and corresponding velocity changes (b, c) from the transverse
component recorded by the 6 m (01) and 50 m (04) borehole stations. (b) is the average velocity change
between stations 01 and 04 obtained from the IRF primary peak at ~0.11 s. (c) represents the average
velocity change in the top 6 m calculated from the IRF secondary peak at ~0.175 s, corresponding to
waves traveling from station 04 to surface then reflected to station 01. The blue horizontal axis ticks in (c)
indicate Julian days in 2010.
158

Figure C3.8. The 1-30 Hz impulse response functions (IRFs, color representing amplitudes) normalized
with the maximum amplitudes (a) and corresponding velocity changes (b, c) from the radial component
recorded by the 6 m (01) and 22 m (03) borehole stations. The layout is the same as Fig. C3.7.
159

Figure C3.9. The 10-20 Hz ACFs (a), velocity changes (b) and 15-30 Hz ACFs (c), velocity changes (d)
from the transverse component at the 22 m borehole station (03). The layout is the same as the middle
panel of Fig. C3.1.
160

Figure C3.10. The 10-30 Hz IRFs (a) and corresponding velocity changes (b, c) from the transverse
component recorded by the 6 m (01) and 22 m (03) borehole stations. The layout is the same as Fig. C3.8.

161
Appendix D: Chapter 4 supplementary materials
This chapter contains supplementary material to Chapter 4. In Fig. D4.1, we present a
synthetic test illustrating that changes in the frequency content of the source will not affect our
travel time variation measurements based on autocorrelation functions (ACFs). Figs A4.2-A4.5
show results from NS and vertical components, with similar patterns as the EW component. Figs
A4.6-A4.7 illustrate the amplitude of thermoelastic strain with different thermal-physical
parameters.

D4.1 Effects of source spectrum variation - simulation
In Fig. D4.1, we demonstrate, based on a synthetic test, that a shift in the peak frequency of
the source spectrum does not affect our estimation of Δt variation from ACF. For the simulation,
we use two Ricker wavelets with dominant frequencies of 4.5 Hz and 3 Hz sampled at 100 Hz,
respectively, as the direct wave S(t), implying >30% peak frequency change in the source
spectrum. We set the reflection coefficient δ = -0.25, and generate seismic recordings with Δt0 =
1.3 s and Δt1 = 1.365 s, suggesting 5% travel time increase, shown as D0 (4.5 Hz) and D1 (3 Hz)
in Fig. D4.1(a). We add random noise to D0 and D1 with signal-to-noise ratio of 4 in the
frequency domain. The ACFs of D0 and D1 are shown as black and red curves in Fig. D4.1(b),
whereas the blue lines outline the tapering window that isolates the reflection signal, i.e. the
window for cross-correlation. The cross-correlation function of the tapered ACFs is illustrated in
Fig. D4.1(c), showing a maximum value at dt = -0.06 s. The estimated travel time variation, 0.06
s, deviates from the true value, 0.065 s, because the data resolution is 0.01 s. The maximum
cross-correlation coefficient is a bit low (~0.5), due to the added noise and the dramatic variation
in peak frequency of the source spectrum. This suggests that the significant change (> 30%) in
162
peak frequency of the source spectrum yields no effect on the Δt variation estimated via cross-
correlation of the tapered ACF.

Figure D4.1. Synthetic test using Ricker wavelets: (a). Two time series with dominant frequencies of 4.5
Hz (D 0; black) and 3 Hz (D 1; red), containing reflection phases at 1.3 s and 1.365 s, respectively. (b). The
normalized autocorrelation functions of D 0 (black) and D 1 (red). The blue vertical lines indicate the time
window used for cross-correlation. (c) The cross-correlation of the D 0 and D 1 autocorrelation functions at
0.5-2 s, which peaks at -0.06 s, implying the reflection phase in D 1 is delayed by 0.06 s with respect to
that in D 0.
163
D4.2 Results from NS and vertical components

Figure D4.2. Two days of continuous seismic recording (gray curve) of the NS (top panel) and vertical
(bottom panel) components. A bandpass filter between 1-5 Hz is applied to the data. A smoothed
envelope (red curves) is obtained using a 10-s-long moving window, and the data after temporal
balancing (Section 4.2.1) is shown in black. The waveform in black is magnified by 200 times for
demonstration purpose.
164

Figure D4.3. Two-day ACFs from NS (a, b) and vertical (c, d) components. The layout is similar to Fig.
4.2.
165

Figure D4.4. Spectrograms of two-day ACF from NS (a, b) and vertical (c, d) components. The layout is
similar to Fig. 4.3.
166

Figure D4.5. Travel time variation (blue curves), peak frequency variation (orange curves), linearly
scaled ground temperature (black solid curves) and best fitting dt/t curves (black dashed curves) from NS
and vertical components. The layout is similar to Fig. 4.4.
(a). NS results
(b). Vertical results
167
D4.3 Thermoelastic strain
The thermoelastic strain in elastic half-space (Berger, 1975) can be expressed as

@@
(,,) =
&%L
&*L

$
M
∙[2(1−)−]
*$A
−
$
M

*MA

1

,(74%$@)
(A4.1a)

