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Quantifying ground deformation of large magnitude earthquakes using optical imgaging systems
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Quantifying ground deformation of large magnitude earthquakes using optical imgaging systems
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i
QUANTIFYING GROUND DEFORMATION OF LARGE MAGNITUDE EARTHQUAKES
USING OPTICAL IMGAGING SYSTEMS
By
Christopher William Douglas Milliner
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSPHY
(GEOLOGICAL SCIENCES)
August 2016
ii
ACKNOWLEDGEMENTS
First and foremost I would like thank my parents, Michael and Jayne, who have worked
tirelessly to give me the support and opportunities I needed to get here.
I would like to thank my adviser James Dolan. It has been an invaluable learning experience,
helping me understand how the endless march of science advances, through careful analysis and
debate. I am truly grateful for his unyielding support and encouragement.
I owe a huge amount of my thanks to James Hollingsworth, who has ‘shown me the ropes’ in
nearly every facet of my doctoral work. I am hugely grateful for the scientific opportunities and
interesting questions he has steered me towards.
I would be remised if I did not thank Amir Allam for his generous help on both questions related
to science and life!
I would like to thank Lee McAuliffe, Rob Zinke, Jessica Grenader, Mark Torres, Jessica
Donovan, Gen Li, and Yaman Oskin for many useful and interesting discussions that have
helped shape a large part of my research.
Last but not least. I owe thanks to Paul Burgess, Bridget Seegers (well all the Seegers), Sylvia
Dee, Elena Perez, Jason Williams, and of course Han Dang for keeping me sane through these
challenging years. A big shout out to my bru Ollie Mulliner!
iii
This dissertation includes parts of the following manuscripts:
1) Milliner, C. W. D., J. F. Dolan, J. Hollingsworth, S. Leprince, F. Ayoub, and C. G.
Sammis, 2015, Quantifying near-field and off-fault deformation patterns of the 1992 Mw
7.3 Landers earthquake, Geochem. Geophys. Geosyst., 16, doi:10.1002/2014GC005693.
2) Milliner, C., Sammis, C., Allam, A.A., Dolan, J.F., Hollingsworth, J., Leprince, S.,
Ayoub, F., 2016, Resolving Fine-Scale Heterogeneity of Co-seismic Slip and the
Relation to Fault Structure, Nat. Sci. Rep. 6, 27201, doi:10.1038/srep27201.
3) Milliner, C. W. D., J. F. Dolan, J. Hollingsworth, S. Leprince, F. Ayoub, in review,
Comparison of near-field and off-fault deformation of the 1992 M
w
7.3 = Landers and
1999 M
w
7.1 = Hector Mine earthquakes: Implications for controls on the distribution of
surface strain. Geophysical Res. Lett.
Contents
ACKNOWLEDGEMENTS ............................................................................................................ ii
ABSTRACT ................................................................................................................................... vi
CHAPTER 1: Introduction ............................................................................................................ 1
1.1 Introduction ...................................................................................................................... 1
CHAPTER 2: Quantifying near-field and off-fault deformation
patterns of the 1992 Mw 7.3 Landers earthquake ........................................................................ 7
2.1 Abstract ................................................................................................................................. 7
2.2 Introduction ........................................................................................................................... 8
2.2.1 Mw 7.3, 1992 Landers Earthquake .............................................................................. 11
2.3 Observations ........................................................................................................................ 12
2.3.1 Cross Correlation of Optical Imagery .......................................................................... 12
2.3.2 Data .............................................................................................................................. 13
2.3.3 Optical Image Cross-Correlation Result ...................................................................... 14
2.4 Methods ............................................................................................................................... 15
2.4.1 Measuring Coseismic Surface Displacement ............................................................... 15
2.4.2 Landers Surface Displacements ................................................................................... 16
2.4.3 Measuring Off-Fault Deformation (OFD) ................................................................... 20
2.4.4 Measuring Fault Zone Width (FZW) ........................................................................... 23
2.5 Discussion ........................................................................................................................... 25
iv
2.5.1 Factors Controlling Off-Fault Deformation (OFD)
and Fault Zone Width (FZW) ............................................................................................... 25
2.5.2 Coseismic Slip Variability ........................................................................................... 30
2.5.3 Implications for Slip Rates and Seismic Hazard.......................................................... 35
2.6 Conclusions ......................................................................................................................... 37
2.7 Figure captions .................................................................................................................... 38
2.7.1 Captions for Supplementary Materials ........................................................................ 42
CHAPTER 3: Resolving Fine-Scale Heterogeneity of
Co-seismic Slip and the Relation to Fault Structure ................................................................ 47
3.1 Abstract ............................................................................................................................... 47
3.2 Introduction ......................................................................................................................... 47
3.3 Methods ............................................................................................................................... 49
3.3.1 Subpixel image correlation of air photos. .................................................................... 49
3.3.2 Measuring displacement. ............................................................................................. 51
3.3.4 Synthetic tests. ............................................................................................................. 52
3.3.5 Estimating the error of the slip profile fractal dimension. ........................................... 53
3.3.6 Bandpass Filter............................................................................................................. 54
3.4 Results ................................................................................................................................. 54
3.4.1 Optical image correlation. ............................................................................................ 54
3.4.2 Spectral analysis of slip distributions. ......................................................................... 56
3.4.4 Analysis of fault system and relation to slip distribution. ........................................... 58
3.5 Discussion ........................................................................................................................... 59
3.6 Conclusion ........................................................................................................................... 61
3.7 Figure Captions ................................................................................................................... 62
3.7.1 Captions for Supplementary Materials ........................................................................ 64
CHAPTER 4: Comparison of near-field and off-fault deformation of the
1992 M
w
7.3 = Landers and 1999 M
w
7.1 = Hector Mine earthquakes:
Implications for controls on the distribution of surface strain. .................................................. 70
4.1 Abstract ............................................................................................................................... 70
4.2 Introduction ......................................................................................................................... 70
4.3 Data and Methods................................................................................................................ 72
4.4 Results ................................................................................................................................. 74
v
4.5 Discussion & Conclusions .................................................................................................. 76
4.6 Figure Captions ................................................................................................................... 81
4.6.1 Captions for Supplementary Materials ........................................................................ 83
CHAPTER 5: Conclusion ............................................................................................................ 86
References ..................................................................................................................................... 88
Chapter 2 Figures .......................................................................................................................... 96
Chapter 3 Figures ........................................................................................................................ 105
Chapter 4 Figures ........................................................................................................................ 108
Appendix A: Quantifying near-field and off-fault deformation
patterns of the 1992 Mw 7.3 Landers earthquake .................................................................... 112
Appendix B: Resolving Fine-Scale Heterogeneity of Co-seismic
Slip and the Relation to Fault Structure ................................................................................... 136
Appendix C: Co-seismic near-field and off-fault surface deformation
patterns of the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine
earthquakes: Implications for controls on the distribution of surface strain ............................ 162
vi
ABSTRACT
Measurements of earthquake surface ruptures provide important insight into the rupture process
and faulting mechanics. Deformation along surface ruptures can range from highly complex
zones of distributed strain to completely localized, along single fault planes. However,
measuring such deformation patterns along surface rupture is highly challenging. Traditional
field geologic surveys are well suited to obtaining detailed measurements of surface fault offset,
but due to the lack of piercing points that extend far from the fault trace, measurement of
distributed deformation is not generally possible. Interferometric Synthetic Aperture Radar
(InSAR), is sensitive to millimeter surface changes, providing good coverage of surface motion
in far field (> 2 from surface rupture), however, due to strong ground shaking typically
decorrelates in the near-field leaving a 1-2 km wide gap of data. While GPS data provides
exceptional temporal resolution of surface motion, due to the cost of instrumentation it also lacks
the necessary spatial coverage to fully characterize the near-field, co-seismic surface deformation
pattern. Thus, due to the limitations of these geodetic and field techniques there is a poor
constraint of the surface motion close to the fault rupture (< 2 km), where deformation is most
complex and observations most important. In this thesis I present optical image correlation
result, which can resolve horizontal surface motion in high spatial detail and precision (1σ = 10
cm), allowing measurement of the amount of distributed deformation and the spatial distribution
of fault slip of large magnitude, continental strike-slip earthquakes. I used the software COSI-
Corr (Co-registration of Optically Sensed Images and Correlation), which can measure
horizontal ground motion to sub-pixel precision, tracking shifts in features between satellite or
air photo imagery taken before and after an event. I present results of the near-field deformation
pattern of the 1992 M
w
= 7.3 Landers and 1999 M
w
= 7.1 Hector Mine earthquakes, events only
vii
20 km apart from one another and part of the same tectonic regime, the Eastern California Shear
Zone, thus providing an excellent opportunity to investigate how deformation patterns may vary
between different fault systems. These results show that for the Landers and Hector Mine events
45 ± 10% and 39 ± 22% of total deformation was accommodated as diffuse deformation over
fault zones averaging 154 m and 121 m in width, respectively. We find that the amount of
distributed deformation is largely controlled by the geometrical fault complexity, and to a lesser
extent the types of near-surface materials; more complex fault zones and unconsolidated material
(e.g., young alluvium) produce larger amounts of OFD. Furthermore, we also find from a
spectral analysis that fault slip is scale invariant and fractal, where Landers has a rougher slip
distribution (fractal dimension of 1.72 ± 0.02 (1σ)) than Hector Mine (fractal dimension of 1.62
± 0.03 (1σ)), which we attribute to Landers having a geometrically ‘rougher’ fault system.
Significant amounts of distributed deformation accommodated during large earthquakes has
basic implications for effective micro-zonation to protect the urban environment, generating
reliable scaling laws that empirically relate displacement to moment magnitude and rupture
length, for meaningful geodetic-geologic slip-rate comparisons, and accurate probabilistic
seismic hazard assessment models.
1
CHAPTER 1:
Introduction
1.1 Introduction
Earthquakes that rupture to surface vary significantly in the degree of strain localization along
their fault lengths, from highly distributed zones of inelastic ‘off-fault’ deformation, to
completely discrete (Rockwell et al., 2002; Treiman et al., 2002; Quigley et al., 2012; Rockwell
and Klinger 2013; Zinke et al., 2014; Gold et al., 2015). The physical mechanisms that
accommodate distributed, ‘off-fault’ deformation (OFD) surface strain can range from warping,
ground boundary sliding, rotation to micro-cracking. Accurate measurements of surface
deformation patterns of large magnitude earthquakes, which necessitates a reliable measurement
of the complex, distributed deformation, is one of the fundamental goals of earthquake geology
and geophysics.
Damage and distributed deformation along faults are known to affect the rupture velocity
Sammis et al., 2009, direction (Shi and Ben-Zion 2006), seismic radiation pattern (Day et al.,
2008), and propagation where structural barriers can arrest the rupture, determining the ultimate
size of the event (Wesnousky 2006). The geologic evolution of fault systems is well understood
from geologic field analysis of exhumed faults (Chester and Chester 1998; Sibson 2003; Frost et
al., 2009), offset geomorphic markers (Shelef and Oskin 2010; Titus et al., 2011), and numerical
(Finzi et al., 2009) and analogue modeling (Tchalenko 1970). Damage zones along crustal faults
initiate as distributed, complex zones of deformation, and with the continual accumulation of slip
through multiple earthquake cycles localize to simpler, more ‘mature’ systems, abandoning
previous mechanically inefficient structures (Tchalenko 1970; Wesnousky 1988; Frost et al.,
2
2009; Shelef and Oskin 2010). Geophysical observations of damage zones from fault-zone head
waves (McGuire and Ben-Zion 2005), trapped waves (Cochran et al., 2009) and double-
difference tomography (Allam et al., 2014) reveal zones of reduced elastic rigidity caused by
micro-cracks that reduces the seismic velocity, that narrow with depth, to < 100 m width within
the seismogenic portions of the crust (3-15 km depth). However, even with these measurements
it is not well known how active these structures are, if they are relict features caused by prior
faulting, and thus what portion of the stored inter-seismic elastic strain energy is released as off-
fault, distributed deformation during co-seismic events.
Following a surface rupturing event the key faulting characteristics, such as the
magnitude and spatial distribution of fault slip, are primarily measured through extensive
geologic field surveys and geodetic techniques, including GPS and satellite radar interferometry
(Sieh et al., 1993; Bürgmann et al., 2000a; Simons et al., 2002). Traditional field geologic
mapping is well suited to obtaining detailed measurements of surface offset, but due to the lack
of piercing points that extend far from the fault trace measurement of distributed deformation is
not generally possible. The primary geodetic approach to measure co-seismic surface motion is
Interferometric Synthetic Aperture Radar (InSAR), that is sensitive to millimeter surface
changes, useful in measuring far-field surface motion (>2 km from surface rupture). However,
InSAR typically decorrelates close to the surface rupture as deformation gradients exceed a
single phase cycle between neighboring radar returns (Bürgmann et al., 2000a), leaving a 1-2 km
wide gap of data. GPS data, on the other hand, while providing exceptional temporal resolution,
due to the cost of instrumentation lacks the necessary spatial coverage to fully characterize the
near-field deformation pattern (< 2 km from surface rupture). Thus, with current field and
geodetic techniques we are left with a significant lack of constraint of the co-seismic, near-field,
3
surface deformation pattern, precluding a precise understanding of the magnitude and width of
distributed deformation, and the spatial variation of fault slip.
The thesis here is to utilize and develop optical image correlation, which uses satellite
and aerial photography images taken before and after an earthquake, that can provide precise and
spatially complete, and detailed measurement of the near-field deformation pattern close to the
fault rupture. Using these technique to improve observations of co-seismic surface deformation
in the near-field (< 2 km), we want to understand what is the magnitude and width of distributed
deformation accommodated during an earthquake? How does distributed deformation vary along
the length of an individual surface rupture, and what are the physical properties of the rupture
that control this variation? Is distributed strain predictable, i.e., can we build empirical relations
that can help estimate the width and magnitude of diffuse strain along a given fault, needed for
seismic hazard analysis? How does distributed deformation vary between earthquakes occurring
on different fault systems? What are the spatial characteristics of co-seismic slip, and how does
slip vary with depth?
Results from Dolan and Haravitch (2014) showed that for immature fault systems surface
fault slip measured by field geologists during co-seismic events is significantly lower than slip at
seismogenic depth (3-10 km) determined from finite-fault inversions. But surface fault slip for
ruptures from mature fault systems was similar to that at depth. Measurements of fault slip by
field geologists primarily captures the discrete, ‘on-fault’ component of displacement and the
hypothesis from the Dolan and Haravitch (2014) study is that a systematic discrepancy of slip at
depth with that at the surface for earthquakes from immature fault systems is due to such
‘missing’ surface slip being accommodated as off-fault, diffuse deformation, missed by geologic
field surveys. The underlying assumption here is that slip at the surface must be similar to that at
4
depth, over geologic timescales this condition must be met, otherwise processes and features at
the surface and within the Earth’s crust would occur that are not observed in nature, such as the
lower crust sliding away with respect to the upper surface. Thus, this result sets up the primary
hypothesis of this body of work, do earthquakes release significant amounts of distributed
deformation and particularly more so for immature faults? If so, how and how much?
In the second chapter, we present results of the near-field deformation pattern of the 1992 M
w
= 7.3 Landers earthquake using optical image correlation, that allows us to measure the total
fault displacement, magnitude and width of distributed deformation in high spatial detail and
precision (1σ = 10 cm). From the deformation maps we found our measurements of
displacement, which captures the total shear accommodated across the fault zone, are
systematically larger than measurements from field geologists, that captures the ‘on-fault’
discrete component of deformation, giving an estimate of the magnitude of off-fault deformation.
For Landers we found the spatial variation of OFD can be correlated with changes in the degree
of fault complexity along the rupture length, more complex fault zones produce larger amounts
of OFD. In addition we also found distinct differences of OFD with the types of near-surface
material, more discrete deformation occurs in areas where the rupture propagates through
consolidated material (e.g., bedrock). These results demonstrate that earthquakes do
accommodate significant amounts of deformation along their rupture length, but also there are
significant variations along their rupture length related to physical properties of the rupture.
In the third chapter, we analyze deformation maps of the 1999 Mw 7.1 Hector Mine
earthquake, produced using the same optical image correlation method and air photo data
described in Chapter 2. This analysis allowed us to measure slip to the same precision and spatial
resolution for both the 1992 Landers and 1999 Hector Mine surface ruptures, where both
5
earthquakes exhibit significant spatial variations along their rupture lengths. By conducting
extensive synthetic tests we found these fluctuations of slip along the fault trace are not
arbitrarily derived by noise from the images, but are reflective of the faulting pattern. From a
spectral analysis we found that Landers has a rougher slip distribution than Hector Mine, the
latter a geometrically ‘smoother’ fault system. We attribute a rougher slip distribution for
Landers due to a geometrically more complex fault system, consistent with recent results from
quasi-static and fully dynamic rupture simulations that show fractal roughness of fault surface
generates a fractal stress field, causing heterogeneous variations in fault slip (Dunham et al.,
2011; Shi and Day 2013).
In the fourth chapter, following from the study outlined in the second chapter, we compare
the magnitude and width of distributed deformation of the Landers and Hector Mine earthquakes
using the same near-field deformation maps presented in Chapter 1 and 2. The overall magnitude
of OFD accommodated along the Hector Mine rupture is similar to that of Landers, with OFD =
39 ± 22% and 45 ± 10%, respectively. We attribute such large magnitudes of OFD to lack of
structural maturity of the ruptured fault systems (with low cumulative offsets of 3-7 km Jachens
et al., 2002). However, spatial variations of OFD along both ruptures indicates there are other
secondary controls. In agreement with the results from Chapter 2, we find statistically significant
correlations of OFD with the degree of fault structure and the types of near-surface material for
Hector Mine, similar to that found for Landers. Significant underestimations of the total fault
displacement by field surveys has basic implications for scaling laws, which use such data to
empirically relate displacement to moment magnitude (M
w
) and rupture length (RL), and we find
such scaling laws are biased, predicting erroneous magnitudes of M
w
and RL not observed in the
studied earthquakes. Such large amounts of OFD accommodated along major fault systems also
6
has basic implications for significantly underestimating geologic fault slip rates, which are
typically taken over narrow aperture distances, which are key inputs to probabilistic seismic
hazard analysis (PSHA) models and meaningful comparisons of geologic-geodetic rates.
Overall, understanding the spatial distribution of coseismic slip along earthquake ruptures
has fundamental implications for better understanding the properties of the source, providing an
effective empirical means to generate realistic synthetic slip distributions to simulate accurate
ground motions for a rupture along a fault of known roughness. Moreover, robust estimates of
the width and magnitude of distributed deformation along a given fault segment, where we
expect permanent ground deformation, has basic implications for effective seismic hazard
analysis and micro-zonation strategies to properly prepare and safeguard infrastructure and the
built environment in close proximity to fault zones.
Each chapter of my dissertation is designed to stand alone and thus there is some unavoidable
redundancy between them.
7
CHAPTER 2:
Quantifying near-field and off-fault deformation patterns of the 1992 Mw 7.3 Landers
earthquake
2.1 Abstract
Co-seismic surface deformation in large earthquakes is typically measured using field mapping
and with a range of geodetic methods (e.g., InSAR, lidar differencing, and GPS). Current
methods, however, either fail to capture patterns of near-field co-seismic surface deformation or
lack pre-event data. Consequently, the characteristics of off-fault deformation and the parameters
that control it remain poorly understood. We develop a standardized method to fully measure the
surface, near-field, co-seismic deformation patterns at high-resolution using the COSI-Corr
program by correlating pairs of aerial photographs taken before and after the 1992 M
w
7.3
Landers earthquake. COSI-Corr offers the advantage of measuring displacement across the entire
zone of surface deformation and over a wider aperture than that available to field geologists. For
the Landers earthquake, our measured displacements are systematically larger than the field
measurements, indicating the presence of off-fault deformation. We show that 46 % of the total
surface displacement occurred as off-fault deformation, over a mean deformation width of 154
m. The magnitude and width of off-fault deformation along the rupture is primarily controlled by
the macroscopic structural complexity of the fault system, with a weak correlation with the type
of near-surface materials through which the rupture propagated. Both the magnitude and width of
distributed deformation are largest in stepovers, bends, and at the southern termination of the
surface rupture. We find that slip along the surface rupture exhibits a consistent degree of
8
variability at all observable length scales and that the slip distribution is self-affine fractal with
dimension of 1.56.
2.2 Introduction
Large-magnitude strike-slip earthquakes that rupture to the surface are an important source of
information for finite-fault inversions and studies of faulting mechanics. In particular, the extent
to which co-seismic fault slip is localized or distributed in the near-surface gives insight into the
initiation, propagation and cessation of dynamic ruptures, the structural evolution of faults, the
use of surface slip data in probabilistic seismic hazard assessment (PSHA), the measurement of
geologic fault slip rates and comparison of these data to geodetic rates (Sammis et al., 2009;
Shelef and Oskin, 2010; Chen and Petersen, 2011; Petersen et al. 2011; Fleming et al., 1994;
Dolan and Haravitch, 2014; Herbert et al., 2014). Constraining the width of the deformation zone
and lateral variations of on- and off-fault displacement may provide predictive information on
the locations of the likely endpoints of future ruptures (e.g., Wesnousky, 2006; 2008; Elliott et
al., 2009; Rockwell and Klinger, 2013).
Surface deformation along co-seismic ruptures typically releases the accumulated inter-
seismic strain energy as a combination of slip along discrete, brittle faults and off-fault, inelastic
deformation expressed physically as warping, granular flow, rigid-block rotation, minor
secondary faulting and/or micro-cracking. Observations of surface deformation patterns from
numerous strike-slip faults demonstrate that the magnitude of off-fault deformation (OFD) can
vary from 0-100 % (e.g., Nelson and Jones, 1987; Rockwell et al, 2002; Treiman et al., 2002;
Kimurah et al., 2004; Shelef and Oskin, 2010; Van Dissen et al., 2011; Quigley et al., 2012) and
9
has been observed to vary systematically according to the structural maturity of the fault
(Milliner et al., 2012; Dolan and Haravitch, 2014). Compliant zones of reduced shear rigidity
surrounding many fault zones are a manifestation of OFD mechanisms damaging the rock over
the entire history of deformation (e.g., Li et al., 1998; Vermilye and Scholz, 1998; Chester and
Chester, 1998; Yamashita, 2000; Ben-Zion et al., 2003; Mamada et al., 2004; Chester et al.,
2005; Lemaitre and Desmorat, 2005; McGuire and Ben-Zion, 2005; Cochran et al., 2009; Frost
et al., 2009; Shelef and Oskin, 2010). These compliant zones are well observed using geodetic
and seismic data with widths measured up to ~2 km (e.g., Fialko et al., 2002; Cochran et al.,
2009). Similar deformation widths are also found from geologic studies that measure distributed
shear accommodated over geologic timescales. For example, Oskin et al. (2008) and Shelf and
Oskin (2010), measured a ~2 km wide zone of distributed deformation for the Calico fault in the
eastern California shear zone and noted that the majority of deformation was confined to a higher
strain 100-200 m-wide fault core. This narrower width is similar to the total observed width of
distributed deformation in many surface ruptures (e.g., McGill and Rubin, 1999; Treiman et al.,
2002; Rockwell et al., 2002; Oskin et al., 2012).
Although off-fault deformation has been observed along many faults, the controls of off-fault
deformation along a co-seismic surface rupture remain poorly understood. Moreover, although a
number of different techniques have been utilized to document OFD patterns, there is as yet no
standard method to robustly and reproducibly measure the characteristics of the complex, near-
field surface deformation in high-resolution with readily available and cost-effective data. For
example, although Interferometric Synthetic Aperture Radar (InSAR) studies reveal the surface
deformation field in exceptional detail, they typically decorrelate close to surface ruptures as
deformation gradients exceed a single phase cycle between neighboring radar returns (e.g.,
10
Burgmann et al., 2000; Simons et al., 2002; Cakir et al., 2003; Fialko, 2004). Field surveys can
provide very precise measurements of on-fault deformation, but they do not typically account for
more subtle, complex off-fault deformation, which can be challenging to measure (e.g., McGill
and Rubin, 1999; Treiman et al., 2002; Rockwell et al., 2002, Shelef and Oskin, 2010; Gold et
al., 2013). GPS data, while providing exceptional temporal resolution, also lacks the necessary
spatial coverage to fully characterize the near-field deformation pattern. Lidar (Light Detection
and Ranging) data have proven to be a valuable tool in studies of near-field surface deformation
(e.g., Oskin et al., 2012; Nissen et al., 2014), but acquisition of lidar data is costly and lidar
differencing requires the existence of pre-existing data, which is not always the case. Cross-
correlation of high-resolution, optical satellite imagery acquired before and after an earthquake
can also reveal the first-order surface deformation patterns in earthquakes (Leprince et al.,
2007a; 2007b; 2008; Ayoub et al., 2009; Konca et al., 2010; Hollingsworth et al., 2013).
However, the relatively coarse spatial resolution (typically > 1 m) of most satellite data inhibits
the detailed analysis of complex and sometimes subtle near-field deformation patterns.
In light of these limitations, the primary goal of this study is to develop a standardized
methodology for the use of cross-correlation of high-resolution, pre- and post-event aerial
photographs to understand patterns of surface deformation. We tested this methodology through
measurements of the near-field ground deformation from the M
w
7.3 1992 Landers earthquake.
Such optical image correlation based on aerial photographs can facilitate measurement of the
distributed inelastic strain, as this technique has the capability to capture the entire deformation
across a fault (e.g., Konca et al., 2010). As part of our analysis, we used numerous statistical tests
to understand whether off-fault deformation and the fault-zone width vary according to any
observable parameters that may facilitate the prediction of strain localization in advance of future
11
large earthquakes. Finally, we discuss the implications of these results for studies of fault
mechanics, the potential underestimation of slip rates, the dynamics of co-seismic ruptures, and
strategies to mitigate damage to the built environment.
2.2.1 Mw 7.3, 1992 Landers Earthquake
The Landers earthquake occurred within an 80-km-wide zone of NNW-trending, right-lateral
faults known as the eastern California shear zone, which accommodates ~25 % of the total
Pacific and North-American plate motion (Humphreys & Weldon, 1994; Dixon et al., 2000;
Oskin et al., 2008; Frankel et al., 2011). The Landers earthquake was generated by rupture of
five distinct faults over a distance of 67 km (Bryant, 1992; 1994; Liu et al, 2003) (Figure 1b).
Rupture initiated near its southern end, on the Johnson Valley fault, and propagated unilaterally
to the north-northwest across two right-stepping, dilational stepovers, before terminating along
the Camp Rock fault (Wald and Heaton, 1994). Detailed mapping of the Landers rupture by field
geologists found particularly complex deformation patterns. For example, McGill and Rubin
(1999) recorded significant variations in offset along 1-2 km stretches of the Emerson fault,
Spotila and Sieh (1995) documented areas of reduced slip (termed ‘slip gaps’) along the
Homestead Valley fault thought to be controlled by fault structural complexity, and Zachariasen
and Sieh (1995) noted distributed, but efficient transfer of slip onto a series of right-stepping en-
echelon faults within the Homestead-Emerson stepover. Although these field studies found
instances of complex deformation patterns along the rupture, they could neither completely
capture the magnitude nor the distribution of off-fault deformation along the entire surface
rupture.
12
Postseismic deformation from the Landers earthquake included poroelastic rebound and up to
15 cm of afterslip at the surface as observed by geodetic surveys seven years following the
earthquake (Peltzer et al., 1998; Fialko, 2004). Slip rate estimates for the Camp Rock fault
indicate <1.4 + 0.6 mm/yr of strain accommodated over the past 50 + 20 ka (Oskin et al., 2008),
with analysis of basement offsets indicating a cumulative displacement of ~3.5 km for the faults
that ruptured in the Landers event (Jachens et al, 2002).
2.3 Observations
2.3.1 Cross Correlation of Optical Imagery
We used the COSI-Corr software (Co-registration of Optically Sensed Images and
Correlation), to correlate pairs of pre- and post-event optical images with sub-pixel precision, in
order to quantify the magnitude and distribution of near-field co-seismic ground deformation
(Leprince et al., 2007a; Ayoub et al., 2009). This technique has been used successfully with
satellite imagery to document surface deformation in earthquakes, landslides, glacier dynamics,
the migration of Martian sand dunes and dikes (Avouac et al., 2006; Leprince et al., 2008;
Bridges et al., 2012; Hollingsworth et al., 2012). Air photos offer the advantage of significantly
greater pixel resolution (1-m) than the satellite data available before the 1992, Landers event,
which allows us to quantify the near-field surface deformation pattern in unprecedented detail.
To produce correlation maps that accurately constrain the ground deformation pattern, the
input aerial photographs must be precisely ortho-rectified (i.e., create a planimetric correct image
where objects are in their true ground geometry) and co-registered before correlation. The COSI-
Corr procedure allows for accurate ortho-rectification of images by taking into account the
13
topography using a digital elevation model (DEM), the internal camera geometry using a camera
calibration report to correct for optical distortions (such as radially increasing incidence angle
from near-nadir at image center to ~30
o
at image edges), and the exterior orientation (look angle
and altitude) determined from ground control points (GCPs) (Ayoub et al., 2009). To co-register
the pre- and post-event photographs, we construct a relative mapping between image pairs using
tie points that relate common features in the image scene. COSI-Corr then applies sub-pixel
image correlation on the set of ortho-images by using an iterative, unbiased processor that
estimates the phase plane in the Fourier domain (Leprince et al., 2007a, 2007b, 2008; Ayoub et
al., 2009). The correlation process yields two correlation maps, representing pixel motion in the
east-west and north-south horizontal directions of the surface displacement field, with an
accuracy of 1/10
th
the size of the input image pixel dimension (Ayoub et al., 2009). The aerial
photographs have 1 m ground-resolution pixel size, which therefore allows detection of
horizontal deformation down to a precision of ~10 cm. This represents a minimum detection
threshold in our correlation maps, and smaller surface displacements cannot be resolved with
these data. Although our methodology does not constrain vertical deformation (see
Hollingsworth et al., 2012), the majority of the deformation in this pre-dominantly strike-slip
earthquake was horizontal (Sieh et al, 1993; Bryant, 1992; 1994; Spotila and Sieh, 1995;
Zachariasen and Sieh, 1995; McGill and Rubin, 1999).
2.3.2 Data
We selected 31 pairs of panchromatic, 1-m-resolution, National Aerial Photography
Program (NAPP) aerial photographs for correlation, purchased from the USGS
(http://earthexplorer.usgs.gov/). Stereo-pair (60 % overlap) pre- and post-event photos were
acquired in July, 1989 and May, 1994, respectively, with 8x8 km footprints and were ortho-
14
rectified using the same 2012, 10 m National Elevation Datum (NED), DEM from the USGS
(http://ned.usgs.gov/). To georeference the post-event aerial photos (i.e., assign absolute ground
co-ordinates), we used 2005, SPOT 5 satellite imagery as the reference ortho-image. To
orthorectify the air photos, GCPs are assumed to have experienced zero ground deformation,
however, as they are collected near the surface rupture the presence of long-wavelength ground
deformation violates this assumption. To correct for this we used a cross-correlation result from
a pair of 10 m, SPOT 5 images, which provides independent information on the ground
deformation (Milliner et al., 2012).
2.3.3 Optical Image Cross-Correlation Result
Our cross-correlation of the optical aerial photographs from before (1989) and after
(1994) the Landers earthquake reveals the detailed surface deformation field associated with the
rupture (Figure 1). From multiple tests we determined the optimal correlation parameters (i.e.
those that suppress noise and decorrelation but retains details of the surface rupture) were a
multi-scale sliding window of 64 to 32 pixels with a step of 6-pixels, which results in a
correlation map of 6 m pixel resolution.
The output correlation maps are found to contain both tectonic and artificial signals. Such
artifacts include scanning distortions from film digitization, radial distortions from unmodelled
lens parameters, and film distortion due to thermomechanical warping of the original
photographic film (Ayoub et al., 2009). Using a series of synthetic tests (detailed in
supplementary information) we found the artificial signals occur at much longer-wavelengths
than the observed shorter-wavelength tectonic signals and do not bias our measurements of
surface displacement (see Figures S1-3), in agreement with Michel and Avouac (2006).
15
Topographic artifacts in the correlation result caused by using only a single post-event DEM to
ortho-rectify both the pre- and post- event photos are corrected for following the procedure of
Ayoub et al., (2009).
2.4 Methods
2.4.1 Measuring Coseismic Surface Displacement
We measured the total surface displacement across the entire width of deformation along
the Landers surface rupture using stacked profiles orientated perpendicular to the fault strike.
The profile lengths ranged from ~2-3 km (perpendicular to fault) and were stacked over a 138-m,
along-strike length (i.e., the fault-parallel displacement is averaged over a 138 m fault-parallel
distance). Thus, each measurement can be considered independent from each other, with a
discretization determined by the stack width (Konca et al., 2010). Testing of different stack
widths indicated an optimal width of 138 m, which allows for suppression of noise in the
correlation maps while minimizing over-smoothing of along-strike changes in surface slip
(Figure S4). Surface displacement is measured from the stacked profiles by manually fitting
linear regressions to the deformation signal on either side of the fault, and the relative difference
of the extrapolated regressions defines the magnitude of the offset accommodated across the
entire fault-zone (Figure 1a). Thus, the COSI-Corr ‘displacement’ value includes both the
localized, on-fault displacement that occurs on the primary fault strand, as well as any off-fault,
distributed inelastic shear accommodated via a range of physical processes.
To reliably understand the slip behavior and detailed pattern of surface strain localization
we need to characterize any error that arises from subjectively measuring the displacement and
16
fault-zone width (FZW). Estimating the width of shear and magnitude of fault offset from the
stacked profiles involves subjectively locating the sometimes subtle inflection point in the profile
on either side of the fault (dashed blue lines in Figure 1a). To quantify the measurement
precision and any possible bias in this procedure, we employed synthetic tests (detailed in
supplementary information), in which we synthetically sheared an image with known and
constant FZW and displacement. Using COSI-Corr we then cross-correlated the synthetically
sheared image with another image of the same location, acquired at a different time (Figure S1).
As the FZW and displacement were kept constant, any deviation from the synthetic, known
values gives a direct quantification of the measurement bias and precision, which reflects
measurement subjectivity and variation in image quality and texture. The synthetic tests reveal a
bias of 0.01 m overestimation with a precision of ± 0.12 m (2 σ) for our displacement
measurements (Figure S3) and an underestimation of 2 m and precision of ± 11.70 m (2 σ) for
the FZW measurements (Figure S4). These values, which are independent of the magnitude of
displacement and width of deformation, allow us to derive an empirical error distribution for the
displacement and FZW measurements, which is then propagated through the pre-existing error in
our COSI-Corr results. Capturing and incorporating this variability is noteworthy given it usually
forms a significant component of the epistemic uncertainty in most studies that measure co-
seismic displacement.
2.4.2 Landers Surface Displacements
In the correlation maps we detected 69 distinct fault segments that accommodated surface
slip larger than our minimum detection threshold (> 10 cm). These agree well with the locations
of fault strands mapped in the field following the earthquake (Bryant, 1992; 1994; Liu et al.,
17
2003 and references therein). We collected a total of 1057 co-seismic, surface displacement
measurements spaced every 138 m along all of the mapped fault traces (Figure 2b), and found a
maximum displacement of 5.58 + 0.14 m (95% confidence interval of measurement precision)
and a mean of 1.52 + 0.70 m (1 σ) and median of 1.00 m. Generally speaking, we found the
highest displacements on structurally simple, single-stranded sections of the Landers rupture,
such as the Homestead fault and parts of the central Emerson fault. Conversely, we found that
co-seismic slip decreases on individual faults in structurally complex areas (e.g., the Kickapoo
and Homestead-Emerson stepovers), due to transfer of total surface slip onto multiple structures.
Our 1057 displacement measurements are distributed in a spatially complex manner
along the rupture and therefore constructing a precise along-strike slip-profile of the 1992
Landers event is a non-trivial task. To overcome this, we developed an algorithm that projects all
1057 of our displacement measurements onto a single, regionally representative ‘fault trace’. To
collapse multiple faults onto a single, regionally representative ‘fault’, we iteratively projected
each individual fault strand sequentially, calculated the component of slip using a cubic
interpolation and added this to eventually construct the cumulative slip distribution (thick, black
line in Figure 3).
The position of the regional ‘fault’ used here agrees well with the macroscopic, 1
st
-order
geometry of the fault system that ruptured during the Landers earthquake (Bryant, 1992; 1994;
Liu et al, 2003 and references therein) as well as the location of faults at depth used in the
inversion of geodetic data (Fialko, 2004). The projection of the displacement measurements also
corrects for slip transfer between branching or parallel fault structures, which if left unaccounted
for can lead to arbitrary along-strike slip variability. As our displacement measurements are
spatially dense, incorporate OFD, and cover the entire Landers rupture, including secondary
18
faults, once projected, the displacement dataset yields a robust and systematically complete
representation of the Landers slip distribution
Generally, the Landers slip profile has a simple, 1
st
-order shape, with two prominent
peaks (labelled i and ii in Figure 3a) and two areas of significantly reduced slip (‘slip gaps’,
labelled iii and iv), the latter likely related to the fault segmentation (which is discussed further
in section 3.1) (Spotila and Sieh, 1995). The COSI-Corr displacement measurements (which
include OFD) exhibit pronounced short-wavelength, along-strike variation, which consistently
occurs along all 69 fault segments (see Figure 3). The slip variation is as large as + 0.5 m over
along-strike distances of ~200 m, which is significantly more than the measurement precision
(95 % confidence interval of + 0.12 m, see supplementary information, Figure S4). As the
observed along-strike slip variability cannot be accounted for by the measurement error, this
suggests the slip heterogeneity reflects the true physical behavior of the faulting and is consistent
with other studies that document co-seismic slip along the Landers rupture (McGill and Rubin,
1999) and other surface ruptures (e.g., Rockwell et al., 2002; Klinger et al., 2006; Rockwell and
Klinger, 2013).
The presence of along-strike slip variability produces along-strike strains, which are
found to vary up to 2.0×10
-3
over ~200 m along-strike distances. Along-strike strain is calculated
as the change in slip per unit distance along-strike and halved in order to determine deformation
on either side of the fault. McGill and Rubin (1999) reported similar magnitudes of along-strike
strain of ~10
-2
for the Landers surface displacement and similar strains of 10
-3
have been
documented for other earthquakes (e.g., Michel and Avouac, 2006; Oglesby, 2008; Elliott et al.,
2009; Oskin et al., 2012; Gold et al., 2013).
19
To understand if there is an underlying structure to the slip variability, and how the
variability changes with different length-scales, we used a spectral analysis by computing the
power spectrum P(k) of the slip distribution (Figure 3) using the Thomson multitaper method
(Thomson, 1982). The spectral analysis shows that the co-seismic slip distribution follows a
power-law decay (Figure 4); we use a linear regression to estimate a decay parameter β of 1.87 +
0.04 (95% confidence interval), with an R
2
= 0.80. Following equation (2), β gives a fractal
dimension D of 1.56 + 0.04, indicating that the co-seismic slip distribution is fractal and scale
invariant (i.e., slip exhibits a statistically consistent degree of variability at all observable length-
scales), (Mandelbrot, 1984). Thus, a more accurate description of ‘variable’ slip is in the fractal
sense, where slip has a consistent (power-law) decay of heterogeneity with decreasing length-
scale. I.e., there is a power-law relation between the amplitude and wavelength of the slip
distribution, where longer wavelength slip perturbations have a larger amplitude and smaller
wavelengths have smaller amplitudes (Figure 4). The linear relation between the Hurst exponent
H (which characterizes the stochastic component of the data and gives a measure of the long-
term memory) and the fractal dimension D in equation (3) (where E is the Euclidean dimension
of the fractal medium), gives a Hurst exponent of 0.44 + 0.04.
P k k
(1)
5
2
D
(2)
1 H E D (3)
20
A Hurst exponent less than 0.5 indicates that co-seismic slip is not random, but rather is
non-persistent with a ‘short-memory’ (i.e., neighboring points of displacement are correlated but
tend to be further away from each other than random) (Turcotte, 1997). In addition to applying
the fractal analysis to the cumulative, projected slip profile (upper black line in Figure 3), we
also applied it to the individual faults (colored lines in Figure 3) and found a similar result.
2.4.3 Measuring Off-Fault Deformation (OFD)
We measured OFD along the 1992 Landers surface rupture by comparing the COSI-Corr
displacement data, which measures the total shear accommodated across a fault, to the
displacement measured in the field, which represents the discrete component of displacement.
Post-earthquake field mapping of the surface rupture produced 763 displacement measurements
(Bryant, 1992; 1994; Liu et al., 2003 and references therein), where we only considered the
horizontal component of displacement because our COSI-Corr measurements cannot constrain
vertical deformation. Off-fault deformation (OFD) is calculated by simply taking the difference
between our COSI-Corr displacement measurements (total displacement) and the field
measurements (on-fault displacement), as described by equation (4).
Off-fault deformation = COSI-Corr displacement – Main strand field displacement. (4)
Field measurements are assumed to primarily capture the discrete, on-fault component of
slip as they typically use piercing points taken over a 1-10 m wide, fault perpendicular aperture
21
and therefore usually do not (and frequently cannot) include precise measurement of the
complex, distributed off fault deformation (McGill and Rubin, 1999; Treiman et al., 2002;
Rockwell et al., 2002; Shelef and Oskin, 2010). This assumption, however, forms a minor
limitation of our calculation of OFD, as in some cases field geologists may successfully capture
some or all OFD (e.g., by using an offset feature that is sufficiently large to span the entire fault-
zone). However, such features, which are almost universally man-made, must be linear,
orientated perpendicular to the fault, and have a precisely known pre-earthquake configuration.
Unsurprisingly such features were rare along the Landers surface rupture and therefore this bias
does not significantly affect our OFD data. Furthermore, post-seismic deformation likely does
not significantly bias our COSI-Corr comparison to the field measurements in calculating OFD,
because, as mentioned above, a maximum of ~15 cm of postseismic afterslip was observed seven
years after the earthquake (Fialko, 2004) (a conservative value given our data are acquired two
years after the earthquake) and also an amount barely detectable with our technique.
We determined the off-fault deformation at points along the surface rupture by iterating
through every COSI-Corr displacement measurement in order to find the nearest corresponding
field displacement point within a 138 m distance (stack width), and then computing the
difference. This difference yields a single value for the OFD at that point along the rupture,
following equation (4). In the 11 instances where field measurements are clearly collected as a
transect across multiple, parallel fault strands, we sum all the field offsets. However, in instances
where multiple field measurements are not strictly collected in such a manner and are
heterogeneously distributed within a single COSI-Corr measurement zone (138 m along-strike
distance), we treat these points as independent measurements and consider only the largest field
displacement. Using only the largest field measurement therefore characterizes the discrete
22
component of displacement occurring on the primary fault strand and thus the OFD calculation
gives a consistent estimation of the amount of inelastic deformation occurring away from the
main surface rupture. The output of this calculation gives a 2D map of OFD at 280 points along
the entire surface rupture (Figure 5). We find the OFD data follow an exponential distribution,
where the median of 0.56 m is ~70 % of the mean value of 0.81 + 0.12 m (2 σ measurement
precision). Comparing each COSI-Corr displacement measurement with the corresponding field
measurement indicates the former is systematically larger (Figure 6). The correlation between
the COSI-Corr and field displacement data is determined using a total least squares method,
which yields a slope of 1.47 that characterizes the relative difference in magnitude between the
two datasets.
As well as calculating OFD in meters we also express it as a percent of deformation that
occurs off the main fault, herein known as OFD%. This is simply defined as: (OFD(m) /COSI-
Corr displacement(m))×100, where at each point along the rupture we normalize for the amount
of total displacement. This normalization is performed for two reasons: i) we want to know the
relative amount of deformation that is accommodated off the fault in relation to how much is
accommodated on the discrete, primary strand. ii) The amount of OFD will arbitrarily be a
function of the amount of displacement at a given site, where the displacement itself varies along
the rupture. This allows for a direct comparison of its variability along the length of the surface
rupture. The OFD% is markedly larger in areas of structural complexity, such as stepovers (e.g.,
the Kickapoo and Homestead-Emerson step-overs), bends in the fault (notably at the bend of the
Emerson fault as it merges into the Camp Rock fault), branching of the main-strand rupture (as
seen in the central portion of the Johnson Valley fault) and the southern termination of the
Landers rupture (Figure 5b). To calculate a reliable mean OFD% value for the entire Landers
23
surface rupture, we spatially resampled the OFD data in order to correct for their spatial
heterogeneity, which if unaccounted for would cause a bias. Downsampling the OFD data into
15 regions equally spaced along the rupture evenly re-weights the data, thereby correcting for the
issue of spatial heterogeneity. From this procedure, we find OFD% for the Landers earthquake
has a mean value of 46 + 10 % (1 σ), following a normal distribution as confirmed by a Lilliefors
test.
2.4.4 Measuring Fault Zone Width (FZW)
The fault-zone width (FZW) is defined as the fault-perpendicular extent of observable
surface shear on either side of the primary, localized fault trace. From the correlation maps the
FZW is measured as the extent of detectable pixel movement found adjacent to a primary main
fault strand. Significantly, our method of measuring the FZW is insensitive to the physical
mechanism(s) accommodating shear across the fault-zone (e.g., warping, block rotation, grain
sliding, or folding), because COSI-Corr is simply detecting shifting of features in the photos that
exist on either side of the primary, discrete fault. Thus, our FZW measurements physically
represent the width of a shear zone accommodating horizontal deformation of > 10 cm (our
detection limit) by any number of possible deformation mechanisms.
A second set of synthetic tests were employed to investigate the degree of artificial
smoothing of the tectonic signal, caused by the use of a sliding window, and how this affects the
estimation of the FZW. This smoothing results from the assumption that during the correlation
process the subset of pixels evaluated within the sliding window have constant displacement. To
correct for this oversimplification, we created a series of synthetic faults of known widths
24
(between 1-155 m wide), and after correlation of the sheared image with a different, un-disturbed
image, we measured the smoothed, synthetic FZW. This gave an empirical calibration curve
(Figure S2), which allows us to reliably recover the true FZW from the smoothed equivalent.
Our results demonstrate that we can reliably resolve a FZW of > 18 m (anything less is still
measured, although the signal saturates and becomes too narrow to be fully resolved).
To measure the FZW of the Landers rupture we used the same stacked profiles that
defined the fault displacement to make a total of 1060 measurements (Figure 7). From these
measurements we found a mean FZW of 154 m, median of 96 m and a maximum of 1160 + 12 m
(2 σ), (located north of the Kickapoo stepover). The FZW varies smoothly along the Landers
rupture and is most pronounced in regions of structural complexity, such as stepovers, kinks, and
bends in the main fault trace, in a manner similar to the OFD result. Notably wide fault-zones
occur in the northern area of the Kickapoo stepover, in the northern region of the Homestead-
Emerson stepover, at the southern termination of the rupture and at a 33° bend in the Emerson
fault. The deformation width defined by the brittle, discrete faults, mapped by field geologists
shortly after the earthquake (Bryant, 1992; 1994; Liu et al., 2003 and references therein),
provides an independent constraint on the fault width, and agrees well with many of our FZW
measurements. However, in some places along the rupture our FZW measurements (a shear zone
accommodating deformation down to the 10-cm scale) are significantly wider than the fault-zone
defined by discrete faults mapped in the field (displacements generally mapped down to the 2 cm
scale). This discrepancy suggests that discrete, brittle faulting is not the only physical mechanism
accommodating strain, and that other processes, which are not easily observed in the field, exist,
such as warping, folding, granular flow, block rotation or micro-cracking, in agreement with
McGill and Rubin (1999).
25
2.5 Discussion
2.5.1 Factors Controlling Off-Fault Deformation (OFD) and Fault Zone Width (FZW)
Both the off-fault deformation (OFD) and fault-zone width (FZW) measurements exhibit
large spatial variability, raising the issue of what observable parameters could be the cause. Our
catalog of 280 OFD measurements and 1060 FZW measurements provides a large database with
which we can test various hypotheses. Here we apply a statistical analysis in order to understand
the range of possible parameters that likely controls the variability of strain localization.
Firstly, we considered the role played by the macroscopic, 1
st
-order fault-zone structural
complexity (complexity that varies on the 10
4
m length scale) in controlling the OFD and FZW.
We characterized the structural complexity of segments of the Landers fault system by
constructing a qualitative, subjective classification scheme that varies from 1-5, with 5 being the
most structurally complex and 1 the simplest. Our criteria for determining the relative level of
fault structural complexity of a region includes the number of faults in the given area, the degree
of segmentation and number of geometrical complexities such as bends, kinks or steps (Figure
8c).
We find OFD positively correlates with the macroscopic structural complexity of the
fault system, as intuitively expected, and as illustrated by the linear regression in Figure 8a.
Specifically, where the fault is more complex, with diffuse faulting spread over an area, we
observe systematically larger OFD%. In contrast, along structurally simple sections of the fault
(e.g., single fault strands), considerably less strain was accommodated off the main surface
rupture. In general, deformation accommodated off the main fault increases by ~10 % from one
26
level of our relative structural complexity index to the next, as expressed by the gradient in our
linear regression (Figure 8a).
The FZW is found to exhibit a positive, but weak, correlation with the fault-zone
complexity (Figure 8b). Specifically, a Monte Carlo simulation involving 10,000 iterations
shows the most probable relation between the FZW and fault zone complexity is positive
(gradient of 0.1). However, due to the large scatter in the data (as illustrated by the ‘error’ bars in
Figure 8b, which show the standard deviation of the data, as opposed to the standard error in the
estimate of the mean), there is ambiguity on the range of possible gradients that could fit the data
(1 σ for slope of 0.1). Nevertheless, as noted above, a basic observation from our analysis is that
the FZW widens in areas of increased structural complexity, such as stepovers or fault
terminations, and narrows in areas of simple fault structure.
Field studies of other surface ruptures have documented that the FZW and OFD vary at
least in some instances, according to the type of the near-surface materials (e.g., Rockwell et al.,
2002; Treiman et al., 2002; Van Dissen et al., 2011; Teran et al., in review; Zinke et al., 2014).
To investigate this, we used geologic maps (Dibblee, 1964a, 1964b; Dibblee, 1967a, 1967b,
1967c) to help categorize the geologic units along the Landers rupture. We hypothesized that the
more consolidated geologic units (e.g., bedrock) would yield lower magnitudes of OFD and
narrower fault zones, and vice versa for less-consolidated units (e.g., young alluvial sediments).
We also assign a third classification for near-surface materials, termed ‘sediment-bedrock
interface’, which describes areas of the rupture where sediment juxtaposes against bedrock. We
find distinct groupings of OFD associated with the type of near-surface materials through which
the rupture propagated (Figure 9a, b, c). As might be expected, ‘sediment-sediment’ units show
large amounts of OFD% (mean of 49 + 24 % (1 σ)), while ‘basement-basement’ units show a
27
surprisingly, large and similar amount of distributed deformation (mean of 52 + 25 %(1 σ)). The
‘sediment-basement interface’ classification in Figure 9b shows a positively skewed distribution
towards strain being more localized, and exhibits lower magnitudes of OFD% (mode of 19 %)
than other near-surface materials.
The FZW also exhibits a distinct and similar pattern as OFD, with the type of near-
surface material (Figure 9d, e, f). Specifically, where the rupture propagated along ‘basement-
sediment interface’, we find the narrowest FZW’s (mean of 55 m), conversely at sites of
‘sediment-sediment’ material the rupture exhibits wider zones of deformation (mean of 155 m)
and in ‘basement-basement’ material we find unusually wide FZWs (mean of 173 m).
Interestingly, the smallest magnitudes and narrowest zones of inelasticity are observed in areas
of ‘basement-sediment interface’ (Figure 9b and e), which likely results from efficient
localization at these sites along strong mechanical contrasts (Martel et al., 1988; Bruhn et al.,
1994; Sibson 2003; Ben-Zion and Sammis 2003). We also found that where the rupture
propagated through ‘basement-basement’ material, the FZWs are unusually wide and OFD
surprisingly large, compared to other material types. We attribute these somewhat
counterintuitive results because the vast majority of bedrock outcrop (84 %) occurs within the
structurally complex Homestead-Emerson stepover.
We compared several parameters with the surface deformation pattern, specifically the
fault complexity, the type of near-surface materials, lateral distance to bedrock (proxy for
sediment thickness), fault orientations (proxy for relation of fault to regional stress field) and
inferred age of alluvial fans (proxy for degree of lithification). Aside from the structural
complexity of the surface rupture and type of near-surface materials through which the rupture
propagated, we note for most of the tested parameters there was no clear correlation with OFD
28
and FZW (see Figures S5-17). We suspect that the overarching correlation we observe between
OFD and the structural complexity of the faults likely obscures and complicates isolating the
effects of other parameters.
Furthermore, an added complication in our analysis is that a component of the variability
in the OFD data is likely statistical noise, derived from inaccuracies of the reported field
displacement measurements. Such inaccuracies can arise due to the subjective and difficult
nature of measuring the true displacement from geomorphic piercing points where the exact pre-
rupture geometry is not known (McGill and Rubin, 1999; Arrowsmith and Rockwell, 2012;
Salisbury et al., 2012; Gold et al., 2013; Scharer et al., 2014). Over- or under-estimation of the
true fault displacement by field surveys will cause under- or over-estimation of OFD in our
calculation (equation (4)), respectively. For this reason, in our analysis we group larger subsets
of OFD data (e.g., Figure 8 and 9) which allows suppression of this effect and to more reliably
constrain possible correlations.
Our analysis of the Landers rupture reveals a mean value of 46 + 10 % (1 σ) of the
surface deformation was accommodated off-the primary fault (although it should be noted OFD
exhibits significant spatial variability along the rupture from 0-90%). But is this large average
value physically reasonable? Following the quasi-static model of fault evolution, faults that have
experienced small cumulative displacements, such as those involved in the Landers rupture (~3.5
km (Jachens et al., 2002)), have not accommodated sufficient strain to localize into simple,
organized, efficient systems (e.g., Wesnousky, 1988; 1990; Frost et al., 2009), and therefore we
expect a relatively large value of OFD (Dolan and Haravitch, 2014). Moreover, our value of
OFD agrees well with the results of Shelef and Oskin (2010), who found OFD of up to 46 + 6 %
29
along the comparably structurally immature (3.5 km cumulative slip (Bartley et al., 1992))
Harper Lake fault.
Damage zones of reduced rigidity with a width of ~2 km have been observed surrounding
the Landers surface rupture using InSAR data (Fialko et al., 2002), and also for the San Andreas,
Calico and San Jacinto faults using geodetic and seismic data (Eberhardt-Phillips and Michael,
1993; Allam and Ben-Zion, 2012; Cochran et al., 2009; Lindsey et al., 2013). In contrast, the
zone of inelastic deformation that we document from the Landers earthquake is much narrower,
with a mean FZW of 154 m. This is similar to the results of seismic studies using fault-zone
trapped waves and waves of reduced velocity, which reveal a damage zone width of ~100 m for
the Landers fault system (Li et al., 1998; Peng et al., 2003). This discrepancy between our single-
event data and observations of damage zones reflecting cumulative deformation, may be a
manifestation of progressive localization of near-surface damage and structural simplification of
the faults that ruptured in the Landers earthquake over geologic time. However, we reiterate that
our analysis can only observe surface deformation to a minimum threshold of ~10 cm using the
COSI-Corr technique. Thus, it is likely that minor amounts of distributed deformation could be
accommodated in a deformation zone wider than what is resolvable in our analysis. Nonetheless,
our data demonstrate that inelastic deformation was predominantly localized to within a < 200 m
wide zone along the faults, much narrower than the typical ~2 km wide deformation zones that
likely reflect the entire, cumulative history of deformation.
There is likely a complex combination of multiple parameters that control strain
localization, many of which remain poorly constrained or are not accounted for at all in this
analysis. For example, the local static and dynamic stresses, the dynamic rupture velocity, and
fracture energy are thought to strongly control the deformation pattern around the propagating
30
rupture tip (e.g., Ben-Zion and Andrews, 1998; Ben-Zion and Shi, 2005; Sammis et al., 2009;
Avouac et al., 2014). Knowledge of the characteristics of the rupture processes at the spatial
scales (>100 m) used here and a more robust characterization of the measurement uncertainty in
field offset measurements, would serve to improve analyses of strain localization. Additional
measurements of surface deformation from other large-magnitude, structurally simpler ruptures
will also help to further clarify the characteristics of co-seismic strain localization.
2.5.2 Coseismic Slip Variability
Understanding co-seismic, surface slip behavior can provide useful information on fault-
zone mechanics, the potential for faults to link together to generate large earthquakes, the
dynamic rupture process, and the likely endpoints of ruptures (e.g., Wesnousky, 2006; 2008;
Elliott et al., 2009; Oskin et al, 2012; Rockwell and Klinger, 2013). Our spatially consistent
dataset documenting fault displacement as well as OFD allows for a detailed discussion of the
faulting kinematics, co-seismic slip variability, and dynamic rupture behavior of the Landers
earthquake.
Theoretical, analog, and geologic studies all suggest that rupture fronts dissipate fracture
energy, and decelerate as they encounter zones of complex, diffuse deformation which in some
cases leads to rupture cessation (e.g., Segall and Pollard, 1980; Schwartz and Coppersmith, 1984;
Barka and Kadinskycade, 1988; Harris et al., 1991; Harris and Day, 1993; Duan and Oglesby,
2005; Wesnousky, 2006; Oglesby, 2008; Biegel et al., 2008; Elliott et al., 2009; Sammis et al.,
2009). The location of two areas of reduced slip (termed ‘slip gaps’ by Spotila and Sieh (1995))
along the surface rupture (labeled iii and iv in Figure 3), can be explained by their spatial
31
relation to the structurally complex Kickapoo and Homestead-Emerson stepovers that in both
cases lie directly to their south. At both structurally complex stepovers we found increased
FZWs and OFD% (in agreement with Michel & Avouac (2006)), where the rupture also
significantly decelerated, as revealed by seismic inversion studies (Wald and Heaton, 1994). This
relationship between abrupt changes in fault slip and the presence of structural barriers that affect
the rupture process has also been well documented in other earthquakes (e.g., Aki, 1979; Spotila
and Sieh, 1995; Klinger et al., 2006; Elliott et al., 2009). The OFD% and FZW also increases
markedly towards the southern termination of the Landers rupture, which suggests that the more
diffuse fault structure there likely acted as a barrier that arrested rupture propagation. In contrast,
our measurements do not provide an explanation for the northern rupture termination where we
observe low OFD and narrow FZWs, where slip was concentrated only within the uppermost few
km along the Camp Rock (Wald and Heaton, 1994).
The co-seismic slip profile for the Landers rupture exhibits strongly heterogeneous along-
strike slip variability (Figure 3). There is no consensus as to whether along-strike co-seismic slip
variability observed at short spatial dimensions is a true reflection of the rupture process or is an
artifact of inadequate characterization of fault displacements and/or missing OFD. For example,
measurements of the co-seismic slip from terrestrial lidar scanning along the M
w
7.2 El-Mayor
earthquake suggest a smooth slip distribution at along-strike wavelengths < 100 m, and that the
slip variability observed in geological field measurements arise primarily from measurement
noise (Gold et al., 2013). In contrast, studies of co-seismic slip distributions from the 1940 M
w
7.1 Imperial, 1999 M
w
7.5 Izmit, and 2001 M
w
7.9 Kokoxili earthquakes, using various field and
remote-sensing techniques that incorporate OFD, suggest that slip variability is a real reflection
of the rupture process (Rockwell et al., 2002; Klinger et al., 2006; Rockwell and Klinger, 2013).
32
Resolving whether co-seismic slip is smooth or truly irregular at short length scales has
important implications for understanding the physics governing the rupture process, and the
estimation of paleoearthquake magnitudes from fault offsets.
As the along-strike slip variability exceeds that of the measurement error, this suggests
the variability is a real signal, reflecting aleatory variability of the rupture process and is not
derived from epistemic uncertainty (i.e. measurement noise). Our synthetic tests, which form an
extensive error analysis of the measurement precision (see Figures S1-4), have allowed us to
quantify and incorporate the various sources of error that were previously thought to be the
major source of the observed slip variability. Furthermore, the slip variability we observe
includes OFD measured on average up to 154 m from the surface rupture (Figure 7), therefore
indicating the variability we measure does not simply arise from missing distributed strain along-
strike, as has been commonly assumed.
These observations raise an obvious question – Are there other potential explanations for
the slip variability we observe? For example, highly diffuse, distal OFD that exists below our
threshold of detection, if accounted for, could smooth the overall along-strike deformation
profile. However, for this effect to discount the near-field variable slip, would require low-
amplitude deformation that occurs over wide fault-perpendicular regions (in order to be
undetectable) that would also have to anti-correlate over the same short along-strike distances as
the co-seismic slip distribution, which seems physically unlikely. Nevertheless, the possible
presence (or absence) of distal, diffuse OFD (> 200 m from rupture) does not negate our
observation that the deformation in the near-field (0-100’s m from surface rupture) is variable. A
second possible mechanism is that displacement variability could be explained by
accommodation of slip in the fault-perpendicular direction. However, our measurements of fault-
33
perpendicular displacement from the correlation results (Figure 1), indicate that such a
mechanism cannot explain the lateral, along-strike slip heterogeneity because these
displacements exist below the noise level (i.e., have an amplitude less than 10 cm).
Fractals are observed widely in many facets of earthquake behavior, such as the
Guttenburg-Richter frequency-magnitude scale (Gutenberg and Richter, 1956; Kanamori and
Anderson, 1975), seismicity distribution across faults (Powers and Jordan, 2010), fault surface
roughness (Brown and Scholz, 1985; Power et al., 1987; Biegel et al., 1989; Power and Tullis,
1988; 1995; Lee and Bruhn, 1996; Renard et al., 2006; Candela et al., 2009), spatial structure of
faults (Aviles et al, 1987; Okubo and Aki, 1987), and spatial distributions of earthquake
hypocenters (Robertson et al., 1995). Noting that the slip distribution is highly heterogeneous,
we used a spectral analysis to show that the slip distribution is self-affine fractal (Figure 4), with
a dimension (D) of 1.56 + 0.04. We believe this is the first study to conclusively find, with direct
observations, that co-seismic slip is scale-invariant (within the observed wavelengths) and self-
affine fractal. Essentially fractal slip means a power-law describes the relation between the slip
amplitude and wavelength over a broad spectrum, indicating that the seemingly complex
‘variability’ actually has a simple and predictable underlying structure. This is in agreement with
modeled fault slip distributions determined from inversion of seismic and geodetic data, which
also exhibit a fractal structure (Mai and Beroza, 2002). Dunham et al. (2011) generated 2D
numerical simulations of dynamic rupture propagation along a non-planar fault of fractal
roughness surrounded by a damage zone, and found that geometrically rough faults produce
significant along-strike slip variability. They suggested that stress variations along the fault result
from surface roughness, which in turn accelerates and decelerates the rupture front, causing slip
heterogeneity Similarly, Dieterich and Smith (2009), using a quasi-static, numerical model, also
34
found a nonplanar, fractal fault surface produces variable along-strike slip. They attributed
highly-variable slip to the generation of backstresses from the geometric irregularities of the fault
surface that acted to resist the applied Coulomb stress driving slip. Thus, if the slip variability
observed here is a manifestation of fault roughness, it is not surprising to find that slip is fractal,
given that many natural fault surfaces also display self-affine fractal roughness (e.g., Power and
Tullis, 1995; Lee and Bruhn, 1996; Renard et al., 2006; Candela et al., 2009). The Hurst
exponent of 0.44 + 0.04 we derived from our analysis of the Landers slip distribution and
equation (3) indicates that co-seismic slip was non-persistent. This value is similar to that found
by Powers and Jordan (2010) from seismicity distributions across aftershock-dominated, small
faults in southern California (such as the Landers-type faults), where the authors also attributed
the observed power-law decay of seismicity distributions to fault surfaces of fractal roughness.
The observed anti-persistence of the slip distribution is the expected result if slip is controlled by
roughness of the fault plane. Each asperity on a fault plane can be viewed as a restraining bend
followed by a releasing bend (or vice-versa). Fault roughness can be viewed as a fractal
distribution of such asperities. In this view, low slip at a restraining bend is necessarily followed
by high slip in the associated releasing bend, resulting in an anti-persistent slip distribution - as
observed.
Our measured slip profile exhibits an apparent roll-off of the spectra at ~70 km (k
c
in
Figure 4), which is arbitrarly related to the length of the Landers rupture. This indicates fractal
slip has an upper physical limit and suggests fractal behavior is limited to a certain range of
spatial frequency bands. We hypothesize that if slip variability is primarily a result of the fault
geometrical roughness, then the lower physical limit could be set by smoothing of the fault
surfaces due to abrasional wear and fracturing, which would alter the fractal properties of the
35
fault surface (initially) at smaller wavelengths. Specifically, this simple mechanism would cause
prefential destruction of smaller, more fragile asperities, while larger-wavelength asperities,
which are physically more robust, will survive, as documented by Sagy et al. (2007), and in the
slip spectra (Figure 4) would produce a second roll-off or ‘whitening’ at higher wavenumbers.
However, as our Nyquist frequency is 69 m (smallest reliably resolvable length scale, defined as
half the sampling frequency of 138 m), our data cannot directly resolve the expected lower limit
to ‘band-limited’ fractal slip. Our results, however, are not necessarily incompatible with those
of Gold et al. (2013), who found using T-lidar data that slip over < 100 m along-strike length
scales along the El-Mayor 2010 earthquake, is smooth. Fractals imply scale-invariant behavior,
and we postulate that smaller-amplitude slip variability could be further embedded within an
apparently smooth slip profile, that would be too subtle to detect given the precision of restoring
geomorphic features using the T-lidar data (2 σ + 0.12 m). This would suggest that the smooth
profile is a good approximation of the 1
st
-order slip variability occurring over the ~100 m length
scale, but that smooth slip is not a true reflection of the underlying rupture process. In order to
resolve this issue, would require ultra-high detailed measurements of fault slip that can detect
centimeter-scale slip variability over < 100 m along-strike length scales.
2.5.3 Implications for Slip Rates and Seismic Hazard
The presence of significant inelastic strain accommodated over a finite fault width along
the Landers rupture has important implications for the use of any surface fault offset
measurements, especially for estimates and interpretation of geologic fault slip rates and paleo-
earthquake magnitudes. For example, if slip rate studies are conducted within a narrow aperture,
36
(i.e., over a few meters to tens of meters), restoration of geologic piercing points will likely miss
a component of off-fault deformation, thus causing an underestimation of the fault slip rate. Such
possible underestimation of fault slip rates, which are used as basic input for probabilistic
seismic hazard assessment (PSHA) models, would lead to an underestimation of the potential
seismic hazard of a region.
Variation of slip over short along-strike distances observed from the Landers data, has
direct implications for estimating the magnitude of paleo-earthquakes using geologic fault
offsets. Specifically, the occurrence of along-strike co-seismic slip variability introduces large
ambiguity and error into what possible earthquake magnitude could have produced the observed
geologic fault offset (Rockwell et al., 2002; Biasi and Weldon, 2006). Furthermore, variable slip
also implies that studies attempting to re-construct slip profiles of historic earthquakes from a
stretch of fault, must be careful when trying to correlate offsets along-strike (e.g., Zielke et al.,
2012).
A simple strategy to avoid underestimating slip rates due to the presence of sometimes
unobservable inelastic, off-fault deformation is to project piercing points over a distance that
traverses the entire fault-zone. But this begs the question, what is the necessary length scale to
capture all the deformation accommodated by an immature fault? The mean width of
deformation of the Landers rupture derived from 1060 FZW measurements is ~150 m (or ~75 m
from either side of the fault trace). We suggest that this is a conservative distance to adequately
capture the majority of deformation across a fault-zone with similar structural maturity to the
faults involved in the Landers event. These FZW measurements thus provide useful information
for future geotechnical zoning studies, as it will provide constraints on the width of the fault-
surface-rupture hazard zone, where we would expect permanent ground deformation and direct
37
destruction to engineered structures (Chen and Petersen, 2011; Petersen et al. 2011.) These
results which show significant off-fault surface deformation accommodated within these fault-
zones, reinforce the wisdom of fault “set-backs” such as those mandated by California Alquist-
Priolo zones.
2.6 Conclusions
We developed a methodology to constrain the near-field, surface deformation pattern,
that facilitates measurement of the co-seismic slip distribution, off-fault deformation, and fault-
zone width using cross-correlation of pre- and post-event aerial photographs. This methodology
is highly versatile and can be applied to historic and recent earthquakes in a cost-effective
manner. This approach is also a useful complement to field investigations, as well as other
remote sensing techniques, such as SAR interferometry, where there is typically a lack of data
within 1-2 km of the rupture.
We applied our methodology to successfully constrain the near-field surface deformation
pattern of the 1992 M
w
7.3 Landers earthquake and the full co-seismic slip distribution down to
10 cm precision. Analysis of this dataset shows that the Landers earthquake accommodated 46 %
of total surface strain as off-fault deformation over a mean deformation-zone width of 154 m.
We also find that the Landers co-seismic slip distribution exhibits a consistent degree of
variability at all observable length scales, and that the variation is neither an artifact, nor random,
but rather is fractal. We attribute the fractal behavior of co-seismic slip to a fault surface of
fractal roughness that likely alters the local stress.
38
Our analysis indicates that the structural complexity of the fault-zone is the dominant
control on the magnitude and width of surface deformation. Off-fault deformation and fault-zone
widths are largest in stepovers, kinks, and bends in the faults, as well at the southern termination
of the Landers rupture. We also observe a correlation with the type of near-surface material
through which the rupture propagated, with surface rupture along bedrock-sediment interfaces
generating less off-fault deformation with relatively narrower fault zones, in contrast to wider,
more distributed deformation where the rupture extended through sediments.
2.7 Figure captions
Figure 1. Correlation maps from 31 aerial image pairs which bracket the Landers earthquake.
Black star shows location of 1992 M
w
7.3 epicenter with map co-ordinates in UTM. (a) North-
south correlation map, positive pixel values indicates movement to the south and negative to the
north. The lower left inset shows fault-parallel displacement within a 138 m wide stacked profile
from X-X’ and illustrates how the displacement and fault-zone width are measured. b) East-west
correlation result with positive pixel values indicating pixel movement to west and negative to
the east. Inset fault map in lower left corner shows annotated Landers surface rupture (Liu et al.,
1993).
Figure 2. (a) Map view of field data compiled from Liu et al (2003) and Bryant (1992; 1994) that
are used to calculate off-fault deformation (OFD), positive values denote right-lateral
displacement, negative left-lateral displacement. (b) Map view of all 1057 displacements
39
measured from the correlation maps. Inset images in lower left corners of a) and b) show
histogram of data.
Figure 3. (a) Landers offset profile from our COSI-Corr displacement measurements plotted as a
function of UTM Northing. Thin multicolored lines show the offset profiles for individual faults.
Thick black line shows the projected, cumulative offset profile for Landers. Green colored
arrows, labelled i and ii, indicate the major peaks of displacement and red colored arrows
labelled iii and iv indicate the areas of reduced slip, termed ‘slip gaps’ (Spotila and Sieh, 1995).
Yellow star denotes the location of the epicenter. Inset map in upper right corner illustrates faults
used in the slip profile with their corresponding colors used in the offset profile. (b) Cumulative,
projected displacement (black line) plotted against UTM Northing, with the field displacement
from Bryant (1992; 1994) and Liu et al. (2003) and references therein, plotted as red dots.
Figure 4. Power spectrum of the along-strike slip as a function of spectroscopic wave number (m
-
1
) in log-log space, computed using the multitaper method (MTM) (Thomson, 1982). The 95 %
lower and upper confidence intervals are plotted as lower and upper gray lines, respectively. The
β parameter, is estimated using a Monte Carlo method with 10,000 simulations (green line
showing the most probable fit) to the power spectral decay beyond the corner wave number (k
c
)
at the ~70 km wavelength. The Monte Carlo yields a β value of 1.87 + 0.04 (95% confidence
interval), with an R
2
of 0.80.
40
Figure 5 (a) Map view of the off-fault deformation (OFD) in meters. Points are computed from
differencing the data in Figure 2a from 2b. (b) Map view of OFD%. Qualitatively, the OFD% is
smaller along structurally simple parts of the rupture (e.g., Johnson Valley fault) and largest in
structurally complex areas (e.g., Homestead-Emerson stepover, bend in the Emerson fault and
sites of branching of the rupture).
Figure 6. Correlation plot of field displacements versus our COSI-Corr displacement
measurements. The gray ellipses denote the 1 σ error in both the x and y direction. Using a total
least-squares approach to fit a linear regression to the observed data, which accounts for errors in
the x and y, the best-fitting model has gradient of 1.47, with R
2
of 0.77, which is in contrast to
the black line with gradient of one.
Figure 7. Map view of all 1060 fault-zone width (FZW) measurements, spaced every 138 m
along the surface rupture. The FZW is plotted as red bars with the histogram in lower left corner.
Inset images shows examples where the FZW increases where the rupture becomes structurally
complex (e.g. at branches, bends or terminations).
Figure 8 (a) Percent of off-fault deformation (OFD%) plotted as a function of the fault zone
complexity. (b) FZW plotted as a function of fault-zone complexity A Monte Carlo simulation
with 10,000 iterations yields an estimate of the slope for the linear regressions in a) as 8.9 + 4.6
(1 σ) and for (b) as 0.1 + 0.1 (1 σ), where the slope in (b) exhibits large ambiguity due to the
large variability of the data. We find a p-value of 0.34 indicating weak statistical significance. c)
41
Map view of Landers surface rupture shown in red lines (Liu et al., 2003). Structural complexity
of the fault zone is delineated by the colored polygon areas, classified from 1 to 5, with 1 being
the structurally simplest and 5 the most complex. We classify the structural complexity on the 1-
10 km length scale so to analyze the macroscopic complexity of the mapped fault traces, with the
following criteria defining each index: 1, straight, continuous single stranded. 2, Segmented,
semi- continuous trace with smaller secondary faulting. 3, Dual-stranded or greater number of
secondary faulting. 4, Abundant secondary faulting, subtle-moderate bends in fault trace. 5, Step-
overs, highly diffuse areas of faulting, macroscopic fault bends. We note that the width of the
deformation was not used as a criterion of fault-zone complexity and these parameters are treated
independently.
Figure 9. (a,b,c) Histograms of OFD% subdivided into ‘sediment-sediment’ (mean 48 %),
‘sediment-basement interface’ (mode of 19 %, which is the global maximum of the population)
and ‘basement-basement’ lithologies (mean 52 %), respectively. Red lines show the best fitting
distributions which are normal, as confirmed by a Lilliefors test, except for b) which is a
positively skewed distribution. (d,e,f) FZWs plotted with same lithological classification, which
are lognormal as confirmed by Lilliefors tests, except for e) which is only slightly negatively-
skewed. ‘Sediment-basement interface’ shows the narrowest FZW with mean of 55 m and
median of 58 m, ‘sediment-sediment’ shows wide FZW with mean of 155 m and median of 84 m
and ‘basement-basement’ shows unusually wide FZWs with mean of 173 m and median of 129
m.
42
2.7.1 Captions for Supplementary Materials
Figure S1 (a) left: Synthetic correlation map of a single dextral fault striking north-south, with a
uniform, prescribed right-lateral displacement of 2m, with map co-ordinates in UTM. This
correlation is produced by using two-different images taken at different times (1989 and 1994) of
the same area, where the eastern half of the most recent image (1994) is displaced to the south.
The hashed rectangle shows the dimensions of the stacked profile orientated perpendicular to our
synthetic fault, with an along-strike width of 138 m and length of 1.75 km. (b) Right, shows the
synthetic deformation signal seen in the stacked profile. The x-axis is distance along profile
length. The y-axis is the pixel movement. The black line is the surface deformation from the
synthetic correlation map in a). Red sub-horizontal dashed lines are the linear regression fits to
the data. Displacement is defined as the difference between the 2 linear regressions where they
intercept the fault trace at x = 0, which in this profile is measured as 2.09 m.
Figure S2. Result from the synthetic tests measuring the FZW from the correlation maps in
comparison to the known, pre-determined true value. The linear regression is our calibration
function, which serves as an empirical tool to correct for the correlation window systematically
and artificially widening the true FZW.
Figure S3. Results from the synthetic tests repeatedly measuring the FZW along a fault of
constant known width of 60m. Blue histogram bars show the binned data measured from the
43
correlation maps. Red line shows our best model fit to the data with a Gaussian distribution.
Green vertical line shows the known, synthetic, pre-determined FZW value (60m).
Figure S4. Results from the synthetic tests repeatedly measuring the displacement along a fault
of constant, known displacement using stacked profiles. Two tests are performed. Test 1: is a
fault with uniform displacement of 0.5 m. Test 2: is a fault with uniform displacement of 2 m. (a)
Blue points are displacement measured plotted along-strike of our synthetic fault. Green
horizontal line shows the true, uniform displacement of the fault. The variability observed is a
reflection of subjectively estimating the displacement, noise in the data and geometric artifacts.
(b) Blue histogram bars show the binned displacement measured from the correlation maps. Red
line shows our best model fit to the data with a Gaussian distribution. Green vertical line shows
the known, synthetic, pre-determined displacement value.
Figure S5. Fault-zone width plotted against off-fault deformation. We find a from a Spearman’s
rank a value of 0.33, indicating that the FZW can only explain a small portion of the variabilty in
the OFD data. We do find however, a p-value < 0.01, indicating that there is a linear relation
between the data and that they are not independent.
Figure S6. COSI-Corr displacement (which represents the total displacement across the fault)
versus fault-zone width plotted.
44
Figure S7. COSI-Corr displacement (which represents the total displacement across the fault)
versus off-fault deformation.
Figure S8. a) Locations of fault-zone width measurement plotted with the geologic maps which
illustrates the range of near-surface materials used in the analysis (Dibblee, 1964a, 1964b;
Dibblee, 1967a, 1967b, 1967c). b) shows enlargement of southern termination of Landers
rupture.
Figure S9 a) Locations of off-fault deformation plotted with the geologic maps which illustrates
the range of near-surface materials used in the analysis (Dibblee, 1964a, 1964b; Dibblee, 1967a,
1967b, 1967c). b) shows an enlargement of the Kickapoo stepover illustrating variation of OFD.
Figure S10. a) Off-fault deformation plotted as a function of horizontal distance to the nearest
outcrop of exposed bedrock which serves as a proxy for thickness of sediment. Larger distances
from the nearest range front would expectedly have thicker amounts of sediment and therefore
larger OFD and FZW. b) Shows fault-zone width plotted as a function of distance to bedrock,
where location of bedrock exposures are determinded from the geologic map (Figure S3).
Figure S11.a) Off-fault deformation plotted against the deviation of fault strike from a regional
strike. The regional strike represents the regional stress field, and thus the deviation a proxy of
the faults optimal orientation to the regional stress field. Faults with large deviations from zero
(the presumed optimal faulting strike) will likely be misaligned with the regional stress field and
likely yield larger OFD and wider FZWs.
45
Figure S12.a)Vertical offset plotted against off-fault deformation (%). Vertical deformation
along a sub-vertical fault-plane can in places producing ponding of sediment against the fault
scarp and therefore produce local areas of thick sediment. Thicker sediment would expectedly
produce larger amounts of OFD.
Figure S13. Fault-zone widths measured in alluvial fans of different inferred ages. Alluvial fan
ages are determinded relatively from multi-spectral aerial images and Google Earth and by
analyzing the degree of desert varnish development, surface texture and relative amount of
incision of each fan. We designate these with informal, local indexes as Q1 through Q4 from
oldest to youngest, where degree of consolidation is expected to increase with age. a) Shows
FZW for Q1, b) FZW for fans measured in Q2, c) FZWs measured in Q3 alluvial fans and d)
FZWs measured in Q4 material.
Figure S14. Off-fault deformation (%) measured in alluvial fans of different inferred ages. Q4 is
the youngest fan, assumed to be the least consolidated and most likely to produce the largest
OFD. Q1 is the oldest observable fan along the surface rupture and assumed to be the most
consolidated and likely to produce least strain accommodated off the primary fault strand.
Alluvial fan ages are determinded relatively from multi-spectral aerial images and Google Earth
and analyzing the degree of desert varnish development, surface texture and relative amount of
incision of each fan. a) Shows OFD for Q1, b) OFD for fans measured in Q2, c) OFD measured
in Q3 alluvial fans and d) OFD measured in Q4 material.
Figure S15 a) Mean OFD with 1 sigma error plotted for different zones of structural complexity
with colored dots denoting different lithologies found within each bin of structural complexity.
b) Mean FZW plotted with 1 sigma error for different zones of structural complexity with
46
colored dots denoting different lithologies found within each bin of structural complexity. We
use three zones of structural complexity instead of five, as used in the main text because this
avoids parsing the data too finley and loosing sample sizes.
Figure S16. a) The Fault length of 69 individual faults plotted against mean displacement found
along the given fault. Blue line shows best fit linear regression with R
2
= 0.58 b) Fault length
plotted against maximum displacement measured along the individual fault. Blue line shows best
fitting linear model with R
2
= 0.52. c) Mean OFD plotted as a function of length of fault. Blue
line shows best fitting linear model with R
2
= 0.10. d) Shows fault length plotted against the
mean fault-zone width of each fault, red line shows best fitting linear model with R
2
= 0.22.
Figure S17 (a) Subset of the north-south correlation result along the southern section of the
Johnson Valley fault, with location of profiles labelled. Color bar shows magnitude of pixel
movement, blue is movement to the north and yellow towards the south. (b) Google earth image
acquired of the same aerial extent as (a), illustrating the types of near-surface material and extent
of the alluvial channel and location of profile transects.(c) Profile drawn across the Holocene
alluvial channel showing the surface deformation signal taken from the correlation result in a).
The signal exhibits a wide fault-zone of 68 m, as delineated by the red, vertical dashed lines and
horizontal arrow. (d) Surface displacement signal from a profile drawn across the Landers
surface rupture from a), within a Pleistocene, more consolidated alluvial fan, which shows a
narrower 18 m fault-zone as delineated by the red, vertical dashed lines.
47
CHAPTER 3:
Resolving Fine-Scale Heterogeneity of Co-seismic Slip and the Relation to Fault Structure
3.1 Abstract
Fault slip distributions provide important insight into the earthquake process. We analyze high-
resolution along-strike co-seismic slip profiles of the 1992 M
w
= 7.3 Landers and 1999 M
w
= 7.1
Hector Mine earthquakes, finding a spatial correlation between fluctuations of the slip
distribution and geometrical fault structure. Using a spectral analysis, we demonstrate that the
observed variation of co-seismic slip is neither random nor artificial, but self-affine fractal and
rougher for Landers. We show that the wavelength and amplitude of slip variability correlates to
the spatial distribution of fault geometrical complexity, explaining why Hector Mine has a
smoother slip distribution as it occurred on a geometrically simpler fault system. We propose as
a physical explanation that fault complexity induces a heterogeneous stress state that in turn
controls co-seismic slip. Our observations detail the fundamental relationship between fault
structure and earthquake rupture behavior, allowing for modeling of realistic slip profiles for use
in seismic hazard assessment and paleoseismology studies.
3.2 Introduction
The spatial pattern of fault slip associated with large earthquakes provides fundamental
insight into rupture mechanics Scholz 2002, faulting processes Wells and Coppersmith 1994 and
seismic radiation Graves et al., 2011. However, our current understanding of co-seismic surface
slip distributions is limited by the inherent drawbacks of standard measurement methodologies:
geodetic data are typically either too sparse to resolve fine-scale heterogeneity (e.g., point Global
48
Positioning System measurements), or adversely affected by strong shaking and deformation
near the surface rupture (e.g., loss of phase coherence in Interferometric Synthetic Aperture
Radar data) Bürgmann et al., 2000b), whereas geologic field measurements typically cannot
include off-fault deformation McGill and Rubin 1999 and are confined to sparse along-fault
locations Gold et al., 2013; Scharer et al., 2014. Co-seismic slip as constrained by these coarse
data has been well-characterized to first order as smooth, semi-elliptical or triangular
distributions with fluctuations related to seismogenic-scale fault segmentation, or off-fault
yielding Scholz 2002; Manighetti et al., 2005; Klinger 2010. However, these first-order models
fail to explain observations from more recent higher-resolution field and geodetic studies, which
have consistently documented high-amplitude, short-wavelength variation of slip, even when
incorporating the effects of off-fault deformation Rockwell et al., 2002; Hudnut et al., 2010;
Leprince et al., 2011; Rockwell and Klinger 2013; Chen et al., 2015. Thus, several key questions
remain: Why does the short-wavelength variability exist? Does this variability follow any
pattern? And what is the physical explanation for this variability?
In this study, we address these questions by generating high-resolution along-strike co-
seismic slip profiles for the 1992 M
w
= 7.3 Landers and 1999 M
w
= 7.1 Hector Mine earthquakes
using subpixel optical image correlation Leprince et al., 2007b. These data allow for the first
time an analysis of the frequency content of co-seismic slip along an entire surface rupture with
high density and number of measurements to high precision. We find from analyzing the fractal
properties of the slip distribution and fault structure, that the along-strike slip variability
correlates with zones of geometrical fault complexity at all scales. From this correlation we infer
that fault complexity gives rise to heterogeneity in the stress field, which in turn causes variable
co-seismic slip.
49
The 1992 M
w
= 7.3 Landers and 1999 M
w
= 7.1 Hector Mine earthquakes are ideal
candidates for investigating and directly comparing co-seismic deformation patterns between two
events for several reasons. First, the two events occurred on kinematically similar NNW-trending
right-lateral fault systems located within the same tectonic regime, the Eastern California Shear
Zone, with epicenters only 20 km apart (see inset map in Fig. 1a). Second, pre- and post-event
high-resolution aerial photographs of 1 m pixel size exist for both earthquakes acquired from the
same optical sensor with similar flight parameters (see Methods). Finally, both ruptures extend
through an arid desert region providing optimal conditions for subpixel correlation between
image pairs acquired at different times as surface features are well preserved, and also the
surface ruptures are not obscured by either vegetation or urban development. Thus, these
conditions allow for complete constraint of the near-field deformation in high-resolution, with
the use of data of comparable spatial resolution and accuracy between the two earthquakes.
3.3 Methods
3.3.1 Subpixel image correlation of air photos.
For the Landers and Hector Mine earthquakes we selected 31 and 21 pairs of stereo-pair
(60% overlap), 1 m resolution, National Aerial Photography Program aerial photographs,
respectively, with 8×8 km footprint (purchased from http://earthexplorer.usgs.gov/). We selected
air photos acquired in 1989, 1994 and 2002, where air photos from the two earlier flight missions
serve as the pre and post Landers data and the latter two serve as the pre and post Hector Mine
data. We note air photos from the 1994 flight mission serve as both the pre-Hector Mine and
post-Landers dataset, giving rise to deformation maps for the two earthquakes derived from the
50
same data acquired from the exact same optical sensor and flight mission, which helps minimize
differences in data quality and accuracy. To produce correlation maps that accurately constrain
the ground deformation pattern, the input aerial photographs must be precisely orthorectified and
co-registered before correlation. The COSI-Corr program
(http://www.tectonics.caltech.edu/slip_history/spot_coseis/download_software.html) allows for
accurate orthorectification of images by taking into account the topography using a digital
elevation model (DEM), the internal camera geometry using a camera calibration report
(https://calval.cr.usgs.gov/calval_osl/calibration_reports/) to correct for optical distortions and
the exterior orientation determined from ground control points (GCPs) Ayoub et al., 2009. To
account for topographic distortion of the images, for both the Landers and Hector Mine events,
we used the same 2012, 10 m National Elevation Dataset DEM that covers both ruptures,
acquired from the USGS (http://ned.usgs.gov/). To georeference the post-event aerial photos, we
used a 2005, 10 m, SPOT 5 image as the reference orthoimage for Landers and a 2000, 10 m,
SPOT 4 image for Hector Mine. To co-register the pre and post-event photographs, we construct
a relative mapping between image pairs using tie points that relates common features between
pre and post-event image pairs. For co-registration GCPs are assumed to have experienced zero-
ground movement, however, this assumption is violated due to long-wavelength ground
deformation, to correct for this we used a correlation result from a pair of 10 m, SPOT 2 images
for Landers and SPOT 4 images for Hector Mine Ayoub et al., 2009 (Supplementary Fig. S1),
which provides independent constraint on ground motion. Topographic artifacts in the
correlation result caused by use of only a single DEM to orthorectify both the pre and post-event
photos are corrected for following the procedure of Ayoub et al. (2009). Once the pre and post-
event air photos are orthorectified, COSI-Corr then applies subpixel image correlation to pairs of
51
selected orthoimages by using an iterative, unbiased processor that estimates the phase plane in
the Fourier domain Leprince et al., 2007b. For image correlation we used a multiscale sliding
window of initial size of 64 and final size of 32 pixels with a step of 6 pixels, resulting in a
correlation map of 6 m pixel resolution.
3.3.2 Measuring displacement.
Displacement is measured using stacked profiles orientated perpendicular to the fault
strike, with lengths of 1-3 km and stack widths of 138 m, where the width defines the
discretization of independent measurement. The optimal stack width of 138 m (23 pixels) is
determined from synthetic tests (Supplementary Fig. S3-7), that gives a noise level of 2σ = 0.12
m in the displacement measurement, a noise level and stack width in agreement with previous
work Michel and Avouac 2006, that allows for suppression of noise while minimizing over-
smoothing along-strike changes in surface slip. Surface displacement is estimated from these
stacked profiles by manually fitting linear regressions to either side of the fault, which are
extrapolated to the fault trace to define the total amplitude of the discontinuity in the vector field,
giving the magnitude of the total shear accommodated across the entire width of deformation (as
shown in inset Fig. 1a,c). Where multiple fault strands exist within a single profile we measure
displacement from each fault independently and simply sum these to give the total displacement
accommodated across the system of faults.
52
3.3.4 Synthetic tests.
Estimating the magnitude of fault offset from the stacked profiles involves subjectively
interpreting and fitting linear regression to the deformation signal, which can potentially lead to
measurement bias and a possible component of artificial along-fault slip variation. To quantify
the measurement precision and any possible bias that may arise in subjectively estimating
displacement, as well as bias imposed by geometrical image distortions (such as scanning,
thermo-mechanical warping or radial distortions) we employed a series of synthetic tests. In
these tests we simulated synthetic fault ruptures through images with pre-determined constant
along-strike fault displacement, where any deviation of the measured displacement from this
known, spatially uniform synthetic value, directly quantifies the artificial amount of variation of
displacement that arises from the subjective nature of estimating displacement, noise or artifacts
within the correlation maps. These tests use the exact images and measurement process (i.e.,
correlation window parameters and stack profile dimensions) as that used to measure
displacement from the real earthquake rupture, therefore allowing us to incorporate and asses the
same noise, artifacts and measurement errors that would affect our real results. We note that we
use MATLAB’s random number generator to produce the synthetic constant displacement so that
the true value is not known when measurements of the displacement are estimated from the
synthetic rupture. The true value is recorded, but not revealed to the user until after the
measurements are complete, therefore avoiding any contamination from subjective bias. From
these tests we derived an empirical error distribution (2σ = 12 cm) for displacement, in
agreement with previous work Michel and Avouac 2006 (see Supplementary Fig. S3-7 and
Supplementary Table S1-3). We note the synthetic tests reveal that the long-wavelength (> 1 km)
geometrical artifacts (e.g., radial distortions, scanning artifacts and thermo-mechanical warping)
53
do not bias our measurement of displacement, as they occur at a wavelength an order of
magnitude greater than the deformation signal (occurring at a length-scale of 1-100 m), (see
Supplementary Fig. S3-7), in agreement with previous studies Michel and Avouac 2006; Ayoub
et al., 2009.
3.3.5 Estimating the error of the slip profile fractal dimension.
To obtain error estimates on the fractal dimension of the slip distributions for both
earthquakes we used a Monte Carlo approach, that allows us to explore a large range of possible
slip distributions given the error in the measurements. We generated 10,000 possible slip
distributions for each earthquake (see Supplementary Fig. S8) by randomly sampling the error of
each displacement measurement point (1081 displacement points for Landers and 470 for Hector
Mine). From each of the simulated 10,000 slip distributions, we measured the fractal dimension
by estimating the slope in the power spectrum from a linear least-squares regression (Fig. 2c and
d) Turcotte 1997, giving a range of possible fractal dimension’s that follow a Gaussian
distribution (1σ of ± 0.02 and ± 0.03 for Landers and Hector Mine, respectively (see
Supplementary Fig. S9)). We note, this method of generating a population of possible slip
distributions (and therefore a distribution of possible fractal dimensions) from modeling the error
of the displacement measurements in the slip profile, rather than simply using the error of the
regression co-efficients of the ‘mean’ displacement profile in the power spectrum (i.e., range of
slopes in Fig. 2c and d), is more robust, as we incorporate the effect of uncertainty originating
from the data itself, as opposed to the error of estimating the power spectrum of a single possible
slip distribution. This approach yields a wider range of possible fractal dimensions of the slip
54
distributions of each earthquake, and therefore gives a more conservative estimate of the
difference of slip roughness between the two events.
3.3.6 Bandpass Filter
In Fig. 2 e and f, we filter the slip distribution of both the 1992 Landers and 1999 Hector
Mine earthquakes using a Butterworth filter Butterworth 1930. This allows us to isolate the
amplitude of slip at specific ranges of frequencies to illustrate how the amplitude of slip
diminishes with decreasing wavelength. The upper and lower cut-off wavelength values for each
band are chosen considering i) numerical stability and ii) illustrative purposes to clearly
demonstrate how the amplitude of slip variation decreases as a function of wavelength. For each
of the 10 bands used to filter the slip distribution shown in Fig. 2 d and e, we used the following
lower and upper cut-off wavelengths respectively for both earthquakes, 0.16-0.20 km, 0.25-0.33
km, 0.33-0.50 km, 0.5-1.00 km, 1.00 -1.43 km, 1.43-1.66 km, 1.66-3.33 km, 3.33-6.66 km, 6.6-
20 km, > 20 km.
3.4 Results
3.4.1 Optical image correlation.
We measured co-seismic fault slip for the two events using the optical image correlation
software COSI-Corr (Co-registration of Optically Sensed Images and Correlation) Leprince et
al., 2007b, which allows for the precise co-registration, orthorectification and subsequent
55
correlation of pairs of pre- and post-event aerial photographs (see Methods for detailed
processing steps). Specifically, to quantify surface motion we track movement of features
between pairs of pre and post-event ortho-air photos using COSI-Corr’s phase correlator that
uses an iterative, unbiased processor that estimates the phase plane in the Fourier domain
Leprince et al., 2007b. The correlation results produced from subpixel matching of the before
and after air photos are presented in terms of 2D horizontal surface deformation maps (Fig. 1).
These reveal the spatial distribution of near-field co-seismic surface deformation as small as 10
cm along multiple fault strands that are consistent between overlapping image pairs and with
almost no decorrelation. Geometrical artifacts in the correlation results yield metric biases, which
can be observed as horizontal ‘streaks’ in Fig. 1 caused by scanning distortion and thermo-
mechanical warping of the film, but are limited to wavelengths (> 1 km) significantly larger than
the deformation signal associated with the width of the earthquake rupture (< 100 m) Michel and
Avouac 2006; Ayoub et al., 2009. Furthermore, a series of synthetic tests have confirmed that
these long-wavelength artifacts exert no influence on our measurements of fault displacement
(See Methods and Supplementary Fig. S2-7), in agreement with previous studies Michel and
Avouac 2006; Ayoub et al., 2009. From the correlation maps, we measured the right-lateral
displacement at points along the surface rupture using 1-3 km-long, 138 m-wide stacked, fault-
normal profiles (dimensions determined from synthetic tests see Methods and Supplementary
Information). We note, the complete constraint of the near-field deformation pattern allows for
measurement of both localized on-fault deformation and distributed off-fault deformation,
meaning each ‘displacement’ measurement represents the total fault-parallel deformation
accommodated across the entire fault zone. By making 1551 such measurements (1081 for
Landers and 470 for Hector Mine) at a uniform along-strike spacing of 138 m, we constructed
56
co-seismic slip distributions (Fig. 2a,b) using the largest number of samples ever reported in a
single study. We note the maximum amplitude of post-seismic afterslip observed from previous
InSAR studies, 10 cm for Landers Fialko 2004a and 6 cm for Hector Mine Jacobs et al., 2002, is
below the noise level and thus does not significantly distort our results.
3.4.2 Spectral analysis of slip distributions.
The slip distributions of both earthquakes exhibit along-fault variability at multiple length
scales, with amplitudes exceeding measurement uncertainty. To understand how the
displacement varies as a function of wavelength, we computed the power spectral density of the
slip distributions using the multi-taper method (Fig. 2c,d)Thomson 1982. The spectral analysis
reveals that the slip amplitude follows a consistent power-law decay over nearly three orders of
magnitude in wavelength, showing slip is scale-invariant and fractal with no characteristic length
scales dominating the frequency domain Mandelbrot 1983; Turcotte 1997. We find that the upper
limit to the power-law behavior is the total length of the rupture; variability cannot exist at scales
larger than that of the entire system. The lower limit is imposed by the image resolution;
variability may well exist at smaller scales but is undetectable given the resolution of the data.
To quantify the degree of roughness of fault slip, we estimated the fractal dimension (D) of both
slip profiles from the power spectrum using the following relation, D = (5- β)/2, where β is the
slope in the power spectrum Turcotte 1997, estimated using a linear least-squares regression past
the corner frequency. The fractal dimension (D) characterizes the degree of slip roughness, for
instance a value of 1 is the dimension of a line and 2 a surface, where higher fractional values
denote an object that is more complex, deviating away from a smooth, straight line and
57
attempting to fill a surface. From the slope in the power spectrum (Fig. 2c and d) we found for
the Landers slip distribution D = 1.72 ± 0.02 (1σ), and for Hector Mine D = 1.62 ± 0.03 (1σ),
indicating both are self-affine Turcotte 1997, with Landers exhibiting a higher degree of
variability. We obtained error estimates on the fractal dimension for both earthquakes using a
Monte Carlo approach that simulates 10,000 possible slip distributions given the error in the
displacement measurement (see Methods and Supplementary Fig. S8,9). From these error
estimates a T-test demonstrates that the Landers slip distribution is statistically rougher than that
of Hector Mine (p-value of << 0.001).
To illustrate the scale-invariant nature of slip, we isolate its amplitude at specific
frequencies using narrow band-pass filters (Fig. 2e,f)Butterworth 1930. This reveals that the slip
variation is organized hierarchically, wherein the amplitude of slip variation decreases with
wavelength. The longest wavelengths, near the fundamental mode, could be characterized as
smooth elliptical or triangular distributions as in previous lower-resolution studies Scholz 2002;
Manighetti et al., 2005 (also see Supplementary Fig. S1 for comparison of our displacement
measurements with coarser results using a 10 m SPOT satellite data that illustrates this). It is
important to note that the amplitude of short-wavelength variability does not imply
unrealistically large along-strike strains; we observe strains of 7×10
-4
for Landers and 4.5×10
-4
for Hector Mine, values that are lower than the irreversible strain limit of the wall-rock (1×10
-3
)
Lockner 1998, and similar to those observed from field and geodetic studies of other earthquake
ruptures McGill and Rubin 1999; Elliott et al., 2009; Gold et al., 2013.
58
3.4.4 Analysis of fault system and relation to slip distribution.
Fault systems are known to exhibit geometrical complexities at all observable length
scales and it has been widely recognized that fault surfaces themselves can be treated as scale-
invariant and fractal Turcotte 1997; Renard et al., 2013. To quantify the relative difference of the
geometrical complexity between the two ruptured fault systems, we applied a boxcounting
method Turcotte 1997 to the rupture traces, measuring fractal dimensions of 1.29 ± 0.02 and 1.15
± 0.02 (2σ) for Landers and Hector Mine, respectively (Supplementary Fig. S10-11). A higher
fractal value for the Landers fault system indicates it is geometrically more complex than Hector
Mine at all scales, which is expected given the rupture propagated through five distinct fault
segments and two structurally complex dilatational stepovers, whereas the Hector Mine rupture
involved only three relatively well-defined faults Sieh et al., 1993; Zachariasen and Sieh 1995;
Treiman et al., 2002 (see fault trace maps in Fig. 3 and Supplementary Fig. S10).
Seismogenic-scale fault segmentation (e.g., macroscopic bends and stepovers) is well-
known to correlate spatially to long-wavelength (~20 km) co-seismic slip variation Klinger et al.,
2006; Klinger 2010; Manighetti et al., 2015. Fault systems, however, are known to be segmented
at not just one length-scale, but at multiple scales Turcotte 1997, as demonstrated above.
Therefore to test whether this relationship holds to smaller wavelengths, we employed a similar
methodology of Klinger et al. (2006), (see their Fig. 9) and Manighetti et al. (2015), (see their
Fig. 2). First, we created three categories of slip variability based on wavelength ( λ): short ( λ <
0.2 km,), intermediate (0.2 km ≤ λ ≤ 2 km), and long ( λ > 2 km), where the shortest wavelength
category is defined by the shortest resolvable changes of slip we can observe, the longest
category defined by macroscopic geometrical fault complexities that relate to macroscopic
changes of slip and the middle category simply defined as the middle of these two endmembers.
59
For these three categories, we highlighted regions of noticeable slip variation (changes in slip
greater than 15 cm, the 2σ measurement uncertainty) on the mapped surface trace (Fig. 3).
Although subjective, this analysis yields clear results for both events; the wavelength and
amplitude of slip variability generally corresponds to the local scale of geometrical complexity.
For example, long-wavelength, large-amplitude slip variability (green arrows in Fig. 3)
corresponds to large-scale macroscopic geometrical features such as kilometer-scale fault bends
or stepovers, whereas shorter-wavelength, smaller-amplitude fluctuations (red arrows)
correspond to sites of smaller-scale fault complexities such as branches and kinks. These results
also illustrate the hierarchical organization of slip; the most common variability is the shortest
wavelength and the least common is the longest wavelength. We note the correlation of areas of
slip variation to sites of geometrical fault complexity are remarkably similar to those observed in
the geomorphic record (Fig. 2 of Manighetti et al., 2015). Combined with the box-counting
analysis of the surface traces, these results demonstrate that a more geometrically complex fault
structure produces a rougher slip distribution; the more complex Landers fault system produces a
rougher slip distribution at all scales, with a higher fractal dimension than the geometrically
simpler Hector Mine event.
3.5 Discussion
Field studies of fractally rough fault surfaces have found that fault roughness evolves
with increasing slip; older, more ‘mature’ faults tend to be smoother with a lower fractal
dimension Wesnousky 1988; Sagy et al., 2007; Brodsky et al., 2011. This is consistent with our
observation that the fractal dimension of the Landers fault system (i.e., degree of geometrical
fault complexity) is higher than that of Hector Mine. The Landers fault system is known to have
60
a slightly lower cumulative displacement (~3.1-3.6 km) than Hector Mine (between 3.4 and 7.8
km, Jachens et al., 2002), indicating it is less structurally mature. Thus, the fractal dimension of
the co-seismic slip distribution may provide a proxy for fault maturity and perhaps vice-versa.
Both quasi-static Dieterich and Smith 2010 and fully dynamic numerical simulations
Dunham et al., 2011; Shi and Day 2013 of earthquake rupture have shown that a fractally rough
fault surface induces a fractal stress field causing a highly variable slip distribution, and that
increasing the roughness of the fault surface leads to a rougher slip distribution (see Fig. 4 of
Dieterich et al. (2009) and Fig. 2 of Dunham et al. (2011)). This therefore provides a possible
physical mechanism for our interpretation that the difference in fractal dimension of the slip
distributions (i.e., roughness) between the two earthquakes can be explained by the relative
difference of the fractal dimension of the fault structures (an overall measure of fault system
roughness). The smoother Hector Mine fault system, with a lower number of sites of geometrical
complexities, likely produces a spatially smoother stress field, resulting in a smoother co-seismic
slip distribution at all scales.
However, a direct comparison between our results and those from quasi-static or dynamic
rupture simulations assessing fault roughness on slip is challenging, given that our study
measures the slip distribution from a heterogeneous 2D fault array, whereas numerical
simulations have so far (i) used only single fault segments of fractal roughness and (ii) have
parameterized rupture at seismogenic depths that are not subject to the same near-surface
conditions as our measurements (e.g., velocity strengthening friction regime). Similarly, it
remains to be seen whether the surface measurements of fractal values persist to depth.
Therefore, although it is tempting to draw direct comparisons between our empirical values and
those derived from finite-fault source inversions Mai and Beroza 2002, the use of different input
61
data, parameterization of the fault geometry, and assumptions about elastic structure used to
determine slip at depth precludes such a comparison with our data. In particular, regularization
and interpolation of the final modeled slip distribution necessarily alters any existing self-
similarity properties of co-seismic slip.
3.6 Conclusion
High-resolution displacement measurements of the 1992 Landers and 1999 Hector Mine
earthquakes indicate that the complex spatial variation of co-seismic slip is a real feature and has
a simple, predictable underlying fractal structure related to the hierarchical geometrical
organization of the fault system. We find that the spatial frequency content of the fault structure
can be observed within the slip distribution, indicating rougher faults systems produce rougher
co-seismic slip at all scales. Synthetic self-affine fractal representations of co-seismic slip can be
easily generated to serve as complex, realistic, and powerful models useful for seismic hazard
analysis and understanding of slip distributions of paleo-earthquakes that are typically
constrained by spatially sparse data. Our study also provides a novel approach for analyzing
surface slip distributions of future earthquakes using high-resolution data, one that can explain
the full heterogeneity of slip with a simple linear fit to the data in the frequency domain. This
framework helps resolve longstanding questions concerning co-seismic slip variability, and
creates a more complete understanding of the relationship between slip and fault structure.
62
3.7 Figure Captions
Figure 1. Correlation maps for the 1992 Landers and 1999 Hector Mine earthquakes.
Deformation maps showing north-south (a,c, left column) and east-west (b,d, right column)
component of displacement with positive values indicating movement to the north and west,
respectively for the (a,b, top) Landers, and (c,d, bottom) Hector Mine events. The inset map in a,
top right, shows the regional location of the 1992 Landers Sieh et al., 1993 and 1999 Hector
Mine Treiman et al., 2002 rupture in red lines overlaid onto a hillshade10 m national elevation
dataset digital elevation model, with yellow stars denoting the location of the epicenter. The inset
figures in Fig. 1a and c show fault-parallel displacement (black line) within a 138 m wide
stacked profile (also shown on the correlation maps as a black rectangle), illustrating how fault
offset is measured using linear regressions (red lines), which are manually fit to the deformation
signal on either side of the fault. A total of 1081 profiles were measured for Landers and 470 for
Hector Mine; these measurements were compiled along-strike to create the co-seismic slip
profiles shown in Fig. 2a,b. The displacement maps were computed using COSI-Corr and plotted
within ENVI 4.8 (http://www.exelisvis.com/ProductsServices/ENVIProducts/ENVI.aspx) and
Arcmap 10.1 (http://www.esri.com/software/arcgis/arcgis-for-desktop). Air photo data compiled
by the U.S. Geological Survey (http://www.usgs.gov).
Figure 2. Analysis of co-seismic slip variation. (top) Slip profiles for a, Landers, and b, Hector
Mine, shown by the black line. (middle) Power spectral density of the slip profiles for c, Landers,
and d, Hector Mine. Both profiles follow fractal distributions with no characteristic frequencies,
red line delineates the corner frequency which is determined by the rupture length (which the
fundamental mode cannot exceed), light gray lines denote the 95% confidence interval on the
63
estimate of the power spectrum and green line the linear least-squares regression with coefficient
of determination (R
2
) of 0.92 and 0.94 for c, and d, respectively. e,f, Band-passed components of
slip profiles at specific wavelengths, vertical red scaling bar defines the amplitude of slip, labels
on y-axis denote the range of wavelength cut-off values used to filter the slip distribution at
specific bands, with arbitrary vertical spacing for illustrative purposes. The band-pass filtering of
slip at specific frequencies illustrates how its amplitude progressively diminishes with shorter
wavelengths, a characteristic of a self-affine fractal distribution. Filters were performed with a
Butterworth filter Butterworth 1930, see Methods for more information on the specific upper and
lower corner wavelength values used for each band.
Figure 3. Correlation of slip variability (black line) to surface trace complexity. Slip profiles for
a, Landers and b, Hector Mine (each plotted to same scale), where colored lines indicate
individual fault slip profiles. Below slip profiles we plot the fault traces mapped in our
correlation results (where colored traces correspond to individual colored slip profiles above),
and the fault traces mapped in the field immediately following the earthquakes (red lines) Bryant
1992; Treiman et al., 2002.
Areas of long-wavelength slip (green, > 2 km along-strike distance) correlate to large-scale jogs
and bends in the fault trace, while intermediate-wavelength (blue, 0.2 – 2 km along-strike
distance) and short-wavelength (red, < 0.2 km along-strike distance) variability tends to correlate
with progressively smaller-scale geometrical features. The > 2 km category of slip variation is
chosen so as to relate macroscopic variations of fault slip to macroscopic areas of structural
complexity along the surface rupture, similar to the approach of Klinger et al. (2006) and
Manighetti et al. (2015). The shortest range of slip variation is chosen as the shortest resolvable
64
variation in fault slip that we can observe along the rupture, with the medium wavelength
category (0.2-2 km) simply defined as the variation of slip found between the two end-members.
3.7.1 Captions for Supplementary Materials
Supplementary Figure S1. Correlation results and slip profiles of Hector Mine and Landers
event using SPOT satellite imagery. a) SPOT correlation result showing north-south motion of
ground surface of Hector Mine earthquake b) SPOT correlation result of Hector Mine earthquake
in east-west direction. c) Slip profile of Hector Mine event, black showing data measured from
air photos presented in main text and red line showing displacement measured from correlation
maps seen in a) and b). d) SPOT correlation result showing north-south motion of ground surface
of Landers earthquake e) SPOT correlation result of Landers earthquake in east-west direction. f)
Slip profile of Landers event, black showing data measured from air photos presented in main
text and red line showing displacement measured from correlation maps seen in a) and b). The
displacement maps were computed using COSI-Corr and plotted within ENVI 4.8
(http://www.exelisvis.com/ProductsServices/ENVIProducts/ENVI.aspx) and Arcmap 10.1
(http://www.esri.com/software/arcgis/arcgis-for-desktop).
Supplementary Figure S2. Illustrates a subset of the images used for the three synthetic tests to
empirically determine the measurement uncertainty. Left column of figure S2 (a, d and g) shows
the pre-event images, middle column of S2 (b, e and h) show post imagery that was synthetically
sheared to produce faults of various widths and displacement (both constant along-strike) and
65
right column shows (c, f and i) correlation result where displacement measurements were taken
from faults running north-south through images (seen as vertical lines juxtaposing different
amounts of ground motion denoted by different colors). Test 1 involves two faults one of supra-
pixel displacement (2.5 m) and sub-pixel displacement (0.4 m). Test 2 involved faults of
different displacement but constant width and test 3 faults of different displacement and different
widths. We note in each of tests 2 and 3 we used two pairs of air photos (two pre- and two post-
event) allowing us to acquire more measurements, giving a total of four pairs of air photos used
for the two tests, where Supplementary Fig. S2 d,e,g and h, show subsets of these air photos. The
displacement maps were computed using COSI-Corr and plotted within ENVI 4.8
(http://www.exelisvis.com/ProductsServices/ENVIProducts/ENVI.aspx) and Arcmap 10.1
(http://www.esri.com/software/arcgis/arcgis-for-desktop). Air photo data compiled by the U.S.
Geological Survey (http://www.usgs.gov).
Supplementary Figure S3. Measurement results from synthetic test 1. a) Slip profiles of
displacement measurements taken from two faults with 2.5 (supra-pixel displacement) and 0.4 m
(sub-pixel displacement). Green lines show the true, synthetic displacment value and blue dots
and line show the displacment measurements aquired from the stacked profiles from the
correlation maps (Fig S2c). b) Shows the histogram of measurements (n = 45, shown as blue
bars) from the supra-pixel displacement test that follow a Gaussian distribution (red line) with a
true, synthetic value of 2.5 m that is labeled by a green vertical line. The offset of the true
synthetic value from the mean measured values is 0.01 m, measurements from the tests yield a
mean of 2.49 m, a 1σ of + 0.04 m and median of 2.49 m. c) Shows the histogram of
measurements (n = 45) from the sub-pixel displacement test (blue bars) that follow a Gaussian
distribution (red line) with a true, synthetic value of 0.4 m that is labeled by a green vertical line.
66
The offset of the true synthetic value from the mean measured values is 0.02 m, measurements
yield a mean of 0.42 m, a 1σ of + 0.038 m and median of 0.42 m.
Supplementary Figure S4. (top) Displacment measurements from test 2 (Supplementary Fig.
S2f), left side of figure shows slip profile of each fault, right side of figure shows the distribution
of data where each row represents the displacement measurements from each of the six synthetic
‘faults’. (bottom) shows the overall distribution of all measurements from test 2 (n = 434), which
has been subtracted from its respective true, known synthetic value. We found an overall mean
(i.e., bias) of -0.0034 m, 1σ of + 0.06 m and median of -0.0029. See Table S2 for statistics for
each fault.
Supplementary Figure S5. (top) Displacment measurements from test 3 (see Supplementary
Fig. S2i), left side of figure shows slip profile of each fault, right side of figure shows the
distribution of data where each row represents the displacement measurements from each of the
six synthetic ‘faults’. (bottom) shows the overall distribution of measurements from test 3 (n =
435), which has been subtracted from its respective true, known synthetic value. We found an
overall mean (i.e., bias) of -0.01 m, 1σ of + 0.06 m and median of -0.01. See Table S3 for
statistics for each fault.
Supplementary Figure S6. a) The variation of displacement measurements (1σ) plotted as a
function of fault zone width. We see no change in the variability of displacement measurement
with the width of the fault zone. That is, a wider fault zone does not make the interpretation of
the deformation signal significantly more ambigious and therefore faults of different widths do
not artificially cause an increase in the variance of the displacement measurements. b)
Displacement measurements from test 3 plotted as function of fault zone width. We find there is
67
no systematic change of the displacement bias (difference from true value) with width of the
fault zone. That is, a wider fault zone does not make it more difficult to accuratley estimate the
displacment measurement.
Supplementary Figure S7. a) and c) show all displacement measurements from tests 2 and 3,
respectively. Power spectrum of synthetic tests 2 and 3 plotted in b) and d) respectively as black
lines (green lines show linear fit), with the real measurements of Landers and Hector Mine fault
slip plotted as blue lines (red line showing linear fit) in b) and d), respectively. The figure clearly
illustrates that the spectra of the synthetic tests have a different slope and significanlty lower
amplitude than the true measurements, indicating the variation of slip observed in the actual
earthquakes is primarily real and reflecting the rupture process as opposed to meaurement
uncertainty. e) Shows the distribution of all displacment measurements aquired from tests 1, 2
and 3 (n = 959), subtracted from their true known value. We find mean (i.e., bias) of 0.02 m, 1σ
of + 0.06 m and median of 0.02 m. We use this distribution as our empirical error distribution
that is used for the measurement uncertainty presented in the main text.
Supplementary Figure S8. Simulated slip distributions for the Landers (top) and Hector Mine
earthquakes (bottom) determined by a Monte Carlo method a) 10,000 possible slip distributions
for the Landers earthquake given the error of the measurements, thick green line shows the mean
slip distribution that is directly measured from the stacked profiles. b) Zoom-in of a 3.5
kilometer area denoted as a red rectangle in a), to illustrate how the Monte Carlo simulation
randomly samples the error to produce different possible slip distributions. Note for illustrative
purposes in b) and d) we only plot 30 possible slip distributions in order to adequately see each
individual simulations. c) 10,000 possible slip distributions for the Hector Mine earthquake,
given the error of the measurements. d) Zoom-in of a 2.5 kilometer area denoted as red rectangle
68
in c), to illustrate how the Monte Carlo simulation randomly samples the error to produce
different possible slip distributions.
Supplementary Figure S9. a) Power spectrum for 10,000 possible slip distributions of the
Landers earthquake produced from randomly sampling the error using Monte Carlo simulations.
Red lines are 10,000 linear regressions fit to each of the 10,000 independently estimated spectra
of the simulated, possible the slip distributions. Green vertical line shows the location of the
corner frequency which delineates the extent of the fitting of the linear regression and
corresponds to the length of surface rupture (67 km). b) Histogram of 10,000 possible fractal
dimensions for the Landers slip distribution, which follow a Gaussian distribution (red line) with
mean of 1.72 and 1σ of + 0.02. c) Power spectrum for 10,000 possible slip distributions of the
Hector Mine earthquake produced from randomly sampling the error using Monte Carlo
simulations. Red lines are 10,000 linear regressions fit to each of the 10,000 independently
estimated spectra of the simulated, possible the slip distributions. Green vertical line shows the
location of the corner frequency which delineates the extent of the fitting of the linear regression
and corresponds to the length of surface rupture (38 km). d) Histogram of 10,000 possible fractal
dimensions for the Hector Mine slip distribution, which follow a Gaussian distribution (red line)
with mean of 1.62 and 1σ of + 0.03.
Supplementary Figure S10. (top) Map view of the surface fault traces of the Landers Bryant
1992 and bottom the Hector Mine rupture Treiman et al., 2002 mapped in the field, with the left
column showing the fault traces in their north-orientated position and right column showing the
fault systems rotated to minimize the amount of image space it occupies. We show here the
actual images used in the boxcounting procedure and therefore do not show scale or north arrow,
69
however, all four images are at the same 1:400,000 scale. We find no significant difference in the
fractal dimension between which orientations are assumed for the fault traces.
Supplementary Figure S11. a) Log-log plot of number of boxes (N
r
) versus size of boxes (r)
from the boxcounting of the surface fault traces. The blue line and solid circles shows the
boxcounting result for the surface fault traces of the Hector Mine event, with the red line
showing the fit giving a D = -1.15 + 0.01. The black line and solid circles shows the boxcounting
result for the surface fault traces of the Landers earthquake, with the green line showing the
linear regression giving a D = -1.29 + 0.01. We note for the purpose of illustrating the difference
in slope between the two fault systems we have shifted the Landers boxcount curve vertically
down the y-axis by a factor of 3.4 in log space.
70
CHAPTER 4:
Comparison of near-field and off-fault deformation of the 1992 M
w
7.3 =
Landers and 1999 M
w
7.1 = Hector Mine earthquakes: Implications for
controls on the distribution of surface strain.
4.1 Abstract
Sub-pixel correlation of pre- and post-event air photos reveals the complete near-field, horizontal
surface deformation patterns for the 1992 M
w
7.3 Landers and 1999 M
w
7.1 Hector Mine
ruptures. Total surface displacement values for both earthquakes are systematically larger than
‘on-fault’ displacements from geologic field surveys, indicating significant distributed, inelastic
deformation occurred along these ruptures. Comparison of these two datasets show 46 ± 10%
and 39 ± 22% of the total surface deformation was distributed over fault zones averaging 154 m
and 121 m in width for the Landers and Hector Mine events, respectively. Spatial variations of
distributed deformation along both ruptures show correlations with the type of near-surface
lithology and degree of fault complexity; larger amounts of distributed shear occur where the
rupture propagated through loose unconsolidated sediments, and areas of more complex fault
structure. These results have basic implications for geologic-geodetic rate comparisons, and
probabilistic seismic hazard analysis.
4.2 Introduction
Analysis of recent co-seismic surface ruptures reveals significant distributed, inelastic,
off-fault deformation (OFD), ranging from highly localized to completely diffuse [e.g., Rockwell
71
et al., 2002; Quigley et al., 2012; Gold et al., 2015; Milliner et al., 2015; Teran et al., 2015].
Such inelastic surface deformation can be accommodated via a range of physical mechanisms,
such as warping, granular flow, rigid-block rotation, and/or micro-cracking [Nelson and Jones
1987; Shelef and Oskin, 2010]. However, understanding how the magnitude and spatial variation
of inelastic deformation may vary along the full length of a surface rupture and between events is
poorly understood. Limiting this understanding are the dearth of comparative analyses of
multiple earthquakes that can resolve near-field strain to the same precision and scale, which
necessarily involves using data of comparable resolution, as well as equivalent measurement
methods (e.g., geologic field surveys, 3D topographic cloud matching, or optical image
correlation), which can otherwise yield arbitrary differences in the amount of observable
deformation. For example, for the 2013 M
w
7.7 Balochistan earthquake, Zinke et al. [2014]
reported 45% OFD, whereas Gold et al. [2015] found 28%, a disagreement attributed to
differences in measurement method and satellite resolution. Accurately understanding the degree
of strain localization and whether there exist systematic differences or similarities between
different earthquakes is key to helping understand fault mechanics, the geologic evolution of
fault systems, and developing effective micro-zonation protocols for the built environment.
Here we use sub-pixel image correlation applied to pairs of before-and-after, high-
resolution air photos of the 1999 M
w
7.1 Hector Mine earthquake to analyze the near-field
surface deformation pattern and quantify the amount of inelastic, distributed deformation along
the surface rupture. We used the same optical image correlation method (COSI-Corr) and air
photos of the same resolution as were used to quantify the near-field surface deformation of the
1992 Landers earthquake [Milliner et al., 2015]. Thus, providing for the first time a robust
comparative analysis of near-field surface deformation patterns between two earthquakes to the
72
same precision and resolution along their full rupture lengths. Along the M
w
7.3 1992 Landers
surface rupture, 46 ± 10% of the total surface shear was accommodated as OFD over average
fault zone widths of 154 m, and the spatial variation of OFD could be explained by variations in
the geometrical structural complexity, but with no clear correlation with the types of near-surface
materials [Milliner et al., 2015]. Both the Landers and Hector Mine events ruptured systems of
structurally immature faults (cumulative displacement of 3-7 km [Jachens et al., 2002]) within
the Eastern California Shear zone (ECSZ) of the Mojave Desert, California, an 80-km-wide
region of NNW-orientated, right-lateral shear.
Herein we seek to understand whether there are common features or systematic
differences in the amount of inelastic deformation between the two surface ruptures, and what
physical properties of the rupture may explain variations between these two seemingly similar
events. We discuss our results in light of their implications for understanding discrepancies
between geodetic and geologic slip rates across the ECSZ, the accuracy of empirical scaling
relations of earthquake surface ruptures derived from field measurements, and use of such data
for probabilistic seismic hazard analysis.
4.3 Data and Methods
To measure the near-field, horizontal surface deformation pattern of the Hector Mine
earthquake, we used the program COSI-Corr (Co-Registration of Optically Sensed Images and
Correlation), which allows for accurate co-registration, orthorectification, and correlation of
pairs of pre- and post-event optical images to sub-pixel precision [Leprince et al., 2007a; 2007b].
We selected 21 pairs of 1-m-resolution National Aerial Photography Program (NAPP) aerial
73
photos for correlation (from http://earthexplorer.usgs.gov/), acquired from July 1994 and May
2002, that cover the entire length of the Hector Mine surface rupture. We produced the
deformation maps following the approach described in Milliner et al. [2015], using the same type
of imagery (NAPP air photos), resolution (1 m), digital elevation model (10 m, 2012 National
Elevation Dataset DEM), correlation method (COSI-Corr phase correlator), and correlation
window parameters (multiscale size of initial 64 to 32 final pixels size with a step of six). This
procedure generated deformation maps of the same resolution (6 m) and comparable precision
(10 cm RMS [1/10
th
of the input image pixel size]) as for the Landers result [Milliner et al.,
2015].
The horizontal fault displacement and fault-zone width (FZW) are measured from the
correlation maps using fault-perpendicular stacked profiles (lengths of 1-3 km; widths of 138 m)
in the same manner outlined in Milliner et al. [2015], where linear regressions are fit to either
side of the fault and extrapolated to the fault trace to approximate the total amplitude and width
of the discontinuity signal (Fig. 1). The COSI-Corr ‘displacement’ measurement thus includes
both the localized, on-fault displacement, and any distributed inelastic shear accommodated
across the entire width of the fault zone.
We estimated OFD along the 1999 Hector Mine rupture by differencing the nearest
geologic field measurements (which captures the on-fault, discrete component of slip) from our
displacement measurements (which captures the total displacement); the same approach
employed for Landers [Milliner et al., 2015]. Field survey measurements are assumed to
primarily capture the discrete, on-fault component of slip because they typically use piercing
points taken over a narrow (1–10 m wide) fault-perpendicular aperture and therefore usually do
not (and frequently cannot) include precise measurement of the complex, distributed off-fault
74
deformation [McGill and Rubin, 1999; Rockwell et al., 2002]. For measurements that capture the
‘on-fault’, discrete component of horizontal displacement, we used 136 field measurements
[Treiman et al., 2002] and 255 measurements derived from a post-event lidar DEM [Chen et al.,
2015]. Displacement measurements between the field and lidar studies yielded values in good
agreement, as both are measured from restoration of offset geomorphic features close to the
primary surface rupture. In the event that multiple field (or lidar) measurements exist when
attempting to co-locate and difference field offsets from our 138-m-wide along-strike averaged
COSI-Corr measurements, we differenced the largest field offset, thereby giving a conservative
lower-bound estimate of OFD.
4.4 Results
The Hector Mine correlation maps reveal a complex system of 22 interconnected right-
lateral, NNW-orientated fault segments with a total rupture length of 45 km (Fig. 1). From the
correlation maps we extracted 470 measurements of fault displacement and 443 measurements of
FZW (synthetic tests show that these measurements are not biased by long-wavelength [> 1 km]
geometrical artifacts, such as thermo-mechanical warping of the film and scanning artifacts, that
occur within the correlation maps [see Michel and Avouac, 2006; Ayoub et al., 2009; Milliner et
al., 2015]). Measurements of displacement follow an exponential distribution, with a mean
displacement of 2.84 m, median of 3.04 m, and a maximum slip of 5.51 m, located in the Bullion
Mountains 7 km south of the epicenter. Measurements of the FZW follow an exponential
distribution with a mean value of 121 m, median of 84 m, and a maximum fault width of 876 m,
found at the southern termination of the rupture. The FZW is notably wider in areas of
geometrical fault complexities, such as in the southern central segment (13.5 km south of the
75
epicenter, where the Bullion Mountain fault branches into the Lavic Lake fault), 3.5 km south of
the epicenter where the main fault bifurcates, at a ~18° bend along the central segment of the
Lavic Lake fault, and at the southern termination of the rupture with 300-876 m of highly
distributed shear.
To visualize the distributed nature of strain along 1999 Hector Mine surface rupture, we
computed the 2D strain field from the correlation maps using a central difference method that is
first order accurate. We first filtered the correlation maps using a non-local means filter that is
specifically adapted to avoid smoothing discrete discontinuities in the vector field (i.e., faults),
which serves to reduce noise that would otherwise degrade calculations of gradients in
displacement [Buades et al., 2006; Rubino et al., 2015]. The strain maps show how shear strain
systematically increases and dilation (trace of the strain tensor) decreases in areas of simple fault
structure where deformation is localized to narrow fault cores, and vice-versa at sites of
geometrical structural complexity, such as fault branches, kinks, bends, and step-overs (Fig. 1d).
The strain maps illustrate the difficulty of incorporating such diffuse deformation in
measurements taken from offset geomorphic features close to the primary fault strand, as is
typically performed in traditional field and lidar analysis of surface ruptures [e.g., Sieh et al.,
1993; Chen et al., 2015].
Comparison of the field and lidar ‘on-fault’ measurements of fault slip with our COSI-Corr
‘total displacement’ measurements show that the latter are systematically larger (Fig. 2e, f),
revealing the spatial variation of OFD at 220 points along the length of the Hector Mine surface
rupture. From this differencing we found a mean OFD of 1.29 m (estimated from both the field
and lidar measurements), and median of 1.01 m. Normalizing each OFD point by the
corresponding total displacement from our COSI-Corr measurements (as displacement itself
76
varies along the rupture) gives the percent of off-fault deformation (OFD%), reflecting the
relative magnitude of OFD compared to the total deformation accommodated at a point across
the fault zone. We found the mean OFD% for the Hector Mine surface rupture of 41 ± 25% (1σ,
n = 86) and 38 ± 17% (1σ, n = 134), derived from comparison with the field and lidar
measurements, respectively, giving an overall mean OFD% of 39 ± 22% (1σ, n = 220).
Qualitatively, the estimates of OFD from the field and lidar datasets both exhibit similar spatial
variations along the rupture length (Fig. 2b). To a first-order, OFD is lowest in the central
segment of the rupture, coincident with the bedrock exposed in the Bullion Mountains, and
generally increases to the north and south, where the rupture passed through surficial
unconsolidated Quaternary sediments. Although our displacement measurements likely include
some post-seismic afterslip because the post-event images were acquired three years after the
Hector Mine event, the effect is likely minor, as InSAR measurements collected one year
following the earthquake detected only 6 cm of surface afterslip [Jacobs et al., 2002], a level
below our threshold of detection (10 cm), and post-seismic velocities from GPS found similarly
small levels of motion [Agnew et al., 2002; Hudnut et al., 2002; Owen et al., 2002].
4.5 Discussion & Conclusions
Our use of the same correlation method and equivalent imagery to quantify the near-field
deformation of the 1999 Hector Mine earthquake as that used by Milliner et al. [2015] to
document the 1992 Landers event allows us to resolve surface deformation to the same
resolution and degree of accuracy, thus facilitating a robust comparison of the magnitude and
spatial variation of inelastic surface deformation in these events. For the Landers and Hector
77
Mine surface ruptures we found similar magnitudes of distributed deformation, with 46 ± 10%
(1σ) and 39 ± 22% (1σ) total surface shear distributed away from the primary fault strand,
respectively. These high percentages are consistent with the structural immaturity of the two
fault systems (both with cumulative displacements of 3-7 km, [Jachens et al., 2002]), and similar
values of distributed deformation have been documented along other structurally immature faults
[e.g., Quigley et al., 2012; Zinke et al., 2014; Gold et al., 2015].
Although the similar structural immaturity of the faults that ruptured in the Landers and
Hector Mine events likely explains the overall large percentages of OFD, spatial variations of
OFD along both surface ruptures indicate there are likely other, secondary physical controls at
work. We explore this by investigating how distributed strain varies as a function of observable
properties along the surface rupture (e.g., the type of near-surface materials and local fault zone
structural complexity), testing the hypothesis that less consolidated materials and more complex
fault zones produce larger magnitudes of distributed strain.
OFD along the Landers rupture from Milliner et al. [2015], was found to be large in areas
of unconsolidated Quaternary sediments (mean OFD of 49 ± 24% [1σ]), lowest at sites where
sediment is juxtaposed against bedrock (positively skewed distribution with a mode of 19%), and
unexpectedly large in areas of bedrock (mean of 52 ± 25% [1σ]), (Fig. 3). The relatively discrete
deformation occurring at sites of sediment-bedrock interfaces suggests that these pre-existing
mechanical interfaces act to localize deformation, as has been found from field investigations
and dynamic rupture simulations [Chester and Logan, 1986; Bruhn et al., 1994; Ben-Zion and
Sammis, 2003; Sibson, 2003 ]. However, although it seems counterintuitive that OFD was largest
in areas of bedrock, the majority of bedrock along the Landers rupture (82%) is exposed in
structurally complex areas, specifically sites of dip-slip faulting that act to exhume bedrock along
78
this predominantly strike-slip fault system. Thus, the interdependency of fault zone complexity
and material type make it particularly difficult to assess the relative effect of each of these
parameters separately. In contrast, the simpler rupture pattern for Hector Mine and the binary
distribution of materials along the rupture (Tertiary bedrock in the central 10 km of the rupture
and unconsolidated Quaternary sediments to the north and south), allows us to better isolate and
more clearly observe the effect of near-surface material type on the degree of strain localization.
From the Hector Mine rupture, we found distinct differences of OFD with the type of material,
with a mean OFD of 45% for sediments and a positively skewed distribution towards
significantly lower OFD (mode of 20%) where the rupture propagated through bedrock (Fig. 3).
To test the effect of fault zone structural complexity on the amount of distributed
deformation for both earthquakes, we quantified the degree of geometrical fault complexity
using a boxcounting method that determines the fractal dimension of 1.5-km-long segments of
the mapped surface rupture (Fig. 3 k,l). Although the fault zone complexity cannot explain all of
the variance in the OFD data (as shown by low R
2
values ranging from 0.26 to 0.68, and
Spearman’s rank correlations ranging from 0.32 and 0.75, for both ruptures), there is a
statistically significant, general first-order positive correlation as evinced by p-values ranging
from 0.01-0.05. Thus, we do not expect fault zone complexity (or near-surface materials) alone
to explain all of the variance in the observed OFD data (where some of the scatter is also likely
due to noise from measurement uncertainty). The remaining, unexplained spatial variation of
OFD could be attributed to other parameters not considered here, such as the thickness of
sediment, fault dip, the state of stress, or the available fracture energy of the propagating rupture
front, properties that should be considered in analysis of future surface ruptures.
79
Geologic slip rates are commonly measured from restoration of offset geomorphic
features (e.g., river channels), over narrow fault-perpendicular distances (< 10 m) where
confidence of the offset geometry is greatest. Such measurements are, however, susceptible to
missing distributed strain, which can result in an underestimation of the long-term slip rate [e.g.,
Dolan and Haravitch, 2014; Gold et al., 2015]. For example, across the ECSZ, a system of six
structurally immature faults, geologic rates are only about half of the geodetic rates, with rates of
≤ 6.2 ± 1.9 mm/yr [Oskin et al., 2008] and 12 ± 2 mm/yr [Bennett et al., 2003; Meade and
Hager, 2005], respectively. Slip rates for the Camp Rock and Pisgah-Bullion faults (segments of
the Landers and Hector Mine ruptures, respectively) were measured from offset of an alluvial
terrace and a pyroclastic deposit, respectively, over < 10-m-wide, fault-perpendicular distances
[Oskin et al., 2008]. Assuming the distributed co-seismic deformation we observe is reflective of
the long-term behavior (where we note offset geologic markers along the neighboring Harper
Lake fault indicate a similar long-term, ‘geologic OFD’ of 45% [Shelef and Oskin, 2010]), such
narrow-aperture geologic rates would likely be underestimated by such an amount. Correcting
the geologic slip rates for 39-45% missed OFD for the six main faults that comprise the ECSZ
would yield rates of 10-11.5 mm/yr, in agreement within 1σ uncertainty of the current geodetic
rates. This implies that the apparent geologic-geodetic slip rate discrepancy, and therefore strain
transient across the ECSZ (a current period of elevated shear loading argued to explain the rate
mismatch), is much smaller than previously suggested [e.g., Dolan et al., 2007; Oskin et al.,
2008]. This example illustrates the necessity of including OFD in all such geologic-geodetic rate
comparisons.
Underestimation of the total surface displacement from field surveys due to missed
distributed strain also has basic implications for empirical scaling laws relating mean
80
displacement (D
mean
) to M
w
and rupture length (RL) [e.g., Wells and Coppersmith, 1994;
Wesnousky, 2008], which are used widely in understanding fault mechanics [Scholz, 2002],
paleo-magnitude estimation [Biasi and Weldon, 2006], and probabilistic seismic hazard analysis
[Field et al., 2014]. For example, our D
mean
values for the 1992 Landers and 1999 Hector Mine
earthquakes are 3.41 m and 2.84 m, respectively, significantly larger than the field equivalents of
2.3 m [Sieh et al., 1993] and 1.56 m [Treiman et al., 2002], respectively. Comparing our D
mean
values (as well as those from the 2013 M
w
7.7 Balochistan and 2010 M
w
7.1 Darfield
earthquakes which include OFD) with the field measured values (which are used to define the
regressions), and measurements from other surface ruptures (Fig. 4), illustrate the significant bias
introduced by missing OFD. Using the empirical scaling relation between D
mean
and M
w
of Wells
and Coppersmith [1994], we obtained seismic moments (M
o
) of 2.35 × 10
27
dyne.cm (M
w
=
7.51) and 1.84 × 10
27
dyne.cm (M
w
= 7.44) for the Landers and Hector Mine ruptures,
respectively, 2.1 and 3.27 times larger than the known geodetic values [Simons et al., 2002;
Fialko, 2004]. Additionally, we also found significant mismatches of our D
mean
values with
those expected from the D
mean
-RL regression [Wesnousky, 2008], where an F-test rejects at the
5% confidence level that our observed D
mean
values would be produced by the observed RL. Our
new D
mean
measurements highlight the problematic nature of existing regressions based on
surface offsets that do not include OFD, which can result in significant over-estimates of M
w
and
RL, key parameters used in probabilistic seismic hazard assessment. We expect future D
mean
measurements that incorporate OFD will lead to higher displacement-length ratios preferentially
for immature fault systems, which typically accommodate more diffuse deformation, also
consistent with the notion that less mature, intra-plate faults generate larger stress drops [Shaw
and Scholz, 2001; Manighetti et al., 2007]. Measurements of the complete near-field, co-seismic
81
deformation pattern that can now be achieved by optical image correlation and lidar differencing,
will lead to a more reliable understanding of faulting mechanics, the total width of distributed
deformation that poses a hazard to the built environment, and assessment of how surface slip
compares to that at seismogenic depths [e.g., Xu et al., 2016].
4.6 Figure Captions
Figure 1. Correlation maps of the 1992 Landers and 1999 Hector Mine earthquakes. (a, b) show
north-south and east-west component of surface motion, respectively, with region of study
shown by gray box within inset, top right of (a). Inset in lower-left of (b) shows fault-parallel
displacement (black line) within a 138 m wide stacked profile, illustrating how fault offset (red
vertical arrow) and fault zone width (blue horizontal arrow) are measured using linear
regressions (green dashed lines). (c) Displacement measurements from the correlation maps,
1058 measurements for Landers and 470 for Hector Mine. (d) Strain maps computed from the
correlation maps (labelled X,Y,Z). Left column shows shear strain, middle, norm of 2D strain
tensor and right, dilation. Top row shows trans-tensional stepover along Landers rupture
(location outlined by dashed box within inset of (a), middle and bottom row shows area of
distributed deformation and transtensional stepover along Hector Mine (outlined by dashed
boxes in a), these examples illustrate distributed deformation along rupture.
Figure 2 Off-fault deformation (a, b) and fault zone width (c,d) measurements for Landers and
Hector Mine. (a) OFD as a percent (OFD%) is computed for Landers by differencing COSI-Corr
measurements from field values [Sieh et al., 1993], result from Milliner et al. [2015], and for
82
Hector Mine differencing from both the field [Treiman et al., 2002] and lidar measurements
[Chen et al., 2015]. (c, d) Map view of fault zone width (FZW) measurements (red lines)
measured from the stacked profiles, spaced every 138 m. Inset images shows examples where the
FZW increases where the rupture becomes structurally complex (e.g., at branches, bends, or
terminations). (e, f) Correlation plots showing the systematic difference of COSI-Corr
displacement measurements versus those from field surveys [Sieh et al., 1993] for Landers and
from field (black dots [Treiman et al., 2002]) and lidar measurements (red dots [Chen et al.,
2015]) for Hector Mine. Total least squares regression (green line) to the data (gray ellipses
indicate 1σ error), has gradient of 1.47, with R
2
of 0.77 for Landers and gradient of 1.38 and R
2
of 0.84 for Hector Mine, both in contrast to the y=x (black lines) indicating OFD.
Figure 3 Off-fault deformation (OFD) as a function of types of near-surface materials (a-e), with
distribution fits (red lines), and fault zone complexity (f-j), for Landers and Hector Mine, in left
and right column, respectively. (a,b) OFD in areas where the rupture propagated through
sediment, exhibited large mean values of OFD of 49 ± 24% and 42 ± 21% for Landers and
Hector Mine, respectively. (c) Histogram of OFD in areas of sediment-bedrock interfaces (only
found along Landers rupture), with a positively skewed distribution (mode of 19%). (d,e)
Histogram of OFD in areas of bedrock, with surprisingly large values of 52 ± 25% for Landers
and significantly lower values for Hector Mine 29 ± 20%. (f, g) OFD where the rupture
propagated through sediment as a function of fault complexity (determined by the fractal
dimension of 1.5 km segments of the fault trace, see (k,l). Higher fractal values denote more
complex fault zones. Spearman rank correlation (ρ
s
) and p-values (p-val) are labelled in upper
left. (h) OFD versus fault complexity for Landers in sediment-bedrock areas. (i,j) OFD versus
83
fault complexity in areas of bedrock only. (k,l) Boxcounting results illustrating areas of
geometrical fault complexity, more complex regions have darker shaded boxes, indicating higher
fractal values.
Figure 4 a) Rupture scaling relationships for large strike-slip earthquakes (blue symbols from
Wesnousky, 2008), including the Darfield (green square), Landers and Hector Mine earthquakes
(cyan squares), and the 2013 Balochistan earthquakes (green square). Green line shows power
law regressions from Wesnousky (2008) with 95% confidence intervals (orange lines), and
regression intervals (red lines). (c) D
mean
vs M
w
scaling relation for strike slip events plotted from
Wells and Coppersmith (1994) (blue circles), and Wesnousky, 2008 (black circles), illustrating
the effect of missing OFD on the scaling relation where D
mean
measured from original field
studies (red diamonds, Sieh et al., 1993; Treiman et al., 2002), with our new values (cyan
squares), and the 2010 Darfield and 2013 Balochistan earthquakes.
4.6.1 Captions for Supplementary Materials
Figure S1. Post-event air photos for the 1992 Landers (left) and 1999 Hector Mine (right) events
acquired in July 1994 and May 2002 respectively, and plotted with the surface ruptures (red
lines). Air photos are 8x8 km footprint with 1 m spatial resolution. We selected 31 pairs and 21
pairs of air photos for the Landers and Hector Mine events respectively
Figure S2. Illustration of estimation of geometrical fault complexity using boxcounting method
with 1.5 km sizes boxes, with left column showing results from Landers rupture and right
column Hector Mine rupture. a and b) Shows boxcounting results plotted on top of surface
84
rupture (red lines), where shading of boxes denotes value of fractal dimension. Higher fractal
values denote more complex fault areas shown by darker shading. These results reveal areas of
simple and complex parts of the surface rupture, the latter for example highlighting step-overs,
where the fault branches, or bends. The fault traces are taken from USGS mapping of the
earthquakes, see supplementary text for more details. c and d) Measurements of off-fault
deformation (OFD) as a percent plotted within the boxes used to estimate the complexity of the
surface rupture. Multiple OFD values within a box are used to compute statistics such as the
mean and standard deviation of OFD within each box, these are then plotted in Fig. 3. e and f)
illustrate a single example of a how the fractal dimension of a particular box is estimated. Blue
line shows counting of boxes that include a fault trace at different box sizes. The smaller the size
of the box the more boxes are needed to cover the surface fault trace, from this power law
relation gives an estimate of the complexity of the fault system within the box. Red lines shows
linear least-squares regression to data (blue), the slope gives the fractal dimension (D).
Figure S3. a) All off-fault deformation as a percent (OFD%) measurements plotted as a function
of fractal dimension (an estimate of the geometrical fault complexity) for the 1992 Landers
rupture. Green line shows the best fit from a linear-least squares regression, red lines show the
confidence intervals of the regression and black lines show the 95% prediction intervals. b) Same
as a) but OFD data from the Hector Mine event.
Figure S4. a) COSI-Corr displacement measurements along the 1992 Landers rupture (same as
that plotted in Fig. 1c) with field measurements from Sieh et al. (1993), illustrating the data used
to compute OFD plotted in Fig. 2a. To compute OFD, we subtract the COSI-Corr measurements
which using 1-2 km long stacked profiles, captures the total surface displacenet from the field
measurements, which capture the discrete, ‘on-fault’ component of displacement. c) COSI-Corr
85
displacement measurements for the 1999 Hector Mine rupture (same as that plotted in Fig. 1c),
with field measurements from Treiman et al. (2002) and Chen et al. (2015), illustrating the data
used to compute OFD.
Figure S5. a) Off-fault deformation along Hector Mine plotted as a function of horizontal
distance to the nearest outcrop of exposed bedrock which serves as a proxy for thickness of
sediment. Larger distances from the nearest range front would expectedly have thicker amounts
of sediment and therefore expectedly larger OFD. b) Same as a) but for the 1992 Landers
rupture.
86
CHAPTER 5:
Conclusion
Using optical image correlation we have managed to measure the near-field deformation pattern
in high spatial resolution of two large magnitude strike-slip earthquakes where geodetic and field
observations have been significantly lacking.
These data have given new insight into the spatial variations of fault slip along a rupture length,
revealing geometrically rougher (less mature) fault systems producer rougher fault slip. The
optical correlation technique we have developed can help image the width of the distributed zone
of deformation that is almost impossible to observe in the field, can provide dense (every 138 m
along the fault) and precise measurement (1σ = 10 cm) of fault slip, and has shown significant
amounts of deformation are accommodated over wide fault zones, with 45 ± 10% and 39 ± 22%
of total deformation accommodated in such a manner for the 1992 Landers and 1999 Hector
Mine earthquake respectively. These results have demonstrated that less mature faults, composed
of zones of complex fault structure and areas where the rupture propagates through
unconsolidated material (such as alluvial sediments) produce significantly larger magnitudes and
wider zones of distributed deformation. Distributed zones of damage can influence the rupture
direction, velocity, propagation and seismic radiation pattern, and is of fundamental importance
in improving the seismic hazard analysis of fault systems. Furthermore, these near-field
measurements also provide vital constraints for finite-fault inversions, indicating the shallow slip
deficit (which has long been a source of major contention in the tectonophysics community
between seismologists, geodesists and earthquake geologists), is largely artificial due to missing
87
near-field data and not properly accounting for significant amounts of distributed deformation
accommodated over wide, complex fault zones.
In the future with improving technology of optical imaging systems and increasing
number of satellites this will give vastly improved spatial and temporal resolution. Such data will
provide a new means to understand faulting mechanics, kinematics interactions and aseismic,
transient processes that have proven difficult to measure with traditional field and geodetic
techniques and will become fruitful sources of information, ultimately giving a better
understanding of earthquake behavior and the hazard it poses to society.
88
References
Agnew, Duncan Carr, Susan Owen, Zheng-Kang Shen, Gregory Anderson, Jerry Svarc, Hadley
Johnson, Kenneth E. Austin, and Robert Reilinger. "Coseismic Displacements from the
Hector Mine, California, Earthquake: Results from Survey-Mode Global Positioning System
Measurements." Bulletin of the Seismological Society of America 92, no. 4 (2002): 1355-
1364.
Allam, AA, Y. Ben-Zion, I. Kurzon, and F. Vernon. "Seismic Velocity Structure in the Hot
Springs and Trifurcation Areas of the San Jacinto Fault Zone, California, from Double-
Difference Tomography." Geophysical Journal International 198, no. 2 (2014): 978-999.
Ayoub, François, Sébastien Leprince, and Jean-Philippe Avouac. "Co-Registration and
Correlation of Aerial Photographs for Ground Deformation Measurements." ISPRS Journal
of Photogrammetry and Remote Sensing 64, no. 6 (2009): 551-560.
Ben-Zion, Yehuda, and Charles G. Sammis. "Characterization of Fault Zones." Pure and Applied
Geophysics 160, no. 3-4 (2003): 677-715.
Biasi, Glenn P., and Ray J. Weldon. "Estimating Surface Rupture Length and Magnitude of
Paleoearthquakes from Point Measurements of Rupture Displacement." Bulletin of the
Seismological Society of America 96, no. 5 (2006): 1612-1623.
Brodsky, Emily E., Jacquelyn J. Gilchrist, Amir Sagy, and Cristiano Collettini. "Faults Smooth
Gradually as a Function of Slip." Earth and Planetary Science Letters 302, no. 1 (2011):
185-193.
Bruhn, Ronald L., William T. Parry, William A. Yonkee, and Troy Thompson. "Fracturing and
Hydrothermal Alteration in Normal Fault Zones." Pure and Applied Geophysics 142, no. 3-
4 (1994): 609-644.
Bryant, WA. "Surface Fault Rupture Along the Johnson Valley, Homestead Valley, and Related
Faults Associated with the M s 7.5 28 June 1992 Landers Earthquake." Fault
Eval.Rept.FER-234, Calif.Div.Mines Geol (1992).
Buades, Antoni, Bartomeu Coll, and Jean-Michel Morel. "The Staircasing Effect in
Neighborhood Filters and its Solution." IEEE Transactions on Image Processing 15, no. 6
(2006): 1499-1505.
Bürgmann, Roland, Paul A. Rosen, and Eric J. Fielding. "Synthetic Aperture Radar
Interferometry to Measure Earth's Surface Topography and its Deformation." Annual
Review of Earth and Planetary Sciences 28, no. 1 (2000a): 169-209.
89
Bürgmann, Roland, Paul A. Rosen, and Eric J. Fielding. "Synthetic Aperture Radar
Interferometry to Measure Earth's Surface Topography and its Deformation." Annual
Review of Earth and Planetary Sciences 28, no. 1 (2000b): 169-209.
Butterworth, Stephen. "On the Theory of Filter Amplifiers." Wireless Engineer 7, no. 6 (1930):
536-541.
Chen, T., SO Akciz, KW Hudnut, DZ Zhang, and JM Stock. "Fault‐Slip Distribution of the 1999
Mw 7.1 Hector Mine Earthquake, California, Estimated from Postearthquake Airborne
LiDAR Data." Bulletin of the Seismological Society of America 105, no. 2A (2015): 776-
790.
Chester, Frederick M., and Judith S. Chester. "Ultracataclasite Structure and Friction Processes
of the Punchbowl Fault, San Andreas System, California." Tectonophysics 295, no. 1
(1998): 199-221.
Cochran, Elizabeth S., Yong-Gang Li, Peter M. Shearer, Sylvain Barbot, Yuri Fialko, and John
E. Vidale. "Seismic and Geodetic Evidence for Extensive, Long-Lived Fault Damage
Zones." Geology 37, no. 4 (2009): 315-318.
Day, Steven M., Sarah H. Gonzalez, Rasool Anooshehpoor, and James N. Brune. "Scale-Model
and Numerical Simulations of Near-Fault Seismic Directivity." Bulletin of the Seismological
Society of America 98, no. 3 (2008): 1186-1206.
Dieterich, James H., and Deborah Elaine Smith. "Nonplanar Faults: Mechanics of Slip and Off-
Fault Damage." In Mechanics, Structure and Evolution of Fault Zones. Springer, 2010,
1799-1815.
Dolan, James F., and Ben D. Haravitch. "How Well do Surface Slip Measurements Track Slip at
Depth in Large Strike-Slip Earthquakes? the Importance of Fault Structural Maturity in
Controlling on-Fault Slip Versus Off-Fault Surface Deformation." Earth and Planetary
Science Letters 388, (2014): 38-47.
Dunham, Eric M., David Belanger, Lin Cong, and Jeremy E. Kozdon. "Earthquake Ruptures
with Strongly Rate-Weakening Friction and Off-Fault Plasticity, Part 2: Nonplanar Faults."
Bulletin of the Seismological Society of America 101, no. 5 (2011): 2308-2322.
Elliott, AJ, JF Dolan, and DD Oglesby. "Evidence from Coseismic Slip Gradients for Dynamic
Control on Rupture Propagation and Arrest through Stepovers." Journal of Geophysical
Research: Solid Earth (1978 –2012) 114, no. B2 (2009).
Fialko, Yuri. "Evidence of Fluid‐filled Upper Crust from Observations of Postseismic
Deformation due to the 1992 Mw7. 3 Landers Earthquake." Journal of Geophysical
Research: Solid Earth (1978 –2012) 109, no. B8 (2004a).
90
Fialko, Yuri. "Probing the Mechanical Properties of Seismically Active Crust with Space
Geodesy: Study of the Coseismic Deformation due to the 1992 Mw7. 3 Landers (Southern
California) Earthquake." Journal of Geophysical Research: Solid Earth (1978 –2012) 109,
no. B3 (2004b).
Field, Edward H., Ramon J. Arrowsmith, Glenn P. Biasi, Peter Bird, Timothy E. Dawson, Karen
R. Felzer, David D. Jackson, Kaj M. Johnson, Thomas H. Jordan, and Christopher Madden.
"Uniform California Earthquake Rupture Forecast, Version 3 (UCERF3)—The Time‐
Independent Model." Bulletin of the Seismological Society of America 104, no. 3 (2014):
1122-1180.
Finzi, Yaron, Elizabeth H. Hearn, Yehuda Ben-Zion, and Vladimir Lyakhovsky. "Structural
Properties and Deformation Patterns of Evolving Strike-Slip Faults: Numerical Simulations
Incorporating Damage Rheology." Pure and Applied Geophysics 166, no. 10-11 (2009):
1537-1573.
Frost, Erik, James Dolan, Charles Sammis, Brad Hacker, Joshua Cole, and Lothar Ratschbacher.
"Progressive Strain Localization in a Major Strike‐slip Fault Exhumed from
Midseismogenic Depths: Structural Observations from the Salzach‐Ennstal‐Mariazell‐
Puchberg Fault System, Austria." Journal of Geophysical Research: Solid Earth 114, no. B4
(2009).
Gold, Peter O., Michael E. Oskin, Austin J. Elliott, Alejandro Hinojosa-Corona, Michael H.
Taylor, Oliver Kreylos, and Eric Cowgill. "Coseismic Slip Variation Assessed from
Terrestrial LiDAR Scans of the El Mayor–Cucapah Surface Rupture." Earth and Planetary
Science Letters 366, (2013): 151-162.
Gold, Ryan D., Nadine G. Reitman, Richard W. Briggs, William D. Barnhart, Gavin P. Hayes,
and Earl Wilson. "On-and Off-Fault Deformation Associated with the September 2013 M W
7.7 Balochistan Earthquake: Implications for Geologic Slip Rate Measurements."
Tectonophysics 660, (2015): 65-78.
Graves, Robert, Thomas H. Jordan, Scott Callaghan, Ewa Deelman, Edward Field, Gideon Juve,
Carl Kesselman, Philip Maechling, Gaurang Mehta, and Kevin Milner. "CyberShake: A
Physics-Based Seismic Hazard Model for Southern California." Pure and Applied
Geophysics 168, no. 3-4 (2011): 367-381.
Hudnut, KW, JM Fletcher, TK Rockwell, JJ Gonzalez-Garcia, O. Teran, and SO Akciz.
2010Earthquake Rupture Complexity Evidence from Field Observations.102.
Hudnut, KW, NE King, JE Galetzka, KF Stark, JA Behr, A. Aspiotes, S. Van Wyk, R. Moffitt, S.
Dockter, and F. Wyatt. "Continuous GPS Observations of Postseismic Deformation
Following the 16 October 1999 Hector Mine, California, Earthquake (Mw 7.1)." Bulletin of
the Seismological Society of America 92, no. 4 (2002): 1403-1422.
91
Jachens, RC, VE Langenheim, and JC Matti. "Relationship of the 1999 Hector Mine and 1992
Landers Fault Ruptures to Offsets on Neogene Faults and Distribution of Late Cenozoic
Basins in the Eastern California Shear Zone." Bulletin of the Seismological Society of
America 92, no. 4 (2002): 1592-1605.
Jacobs, Allison, David Sandwell, Yuri Fialko, and Lydie Sichoix. "The 1999 (Mw 7.1) Hector
Mine, California, Earthquake: Near-Field Postseismic Deformation from ERS
Interferometry." Bulletin of the Seismological Society of America 92, no. 4 (2002): 1433-
1442.
Klinger, Yann. "Relation between Continental Strike‐slip Earthquake Segmentation and
Thickness of the Crust." Journal of Geophysical Research: Solid Earth (1978 –2012) 115,
no. B7 (2010).
Klinger, Y., R. Michel, and G. C. P. King. "Evidence for an Earthquake Barrier Model from
Mw ∼ 7.8 Kokoxili (Tibet) Earthquake Slip-Distribution." Earth and Planetary Science
Letters 242, no. 3–4 (2006): 354-364.
Leprince, S., KW Hudnut, SO Akciz, A. Hinojosa-Corona, and JM Fletcher. "Surface Rupture
and Slip Variation Induced by the 2010 El Mayor–Cucapah Earthquake, Baja California,
Quantified using COSI-Corr Analysis on Pre-and Post-Earthquake LiDAR Acquisitions."
EP41A –0596 (2011).
Leprince, Sébastien, François Ayoub, Yann Klingert, and J-P Avouac. 2007aCo-Registration of
Optically Sensed Images and Correlation (COSI-Corr): An Operational Methodology for
Ground Deformation Measurements.1943-1946.
Leprince, Sébastien, Sylvain Barbot, François Ayoub, and J-P Avouac. "Automatic and Precise
Orthorectification, Coregistration, and Subpixel Correlation of Satellite Images, Application
to Ground Deformation Measurements." Geoscience and Remote Sensing, IEEE
Transactions on 45, no. 6 (2007b): 1529-1558.
Lockner, David A. "A Generalized Law for Brittle Deformation of Westerly Granite." Journal of
Geophysical Research: Solid Earth (1978 –2012) 103, no. B3 (1998): 5107-5123.
Mai, P. Martin, and Gregory C. Beroza. "A Spatial Random Field Model to Characterize
Complexity in Earthquake Slip." Journal of Geophysical Research: Solid Earth (1978 –
2012) 107, no. B11 (2002): ESE 10-1-ESE 10-21.
Mandelbrot, Benoit B. The Fractal Geometry of Nature. Macmillan, 1983.
Manighetti, Isabelle, Michel Campillo, C. Sammis, PM Mai, and G. King. "Evidence for Self‐
similar, Triangular Slip Distributions on Earthquakes: Implications for Earthquake and Fault
Mechanics." Journal of Geophysical Research: Solid Earth (1978 –2012) 110, no. B5
(2005).
92
Manighetti, I., C. Caulet, L. De Barros, C. Perrin, F. Cappa, and Y. Gaudemer. "Generic Along-
Strike Segmentation of Afar Normal Faults, East Africa: Implications on Fault Growth and
Stress Heterogeneity on Seismogenic Fault Planes." Geochemistry, Geophysics, Geosystems
16, no. 2 (2015): 443-467.
Martel, Stephen J., David D. Pollard, and Paul Segall. "Development of Simple Strike-Slip Fault
Zones, Mount Abbot Quadrangle, Sierra Nevada, California." Geological Society of
America Bulletin 100, no. 9 (1988): 1451-1465.
McGill, Sally F., and Charles M. Rubin. "Surficial Slip Distribution on the Central Emerson
Fault during the June 28, 1992, Landers Earthquake, California." Journal of Geophysical
Research: Solid Earth (1978 –2012) 104, no. B3 (1999): 4811-4833.
McGuire, Jeff, and Yehuda Ben-Zion. "High-Resolution Imaging of the Bear Valley Section of
the San Andreas Fault at Seismogenic Depths with Fault-Zone Head Waves and Relocated
Seismicity." Geophysical Journal International 163, no. 1 (2005): 152-164.
Michel, Rémi, and Jean‐Philippe Avouac. "Coseismic Surface Deformation from Air Photos:
The Kickapoo Step Over in the 1992 Landers Rupture." Journal of Geophysical Research:
Solid Earth (1978 –2012) 111, no. B3 (2006).
Milliner, Christopher WD, James F. Dolan, James Hollingsworth, Sebastien Leprince, Francois
Ayoub, and Charles Sammis. "Quantifying Near‐field and Off‐fault Deformation Patterns of
the 1992 Mw 7.3 Landers Earthquake." Geochemistry, Geophysics, Geosystems (2015).
Nelson, Michael R., and Craig H. Jones. "Paleomagnetism and Crustal Rotations Along a Shear
Zone, Las Vegas Range, Southern Nevada." Tectonics 6, no. 1 (1987): 13-33.
Oskin, Michael, Lesley Perg, Eitan Shelef, Michael Strane, Emily Gurney, Brad Singer, and
Xifan Zhang. "Elevated Shear Zone Loading Rate during an Earthquake Cluster in Eastern
California." Geology 36, no. 6 (2008): 507-510.
Owen, S., G. Anderson, DC Agnew, H. Johnson, K. Hurst, R. Reilinger, Z-K Shen, J. Svarc, and
T. Baker. "Early Postseismic Deformation from the 16 October 1999 Mw 7.1 Hector Mine,
California, Earthquake as Measured by Survey-Mode GPS." Bulletin of the Seismological
Society of America 92, no. 4 (2002): 1423-1432.
Quigley, M., R. Van Dissen, N. Litchfield, P. Villamor, B. Duffy, D. Barrell, K. Furlong, T.
Stahl, E. Bilderback, and D. Noble. "Surface Rupture during the 2010 Mw 7.1 Darfield
(Canterbury) Earthquake: Implications for Fault Rupture Dynamics and Seismic-Hazard
Analysis." Geology 40, no. 1 (2012): 55-58.
Renard, François, Thibault Candela, and Elisabeth Bouchaud. "Constant Dimensionality of Fault
Roughness from the Scale of Micro‐fractures to the Scale of Continents." Geophysical
Research Letters 40, no. 1 (2013): 83-87.
93
Rockwell, Thomas K., and Yann Klinger. "Surface Rupture and Slip Distribution of the 1940
Imperial Valley Earthquake, Imperial Fault, Southern California: Implications for Rupture
Segmentation and Dynamics." Bulletin of the Seismological Society of America 103, no. 2A
(2013): 629-640.
Rockwell, Thomas K., Scott Lindvall, Tim Dawson, Rob Langridge, William Lettis, and Yann
Klinger. "Lateral Offsets on Surveyed Cultural Features Resulting from the 1999 Izmit and
Düzce Earthquakes, Turkey." Bulletin of the Seismological Society of America 92, no. 1
(2002): 79-94.
Rubino, V., N. Lapusta, AJ Rosakis, S. Leprince, and JP Avouac. "Static Laboratory Earthquake
Measurements with the Digital Image Correlation Method." Experimental Mechanics 55,
no. 1 (2015): 77-94.
Sagy, Amir, Emily E. Brodsky, and Gary J. Axen. "Evolution of Fault-Surface Roughness with
Slip." Geology 35, no. 3 (2007): 283-286.
Sammis, Charles G., Ares J. Rosakis, and Harsha S. Bhat. "Effects of Off-Fault Damage on
Earthquake Rupture Propagation: Experimental Studies." Pure and Applied Geophysics 166,
no. 10-11 (2009): 1629-1648.
Scharer, KM, JB Salisbury, J. R. Arrowsmith, and TK Rockwell. "Southern San Andreas Fault
Evaluation Field Activity: Approaches to Measuring Small Geomorphic offsets—
Challenges and Recommendations for Active Fault Studies." Seismological Research
Letters 85, no. 1 (2014): 68-76.
Scholz, Christopher H. The Mechanics of Earthquakes and Faulting. Cambridge university
press, 2002.
Shelef, Eitan, and Michael Oskin. "Deformation Processes Adjacent to Active Faults: Examples
from Eastern California." Journal of Geophysical Research: Solid Earth 115, no. B5 (2010).
Shi, Zheqiang, and Yehuda Ben-Zion. "Dynamic Rupture on a Bimaterial Interface Governed by
Slip-Weakening Friction." Geophysical Journal International 165, no. 2 (2006): 469-484.
Shi, Zheqiang, and Steven M. Day. "Rupture Dynamics and Ground Motion from 3-D Rough-
Fault Simulations." Journal of Geophysical Research: Solid Earth 118, no. 3 (2013): 1122-
1141.
Sibson, Richard H. "Thickness of the Seismic Slip Zone." Bulletin of the Seismological Society
of America 93, no. 3 (2003): 1169-1178.
Sieh, K., L. Jones, E. Hauksson, K. Hudnut, D. Eberhart-Phillips, T. Heaton, S. Hough, K.
Hutton, H. Kanamori, A. Lilje, S. Lindvall, S. F. McGill, J. Mori, C. Rubin, J. A. Spotila, J.
Stock, H. K. Thio, J. Treiman, B. Wernicke, and J. Zachariasen. "Near-Field Investigations
94
of the Landers Earthquake Sequence, April to July 1992." Science (New York, N.Y.) 260, no.
5105 (1993): 171-176.
Simons, Mark, Yuri Fialko, and Luis Rivera. "Coseismic Deformation from the 1999 Mw 7.1
Hector Mine, California, Earthquake as Inferred from InSAR and GPS Observations."
Bulletin of the Seismological Society of America 92, no. 4 (2002): 1390-1402.
Tchalenko, JS. "Similarities between Shear Zones of Different Magnitudes." Geological Society
of America Bulletin 81, no. 6 (1970): 1625-1640.
Teran, Orlando J., John M. Fletcher, Michael E. Oskin, Thomas K. Rockwell, Kenneth W.
Hudnut, Ronald M. Spelz, Sinan O. Akciz, Ana Paula Hernandez-Flores, and Alexander E.
Morelan. "Geologic and Structural Controls on Rupture Zone Fabric: A Field-Based Study
of the 2010 Mw 7.2 El Mayor–Cucapah Earthquake Surface Rupture." Geosphere 11, no. 3
(2015): 899-920.
Thomson, David J. "Spectrum Estimation and Harmonic Analysis." Proceedings of the IEEE 70,
no. 9 (1982): 1055-1096.
Titus, Sarah J., Mark Dyson, Charles DeMets, Basil Tikoff, Frederique Rolandone, and Roland
Bürgmann. "Geologic Versus Geodetic Deformation Adjacent to the San Andreas Fault,
Central California." Geological Society of America Bulletin 123, no. 5-6 (2011): 794-820.
Treiman, Jerome A., Katherine J. Kendrick, William A. Bryant, Thomas K. Rockwell, and Sally
F. McGill. "Primary Surface Rupture Associated with the Mw 7.1 16 October 1999 Hector
Mine Earthquake, San Bernardino County, California." Bulletin of the Seismological Society
of America 92, no. 4 (2002): 1171-1191.
Turcotte, Donald L. Fractals and Chaos in Geology and Geophysics. Cambridge university
press, 1997.
Wells, Donald L., and Kevin J. Coppersmith. "New Empirical Relationships among Magnitude,
Rupture Length, Rupture Width, Rupture Area, and Surface Displacement." Bulletin of the
seismological Society of America 84, no. 4 (1994): 974-1002.
Wesnousky, Steven G. "Displacement and Geometrical Characteristics of Earthquake Surface
Ruptures: Issues and Implications for Seismic-Hazard Analysis and the Process of
Earthquake Rupture." Bulletin of the Seismological Society of America 98, no. 4 (2008):
1609-1632.
Wesnousky, Steven G. "Predicting the Endpoints of Earthquake Ruptures." Nature 444, no. 7117
(2006): 358-360.
Wesnousky, Steven G. "Seismological and Structural Evolution of Strike-Slip Faults." (1988).
95
Zachariasen, Judith, and Kerry Sieh. "The Transfer of Slip between Two En Echelon Strike‐slip
Faults: A Case Study from the 1992 Landers Earthquake, Southern California." Journal of
Geophysical Research: Solid Earth (1978 –2012) 100, no. B8 (1995): 15281-15301.
Zinke, Robert, James Hollingsworth, and James F. Dolan. "Surface Slip and Off‐fault
Deformation Patterns in the 2013 MW 7.7 Balochistan, Pakistan Earthquake: Implications
for Controls on the Distribution of Near‐surface Coseismic Slip." Geochemistry,
Geophysics, Geosystems 15, no. 12 (2014): 5034-5050.
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Chapter 2 Figures
Figure 1
97
Figure 2
98
Figure 3
99
Figure 4
100
Figure 5
101
Figure 6
102
Figure 7
103
Figure 8
104
Figure 9
105
Chapter 3 Figures
Fig. 1
106
Fig. 2
107
Fig. 3
108
Chapter 4 Figures
Fig. 1
109
Fig. 2
110
Fig. 3
111
Fig. 4
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Appendix A: Quantifying near-field and off-fault deformation patterns of the 1992 Mw 7.3
Landers earthquake
Introduction
The supplementary text includes detailed results of our synthetic tests, which are a similar but
more detailed analysis than the study of Michel and Avouac (2006). The supplementary figures
are split into two parts, the first are results relating to our synthetic tests (Figures S1-S4), the
second (Figures S5-S17) are results from our statistical analysis of the control of various
parameters on our COSI-Corr displacement, off-fault deformation (OFD) and fault-zone width
(FZW) data. For these synthetic tests we use two different images taken at different times in
order to incorporate the effect of different images textures and quality.
The COSI-Corr displacement (n = 1057), OFD (n = 280) and FZW (n = 1060) data are
acquired from stacked profiles from the correlation maps. The tested parameters we considered
include the inferred age of alluvial fans (proxy for degree of lithification), horizontal distance to
nearest bedrock exposure (a proxy for sediment thickness), fault strike relative to an optimal
orientation (a proxy for stress field), and fault length (a proxy for structural maturity). We infer
the ages of alluvial fans from the development of desert varnish, surface texture and relative
amount of incision between fan surfaces from false-color composite aerial photography and
Google Earth imagery. The horizontal distance to bedrock is determined from the same geologic
maps used in the main article. We also analyze how the COSI-Corr displacement, FZW and OFD
scale with each other.
113
The figures here present useful information on how the tested parameters show a control
(or lack of) with our data that serves as a supplement to the results in the main text. The majority
of the parameters presented here yield in most cases no discernable relation with our surface
deformation data. However, several of these comparisons do appear to exhibit a systematic
relationship. Specifically figure 10 shows a weak correlation between our data (COSI-Corr
displacement, OFD and FZW) with the fault length. As might be expected longer faults can host
larger displacements and wider fault-zones, while OFD should decrease as the fault matures and
lengthens.
We also provide a table (Table S1), which contains all the measurements made and used
in our statistical analysis that were extracted from our correlation maps. Note there are numerous
nan values in the OFD column, which represents no OFD was found, because we could only
measure OFD where a COSI-Corr measurement could be sufficiently matched with a nearby
field measurement at that location.
Synthetic tests
During the correlation process, the correlation window analyses a subset of pixels within
the input aerial image and finds similar pixel pattern in the corresponding image that brackets the
event. Therefore the correlation window essentially averages the tectonic deformation over the
region defined by the window size. From this process of averaging, the sliding window is
thought to smooth the resulting correlation maps, thus adding an ‘artificial’ FZW to the real
width. Therefore, before we can measure the FZW reliably, we first need to understand the
correlation process. Specifically we need to constrain the magnitude of the artificial ‘smoothing’
114
and understand whether this process is linear, predictable, and therefore correctable. We also
perform additional tests, the results of which constitute a powerful tool that uniquely constrains
the measurement bias and precision when subjectively estimating the FZW and displacement
from the stacked profiles.
Test A – Correlation window
The correlation process measures the average displacement over a given correlation
window [Leprince et al., 2007a; 2007b]. On a first approximation, the correlation process can
then be modeled as a simple convolution such as:
obs tr corr
d d h (S1)
Where h
corr
is the convolution kernel, which is in our case a Hanning window, d
tr
is the
theoretical displacement to be measured, * represents the convolution operator, and d
obs
is the
displacement observed through the correlation process. By the properties of the convolution, the
support of d
obs
is therefore the sum of the supports of d
tr
and h
corr
. In our case, the FZW can be
modeled as the support of the derivative of the offset across the fault displacement, such that:
obs tr
corr
dd
h
xx
(S2)
115
supp supp supp
obs tr
obs corr
dd
FZW h
x dx
(S3)
supp
obs th corr
FZW FZW h (S4)
If no OFD where to be present, the theoretical offset would be an ideal step function, and
its derivative an ideal Dirac delta function of null support [see equation (S2)]. A fault with no
OFD would be measured with a FZW equal to the support of the correlation window, and
generally, the observed FZW is biased by the support of the correlation window. Knowing the
correlation window, we can therefore correct the observed measurement of the FZW to recover
the true FZW. In practice, because the Hanning window quickly tapers down at the edges, its
effective support can be expected to be about half its exact support. We therefore determine this
correction term empirically.
To determine the artificial FZW (h
corr
) on a fault of known displacement and width, we
imposed a synthetic earthquake in one of our post-event aerial image. In MATLAB we simply
shift one half of a post-event, aerial image by a known amount, thereby imitating a rupture on a
fault. We correlate the artificially dextrally sheared image with a different non-disturbed pre-
event image (Figure S1a) using the same processing procedure in COSI-Corr that we use to
produce our real dataset [Leprince et al., 2007a; 2007b]. We measured the FZW from the
correlation images using stacked profiles in the same manner as we implemented in our true
dataset. To shift image pixels by a non-integer amount, we applied a cubic interpolation to one
side of the deformed image.
116
We performed 39 synthetic tests with an array of faulting styles, widths and
displacements expected in a real environment. Figure S2 shows as expected; the observed
synthetic FZW (d
obs
) is systematically larger than the true synthetic FZW (d
tr
) by an amount
approximately half the window size. Figure S2 shows our empirically derived calibration
function with slope of 1.04, which unequivocally shows the linear and predictable nature of this
problem. We found for multiple tests that supp(d
corr
) is consistently 18 pixels, which is illustrated
by the goodness-of-fit for our linear model. Therefore, to determine the true FZW (d
tr
), no matter
the true width of deformation, one can use the calibration function to correct for h
corr
by simply
subtracting supp(d
corr
) from the observed FZW (d
h
). Importantly, the synthetic tests reveal the
observed step signal seen in the stacked profiles cannot be produced by any other process except
by strain release occurring over a finite width.
Knowing the synthetic displacement and FZW value allows robust estimation of any
measurement bias, because we can directly compare the values to those subjectively estimated.
When shearing an image synthetically, we applied uniform displacement to the entire fault,
which also has a constant FZW along-strike. Repeatedly measuring the displacement and FZW
along-strike of our synthetic fault across different parts of the correlation image therefore gives
multiple independent measurements. This consequently yields an empirical distribution of the
FZW and displacement measurement. When measuring both the FZW and displacement, as
described below, the true values were not revealed to the user, in order to not influence the
measurements.
a
)
117
Test B - FZW measurement uncertainty
We performed 71 independent measurements of the FZW of the synthetic fault using
stacked profiles, shown in Figure S3. The synthetic fault has a known, pre-determined FZW of
60 m. Subjectively picking the FZW of a fault multiple times expectedly produces an empirical
distribution which is Gaussian, with a mode that exactly matches the true FZW. These tests
demonstrate that when subjectively estimating the FZW there is minor measurement bias
present, with ~2.00 m underestimation of the true FZW. From the Gaussian distribution seen in
Figure S3 we derive an empirical measurement uncertainty of + 12 m (2σ). This empirical
uncertainty value is consistent for any width of fault-zone because it is related to the correlator
window size, which is constant during the correlating process.
Test C – Displacement uncertainty
We also charaterize the measurement distribution for the displacement measurements
from the synthetic tests, the results of which are shown in Figure S4. We apply two tests, one for
a fault with supra-pixel movement of 2 m displacement and another with sub-pixel movement of
50 cm displacement. The tests indicate there is minor amount of measurement bias, with a small
overestimation of the true displacment by 0.01 m. Both the sub- and supra-pixel displacement
tests yield the same behavior with a 1 sigma measurement precision of + 0.07 m and + 0.05 m,
respectively, which is in agreement with the results of Michel and Avouac (2006). The very tight
precision and nearly zero measurement bias is reflective of the robustness of the correlation
procedure, the quality of the aerial images, and the use of profile stacking to suppress noise.
118
Furthermore, Figure S4a shows that subjectively estimating the displacement produces a small
amount of artificial, along-strike slip variability + 0.05 m at the 1 σ level.
Supplementary figures
Figure S1 (a) left: Synthetic correlation map of a single dextral fault striking north-south, with a
uniform, prescribed right-lateral displacement of 2m, with map co-ordinates in UTM. This
correlation is produced by using two-different images taken at different times (1989 and 1994) of
the same area, where the eastern half of the most recent image (1994) is displaced to the south.
The hashed rectangle shows the dimensions of the stacked profile orientated perpendicular to our
synthetic fault, with an along-strike width of 138 m and length of 1.75 km. (b) Right, shows the
119
synthetic deformation signal seen in the stacked profile. The x-axis is distance along profile
length. The y-axis is the pixel movement. The black line is the surface deformation from the
synthetic correlation map in a). Red sub-horizontal dashed lines are the linear regression fits to
the data. Displacement is defined as the difference between the 2 linear regressions where they
intercept the fault trace at x = 0, which in this profile is measured as 2.09 m.
120
Figure S2. Result from the synthetic tests measuring the FZW from the correlation maps in
comparison to the known, pre-determined true value. The linear regression is our calibration
function, which serves as an empirical tool to correct for the correlation window systematically
and artificially widening the true FZW.
121
Figure S3. Results from the synthetic tests repeatedly measuring the FZW along a fault of
constant known width of 60m. Blue histogram bars show the binned data measured from the
correlation maps. Red line shows our best model fit to the data with a Gaussian distribution.
Green vertical line shows the known, synthetic, pre-determined FZW value (60m).
122
Figure S4. Results from the synthetic tests repeatedly measuring the displacement along a fault
of constant, known displacement using stacked profiles. Two tests are performed. Test 1: is a
fault with uniform displacement of 0.5 m. Test 2: is a fault with uniform displacement of 2 m. (a)
Blue points are displacement measured plotted along-strike of our synthetic fault. Green
horizontal line shows the true, uniform displacement of the fault. The variability observed is a
reflection of subjectively estimating the displacement, noise in the data and geometric artifacts.
(b) Blue histogram bars show the binned displacement measured from the correlation maps. Red
line shows our best model fit to the data with a Gaussian distribution. Green vertical line shows
the known, synthetic, pre-determined displacement value.
123
Figure S5. Fault-zone width plotted against off-fault deformation. We find a from a Spearman’s
rank a value of 0.33, indicating that the FZW can only explain a small portion of the variabilty in
the OFD data. We do find however, a p-value < 0.01, indicating that there is a linear relation
between the data and that they are not independent.
124
Figure S6. COSI-Corr displacement (which represents the total displacement across the fault)
versus fault-zone width plotted.
125
Figure S7. COSI-Corr displacement (which represents the total displacement across the fault)
versus off-fault deformation.
126
Figure S8. a) Locations of fault-zone width measurement plotted with the geologic maps which
127
illustrates the range of near-surface materials used in the analysis [Dibblee, 1964a, 1964b;
Dibblee, 1967a, 1967b, 1967c]. b) shows enlargement of southern termination of
128
Figure S9 a) Locations of off-fault deformation plotted with the geologic maps which illustrates
the range of near-surface materials used in the analysis [Dibblee, 1964a, 1964b; Dibblee, 1967a,
1967b, 1967c]. b) shows an enlargement of the Kickapoo stepover illustrating variation of OFD.
Figure S10. a) Off-fault deformation plotted as a function of horizontal distance to the nearest
outcrop of exposed bedrock which serves as a proxy for thickness of sediment. Larger distances
from the nearest range front would expectedly have thicker amounts of sediment and therefore
larger OFD and FZW. b) Shows fault-zone width plotted as a function of distance to bedrock,
where location of bedrock exposures are determinded from the geologic map (Figure S3).
129
Figure S11.a) Off-fault deformation plotted against the deviation of fault strike from a regional
strike. The regional strike represents the regional stress field, and thus the deviation a proxy of
the faults optimal orientation to the regional stress field. Faults with large deviations from zero
(the presumed optimal faulting strike) will likely be misaligned with the regional stress field and
likely yield larger OFD and wider FZWs.
130
Figure S12.a)Vertical offset plotted against off-fault deformation (%). Vertical deformation
along a sub-vertical fault-plane can in places producing ponding of sediment against the fault
scarp and therefore produce local areas of thick sediment. Thicker sediment would expectedly
produce larger amounts of OFD.
131
Figure S13. Fault-zone widths measured in alluvial fans of different inferred ages. Alluvial fan
ages are determinded relatively from multi-spectral aerial images and Google Earth and by
analyzing the degree of desert varnish development, surface texture and relative amount of
incision of each fan. We designate these with informal, local indexes as Q1 through Q4 from
oldest to youngest, where degree of consolidation is expected to increase with age. a) Shows
FZW for Q1, b) FZW for fans measured in Q2, c) FZWs measured in Q3 alluvial fans and d)
FZWs measured in Q4 material.
132
Figure S14. Off-fault deformation (%) measured in alluvial fans of different inferred ages. Q4 is
the youngest fan, assumed to be the least consolidated and most likely to produce the largest
OFD. Q1 is the oldest observable fan along the surface rupture and assumed to be the most
consolidated and likely to produce least strain accommodated off the primary fault strand.
Alluvial fan ages are determinded relatively from multi-spectral aerial images and Google Earth
and analyzing the degree of desert varnish development, surface texture and relative amount of
incision of each fan. a) Shows OFD for Q1, b) OFD for fans measured in Q2, c) OFD measured
in Q3 alluvial fans and d) OFD measured in Q4 material.
133
Figure S15 a) Mean OFD with 1 sigma error plotted for different zones of structural complexity
with colored dots denoting different lithologies found within each bin of structural complexity.
b) Mean FZW plotted with 1 sigma error for different zones of structural complexity with
colored dots denoting different lithologies found within each bin of structural complexity. We
use three zones of structural complexity instead of five, as used in the main text because this
avoids parsing the data too finley and loosing sample sizes.
134
Figure S16. a) The Fault length of 69 individual faults plotted against mean displacement found
along the given fault. Blue line shows best fit linear regression with R
2
= 0.58 b) Fault length
plotted against maximum displacement measured along the individual fault. Blue line shows best
fitting linear model with R
2
= 0.52. c) Mean OFD plotted as a function of length of fault. Blue
line shows best fitting linear model with R
2
= 0.10. d) Shows fault length plotted against the
mean fault-zone width of each fault, red line shows best fitting linear model with R
2
= 0.22.
135
Figure S17 (a) Subset of the north-south correlation result along the southern section of the
Johnson Valley fault, with location of profiles labelled. Color bar shows magnitude of pixel
movement, blue is movement to the north and yellow towards the south. (b) Google earth image
acquired of the same aerial extent as (a), illustrating the types of near-surface material and extent
of the alluvial channel and location of profile transects.(c) Profile drawn across the Holocene
alluvial channel showing the surface deformation signal taken from the correlation result in a).
The signal exhibits a wide fault-zone of 68 m, as delineated by the red, vertical dashed lines and
horizontal arrow. (d) Surface displacement signal from a profile drawn across the Landers
136
surface rupture from a), within a Pleistocene, more consolidated alluvial fan, which shows a
narrower 18 m fault-zone as delineated by the red, vertical dashed lines.
Appendix B: Resolving Fine-Scale Heterogeneity of Co-seismic Slip and the Relation to
Fault Structure
Validation of displacement measurements using SPOT data
To validate our displacement measurements derived from the 1 m National Aerial
Photography Program (NAPP) air photos we used an independent dataset that can also measure
the deformation field and slip distributions of both the Landers and Hector Mine earthquakes.
Our independent data consists of pre- and post-event 10 m SPOT imagery that cover both
earthquakes in space and time, giving an independent constraint on the surface deformation field
and slip distribution, which is produced from the same COSI-Corr procedure as that used for the
air photos.
The Landers SPOT correlation (Supplementary Fig. S1 a,b) is produced from a pre-event,
1991, 10 m SPOT 2 image, and a post-event, 1993, 10 m SPOT 2 image. For Hector Mine we
produced the correlation maps (Supplementary Fig. S1 d,e) from pre-event 1993, 10 m SPOT 4
imagery and post-event imagery from a 2000, 10 m SPOT 4 image. For both earthquakes we
used a multi-scale correlation window of initial 64 pixels and final of 32 pixels with a step size
of 8 pixels, similar correlation parameter as that used for the air photo data, and applied a non-
local means filter to the correlation result to suppress noise. To measure the displacement we
used stacked profiles of 2.5km width, spaced with the same distance along the surface rupture.
137
Comparing the slip distribution from the SPOT correlation to the air photos we find an
excellent agreement at the first-order scale (Supplementary Fig. S1). The overall smoothness of
the SPOT result is a function of a (i) coarser pixel resolution (10 m of SPOT data compared to 1
m air photos), (ii use of a non-local means filter to reduce noise in the correlation result and (iii)
use of wide stacked profiles (2.5 km compared to 138 m in the air photos) with also the same
coarse measurement discretization. Therefore the excellent agreement between these two
different geodetic datasets at the first-order scale, which is what the SPOT imagery can resolve,
provides a robust validation of our displacement measurements.
Synthetic tests
To quantify the measurement precision and any possible bias in estimating displacement
we employed synthetic tests. Specifically, we design these tests to capture and quantify how the
estimation of displacement measurement is effected by (i) noise and geometrical artifacts within
the correlation maps and (ii) the subjective manner when interpreting the deformation signal
within the stacked profiles. To do this we create a synthetic rupture through the air photos with
pre-determined displacement that is constant along the fault, which is then measured using
stacked profiles in order to quantify how well we can recover the spatially uniform values. Thus
when measured if any spatial variation of displacement does arise that deviates from the known
constant value, this directly constrains the effect of noise, long-wavelength geometrical artifacts
(such as scanning, thermo-mechanical warping or radial distortion) from the correlation maps
and the subjective interpretation of estimating displacement.
138
To simulate a synthetic rupture on a ‘fault’ we simply shift one half of a post-event, aerial
image by a pre-determined amount. To generate a displacement for the synthetic fault rupture
without it being known to the user when measuring displacement we use MATLAB’s random
number generator, where the value is recorded and only revealed until after the measurements
are complete, therefore allowing us to conduct measurements of displacement without knowing
the true value and biasing the results. We correlate the artificially dextrally sheared image with a
different non-disturbed pre-event image (Supplementary Fig. S2) using the same processing
procedure in COSI-Corr that we use to produce our real dataset. We measure displacement using
stacked profiles of 138 m width and lengths up to a maximum of 3 km. Where multiple fault
strands exist within a single profile we measure displacement from each fault independently and
simply sum these to give the total displacement accommodated across the system of faults.As the
images are aquired over areas that contain real tectonic deformation, which are areas we want to
neglect from our tests (as this would contaminate our synthetic known ruptures), we simply used
information from the real correlation result (Fig. 1 of the main text) to help avoid such areas. To
shift image pixels by a non-integer amount, we applied a cubic interpolation to one side of the
deformed image. In total we used five image pairs, one pair from the Landers (Supplementary
Fig. 2 a and b) event and four pairs from the Hector Mine event (Supplementary Fig. 2 d, e, g
and h), where each pair contains a pre and post-event image..
As the synthetic offset is determined to be constant along the entire fault length, any
deviation of the measurements from the synthetic, known values gives a direct quantification of
the measurement bias and precision, which reflects measurement subjectivity and variation in
image quality and texture. Furthermore repeatedly measuring the displacement along-strike of
our synthetic fault across different parts of the correlation image gives multiple independent
a
)
139
measurements of displacement. We estimate measurement bias by simply subtracting the average
displacement (from a large sample) that we measure from the correlation maps, to the true,
known synthetic displacement value. To avoid biasing the measurements, the true, pre-
determined synthetic fault offset values were chosen using a random number generator and were
not revealed to the user until the measurements from the correlation maps were completed.
In total we performed three types of synthetic tests that utilized an array of faulting styles,
widths and displacements expected in a real environment from imagery acquired over both the
Landers and Hector Mine events, that are outlined in detail below (Supplementary Fig. S2).
Results
The first test involved imagery associated with the Landers event with the aim of
understanding whether COSI-Corr’s sub-pixel correlation behaves differently when evaluating
fault displacement that exceeds a pixel dimension i.e., ‘supra’ pixel fault movement. To test
whether COSI-Corr gives consistent results and does not artificially alter displacement if the
fault movement exceeds a pixel dimension, we used one fault with supra-pixel movement of 2.5
m and a second with sub-pixel movement of 0.4 m displacement (where the image pixel
resolution we use is 1 m). We used fault lengths of ~7 km that span the entire image and aquired
45 displacement measruements for each fault. We note this first test is similar to that conducted
by ref. 40 found in the supplementary file, and we re-performed this test in order to establish
consistentcy between the two studies.
The first synthetic test reveals an overall bias of 0.02 m with a precision of + 0.04 m (1σ)
for our displacement measurements (Supplementary Fig. S3). Specifically, both the sub- and
140
supra-pixel displacement tests yield the same behavior with a 1σ measurement precision of +
0.041 m and + 0.038 m, respectively, in agreement with previous studies
1,2
.
The second and third tests involved imagery used for the correlation of the 1999 Hector
Mine event, again, from locations that contain no real tectnoic deformation. Specifically, the
second test invovles performing additional displacement measurements, similar to the first test,
in order to understand whether the measurement uncertainity is different from the correlation
produced by air photos associated with the Hector Mine earthquake in comparison to air photos
used for the Landers event (even though the post-Landers and pre-Hector Mine are derived from
the same 1994, NAPP flight mission). For test 2 we implemented six faults of equal length and
spacing but with different magnitudes of displacement, that were set constant along-strike
(Supplementary Fig. S2 d,e,f). In total we collected 434 displacement measurements, finding an
overall bias of 0.01 m and precision (1σ) of + 0.06 m (Supplementary Fig.S 4c). Importantly, we
found no discernable diffference of the measurement precision or accuracy derived from the
Landers air photos (test 1, with a bias of 0.02 m and 1σ of + 0.04 m) or the Hector Mine imagery
(see Table S1 and S2 and Supplementary Fig. S3 and S4).
The third test involved changing the width of deformation to understand whether a wider
fault zone causes the measurement estimation to be more amibigous and therefore more difficult
to interpret and adequatley extract the true displacement. To simulate ‘faults’ of various widths
we simply varied the number of multiple parallel fault strands within a synthetic ‘fault zone’. We
simulated six different main ‘fault zones’ with widths of 1, 25, 50, 100, 125 and 150 m, that are
of constant width and displacment along-strike. We simulate widths that are similar to those
observed in the real correlation results and that observed from
1,3,4
. From this third test we
collected 435 displacement measurements and found an overall measurement bias of 0.02 m and
141
precision of 1σ + 0.06 m (Supplementary Fig. S5). Importantly, we found the displacement bias
and precision is not significantly affected by the width of deformation (Supplementary Fig. S6).
The similar level of bias and precision found in test 3 to that of test 1 and 2, again indicates the
width of deformation has an unnoticeable effect on the estimation of displacement in the stacked
profiles.
For all three tests we found the spectrum of these results is close to but does not follow white
noise (Supplementary Fig. S7), in agreement with a previous and similar analysis
2
and
importantly, nor do they have the same slope in the power spectrum as the real displacement
measurements reported in the main text. The slope of the slip spectra for tests 2 and 3 are 0.31
(corresponding to a fractal dimension [D] = 2.34) and 0.47 (D = 2.26), respectively
(Supplementary Fig. S7 b and d). Furthermore, we note that both the slope and the power of the
synthetic slip in the spectra are significantly diferrent (and less in power) than that found in the
real results presented in the main text, again indicating variation of slip induced by measurement
subjectivity and noise within the images, is insufficient in amplitude across a broad range of
frequencies to cause the observed amplitude of slip variaiton that is observed in our real
correlation maps (Fig. 1).
From all three synthetic tests, we found a consistent value for the measurement bias and
precision of displacement when estimated from the stacked profiles. From a total of 959
displacement measurements from the three synthetic tests, we found an overall measurement bias
of 0.02 m and precision (1σ) of + 0.06 m with no observable systematic variation as a function
of the air photos used (Landers or Hector Mine flight missions), fault width or magnitude of
displacement. Using these results we derived an empirical error distribution for the displacement
measurements (Supplementary Fig. S7c), which we propagate through the pre-existing error in
142
COSI-Corr, that forms the basis of the measurement uncertainty found in the main text. The
small precision and measurement bias is reflective of the robustness of the correlation procedure,
the quality of the aerial images, and the use of profile stacking to suppress noise. These tests also
confirm the width of our stacked profiles is appropriate, a width that reduces noise to a low level
of uncertainty (1σ = 0.06 m), the same as that observed from ref. 17, that found using the same
Landers images used here, this value of uncertainty is the base level of noise in the correlation
result between the before and after images. Thus, these results and their agreement with previous
work indicate a stack profile of 138 m width is sufficient to reduce noise to its floor level, but not
unnecessarily wide to ‘over-smooth’ displacment along the surface rupture. We note that Figs.
S3, S4, S5 and S7 show no evidence of long-wavelength artifacts (such as scanning, thermo-
mechanical warping or radial distortions) biasing the displacement measurements, as we found
the mean measured displacement values were consistent with the true synthetic value with no
systematic offset. We note the synthetic rupture occurs in areas where scanning and thermo-
mechanical distortions are present in the images (as can be observed in the correlation result of
Supplementary Fig. S2c) and we find these geometric distortions do not influence or offset the
measured displacement from the true value. We note our results showing the long-wavelength
artifacts do not bias our measurement of displacment, a signal which occurs over <100 m length
scales is in agreement with previous studies
16,17,40
.”
143
Estimating the statistical difference between the fractal dimensions of the 1992 Landers
and 1999 Hector Mine slip distributions.
From each of the simulated 10,000 slip distributions for the Landers and Hector Mine
earthquakes, derived using the Monte Carlo approach (see Methods), the fractal dimension was
estimated from the slope in the power spectrum beyond the corner frequency from a linear
regression calculated using a least-squares approach (Fig. 2b and e)
5
. The corner frequency (red
vertical lines in Fig. 2 c and d) in both cases are determined by the rupture length which limits
the long possible wavelength (i.e. the fundamental mode) of slip that can occur along the rupture.
For a total of 20,000 slip distributions (10,000 for each earthquake), we found that the
estimate of the fractal dimension follows a Gaussian distribution with a 1σ of + 0.02 and + 0.03
for Landers and Hector Mine, respectively (Supplementary Fig. S9). Using a T-test we compared
the statistical significance of the difference between the fractal dimension of the Landers (1.72 +
0.02) and Hector Mine slip distribution (1.62 + 0.03) using the values obtained from the Monte
Carlo simulations. We found the T-test rejects the null hypothesis that the fractal dimension of
the Landers and Hector Mine slip distributions are drawn from the same distribution, with a p-
value of 0.0014, well below our confidence level of 5%.
Boxcounting of the Landers and Hector Mine fault systems
Fault systems and fractures have been shown to follow fractal distributions and previous
studies have characterized the fractal properties of faults using boxcounting methods
41,42
. Here
we used a boxcounting method to estimate D in order to quantify which fault system, Landers or
Hector Mine is more complex and whether the geometrical complexities that compose these
144
faults systems can be considered scale invariant and fractal structures. The boxcounting method
allows one to draw log-log plots of the number of boxes required to cover the object (N
r
), in this
case the mapped fault traces, against the size of the box (r). The slope of the log-log plot
provides an estimation of D, that is between 1 and 2 in this case.
To be considered a fractal object the boxcounting curve needs to follow a straight line in
log space, defined by the following relation: log(N
r
) = a + D * log(1/r)
5
. To estimate the fractal
dimension we used boxes of decreasing size and count the number of them that cover the
mapped surface fault traces (Supplementary Fig. S10). We use boxes of sufficient size that
adequately covers a range of spatial scales similar to that of the distance between individual fault
strands.
The fault traces were acquired from the USGS
(http://earthquake.usgs.gov/hazards/qfaults/google.php), and were produced by careful mapping
immediately after both earthquakes
3,8
. Therefore importantly the fault traces analyzed here
represent the faulting directly involved in the rupture and are not inactive and therefore irrelevant
structures.
To minimize any possible distortions or avoid introducing any potential artifacts, we take
a single high resolution image that includes both the fault systems of Hector Mine and Landers,
as they are fortuitously only 20 km apart. Therefore both fault traces are projected in the same
map projection system (UTM WGS-84, Zone 11N) causing minimal distortion to the geometry
of the fault traces and imaged at the same resolution (700 dots per inch) and scale
(1:400,000).We then split the image into two in order to appropriately separate the Landers and
Hector Mine fault systems and then apply the boxcounting analysis separately to each image
145
(Supplementary Fig. S10). Thus from this procedure we can be confident any difference in the
estimation of the fractal D from the boxcounting method is primarily a reflection of fault
geometrical complexity rather than a reflection of any spurious artifacts.
Results
We analyze the boxcounting curve over more than 2 orders of magnitude (10
2
–10
4
pixels). From a linear regression to the boxcounting curve we find a fractal dimension of 1.29 +
0.01 with R
2
= 0.98 for the Landers fault system and 1.15 + 0.01 with R
2
= 0.99 for the Hector
Mine rupture, which is seen in Supplementary Fig. S11 as a steeper curve. Thus, the boxcounting
method clearly indicates the Landers surface rupture has a more complex geometry than the
Hector Mine rupture, which can also be easily validated with a simple visual comparison of the
two surface fault traces of the two earthquakes (Supplementary Fig. S10). We also tested
whether the initial box size affects the estimation of the fractal dimension by rotating the faults
(Supplementary Fig. S10). We find an insignificant difference when varying the initial box size
(by rotating the images of the fault traces) with a difference of 0.0023 and 0.0062 in the fractal
dimension for the Hector Mine and Landers surface fault traces respectively.
146
Supplementary Figure S1. Correlation results and slip profiles of Hector Mine and Landers
event using SPOT satellite imagery. a) SPOT correlation result showing north-south motion of
ground surface of Hector Mine earthquake b) SPOT correlation result of Hector Mine earthquake
in east-west direction. c) Slip profile of Hector Mine event, black showing data measured from
air photos presented in main text and red line showing displacement measured from correlation
maps seen in a) and b). d) SPOT correlation result showing north-south motion of ground surface
of Landers earthquake e) SPOT correlation result of Landers earthquake in east-west direction. f)
Slip profile of Landers event, black showing data measured from air photos presented in main
text and red line showing displacement measured from correlation maps seen in a) and b). The
displacement maps were computed using COSI-Corr and plotted within ENVI 4.8
147
(http://www.exelisvis.com/ProductsServices/ENVIProducts/ENVI.aspx) and Arcmap 10.1
(http://www.esri.com/software/arcgis/arcgis-for-desktop).
Supplementary Figure S2. Illustrates a subset of the images used for the three synthetic tests to
empirically determine the measurement uncertainty. Left column of figure S2 (a, d and g) shows
the pre-event images, middle column of S2 (b, e and h) show post imagery that was synthetically
sheared to produce faults of various widths and displacement (both constant along-strike) and
right column shows (c, f and i) correlation result where displacement measurements were taken
148
from faults running north-south through images (seen as vertical lines juxtaposing different
amounts of ground motion denoted by different colors). Test 1 involves two faults one of supra-
pixel displacement (2.5 m) and sub-pixel displacement (0.4 m). Test 2 involved faults of
different displacement but constant width and test 3 faults of different displacement and different
widths. We note in each of tests 2 and 3 we used two pairs of air photos (two pre- and two post-
event) allowing us to acquire more measurements, giving a total of four pairs of air photos used
for the two tests, where Supplementary Fig. S2 d,e,g and h, show subsets of these air photos. The
displacement maps were computed using COSI-Corr and plotted within ENVI 4.8
(http://www.exelisvis.com/ProductsServices/ENVIProducts/ENVI.aspx) and Arcmap 10.1
(http://www.esri.com/software/arcgis/arcgis-for-desktop). Air photo data compiled by the U.S.
Geological Survey (http://www.usgs.gov).
149
Supplementary Figure S3. Measurement results from synthetic test 1. a) Slip profiles of
displacement measurements taken from two faults with 2.5 (supra-pixel displacement) and 0.4 m
(sub-pixel displacement). Green lines show the true, synthetic displacment value and blue dots
and line show the displacment measurements aquired from the stacked profiles from the
correlation maps (Fig S2c). b) Shows the histogram of measurements (n = 45, shown as blue
bars) from the supra-pixel displacement test that follow a Gaussian distribution (red line) with a
true, synthetic value of 2.5 m that is labeled by a green vertical line. The offset of the true
synthetic value from the mean measured values is 0.01 m, measurements from the tests yield a
mean of 2.49 m, a 1σ of + 0.04 m and median of 2.49 m. c) Shows the histogram of
measurements (n = 45) from the sub-pixel displacement test (blue bars) that follow a Gaussian
distribution (red line) with a true, synthetic value of 0.4 m that is labeled by a green vertical line.
The offset of the true synthetic value from the mean measured values is 0.02 m, measurements
yield a mean of 0.42 m, a 1σ of + 0.038 m and median of 0.42 m.
150
151
Supplementary Figure S4. (top) Displacment measurements from test 2 (Supplementary
Fig. S2f), left side of figure shows slip profile of each fault, right side of figure shows the
distribution of data where each row represents the displacement measurements from each of the
six synthetic ‘faults’. (bottom) shows the overall distribution of all measurements from test 2 (n
= 434), which has been subtracted from its respective true, known synthetic value. We found an
overall mean (i.e., bias) of -0.0034 m, 1σ of + 0.06 m and median of -0.0029. See Table S2 for
statistics for each fault.
152
Supplementary Figure S5. (top) Displacment measurements from test 3 (see Supplementary
Fig. S2i), left side of figure shows slip profile of each fault, right side of figure shows the
distribution of data where each row represents the displacement measurements from each of the
six synthetic ‘faults’. (bottom) shows the overall distribution of measurements from test 3 (n =
153
435), which has been subtracted from its respective true, known synthetic value. We found an
overall mean (i.e., bias) of -0.01 m, 1σ of + 0.06 m and median of -0.01. See Table S3 for
statistics for each fault.
Supplementary Figure S6. a) The variation of displacement measurements (1σ) plotted as a
function of fault zone width. We see no change in the variability of displacement measurement
with the width of the fault zone. That is, a wider fault zone does not make the interpretation of
the deformation signal significantly more ambigious and therefore faults of different widths do
not artificially cause an increase in the variance of the displacement measurements. b)
Displacement measurements from test 3 plotted as function of fault zone width. We find there is
no systematic change of the displacement bias (difference from true value) with width of the
fault zone. That is, a wider fault zone does not make it more difficult to accuratley estimate the
displacment measurement.
154
Supplementary Figure S7. a) and c) show all displacement measurements from tests 2 and 3,
respectively. Power spectrum of synthetic tests 2 and 3 plotted in b) and d) respectively as black
lines (green lines show linear fit), with the real measurements of Landers and Hector Mine fault
slip plotted as blue lines (red line showing linear fit) in b) and d), respectively. The figure clearly
illustrates that the spectra of the synthetic tests have a different slope and significanlty lower
amplitude than the true measurements, indicating the variation of slip observed in the actual
earthquakes is primarily real and reflecting the rupture process as opposed to meaurement
uncertainty. e) Shows the distribution of all displacment measurements aquired from tests 1, 2
and 3 (n = 959), subtracted from their true known value. We find mean (i.e., bias) of 0.02 m, 1σ
155
of + 0.06 m and median of 0.02 m. We use this distribution as our empirical error distribution
that is used for the measurement uncertainty presented in the main text.
Supplementary Figure S8. Simulated slip distributions for the Landers (top) and Hector Mine
earthquakes (bottom) determined by a Monte Carlo method a) 10,000 possible slip distributions
for the Landers earthquake given the error of the measurements, thick green line shows the mean
slip distribution that is directly measured from the stacked profiles. b) Zoom-in of a 3.5
kilometer area denoted as a red rectangle in a), to illustrate how the Monte Carlo simulation
randomly samples the error to produce different possible slip distributions. Note for illustrative
purposes in b) and d) we only plot 30 possible slip distributions in order to adequately see each
individual simulations. c) 10,000 possible slip distributions for the Hector Mine earthquake,
given the error of the measurements. d) Zoom-in of a 2.5 kilometer area denoted as red rectangle
156
in c), to illustrate how the Monte Carlo simulation randomly samples the error to produce
different possible slip distributions.
Supplementary Figure S9. a) Power spectrum for 10,000 possible slip distributions of the
Landers earthquake produced from randomly sampling the error using Monte Carlo simulations.
Red lines are 10,000 linear regressions fit to each of the 10,000 independently estimated spectra
of the simulated, possible the slip distributions. Green vertical line shows the location of the
corner frequency which delineates the extent of the fitting of the linear regression and
corresponds to the length of surface rupture (67 km). b) Histogram of 10,000 possible fractal
dimensions for the Landers slip distribution, which follow a Gaussian distribution (red line) with
mean of 1.72 and 1σ of + 0.02. c) Power spectrum for 10,000 possible slip distributions of the
Hector Mine earthquake produced from randomly sampling the error using Monte Carlo
simulations. Red lines are 10,000 linear regressions fit to each of the 10,000 independently
157
estimated spectra of the simulated, possible the slip distributions. Green vertical line shows the
location of the corner frequency which delineates the extent of the fitting of the linear regression
and corresponds to the length of surface rupture (38 km). d) Histogram of 10,000 possible fractal
dimensions for the Hector Mine slip distribution, which follow a Gaussian distribution (red line)
with mean of 1.62 and 1σ of + 0.03.
Supplementary Figure S10. (top) Map view of the surface fault traces of the Landers
8
and
bottom the Hector Mine rupture
3
mapped in the field, with the left column showing the fault
traces in their north-orientated position and right column showing the fault systems rotated to
158
minimize the amount of image space it occupies. We show here the actual images used in the
boxcounting procedure and therefore do not show scale or north arrow, however, all four images
are at the same 1:400,000 scale. We find no significant difference in the fractal dimension
between which orientations are assumed for the fault traces.
Supplementary Figure S11. a) Log-log plot of number of boxes (N
r
) versus size of boxes (r)
from the boxcounting of the surface fault traces. The blue line and solid circles shows the
boxcounting result for the surface fault traces of the Hector Mine event, with the red line
showing the fit giving a D = -1.15 + 0.01. The black line and solid circles shows the boxcounting
result for the surface fault traces of the Landers earthquake, with the green line showing the
linear regression giving a D = -1.29 + 0.01. We note for the purpose of illustrating the difference
in slope between the two fault systems we have shifted the Landers boxcount curve vertically
down the y-axis by a factor of 3.4 in log space.
159
Supplementary Table S1 Statistics of measurements from synthetic test 1 for two faults of sub-
pixel displacement (row 2) and supra-pixel displacement (row 3).
True fault
displacement
(m)
Mean
measured
displacement
(m)
1σ of measured
displacement (m)
Bias (i.e. mean
difference of
measured value to
known true value)
(m)
Number of
measurements
on fault
0.40 0.42 0.04 0.02 47
2.50 2.49 0.04 -0.01 47
Supplementary Table S2. Statistics of measurements of test 2 with six faults of different
displacements, with constant widths.
True fault
displacement
(m)
Mean
measured
displacement
(m)
1σ of
displacement
measurement (m)
Bias (i.e. mean
difference of
measured value to
known true value)
(m)
Number of
measurements
on fault
3.30 3.30 0.05 0.00309 79
160
1.30 1.29 0.05 0.00672 79
3.30 3.31 0.06 0.01 77
3.20 3.18 0.06 -0.02 76
3.40 3.39 0.06 -0.01 64
2.00 1.99 0.06 -0.01 59
Supplementary Table S3. Statistics of measurements of test 3, from siz faults with different
displacements and widths of deformation.
Fault
width
True fault
displaceme
nt (m)
Mean
measured
displaceme
nt (m)
1σ of
displacement
measurement
(m)
Bias (i.e.
mean
difference
of measured
value to
known true
Number of
measurements on
fault
161
value) (m)
0 1.80 1.82 0.07 0.02 74
25 2.60 2.57 0.05 -0.03 76
50 2.60 2.58 0.05 -0.02 75
100 1.40 1.37 0.05 -0.03 71
125 2.00 1.99 0.06 -0.01 74
150 1.80 1.78 0.05 -0.02 67
162
Appendix C: Co-seismic near-field and off-fault surface deformation patterns of the 1992
Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes: Implications for controls on
the distribution of surface strain
Introduction
The supporting material listed here outlines the description of processing steps to co-register,
orthorectify and correlate the air photos using the program COSI-Corr (Text S1), information on
how displacement measurements were collected (Text S2), description of how strain maps were
calculated (Text S3), methodological procedure of quantifying the geometrical fault complexity
using a boxcounting method to estimate the fractal dimension (Text S4), and a brief description
of how the M
w
and surface rupture length (SRL) were estimated for the Landers and Hector
Mine events using empirical scaling relations with our mean displacement values (Text S5).
These descriptions are supported with figures (Fig. S1-S6), which help illustrate these
explanations. There are also two tables providing the measurements of displacement, fault zone
width and off-fault deformation, which due to their lengths are provided separately from this file.
Air Photo Correlation Method
For the Landers and Hector Mine earthquakes we selected 31 and 21 pairs of stereo-pair (60%
overlap), 1 m resolution, National Aerial Photography Program aerial photographs, respectively,
with 8×8 km footprint (purchased from http://earthexplorer.usgs.gov/). We selected air photos
acquired in 1989, 1994 and 2002, where air photos from the two earlier flight missions serve as
the pre and post Landers data and the latter two serve as the pre and post Hector Mine data. We
note air photos from the 1994 flight mission serve as both the pre-Hector Mine and post-Landers
dataset, giving rise to deformation maps for the two earthquakes derived from the same data
163
acquired from the exact same optical sensor and flight mission, which helps minimize
differences in data quality and accuracy. To produce correlation maps that accurately constrain
the ground deformation pattern, the input aerial photographs must be precisely orthorectified and
co-registered before correlation. The COSI-Corr program
(http://www.tectonics.caltech.edu/slip_history/spot_coseis/download_software.html) allows for
accurate orthorectification of images by taking into account the topography using a digital
elevation model (DEM), the internal camera geometry using a camera calibration report
(https://calval.cr.usgs.gov/calval_osl/calibration_reports/) to correct for optical distortions and
the exterior orientation determined from ground control points (GCPs) [Ayoub et al., 2009]. To
account for topographic distortion of the images, for both the Landers and Hector Mine events,
we used the same 2012, 10 m National Elevation Dataset DEM that covers both ruptures,
acquired from the USGS (http://ned.usgs.gov/). To georeference the post-event aerial photos, we
used a 2005, 10 m, SPOT 5 image as the reference orthoimage for Landers and a 2000, 10 m,
SPOT 4 image for Hector Mine. To co-register the pre and post-event photographs, we construct
a relative mapping between image pairs using tie points that relates common features between
pre and post-event image pairs. For co-registration GCPs are assumed to have experienced zero-
ground movement, however, this assumption is violated due to long-wavelength ground
deformation, to correct for this we used a correlation result from a pair of 10 m, SPOT 2 images
for Landers and SPOT 4 images for Hector Mine [Ayoub et al., 2009] (Supplementary Fig. S1),
which provides independent constraint on ground motion. Topographic artifacts in the
correlation result caused by use of only a single DEM to orthorectify both the pre and post-event
photos are corrected for following the procedure of ref. 17. Once the pre and post-event air
photos are orthorectified, COSI-Corr then applies subpixel image correlation to pairs of selected
164
orthoimages by using an iterative, unbiased processor that estimates the phase plane in the
Fourier domain [Leprince et al., 2007]. For image correlation we used a multiscale sliding
window of initial size of 64 and final size of 32 pixels with a step of 6 pixels, resulting in a
correlation map of 6 m pixel resolution.
Measuring displacement.
Displacement is measured using stacked profiles orientated perpendicular to the fault strike,
with lengths of 1-3 km and stack widths of 138 m, where the width defines the discretization of
independent measurement. The optimal stack width of 138 m (23 pixels) is determined from
synthetic tests (see Milliner et al. [2015] and its supporting information), that gives a noise level
of 2σ = 0.12 m in the displacement measurement, a noise level and stack width in agreement
with previous work [Michel and Avouac 2006], that allows for suppression of noise while
minimizing over-smoothing along-strike changes in surface slip. Surface displacement is
estimated from these stacked profiles by manually fitting linear regressions to either side of the
fault, which are extrapolated to the fault trace to define the total amplitude of the discontinuity in
the vector field, giving the magnitude of the total shear accommodated across the entire width of
deformation (as shown in inset Fig. 1a,c).
For more information on synthetic tests used to calibrate the measurement of the fault-
zone and synthetic used to quantify the measurement uncertainty due to our subjective estimation
of displacement, see Milliner et al. [2015] and its supporting materials.
165
Calculating strain from the correlation maps
We computed all 3 independent components of strain, the norm of strain, and dilation using a
central difference method that is 1
st
order accurate. Here we list the equations used to calculate
strain. In the supplementary figures we also show additional areas of interest where strain varies
in areas of structural complexities.
Below are the equations for calculating strain, s is the dx, step size, which is the pixel resolution
of the correlation images of 6 m. We note the NLM filtering still preserves the original pixel
dimension of the correlation maps. Notation below refers to Cartesian co-ordinates, however,
origin is located at 1,1 pixel location (i.e., top left corner of image), with x increasing from left to
right and y increasing from top to bottom. The norm of the strain tensor (N
ε
)
is computed as the
Euclidean norm, dilation the trace of the strain tensor [tr( ε)].
𝜀 𝑥𝑥
=
𝑢 𝑥 (𝑥 +1,𝑦 )− 𝑢 𝑥 (𝑥 −1,𝑦 )
2𝑠 (S5)
𝜀 𝑦𝑦
=
𝑢 𝑦 (𝑥 ,𝑦 +1)− 𝑢 𝑦 (𝑥 ,𝑦 +1)
2𝑠 (S6)
𝜀 𝑦𝑥
=
1
2
{
𝑢 𝑦 (𝑥 +1,𝑦 )− 𝑢 𝑦 (𝑥 −1,𝑦 )
2𝑠 +
𝑢 𝑥 (𝑥 ,𝑦 +1)− 𝑢 𝑥 (𝑥 ,𝑦 +1)
2𝑠 } (S7)
𝑁 𝜀 = √
∑ ∑ 𝜀 𝑖𝑗
2 𝑛 𝑗 =1
𝑛 𝑖 =1
(S8)
166
Estimating fractal dimension of fault structure
Fault systems and fractures have been shown to follow fractal distributions and previous
studies have characterized the fractal properties of faults using boxcounting methods
41,42
. Here
we used a boxcounting method to estimate D in order to quantify which fault system, Landers or
Hector Mine is more complex and whether the geometrical complexities that compose these
faults systems can be considered scale invariant and fractal structures. The boxcounting method
allows one to draw log-log plots of the number of boxes required to cover the object (N
r
), in this
case the mapped fault traces, against the size of the box (r). The slope of the log-log plot
provides an estimation of D, that is between 1 and 2 in this case.
To be considered a fractal object the boxcounting curve needs to follow a straight line in
log space, defined by the following relation: log(N
r
) = a + D * log(1/r) Turcotte 1997]. To
estimate the fractal dimension we used boxes of decreasing size and counted the number of them
that cover the mapped surface fault traces (Fig. S2e,f). We used boxes of sufficient size that
adequately covers a range of spatial scales similar to that of the distance between individual fault
strands.
The fault traces were acquired from the USGS
(http://earthquake.usgs.gov/hazards/qfaults/google.php), and were produced by careful mapping
immediately after both earthquakes [Bryant 1992; Treiman et al., 2002.] Therefore importantly
the fault traces analyzed here represent the faulting directly involved in the rupture and are not
inactive and therefore irrelevant structures (see Fig. S6 for fault traces used).
To minimize any possible distortions or avoid introducing any potential artifacts, we take
a single high resolution image that includes both the fault systems of Hector Mine and Landers,
167
as they are fortuitously only 20 km apart. Therefore both fault traces are projected in the same
map projection system (UTM WGS-84, Zone 11N) causing minimal distortion to the geometry
of the fault traces and imaged at the same resolution (700 dots per inch) and scale
(1:400,000).We then split the image into two in order to appropriately separate the Landers and
Hector Mine fault systems and then apply the boxcounting analysis separately to each image
(Supplementary Fig. S6). Thus from this procedure we can be confident any difference in the
estimation of the fractal D from the boxcounting method is primarily a reflection of fault
geometrical complexity rather than a reflection of any spurious artifacts.
We tested different box sizes and chose a final box width of 1.5 km (see Fig. S6), larger
values of 3 km and 6 km, were too coarse, providing too few boxes to adequately cover the
ruptures (for box size of 6 km it gave only 9 measurements of fault complexity along the Landers
and 6 points along the Hector Mine) and included fault strands that were essentially irrelevant to
local fault complexity neighboring the measurement of off-fault deformation. Box sizes smaller
than 1.5 km started to reduce the available wavenumbers to acquire robust estimates of the
fractal dimension, and also start to reduce the number of OFD points within a box, therefore
giving less robust constraints on the amount of OFD that relates to each box, and thus we
subjectively settled on a box width of 1.5 km, which we felt provided the best of both resolution
(i.e., number of boxes along the rupture) and stable estimates of fractal dimension that included a
sufficient number of OFD points. We also present in Fig. S7 the OFD% plotted with fractal
dimension that is not subdivided into the lithologies, which shows significant scatter. This
justifies partitioning the OFD% into the different types of near-surface material, where the
scatter can be better understood as the near-surface materials is an important parameter
controlling OFD and itself a source of variation.
168
Derivation of M
w
and Rupture length estimates using empirical scaling relations
To investigate whether we would have accurately estimated the Mw potential of the Landers and
Hector Mine earthquakes from surface rupture characteristics that we measured, as would be
employed in geologic field or paleo-seismic analysis, we used the Dmean versus Mw regressions
from global strike-slip earthquakes to derive estimates of moment magnitude (Mw) from Wells
and Coppersmith [1994].
M
w
= 7.04(±0.05) + 0.89(±0.09)∙log(D
mean
) (S9)
For Landers we used: D
mean
= 3.41. For Hector Mine we used D
mean
= 2.84. Using [Wells &
Coppersmith, 1994] we find M
w
= 7.51 for Landers and M
w
= 7.44 for Hector Mine. We convert
moment magnitude (M
w
) to seismic moment (M
o
) using the following relation from Kanamori
and Hanks [1979]:
𝑀𝑜 = 10
1.5 𝑀𝑤 +16.1
(S10)
From this we find M
o
= of 2.35 × 10
27
dyne.cm and M
o
= 1.84 × 10
27
dyne.cm for
Landers and Hector Mine, respectively.
169
Figure S1. Post-event air photos for the 1992 Landers (left) and 1999 Hector Mine (right) events
acquired in July 1994 and May 2002 respectively, and plotted with the surface ruptures (red
lines). Air photos are 8x8 km footprint with 1 m spatial resolution. We selected 31 pairs and 21
pairs of air photos for the Landers and Hector Mine events respectively
170
171
Figure S2. Illustration of estimation of geometrical fault complexity using boxcounting method
with 1.5 km sizes boxes, with left column showing results from Landers rupture and right
column Hector Mine rupture. a and b) Shows boxcounting results plotted on top of surface
rupture (red lines), where shading of boxes denotes value of fractal dimension. Higher fractal
values denote more complex fault areas shown by darker shading. These results reveal areas of
simple and complex parts of the surface rupture, the latter for example highlighting step-overs,
where the fault branches, or bends. The fault traces are taken from USGS mapping of the
earthquakes, see supplementary text for more details. c and d) Measurements of off-fault
deformation (OFD) as a percent plotted within the boxes used to estimate the complexity of the
surface rupture. Multiple OFD values within a box are used to compute statistics such as the
mean and standard deviation of OFD within each box, these are then plotted in Fig. 3. e and f)
illustrate a single example of a how the fractal dimension of a particular box is estimated. Blue
line shows counting of boxes that include a fault trace at different box sizes. The smaller the size
of the box the more boxes are needed to cover the surface fault trace, from this power law
relation gives an estimate of the complexity of the fault system within the box. Red lines shows
linear least-squares regression to data (blue), the slope gives the fractal dimension (D).
172
Figure S3. a) All off-fault deformation as a percent (OFD%) measurements plotted as a function
of fractal dimension (an estimate of the geometrical fault complexity) for the 1992 Landers
rupture. Green line shows the best fit from a linear-least squares regression, red lines show the
confidence intervals of the regression and black lines show the 95% prediction intervals. b) Same
as a) but OFD data from the Hector Mine event.
173
174
Figure S4. a) COSI-Corr displacement measurements along the 1992 Landers rupture (same as
that plotted in Fig. 1c) with field measurements from Sieh et al. (1993), illustrating the data used
to compute OFD plotted in Fig. 2a. To compute OFD, we subtract the COSI-Corr measurements
which using 1-2 km long stacked profiles, captures the total surface displacenet from the field
measurements, which capture the discrete, ‘on-fault’ component of displacement. c) COSI-Corr
displacement measurements for the 1999 Hector Mine rupture (same as that plotted in Fig. 1c),
with field measurements from Treiman et al. (2002) and Chen et al. (2015), illustrating the data
used to compute OFD.
175
Figure S5. a) Off-fault deformation along Hector Mine plotted as a function of horizontal
distance to the nearest outcrop of exposed bedrock which serves as a proxy for thickness of
sediment. Larger distances from the nearest range front would expectedly have thicker amounts
of sediment and therefore expectedly larger OFD. b) Same as a) but for the 1992 Landers
rupture.
Abstract (if available)
Abstract
Measurements of earthquake surface ruptures provide important insight into the rupture process and faulting mechanics. Deformation along surface ruptures can range from highly complex zones of distributed strain to completely localized, along single fault planes. However, measuring such deformation patterns along surface rupture is highly challenging. Traditional field geologic surveys are well suited to obtaining detailed measurements of surface fault offset, but due to the lack of piercing points that extend far from the fault trace, measurement of distributed deformation is not generally possible. Interferometric Synthetic Aperture Radar (InSAR), is sensitive to millimeter surface changes, providing good coverage of surface motion in far field (> 2 from surface rupture), however, due to strong ground shaking typically decorrelates in the near-field leaving a 1-2 km wide gap of data. While GPS data provides exceptional temporal resolution of surface motion, due to the cost of instrumentation it also lacks the necessary spatial coverage to fully characterize the near-field, co-seismic surface deformation pattern. Thus, due to the limitations of these geodetic and field techniques there is a poor constraint of the surface motion close to the fault rupture (< 2 km), where deformation is most complex and observations most important. In this thesis I present optical image correlation result, which can resolve horizontal surface motion in high spatial detail and precision (1σ = 10 cm), allowing measurement of the amount of distributed deformation and the spatial distribution of fault slip of large magnitude, continental strike-slip earthquakes. I used the software COSI-Corr (Co-registration of Optically Sensed Images and Correlation), which can measure horizontal ground motion to sub-pixel precision, tracking shifts in features between satellite or air photo imagery taken before and after an event. I present results of the near-field deformation pattern of the 1992 Mw = 7.3 Landers and 1999 Mw = 7.1 Hector Mine earthquakes, events only 20 km apart from one another and part of the same tectonic regime, the Eastern California Shear Zone, thus providing an excellent opportunity to investigate how deformation patterns may vary between different fault systems. These results show that for the Landers and Hector Mine events 45 ± 10% and 39 ± 22% of total deformation was accommodated as diffuse deformation over fault zones averaging 154 m and 121 m in width, respectively. We find that the amount of distributed deformation is largely controlled by the geometrical fault complexity, and to a lesser extent the types of near-surface materials
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Milliner, Christopher William Douglas
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Quantifying ground deformation of large magnitude earthquakes using optical imgaging systems
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Doctor of Philosophy
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Geological Sciences
Publication Date
07/21/2016
Defense Date
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