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Mapping the Moho in southern California using P receiver functions

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Mapping the Moho in southern California using P receiver functions

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MAPPING THE MOHO IN SOUTHERN CALIFORNIA USING P RECEIVER
FUNCTIONS

by

Panxu Zhang

A Thesis Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
MASTER OF SCIENCE
(GEOLOGICAL SCIENCES)

December 2012

Copyright 2012 Panxu Zhang
ii
Acknowledgements

I thank my advisor, Meghan Miller, for her mentoring, support and guidance throughout
the past two years. Meghan is always patient with me and shares with me her knowledge
and experience in science. Her guidance helps me in all the time of research and
writing. This thesis would not have been possible without her help and support. I thank
David Okaya, Iain Bailey, and Daoyuan Sun for their help and advice in discussion,
providing codes and reviewing the draft. I also thank other members of my thesis
committee, James Dolan, Charles Sammis, for their patience and advice.
My Master’s study is funded by Department of Earth Sciences of USC and Southern
California Earthquake Center. I am grateful to Meghan Miller, Thomas Jordan, John
McRaney and Cindy Waite for providing me the opportunity to study in USC.
Finally I thank my family for their forever caring, encouragement and unconditional
support.

iii
Table of Contents
Acknowledgements ii
List of Figures v
Abstract x
Chapter 1 Introduction 1
1.1 San Andreas Fault System 2
1.2 Rheology of the Lower Crust 4
1.3 Goals of this Study 6
Chapter 2 Data and Methodology 9
2.1 Data 9
2.2 Receiver Function Methodology 10
2.2.1 Introduction of Receiver Function 10
2.2.2 Data Processing 13
2.2.3 Depth Conversion 16
2.3 CCP Stacking 19
2.4 Synthetic Modeling: Finite Difference Method 21
2.4.1 Equation of Elastic Wave and Finite-Difference Implementation 23
2.4.2 Source Function 26
2.4.3 Boundary Condition 27
2.4.4 Stability and Dispersion Condition 28
Chapter 3 Mapping the Moho in Southern California 31
3.1 Moho Depth Map in Southern California 34
3.2 San Gabriel Mountains 38
Chapter 4 Regional Study in San Jacinto Fault 42
4.1 Tectonic Setting 42
4.2 Receiver Gathers 44
4.3 Bootstrap Error Estimation 51
4.4 CCP imaging 53
4.5 Synthetic Results 56
4.5.1 Model Description 56
4.5.2 Synthetic Receiver Functions 58
4.5.3 Vertical Resolvability and Horizontal Effect Test 63
Table 1: Mean and standard deviation for the Moho depth of the eleven stations 52
Chapter 5 Discussion and Conclusion 69
5.1 Rheology of the Lower Crust and the Upper Mantle 69
5.2 Deformation in the Lower Crust beneath Strike-slip Faults 73
iv
References 81
Appendices 91
Appendix I: Stations Information 91
Appendix II: Event Information 95
Appendix III: Transverse Receiver Gathers for 11 Stations in the San Jacinto
Fault zone 100
Appendix IV: Radial Receiver Gathers for 97 Stations in Southern California 104

v
List of Figures
1.1 Diagram of the tectonic history of southern California. (Made by
Kious et al., 2001)
1.2 Map of faults in southern California. Arrows represent relative plate
motion. Average slip rate between the North American plate and
Pacific plate is 55 mm/yr, along the San Jacinto Fault Zone vary
between 8-20mm/yr, and along the San Andrea Fault vary between
10-30 mm/yr.
2.1 Map of all broadband seismic stations used in the study including
SCSN and USArray (red triangles). The figure on the right shows
teleseismic events from 2000 to 2011 with magnitude greater than
6.0 and great circle distance between 35 to 90 degrees which were
used in the analysis. The events are grouped by colors on NE
(yellow), NW (green), SE (blue), SW (red) directions.
2.2 (a) Diagram of the P receiver function; (b) an example of P receiver
function
2.3 (a) Three-component waveform (top: east, middle: north, bottom:
vertical component) for 2002/11/17 earthquake recorded at station
CRY; predicted arrival time for direct P and PP are calculated by
Taup software (Crotwell et al., 1999) using PREM model
(Dziewonski and Anderson, 1981). (b) Corresponding radial (top)
and transverse (bottom) receiver functions.
2.4 (a) The amplitude at time=0 is negative and the maximal spike is not
at t=0; (b) Maximal spike is not at t=0 and the second largest spike
exceeds 75% of the largest spike; (c) A good receiver function
2.5 Comparison of average 1d SCEC CVM (ref) and other classic 1d
velocity models: ak135 (Kennett et al., 1995), PREM (Dziewonski
and Anderson, 1981), iasp91 (Kennett and Engdahl, 1991), TNA
(Tectonic North America velocity model, Grand and Helmberger
1984).
2.6 Map of stations in San Jacinto fault area.
2

3

9

10

14

15

16

18

vi
2.7 1D velocity models extracted from SCEC 3D CVM for three selected
AZ network stations near San Jacinto Fault: CRY, SND and KNW,
whose locations are shown in the map on figure 2.6.
2.8 (top) Schematic diagram for common midpoint (CMP) stacking;
(bottom) Common conversion point (CCP) stacking.
2.9 (a) Map of San Jacinto Fault zone region. Fault traces are shown as
gray lines on the map. Positions of cross sections are plotted on map
on the left. Red crosses represent stations used. (b) Common
conversion points (CCP) stacking of P receiver functions along three
profiles in San Jacinto Fault Zone. Locations of Elsinore fault and
San Jacinto fault as well as possible Moho boundary are marked on
the stacking profiles. Note that small Moho offset can be seen
beneath major faults.
2.10 Velocity models with four possible geometries: 1) a step in the Moho
(blue), 2) a 5 km wide and 10 km vertically offset ramp (green), 3) a
15 km wide and 10 km vertically offset ramp (red), 4) a flat Moho at
30 km depth (light blue).
2.11 Teleseismic source function used in this study. (top) Source function
as a time series; (bottom) Spectrum of the source function.
2.12 An example of the synthetic teleseismic waveform for the step model
in this study. From top to bottom, they are vertical, x, y components
respectively.
3.1 Topographic map in southern California with major tectonic
provinces are labeled. Red triangles represent broadband seismic
stations used in this study.
3.2 Interpolated Moho depth map in southern California. The faults are
plotted in gray lines. Data points used to produce this map are plotted
in Figure 3.3.
3.3 Map of the data points used to produce Figure 3.2. The data points
are the surface projections of P-to-S conversion points calculated at
the Moho depth for that station.
19

20

21

23

27

30

31

37

37

vii
3.4 Topographic map in the San Gabriel Mountains region. Yellow
triangles represent the broadband seismic station stations. Receiver
gathers profiles for four selected stations are shown in Figure 3.4.
Profiles for other stations are shown in Appendix B.
3.5 Receiver gathers profiles for four broadband seismic stations in the
San Gabriel Mountains area. The receiver gathers are plotted and
colored by back azimuth bins: yellow, blue, red and green represent
NE, SE, SW and NW respectively. The locations of these stations are
shown in Figure 3.3.The second positive arrivals at around 4 s are
considered as the converted signal at the Moho.
4.1 Geologic map of San Jacinto Fault Zone area (Jennings, 1977;
modified by USGS)
4.2 Map of the San Jacinto Fault zone area. Fault traces are indicated by
the light grey lines. The red triangles represent the broadband seismic
stations used in this study. Crosses are the P to SV converted points
for all the used events calculated at the depth of 30 km. The color of
yellow, green, red, and blue represent NE, NW, SW, SE directions
respectively, which corresponds with the colors used in Figure 4.3.
4.3 Radial component RF gathers profile for the 11 seismic stations. The
locations of the stations are shown on Figure 4.2. The receiver
gathers are plotted by back azimuth. The first positive arrival at 0 s is
the direct P arrival, and the second positive arrival at around 4 s is the
converted wave signal from the Moho (Pms). The other following
arrivals are considered as multiples.
4.4 Common conversion points (CCP) stacking of P receiver functions
along three profiles in San Jacinto Fault Zone. Fault traces are shown
as grey lines on the map. Positions of cross sections are plotted on
map on the left. Red crosses represent stations used. The yellow
triangle is station CRY. Locations of Elsinore fault (EF), Coyote
Creek Fault (CCF) and San Jacinto fault (SJF) as well as possible
Moho boundary are marked on the stacking profiles. Note that small
Moho offset can be seen beneath major faults.
4.5 Velocity models with four possible geometries in a two dimensional
38

39

44

45

48

54

58
viii
model of homogeneous elastic media, with a width of 500 km and
depth of 300 km.: 1) a step in the Moho (blue), 2) a 5 km wide and
10 km vertically offset ramp (green), 3) a 15 km wide and 10 km
vertically offset ramp (red), 4) a flat Moho at 30 km depth (light
blue). 101 stations with spacing of 1km are placed linearly and
symmetrically along the surface, and station 48 represents station
CRY from our observational data.
4.6 Receiver function gathers for station CRY.
4.7 A-F: Synthetic receiver gathers for CRY (station 48) plotted by back
azimuth for six different models. Red pulses are positive and blue are
negative. Note the variation in signal for the first positive signal after
the primary P arrival.
4.8 Synthetic receiver gathers with plane waves originating from SE
direction for model with a step in Moho (right) compared to the
model with a 15 km ramp in Moho (left)
4.9 Synthetic gathers with a plane wave originating from SW direction
for the model with a step in Moho (right) compared to the model with
a 15 km ramp in Moho (left)
4.10 RF gathers profiles for 10, 7.5, 5, and 2.5 km step models.
4.11 A series of synthetic receiver gather profiles for the 10-km step model
to test horizontal effect. The bottom row panels are for stations +10,
+20, +30 km right of the fault (shallow Moho). The top row shows
-30, -20, -10 km left of the fault (deeper Moho). The middle row
shows the station directly over the fault. Within each receiver gather
profile, the fault trace runs along back azimuth (BAZ) 0 deg (north)
and 180 deg (south), separating the shallow Moho (BAZ 0-180 deg)
from the deep Moho (BAZ 180-360 deg).
5.1 Schematic view of three models for the strength of continental
lithosphere. a) Jelly sandwich model which describes a strong upper
crust, weak lower crust and strong upper mantle (e.g., Chen and
Molnar, 1983; Hirth and Kohlstedt, 2003); b) Crème Brulee model
which has a strong upper crust and weak lower crust and upper
mantle (Jackson, 2002); and c) Banana split model with relative

61
62

63

64

65
67

70

ix
weakness of all three layers (Zoback et al., 1987). [Made by
Burgmann and Dresen, 2008]
5.2 A schematic for our interpreted structure beneath the San Jacinto
Fault zone. The Moho is offset by ~ 10 km vertically within 5 km
width. The strain is localized within the fault zone.

76

x
Abstract
The degree to which faults are localized or distributed within the continental lithosphere
has long been a controversial subject. This thesis presents a study of the variation for the
crustal thickness in southern California. The goal is to study strain deformation at depth
by investigating the variations of the Moho beneath strike-slip faults. The data used in
this study are broadband teleseismic waveforms from 2000 to 2011 recorded by the
Southern California Seismic Network (SCSN) and USArray. The P Receiver Function
(RF) method is used to process the teleseismic events to image the Moho. Synthetic
modeling in 3D elastic media using a finite difference algorithm is conducted to constrain
the geometry of the Moho.
The first part of this thesis presents a map of Moho depth in southern California. The
estimated average Moho depth is 30 km but has a range between 18 and 41 km. A
shallow Moho of 18-20 km is observed in the Salton Trough and the Inner Continental
Borderland. There is a general correlation of a deeper Moho beneath mountains, such as
the Peninsular Range, eastern Transverse Ranges and western Transverse Ranges. The
deeper Moho beneath these areas is consistent with the presence of the mountain root.
Moreover, using a similar broadband seismic data and P receiver function technique as
Yan and Clayton (2007), our receiver gather analyses confirm the previous conclusion of
a vertical Moho offset beneath the San Gabriel Mountains.
xi
The second part of the thesis involves a detailed study of the Moho beneath the San
Jacinto fault zone. First, receiver gathers as a function of back azimuth were analyzed.
Receiver gathers at certain stations near the San Jacinto fault trace show a strong back
azimuthal variation. These back-azimuthal variations of the Moho signal indicate
three-dimensional complexity beneath the central San Jacinto fault that may suggest
variations of Moho depth. A SW-NE stacking profile across the Elsinore, San Jacinto,
and San Andreas faults indicates an 8~10 km vertical offset structure beneath the San
Jacinto fault. In order to constrain the geometry of the Moho in this area, 3D synthetic
modeling using finite difference algorithm was conducted to confirm the interpretation of
the Moho offset. Six possible geometries were constructed: one with a 10 km vertical
step in the Moho, one with a 5-km-wide and 10-km vertically offset ramp, one with a
15-km-wide and 10-km vertically offset ramp, one with a flat Moho but with 10%
velocity contrast across the fault, and one with a flat Moho but with 20% velocity
contrast across the fault. The synthetic receiver gathers were plotted and analyzed both as
a function of back azimuth and incident angles. Our basic conclusion is that the Moho
model with a vertical step of 10 km best fits the data.
Our results support the idea that the lower crust is strongly coupled to and deforms with
the upper crust. For the deformation observed beneath the strike-slip faults, our
back-azimuth RF analysis and synthetic modeling found a 10-km Moho step beneath the
xii
San Jacinto fault. This result suggests that the fault extends through the entire crust and
that the strain in the lower crust is localized within a narrow zone beneath this major
strike-slip fault.

1
Chapter 1 Introduction
Southern California has a very complex tectonic history, primarily due to its transition
from a convergent plate boundary to a transform plate boundary over past 30 Ma years
(Atwater, 1970; Atwater and Molnar, 1973; Atwater, 1989; Harden, 1997; Irwin, 1990;
Wallace, 1990). Figure 1.1 shows the tectonic evolution of the southern California during
this time period. Thirty Ma years ago, this portion of the western edge of the North
American plate was a convergent margin, where the Farallon plate was subducted
eastward beneath the North American plate (Figure 1.1a). Around 28 million years ago,
the divergent boundary between the Farallon plate and the Pacific plate encountered the
North American plate, resulting in the initiation of the San Andreas fault system. Two
triple junctions were formed: the Mendocino Triple Junction in the northwest which has
been migrating to the north, and the Rivera Triple Junction in the southeast, which has
been migrating to the south (Figure 1.1b). Due to the migrations of these triple junctions,
the principal movement in the early development of the San Andreas fault system is shear
motion along the transform boundary (Figure 1.1c). At some point during southward
migration of the triple junction, the transform boundary jumped eastward to a position
within the North American plate (Figure 1.1d). The southern section of the modern San
Andreas fault was formed by similar eastward jumps at ~4 Ma, resulting in the opening
of the Gulf of California (Wallace, 1990; Irwin, 1990). Some of the major faults in
2
southern California, such as the Elsinore, and San Jacinto faults may represent these
earlier positions of the transform (Irwin, 1990).

Figure 1.1: Diagram of the tectonic history of southern California. (made by Kious et al., 2001)

1.1 San Andreas Fault System
The San Andreas fault is a right-lateral strike-slip fault and is one of the most studied and
active strike-slip faults in the world (Figure 1.2). The average slip rate in southern
California is 49-55 mm/year based on paleoseismology and geodetic studies (Sharp, 1981;
Bennett et al., 1996; Bourne et al., 1997), yet how slip rates are partitioned between each
3
fault segments is still debated (Becker et al., 2005; Bennett et al., 1996). The southern
portion of the San Andreas fault system primarily consists of three strike-slip faults: the
San Andreas, San Jacinto and Elsinore faults (Figure 1.2). At the surface, these three
faults are parallel, discrete and independent traces. However, whether these faults extend
into the lower crust as discrete individual faults or form as a whole zone of distributed
deformation is not clear. These discrete fault branches that comprise the southern segment
of San Andreas Fault system make it an ideal place to study continental deformation.

Figure 1.2: Map of faults in southern California. Arrows represent relative plate motion. Average slip rate
between the North American plate and Pacific plate is 55 mm/yr, along the San Jacinto Fault Zone vary
between 8-20mm/yr, and along the San Andrea Fault vary between 10-30 mm/yr.

4
1.2 Rheology of the Lower Crust
Based on rheological characteristics, the lithosphere can be divided into three layers: the
upper crust, the lower crust, and the upper mantle (e.g., Barrell, 1914; Burgmann and
Dresen, 2008). The upper crust is believed to be brittle with its strain is accommodated in
the form of earthquakes (Byerlee, 1978). However, how strain is accommodated in the
lower crust and the upper mantle is debated. Burgmann and Dresen (2008) summarize
three different models for the lithosphere based on strength: a) a strong upper crust,
relative weak lower crust and strong upper mantle; b) a strong upper crust, strong lower
crust and weak upper mantle; c) relative weakness of all three layers. Some continued
questions on this subject include: a) whether the strain in the lower crust is localized or
distributed; b) the coupling relationship between the crust and upper mantle; and c) the
strength of lower crust.
One way to address these questions is to study the deformation within the lower crust by
mapping the Moho discontinuity. The Moho is defined as the boundary between
the crust and the mantle, which was first identified by Mohorovičić (1909) with
earthquake travel time data. At the Moho boundary, there is a major change in seismic
wave velocity and chemical composition from intermediate and mafic crustal rocks to an
ultramafic mantle (e.g., Anderson, 1989; Plummer et al., 1996). The velocity of P waves
increases from about 6.4 km/s to 7.6 km/s, and the velocity of S waves increases from 3.7
5
km/s to 4.4 km/s (Anderson, 1989).
The depth variation for the Moho beneath strike-slip faults is of particular interest to
geophysical and geological studies. The Moho topography is closely related to strain
localization within the lower crust and a vertical separation of the Moho may represent
highly localized strain at depth and imply relative strength of the lower crust and upper
mantle. Strike-slip faults can have large lateral offsets at the surface, but how the strain is
developed at depth within the fault zone is controversial. There are two competing
viewpoints regarding this subject (e.g., Savage and Burford, 1973; England et al., 1985;
Platt and Becker, 2010). One possibility is that the lower crust is rigid and that strike-slip
faults are discrete, independent structures. From this viewpoint, the strike-slip fault will
cut through the entire crust, and deformation in the lower curst and upper mantle is
concentrated on the narrow fault zone. This viewpoint is supported by seismic studies in
San Gabriel Mountain (Yan et al., 2007), northern California (Parsons, 1998), Dead Sea
Transform (Weber et al., 2004), Walls Boundary strike-slip fault in Scotland (McGeary,
1989), and Altyn Tagh fault in Tibet (Wittlinger et al., 1998; Herquel et al., 1999).
The alternative viewpoint is that the lower crust has low strength and deformation in the
lower crust and upper mantle is distributed over a broad region. This interpretation is
supported by many rock mechanics laboratory experiments (e.g., Hirth and Kohlstedt,
2003). However, more seismic evidence supports the first view. As discussed above,
6
previous studies indicate that the San Andreas fault penetrates through the whole crust in
Northern (Parsons, 1998) and Central California (McBride and Brown, 1986), as well as
beneath the San Gabriel Mountains (Yan et al., 2007). But whether its southern
branches (e.g., San Jacinto and Elsinore faults) have the same features or not remains
unclear.
Geodetic studies (Figure 1.2) suggest that the San Andreas and San Jacinto fault systems
accommodate the majority of the 45mm/yr plate motion between the North American
Plate and Pacific Plate in southern California: the San Andreas fault rate varies between
10-30 mm/yr, and slip rate along the San Jacinto Fault Zone varies between 8-20 mm/yr
(e.g., Fialko, 2006; Becker et al., 2005; Kendrick et al. 2002). Compared to the San
Andreas fault, the San Jacinto fault is a relatively young fault that initiated around 1.0-1.5
Ma (Langenheim et al., 2004). This project investigates whether this less mature fault has
the same strain localization feature as that found in the more mature San Andreas fault
(Parsons, 1998; McBride and Brown, 1986; Yan et al., 2007; Zhu et al., 2000; Zhu, 2002),
more generally whether these faults exhibit discrete vertical step in Moho depth.

1.3 Goals of this Study
In this study we have attempted to map the Moho in southern California using P receiver
7
functions to help answer these outstanding questions. There are previous receiver
function studies, but most of them are large scale, for example, the whole of western
North America (e.g., Ozalaybey and Savage, 1995; Hartog and Schwartz, 2001; Ramesh,
2002; Abt et al., 2010; Gilbert, 2012; Levander and Miller, 2012). Zhu et al. (2000) and
Yan et al. (2007) have conducted studies similar to ours in southern California, but there
are still several issues that are not clear. Zhu (2000) and Yan et al. (2007) suggest an
offset structure for the Moho beneath the San Gabriel Mountains using the receiver
function technique, but their conclusion is still in debate due to the contrasting result
found in other teleseismic travel times study (Kohler and Davis, 1997) and a Pn travel
times study (Hearn, 1984). In this study we conduct back azimuth analysis of receiver
functions in the same region to better understand this subsurface structure.
Besides placing an emphasis on these highly debated subjects, we have also improved
upon a technical portion of receiver function processing. First, previous receiver function
studies (e.g., Zhu, 2000, 2002; Zhu and Kanamori, 2000; Yan and Clayton, 2007) use
standard 1D velocity model such as ak135 (Kennett et al., 1995), PREM (Dziewonski and
Anderson, 1981), iasp91 (Kennett and Engdahl, 1991), TNA (Grand and Helmberger
1984) for depth conversion. However, the crust and lithosphere beneath southern
California is very complex, and a 1D standard velocity model may not be sufficient or
appropriate. Therefore, a regional velocity model is required for properly imaging and
8
interpreting the subsurface structure beneath southern California. In this study a series of
1D averaged velocity models extracted from the SCEC 3D Community Velocity Model
(Kohler et al., 2003; Pleasch et al., 2009) to be applied in the depth conversion process.
Second, studying receiver functions as a function of back azimuth is very helpful in terms
of better understanding subsurface structure, but previous studies (Zhu, 2000; Yan et al.,
2007) do not include events from the northeast due to lack of deep earthquakes in the
Mid-Atlantic Ridge area. Therefore, some information could be missing due to lack of
data from this back azimuth bin. This study provides full back azimuth coverage by
selecting ~20 good quality teleseismic events from the northeast direction but at
shallower depth.
In the following chapters, Chapter 2 provides a basic description of data and
methodology used in this study. Chapter 3 first provides a map for Moho depth in
southern California, and different tectonic blocks are shown and discussed. Then detailed
receiver function analysis is conducted in the San Gabriel Mountains to better understand
the debated structure. Later in Chapter 4, the same receiver function analysis is applied in
the San Jacinto Fault region to study the subsurface structure beneath the strike-slip fault.
In addition, synthetic modeling for six possible crustal structures is conducted to better
constrain the Moho geometry. Chapter 5 includes discussion of the work and avenues for
further study.
9
Chapter 2 Data and Methodology
2.1 Data
The data used in this study are 112 teleseismic events from 2000 to 2011 recorded by
ninety-seven broadband stations of the Southern California Seismic Network (SCSN) and
USArray transportable array (TA) (Figure 2.1, Appendix I and II). The events are selected
based on the following three conditions: moment magnitude greater than 6.0, great circle
distances between 30 to 95 degrees, and depth between 25 km to 700 km. With these
requirements no events from the northeast direction were identified, therefore the depth
range for this particular direction was broadened to 5-700 km in order to get better
azimuth coverage. As a result, 33 more events were included.

Figure 2.1: Map of all broadband seismic stations used in the study including SCSN and USArray (red
triangles). The figure on the right shows teleseismic events from 2000 to 2011 with magnitude greater
than 6.0 and great circle distance between 35 to 90 degrees which were used in the analysis. The
events are grouped by colors on NE (yellow), NW (green), SE (blue), SW (red) directions.
10
2.2 Receiver Function Methodology
2.2.1 Introduction of Receiver Function
The receiver function method (Langston, 1977; Vinnik, 1977) is a widely used technique
to detect velocity discontinuities beneath seismic stations using teleseismic events
recorded at three-component broadband seismic stations.

Figure 2.2: a) Diagram of the P receiver function; when teleseismic P waves travel through the velocity
discontinuity, part of the P wave converts into S wave, resulting in Pp and Ps phases. b) An example of P
receiver function, Ps signal is marked.
As can be seen from Figure 2.2, when a teleseismic P wave travel across a velocity
discontinuity, part of the P wave converts into an SV wave. The P-to-SV conversion is
11
called a Ps phase. In a three component seismogram, the direct P wave energy mostly
appears on the vertical component, and the Ps phase appears most on the horizontal
components because the SV wave is polarized in the horizontal direction. The Ps phase
has a similar shape to the direct P arrival and follows it by the amount of time which is
proportional to the depth of the discontinuity. The depth to the discontinuity can then be
determined by the subsurface velocity structure and the difference in travel time between
the direct P arrival and Ps arrival. However, it is not easy to pick the Ps phase from
seismograms because the Ps phase is usually obscured by the coda of the P wave, which
is caused by both the propagation path and source effects (Shearer, 2009). Therefore, the
Ps phase can be extracted by deconvoluting the vertical component from the horizontal
components. The deconvoluted waveform is termed a receiver function.
Receiver function analysis is a useful technique to image the structure of the Earth. It is
relatively simple to conduct and the result can be straightforward and powerful. This
section explains the receiver function in a theoretical way. The detailed procedure and
parameter settings are discussed in section 2.2.2.
In general, a seismogram can be written as a convolution of a source effect, a propagation
effect and a near surface structure effect:
𝑤 ( 𝑡 ) = 𝑠 ( 𝑡 ) ∗ 𝑝 ( 𝑡 ) ∗ 𝑛 ( 𝑡 ) (1)
12
Where w(t) represents a seismic waveform, s(t) represents the source effect, p(t)
represents the propagation effect and n(t) represents the near surface structure effect.
Receiver functions are based on deconvoluting the incoming vertical component from the
radial component in order to remove the effects from source and propagation path, and
therefore focus on the near surface structure.
In mathematical terms, the radial and transverse components of the receiver function are
defined by:
𝐸 _ 𝑅 ( 𝑤 ) =
𝑅 ( 𝑤 ) 𝑍 ∗
( 𝑤 )
𝑍 ( 𝑤 ) 𝑍 ∗
( 𝑤 )
(2)
𝐸 _ 𝑇 ( 𝑤 ) =
𝑇 ( 𝑤 ) 𝑍 ∗
( 𝑤 )
𝑍 ( 𝑤 ) 𝑍 ∗
( 𝑤 )
(3)
Where 𝑅 ( 𝑤 ) = 𝑠 ( 𝑤 ) 𝑝 ( 𝑤 ) 𝑛 _ 𝑟 ( 𝑤 ) , 𝑍 ( 𝑤 ) = 𝑠 ( 𝑤 ) 𝑝 ( 𝑤 ) 𝑛 _ 𝑧 ( 𝑤 ) ,
𝑇 ( 𝑤 ) = 𝑠 ( 𝑤 ) 𝑝 ( 𝑤 ) 𝑛 _ 𝑡 ( 𝑤 ). which is the Fourier transform of eq. (1), and w is the angular
frequency 2 𝜋𝑓 .
Since radial, transverse, and vertical components share the same source effect and
propagation path, which means they have the same s(w) and p(w), therefore the
deconvolution result of eq.(2) and eq.(3) will only depend on near surface structure
beneath the receiver. Therefore, it provides a useful approach to study the structure
beneath a station while reducing the effects from the source and propagation.
13
2.2.2 Data Processing
In this study, the continuous 3 component seismograms are first cut between 30 s before
the first P arrival and 90 s following for each earthquake, and then are processed to
remove the mean and trend, and band-pass filtered by a fourth order Butterworth filter
with corner frequencies of 0.02 and 1.5 Hz, to include the useful frequencies for a
teleseismic event. The two horizontal components are rotated to be parallel and
perpendicular to the "great circle path", which are respectively called radial and
transverse components. Then the vertical component is deconvoluted from the radial
component with a Gaussian filter width of 1.5 Hz using an iterative, time-domain
deconvolution algorithm following Ligorria and Ammon (1999). The resulting
source-equalized time series are P receiver functions. Figure 2.3 shows a
three-component waveform profile for station CRY and its corresponding receiver
functions. The Ps phase is not obvious on the seismogram, but is clearly enhanced in
the receiver function.
14

Figure 2.3: (a) Three-component waveform (top: east, middle: north, bottom: vertical component) for
2002/11/17 earthquake recorded at station CRY; predicted arrival time for direct P and PP are calculated by
Taup software (Crotwell et al., 1999) using the PREM model (Dziewonski and Anderson, 1981). (b)
Corresponding radial (top) and transverse (bottom) receiver functions.
Raw receiver functions chosen for further analysis are automatically selected based on
the four following criteria. First, the amplitude at time equal to 0 should be positive and
the maximal spike should be at t=0 to ensure the direct P arrival always appears at time
zero. Secondly, the second largest spike should not exceed 75% of the largest spike;
otherwise it indicates that another phase or noise is contaminating the signal. Thirdly, the
signal to noise ratio is required to be greater than 10. Finally, the Root Mean Square
15
(RMS) misfit must be less than 0.5 so that the deconvolution will work properly. Figure
2.4 shows two examples of bad receiver functions that were discarded. As a result, 4505
qualified receiver functions are automatically selected out of 6955 initial ones in total.

Figure 2.4: Examples of receiver functions for station CRY . (a) The amplitude at time=0 is negative and
the maximal spike is not at t=0; (b) The maximum spike is not at t=0 and the second largest spike exceeds
75% of the largest spike; (c) A good receiver function.
16

Figure 2.5: comparison of average 1d SCEC CVM (Pleasch et al., 2009) and other classic 1d velocity
models: ak135 (Kennett et al., 1995), PREM (Dziewonski and Anderson, 1981), iasp91 (Kennett and
Engdahl, 1991), TNA (Tectonic North America velocity model, Grand and Helmberger 1984).

2.2.3 Depth Conversion
Receiver functions are time series. In order to obtain Moho depth information, a
procedure named depth conversion needs to be applied. There are two parameters in
determining the location of the velocity discontinuity from the receiver functions: the
time delay of P-to-S conversion relative to direct P-wave and the reference velocity
model. The time delay can be well determined from receiver functions, but the velocity
structure of the subsurface is more complex and variable. There are various 1D velocity
models available, such as ak135 (Kennett et al., 1995), PREM (Dziewonski and Anderson,
1981), iasp91 (Kennett and Engdahl, 1991), Tectonic North America velocity model
17
(TNA) (Grand and Helmberger 1984). However, there are large variations between them,
and each of these velocity models usually best represents one particular region. Therefore,
an appropriate velocity model is the key in accurately locating the subsurface feature of
interest.
Since the receiver function method assumes the incident angle of the teleseismic wave is
near vertical, it can be assumed that the velocity structure that each seismic ray travels
through is near vertical and therefore can be considered as one dimensional. Therefore in
this analysis the receiver functions were depth converted using a 1D model. To improve
reliability and accuracy, 1D velocity models at each P-to-SV conversion for the
station-event pairs were extracted from the SCEC 3D Community Velocity Model
(Pleasch et al., 2009; Kohler et al., 2003). Figure 2.5 shows as large as 10% variation
between an averaged 1D SCEC velocity model and other commonly used 1D velocity
models: ak135 (Kennett et al., 1995), PREM (Dziewonski and Anderson, 1981), iasp91
(Kennett and Engdahl, 1991), Tectonic North America velocity model (TNA) (Grand and
Helmberger 1984).
The first step in depth conversion is to calculate the locations of P to S converted points
at 30 km, which is assumed to be the approximate depth of the crust-mantle boundary at
southern California based on previous receiver function estimates by Zhu and Kanamori
(2000). Then a 1D velocity model is extracted at those piercing points from the SCEC 3D
18
Community Velocity Model (Pleasch et al., 2009; Kohler et al., 2003). Thus each
signal-event pair has a unique velocity model for depth conversion based on prior,
independent local seismic velocity information. Figure 2.7 shows the extracted 1D SCEC
velocity models for three selected AZ network stations, which are marked on Figure 2.6.
In Figure 2.7, it can be seen that station CRY, SND, and KNW are close to each other,
5%-15% Vs contrasts are observed between depths of 0 and 50 km. Thus, by using a
unique one dimensional velocity model for each conversion point many artifacts can be
prevented, which could be a result of applying an inappropriate constant 1D velocity
model.

Figure 2.6: Map of stations in San Jacinto fault area. Crosses represent surface projections of P-to-S
conversions at Moho depths. These piercing points are colored and grouped by four directions, NE, SE, SW,
NW respectively, which correspond to the colors in Figure 2.1.
19

Figure 2.7: 1D velocity models extracted from SCEC 3D CVM for three selected AZ network stations near
San Jacinto Fault: CRY , SND and KNW, whose locations are shown in the map in Figure 2.6.

2.3 CCP Stacking
Common midpoint stacking is a commonly used technique in reflection seismology to
reduce noise and enhance data quality (e.g., Yilmaz, 1987). In reflection seismology, the
P-P reflection has a symmetrical ray path. Its reflected point projected at the surface is the
halfway point between source and receiver, which is also called the midpoint (Figure 2.8).
The set of traces recorded from different source-receiver pairs that have the same
common midpoint (CMP) is called a CMP gather. By stacking the CMP gathers that share
the same midpoint the multiples and random noise can be attenuated and the signal can
be enhanced. The application of this technique to converted-waves is named as common
conversion point (CCP) stacking (Clouser and Langston, 1995).
20

Figure 2.8: (top) Schematic diagram for common midpoint (CMP) stacking; (bottom) Common conversion
point (CCP) stacking.
For CCP stacking, receiver functions are first projected onto their ray paths calculated
using a 1D velocity model. In this study 1D velocity model averaged from the SCEC 3D
CVM (Pleasch et al., 2009) is used. The projected paths for the profiles are plotted as
black dashed lines on the map of Figure 2.9a. Then the subsurface region of interest is
divided into the bins with width of 100 km, length of 2 km, and height of 1 km. The
amplitudes of the receiver functions within the bin are summed and averaged to obtain
the average amplitude. Neighboring bins overlap by 3 km along the profile was used to
make sure a smooth CCP stacking image. Figure 2.9b shows the result of the CCP
21
stacking in the San Jacinto Fault Zone. The red amplitude at about 30 km is interpreted as
the Moho discontinuity. It can be seen that the Moho is not flat but has some depth
variations. The details of the CCP stacking result are discussed in Chapter 4.

Figure 2.9: (a) Map of San Jacinto Fault zone region. Fault traces are shown as gray lines on the map.
Positions of cross sections are plotted on map on the left. Red crosses represent stations used. (b) Common
conversion points (CCP) stacking of P receiver functions along three profiles in San Jacinto Fault Zone.
Locations of Elsinore fault (EF) and San Jacinto fault (SJF) as well as possible Moho boundary are marked
on the stacking profiles. Note that a small Moho offset can be seen beneath major faults.

2.4 Synthetic Modeling: Finite Difference Method
Synthetic modeling is used to provide a link between observed seismograms and the
22
interpreted geological structure. The input model for the synthetics is a quantitative
description of the interpreted geological structure, which defines the velocity and density
distribution, and possible offset or structures of interest. The interpreted model is then
tested by comparing the match between the synthetic modeling results and observed
seismograms. An optimal model can subsequently be reached by modifying the input
parameters based on the comparison.
Synthetic modeling in 3D elastic media using finite difference algorithm (Graves, 1996;
Okaya et al., 2003) are conducted for five different models to constrain the geometry of
the Moho and test the robustness of its features. The homogeneous elastic media has a
width of 500 km, length of 500 km and depth of 300 km. The models tested are shown in
Figure 2.10, which include one with a step in the Moho, a 5 km wide and 10 km vertical
ramp, a 10 km wide and 10 km vertical ramp, a flat Moho at 30km depth, and a flat Moho
but two velocity blocks across a vertical fault.
23

Figure 2.10: Velocity models with four possible geometries: 1) a step in the Moho (blue), 2) a 5 km wide
and 10 km vertically offset ramp (green), 3) a 15 km wide and 10 km vertically offset ramp (red), 4) a flat
Moho at 30 km depth (light blue).

2.4.1 Equation of Elastic Wave and Finite-Difference
Implementation
Graves (1996) describes the implementation of Finite-Difference method for 3D elastic
wave. The equations of elastic wave in 3D isotropic media can be derived from the
following equations:
Equations for momentum conservation:
𝜌 𝜕 2
𝑢 𝑥 𝜕 𝑡 2
=
𝜕 𝜏 𝑥𝑥
𝜕𝑥
+
𝜕 𝜏 𝑥𝑦
𝜕𝑦
+
𝜕 𝜏 𝑥𝑧
𝜕𝑧
+ 𝑓 𝑥
𝜌 𝜕 2
𝑢 𝑦 𝜕 𝑡 2
=
𝜕 𝜏 𝑥𝑦
𝜕𝑥
+
𝜕 𝜏 𝑦 𝑦 𝜕𝑦
+
𝜕 𝜏 𝑦 𝑧 𝜕𝑧
+ 𝑓 𝑦 (4)
𝜌 𝜕 2
𝑢 𝑧 𝜕 𝑡 2
=
𝜕 𝜏 𝑥𝑧
𝜕𝑥
+
𝜕 𝜏 𝑦 𝑧 𝜕𝑦
+
𝜕 𝜏 𝑧𝑧
𝜕𝑧
+ 𝑓 𝑧
24

Stress-strain relation (Hooke’s Law):
𝜏 𝑥𝑥 = ( 𝜆 + 2 𝜇 )
𝜕 𝑢 𝑥 𝜕𝑥
+ 𝜆 (
𝜕 𝑢 𝑦 𝜕𝑦
+
𝜕 𝑢 𝑧 𝜕𝑧
)
𝜏 𝑦𝑦
= ( 𝜆 + 2 𝜇 )
𝜕 𝑢 𝑦 𝜕𝑦
+ 𝜆 (
𝜕 𝑢 𝑥 𝜕𝑥
+
𝜕 𝑢 𝑧 𝜕𝑧
)
𝜏 𝑧𝑧
= ( 𝜆 + 2 𝜇 )
𝜕 𝑢 𝑧 𝜕𝑧
+ 𝜆 (
𝜕 𝑢 𝑥 𝜕𝑥
+
𝜕 𝑢 𝑦 𝜕𝑦
)

(5)
𝜏 𝑥𝑦 = 𝜇 (
𝜕 𝑢 𝑥 𝜕𝑦
+
𝜕 𝑢 𝑦 𝜕𝑥
)
𝜏 𝑥𝑧 = 𝜇 (
𝜕 𝑢 𝑥 𝜕𝑧
+
𝜕 𝑢 𝑧 𝜕𝑥
)
𝜏 𝑦𝑧
= 𝜇 (
𝜕 𝑢 𝑦 𝜕𝑧
+
𝜕 𝑢 𝑧 𝜕𝑦
)
Where 𝜆 , 𝜇 are Lamé parameters, 𝑓 𝑥 , 𝑓 𝑦 , 𝑓 𝑧 are the body force components, 𝜌 is the
density, 𝑢 𝑥 , 𝑢 𝑦 , 𝑢 𝑧 are the displacements along x, y, z axis separately, 𝜏 𝑖𝑗 is the stress
tensor at i plane along j axis.
Considering
∂
2
u
y
∂ t
2
=
∂ v
x
∂ t
, equations (4) can be rewritten as:
𝜕 𝑣 𝑥 𝜕 𝑡 =
1
𝜌 (
𝜕 𝜏 𝑥𝑥
𝜕𝑥
+
𝜕 𝜏 𝑥𝑦
𝜕𝑦
+
𝜕 𝜏 𝑥𝑧
𝜕𝑧
+ 𝑓 𝑥 )
𝜕 𝑣 𝑦 𝜕 𝑡 =
1
𝜌 (
𝜕 𝜏 𝑥𝑦
𝜕𝑥
+
𝜕 𝜏 𝑦 𝑦 𝜕𝑦
+
𝜕 𝜏 𝑦 𝑧 𝜕𝑧
+ 𝑓 𝑦 )
𝜕 𝑣 𝑧 𝜕 𝑡 =
1
𝜌 (
𝜕 𝜏 𝑥𝑧
𝜕𝑥
+
𝜕 𝜏 𝑦 𝑧 𝜕𝑦
+
𝜕 𝜏 𝑧𝑧
𝜕𝑧
+ 𝑓 𝑧 )

(6)

25
If we take time derivative on both sides of equations (5), and substitute equation
𝜕 𝑢 𝑖 𝜕𝑡
= 𝑣 𝑖 ,
the results can be written as follows:
𝜕 𝜏 𝑥𝑥 𝜕𝑡
= ( 𝜆 + 2 𝜇 )
𝜕 𝑣 𝑥 𝜕𝑥
+ 𝜆 (
𝜕 𝑣 𝑦 𝜕𝑦
+
𝜕 𝑣 𝑧 𝜕𝑧
)
𝜕 𝜏 𝑦𝑦
𝜕𝑡
= ( 𝜆 + 2 𝜇 )
𝜕 𝑣 𝑦 𝜕𝑦
+ 𝜆 (
𝜕 𝑣 𝑥 𝜕𝑥
+
𝜕 𝑣 𝑧 𝜕𝑧
)
𝜕 𝜏 𝑧𝑧
𝜕𝑡
= ( 𝜆 + 2 𝜇 )
𝜕 𝑣 𝑧 𝜕𝑧
+ 𝜆 (
𝜕 𝑣 𝑥 𝜕𝑥
+
𝜕 𝑣 𝑦 𝜕𝑦
)

(7)
𝜕 𝜏 𝑥𝑦 𝜕𝑡
= 𝜇 (
𝜕 𝑣 𝑥 𝜕𝑦
+
𝜕 𝑣 𝑦 𝜕𝑥
)
𝜕 𝜏 𝑥𝑧 𝜕𝑡
= 𝜇 (
𝜕 𝑣 𝑥 𝜕𝑧
+
𝜕 𝑣 𝑧 𝜕𝑥
)
𝜕 𝜏 𝑦𝑧
𝜕𝑡
= 𝜇 (
𝜕 𝑣 𝑦 𝜕𝑧
+
𝜕 𝑣 𝑧 𝜕𝑦
)
By applying the Finite-Difference method in time, the left side of equations (6) and (7)
can be written as:
𝑣𝑒 𝑙 ( 𝑖 + 1) − 𝑣𝑒 𝑙 ( 𝑖 )
∆ 𝑡 (8)
𝑠𝑡 𝑟 𝑒 𝑠𝑠 ( 𝑡 + 1) − 𝑠𝑡 𝑟 𝑒 𝑠𝑠 ( 𝑡 )
∆ 𝑡
By applying the finite-difference method in space, the right side of equations (6) and (7)
can be written as:
𝑠𝑡 𝑟 𝑒 𝑠𝑠 ( 𝑖 + 1) − 𝑠𝑡 𝑟 𝑒 𝑠𝑠 ( 𝑖 )
∆ 𝑖
𝑣𝑒 𝑙 ( 𝑖 + 1) − 𝑣𝑒𝑙 ( 𝑖 )
∆ 𝑖 (9)
Then the continuous elastic wave equations are written as a discrete system, and can be
26
solved by a staggered-grid finite-difference technique (e.g., Virieux, 1986; Levander,
1988; Randall, 1989). More details about the implementation are described by Graves
(1996).
2.4.2 Source Function
A source function is a temporal equation used to describe the seismic source. In general,
the characteristics of a seismic source signal include generation an impulsive source,
band-limited and time-varying waves. There are various shapes for source function, such
as a boxcar, triangle, or Gaussian. The detailed difference between each source function
matters little in receiver functions because in later processing, the source function is
removed by deconvolution when generating a synthetic receiver function. But we chose a
Gaussian shape for this study because of its simplified mathematical form.
Figure 2.11 shows the teleseismic source function used in this study. It is generated with a
frequency band of 0.33-2 Hz. The upper figure is in the function of time and the lower
figure is in the function of frequency. The length of the source time function represents
the duration of energy radiation. The amplitude of the source time function represents the
amount of energy released in the earthquake. As can be seen in the top figure, the
tele-pulse is one Gaussian shape pulse, which indicates that most energy is released in the
main rupture. As can be seen from the spectrum (bottom figure), at low frequency (0-0.4
27
Hz), the amplitude is relatively flat and equal to the maximal amplitude in the time series.
Then the amplitude starts to decrease at 0.4 Hz, and falls to zero at 0.8 Hz.

Figure 2.11: Example of the teleseismic source function used in this study. (top) Source function as a time
series; (bottom) Spectrum of the source function.

2.4.3 Boundary Conditions
The boundary conditions are very important for synthetic modeling. In these synthetic
simulations, a free surface at the top represents the surface of the Earth. The free surface
satisfies zero-stress condition where the values of pressure of all nodes above free surface
are set as zero. Due to the finite volume of the model, there are boundaries at bottom and
around the volume, which are unrealistic for the Earth. As a result, reflected waves are
produced at these boundaries, which would disturb the waves that are of interest to our
28
study. Therefore absorbing boundaries, which are in practice attenuating zones, are set at
the bottom and around to eliminate unnecessary reflecting waves. In this study, the
attenuate coefficient is set as 0.0015, which means the energy will decrease in rate of
exponential function
𝑔 = exp (( −0.0015 𝑥 )
2
) (10)
where x is the relative coordinate in the absorbing zone and in this study the width of the
pad zone in nodes is set as 64.

2.4.4 Stability and Dispersion Conditions
Energy radiation from an earthquake can be described as a continuous system. However,
the synthetic modeling is a discrete system, in which several factors, such as grid spacing,
time spacing, minimum and maximum wave speed, and source frequency interplay with
each other. As described by Okaya et al. (2003), in order to keep the synthetic modeling
stable and reliable, two conditions have to be satisfied.
First, a stability condition is set up to make the finite difference wave equation stable.
𝑉 𝑚𝑎𝑥
∗
𝐷 𝑡 𝐷 𝑥 < 0.50 (11)
Where 𝑉 𝑚𝑎𝑥
is the maximal velocity in the system (P wave), Dt is the finite time
29
difference, and Dx is the volume grid spacing. In this study, the Dt, Dx, and 𝑉 𝑚𝑎𝑥
is set
as 0.025 s, 0.5 km and 8.21 km/s respectively.
Second, a seismic wavelet will disperse if the grid spacing is too large with respect to the
pulse shape. Therefore, constraints are applied to these parameters to avoid dispersion as
described by equation (12).
𝑉 𝑚𝑖𝑛 ∗
𝑓 𝑚𝑎𝑥 𝐷 𝑥 > 2.8 (12)
Where 𝑉 𝑚𝑖𝑛 is the minimal velocity in the system (S wave), 𝑓 𝑚𝑎𝑥
is the maximal
frequency for the source function, and Dx is the volume grid spacing. In this study, the
𝑓 𝑚𝑎𝑥
, Dx, and 𝑉 𝑚𝑎𝑥
are set as 0.7 Hz, 0.5 km and 2.78 km/s respectively. Nx, Ny, Nz are
set as 500 km, 300km and 300 km, where Nx, Ny and Nz are the width, length, and height
of the volume respectively.
Figure 2.12 shows an example of the synthetic teleseismic waveform for the 10 km step
model in this study. From top to bottom, they are vertical, x and y components
respectively. The seismograms are relative simple and have no noise. The direct P arrival
can be seen in both the vertical and x components, but are not shown on y component as
the y plane is set as perpendicular to the particle motion of the P wave.
30

Figure 2.12: an example of the synthetic teleseismic waveform for the step model in this study. From top to
bottom, they are vertical, x, y components respectively. P, Ps and S arrivals are labeled.
In order to match the real data, which has full 360 degree back azimuth coverage, elastic
plane wave is introduced to simulate teleseismic waves from 0 to 360 degree back
azimuths with 10 degree spacing. Then synthetic seismograms are cut, bandpassed,
rotated, and deconvoluted using the same method described in Section 2.2.2 to generate P
receiver functions.
Using data and methodology described in this Chapter, a map for Moho depth in southern
California is produced and discussed in Chapter 3, and a detailed receiver function study
and synthetic modeling are conducted in Chapter 4 for the San Jacinto Fault zone.
31
Chapter 3 Mapping the Moho in Southern California

Figure 3.1: Topographic map in southern California with major tectonic provinces are labeled. Red
triangles represent broadband seismic stations used in this study. Station information is shown in
Appendix I.

Southern California provides an ideal natural laboratory to study the strain deformation at
depth. It consists of several different tectonic provinces, such as strike-slip faults of the
San Andreas Fault system and continental rifting system in Salton Trough (Figure 3.1).
Besides, southern California experienced extensive compression and extension during
past ~100 million years, resulting in different topographic expressions, such as mountains
and basins (Figure 3.1). It is reasonable to expect that these tectonic and topographic
32
differences at surface could be accompanied by differences at depth. The dominant
tectonic feature in southern California is the San Andreas fault system, which is the
transform boundary between Pacific plate and North American plate. At the latitude of
Los Angeles, the San Andreas Fault bends to the east-west along the Transverse Ranges.
Details about the tectonic history of the rotation of the Transverse block and the bending
of the San Andreas Fault are discussed in Chapter 1. At the southeastern end of the fault
lies the Salton trough, which is a modern continental rifting center associated with the
opening of the Gulf of California (Atwater, 1970; Oskin et al., 2001; Lekic et al., 2011).
To the west of the Salton Trough lies the north-south oriented Peninsular Range, which
consists of Mesozoic batholiths (Gromet and Silver, 1987; Wallace, 1990). To the north of
the Peninsular Range lies the Mojave Desert, which is bounded by the San Andreas fault
and the left-lateral Garlock fault. To the southeast of the Mojave Desert lies the Eastern
California Shear Zone, where several right-lateral strike-slip faults are thought to
accommodate 20%–25% of total relative motion between the Pacific and North America
plates (Dokka and Travis, 1990; McClusky et al., 2001; Dixon et al., 2003).
It is of particular interest to study the crustal thickness variations beneath these
significantly different tectonic provinces. Moreover, southern California has a good
coverage of broadband seismic instrumentation, with much more densely spaced seismic
stations in the Los Angeles basin and the region surrounding San Jacinto Fault zone
33
(Figure 3.1), which can then be used to image the crustal and lithospheric structure.
During the past decades, many efforts have been made to study the crustal structure in
southern California. These studies includes seismic refraction (Kanamori and Hadley,
1975; Fuis et al., 2001; Godfrey et al., 2002; Lutter et al., 2004), seismic reflection (Li et
al., 1992; Malin et al., 1995; Dinger and Shearer, 1997), seismic tomography (Hearn,
1984; Zhao and Kanamori, 1992; Yang and Forsyth, 2006; Tape et al., 2009, 2010), slip
rates geodynamic modeling (Meade and Hager, 2005; Fay et al., 2008), and teleseismic
converted wave imaging (Kohler, 1999; Zhu, 2000; Zhu and Kanamori, 2000; Zhu, 2002;
Ramesh, 2002; Lekic et al., 2011; Levander and Miller, 2012; Yan and Clayton, 2007a,
b).
In general, the averaged Moho depth in southern California is between 28-30 km (Zhu
and Kanamori, 2000; Yan and Clayton, 2007). A relatively shallow Moho (18-22 km) has
been observed beneath the (18-22 km) beneath the Salton Trough and Continental
Borderland (Dinger and Shearer, 1997; Zhu and Kanamori, 2000; Yan and Clayton, 2007).
A deeper Moho of 33-39 km is observed beneath Sierra Nevada, Peninsula Range, and
eastern Transverse Ranges (Hearn, 1984; Dinger and Shearer, 1997; Zhu and Kanamori,
2000; Godfrey et al., 2002; Yan and Clayton, 2007), which is consistent with mountain
roots in Airy’s isostasy model (Airy, 1855). According to Airy, the root zone compensates
for the elevated mountain, therefore the Earth’s crust and mantle are in a state
34
of gravitational equilibrium. But in more detailed studies of the Moho beneath the
central and western Transverse Ranges, the structure is still debated. Zhu and Kanamori
(2000) and Yan and Clayton (2007) suggest a shallower Moho of 28-31 km beneath
central Transverse Ranges. In contrast, Kohler and Davis (1997) found a continuous deep
Moho of 40 km beneath central Transverse Ranges using teleseismic travel times. For the
eastern Transverse Ranges, previous receiver function studies suggest an offset structure
for the Moho beneath San Gabriel Mountains (Zhu, 2000, 2002; Yan and Clayton, 2007).
However, Dinger and Shearer (1997) found continuous Moho of 33 km beneath the
eastern Transverse Ranges using Pmp arrivals. Hearn (1984) also found a continuous but
shallow Moho beneath the San Gabriel Mountain using Pn travel times study. Therefore,
section 3.2 provides a detailed receiver function analysis trying to clarify this debate.

3.1 Moho Depth Map in Southern California
Figure 3.2 shows an interpolated Moho depth map in southern California, which uses
4505 receiver functions that were stacked and averaged. As described in Chapter 2, the
receiver functions are first converted from time series into depth. The 1D velocity model
used in depth conversion is extracted from SCEC 3D Community Velocity Model
(Pleasch et al., 2009). Then the converted RFs of each station are grouped into four
quadrants (NE, SE, SW, and NW) by back azimuths. For groups with more than five RFs,
35
the RFs are stacked and averaged to get averaged Moho depth. Data points are plotted in
Figure 3.3, which are surface projections of P-to-S conversion points at the Moho depth.
A Delaunay Triangulation algorithm (Shewchuk, 1996) is applied for interpolation with
the grid size of 0.02 degree, and then the grid file is filtered by a cosine function with
width of 80 km to smooth the map. Error estimation for these piercing points in San
Jacinto fault zone is shown in Section 4.3.
The major features of our results agree with previous studies in the same region. A
shallow Moho of 18-22 km is observed beneath the Salton Trough, which agree with
other receiver function and travel times studies (Hearn, 1984; Dinger and Shearer, 1997;
Zhu and Kanamori, 2000; Yan and Clayton, 2007), and is consistent with previous reports
of rifting and upwelling of the asthenosphere in this region (Yang and Forsyth, 2006; Fay
et al., 2008; Lekic et al., 2011). A deeper Moho of 37-39 km is observed beneath the
Peninsular Ranges, which indicates the existence of a mountain root. The Moho beneath
the southern part of the Sierra Nevada is between 35-40 km, which agrees with previous
Moho observations (Dinger and Shearer, 1997; Zhu and Kanamori, 2000; Yan and
Clayton, 2007). Yet evidence of foundering root reported by other receiver function
studies (e.g., Zandt et al., 2004; Frassetto et al., 2011) is not observed in this study. A
relatively deep Moho of 38 km is observed beneath the eastern Transverse Range,
suggestive of a mountain root, and a shallower Moho of 28-30 km found in the central
36
Transverse Ranges suggest there is no mountain root beneath this region. These results
agree with other previous studies (Zhu and Kanamori, 2000; Yan and Clayton, 2007).
Deep Moho of 35-39 km can be seen beneath the San Gabriel Mountains.
As discussed above, the Figure 3.2 is produced by the triangulation interpolation and
filtering, where the data is filtered and smoothed. Therefore, the map mostly represents
the broad-scale features of the Moho instead of fine-scale variations. Yan and Clayton
(2009) conducted receiver gather analysis and synthetic waveform modeling for this
region, and suggested that a notch structure Moho beneath the eastern San Gabriel
Mountains. Section 3.2 provides detailed back azimuth analysis for the receiver functions
here. Similarly, as can be seen from Figure 3.3, the receiver functions in the San Jacinto
Fault zone show significant variations for the Moho depth, ranging from 20-38 km. To
better understand the crustal variation and strain localization beneath strike-slip fault
zone, Chapter 4 provides a detailed study of receiver gather analysis and synthetic
modeling in the San Jacinto Fault zone.
37

Figure 3.2: Interpolated Moho depth map in southern California. The faults are plotted in gray lines. Data
points used to produce this map are plotted in Figure 3.3.

Figure 3.3: Map of the data points used to produce Figure 3.2. The data points are the surface projections of
P-to-S conversion points calculated at the Moho depth for that station. Error estimation for these piercing
points in San Jacinto fault zone is shown in Section 4.3.
38
3.2 San Gabriel Mountains
As discussed above, crustal structure beneath the San Gabriel Mountains is particularly
complicated (Figure 3.3). Kohler and Davis (1997) suggest deep Moho of 40 km beneath
the San Gabriel Mountains through teleseismic travel times study, Godfrey et al. (2002)
found similar result of root beneath the San Gabriel Mountains using refraction data
recorded by LARSE-I experiment, but no deep Moho is found by Pn travel times (Hearn,
1984) nor Pmp travel times study (Dinger and Shearer, 1997). In contrast to the
continuous Moho structure found by the above studies, receiver function studies suggest
an offset structure for the Moho beneath the San Gabriel Mountains (Zhu, 2000, 2002;
Yan and Clayton, 2007). Yan and Clayton (2009) conducted synthetic waveform
modeling and suggest that a notch structure best fit their observations.

Figure 3.4: Topographic map in the San Gabriel Mountains region. Yellow triangles represent the
broadband seismic station stations. Receiver gathers profiles for four selected stations are shown in Figure
3.5. Profiles for other stations are shown in Appendix B.
39

Figure 3.5: Receiver gathers profiles for four selected broadband seismic stations in the San Gabriel
Mountains area. The locations of these stations are shown in Figure 3.4. The receiver gathers are plotted
and colored by back azimuth bins: yellow, blue, red and green represent NE, SE, SW and NW respectively.
The second positive arrivals at around 4 s are considered as the converted signal at the Moho.
40
Figure 3.5 shows receiver gathers profiles for four selected broadband seismic stations in
the San Gabriel Mountains area. Profiles for additional stations are shown in Appendix B.
The receiver gathers are plotted and colored by back azimuth bins: yellow, blue, red and
green represent NE, SE, SW and NW respectively. The locations of these stations are
shown in Figure 3.4. The second positive arrivals at around 4 s are considered as the
converted signal at the Moho. It can be seen that the arrival times of the Moho signal for
all four stations appears variable in back azimuth. For example, for station BFS, the
arrival times of the Moho signal for bin NE (yellow) and SE (blue) increase gradually
with back azimuth from 2 s to 4.5 s, and for bin SW (red) and NW (green), they do not
change with back azimuth and remain at 4.5 s. The profile is consistent with the analysis
for the same station by Yan and Clayton (2007).
For other three stations, the arrival times of the Moho signals show similar pattern as
station BFS. For these receivers the Moho signals arrive 2 s earlier at bin NE (yellow)
and SE (blue) than those at bin SW (red) and NW (green), and they increases gradually to
4.5 s with the increase of back azimuth for bins of NE and SE. These strong back azimuth
dependences suggest variation for the Moho beneath eastern and western sides of the San
Gabriel Mountains and indicate a possible Moho offset beneath this region. The
implication of the Moho offset is consistent with the offset structure beneath the San
Gabriel Mountains reported by Zhu and Kanamori (2000) and Yan and Clayton (2007).
41
As shown above, our results for the San Gabriel Mountains are consistent with other
previous receiver function studies in the same region by Zhu and Kanamori (2000) and
Yan and Clayton (2007). For the broader southern California region, we observed a
general correlation of a deeper Moho beneath mountains, such as beneath the Peninsular
Range and both the eastern and western Transverse Ranges (Section 3.1), but evidence of
a mountain root is not observed beneath central Transverse Ranges. These variations
could be the result of intense compression or extension in these provinces, and suggest
that the lower crust is strongly coupled and deformed with the upper crustal blocks. A
similar type of analysis is applied into the San Jacinto Fault in Chapter 4 to study the
Moho structure and strain localization beneath the strike-slip fault zone. Chapter 4 also
provides synthetic modeling to better constrain and confirm the interpreted structure.

42
Chapter 4 Regional study of the San Jacinto Fault
4.1 Tectonic Setting
The San Jacinto fault is a right-lateral strike-slip fault that extends for 230 km
southeastward from the San Gabriel Mountains to the Salton Trough (Figure 1.2, Figure
4.1). It is one of the most seismically active branches of the San Andreas system in
southern California (e.g. Sanders and Kanamori 1984). The San Jacinto fault is thought to
have formed between 1.0-1.5 Ma ago (Langenheim et al. 2004) and the total accumulated
slip is estimated to be 24 km (Rockwell et al. 1990; Kirby et al. 2007), with estimated slip
rate that vary between 8 to 20 mm/year (Kendrick et al. 2002; Rockwell 2003; Fay and
Humphreys 2005; Fialko 2006). Geodetic studies suggest that together the San Andreas
and San Jacinto fault systems accommodate the majority of the 45 mm/yr plate motion
caused by the NW-SE movements between the North American Plate and Pacific Plate
(e.g., Fialko 2006), the slip rates along the San Andrea fault vary between 10-30 mm/yr
(e.g. Kendrick et al. 2002; Becker et al., 2005; Fialko, 2006).
The San Jacinto fault zone is not a single continuous fault, but instead consists of
multiple segments (Figure 4.2). For example, the Coyote Creek fault is a major strand of
the San Jacinto fault zone. It starts in the Coyote Creek area and extends parallel to the
San Jacinto fault (Figure 4.2). These segments exhibit different properties and behaviors,
43
such as slip rate and seismicity, both at the surface and at depth (Wechsler et al., 2009;
Salisbury et al., 2011; Morton et al., 2012). It is of particular interest for geological and
geophysical researchers to determine whether these discrete segments extend deep into
the lower crust as relatively discrete ductile shear zone or as wide zones of distributed
shear. Thus the San Jacinto fault zone provides an excellent natural laboratory for
studying lithospheric strength and the coupling relationship between the lower crust and
the mantle.
Figure 4.1 is a generalized geologic map of the region showing the variations in the rock
types in the San Jacinto fault zone (Jennings, 1977; Wallace, 1990). The majority of the
rocks are Mesozoic plutonic rocks of the southern California batholiths (light purple in
Figure 4.1) and similar-aged metamorphic rocks (dark purple in Figure 4.1). Both of
these rock types have relatively high seismic velocity (Vp = 3.6 – 5.0 km/s Barton, 2007).
But there are also Quaternary deposits (dark yellow in Figure 4.1) with relatively low
seismic velocity (Vp = 1.4 – 4.2 km/s, Barton, 2007) near the fault trace. The distribution
of these rock types at depth is unclear.
44

Figure 4.1: Geologic map of San Jacinto Fault Zone area (Jennings, 1977; modified by USGS). The area in
black box is shown in Figure 4.2.

4.2 Receiver Gathers
To better understand the subsurface structure beneath the San Jacinto Fault Zone (SJFZ),
receiver gathers profiles grouped by back-azimuth for 11 stations in the region (Figure
4.2). The locations of P to SV converted points for all events are calculated at the depth of
30 km and marked as crosses on the figure. As can be seen from the map, there is good
45
coverage within a 30 km by 100 km area centered along the fault. The teleseismic
waveform data are band-pass filtered (0.02–1.5 Hz) and then a time–domain
deconvolution techniques were applied to obtain the RFs. Details on data selection,
deconvolution and stacking are described in Chapter 2.

Figure 4.2: Map of the San Jacinto Fault zone area. Fault traces are shown as light grey lines. The red
triangles represent the broadband seismic stations used in this study. Crosses are the P to SV converted
points for all the used events calculated at a depth of 30 km. The color of yellow, green, red, and blue
represent NE, NW, SW, SE directions respectively, which corresponds with the colors used for the receiver
functions in Figure 4.3.
Figure 4.3 shows the radial component of receiver function (RF) gathers for 11 seismic
stations in SJFZ area. Transverse RF gathers are shown in Appendix A. Radial and
46
transverse RFs are defined in Section 2.2.1 (Equations (2) and (3)). The RF gathers are
plotted by back azimuth and four back azimuth bins are divided and colored
corresponding to the piercing points in Figure 4.2, where NE, NW, SE and SW are
colored by yellow, green, red, and blue respectively. The time window shown is between
0 to 15 s, which is long enough to include direct P signal, converted wave signal from the
Moho, and multiple reflected/converted signals from the Moho. The first positive arrival
at 0 s is the direct P arrival, and the second positive arrival at around 4 s is the converted
wave signal from the Moho (Pms). The other subsequent signals are considered multiple
reflected/converted signals from the Moho, such as PpPms, which is the secondary
converted phase at the Moho discontinuity and arrives at 10s in the profiles (Figure 4.3).
These multiples can be used in H-K receiver function studies to better constrain the Moho
depth (e.g., Zhu and Kanamori, 2000). In this study we do not use the H-K technique
because of the strong back azimuth dependence of the multiples makes application of this
technique difficult.
For stations that are very near the fault trace, such as TRO and KNW (Figure 4.2), the
signals become very complicated (Figure 4.3). There are additional phases before and
after the converted signal from Moho at ~ 4 s. Moreover, the arrival times of Pms signals
recorded at KNW show strong back azimuth dependence. For example, the Pms signal
arrives at 4 s from the SE direction, at 5 s from the SW direction, and arrives at 4.5 s from
47
the NW direction. Another interesting feature for the RFs at station TRO is its signal
pattern for SW bin. There is a negative phase at 6 s, which is 2.0 s later than the phase
associated with Pms for SW group (red) at station TRO. This negative phase is appears
throughout the events in the SW bin and has a similar amplitude as that of the Pms.
Moreover, there is an additional positive phase with amplitude slightly larger than Pms
follows ~1 s after the negative phase. The map of piercing point (Figure 4.2) shows that
the SW bin (red) of TRO is located across the fault trace, which implies that the negative
phase could be caused by the subsurface structure beneath the fault trace.
For stations located away from the fault zone (Figure 4.3, >5 km to the fault trace), such
as BZN, FRD, PFO and RDM, the delay times of Pms with respect to the direct P are
consistent within each back azimuth bin for the single station. However, the delay times
of Pms with respect to direct P have variations as large as 25% for the different stations in
the region. For stations located on the northwest side of the fault, such as RDM, the delay
times of Pms with respect to the direct P are 5 s. For stations east of the fault, such as
PFO, the delay times are 3.5 s. Using the SCEC average 1D model (averaged from SCEC
3D CVM by Pleasch et al., 2009)) for conversion, the time difference of 1.5 s amounts to
~10 km difference.
For stations that are located within 5 km to the fault trace, the delay time of Pms with
respect to the direct P shows a complicated pattern. For station CRY, the delay time of
48
Pms with respect to the direct P varies with different back azimuths. For the back azimuth
bin of SE (blue), it increases rapidly from 3 to 4.5 s; for the back azimuth bin of SW (red),
it decreases slightly from 5 s to 4 s; and for the back azimuth bin of NW (green), it
remains at 4 s. If the RFs which are deconvoluted in the time-domain are converted into
depth using the SCEC average 1D model (averaged from SCEC 3D CVM by Pleasch et
al., 2009), a ~8 km offset at the Moho depth between two sides of the fault is inferred.
This feature also exists with other 1D velocity model such as PREM (Dziewonski and
Anderson, 1981) and TNA (Grand and Helmberger 1984).

Figure 4.3: Radial component RF gathers profile for the 11 seismic stations. The locations of the
stations are shown on Figure 4.2. The receiver gathers are plotted by back azimuth. The first positive
arrival at 0 s is the direct P arrival, and the second positive arrival at around 4 s is the converted wave
signal from the Moho (Pms). The other following arrivals are considered as multiples.
49

Figure 4.3: continued
50

Figure 4.3: continued
Besides radial RF gathers shown in Figure 4.3, transverse RF gathers are shown in
Appendix A. Theoretical part of radial and transverse RF is discussed in Section 2.2.1
(Equations (2) and (3)). Transverse RF is closely related to anisotropic structure. For pure
isotropic structure, the transverse RF is all zero. For anisotropic structure, any energy
shown in transverse RF is caused by the anisotropy or dipping structure (Savage, 1998).
As can be seen from Appendix A, all transverse RFs appear strong energy, which indicate
strong anisotropy beneath the San Jacinto Fault Zone. Moreover, for stations near the
fault trace, such as CRY, KNW, TRO, their transverse RFs show as strong back azimuth
dependence as their radial RFs (Figure 4.3). The arrival times of their second positive
signals change in four back azimuth bins. These anisotropic features shown by transverse
51
RFs suggest that the subsurface beneath the fault zone is undergoing strong deformation.

4.3 Bootstrap Error Estimation
In order to determine an estimate of the error and stability of the results we used
bootstrap error estimation (Efron and Tibshirani, 1993). Bootstrap error estimation
involves two steps. First, each station has several RFs as an original set. Then a new set
of receiver functions is created for each station by randomly sampling and replacing from
the original set. The size of the new set is the same as the original one but may consist of
duplicates of certain receiver functions. Second, an average is calculated from the new set.
The above two procedures are repeated for 300 times for 300 receiver functions at each
station. Then mean value and standard deviation for the 300 receiver functions are
calculated. Table 1 lists the mean value and standard deviation for the Moho depth of the
eleven stations in the San Jacinto region (Figure 4.2).

52
Table 1: Mean and standard deviation for the Moho depth of the eleven stations
Station
Average Depth for
the Moho (km)
Standard
Deviation (km)
BVDA2 30.0664 1.6565
BZN 27.3801 0.863
CRY 29.7978 2.3089
FRD 29.6646 0.7594
KNW 23.0379 1.7938
LVA2 30.1892 1.8473
PFO 25.753 1.2226
RDM 32.2809 2.1271
SND 35.6486 1.3498
TRO 24.9077 0.9509
WMC 28.1272 3.0339
As can be seen from Table 1, the average Moho depth is up to 35 km on the west side of
SJF and as shallow as 25 km on the east side of SJF. Meanwhile, the stations that are
close to the fault trace, such as CRY, WMC, RDM, usually have larger standard
deviation than other distant stations.
53
Possible reasons for the error includes: 1) human error produced in picking the Moho
signal. Since the signal from the Moho is not a perfect pulse but with some width, there
will be errors when the arrival time of the Moho is determined by hand. This kind of error
should not be larger than half of the width of the pulse (less than 3 km) and therefore is
not significant. 2) At certain stations, such as TRO and KNW, there exist two signals
from the Moho, with 2-3 s time difference in their arrival times. Either of them could be a
signal from the Moho, but corresponding to different Moho depths. If the earlier one is
considered as the signal from the Moho, the latter one should be diffraction or multiple; if
the latter one is considered as the signal from the Moho, the earlier one should be the
signal from a middle-crustal structure. Determining the Moho signal is based on
experience and consistency with nearby receiver functions. 3) Other factors might cause
large noise that could lead to errors in the receiver functions. These factors include a)
quality of the equipment b) geologic feature such as the damage rock in the fault zone.
But this kind of error is considered to be systematic and difficult to estimate its
significance.

4.4 CCP imaging
Besides back azimuth analysis for receiver gather profiles, common conversion point
(CCP) stacking is used in this section to provide a straightforward image of the
54
subsurface structure. Figure 4.4 shows CCP stacking images for three cross sections that
run perpendicular to the San Jacinto Fault. The cross section locations are plotted as blue
lines on the left map of Figure 4.4. The receiver functions used in each cross section are
projected onto the profiles along the black dashed paths. These were then stacked to
produce the structural image on right side of Figure 4.4. More detailed information about
the methodology used CCP stacking is discussed in Section 2.3.

Figure 4.4: Common conversion points (CCP) stacking of P receiver functions along three profiles in
San Jacinto Fault Zone. Fault traces are shown as grey lines on the map. Positions of cross sections are
plotted on map on the left. Red crosses represent stations used. The yellow triangle is station CRY.
Locations of Elsinore fault (EF), Coyote Creek Fault (CCF) and San Jacinto fault (SJF) as well as
possible Moho boundary are marked on the stacking profiles. Note that small Moho offset can be seen
beneath major faults.
55
The left side of Figure 4.4 shows the CCP stacking results for the three profiles. The
second positive amplitude (red) is labeled as the converted wave signal at the Moho
discontinuity (Pms). The second blue amplitude represents a negative gradient in the
velocity, which we interpreted as the lithosphere and asthenosphere boundary (LAB). In
this study we would not discuss further into the interpretation of the LAB because it is
not the topic of this study. Locations of Elsinore fault and San Jacinto fault are labeled on
the top of each cross section. It can be seen that the Moho is not flat and has some
variation in topography.
On A-A’ and B-B’ profiles, the Moho is offset up on the northeastward side of the San
Jacinto Fault by approximately 5-10 km. This offset is consistent with the result of
receiver gathers profile of station CRY, which is located between A-A’ and B-B’ (yellow
triangle in Figure 4.2). But on the C-C’ profile, the Moho is offset down northeastward
side of the fault by ~ 5 km. On C-C’ cross section across the northern part of Coyote
Creek Fault that runs parallel to the main SJF trace, and the Coyote Creek Fault is not in
the other profiles (AA’ and BB’). This implies that these smaller discrete faults extend at
least to the base of the crust as separate ductile shear zone. The reversal of vertical
separation direction across the Moho could be related to horizontal offset of laterally
varying Moho “topography”.
For LAB, there exist some variations. On the CC’ profile, it is offset down northeastward
56
beneath the SJF, but on AA’ and BB’ profiles, there is no obvious offset beneath SJF.
Considering the fact that only CC’ profile across the Coyote Creek Fault, it is possible
that the LAB offset beneath CC’ profile is caused by the fault. Meanwhile, the LAB
offset beneath CC profile has similar trend as the Moho offset, which implies that the
Coyote Creek Fault might extend into the lithosphere. The LAB beneath the Elsinore
fault is noisy and difficult to interpret. The largest uncertainty in the LAB signal is likely
due to contamination of the signal due to the multiples as P phases arrive prior to S
phases. Therefore, for interpretation of deeper structure such as the LAB, S receiver
functions that use S-to-p conversions can be better as it avoid contamination of crustal
multiples to provide a more reliable and resolvable result (Yuan et al., 2006).

4.5 Synthetic Results
4.5.1 Model Description
As discussed in the receiver gathers profile and CCP stacking in Section 4.2 and 4.4, an
8-10 km Moho offset is interpreted beneath the San Jacinto Fault. But the geometry of the
offset is not well understood. In this section synthetic modeling is used to better quantify
the geometry of the offset. Six possible geometries are constructed for the synthetic
modeling: one with a 10 km step in the Moho, one with a 5 km wide and 10 km vertically
57
offset ramp, one with a 15 km wide and 10 km vertically offset ramp (Figure 4.5).
Besides, using the tomography study of Allam and Ben-Zion (2012), which suggest a ~20%
Vp velocity contrast and ~15% Vs velocity contrast in the top few kilometers in the San
Jacinto Fault Zone, we chose models of flat Moho at 30 km depth but with velocity
contrast of 10% and 20% in the crust to better understand how much the velocity contrast
contributes to the apparent depth variation in the receiver gathers.
Figure 4.5 describes the models used in this study. Station 48 is designed to represent
station CRY from our observations, whose receiver gathers show strong back azimuth
dependence (Figure 4.3) and lead to the interpretation of a Moho 10 km offset across the
San Jacinto Fault. An elastic plane wave is introduced to simulate teleseismic waves from
0 to 360 degree back azimuths with 10 degree spacing to match the real data, which has a
full coverage of all back azimuths. Details of the synthetic methodology are discussed in
Section 2.4.
58

Figure 4.5: Velocity models with four possible geometries in a two dimensional model of homogeneous
elastic media, with a width of 500 km and depth of 300 km.: 1) a step in the Moho (blue), 2) a 5 km wide
and 10 km vertically offset ramp (green), 3) a 15 km wide and 10 km vertically offset ramp (red), 4) a flat
Moho at 30 km depth (light blue). 101 stations with spacing of 1km are placed linearly and symmetrically
along the surface, and station 48 represents station CRY from our observational data.
The receiver function method requires the incident plane to be nearly vertical. As a result,
a very limited range of incident angles qualify for the computational experiment. In the
first set of simulations the incident angle is fixed and the back azimuths are increased by
every 10 degrees (Figure 4.7). For the second set of simulations the back azimuth is fixed
at SE (135 deg) and SW (315 deg) direction respectively, and incident angle increases
gradually to study further details (Figures 4.8 and 4.9).

59
4.5.2 Synthetic Receiver Function Results
Synthetic seismograms are cut, bandpassed, rotated, and deconvoluted using the same
methodology and parameters as the observational data was to generate P synthetic
receiver functions. Section 2.4 provides more details about the methodology of synthetic
modeling and section 2.2.2 describes the processing of the seismograms.
As discussed in section 4.2 the receiver gathers of station CRY show a strong back
azimuthal variation of the Moho signal (Figure 4.6). The arrival times of the Moho signal
increase with the back azimuth within the NE and SE bins. Figure 4.2 shows that the
piercing points from these two quadrants (yellow and blue) are located at the fault trace.
When this difference in time is converted into the depth, an 8~10 km offset beneath the
San Jacinto Fault is inferred.
Figure 4.7 presents the synthetic receiver functions for station 48, which represents the
location of station CRY , which is closest to the surface trace of the fault and has very high
signal to noise ratios. The results are shown for model of a) a flat Moho, b) Moho with
a 10 km vertical step, c) Moho with a 5 km wide and 10 km vertical ramp, d) Moho with
a 15 km wide and 10 km vertical offset ramp, e) flat Moho but with 10% velocity contrast,
and f) flat Moho but with 20% velocity contrast. The first positive arrival at 0 s is the
direct P arrival, and the second positive arrival at around 4 s is the converted wave signal
60
from the Moho. The other following arrivals are considered as multiples and not
important in this study. One feature that distinguish model e) and f) is the clear variation
of the arrival times for the direct P wave, which is inconsistent with model a), b), c) and
d), and the observations. Additionally, the direct P pulses for model e) and f) are wider
than that for the other models. As can be seen from the top of Figure 4.7, there is no
obvious variation for direct P arrival in the profile of CRY, which is consistent with
synthetic results in model a), b), c), and d). The inconsistency of the direct P between
model e), f) and the observation implies that the velocity contrast in SJFZ should be
much less at depth and contribute less to the variation we observe in the receiver gathers.
One important result is that the synthetics in Figure 4.7 b), c) and d) show a back
azimuthal dependence for the converted wave signal from the Moho. The arrival times of
the second positive arrivals in b), c) and d) decrease with the increase of the back azimuth
in the bin of NE direction, then increase as the back azimuth increases in the bin of SE
direction. The earliest arrival time of ~2.5 s comes from a back azimuth of 100 degrees.
The latest arrival time of ~ 3.5 s for the Moho signal is reached at the back azimuth of
250 degrees.
Another significant feature that distinguishes model b), c) and d) from model e) and f) is
the splitting of the second arrivals at 3-4.5 s that can be seen on the b), c) and d) profiles,
forming a convex shape in the receiver gathers. The splitting is considered to be caused
61
by change of velocity at the offset. In addition, by comparing model b), c) and d), which
have different widths of the offset, it can be seen that the width of the convex shape is
inversely proportional to the width of the offset. Meanwhile, a larger magnitude convex
shape can be seen in the receiver gathers for station CRY, which fits b) and c) better than
d) in Figure 4.7. The convex shape is very wide for CRY, which indicates that the offset
should be very sharp, with width no more than 5 km.

Figure 4.6: Receiver function gather for station CRY .
62

Figure 4.7: A-F: Synthetic receiver gathers for CRY (station 48) plotted by back azimuth for six
different models. Red pulses are positive and blue are negative. Note the variation in signal for the
first positive signal after the primary P arrival.
To better distinguish the difference between the model with step in the Moho and the one
with 15 km ramp in the Moho, synthetic receiver functions are calculated with regularly
spaced plane wave incident angles (Figures 4.8 and 4.9).
Figure 4.8 shows synthetic receiver gathers with plane waves originating from SE
direction (back azimuth of 135 degrees). One obvious feature on both profiles is that the
amplitude of both direct P and converted phase from the Moho increase with the incident
angle. For the model with a step in Moho (right), the second signal, which comes from
the Moho, splits into two pulses. The splitting is considered to be caused by the dramatic
63
change in depth (both in the step and ramp models) of the Moho. When the change in
velocity becomes smaller, the splitting becomes less obvious. For the model with a 15 km
ramp in Moho (left), the splitting in Moho signal is not observed compared with the step
model (right).
Figure 4.9 shows the synthetic receiver gathers using plane waves from SW direction
(back azimuth of 225 degrees). There is a clear trend for the amplitude of both direct P
and Moho signals increase with the incident angle. For the model with a step in Moho
(right), small positive amplitude can be observed at ~1.5s between direct P and Moho
arrival at larger incident angles (25 to 35 degrees). Same signal is not observed for the
model with a 15 km ramp in Moho (left) because the change of velocity becomes smaller.

Figure 4.8: Synthetic receiver gathers with plane waves originating from SE direction for model with a step
in Moho (right) compared to the model with a 15 km ramp in Moho (left)
64

Figure 4.9: Synthetic gathers with a plane wave originating from SW direction for the model with a step in
Moho (right) compared to the model with a 15 km ramp in Moho (left)

4.5.3 Vertical Resolvability and Horizontal Effect Test
It is very important to know how narrow a vertical step the RF can resolve. Thus,
synthetic RF modeling for 10, 7.5, 5, and 2.5 km step models are conducted to test its
vertical resolvability. Figure 4.10 shows the results for this test. It can be seen that the RF
can resolve step structure at vertical distance of 10, 7.5, 5 km but cannot resolve at 2.5
km. Furthermore, by comparing the results with the real data (Figure 4.6), the 10 and 7.5
km step model best fit the real data. Therefore, our initial interpretation of an 8–10 km
Moho step is reasonable.
65

Figure 4.10: RF gather profiles for 10, 7.5, 5, and 2.5 km step models.
The receiver gather profile is also highly sensitive to the perpendicular distance of the
station to the fault step. The farther away, the more narrow the back-azimuth window that
will express the presence of the fault. Figure 4.11 shows a series of synthetic receiver
gather profiles for the 10-km step model to test horizontal effect. As can be seen from
Figure 4.5, the fault offset is located beneath station 50. The Moho is set at 35 km depth
to the left of the fault, and at 25 km depth to the right of the fault. Back azimuth between
0-180 deg are for the right side (shallow Moho), whereas 180-360 deg will see the left
side (deeper Moho). For Figure 4.11, the bottom row panels are for stations +10, +20,
66
+30 km right of the fault (shallow Moho). The top row shows -30, -20, -10 km left of
the fault (deeper Moho). The middle row shows the station directly over the fault. It can
be seen that the +30 km panel shows a flat and shallow Moho, and the -30 km panel
shows a flat and deep Moho. It indicates that the fault step does not affect stations further
than 30 km away. At 0 km, effects caused by the step appear in the full back-azimuth
range (both side of the fault). For east side (0-180 deg), there are two curving pulses
appearing between 2-4 s, and the arrival times of these pulses change with the back
azimuths. For west side (180-360 deg), there are three pulses appearing between 1.5-4 s.
For -20 and -10 km panels, there is no obvious step feature (triple-bump) shown in west
back azimuth (180-360 deg). There is a step feature (curving double-bump) shown in
20-180 deg for -10 km panel, and in 50-150 deg for -20 km panel. Similarly, for +20 and
+10 km panels, there is no obvious step feature (curving double-bump) shown in east
back azimuth (0-180 deg), but there is step feature (triple-bump) shown in 200-340 deg
for +10 km panel, and in 230-330 deg for +20 km panel. These features confirm the
assumption that receiver gather profile is highly sensitive to the perpendicular distance of
the station to the fault step, and the farther away, the more narrow the back-azimuth
window that will express the presence of the fault.
67

Figure 4.11: A series of synthetic receiver gather profiles for the 10-km step model to test horizontal effect.
The bottom row panels are for stations +10, +20, +30 km right of the fault (shallow Moho). The top row
shows -30, -20, -10 km left of the fault (deeper Moho). The middle row shows the station directly over the
fault. Within each receiver gather profile, the fault trace runs along back azimuth (BAZ) 0 deg (north) and
180 deg (south), separating the shallow Moho (BAZ 0-180 deg) from the deep Moho (BAZ 180-360 deg).
Therefore, synthetic modeling results show that a model of Moho with an 8-10 km step
best fits our observations. Together with the back azimuth analysis and CCP image, we
68
interpret that the Moho beneath the San Jacinto Fault zone is offset by 8-10 km in depth
over a lateral distance of less than 5 km. Chapter 5 provides a detailed discussion of our
interpretation and remaining questions for future study.

69
Chapter 5 Discussion and Conclusion
Our results show depth variations for the Moho in southern California, which can be
strongly connected to tectonic regions. In our detailed study of the San Jacinto fault we
find that there is a vertical separation of the Moho of 8-10 km over a lateral distance of
less than 5 km. We conclude that this step in the Moho is related to the rheology of the
lower crust and the upper mantle and could provide implications for the strain
localization beneath the strike-slip fault.
5.1 Rheology of the Lower Crust and the Upper Mantle
It is commonly believed that the lithosphere consists of three rheologically different
layers: the upper crust, the lower crust and the upper mantle (e.g., Barrell, 1914;
Burgmann and Dresen, 2008). Moreover, it is widely accepted that the upper crust is
brittle and therefore can accommodate strain in form of elastic earthquakes (Byerlee,
1978). However, the rheology and strength of the lower crust and the upper mantle are
still debated (e.g., Jackson, 2002; Burov and Watts, 2006). There are three competing
models (Figure 5.1): a) Jelly sandwich model (Figure 5.1a), which describes a strong
upper crust, relatively weak lower crust, and strong upper mantle (e.g., Chen and Molnar,
1983; Hirth and Kohlstedt, 2003); b) Crème Brulee model (Figure 5.1b), which has a
strong upper crust, strong lower crust, and weak upper mantle (Jackson, 2002); and c)
70
Banana split model (Figure 5.1c), with relative weakness of all three layers (Zoback et al.,
1987).

Figure 5.1: Schematic view of three models for the strength of continental lithosphere. a) Jelly sandwich
model which describes a strong upper crust, relative weak lower crust and strong upper mantle (e.g., Chen
and Molnar, 1983; Hirth and Kohlstedt, 2003); b) Crème Brulee model which has a strong upper crust,
strong lower crust and weak upper mantle (Jackson, 2002); and c) Banana split model with relative
weakness of all three layers (Zoback et al., 1987). [Figure made by Burgmann and Dresen, 2008]
Evidence from laboratory experiments and synthetic modeling suggests that rock
rheology is affected by many different factors, including: mineralogy, presence or
absence of water and partial melt, mineral grain size, temperature, and pressure (e.g.,
Bystricky and Mackwell, 2001; Hirth and Kohlstedt, 2003; Freed and Burgmann, 2004;
Dimanov and Dresen, 2005; Chen et al., 2006; Burgmann and Dresen, 2008). For
example, Hirth and Kohlstedt (2003) conducted rock mechanics experiments for a strong
upper mantle. Their results suggest that the presence of water and partial melt weaken the
upper mantle, where as an increase in stress increases the strength, yet an increase of
temperature causes reduction in strength. Therefore, they infer a strong upper mantle is
71
likely to be cold and dry, which can be seen beneath the cold and dry Precambrian
continental craton (Hirth and Kohlstedt, 2003). Unfortunately, conditions pertaining to
the upper mantle beneath Phanerozoic continents are not clearly understood, and fewer
experimental data are available due to the complexity of both the composition and the
structure beneath these active regions. Other experiments on pyroxenes, which are major
mineral components in lower crustal granulites and upper mantle peridotites, suggest
decreasing grain size will weaken the samples (Bystricky and Mackwell, 2001; Chen et
al., 2006). Although the extrapolation of laboratory data does improve our knowledge of
rock mechanics, the reliability of laboratory experiments is still debated because of the
significant differences between experiment and nature in both spatial and temporal scales
(Burgmann and Dresen, 2008).
Geodetic studies regarding post-seismic deformation of large earthquakes also provide
insight into rheology at depth (Savage and Svarc, 1997; Deng et al., 1998; Pollitz et al.,
2001; Owen et al., 2002; Kenner and Segall, 2003; Fialko, 2004; Freed and Burgmann,
2004;). Some studies support a relatively weak lower crust (Deng et al., 1998; Kenner
and Segall, 2003), but other studies suggest a relatively strong lower crust (Savage and
Svarc, 1997; Owen et al., 2002; Fialko, 2004). Pollitz et al (2001) and Freed and
Burgmann (2004) studied post-seismic deformation after the Landers and Hector Mine
earthquakes, and they found that the upper mantle is strong and some of the initial
72
post-seismic relaxation was released in form of elastic earthquake stress.
From our PRF analysis we produced a map of the Moho topography beneath southern
California. As can be seen from Figure 3.2, there are clear depth variations for the
different tectonic provinces. A very shallow Moho of around 20 km is observed in the
Salton Trough, where continental rifting is occurring (e.g., Atwater, 1989). The thinning
of the crust in this region indicates that the lower crust is strongly coupled and deformed
with the upper crust. Lekic et al. (2011) used teleseismic S receiver function analysis and
found a thin lithosphere in this region, which they infer that the upper mantle is also
coupled to and deforms with the crust.
For those provinces that have experienced intensive compression, such as the Transverse
Ranges, San Gabriel Mountains, and San Bernardino Mountains, the Moho structure is
much more complicated. A deep Moho of 34-39 km is observed beneath the San
Bernardino Mountains. A shallower Moho of 28 km is observed in the central Transverse
Ranges, while a deeper Moho of 35 km is observed in the eastern and western Transverse
Ranges. These variations are the result of the compressive stress, and suggest that the
lower crust is strongly coupled and deformed with the upper crustal blocks. Moreover,
using the same broadband seismic data and P receiver function technique as Yan and
Clayton (2007), our receiver gather analysis (Section 3.2) confirms their conclusion of a
vertical Moho step beneath the San Andreas fault in the San Gabriel Mountains (Zhu,
73
2000; Zhu, 2002; Yan and Clayton, 2007).
5.2 Deformation in the Lower Crust beneath Strike-slip
Faults
The degree of strain localization at depth beneath strike-slip faults is of particular interest.
As discussed above, experimental and geodetic studies have several disadvantages and
challenges. Documenting the deformation at depth beneath strike-slip faults provides
another approach to study the rheology of the lower crust and the upper mantle.
It is commonly believed that the deformation in the upper crust along a strike-slip fault is
concentrated into a very narrow zone (Byerlee, 1978). But whether the deformation in the
lower crust and upper mantle is localized or distributed is still debated (Holbrook et al.,
1996; Henstock et al., 1997; Wilson et al., 2004; Yan et al., 2007). Distributed
deformation implies weakness, whereas localized strain suggests strength. Platt and Behr
(2011) suggest that the cumulative width of ductile shear zones in the lower crust and the
upper mantle could reach as wide as hundreds kilometers for quartz-rich material, or as
narrow as a few meters for feldspathic material. Many rock mechanics experiments and
geodetic studies provide evidence to support the viewpoint of a relatively weak lower
crust (Deng et al., 1998; Kenner and Segall, 2003; Hirth and Kohlstedt, 2003), however,
little seismic evidence is found. Most seismic studies of other strike-slip faults suggest
74
that these faults cut through the entire crust (McGeary, 1989; Henstock et al., 1997;
Parsons, 1998; Zhu, 2000; Zhu, 2002; Weber et al., 2004; Yan et al., 2007). For example,
Henstock et al.’s (1997) study of the crustal structure beneath northern California using
seismic reflection data indicates that the top of the lower crust is offset by 5 km, and the
Moho is offset 2 km over a lateral distance of less than 5 km beneath both the San
Andreas and Maacama strike-slip faults. Similarly, Parsons (1998) suggested that the
Hayward fault extends into the lower crust in San Francisco Bay area from seismic
reflection data, and inferred that strain is localized along high-angle faults throughout the
crust. From seismic reflection profiles, McGeary (1989) suggested that the Moho is
vertically separated by 2–3 km over a lateral distance of less than 6 km beneath the Walls
Boundary strike-slip fault in Scotland. Weber et al. (2004) showed that the seismic crustal
basement is vertically displaced by 3–5 km under the Dead Sea Transform, using seismic
reflection and refraction data. Furthermore, evidence from tomography and shear wave
splitting suggests that the strike-slip system extends through the entire lithosphere
beneath the Altyn Tagh fault in Tibet (Wittlinger et al., 1998; Herquel et al., 1999). Yan et
al. (2007) and Zhu et al. (2000, 2002) studied the Moho beneath the San Gabriel
Mountains using receiver functions, and both groups suggested a notch structure vertical
offset of the Moho beneath the San Andreas fault. Our receiver gather analysis using the
same data, but a more precise velocity model, confirms their conclusions (Section 3.2).
75
For our study in the San Jacinto Fault zone (SJF), as discussed in Section 4.4, our CCP
stacking result shows that the Moho depth is 32 ~ 35 km in the west side of the SJF and
25 ~ 28 km on the east side of the fault. Moreover, there is a vertical Moho step directly
beneath the San Jacinto fault. The vertical offset structure is estimated to be ~10 km
(Figure 4.5). Evidence from the receiver gathers further supports this inference. There
appears to be strong back azimuth dependence in the receiver gathers for several stations
located on the fault trace, and the map shows that their piercing points are located on
either side of the fault (Figure 4.2). The vertical step indicates that the fault extends
throughout the entire the crust as a discrete shear zone. Although Allam et al. (2012)
propose a high velocity contrast across the SJF, our synthetic modeling results suggest
that a velocity contrast as large as 20% across the SJF is not a major contributor to the
interpreted offset (Figure 4.7). The synthetic modeling results also refute the Moho model
with a 15-km-wide ramp structure, and suggest that the model with a vertical step or a
<5-km-wide ramp more accurately represents the data. These results indicate that the
deformation in the lower crust is concentrated in a narrow zone (less than 5 km wide)
rather than being distributed in a broad zone. Figure 5.2 shows a schematic for our
interpreted structure beneath the San Jacinto Fault zone. These results also allow us to
infer a relatively strong lower crust beneath the central SJF, which agrees with estimates
that the seismogenic zone in the central SJF extends as deep as 20 km (Figure 2e in
76
Wdowinski, 2009). Our interpretation of strain localization beneath the SJF agrees with
other receiver function, reflection and refraction studies beneath the San Gabriel
Mountains, and beneath the northern and central part of the San Andreas fault (McBride
and Brown, 1986; Henstock et al., 1997; Parsons, 1998; Zhu, 2000; Zhu 2002; Yan et al.,
2007), and along other major strike-slip faults (McGeary, 1989; Weber et al., 2004). In
contrast, our results differ from the conclusion of Wilson et al.’s (2004) study of the
Marlborough strike-slip fault system in New Zealand.

Figure 5.2: A schematic for our interpreted structure beneath the San Jacinto Fault zone. The Moho is offset
by ~ 10 km vertically within 5 km width. The strain is localized within the fault zone.
As shown in Figure 4.7, our synthetic modeling results suggest that even a velocity
contrast as large as 20% across the SJF is not a major contribution to the interpreted
77
vertical step beneath the SJF. However, it is possible that the Moho offset structure could
be related to the juxtaposition of two blocks with different Moho depths along the fault.
Based on geologic studies, the total cumulative strike slip accumulated on the SJF is
estimated to be 24 km since its initiation at 1.5 Ma (Rockwell et al. 1990; Langenheim et
al. 2004; Kirby et al. 2007). Although the majority of the rocks on either side of the SJF
are lithologically similar (granitic and metamorphic rocks - see Figure 4.1 for more
details), the total slip of 24 km is far enough to cause the juxtaposition of two blocks with
different Moho depths. Furthermore, Sharp (1965) suggests the southwestern block has
risen between 0.5 and possibly 8 miles (0.8 – 13 km) near Anza based on geometric
extrapolation of the various geologic contacts. The estimated vertical component of this
differential uplift at the surface is consistent with the estimated height of vertical Moho
step at depth.
The Moho offset structure could also be a result of the build up and rotation by
compressive stress (Peacock et al., 1988; Crampin et al., 1990; Aster and Shearer, 1992;
Hartse et al., 1994), which also causes the ANZA seismic gap. Evidence from shear wave
splitting suggests that major orientation of the stress field in the SJFZ is north-south, but
shear wave splitting results at station KNW show a 𝑁 40° 𝑊 direction of maximum
compressive stress (Peacock et al., 1988; Crampin et al., 1990; Aster and Shearer, 1992).
Hartse et al. (1994) propose a model to describe the change of the stress field, in which a
78
block rotation is superimposed on the right-lateral strike-slip motion. Their proposed
model satisfies the first-order observations of stress orientation, faulting, and horizontal
surface strain. Therefore, we must also consider that the Moho offset could be a result of
this type of block rotation.
Our results of Moho depth variations in southern California (discussed in Chapter 3 and
Section 5.1) and Moho offset beneath the San Jacinto fault zone (discussed in Chapter 4
and Section 5.2) suggest that strain is highly localized within the lower crust, and we
therefore infer a relatively strong lower crust. As can be seen from Figure 5.1, model b)
(“Crème Brulee”) has a strong lower crust, with an absolute differential stress value of
250~500 MPa, which is consistent with our result. Evidence to support the idea of a weak
lower crust (models a and c) is not found in this study. But for upper mantle strengths,
our initial CCP stacking result (Figure 4.4 and Section 4.4) also shows variations for the
depth of the lithosphere and asthenosphere boundary (LAB), which suggest that the SJF
may be a discrete ductile shear zone throughout the entire lower lithosphere. This, in turn,
is consistent with the inference of a strong upper mantle. But while our results suggest
that the strength of the lower crust and the upper mantle should be strong enough for the
strain localization, their relative strength of them cannot be determined by this study.
Based on the above discussions, we suggest a series of potential avenues for future work.
First, some evidence suggests that a strike-slip system can extend entirely through the
79
lithosphere, as seen for the Altyn Tagh Fault in Tibet (Wittlinger et al., 1998; Herquel et
al., 1999). But the structure of the lithosphere beneath other strike-slip faults is still not
well understood, including the San Jacinto fault. Our initial results from CCP stacking of
receiver functions beneath the SJF show a variation in depth for the lithosphere
ashenosphere boundary (LAB). It would be worthwhile to use S receiver functions, with
back azimuthal analysis and synthetic modeling to study whether there is a vertical step at
the LAB depth beneath the SJF. S receiver functions could avoid the complication of
multiples of P receiver function at LAB depths. Synthetic modeling could then be
conducted to confirm and constrain the geometry of the LAB. Second, the Moho offset
we observe beneath SJF (Figure 4.4, 4.6, 4.7) provides a possible model for numerical
modeling. As discussed above, our results suggest that the strength of the lower crust and
the upper mantle should be strong enough for the strain localization, but the relative
strength between the lower crust and the upper mantle is still not well understood. More
evidence from geodynamic modeling is needed to decide which model best fits the
rheology in southern California. Moreover, geodynamic modeling could be conducted to
test the rheological features beneath less structurally mature fault zones and compare to
more mature fault zones such as the San Andreas. Third, the evidence of the Moho offset
supports the idea of a strong lower crust, however, because of the limited coverage of the
seismic array currently available more detailed analysis is currently impossible. With
80
more stations and more data it may be possible to better determine whether the strong
lower crust exists only near the fault zone or if it also exists away from the fault zone.
Additional coverage of broadband seismic stations plus a combination of geodetic or
laboratory experiment is needed to solve this question.

81
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91
Appendices
Appendix I and II provides information for the stations and events used in this study.
Appendix III provides the transverse RF gathers for the stations in the San Jacinto Fault
zone. Appendix IV provides a collection of radial RF gathers for all stations in southern
California. In general, radial RF can be related to isotropic structure, and transverse RF
are related to anisotropic structure. The methodology and theoretical definition of radial
and transverse RF is described in Section 2.2.1 (Equations (2) and (3)).
Appendix I: Stations Information

Network Station Latitude Longitude
AZ BVDA2 33.3265 -116.366
AZ BZN 33.4915 -116.667
AZ CPE 32.8889 -117.105
AZ CRY 33.5654 -116.737
AZ FRD 33.4947 -116.602
AZ HWB 33.0262 -116.96
AZ KNW 33.7141 -116.712
AZ LVA2 33.3516 -116.562
AZ MONP 32.8927 -116.423
AZ MONP2 32.892 -116.422
AZ PFO 33.6117 -116.459
AZ RDM 33.63 -116.848
AZ SCI2 32.915 -118.488
AZ SMER 33.4577 -117.171
AZ SMER2 33.4577 -117.171
AZ SND 33.5519 -116.613
AZ SOL 32.841 -117.248
92
AZ TRO 33.5234 -116.426
AZ WMC 33.5736 -116.675
BK BDM 37.954 -121.866
BK CMB 38.0345 -120.387
BK CVS 38.3453 -122.458
BK FARB 37.6978 -123.001
BK GASB 39.6547 -122.716
BK HOPS 38.9935 -123.072
BK HUMO 42.6071 -122.957
BK JCC 40.8175 -124.03
BK JRSC 37.4037 -122.239
BK KCC 37.3236 -119.319
BK MCCM 38.1448 -122.88
BK MNRC 38.8787 -122.443
BK MOD 41.9025 -120.303
BK ORV 39.5545 -121.5
BK PACP 37.008 -121.287
BK PKD 35.9452 -120.542
BK SAO 36.764 -121.447
BK WDC 40.5799 -122.541
BK WENL 37.6221 -121.757
BK YBH 41.732 -122.71
CI ADO 34.5505 -117.434
CI ARV 35.1269 -118.83
CI BAK 35.3444 -119.104
CI BAR 32.68 -116.672
CI BBR 34.2623 -116.921
CI BC3 33.6552 -115.454
CI BEL 34.0006 -115.998
CI BFS 34.2388 -117.659
CI CHF 34.3334 -118.026
CI CIA 33.4019 -118.415
CI CWC 36.4399 -118.08
CI DAN 34.6375 -115.381
CI DEC 34.2535 -118.334
CI DGR 33.65 -117.009
CI DJJ 34.1062 -118.455
CI DVT 32.6591 -116.101
93
CI EDW2 34.8811 -117.994
CI FMP 33.7126 -118.294
CI FUR 36.467 -116.863
CI GLA 33.0515 -114.827
CI GMR 34.7846 -115.66
CI GRA 36.9961 -117.366
CI GSC 35.3018 -116.806
CI HEC 34.8294 -116.335
CI IRM 34.1574 -115.145
CI ISA 35.6628 -118.474
CI LGU 34.1082 -119.066
CI LRL 35.4795 -117.682
CI MLAC 37.6302 -118.836
CI MPM 36.058 -117.489
CI MPP 34.8885 -119.814
CI MUR 33.6 -117.195
CI MWC 34.2236 -118.058
CI NEE2 34.7676 -114.619
CI OSI 34.6145 -118.724
CI PASC 34.1714 -118.185
CI PDM 34.3034 -114.142
CI PHL 35.4077 -120.546
CI PLM 33.3536 -116.863
CI RCT 36.3052 -119.244
CI RPV 33.7435 -118.404
CI RRX 34.8753 -116.997
CI SBC 34.4408 -119.715
CI SCI2 32.9799 -118.547
CI SCZ2 33.9954 -119.635
CI SDD 33.5526 -117.662
CI SHO 35.8995 -116.275
CI SLA 35.8909 -117.283
CI SMM 35.3142 -119.996
CI SNCC 33.2479 -119.524
CI SVD 34.1065 -117.098
CI SWS 32.9451 -115.8
CI TIN 37.0542 -118.23
CI TUQ 35.4358 -115.924
94
CI USC 34.0192 -118.286
CI VCS 34.4836 -118.118
CI VES 35.8409 -119.085
CI VTV 34.5606 -117.33

95
Appendix II: Events Information

Event data Time Latitude Longitude Depth(km) Magnitude(MB)
2000-01-28 16:39:24 26.066 124.504 194 6.1
2000-07-07 15:46:49 51.464 179.994 69 6.4
2000-07-10 9:58:18 46.86 145.403 358 6.2
2000-07-20 18:39:19 36.625 140.961 49 6
2000-08-19 17:26:27 43.803 147.173 63 6
2000-10-27 4:21:51 26.277 140.522 387 6.1
2000-11-13 15:57:21 42.542 144.758 33 6.1
2000-12-19 13:11:47 11.782 144.76 33 6.3
2001-03-15 13:02:43 -32.237 -71.318 47 6.3
2001-04-14 23:27:30 30.201 141.761 33 6.1
2001-04-19 3:13:29 -7.412 155.924 33 6
2001-06-23 21:27:35 -17.092 -72.373 33 6.3
2001-08-28 6:56:09 -21.484 -69.951 66 6
2001-11-22 4:17:26 -31.045 -176.663 33 6
2002-01-16 23:09:52 15.611 -93.111 76 6.1
2002-02-01 21:55:20 45.544 136.656 353 6.1
2002-03-28 4:56:21 -21.601 -68.13 122 6.3
2002-04-01 19:59:32 -29.483 -71.069 67 6.2
2002-04-18 16:08:36 -27.535 -70.6 62 6.2
2002-04-20 15:59:57 -16.414 173.235 33 6
2002-04-26 16:06:08 13.404 144.599 86 6.6
2002-06-18 13:56:22 -30.754 -70.964 53 6
2002-06-28 17:19:30 43.747 130.702 566 6.8
2002-08-14 13:57:56 14.19 146.13 65 6.1
2002-08-19 11:01:01 -21.697 -179.505 580 6.7
2002-09-15 8:39:31 44.858 130.078 578 6.3
2002-09-24 3:57:22 -31.429 -68.96 120 6.3
2002-10-04 19:05:49 -20.855 -178.957 621 6.1
2002-10-12 20:09:11 -8.27 -71.695 533 6.5
2002-10-16 10:12:21 51.905 157.357 102 6.2
2002-11-17 4:53:50 47.979 146.276 499 6.9
2003-01-04 5:15:04 -20.516 -177.757 377 6
96
2003-01-07 0:54:52 -33.572 -69.762 111 6
2003-03-31 1:06:51 -6.195 151.304 33 6
2003-04-29 13:53:16 43.668 147.757 61 6.1
2003-05-03 5:03:02 -15.166 -173.792 33 6.3
2003-05-26 9:24:32 38.901 141.446 68 6.8
2003-06-16 22:08:01 55.489 159.942 174 6.3
2003-06-20 6:19:38 -7.537 -71.62 556 6.4
2003-07-25 9:37:48 -1.487 149.63 42 6.4
2003-07-27 6:25:33 47.173 139.244 481 6.5
2003-11-06 10:38:04 -19.253 168.84 114 6
2003-11-11 18:48:25 22.315 143.228 114 6
2003-11-12 8:26:44 33.319 136.893 396 6.3
2004-01-25 11:43:11 -16.84 -174.168 130 6.5
2004-04-14 1:54:09 55.185 162.649 51 6
2004-06-10 15:19:57 55.713 160.031 184 6.3
2004-07-15 4:27:14 -17.674 -178.755 566 6.5
2004-07-22 9:45:18 26.545 128.888 44 6.1
2005-01-18 14:09:06 42.915 144.882 42 6.3
2005-02-05 3:34:24 15.989 145.851 139 6.3
2005-02-08 14:48:21 -14.246 167.277 206 6.1
2005-03-21 12:23:54 -24.908 -63.395 579 6.1
2005-04-10 22:22:15 35.601 140.37 43 6.1
2005-04-11 14:54:06 -7.342 -77.846 130 6.2
2005-05-21 5:11:34 -3.285 -80.847 39 6.1
2005-06-13 22:44:33 -19.934 -69.028 117 6.9
2005-07-23 7:34:57 35.506 139.933 66 6
2005-09-09 7:26:43 -4.543 153.457 90 6.3
2005-09-21 2:25:07 43.884 146.159 99 6.1
2005-09-23 13:48:31 16.125 -87.5 30 6
2005-10-05 10:07:26 -20.572 -174.282 48 6
2005-10-15 15:51:07 25.295 123.316 185 6.1
2005-11-17 19:26:56 -22.263 -67.784 163 6.1
2005-11-28 16:41:32 20.302 146.007 42 6.1
2005-12-03 16:10:40 29.364 130.24 30 6
2006-01-02 22:13:40 -19.926 -178.169 583 6.4
2006-01-06 3:40:01 6.652 -82.278 25 6
2006-02-02 12:48:43 -17.767 -178.362 598 6
2006-02-14 15:27:24 20.84 146.178 48 6.2
97
2006-05-16 10:39:24 -31.527 -179.303 152 6.7
2006-05-22 13:08:01 54.307 158.394 183 6
2006-07-16 11:42:45 -28.667 -72.426 34 6
2006-08-17 11:11:35 55.665 161.693 55 6.1
2006-08-24 21:50:36 51.159 157.493 43 6
2006-09-01 10:18:52 -6.822 155.535 46 6.2
2006-09-22 2:32:26 -26.737 -63.013 599 6
2006-09-29 13:08:25 10.91 -61.65 53 6.1
2006-10-20 10:48:57 -13.441 -76.577 32 6
2007-02-17 0:02:57 41.866 143.511 35 6
2007-03-09 3:22:42 43.214 133.552 442 6.1
2007-04-29 12:41:57 52.037 -179.977 117 6.4
2007-05-06 21:11:52 -19.41 -179.344 678 6
2007-05-30 20:22:12 52.144 157.313 116 6.4
2007-07-16 14:17:37 36.788 134.897 349 6.2
2007-08-01 17:08:51 -15.737 167.745 120 6.2
2007-09-03 16:14:53 45.795 150.051 97 6.3
2007-09-26 4:43:17 -3.904 -79.164 99 6.2
2007-10-02 18:00:08 54.581 -161.768 48 6.2
2007-10-05 7:17:54 -25.243 179.414 535 6
2007-10-21 10:24:52 -6.325 154.753 47 6
2007-11-16 3:13:00 -2.271 -77.804 123 6.3
2007-11-29 19:00:19 14.943 -61.244 146 6.8
2007-12-13 15:51:29 -15.178 -172.402 33 6
2007-12-16 8:09:19 -22.914 -70.06 58 6.1
2008-02-04 17:01:29 -20.123 -70 32 6.1
2008-04-09 12:46:12 -20.089 168.852 33 6.2
2008-05-09 21:51:29 12.506 143.179 76 6.1
2008-06-03 16:20:51 -10.464 161.32 89 6.2
2008-06-26 21:19:15 -20.762 -173.329 38 6
2008-07-05 2:12:04 53.888 152.869 636 6.7
2008-07-08 7:42:10 27.506 128.358 43 6
2008-07-23 15:26:19 39.802 141.463 108 6.7
2008-09-08 18:52:08 -13.514 166.967 122 6.4
2008-09-13 9:32:01 4.779 -75.489 132 6
2008-10-12 20:55:42 -20.06 -64.94 356 6
2008-11-21 7:05:35 -8.948 159.558 118 6
2009-02-15 9:24:31 40.245 142.225 33 6
98
2009-04-18 2:03:52 -28.933 -177.418 65 6
2009-04-21 5:26:11 50.793 155.052 152 6
2009-07-04 6:49:35 9.612 -78.962 38 6
2009-08-09 10:55:55 33.122 138.026 297 6.5
2009-08-10 20:07:07 34.778 138.276 26 6.1
2009-10-07 22:18:37 -12.762 164.78 36 6.7
2009-12-10 2:30:52 53.428 152.712 656 6
2009-07-07 19:11:46 75.351 -72.453 19 6
2009-03-06 10:50:29 80.324 -1.853 9 6.4
2005-04-02 12:52:36 78.607 6.098 10 6.1
2008-02-21 2:46:17 77.08 18.573 10 6
2009-08-20 6:35:04 72.2 0.944 6 6
2011-01-29 6:55:26 70.936 -6.679 6 6.2
2004-04-14 23:07:39 71.067 -7.747 12.2 6
2008-05-29 15:46:00 64.004 -21.012 10 6.2
2009-04-06 1:32:39 42.334 13.334 8.8 6.3
2003-05-21 18:44:20 36.964 3.634 12 6.7
2010-04-11 22:08:12 36.965 -3.542 609.8 6.3
2007-02-12 10:35:21 35.796 -10.334 10 5.9
2007-04-07 7:09:25 37.306 -24.494 8 6
2007-04-05 3:56:50 37.306 -24.621 14 6.2
2003-04-02 3:43:11 35.28 -35.729 10 6.1
2010-05-25 10:09:05 35.336 -35.924 10 6.3
2009-06-06 20:33:28 23.864 -46.105 14 6
2003-05-14 6:03:35 18.266 -58.633 41.5 6.6
2001-10-17 11:29:09 19.354 -64.932 33 5.8
2008-10-11 10:40:14 19.161 -64.833 23 6
2004-03-08 23:39:11 10.48 -43.919 10 6
2011-07-27 23:00:30 10.801 -43.393 10 5.9
2008-02-08 9:38:14 10.671 -41.899 9 6.9
2007-08-20 22:42:29 8.038 -39.248 10 6.5
2008-09-10 13:08:14 8.092 -38.718 10 6.6
2004-01-16 18:07:55 7.641 -37.704 10 6.2
2008-05-23 19:35:34 7.313 -34.897 9 6.5
2006-06-05 6:27:07 1.175 -28.065 10 5.9
2007-07-03 8:26:00 0.715 -30.272 10 6.1
2011-05-15 13:08:13 0.569 -25.647 10 6.1
2006-03-09 17:55:55 0.791 -26.125 10 5.9
99
2008-08-11 23:38:38 -1.02 -21.843 13 6
2008-04-24 12:14:49 -1.182 -23.471 10 6.4

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Appendix III: Transverse Receiver Gathers for Stations in the
San Jacinto Fault Zone
This appendix provides the transverse RF gathers for 11 broadband stations in the San
Jacinto Fault zone (Figure III.1). Radial RF gathers for this region are shown and
discussed in Chapter 4 (Section 4.2, Figure 4.3). As described in Section 2.2.1, transverse
RF can be related to anisotropic structure. For a purely isotropic structure, the transverse
RF would be zero. Energy shown in transverse RF is caused by a dipping structure or
anisotropy (Savage, 1998).

Figure III.1: Map in the San Jacinto Fault zone. Yellow triangles represent stations used in this study.
It can be seen that in all of the transverse RFs there is strong energy, which indicate
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anisotropy or dipping beneath the San Jacinto Fault Zone. Moreover, for stations near the
fault trace, such as CRY, KNW, TRO, their transverse RFs show as strong back azimuth
dependence as their radial RFs (Figure 4.3). The arrival times of their second positive
signals change in four back azimuth bins.

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Appendix IV: Radial Receiver Gathers for 97 Stations in
Southern California

Figure IV.1: Map of southern California. Yellow triangles with names labeled represent 97 stations
used in this study. Detailed maps of the San Jacinto Fault zone and the San Gabriel Mountains regions
(black boxes) are shown in Figure A.1 and A.3 respectively.
This appendix provides a collection of radial RF gathers for all stations in southern
105
California. Figure IV .1 shows a map of southern California. Yellow triangles with names
labeled represent 97 stations used in this study. Detailed maps of the San Jacinto Fault
zone and the San Gabriel Mountains regions (black boxes) are shown in Figure III.1 and
IV.2 respectively. Back azimuth analysis for RF gathers in the San Jacinto fault zone is
discussed in Section 4.2, and for RF gathers in the San Gabriel Mountains region is
discussed in Section 3.2.

Figure IV .3: Map in the San Gabriel Mountains. Yellow triangles represent stations used in this study.

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Abstract (if available)

Abstract The degree to which faults are localized or distributed within the continental lithosphere has long been a controversial subject. This thesis presents a study of the variation for the crustal thickness in southern California. The goal is to study strain deformation at depth by investigating the variations of the Moho beneath strike-slip faults. The data used in this study are broadband teleseismic waveforms from 2000 to 2011 recorded by the Southern California Seismic Network (SCSN) and USArray. The P Receiver Function (RF) method is used to process the teleseismic events to image the Moho. Synthetic modeling in 3D elastic media using a finite difference algorithm is conducted to constrain the geometry of the Moho. ❧ The first part of this thesis presents a map of Moho depth in southern California. The estimated average Moho depth is 30 km but has a range between 18 and 41 km. A shallow Moho of 18-20 km is observed in the Salton Trough and the Inner Continental Borderland. There is a general correlation of a deeper Moho beneath mountains, such as the Peninsular Range, eastern Transverse Ranges and western Transverse Ranges. The deeper Moho beneath these areas is consistent with the presence of the mountain root. Moreover, using a similar broadband seismic data and P receiver function technique as Yan and Clayton (2007), our receiver gather analyses confirm the previous conclusion of a vertical Moho offset beneath the San Gabriel Mountains. ❧ The second part of the thesis involves a detailed study of the Moho beneath the San Jacinto fault zone. First, receiver gathers as a function of back azimuth were analyzed. Receiver gathers at certain stations near the San Jacinto fault trace show a strong back azimuthal variation. These back-azimuthal variations of the Moho signal indicate three-dimensional complexity beneath the central San Jacinto fault that may suggest variations of Moho depth. A SW-NE stacking profile across the Elsinore, San Jacinto, and San Andreas faults indicates an 8~10 km vertical offset structure beneath the San Jacinto fault. In order to constrain the geometry of the Moho in this area, 3D synthetic modeling using finite difference algorithm was conducted to confirm the interpretation of the Moho offset. Six possible geometries were constructed: one with a 10 km vertical step in the Moho, one with a 5-km-wide and 10-km vertically offset ramp, one with a 15-km-wide and 10-km vertically offset ramp, one with a flat Moho but with 10% velocity contrast across the fault, and one with a flat Moho but with 20% velocity contrast across the fault. The synthetic receiver gathers were plotted and analyzed both as a function of back azimuth and incident angles. Our basic conclusion is that the Moho model with a vertical step of 10 km best fits the data. ❧ Our results support the idea that the lower crust is strongly coupled to and deforms with the upper crust. For the deformation observed beneath the strike-slip faults, our back-azimuth RF analysis and synthetic modeling found a 10-km Moho step beneath the San Jacinto fault. This result suggests that the fault extends through the entire crust and that the strain in the lower crust is localized within a narrow zone beneath this major strike-slip fault.

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Asset Metadata

Creator Zhang, Panxu (author)

Core Title Mapping the Moho in southern California using P receiver functions

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geological Sciences

Publication Date 10/04/2012

Defense Date 10/04/2012

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

Tag Moho,OAI-PMH Harvest,receiver function,Southern California

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Miller, Meghan S. (committee chair), Dolan, James F. (committee member), Okaya, David (committee member), Sammis, Charles G. (committee member)

Creator Email panxu.zhang@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-101805

Unique identifier UC11289858

Identifier usctheses-c3-101805 (legacy record id)

Legacy Identifier etd-ZhangPanxu-1227.pdf

Dmrecord 101805

Document Type Thesis

Rights Zhang, Panxu

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