AA
(,,) =
&%L
&*L
∙−
$
M
(2−)
*$A
+
*MA

1

,(74%$@)
(A4.1b)
where represents the horizontal coordinates, is the depth and is the angular frequency.
Here is the Poisson’s ratio, is the coefficient of linear thermal expansion, is the thermal
diffusivity of the elastic half-space, and ≅ (1+)(/2)
&/+
considering ≪ /
+
.
1
and
= 2/ are the amplitude and wavenumber of the temperature field with being the
wavelength. Considering a fully decoupled layer with a thickness of
=
on top of the elastic half-
space (Ben-Zion & Leary, 1986), the thermoelastic strain at the underlying half-space is
generated by the delayed and attenuated (by
*MA
&
) temperature field at the bottom of the
decoupled layer. We define the volumetric strain as the summation of horizontal and vertical
strains,
@@
+
@@
+
AA
, assuming an isotropic deformation in the two horizontal directions, and
present the amplitude of volumetric strain in Figs A4.6-A4.7 based on simulation using different
thermal-physical parameters.
168

Figure D4.6. Amplitude of thermoelastic strain calculated at different depths y, 0.1 m (a, b, c) and 200 m
(d, e, f) relative to the bottom of the decoupled layer and with different wavelengths 0.5 km (a, d), 3 km
(b, e) and 15 (c, f) of temperature field. Here we assume the decoupled surface layer is 0.1 m thick (yb)
with thermal diffusivity of 2 × 10
-8
m
2
/s. The Poisson’s ratio in half-space is set to 0.3. Results are
computed for the elastic half-space with and ranging from 2 × 10
-8
- 10
-8
m
2
/s and 10
-5
- 10
-3
°C
-1
,
respectively.
169

Figure D4.7. Amplitude of thermoelastic strain calculated at different depths y, 0.1 m (a, b, c) and 200 m
(d, e, f) relative to the bottom of the decoupled layer and with different Poisson’s ratio 0.1 (a, d), 0.3 (b,
e) and 0.5 (c, f). Here we assume the decoupled surface layer is 0.1 m thick (yb= 0.1 m) with thermal
diffusivity of 2×10
-8
m
2
/s. The wavelength of temperature field is set to 15 km. Results are computed
for the elastic half-space with and ranging from 2 × 10
-8
- 10
-8
m
2
/s and 10
-5
- 10
-3
°C
-1
, respectively.
170
Appendix E: Chapter 5 supplementary materials

Figure E5.1. Normalized instrument responses of STS5 (solid/dotted, HH/BH), Trillium120-PH (densely
dashed/loosely dashed, HH/BH) and HS-1-LT (dashdotted, i.e. B084) sensors, with the vertical lines
indicating the corresponding frequencies of sensitivity (STS5, 0.5 Hz for HH, 0.2 Hz for BH;
Trillium120-PH, 0.6 Hz for HH, 0.2 Hz for BH; HS-1-LT, 20 Hz). The responses of HH and BH
components overlap with each other below the 20 Hz Nyquist frequency of the BH components.

171

Figure E5.2. HHN component results (a. waveforms; b. coherogram; c-d. spectrograms of PY01 and
PY02) on Julian day 114, 2016 at stations 01 and 02 of the PY array. The layout is the same as Fig. 5.2.
172

Figure E5.3. (a) HHN and (b) HHZ coherograms (top panel) and spectrograms in (m/s)2/Hz (bottom two
panel) at stations PY01 and B084 on Julian day 114, 2016. The layouts of (a) and (b) are the same as Fig.
5.5.

Figure E5.4. Three-year HHN coherograms from three (a, c, e) STS5 and three (b, d, f) Trillium 120PH
station pairs. The layout is the same as Fig. 5.6.
173

Figure E5.5. Three-year HHZ coherograms from three (a, c, e) STS5 and three (b, d, f) Trillium 120PH
station pairs. The layout is the same as Fig. 5.6.
174

Figure E5.6. Three-year HHE coherograms from three station pairs (a. 01-04; b. 05-06; c. 09-10) with
one STS5 sensor and one Trillium 120PH sensor. Each plot is labeled with the corresponding station
codes and interstation distances.

Figure E5.7. Three-year (a) HHE, (b) HHN and (c) HHZ median coherences from six station pairs with
different sensor types (one STS5 and one Trillium 120PH). Interstation distances are 65 m for 01-04/02-
03, 340 m for 05-06, 360 for 07-08, 740 m for 09-10 and 760 m for 11-12.
175

Figure E5.8. (a). All the teleseismic events in 2015-2017 with magnitude larger than 7. The triangle
shows the PY array location. (b) and (c) are HHN and HHZ coherences from all teleseismic events,
calculated with the same parameter settings as Fig. 5.8(c). Only two events exhibit minimum HHN
coherence values below 0.95.
176

Figure E5.9. (a, c) cross-station (01-02) seismic coherograms from (a) BHN and (c) BHZ components.
(b, d) cross-channel (BHN-BDO; BHZ-BDO) coherograms at station 01. All the coherograms are
calculated with the same parameter settings as Fig. 5.12.

Figure E5.10. High-coherence frequency bands of (a) HHN and (b) HHZ component in five STS5 station
pairs (same stations as in Fig. 5.13). The vertical bars represent the frequency bands where the coherences
are larger than 0.95, with solid lines indicating the upper and lower bounds. The station codes and
interstation distances are labeled on the right.
177

Figure E5.11. Results from five STS5 stations pairs (same stations as in Fig. 5.14). From top to bottom
are the results for HHE, HHN and HHZ components, respectively. (a) displays the misfit functions with
y0=0.01 and y1=0.005 fixed at the best-fitting model. The crosses indicate the minimums of the misfit
functions, located at ( 0,) equaling to (92,160) for HHE, (96,150) for HHN, and (0,19) for HHZ. (b)
shows the corresponding absolute gradients (solid lines) with the best fitting boxcar functions (thick
dashed lines) from the three components.

Figure E5.12. The lower bounds of the high-coherence frequency bands (solid lines) and the best-fitting
boxcar functions (thick dashed lines) with modified amplitudes for (a) HHN and (b) HHZ components in
five STS5 station pairs (similar to Fig. 5.14). Station codes and interstation distances are labeled on the
right.
178
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Abstract (if available)

Abstract I developed several seismologically-based tools for imaging and monitoring fault zones, especially the shallow materials (top hundred meters) with high spatial-temporal resolutions. This thesis includes analyses of fault zone phases (e.g. P- and S- waves, fault zone head waves, and fault zone trapped waves) for internal structures of the San Jacinto Fault Zone (SJFZ) in southern California (SoCal) at two sites (Sage Brush and Ramona Reservation), monitoring materials in the top hundred meters using seismic interferometry at the Garner Valley in SoCal, and at the site of NASA’s Interior Exploration using Seismic Investigations, Geodesy and Heat Transport (InSight) mission on Mars. I also investigate wavefield characteristics with coherence at Piñon Flats in SoCal to study the dynamics of shallow materials. ❧ With seismic recordings from the linear dense arrays crossing the SJFZ at Sage Brush and Ramona Reservation, I image the fault internal structures at the two sites with resolution comparable to the station spacing (10-30 m) which cannot be achieved with traditional regional-scale imaging techniques. Waveform changes are analyzed to identify the location of the main seismogenic fault. Delay times of P-waves from local and teleseismic events are used to estimate variations of seismic velocities across the fault zone structure. Fault zone head waves that propagate exclusively along a bimaterial interface (i.e. the interface which separates two crustal blocks with distinctive seismic velocities) are identified to image the properties (e.g. location, depth extent) of fault-related bimaterial interfaces. P- and S- type fault zone trapped waves are indicative of constructively interfering seismic energy within fault damage zones resulted from the asymmetric rock damages related to earthquake ruptures with preferred propagation direction. Analyses of these signals at the two sites provide detailed imaging of internal fault structures and suggest consistent preferred propagation of earthquake ruptures to the NW. ❧ Along with imaging the subsurface structures, I monitor temporal variations and resolve susceptibility of the shallow materials to various loadings (e.g. strong ground motions from earthquakes, thermal elastic strains). At the Garner Valley Downhole Array in SoCal, the direct P- and S- wave travel times between surface and borehole stations are used to study the velocity structures in the top 150 m. Temporal changes at different depth ranges of seismic velocities after the 2010 M7.2 El Mayor-Cucapah earthquake are estimated using autocorrelations of data in moving time windows and seismic interferometry between multiple station pairs. Autocorrelations of single-station seismic data on Mars also reveal daily variations of seismic velocities on Mars, especially in the top ~20 m, in response to thermoelastic strains. The results suggest up to 10% temporal variation of seismic velocities in response to a dynamic strain level of 10⁻⁷ in the top ~20 m weak sediment materials. ❧ An innovative way to study the behavior of shallow material is to investigate the coherence, a value ranging from 0 to 1, that evaluates the similarity between two recordings and depends on frequency and interstation distance, and is sensitive to minute discrepancies between seismic recordings. Analysis of coherence in different frequency bands at the Piñon Flats Observatory array and a collocated 148 m deep borehole station reveals influence on seismic recordings from atmospheric loadings, anthropogenic activities, thermoelastic strains, and potential near-surface failures.

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Asset Metadata

Creator Qin, Lei (author)

Core Title High-resolution imaging and monitoring of fault zones and shallow structures: case studies in southern California and on Mars

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Geological Sciences

Publication Date 04/15/2021

Defense Date 03/16/2021

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

Tag coherence of seismic data,fault zone imaging,OAI-PMH Harvest,temporal changes of shallow materials

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Ben-Zion, Yehuda (committee chair), Corsetti, Frank (committee member), Leahy, Richard (committee member), Sammis, Charles (committee member)

Creator Email qinqiu48@163.com,qinqiu48@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-444567

Unique identifier UC11667605

Identifier etd-QinLei-9448.pdf (filename),usctheses-c89-444567 (legacy record id)

Legacy Identifier etd-QinLei-9448.pdf

Dmrecord 444567

Document Type Dissertation

Rights Qin, Lei

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA