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Seismicity distribution near strike-slip faults in California

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Seismicity distribution near strike-slip faults in California

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SEISMICITY DISTRIBUTION NEAR STRIKE-SLIP FAULTS

IN CALIFORNIA

by

Peter Marion Powers

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

August 2009

Copyright 2009 Peter Marion Powers
ii
Acknowledgements
This research was supported by the Southern California Earthquake Center. SCEC is
funded by NSF Cooperative Agreement EAR-0106924 and USGS Cooperative
Agreement 02HQAG0008. The results presented here have benefited greatly from
discussions and interaction with the greater SCEC community, and I am particularly
grateful to Bill Ellsworth, Egill Hauksson, Peter Shearer, Cliff Thurber and their
respective co-authors for publishing high-quality relocated earthquake catalogs, without
which this work would not have been possible. Efforts on the part of the SCEC Unified
Structural Representation group are also appreciated, and I thank Jim Dieterich and
Deborah Smith for their insight and opinion.
I am truly grateful that my advisor, Tom Jordan, had the vision to support a student
with dual interests in geosciences and information technology. His own varied interests
and perspective were an invaluable part of our scientific discussions, and his fostering of
the SCEC summer IT intern program afforded me the opportunity to significantly
enhance my programming skills. Others at USC that have helped me, in both scholarly
and social contexts, include Greg Davis, James Dolan, Yehuda Ben-Zion, Charlie
Sammis, Thorsten Becker, Kurt Frankel, and Jeremy Zechar.
Lastly, I thank my parents, who were forever supportive of my interests and
aspirations growing up, and my wife, Catherine, who will continue to encourage me,
moving forward.
iii
Table of Contents
Acknowledgements ii
List of Tables iv
List of Figures v
Abstract xi
Introduction 1
Chapter 1: Catalog Analysis 7
Fault referenced seismicity catalogs 7
Intercatalog location uncertainties 18
Catalog-specific location uncertainties 22
Chapter 2: Scaling Analysis 27
Fault-normal seismicity distribution 27
Analysis of bias 39
Chapter 3: Fault-Seismicity Model 45
Rough fault loading model 45
Evolutionary aspects of near-fault seismicity 55
Chapter 4: Near-Fault Earthquake Triggering 63
Aftershock distributions 64
Aftershock statistics 65
Aftershock model 76
Parameter estimation 78
Conclusions 84
References 87
Appendix A: Fault segment catalog summaries 96
Appendix B: Catalog analysis results 149
Appendix C: Uniform reduction of error 155
Appendix D: Scaling analysis 161
Appendix E: Fault catalog weighting analysis 188
Appendix F: Fault segment subsets 193

iv
List of Tables
Table 1: Earthquake catalog sources 8
Table 2: Earthquake catalog statistics 11
Table 3: Fault segment catalogs 12
Table 4: Intercatalog error estimates 20
Table 5: Catalog-specific error estimates 25
Table 6: Comparison of jackknife resampling and maximum likelihood
error estimates 35
Table 7: Apparent fault-normal scaling parameters 38
Table 8: Bias-corrected scaling parameters 42
Table 9: Individual fault data 56
Table B–1: Intercatalog event variation for SoCal faults 150
Table B–2: Catalog-specific event variation for SoCal faults 151
Table B–3: Intercatalog event bias for SoCal faults 152
Table B–4: Catalog-specific event bias for SoCal faults 153
Table B–5: Intercatalog event bias and variation for NoCal faults 154

v
List of Figures
Figure 1: Map of northern California showing locations of seismicity samples 3
Figure 2: Map of southern California showing locations of seismicity samples 4
Figure 3: Depth distributions of relocated earthquakes in the fault segment
catalogs 5
Figure 4: Example of intercatalog earthquake location variation 14
Figure 5: Example of how a fault-seismicity based coordinate system localizes
events on a fault and minimizes artificial fault-normal dispersion 15
Figure 6: Frequency-magnitude distributions for the large-fault classes in
SoCal and NoCal 17
Figure 7: Sample uniform reduction of error analysis for NoCal Faults 23
Figure 8: Fault-normal earthquake density distributions for large SoCal faults 28
Figure 9: Fault-normal earthquake density distributions for small faults and
aftershock-dominated fault segments in SoCal 29
Figure 10: Fault-normal earthquake density distributions for large NoCal faults 30
Figure 11: Fault-normal earthquake density distributions for the Parkfield
fault segments 31
Figure 12: Maximum likelihood solutions and errors for

!
! and

!
d 33
Figure 13: Downweight analysis results for small SoCal faults 36
Figure 14: Theoretical relationship between an observed inner scale,

!
d , and
the true value of d plotted for various γ 41
Figure 15: Sample result from simulation analysis of parameter bias 43
Figure 16: Schematic representation of the RFL (rough fault loading) model
that explains observations of near-fault seismicity distribution 46
Figure 17: Schematic power spectrum, P
X
(y
k
), for the RFL model as a
function of along-strike wavenumber 48
Figure 18: Relationship between fault-core multiplicity and damage zone width 53
vi
Figure 19: Correlations between scaling parameters,

!
! and

!
d , and on-fault
earthquake density !
0
/LW and fault width W for related subsets
of faults 59
Figure 20: Correlations between scaling parameters,

!
! and

!
d , and cumulative
offset and aseismicity factor for related subsets of faults 61
Figure 21: Aftershock sources for SoCal and NoCal 66
Figure 22: Example of near-fault bias in aftershock distributions 67
Figure 23: Frequency-magnitude distribution of mainshocks and aftershocks
(T = 1.5 days)selected for this study from SoCal and NoCal 68
Figure 24: Average rate of M ≥ 2 earthquakes in SoCal as a function of time
t after triggering mainshocks of varying magnitude 70
Figure 25: Average rate of M ≥ 2 earthquakes in NoCal as a function of time
t after triggering mainshocks of varying magnitude 71
Figure 26: Aftershock productivity as a function of mainshock magnitude for
aftershocks where m
0
= 2 72
Figure 27: Aftershock productivity as a function of mainshock magnitude for
aftershocks where m
0
= 0 74
Figure 28: Aftershock productivity as a function of distance from SoCal
mainshocks 75
Figure 29: Contours of the p.d.f. of near-fault aftershock distribution for
different values of x
0
77
Figure 30: On-fault aftershock distributions 81
Figure 31: Synthetic aftershocks sequences derived using the preferred model
parameters for SoCal and NoCal 83
Figure A–1: Summary of catalog data for Box 1, Garlock (East) 97
Figure A–2: Summary of catalog data for Box 2, Garlock (Central) 98
Figure A–3: Summary of catalog data for Box 3, Garlock (West) 99
Figure A–4: Summary of catalog data for Box 4, Lenwood - Lockhart 100
vii
Figure A–5: Summary of catalog data for Box 5, San Andreas (Mojave) 101
Figure A–6: Summary of catalog data for Box 6, Santa Cruz - Catalina Ridge 102
Figure A–7: Summary of catalog data for Box 7, Palos Verdes 103
Figure A–8: Summary of catalog data for Box 8, Newport - Inglewood (North) 104
Figure A–9: Summary of catalog data for Box 9, Newport - Inglewood (South) 105
Figure A–10: Summary of catalog data for Box 10, Elsinore - Temecula 106
Figure A–11: Summary of catalog data for Box 11, San Jacinto (Anza) 107
Figure A–12: Summary of catalog data for Box 12, Elsinore - Coyote Mtn. 108
Figure A–13: Summary of catalog data for Box 13, Cerro Prieto 109
Figure A–14: Summary of catalog data for Box 14, Imperial 110
Figure A–15: Summary of catalog data for Box 15, San Andreas (Coachella) 111
Figure A–16: Summary of catalog data for Box 16, Scodie Lineament 112
Figure A–17: Summary of catalog data for Box 17, San Jacinto (Anza) 113
Figure A–18: Summary of catalog data for Box 18, San Jacinto (Anza) 114
Figure A–19: Summary of catalog data for Box 19, San Jacinto (Anza) 115
Figure A–20: Summary of catalog data for Box 20, San Jacinto (Coyote Ck.) 116
Figure A–21: Summary of catalog data for Box 21, San Jacinto (Anza) 117
Figure A–22: Summary of catalog data for Box 22, San Jacinto (Coyote Ck.) 118
Figure A–23: Summary of catalog data for Box 23, San Jacinto (Anza) 119
Figure A–24: Summary of catalog data for Box 24, San Jacinto (Borrego) 120
Figure A–25: Summary of catalog data for Box 25, Superstition Mtn. 121
Figure A–26: Summary of catalog data for Box 26, Elmore Ranch 122
Figure A–27: Summary of catalog data for Box 27, Elmore Ranch (W. ext.) 123
Figure A–28: Summary of catalog data for Box 28, Elmore Ranch (W. ext.) 124
viii
Figure A–29: Summary of catalog data for Box 29, Elsinore 125
Figure A–30: Summary of catalog data for Box 30, Joshua Tree 126
Figure A–31: Summary of catalog data for Box 31, Joshua Tree 127
Figure A–32: Summary of catalog data for Box 32, Joshua Tree 128
Figure A–33: Summary of catalog data for Box 33, Joshua Tree 129
Figure A–34: Summary of catalog data for Box 34, Landers 130
Figure A–35: Summary of catalog data for Box 35, Landers 131
Figure A–36: Summary of catalog data for Box 36, Landers 132
Figure A–37: Summary of catalog data for Box 37, Landers 133
Figure A–38: Summary of catalog data for Box 38, Landers 134
Figure A–39: Summary of catalog data for Box 39, Hector Mine 135
Figure A–40: Summary of catalog data for Box 40, Hector Mine 136
Figure A–41: Summary of catalog data for Box 41, Hector Mine 137
Figure A–42: Summary of catalog data for Box 42, Hayward (North) 138
Figure A–43: Summary of catalog data for Box 43, Hayward (South) 139
Figure A–44: Summary of catalog data for Box 44, Calaveras (North) 140
Figure A–45: Summary of catalog data for Box 45, Calaveras (Central) 141
Figure A–46: Summary of catalog data for Box 46, Calaveras (South) 142
Figure A–47: Summary of catalog data for Box 47, Sargent 143
Figure A–48: Summary of catalog data for Box 48, SAF Creeping (North) 144
Figure A–49: Summary of catalog data for Box 49, SAF Creeping (Central) 145
Figure A–50: Summary of catalog data for Box 50, SAF Creeping (South) 146
Figure A–51: Summary of catalog data for Box 51, SAF Parkfield (North) 147
Figure A–52: Summary of catalog data for Box 52, SAF Parkfield (South) 148
ix
Figure C–1: Uniform reduction of error, large SoCal faults 156
Figure C–2: Uniform reduction of error, small SoCal faults 157
Figure C–3: Uniform reduction of error, aftershock-dominated segments 158
Figure C–4: Uniform reduction of error, large NoCal faults 159
Figure C–5: Uniform reduction of error, Parkfield segments 160
Figure D–1: Scaling analysis of large SoCal faults (all events) 162
Figure D–2: Scaling analysis of large SoCal faults (independent events) 164
Figure D–3: Scaling analysis of large SoCal faults (clustered events) 166
Figure D–4: Scaling analysis of small SoCal faults (all events) 168
Figure D–5: Scaling analysis of small SoCal faults (independent events) 170
Figure D–6: Scaling analysis of small SoCal faults (clustered events) 172
Figure D–7: Scaling analysis of aftershock-dominated segments (all events) 174
Figure D–8: Scaling analysis of large NoCal faults (all events) 176
Figure D–9: Scaling analysis of large NoCal faults (independent events) 178
Figure D–10: Scaling analysis of large NoCal faults (clustered events) 180
Figure D–11: Scaling analysis of Parkfield segments (all events) 182
Figure D–12: Scaling analysis of Parkfield segments (independent events) 184
Figure D–13: Scaling analysis of Parkfield segments (clustered events) 186
Figure E–1: Downweight analysis of large SoCal faults 189
Figure E–2: Downweight analysis of small SoCal faults 190
Figure E–3: Downweight analysis of aftershock-dominated segments 191
Figure E–4: Downweight analysis of large NoCal faults 192
Figure F–1: Scaling analysis of the Garlock fault [1,2,3]. 194
Figure F–2: Scaling analysis of the Newport – Inglewood fault [8,9]. 195
x
Figure F–3: Scaling analysis of the Elsinore fault [10,12]. 196
Figure F–4: Scaling analysis of the San Jacinto fault [11]. 197
Figure F–5: Scaling analysis of the Imperial fault [14]. 198
Figure F–6: Scaling analysis of the San Andreas fault at Coachella [15]. 199
Figure F–7: Scaling analysis of the Hayward fault [42,43]. 200
Figure F–8: Scaling analysis of the Calaveras fault [44,45,46]. 201
Figure F–9: Scaling analysis of the creeping section of the
San Andreas fault [48,49,50]. 202
xi
Abstract
Hypocenters of small, relocated earthquakes are used to constrain how seismicity
rates vary with distance from strike-slip faults in California. Stacks of events in a fault-
referenced coordinate system show that out to a fault-normal distance x of 3-6 km,
seismicity obeys a power-law ~ (1+ x
2
/d
2
)
!" /2
, where γ is the asymptotic roll-off rate
and d is a near-fault inner scale. These results are compatible with a ‘rough fault loading’
model in which the inner scale d measures the half-width of a volumetric damage zone
and the roll-off rate γ is governed by stress variations due to fault roughness. Two-
dimensional numerical simulations by J. Dieterich and D. Smith indicate that γ is
approximately equal to the fractal dimension of along-strike roughness. Results of a
multi-catalog error analysis and catalog simulations are used to correct the estimates of γ
and d for mislocation bias. Near-fault seismicity is more localized on faults in Northern
California (NoCal:d = 50±20m , ! =1.51±.05 ) than in Southern California (SoCal:
d = 210±40m , ! = 0.97±.05 ). The Parkfield region has a damage-zone half-width
(d =120±30m ) consistent with the SAFOD drilling estimate and its high roll-off rate
(! = 2.30±.25 ) indicates a relatively flat roughness spectrum:

~ k
!1
vs.

k
!2
for NoCal
and

k
!3
for SoCal. Fault surfaces in SoCal are therefore nearly self-similar, and their
roughness spectra are redder than in NoCal, consistent with the macroscopic complexity
of the observed fault traces. The damage-zone widths—the first direct estimates averaged
over the seismogenic layer—can be interpreted in terms of an across-strike ‘fault-core
multiplicity’ that is ~1 in NoCal, ~2 at Parkfield, and ~3 in SoCal. The localization of
xii
seismicity near individual faults correlates with cumulative offset, seismic productivity,
and aseismic slip, consistent with a model in which faults originate as branched networks
with broad, multi-core damage zones and evolve towards more localized, lineated
features with low fault-core multiplicity, thinner damage zones, and less seismic
coupling. The spatial distribution of aftershocks is modified by the presence of faults and
is well described by an elliptical kernel, in which an aspect parameter scales with
distance from a fault.

1
Introduction
California, with its dense, well-mapped network of faults and high-quality earthquake
catalogs, is an excellent setting to investigate seismicity variations in space and time.
Earthquake catalogs constructed using improved hypocenter relocation techniques
[Ellsworth, et al., 2000; Hauksson and Shearer, 2005; Shearer, et al., 2005; Thurber, et
al., 2006] are revealing new details about the 3D geometry of fault networks [Yule and
Sieh, 2003; Carena, et al., 2004] and ruptures of large earthquakes [Liu, et al., 2003],
properties of nascent faults [Bawden, et al., 1999], earthquake streaks observed on
creeping sections [Rubin, et al., 1999; Waldhauser, et al., 1999; Waldhauser, et al., 2004;
Shearer, et al., 2005; Thurber, et al., 2006], and the space-time behavior of earthquake
swarms [Vidale and Shearer, 2006]. These studies, as well as extensive research on the
fractal character of fault systems [Tchalenko, 1970; King, 1983; Okubo and Aki, 1987;
Hirata, 1989; Robertson, et al., 1995; Ouillon, et al., 1996; Kagan, 2007], have raised a
number of interesting issues regarding the relationship of small earthquakes to major
faults.
This study examines how seismicity rate varies normal to near-vertical strike-slip
faults in California and what bearing the results have on stress heterogeneity, damage
zones, degree of seismic coupling, and earthquake triggering statistics. Strike-slip faults
were chosen because their locations are constrained by mapped surface traces and their
approximate bilateral symmetry makes the seismicity distributions simpler to interpret
than those of normal and reverse faults. To reveal systematic scaling relationships, data
were aggregated from fault segments in a common class, as defined by geographic
2
region, fault length, and aftershock activity. The analysis was restricted to small
earthquakes (M
W
< 5), which were treated as point sources. Examined this way, the near-
fault seismicity shows a power-law decay away from the fault surface [Powers and
Jordan, 2005; 2007].
A comparison of results from selected fault segments in northern California (NoCal),
between Parkfield and the San Francisco Bay (Fig. 1), and a more extensive distribution
of faults in southern California (SoCal, Fig. 2) highlights regional variations in the fault-
normal distribution of seismicity. In NoCal, the fault segments are on or sub-parallel to
the San Andreas master fault, a larger percentage of the faults are creeping [Irwin, 1990],
and little seismicity extends below 10 km [Hill, et al., 1990] (Fig. 3). In contrast, the
SoCal segments have deeper seismicity [Hauksson, 2000], show little or no creep [Bodin,
et al., 1994; Lyons and Sandwell, 2003; Shearer, et al., 2005], and often intersect at high
angles. The spatial distribution of seismicity near smaller faults in SoCal (e.g. splays of
large faults and unmapped secondary faults) was also examined to see how fault length
and along-fault variations affect the scaling relations. To constrain how the scaling
relations are modified by aftershock activity, each dataset was declustered and fault
segments that ruptured during large (M
W
> 6) earthquakes were considered. To assess the
bias and variance in the scaling parameters caused by event mislocation, the errors
estimated by the hypocenter location algorithms were supplemented with constraints
from an intercatalog location error analysis and statistical simulations.
The results of the near-fault seismicity analysis provide measures of shear
localization on faults, indirect evidence that fault damage zones extend through the
3

Figure 1. Map of northern California (NoCal) showing locations of seismicity samples
(grey boxes with reference numbers; see Table 3). Black lines delineate large faults and
the heavy black line marks the San Andreas fault. Dark-grey dots mark the locations of
1.5 < M ≤ 2.5 earthquakes (1984–2002). Reference label background shades (colors in
electronic version) reflect the fault-normal intercatalog location uncertainty of each
segment: !
TN
x
for the Parkfield segments (51 and 52); !
UN
x
for all others.
4

Figure 2. Map of southern California (SoCal) showing locations of seismicity samples
(with reference numbers; see Table 3). Black lines delineate large faults and the heavy
black line marks the San Andreas fault. Grey boxes with reference numbers in circles (1–
15) indicate the limits of seismicity samples about large strike-slip faults; reference
numbers in squares indicate the locations of samples about small (16–29) and aftershock-
dominated (30–41) fault segments. Dark-grey dots mark the locations of 1.5 < M ≤ 2.5
earthquakes (1984–2002). Reference label background shades (colors in electronic
version) reflect the fault-normal intercatalog location uncertainty, !
PS
x
, of each segment.
5

Figure 3. Depth distributions of relocated earthquakes in the fault segment catalogs.
Events from (a) catalog H and (b) catalog P in SoCal, and (c) catalogs U and T in NoCal.
The darker shaded bars mark the medial 90% of all events in the catalogs. Note that
seismicity is generally shallower in NoCal (c). The downward bias in catalog H (a) is
likely an artifact of the 3D velocity model used for earthquake relocation.
6

seismogenic crust, and are consistent with a model of fault behavior that incorporates slip
on a fractal fault. This model, in conjunction with fault width data, on-fault earthquake
density, cumulative offset, and aseismic slip rate, illuminates how the rate of small
earthquakes varies during fault evolution. The structure of a fault damage zone at depth,
as defined by seismicity, is comparable to results from studies of exhumed faults and
drilling.
These results also have immediate application to earthquake forecasting methods that
rely on spatial models of earthquake triggering. The strong near-fault bias of seismicity
suggests that aftershock statistics may be modified by the presence of faults, and
examination of aftershock clusters within the filtered data sets shows this to be the case.
Close to a fault, contours of aftershock distributions are elliptical in shape and exhibit a
bias towards the fault; at greater distances, their distribution tends toward isotropic. This
variation can be described by a spatial kernel of aftershock distribution that incorporates
elements of the near-fault seismicity scaling relation, the distance of a mainshock from a
fault, and an aspect parameter that governs strike-parallel elongation.

7
Chapter 1: Catalog analysis
Fault-referenced seismicity catalogs
Hypocenters from six earthquake catalogs—three in SoCal, two in NoCal, and one for
the Parkfield region (Table 1)—were used to constrain near-fault seismicity distributions
and their uncertainties. The Southern California Seismic Network (SCSN) is the southern
part of the California Integrated Seismic Network (CISN), a region within the Advanced
National Seismic System (ANSS). The SCSN catalog (here abbreviated as ‘S’; available
at http://www.data.scec.org) is the standard catalog for SoCal and contains events
reported by all networks in the region. It includes some estimates of hypocentral errors,
but all events have a ‘quality’ designation indicative of maximum horizontal and vertical
location uncertainties.
Hauksson and Shearer [2005] relocated events (catalog ‘H’; available at
http://www.data.scec.org) from the SCSN using the double-difference algorithm of
Waldhauser and Ellsworth [2000]. They cross-correlated waveforms to measure travel-
time differences and relocated seismicity in a three-dimensional (3D) velocity model. For
events lacking sufficient data for double-differencing (< 10%), they determined
hypocenters using Hauksson’s [2000] relocation method. They also evaluated errors
using this method, because the double-difference code does not compute hypocentral
location errors for large datasets.
Shearer et al. [2005] relocated events (catalog ‘P’; available at
http://www.data.scec.org) using a source-specific station term algorithm [Richards-
Dinger and Shearer, 2000] that employs a layered (1D) velocity model. Using event-
8

Region
Sources
ID
a
type
Southern California (SoCal)
SCSN S standard
Shearer et al. (2005) P relocated
Hauksson and Shearer (2005) H relocated
Northern California (NoCal
NCSN N standard
Ellsworth et al. (2000) U relocated
Thurber et al. (2006) – Parkfield T relocated
a
Used to reference catalog in equations and text.

Table 1. Earthquake catalog sources.

9
similarity data from a waveform cross-correlation analysis, they further refined the
locations of spatially related events (~60%) via a cluster analysis. Hypocentral errors
reported by Shearer et al. [2005] correspond to the relative locations of events in each
cluster.
The catalog of the Northern California Seismic Network (NCSN, abbreviated ‘N’;
available at http://www.ncedc.org/ncsn) is the standard catalog for the northern part of
the CISN. Ellsworth et al. [2000] relocated a subset of the NCSN events in the San
Francisco Bay area (catalog ‘U’; available at http://pubs.usgs.gov/of/2004/1083) using
the double-difference algorithm of Waldhauser and Ellsworth [2000]. The catalog does
not include hypocentral location errors, but Ellsworth et al. [2000] report average
horizontal and vertical location uncertainties of 0.1 km and 0.5 km respectively.
On the creeping section of the San Andreas fault in the vicinity of Parkfield, relocated
events (denoted catalog ‘T’; available at http://www.seismosoc.org/publications/
BSSA_html/bssa_96-4b/05825-esupp/) were taken from Thurber et al. [2006]. They
constructed an improved 3D wavespeed model to first determine station corrections and
then relocated events via double-difference using a combination of event cross-
correlation differential times and travel-time differences from NCSN phase picks. The
catalog does not include any hypocentral error information.
To facilitate an error analysis, each of the six catalogs was trimmed to events that
occurred between the beginning of 1984 and the end of 2002. To allow for intercatalog
comparisons, the events were required to have hypocenters in both NoCal catalogs (N
and U or T and U) or in all three SoCal catalogs (S, P, and H). The NoCal catalogs, T and
10
U, do not overlap geographically and may only be compared independently to catalog N,
whereas the SoCal catalogs span the entire lower half of the state and may be compared
collectively. Events identified as quarry blasts or ones with intercatalog separations
greater than 10 km were discarded.
Catalogs of earthquakes for five classes of near-vertical strike slip faults (Tables 2
and 3; Figs. 1 and 2) were constructed: large NoCal faults, the San Andreas fault at
Parkfield, large SoCal faults, small SoCal faults, and fault segments with abundant
aftershocks of major SoCal earthquakes. For large faults, only relatively straight
segments of named, through-going faults were chosen (e.g. Figs. 4 and 5), and those
segments with earthquake density of less than one event per km were eliminated. Fault
junctions and zones of structural complexity were also avoided. In SoCal, the SCEC
Community Fault Model (CFM) [Plesch, et al., 2007`; available at
http://structure.harvard.edu/cfm] was the guide for fault selection; in NoCal, where faults
are well defined by near-vertical seismicity distributions, surface traces were used. Where
the surface trace or seismicity along a particular fault indicates significant changes in
strike or fault-strand overlap, fault selection was restricted to smaller fault segments; e.g.
the Hayward fault (Fig. 1; segments 42-43) and Garlock fault (Fig. 2; segments 1-3).
Large fault lengths, L
k
in Table 3, average 21 km in NoCal and 47 km in SoCal.
Small and aftershock-dominated SoCal faults in were identified by sets of
earthquakes that define linear structural features of shorter length (average ~ 9 km). The
small-fault class comprises splays off larger faults and unmapped secondary faults.
Aftershock-dominated segments were selected from faults activated by the 1992 Joshua
11

Region
N
T

a
b M
c
(events)
Southern California (SoCal)
SCSN catalog 291,541 0.9 2.0
Fault classes:
Large 11,095 0.9 1.9
Small 8,966 0.8 1.5
Aftershock-Dominated 19,849 0.9 1.8
Northern California (NoCal)
NCSN catalog 47,711 0.8 1.2
Fault classes:
Large 16,881 0.7 1.2
Parkfield 3,897 0.9 1.2
a
All events common to regional and relocated catalogs in Table 1.

Table 2. Earthquake catalog statistics.

12

Fault Class (Down-weight level N
0
, Fitting distance x
max
) size N
k
L
k
W
k

a
Ref. Segment Name (events) (km) (km)
SoCal Large (N
0
= 1000, x
max
= 6 km)
1 Garlock (East) 565 56.3 13.0
2 Garlock (Central) 566 27.3 8.0
3 Garlock (West) 534 45.1 8.7
4 Lenwood - Lockhart 92 31.9 10.0
5 San Andreas (Mojave) 742 96.9 10.9
6 Santa Cruz - Catalina Ridge 70 62.5 15.1
7 Palos Verdes 115 51.6 14.6
8 Newport - Inglewood (North) 226 34.7 14.4
9 Newport - Inglewood (South) 182 79.0 17.1
10 Elsinore - Temecula 554 54.0 13.8
11 San Jacinto (Anza) 5,027 37.7 17.4
12 Elsinore - Coyote Mtn. 415 23.6 12.0
13 Cerro Prieto 572 39.4 16.6
14 Imperial 1,179 21.2 14.1
15 San Andreas (Coachella) 256 40.7 8.3
Total (N
T
): 11,095 702.0
Length-weighted average: 13.2
SoCal Small (N
0
= 700, x
max
= 2.5 km)
16 Scodie Lineament 1,274 15.0 9.6
17 San Jacinto (Anza) 1,166 11.0 11.3
18 San Jacinto (Anza) 1,020 5.8 14.8
19 San Jacinto (Anza) 978 4.6 14.0
20 San Jacinto (Coyote Ck.) 484 7.0 12.5
21 San Jacinto (Anza) 326 5.0 10.9
22 San Jacinto (Coyote Ck.) 853 6.8 11.6
23 San Jacinto (Anza) 359 6.4 9.6
24 San Jacinto (Borrego) 443 7.5 9.9
25 Superstition Mtn. 258 12.8 12.8
26 Elmore Ranch 318 19.9 11.2
27 Elmore Ranch (western ext.) 177 6.8 8.9
28 Elmore Ranch (western ext.) 382 9.5 10.7
29 Elsinore 928 7.9 11.2
Total (N
T
): 8,966 126.0
Length-weighted average: 9.2
a
From relocated catalogs P, U, & T as described in text.

Table 3. Fault segment catalogs.
13

Fault Class (Down-weight level N
0
, Fitting distance x
max
) size N
k
L
k
W
k

a
Ref. Segment Name (events) (km) (km)
SoCal Aftershock-Dominated (N
0
= 1500, x
max
= 3 km)
30 Joshua Tree 1,068 6.6 8.0
31 Joshua Tree 2,338 7.5 8.0
32 Joshua Tree 1,815 4.9 8.4
33 Joshua Tree 861 6.2 9.1
34 Landers 873 5.5 11.0
35 Landers 669 10.3 8.7
36 Landers 1,855 10.7 9.5
37 Landers 2,539 7.0 7.0
38 Landers 1,334 5.7 7.9
39 Hector Mine 984 11.2 8.4
40 Hector Mine 2,872 14.3 8.8
41 Hector Mine 2,641 11.2 8.6
Total (N
T
): 19,849 101.1
Length-weighted average: 8.2
NoCal Large (N
0
= 1500, x
max
= 3 km)
42 Hayward (North) 336 44.3 10.7
43 Hayward (South) 674 45.9 10.8
44 Calaveras (North) 2,958 13.1 7.1
45 Calaveras (Central) 508 8.2 5.9
46 Calaveras (South) 1,200 17.9 7.1
47 Sargent 1,083 10.9 7.7
48 San Andreas Creeping (North) 1,229 12.2 7.6
49 San Andreas Creeping (Central) 3,012 14.9 8.0
50 San Andreas Creeping (South) 5,881 21.8 8.3
Total (N
T
): 16,881 189.4
Length-weighted average: 7.9
NoCal Parkfield (no downweight, x
max
= 3 km)
51 San Andreas Parkfield (North) 3,417 32.4 8.3
52 San Andreas Parkfield (South) 480 31.9 10.1
Total (N
T
): 3,897 64.2
Length-weighted average: 8.4
a
From relocated catalogs P, U, & T as described in text.

Table 3 (Continued)
14

Figure 4. Example of intercatalog earthquake location variation. (a) Map of the Elsinore
fault (segment 10, Fig. 2) showing relocated seismicity of catalog P and historic (heavy
black lines), Holocene (thin black lines), and Late Quaternary (thin grey lines) faults. (b)
Depth section across the map showing locations of events in the standard catalog S
relative to an initial, 3D fault-model based estimate of the fault trace (heavy dashed line);
earthquakes are the same magnitude ranges as on the map. (c) Fault-normal distribution
of events. (d) Depth section across the map for relocated catalog P. (e) Fault-normal
seismicity distribution of relocated events. Note the difference in horizontal bias (black
arrow in c and e) of peak seismicity between the standard and relocated catalog.
15

Figure 5. Example of how a fault-seismicity based coordinate system localizes events on
a fault and minimizes artificial fault-normal dispersion. (a) Map of the southern Hayward
fault (segment 43, Fig. 1) showing relocated seismicity of catalog U; fault age
representations are the same as in Fig. 4. The fault strand cutting across the lower right
corner of the map is the northern Calaveras fault. (b) Fault-normal depth section across
the fault trace prior to aligning coordinate system to relocated seismicity; earthquakes are
the same magnitude ranges as in the map, and the heavy dashed line marks the depth
projection of the fault surface-trace. (c) Fault-normal distribution of events. (d) Fault-
normal depth section across the fault trace after aligning coordinate system to a best-fit
plane to relocated seismicity. (e) Realigned fault-normal distribution. Note that the
change of coordinate system focuses the event distribution on the fault.
16

Tree (M
W
6.1), 1992 Landers (M
W
7.3), or 1999 Hector Mine (M
W
7.1) earthquakes.
Although the seismicity in the aftershock-dominated class spans the entire 19-year length
of the source catalogs, it is dominated by aftershocks from these large events. The
seismicity of the small-fault class is more uniformly distributed in time.
Only the most recently updated magnitude values from catalogs S and N were used in
the analysis; these are generally reported as local magnitude, although there are a few
events for which magnitudes were computed using other means. The maximum-
likelihood Gutenberg-Richter b-values [Aki, 1965] for the NoCal and SoCal catalogs are
0.8 and 0.9, respectively (Table 2 and Fig. 6). NoCal has a lower magnitude of
completeness (M
c
= 1.2) than SoCal (M
c
= 2.0), reflecting its smaller area and higher
station density.
Hypocenters in each catalog were also filtered in depth to focus on the central part of
the seismogenic crust. Averaged across all fault segments, 90% of seismicity falls
between 2 and 10 km for catalogs U and T and 2.5 and 17 km for catalog P (Fig. 3). The
upper 5% of events tend to occur within 2 km of the free surface, and so 2 km was taken
as an upper truncation depth. The lower cutoff shows significant variation reflecting
regional differences in seismogenic thickness [Hauksson, 2000; Magistrale, 2002]. The
lower truncation depth was therefore set to exclude the deepest 5% of hypocenters in
each fault catalog. The differences between the lower and upper truncation depths for the
kth fault segment determined the segment width W
k
; values for each fault segment catalog
are listed with the fault lengths L
k
in Table 3 and detailed maps of each are provided in
Appendix A.
17

Figure 6. Frequency-magnitude distributions for the large-fault classes in (a) SoCal and
(b) NoCal. In each figure, the black line represents the cumulative frequency-magnitude
distribution for all events common to both regional and relocated catalogs used in this
study. For each fault segment, only events within x
max
km of a fault, the outer limit of a
seismicity scaling zone derived from the seismicity analysis (see Figs. 7–10), were
considered. In NoCal, the maximum likelihood b-value of near fault seismicity is lower
(b = 0.7) than the regional average (b = 0.9); in SoCal, b-values are about the same.
18

A fault-oriented coordinate system was established for each fault segment by fitting a
plane to the seismicity. An initial estimate of the fault plane was derived from the CFM
or, in the absence of a fault model, from a vertical plane that approximated the mapped
surface or epicenter trace (e.g., Fig. 5). The parameters of the plane were perturbed to
obtain a least-squares fit to relocated hypocenters from catalogs P, U or T within 2 km of
this initial fault plane.
The hypocenters from the relevant relocated catalog were transformed into a local
Cartesian system defined by an origin at one end of the surface trace of the best-fit fault
plane, a near-vertical z-axis, a y-axis along the fault strike, and an x-axis perpendicular to
the fault plane. A final, fault-referenced catalog was then constructed by eliminating
events with relocated x coordinates greater than ±15 km, relocated y coordinates beyond
the ends of the fault segment, and relocated z coordinates outside the depth limits
described above. The fault-segment catalogs are summarized in Table 3 and detailed
maps of each are provided in Appendix A.
Intercatalog location uncertainties
A proper description of near-fault seismicity distributions requires careful attention to
mislocation errors. Information about such errors can be determined from comparisons of
hypocenters determined by different methods [e.g. Shearer, et al., 2005]. In the present
study, the intercatalog comparisons have been quantified on a fault-segment basis. For
the kth fault segment with N
k
events common to the catalog pair A and B, the intercatalog
fault-normal bias is defined by
19
b
AB
kx
=
1
N
k
(x
A
i
! x
B
i
)
i"k
#
, (1)
and the fault-normal variance by
(!
AB
kx
)
2
=
1
N
k
"1
(x
A
i
" x
B
i
"b
AB
kx
)
2
i#k
$
. (2)
Here, x
A
i
is the fault-normal coordinate of the ith event, and the summation implied
byi!k is over all N
k
events associated with the kth fault segment. Similar expressions
can be written for the fault-parallel and near-vertical directions. The intercatalog bias and
variance computed for each catalog pair (UN and TN in NoCal and HS, PS, and HP in
SoCal) are listed by individual fault segment in Appendix B.
For each coordinate of the fault-oriented reference frame, the mean intercatalog bias
for a fault class was computed by taking the absolute values of the segment biases,
weighting them by the number of events for each segment, and averaging over all
segments. Likewise, the mean standard deviation was calculated as the square-root of the
event-weighted segment variances. These averages are given in Table 4. For all classes,
the intercatalog biases and standard deviations are largest for the z coordinate, reflecting
the uncertainty in estimating hypocentral depth. No systematic differences are observed
between the horizontal coordinates. In SoCal, the z-coordinate statistics are especially
large, in part because shallow events in the early part of Catalog S were often assigned a
default depth of 6 km, and also because the velocity model used to relocate events in
Catalog H tends to bias events downward (Fig. 3). Because the fault-normal distribution
of seismicity is of greatest interest, this discussion focuses on b
AB
x
and !
AB
x
.

20

Fault Class Bias (km)
a
catalog pair (AB)
b
x
AB
b
y
AB
b
z
AB
!
x
AB
!
x
AB
b
!
y
AB
!
z
AB
SoCal Large:
HS 0.74 0.61 1.36 1.14 0.75 1.23 3.09
PS 0.57 0.33 1.36 1.08 0.72 1.16 3.12
HP 0.59 0.35 1.06 0.74 0.25 0.77 2.15
SoCal Small:
HS 0.47 0.23 1.69 0.80 0.60 0.82 2.62
PS 0.43 0.24 0.96 0.75 0.58 0.77 2.41
HP 0.24 0.37 0.98 0.40 0.15 0.45 1.52
SoCal Aftershock-Dominated:
HS 0.18 0.22 2.06 0.62 0.42 0.70 2.25
PS 0.24 0.27 1.09 0.55 0.39 0.63 1.97
HP 0.17 0.14 0.97 0.41 0.19 0.44 1.49
NoCal:
UN (Large) 0.10 0.03 0.15 0.30 0.15 0.24 0.52
TN (Parkfield) 0.47 0.13 0.60 0.68 0.42 0.32 0.82
a
Event-weighted mean absolute values.
b
!
x
AB
estimated by uniform reduction.
Standard Deviation (km)

Table 4. Intercatalog error estimates – see Appendix B for individual fault values.
21
The intercatalog statistics for well-instrumented Parkfield region are higher than those
of the NoCal fault class, particularly the fault-normal values (e.g., !
TN
x
= 0.62 km vs.
!
UN
x
= 0.31 km). These differences are primarily due to the strong velocity contrast
across the San Andreas fault near Parkfield, which is modeled in the Thurber et al.
[2006] relocations but not in the standard catalog.
The intercatalog statistics for the large SoCal faults (e.g., !
PS
x
= 1.04 km) are also
substantially higher than for the NoCal fault class, which is likely due to several factors.
The southern region has a more heterogeneous crustal structure than the northern region,
such as larger and deeper sedimentary basins, increasing the location errors. Moreover,
the faults sampled in NoCal were restricted to well-instrumented regions of the San
Andreas system near the center of the NCSN. In SoCal, a number of the large faults are
peripheral to the SCSN, and they invariably show bigger intercatalog variations (Fig. 2).
For instance, !
PS
x
for the coastal Newport-Inglewood fault (segments 8-9) is 2.1 km, and
it reaches 2.7 km for the Cerro Prieto fault (segment 13), which is located in Mexico
outside the SCSN. In contrast, the values for the more centrally located San Jacinto fault
(segments 17-24) are less than 1 km.
In SoCal, the large-fault class has a higher intercatalog standard deviation than either
the small-fault or aftershock classes (e.g., !
PS
x
= 1.04 km, 0.75 km, 0.55 km,
respectively). The fault-normal biases show a similar ordering (e.g., b
PS
x
= 0.54 km, 0.43
km, 0.23 km). Network geometry again plays a role, because the latter two classes
comprise segments that tend to be more centrally located within the SCSN. In addition,
the estimator given by equation (1) accounts only for a constant translational bias; for
22
long segments, other parameters, such as a rotational bias, may be needed to represent the
catalog differences, especially for faults on the periphery of the network. The inadequacy
of the bias model acts to increase the apparent intercatalog variance.
The standard deviations between the two relocated SoCal catalogs (HP) are
consistently lower than those involving the standard catalog (HS and PS), satisfying the
expectation that relocation reduces the hypocentral variance (Table 4). However,
histograms of the fault-normal differences for all three catalog combinations show heavy-
tailed distributions with outliers that dominate the variance estimates. Most of these
outliers can be explained by the way the different location algorithms respond to
anomalous travel times (e.g., picking blunders, large path anomalies). To account for
outliers, a method of uniform reduction [Jeffreys, 1932; Buland, 1986] was applied in
which the differences are modeled as the superposition of a Gaussian distribution and a
nearly uniform distribution (Fig. 7 and Appendix C). The standard deviations of the best-
fit Gaussians are listed in Table 4. The largest reductions, more than 80% in variance, are
obtained for the HP intercatalog differences. The reduced standard deviations were used
to characterize the event mislocations in a subsequent error analysis of the fault-normal
scaling parameters.
Catalog-specific location uncertainties
If the event location errors from the three SoCal catalogs are assumed to be
statistically independent—possibly a poor assumption—then the catalog-specific biases,
b
A
kx
, and standard deviations, !
A
kx
, may be determined by solving the three equations for
intercatalog bias,
23

Figure 7. Sample uniform reduction of error analysis for NoCal faults. Logarithmic (a)
and linear (b) distributions of fault-normal intercatalog location variation between
matching events in catalogs U and N, less the intercatalog bias of the corresponding fault
segment. The dashed line marks a Gaussian distribution with a standard deviation
computed from the intercatalog values. The solid line is a Gaussian fit to the observations
that ignores the outliers (heavy tails) of the observed distribution and provides an
improved estimate of fault-normal location uncertainty. See Appendix C for analyses of
all fault classes.
24

b
AB
kx
=b
A
kx
!b
B
kx
, (3)
and the three for intercatalog variance,
!
AB
kx
( )
2
= !
A
kx
( )
2
+ !
B
kx
( )
2
, (4)
where AB = {PS, HS, HP}. Equations (3) are not linearly independent, and were therefore
subjected to the additional constraint that the biases of the individual catalogs should sum
to zero, which minimizes the overall bias. Similar sets of equations can be solved for the
fault-parallel and depth directions. The values presented in Table 5 are the averaged,
event-weighted absolute values of the fault-segment biases (see Appendix B for
individual fault-segment data).
The σ-values for the relocated catalogs are substantially smaller than those for the
standard SCSN catalog, as expected from the intercatalog comparisons, and the σ -values
for the Shearer et al. [2005] catalog are in all cases smaller than those for the Hauksson
and Shearer [2005] catalog. In particular, the values of !
P
x
obtained from the reduced
intercatalog standard deviations are only about half the size of !
H
x
, which is consistent
with the qualitative observation that the cluster-analysis relocation method used to
develop the P catalog provides significantly better localization of hypocenters into fault-
like structures [Shearer, et al., 2005]. For this preferred SoCal catalog, the fault-normal
standard deviations are less than 0.1 km for all three fault classes. As noted above, the
linear removal of bias did not consider possible intercatalog rotations, which could skew
the intercatalog variance to higher values, whereas possible correlations in the hypocenter

25

Fault Class Bias (km)
ab
Standard Deviation (km)
a
Catalog Error (km)
catalog (A)
b
x
A
b
y
A
b
z
A
!
x
A
!
x
A
c
!
y
A
!
z
A
horiz. vert.
SoCal Large:
S (standard) 0.37 0.29 0.76 0.98 0.71 1.07 2.71 2.35 4.49
P (relocated) 0.28 0.13 0.69 0.45 0.09 0.45 1.55 0.04 0.21
H (relocated) 0.40 0.32 0.72 0.58 0.23 0.62 1.50 0.15 0.25
SoCal Small:
S (standard) 0.28 0.12 0.88 0.72 0.58 0.73 2.28 1.96 3.52
P (relocated) 0.18 0.19 0.30 0.19 0.07 0.24 0.78 0.03 0.13
H (relocated) 0.22 0.18 0.82 0.35 0.14 0.38 1.30 0.10 0.17
SoCal Aftershock-Dominated:
S (standard) 0.13 0.16 1.05 0.50 0.38 0.59 1.83 1.76 3.26
P (relocated) 0.13 0.12 0.16 0.21 0.08 0.22 0.71 0.04 0.25
H (relocated) 0.10 0.06 1.01 0.36 0.17 0.38 1.30 0.19 0.33
NoCal Large:
N (standard) — — — — — — — 0.30 0.62
U (relocated)
d
— — — — — — — 0.10 0.50
NoCal Parkfield:
N (standard) — — — — — — — 0.56 0.95
T (relocated) — — — — — — — N.R. N.R.
N.R. = not reported
a
Computed assuming statistical independence.
b
Event-weighted mean absolute values.
c
!
x
A
estimated by uniform reduction.
d
Catalog averages as reported by Ellsworth et al. (2000).

Table 5. Catalog-specific error estimates – see Appendix B for individual fault values.
26

errors between different catalogs would skew them to lower values. On balance, !
P
x
≈ 0.1
km appears to be a good estimate.
Table 5 also presents a comparison of the results of the intercatalog error analysis
with formal location errors listed in the individual catalogs. The standard deviations in
depth from the latter sources are always larger than the corresponding mean horizontal
standard deviation, in rough agreement with the intercatalog analysis, but the magnitudes
are rather different. The mislocation errors included in the standard network catalogs are
substantially larger than the values computed here. The reverse is generally true for the
relocated catalogs, though the agreement is much better. Further checks on the
mislocation errors from seismicity modeling, described in Chapter 2, support the
intercatalog analysis.

27
Chapter 2: Scaling Analysis
Fault-normal seismicity distribution
Because strike-slip faults in California are nearly vertical, the scaling relations
developed here use the fault-normal distance | x | as the independent variable and ignore
bilateral asymmetry in seismicity. After stacking the seismicity data in each fault group,
the earthquake density was computed as a function of distance | x | using a nearest-
neighbor method [Silverman, 1986] in which bin widths are adjusted to contain q-
neighboring events. For each data set, a q-value was selected that yielded an adequate
point density for deriving fault-normal scaling relations (10 ≤ q ≤ 50).
Logarithmic plots of earthquake density versus | x | for each regional catalog indicate
fault-normal distributions that have flat peaks within a few hundred meters of the fault,
roll off as an inverse power-law for about an order of magnitude in distance, and merge
with irregular backgrounds at distances less than 10 km (Figs. 8-11 and Appendix D).
Near the fault, the observed distributions can be described by the functional form:
!(x)=!
0
d
m
x
m
+d
m
"
#
$
%
&
'
(
m
.
(5)
In this expression d is an inner scale that removes the power-law singularity on the fault,
γ is the asymptotic roll-off of seismicity away from the fault, and the exponent m controls
the shape of the distribution for x ~ d; i.e., the sharpness of the corner on a logarithmic
plot. When varying the latter parameter, the best fits to the observed fault-normal
distributions were obtained for m ≈ 2.
28

Figure 8. Fault-normal earthquake density distributions for large SoCal faults.
Distributions for (a) relocated catalog P, (b) relocated catalog H, and (c) standard catalog
S using a nearest-neighbor bin interval of q = 50 events. In each figure, the heavy dashed
line marks the limit to which the data were fit, x
max
; beyond this limit, background
seismicity dominates. The black line is a maximum likelihood fit of an inverse power-
law, with asymptotic slope

!
! , to observations within that limit. The inner scale of the
distribution is described by

!
d .
29

Figure 9. Fault-normal earthquake density distributions for (a) small faults and (b)
aftershock-dominated fault segments in SoCal. Both figures use events from relocated
catalog P with a bin interval of q = 50 events. Figure features are the same as in Fig. 8.
30

Figure 10. Fault-normal earthquake density distributions for large NoCal faults.
Distributions for (a) relocated catalog U and (b) standard catalog N using a nearest-
neighbor bin interval of q = 20 events. In each figure, the heavy dashed line marks the
limit to which the data were fit, x
max
; beyond this limit, background seismicity dominates.
As in Figs. 8 and 9, the black line is a maximum likelihood fit of an inverse power-law to
observations within that limit.
31

Figure 11. Fault-normal earthquake density distributions for the Parkfield fault segments.
Distributions for (a) relocated catalog T and (b) standard catalog N using a nearest-
neighbor bin interval of q = 10 events. Figure features are the same as in Fig. 10.
32

Assuming m = 2, a maximum-likelihood fit of equation (5) to the binned data was
computed for each fault group out to a maximum fault-normal distance x
max
, chosen such
that the relative contributions from background seismicity were small; the values of x
max

for each fault class are listed in Table 3. The expected number of events in the jth bin of
width Δx is the integral:
n
j
= !(x)
|x
j
|"#x
|x
j
|
$
dx .
(6)
The observed value, n
j
, in each bin is assumed to be Poisson distributed, which yields the
log-likelihood function [e.g. Boettcher and Jordan, 2004]:
!("
0
,#,d)= n
j
ln n
j
(x) $
%
&
'
( n
j
(x) $
%
&
'
( ln(n
j
!)
{ }
j=1
J
bins
)
, (7)
Maximizing (7) using a linear approximation to ν(x) over each binning interval (adequate
for the small intervals used here) yields the estimates

!
!
0
,

! ! , and

!
d . These estimates
have correlated errors. However, note that the maximum likelihood estimator for

!
!
0
is
N
max
(1+x
2
/
0
x
max
!
d
2
)
"# /2
dx , where N
max
is the cumulative number of events out to x
max
.
If N
max
is large, its relative error is small (~

N
max
!1/2
) and uncorrelated with the errors in

!
!
and

!
d . The latter are positively correlated, as shown in Fig. 12 (see also Appendix D),
which plots the maximum-likelihood estimates and confidence intervals for the various
fault groups in the

!
! -

!
d plane.
33

Figure 12. Maximum likelihood solutions and errors for

!
! and

!
d . Values for (a) large
SoCal faults, (b) large NoCal faults, and (c) Parkfield showing the positive correlation
between scaling parameters. Light grey and black ovals mark the 68% and 95%
confidence bounds, respectively.
34

The error estimates from the maximum-likelihood procedure were checked with those
derived from jackknife resampling [Efron, 1979]. Generally speaking, the two were in
agreement, but where they differed, the larger estimate was used (Table 6). In
experimenting with the lower magnitude cutoff and depth ranges, the results were found
to be robust. Varying bin width, q, likewise yielded little variation in the results.
An important issue is the weighting of individual fault segments in the seismicity
stacking. Owing to the variability in seismicity rates, the number of earthquakes per fault
segment ranges from a hundred to several thousand (Table 3), and any results will depend
on how each is weighted. In the stacking procedure, a positive weighting factor w
k
was
applied to each event in the kth fault-segment catalog, which was computed by the
formula,
w
k
= min 1,N
0
/N
k
[ ]
, (8)
where N
0
is a ‘down-weight level’ that was held constant for each fault group. N
0
was
then set to vary from N
min
, the minimum of all catalog sizes N
k
in each fault group, to
N
max
, the maximum in each group. The latter bound corresponds to ‘one-event-one-vote’
(w
k
= 1), whereas the former corresponds to ‘one-catalog-one-vote’ (w
k
~ 1 / N
k
). For
intermediate values, events from catalogs larger than N
0
were down-weighted by the ratio
N
0
/ N
k
, while those from smaller catalogs received unit weight. In experimenting with a
range of down-weight levels for each structural group, the maximum-likelihood estimates
for most of the parameters were found to be stable across a wide range between N
min
and
N
max
(Fig. 13). Table 3 lists the actual values used in deriving the parameter values
discussed below (see Appendix E for the analyses of all fault classes).

35

Fault Class
catalog JK ML JK ML JK ML JK ML JK ML JK ML
S. California Large Faults:
S (raw) 0.044 0.030 0.054 0.085 0.038 0.030 0.057 0.090 0.115 0.115 0.106 0.185
P (relocated) 0.037 0.018 0.013 0.030 0.037 0.016 0.022 0.034 0.045 0.054 0.006 0.044
H (relocated) 0.031 0.020 0.032 0.032 0.030 0.016 0.055 0.042 0.036 0.052 0.016 0.054
S. California Small Faults:
S (raw) 0.110 0.304 0.051 0.114 0.134 0.444 0.064 0.180 0.115 0.535 0.045 0.170
P (relocated) 0.052 0.081 0.016 0.016 0.053 0.082 0.016 0.025 0.058 0.174 0.019 0.032
H (relocated) 0.060 0.087 0.019 0.022 0.060 0.096 0.017 0.027 0.078 0.194 0.029 0.044
S. California Aftershocks:
S (raw) 0.106 0.102 0.035 0.042 — — — — — — — —
P (relocated) 0.077 0.066 0.019 0.022 — — — — — — — —
H (relocated) 0.069 0.060 0.018 0.022 — — — — — — — —
N. California Large Faults:
N (raw) 0.051 0.058 0.024 0.011 0.061 0.096 0.025 0.020 0.063 0.070 0.025 0.018
U (relocated) 0.037 0.040 0.008 0.009 0.047 0.068 0.013 0.012 0.048 0.054 0.006 0.008
Clusters
!
"
!
d
!
d
Whole Catalog
!
d
!
"
!
"
Declustered

Table 6. Comparison of jackknife (JK) resampling and maximum likelihood (ML)
error estimates (selected values bold).

36

Figure 13. Downweight analysis results for small SoCal faults. (a)

!
! and (b)

!
d vary
with downweight value across the different catalogs. In both figures, the dashed gray line
marks the selected value of N
0
= 700. Note that parameter estimates are largely stable
within error for most downweight values. Only at low values of N
0
do parameters start to
vary as more box-catalogs, including those with few events, are weighted equally (see
Appendix E for the analyses of all fault classes).

37
For all structural groups, there is a well-defined scaling region of at least an order of
magnitude in fault-normal distance where the earthquake density shows a power-law roll
off before it merges with the background seismicity (Figs. 8-11 and Appendix D). In
Table 7, the maximum-likelihood estimates of

!
! and

!
d are listed by fault group. To
assess the effects of earthquake clustering, the fault-segment catalogs were declustered
using the algorithm of Reasenberg [1985] and the declustered catalogs and the event
clusters analyzed for the distribution parameters.
Table 6 shows interesting variations across the fault groups and catalog types.
Comparing the relocated catalogs P and U, seismicity decays away from the large SoCal
faults at a significantly lower rate (

!
! = 0.98 ± 0.04) than it decays in NoCal (1.60 ± 0.04)
or for the small SoCal faults (1.37 ± 0.08). In SoCal, clustered events decay more rapidly
than independent events, in agreement with the higher decay rate for aftershocks of large
SoCal earthquakes (

!
! = 1.50 ± 0.08).
For the larger faults, the apparent inner scale

!
d for relocated catalogs is smaller in
NoCal (0.08 ± 0.01 km) than in SoCal (0.23 ± 0.03 km). The former is comparable to the
relocation uncertainty. Significantly higher values are obtained for the standard catalogs
(0.6-0.8 km), consistent with more dispersion due to mislocation.
The robustness of these results was checked by relaxing the assumption of
bilateral symmetry used in stacking and interpreting the seismicity distributions (e.g.,
Figs. 7-10). After identifying which side of each fault segment had more events for | x | ≤
x
max
, the data for each of the five fault classes was restacked, preserving any asymmetry

38

Fault Class Whole Catalog Declustered Clusters
Catalog
(km) (km) (km)
SoCal Large:
S (standard) 0.88 ± 0.09 1.19 ± 0.04 0.86 ± 0.09 1.12 ± 0.04 0.95 ± 0.19 1.51 ± 0.12
P (relocated) 0.23 ± 0.03 0.98 ± 0.04 0.24 ± 0.03 0.93 ± 0.04 0.24 ± 0.04 1.22 ± 0.05
H (relocated) 0.27 ± 0.03 0.98 ± 0.03 0.28 ± 0.05 0.94 ± 0.03 0.27 ± 0.05 1.18 ± 0.05
SoCal Small:
S (standard) 0.79 ± 0.11 1.90 ± 0.30 0.86 ± 0.18 1.86 ± 0.44 0.73 ± 0.17 2.17 ± 0.54
P (relocated) 0.19 ± 0.02 1.37 ± 0.08 0.19 ± 0.03 1.27 ± 0.08 0.22 ± 0.03 1.62 ± 0.17
H (relocated) 0.23 ± 0.02 1.44 ± 0.09 0.22 ± 0.03 1.35 ± 0.10 0.27 ± 0.04 1.71 ± 0.19
SoCal Aftershock-Dominated:
S (standard) 0.55 ± 0.04 1.63 ± 0.11 — — — —
P (relocated) 0.33 ± 0.02 1.50 ± 0.08 — — — —
H (relocated) 0.31 ± 0.02 1.44 ± 0.07 — — — —
NoCal Large:
N (standard) 0.16 ± 0.02 1.68 ± 0.06 0.18 ± 0.03 1.73 ± 0.10 0.15 ± 0.02 1.66 ± 0.07
U (relocated) 0.08 ± 0.01 1.60 ± 0.04 0.10 ± 0.01 1.62 ± 0.07 0.07 ± 0.01 1.61 ± 0.05
NoCal Parkfield:
N (standard) 0.89 ± 0.09 3.86 ± 0.60 0.93 ± 0.12 4.64 ± 0.77 0.85 ± 0.19 5.57 ± 1.60
T (relocated) 0.13 ± 0.02 2.52 ± 0.22 0.14 ± 0.02 2.50 ± 0.24 0.10 ± 0.03 2.70 ± 0.78

˜ !

˜ !

˜
d

˜
d

˜
d

˜ !

Table 7. Apparent fault-normal scaling parameters.

39
in seismic abundance. The values of d obtained from these asymmetric distributions were
essentially the same as those from the symmeterized distributions. The estimates of γ on
the less abundant side were slightly higher than those on the more abundant side, but the
magnitude of the difference (~ 0.1) was statistically marginal. Notably though, on the
side with fewer events, the scaling region extended to greater distances from the fault, in
some cases by an order of magnitude, before merging with the background seismicity.
Fault maps show that the truncation of the scaling region on the abundant side can
generally be explained by the seismicity increase from another fault branch proximate to
the target fault segment, a common feature of the San Andreas system (e.g., Fig. 5).
Analysis of Bias
The results in Table 6 are likely biased by hypocenter mislocation in two ways and
both a theoretical approach and Monte Carlo simulations were used to assess the
significance of the effect. In this analysis, it is assumed that the true fault-normal
seismicity is governed by the distribution ν(x) in equation (5), and that the catalogs have
independent, identically distributed mislocation errors approximated by a zero-mean
Gaussian probability density function (p.d.f.),
g
A
(x)=
1
!
A
x
2"
exp #x
2
/2(!
A
x
)
2
$
%
&
'
,
(9)
where

!
A
x
is the standard error for catalog A. The p.d.f. for the observed seismicity can
then be computed as the convolution of the two (normalized) distributions:
p
A
(x)= !(x"#)g
A
(#)d#
"$
$
%
/ !(#)d#
"$
$
%
. (10)

40
A little analysis shows that, if !
A
x
/d is not too large (less than 5 or so), p
A
(x) can be
approximated by equation (5) with an asymptotic slope

!
! = ! and an inner scale

!
d
computed as the intersection of the small-x probability density with the large-x
asymptote,

d /
!
d
( )
!
= 2 /" 1+(#
A
x
x /d)
m
$
%
&
'
(! /m
e
(x
2
/2
dx
0
)
*
. (11)
The bias correction

d!
!
d derived by solving (11) is only weakly dependent on the shape
parameter m, so it was fixed at the best-fit value (m = 2). Fig. 14 plots

!
d versus d for !
A
x

= 0.1 km, appropriate for A = P, U, and T; the correction is small for d >!
A
x
and
decreases with γ. The bias-corrected estimates of d obtained from (11) are listed in Table
8. The largest correction, for large-fault seismicity in NoCal, changes the estimated inner
scale from 0.08 km to 0.05 km, a difference of only 30 m. Note that the magnitude of bias
in this worst case, 0.03 km, is smaller than the quadratic estimator d
2
+!
A
2
"d = 0.05
km.
The small size of the bias correction was verified using the following Monte
Carlo method. Synthetic catalogs that satisfied (12) were generated and subsequently
perturbed with Gaussian noise (!
A
x
= 0.1 km). A likelihood score of their fit to the
distribution curves obtained from the actual data was then computed. The values of d and
γ that maximized the likelihood for many (~50) catalog realizations are listed in Table 8;
an example of a single realization is presented in Fig. 15. The estimates of d are nearly
identical to the theoretically corrected values. Moreover, the simulations provided bias

41

Figure 14. Theoretical relationship between an observed inner scale,

!
d , and the true
value of d plotted for various γ. Theory assumes that an observed fault-seismicity scaling
distribution is the product of the true distribution convolved with a Gaussian noise
function with standard deviation of 0.1 km. Only at d < 0.2 km do the observed and true
values diverge significantly.

42

Theoretical
a
Simulated
a
Fault Class Catalog d (km)
SoCal Large P 0.21 0.21 ± 0.04 0.97 ± 0.05
SoCal Small P 0.17 0.16 ± 0.03 1.32 ± 0.10
SoCal Aftershock-Dominated P 0.31 0.31 ± 0.03 1.48 ± 0.10
NoCal Large U 0.05 0.05 ± 0.02 1.51 ± 0.05
NoCal Parkfield T 0.11 0.12 ± 0.03 2.30 ± 0.25
a
Bias corrections computed assuming !
x
A
= 0.1 km.
d (km) "

Table 8. Bias-corrected scaling parameters.

43

Figure 15. Sample result from simulation analysis of parameter bias. In each simulation,
synthetic distributions were perturbed with Gaussian noise (!
A
x
= 0.1 km) until a
combination of γ and d were found that maximized the likelihood score of the fit to the
original distribution. The simulation result pictured is for large SoCal faults and
illustrates a good correlation between a perturbed synthetic distribution (dots) and the
observed distribution (dashed line) for catalog P.

44
corrections for γ, which are not zero (as the asymptotic theory predicts) owing to the
positive correlation between the estimators of d and γ arising from a finite range of x (see
Fig. 11). However, the corrections to γ are also small, 10% (for catalog T) or less.
45
Chapter 3: Fault-Seismicity Model
Rough fault loading model
The multi-catalog analysis of earthquake hypocenters in California revealed that the
seismicity in the vicinity of strike-slip faults can be represented by a three-parameter
distribution:

!(x) = !
0
d
2
x
2
+d
2
"
#
$
$
%
&
'
'
( /2
,

|x | ! x
max
. (12)
The constant

!
0
describes the fault-normal seismic intensity (in events/km) on the fault
surface. Using the data in Table 3, the intensity ν(x) can be normalized by the total fault
length ! L
k
, as plotted in Figs. 8-11 and Appendix D, or by the total fault area ! L
k
W
k
,
which yields a spatial seismic density for the catalog interval T = 19 a. The inner scale d
measures the half-width of a near-fault region where the seismic intensity is flat ( ~!
0
),
and the exponent γ specifies the power-law roll-off of seismic intensity in the scaling
region d < x! x
max
.
Fig. 16 presents a conceptual ‘rough faulting loading’ (RFL) model that is used to
explain the seismicity behavior. The model derives from the observation that fault
surfaces can be described by a self-affine (fractal) complexity over a large range of
spatial scales [Power and Tullis, 1995; Lee and Bruhn, 1996; Renard, et al., 2006] and
evolve in time towards surfaces that are less complex in the direction of slip [Wesnousky,
1988; Stirling, et al., 1996; Sagy, et al., 2007; Finzi, et al., in press]. Here ‘complexity’
refers to the fractal branching of faults into multiple surfaces [e.g. King, 1983; Hirata,
46

Figure 16. Schematic representation of the RFL (rough fault loading) model that explains
observations of near-fault seismicity distribution. (a) Tectonic loading of a self-affine
fault generates a heterogeneous stress field that yields a power-law decay of seismicity
over a scaling region via stress-relaxation [modified from Dieterich and Smith, 2006]. (b)
Towards the fault core, small scale stress heterogeneities of the rough fault are attenuated
by low fracture strength across a damage zone of width 2d km. (c) Illustration of how
observed seismicity rates vary with distance from a fault (solid black line). The scaling
region likely extends beyond x
max
, as indicated by the dashed black line, but is masked by
interference from proximal fault branches. Stress field in (a) is colored in electronic
version.
47
1989] as well as the fractal roughness of individual fault surfaces [e.g. Lee and Bruhn,
1996; Renard, et al., 2006; Sagy, et al., 2007]. In building a simple model, a single fault
surface is considered, whose deviations from the planar approximation x = 0 define a
fault-normal topography [Saucier, et al., 1992; Chester and Chester, 2000; Dieterich and
Smith, 2006]. The along-strike (constant-z) profile of this topography is the realization of
a stationary stochastic process X(y) that has zero expectation, X(y) = 0 , and a
variogram
2!
2
("y) = [X(y+"y)# X(y)]
2
1/2
. (13)
If the surface is self-affine, then ! ~"y
H
, where 0 ≤ H ≤ 1 is the Hausdorff measure
(sometimes referred to as the Hurst exponent) of the along-strike profile [Feder, 1988;
Turcotte, 1997].
It is assumed the self-affine scaling of fault roughness breaks down above some outer
scale !y
outer
related to the characteristic segmentation length L
k
. At profile separations
larger than !y
outer
, the variogram (13) levels off to 2!
"
, where !
"
# X
2
(y)
1/2
is the
root-mean-square (rms) topographic fluctuation. The power spectrum P
X
(k
y
) is then the
Fourier transform of the autocovariance function C
X
(!y)="
#
2
$"
2
(!y) . P
X
(k
y
) plateaus
at a value ~!
"
2
below the characteristic wavenumber 1/!y
outer
and rolls off as k
y
!2H!1

above this characteristic wavenumber (Fig. 17).
The widths of the seismicity scaling regions, x
max
= 3-7 km, are much smaller than the
average segmentation lengths in Table 3, so a seismicity cutoff associated with !y
outer
is
48

Figure 17. Schematic power spectrum, P
X
(k
y
), for the RFL model as a function of along-
strike wavenumber. The spectrum includes upper and lower cutoffs associated with
outer,!y
outer
"1
, and inner, !y
inner
"1
, scales, as well as a scaling region with slope !(2H +1) ,
where H is the Hausdorff measure. The inner and outer scales are beyond the resolution
of the analysis, which only captures the scaling region (grey box). Regional variation in
seismicity rates are found to correlate with different levels of fault roughness, as
measured by H (inset).
49
not observed. Instead, the scaling regions are limited by the background seismicity from
proximate faults; i.e., the values of x
max
are related to fault branching rather than fault
roughness.
In the scaling region !youter
, the tectonic loading of a self-affine fault will
generate near-fault stress heterogeneity characterized by stress lobes with a power-law
size distribution, as illustrated in Fig. 16. Dieterich and Smith [2006] have used two-
dimensional numerical simulations based on Dieterich’s [1994] rate- and state-dependent
model of seismic nucleation to calculate the fault-normal seismic intensity ν(x) from this
type of stress loading. They obtain a power-law decay in seismicity that satisfies ν ~ | x |
–
D
, where D = 2 – H is the fractal dimension of the along-strike profile.
If this 2D approximation applies to strike-slip faults in California, then γ ≈ D, and the
data from Table 8 yield a low fractal dimension for large-fault roughness in SoCal: D ≈ 1,
consistent with self-similar scaling (H = 1). For the small-fault and aftershock-dominated
classes in SoCal and the large NoCal faults, D ≈ 3/2, which corresponds to a process with
an exponential correlation function (brown noise). Fault traces and profiles across
exposed and laboratory-generated fault surfaces typically range between these fractal
dimensions [Power and Tullis, 1995; Lee and Bruhn, 1996; Renard, et al., 2006], as do
profiles across other types of geologic surfaces [Brown and Scholz, 1985; Goff and
Jordan, 1988; Brown, 1995]. The seismicity roll-off rate for Parkfield is significantly
higher, γ = 2.3 ± 0.25, consistent with H ≈ 0, D ≈ 2. For this type of fault roughness, the
power spectrum decays as 1/k
y
(pink noise). Pink spectra have been observed on a few
normal-fault scarps in the direction of slip [Sagy, et al., 2007].
50
Of course, the validity of the fractal quantification can be questioned owing to the
simplicity of the calculations (e.g., the Dieterich-Smith model doesn’t account for
aftershock diffusion) and the likely role of 3D effects, including fault branching [e.g.
King, 1983; Hirata, 1989] and roughness anisotropy [e.g. Lee and Bruhn, 1996; Renard,
et al., 2006]. Nevertheless, these data do suggest that the wavenumber spectra of large
SoCal faults are ‘redder’ than those of NoCal; this inference agrees with observations that
many of the large faults in SoCal are macroscopically complex [Okubo and Aki, 1987;
Wesnousky, 1988; 1990]. By the same token, if the roughness amplitude at short scales
(say, Δy ~ centimeters) is assumed to be similar for all strike-slip faults in California, as
depicted in Fig. 17, then Parkfield should have the lowest along-strike roughness
amplitude at long scales among the fault classes in Table 8. The Parkfield segments of the
San Andreas fault are indeed quite straight. Some evolutionary aspects of the RFL model
related to fault complexity are discussed in the next section.
Equally interesting is the interpretation of d. For the fault classes in Table 8, this inner
scale of the seismicity distribution varies from 50 m to around 300 m. An inner scale of
fault roughness, !y
inner
, could be added to the RFL model, as depicted in Fig. 17, below
which !("y)# 0 . Such a cutoff would cause the stress-loading amplitudes to level off in
a near-fault region of width d ~ !y
inner
. However, the available data suggest that the self-
affine scaling of fault roughness continues to much smaller dimensions than d, perhaps
even to microscopic scales [Power and Tullis, 1995; Sagy, et al., 2007].
Rather than reflecting a cutoff in surface roughness, d may be interpreted as the half-
width of a volumetric ‘damage zone’, where small-scale stress heterogeneity is attenuated
51
by low rock strength (Fig. 16). Damage zones with dimensions of tens to hundreds of
meters are widely recognized features of exhumed strike-slip faults [Chester and Logan,
1986; Chester, et al., 1993; Ben-Zion and Sammis, 2003; Chester, et al., 2005; Rockwell
and Ben-Zion, 2007], and they have been used to explain vertical low velocity zones of
comparable dimensions inferred from fault-zone guided waves [Li, et al., 1990]; these
low-velocity zones extend at least to several kilometers [Ben-Zion, et al., 2003; Peng, et
al., 2003; Lewis, et al., 2005] and perhaps deeper [Li, et al., 2004; Wu, et al., 2008]. Drill
samples across the Nojima fault, which ruptured in the 1995 Kobe earthquake, indicate
that shear strength is significantly reduced and the permeability increased within a
damage zone surrounding the fault core [Lockner, et al., 1999]. A reduction in fracture
strength by increased fluid pressures [Unsworth, et al., 1997] and the formation of talc
and other low-strength minerals within the damage zone [Morrow, et al., 2000; Moore
and Rymer, 2007] is the preferred explanation of the near-fault stress homogenization
implied by the inner scale d.
The best data on damage-zone dimensions at seismogenic depths in California come
from recent borehole measurements near Parkfield by the San Andreas Fault Observatory
at Depth (SAFOD) project. In 2007, SAFOD drilling encountered two principal slip
surfaces at measured depths of 3194 m and 3301 m, which were embedded in a zone of
variably damaged rock approximately 250 m in fault-normal width [Chester, et al., 2007;
Zoback, et al., 2008]. This value, obtained near the top of the seismogenic zone, is
consistent with local studies of fault-zone guided waves, which sample somewhat deeper
52
[Korneev, et al., 2003; Li, et al., 2004], and it agrees with our Parkfield value of 2d = 240
± 20 m, which averages over the entire seismogenic zone.
For large NoCal faults, the damage-zone width inferred from Table 8 is 100 ± 20 m,
in line with geologic estimates from large exhumed strike-slip faults [Chester, et al.,
2004], faults exposed in mines [Wallace and Morris, 1986], and studies of fault-zone
trapped waves elsewhere [Ben-Zion, et al., 2003; Lewis, et al., 2005]. The narrow damage
zone is consistent with a simple fault geometry comprising a single fault core bounded on
one or both sides by a variably fractured material (Fig. 18a), similar to exposures of the
San Gabriel, San Andreas, and San Jacinto faults [Chester, et al., 2004; Dor, et al., 2006].
Such a single-core fault is said to have a ‘fault-core multiplicity of one’. In this
terminology, the double-core Punchbowl fault [Chester, et al., 2004] and the San Andreas
fault at SAFOD have a fault-core multiplicity of two, which approximately doubles the
damage-zone width (Fig. 18b).
The average damage-zone width obtained for the small SoCal fault class is
significantly larger than at Parkfield: 2d = 320 ± 20 m, suggesting a fault-core
multiplicity greater than two—i.e., wider, more complex fault zones comprising multiply
braided fault cores (Fig. 18c). There are no observations from SoCal that independently
confirm this hypothesis, but some strike-slip faults exposed elsewhere have
anastomosing, multi-core damage zones at least several hundred meters in fault-normal
width [Wallace and Morris, 1986; Faulkner, et al., 2003].
The same line of reasoning would attribute an even higher multiplicity to the large
SoCal faults, for which 2d = 420 ± 20 m. In the case of long faults, however, an increase
53

Figure 18. Relationship between fault-core multiplicity and damage zone width. Each
figure shows fault cores (heavy black lines) embedded in a damage zone that is
surrounded by largely undamaged host rock. Damage intensity is indicated above each
figure [after Chester, et al., 2004]. (a) The damage zone width about a single fault core is
narrow, comparable to NoCal faults. (b) The width of fault damage zones with a
multiplicity of two (paired) is consistent with our observations of the San Andreas fault at
Parkfield and field studies of the exhumed Punchbowl fault [Chester, et al., 2004]. (c)
Fault damage zones with a fault multiplicity greater than two are comparable to SoCal
faults, and are manifested as multiple braided or anastamosing fault cores [modified from
Faulkner, et al., 2003].
54
in the apparent damage-zone width caused by along-strike variability of the fault-core
surfaces must be taken into account. In a self-similar model (H = 1), the along-strike rms
topography of the large faults, !("y
outer
) ≈ !
"
, should be about five times that of the
small faults (which are about one-fifth as long; see Table 3). Assuming the fault-normal
topography is approximately Gaussian, its contribution to d may be estimated by
replacing !
A
x
with !("y) in equation (11). A calculation shows that the entire difference
between the large and small faults can be explained if !
"
≈ 180 m. Large SoCal faults in
show at least this much variability (e.g., Fig. 4). A fault-core multiplicity of order three
can therefore explain the observed d-values for both the large and small SoCal fault
classes.
For aftershock-dominated faults, 2d = 620 ± 20 m, the highest of all fault classes.
Because these fault segments are quite short (~8 km), the rms topography of the fault
surfaces should not contribute significantly to the apparent damage-zone width.
Mislocation errors might be somewhat higher for the aftershock-dominated faults (e.g.,
owing to saturation of network-processing capabilities during times of high seismicity),
but enhanced mislocation bias as an explanation of higher apparent width may be
discounted, because the subcatalogs of clustered seismicity extracted from the other fault
classes do not show an increase in

!
d relative to unclustered seismicity (Table 6). More
likely, the immature faults of the Eastern California Shear Zone that were activated by
the Joshua Tree-Landers-Hector Mine sequence are just more complex than typical SoCal
faults, as suggested by the broad (~2 km) compliant zones of induced, and in two cases
55
retrograde, deformation observed following the Hector Mine mainshock [Fialko, et al.,
2002].
A speculative possibility is that the effective width of the damage zone increases in
response to strong shaking during large earthquakes and subsequently decreases by
logarithmic healing. This mechanism is consistent with the studies of fault-zone guided
waves following the Landers and Hector mine earthquakes, which indicate significant
healing on a decadal time scale [Li, et al., 1998; Li, et al., 2003]. We note, however, that
the fault-zone waveguides do not appear to be anomalously wide in the Landers region
[Li, et al., 2000].
Evolutionary aspects of near-fault seismicity
The short-term response of fault zones to shaking during large earthquakes and the
well-documented long-term evolution of strike slip faults in California [Wesnousky,
1988; Stirling, et al., 1996; Sagy, et al., 2007] indicate the RFL model may have
implications for fault evolution. To augment the geographic variation observed in the
results for the aggregated fault classes in Table 8, estimates of the seismicity parameters
are provided for 10 individual faults with adequate earthquake rates, taken from the large-
fault classes for northern and southern California (Table 9). In three cases, the seismicity
catalogs for individual faults correspond to fault segments listed in Table 3 and mapped
in Figs. 1 and 2: segments 11(San Jacinto), 14 (Imperial), and 15 (Coachella segment of
the San Andreas); the other seven are aggregates of two or three segments. For instance,
the Hayward fault spans two segments (42 and 43) with similar geologic histories and
slip rates, and the creeping section of the San Andreas spans three (48-50).

56

N
T
L W
a
!
0
/ LW
(events) (km) (km) (km) (events/km
3
)
Garlock GA 1, 2, 3 1665 0.29 1.07 128.7 12.4 1.0
Newport - Inglewood NI 8, 9 408 0.20 0.84 113.7 18.3 0.16
Elsinore EL 10, 12 969 0.53 0.93 77.7 15.2 0.46
San Jacinto SJ 11 5027 0.25 0.96 37.7 19.4 6.7
Imperial IM 14 1179 0.32 2.53 21.2 7.0 20.0
San Andreas (Coachella) SAco 15 256 0.77 2.95 40.7 10.3 0.62
Hayward Fault HA 42, 43 1010 0.21 1.37 90.3 12.8 1.8
Calaveras CA 44, 45, 46 4666 0.06 1.73 39.2 8.9 130.0
San Andreas (Creeping) SAcr 48, 49, 50 10122 0.09 1.63 48.9 10.1 120.0
San Andreas (Parkfield) SApa 51, 52 3897 0.14 2.52 64.2 11.2 35.0
a
Length-weighted average.
Fault name ID Segment #

˜
d

˜ "

Table 9. Individual fault data.

57

Aseismicity Factor
(km) Refs. Refs.
Garlock GA 12 – 64 Powell, 1993 0.0 —
Stirling et al., 1996
Newport - Inglewood NI 5 ± 5 Stirling et al., 1996 0.0 —
Elsinore EL 12 ± 3 Stirling et al., 1996 0.0 —
San Jacinto SJ 28 Powell, 1993 0.0 —
Imperial IM ? – 185 Powell, 1993 0.2 Genrich et al., 1997
Shearer, 2002
San Andreas (Coachella) SAco 160 – 185 Powell, 1993 0.2 Lyons & Sandwell, 2003
Hayward Fault HA 100 ± 5 Graymer et al., 2002 0.61 ± 0.19 WGCEP, 2007
Lienkaemper et al.. 2001
Calaveras CA 160 ± 5 Graymer et al., 2002 0.77 ± 0.24 WGCEP, 2007
Galehouse & Lienkaemper, 2003
San Andreas (Creeping) SAcr 315 ± 10 Matti & Morton, 1993 0.62 ± 0.18 WGCEP, 2007
San Andreas (Parkfield) SApa 315 ± 10 Matti & Morton, 1993 0.77 ± 0.09 WGCEP, 2007
Cumulative Offset
ID Fault name

Table 9 (Continued)

58

The same maximum likelihood procedure was employed in fitting equation (5) to the
individual fault catalogs. Because these catalogs comprise fewer events, the estimation
uncertainties are larger than in Table 8, and mislocation-bias corrections, which are small
enough to be ignored in the following comparisons, were not applied. The seismicity
parameters exhibit interesting internal correlations. In particular, the seismicity is more
localized—γ is larger and d is smaller—on faults with higher seismic productivity
!
0
/LW (Figs. 19a,b), and it is less localized where the seismogenic zone, as measured
by W, is thicker (Figs. 19c,d).
Table 8 also lists cumulative offsets on the individual faults and their aseismicity
factors. Cumulative offset values for each fault were aggregated from the literature, with
uncertainties and range estimates reported where available. Following Wisely et al.
[2007], the aseismicity factor (AF) was computed as the ratio of the aseismic slip rate to
the long-term slip rate over the full thickness of the seismogenic zone; i.e., AF = 0
corresponds to a locked fault, and AF = 1 to stable sliding. The AFs in Table 9, which are
weighted by N
k
, were primarily derived from the slip data compiled by Wisely et al.
[2007] for the 2007 Working Group on California Earthquake Probabilities [WGCEP,
2007], supplemented with a few additional studies. Faults that exhibit steady or transient
surface creep thought to be a dynamic (short-term) or static (long-term) response to some
large, regional event [e.g. (Superstition Hills/ Elmore Ranch) McGill, et al., 1989;
(Landers) Bilham and Behr, 1992; Bodin, et al., 1994; (Loma Prieta) Lienkaemper, et al.,
1997; Rymer, 2000; (Hector Mine) Rymer, et al., 2002] were not included. However,

59

Figure 19. Correlations between scaling parameters,

!
! and

!
d , and on-fault earthquake
density !
0
/LW and fault width W for related subsets of faults. Fault names (see Table 8)
are indicated as follows: CA (Calaveras), EL (Elsinore), GA (Garlock), HA (Hayward),
NI (Newport-Inglewood), PA (Parkfield), SAcr (San Andreas–Creeping), SAco (San
Andreas–Coachella Valley), IM (Imperial), and SJ (San Jacinto). Note that smaller and
more productive faults exhibit greater localization of seismicity (small

!
d , large

!
! ).
Correlation coefficients R in parenthesis are values for which outliers were not included.
In (c), SAco and SApa were removed; in (d), SAco and IM were removed.

60
nonzero AFs were assigned to the Coachella Valley [Lyons, et al., 2002] and Imperial
Valley segments of the San Andreas fault, because they have exhibited transient creep
over the full width of the seismogenic crust. In the case of the Imperial Valley fault,
aseismic slip over the seismogenic crust is inferred by reevaluating Bilham and Behr’s
[1992] fault model in light of new estimates of seismogenic thickness [Shearer, 2002].
Although the scatter is high, seismicity tends to localize with increasing cumulative
offset (Figs. 20a,b), conforming to the notion that faults evolve towards more linear,
focused structures. Wesnousky [1988] observed greater localization of surface traces with
increasing cumulative offset on fault length scales of hundreds of kilometers. Here, a
similar localization in the seismicity is observed at fault length scales of tens of
kilometers. Seismic localization also correlates with AF (Figs. 20c,d).
These data and the RFL model are consistent with a simple narrative for fault
evolution. Faults initiate as multiple overlapping strands and coalesce into through-going
structures over time. Younger, rougher faults are characterized by multiple fault cores
(high multiplicity) and correspondingly wide damage zones. As offset progresses, a fault
zone localizes and its roughness spectrum is whitened by a steady decrease in its low-
wavenumber components, which localizes the near-fault seismicity by increasing the roll-
off rate, γ (decreasing H). This localization also reduces the fault-core multiplicity,
eventually to a single or paired core, thus reducing the damage-zone width, 2d. Fault
localization and smoothing promotes aseismic slip. Consequently, stressing rates increase
markedly at the boundaries between steadily slipping and locked patches of a fault,
driving up the seismic productivity per unit fault area, !
0
/LW .

61

Figure 20. Correlations between scaling parameters,

!
! and

!
d , and cumulative offset and
aseismicity factor (a measure of aseismic slip on a fault) for related subsets of faults.
Fault names (see Table 9) are the same as in Fig. 19. High aseismicity factors tend to be
associated with more localized faults. Localization also increases with cumulative offset
reflecting fault evolution towards more linear, focused structures. Correlation coefficients
R in parenthesis are values for which outliers were not included. In (b), SAco was
removed; in (c), SAco and IM were removed; in (d), SAco was removed.

62
In the real world, various combinations of additional factors may ultimately govern
the behavior of a fault. Even if the geology of a fault at depth were known, the
interrelated factors of pore pressure, frictional strength, and heat flow will produce
widely varying conditions for small earthquake nucleation. Such variability is likely
responsible for outliers such as the Coachella Valley segment of the San Andreas fault
(SAco in Figs. 19 and 20). For example, the Coachella Valley segment is comparable to
Parkfield in terms of cumulative offset and fault width, but the Parkfield segment is
known to contain serpentinite [Irwin and Barnes, 1975; Zoback, et al., 2008] and
metamorphic fluids [Unsworth, et al., 1997; Bedrosian, et al., 2004] that likely encourage
aseismic slip along a narrow zone. The Coachella Valley segment, on the other hand,
may be dry and therefore have a larger d, lower seismicity, and less aseismic slip.

63
Chapter 4: Near-Fault Earthquake Triggering
The robust scaling between seismicity and distance from a fault and the increased
localization of aftershocks on faults in SoCal have important implications for earthquake
forecasting and prediction. Systematic earthquake forecasting requires the best possible
models of regional seismicity in order to accurately predict the future rate and
distribution of earthquakes. Epidemic-Type Aftershock Sequence (ETAS)[Ogata, 1988]
models of triggered seismicity, which incorporate the Gutenberg-Richter frequency-
magnitude distribution [Gutenberg and Richter, 1944] and the modified Omori Law for
aftershock decay [Utsu, et al., 1995], do a good job of predicting observed earthquake
patterns, excepting the largest events [Helmstetter and Sornette, 2002; Helmstetter, et al.,
2003; Helmstetter and Sornette, 2003; Helmstetter, et al., 2006]. However, these models
so far only incorporate the fault structure that controls earthquake distribution to a limited
extent. When spatial constraints are integrated into ETAS models, they usually take the
form of an isotropic radial power-law or exponential decay away from an event [Ogata,
1998; Zhuang, et al., 2004] but do not introduce any fault bias. Although the largest
events in such models may be described by elliptical kernels [Ogata, 1998], they are
conditioned on knowing the distribution of aftershocks a priori and do not consider off-
fault events.
Earthquake-aftershock sequences typically show that faults at or near a mainshock
control the distribution of subsequent aftershocks [e.g. Hauksson, et al., 1993], so
incorporation of fault-seismicity scaling relations could improve ETAS spatial kernels.
64
The following chapter demonstrates that the distributions of aftershocks of small
earthquakes (M 2.5–4.5) vary systematically with distance from a fault and presents a
model that could potentially be used to improve earthquake forecasting.
Aftershock distributions
To assess the broad characteristics of near-fault aftershock distributions, sets of
mainshock-aftershock sequences were culled from the fault catalogs used in the
preceding seismicity analysis. In NoCal, only the large faults were considered (i.e.
Parkfield was not included). In SoCal, mainshock-aftershock sequences from both the
large and small fault classes were combined. For each mainshock-aftershock catalog,
earthquakes were selected that followed M 2.5–4.5 mainshocks within a window T days.
To limit the effect of regional dynamic and secondary aftershock triggering, the 30 days
following any M>5.5 earthquake were clipped from the source catalogs. To eliminate
sequence overlap and duplication, the following rules were applied to qualifying
mainshocks occurring within 20 km of and T days following an earlier mainshock: (1) if
the event magnitude is larger, terminate the current aftershock sequence or (2) if the
event is smaller, no longer consider it a qualifying mainshock and continue the current
sequence.
To allow the greatest flexibility when exploring various models and their parameters,
regional aftershock sets were initially created for T = [0.5, 1, 1.5, 2, 5, 10, 20] days. As
with the seismicity analysis, mainshock-aftershock sequences were consolidated on the
positive x side of a fault. For each shifted mainshock, the corresponding aftershock
distribution was mirrored. This preserved any fault bias and placed some aftershocks on
65
the –x side of a fault. The catalogs of mainshock-aftershock sequences were also limited
to mainshocks at a maximum distance of 7 km from a fault, the approximate half-width
of major fault strand separation.
A similar pattern of aftershock distribution emerges in both SoCal and NoCal (Fig.
21): near a fault, aftershock distributions exhibit strike-parallel elongation; with
increasing distance, their elliptical aspect approaches an isotropic distribution. The near-
fault elongation of aftershocks is more pronounced in NoCal than in SoCal, probably
reflecting a combination of fault characteristics such as on-fault productivity, damage
zone width, and the tendency for small earthquakes to be distributed in streaks. Close
inspection of near-fault events shows that aftershock distributions are also biased towards
the fault (Fig. 22). For short T, these characteristics of near-fault aftershock distributions
are well-defined; for long T, there is increased contamination by background events.
Aftershock statistics
Construction of an empirical model of near-fault aftershock distribution requires
knowing if and possibly why the underlying events deviate from established spatio-
temporal and frequency-magnitude statistics. Because seismicity rate decays so rapidly
with distance from a fault, variations in both on- and off-fault aftershock statistics are
explored. For the purpose of this analysis mainshocks in the interval 0–0.5 km from a
fault are considered ‘on-fault’, and those between 0.5 and 7 km ‘off-fault’.
Frequency-magnitude statistics of mainshock-aftershock sets in both NoCal and
SoCal are consistent with values determined for the source fault-catalogs and regional
values (Fig. 23, Table 2). To validate the temporal distribution of selected aftershocks,
66

Figure 21. Aftershock sources for (a) SoCal and (b) NoCal. In each figure, aftershocks
are plotted relative to their corresponding mainshock, each of which has been shifted to a
fault parallel position of y = 0 km. The duration of the individual aftershock sets is T =
1.5 days. Note the near- and on-fault stretching of the aftershock distributions that decays
to an isotropic form with distance.
67

Figure 22. Example of near-fault bias in aftershock distributions. In this figure,
aftershock sequences (T = 1.5 days) were selected for mainshocks in the interval x = 0.2–
0.4 km. The aftershock sequences were then stacked by shifting them to mainshock y = 0
km and x = 0.23 km, the median x of the selected mainshocks. (a) Fault-normal, nearest
neighbor histogram of aftershocks; arrow indicates median mainshock distance from
fault. The black line is the fault-parallel integral of the preferred model parameters [γ =
1.2, d = 0.2, A
0
= 4, β = 2.7, h = 0.03] for SoCal. (b) Map view of the same; black circle
indicates the stack point. Note the distinct bias towards the fault, particularly visible in
(a).
68

Figure 23. Frequency-magnitude distribution of mainshocks and aftershocks (T = 1.5
days)selected for this study from (a) SoCal and (b) NoCal. Both magnitude of
completeness, M
C
, and b-value are consistent with those determined for the complete
fault catalogs in each region. The order of magnitude drop in abundance from
mainshocks to aftershocks is a reflection of Båth’s Law.
69

longer (T = 30 days) mainshock-aftershock sequences were selected for each region and
aftershocks were stacked on their mainshock origin time (Figs. 24 and 25). To assess
productivity across different magnitude intervals, the aftershock stacks were subdivided
into groups defined by 0.5 M mainshock magnitude intervals. To permit comparison with
other studies [e.g. Helmstetter, 2003; Helmstetter, et al., 2005], only aftershocks of M ≥ 2
were initially included. Nearest-neighbor binning was used to illustrate the decay of
events with time. In each region, the Omori Law for aftershock decay [Utsu, et al., 1995]
is recovered with temporal decay exponent p ≈ 0.9 ± 0.1, as expected. Values of p were
computed using a least-squares fit (considering all magnitude ranges simultaneously) to
the steepest part of the distribution, which maintains a consistent slope from a roll off at
short time t = 0.002 days (~3 minutes) out to a slope break at t = 1 to 2 days. The slope
break time marks the onset of background contamination in the aftershock selection
process, indicating that sequences for which T = 1.5 days provide highest ratio of
triggered to independent events.
Aftershock productivity increases exponentially as a function mainshock magnitude
m
!
according to K(m
!
)=K
0
10
"(m
!
#m
0
)
where K(m
!
) represents the seismicity rate per
day for m ≥ m
0
at time t = 1 day after the mainshock occurrence. For the mainshock-
aftershock sequences considered here, small magnitude mainshocks are significantly
more productive (high K
0
, low α) than the southern California regional average (Fig. 26)
of Helmstetter et al.[2005], even though a minimum aftershock magnitude cutoff of m
0
=
2 results in some poorly sampled magnitude intervals (e.g. M 4–4.5 in SoCal, Fig. 26).
On-fault productivity mimics that of the full dataset in each region because most events
70

Figure 24. Average rate of M ≥ 2 earthquakes in SoCal as a function of time t after
triggering mainshocks of varying magnitude, increasing from (a) to (d). Dots represent
the distribution of aftershocks binned in time by nearest-neighbor method with q events.
The black line is a least-squares fit (that includes all four data sets) with slope p to the
steepest part of the distribution, clipped at 0.002 days (~ 3 min) and the break in slope at
~1.0 day. The break in slope marks the onset time of background contamination in
aftershock selection.
71

Figure 25. Average rate of M ≥ 2 earthquakes in NoCal as a function of time t after
triggering mainshocks of varying magnitude, increasing from (a) to (d). Dots represent
the distribution of aftershocks binned in time by nearest-neighbor method with q events.
The black line is a least-squares fit (that includes all four data sets) with slope p to the
steepest part of the distribution, clipped at 0.002 days (~ 3 min) and the break in slope at
~1.0 day. The break in slope marks the onset time of background contamination in
aftershock selection.
72

Figure 26. Aftershock productivity as a function of mainshock magnitude for aftershocks
where m
0
= 2. Black squares with errors indicate the range of possible values for α,
derived from the aftershock rates in Fig 25 . In both SoCal and NoCal, the distribution of
values does not follow a consistent trend due to poor sampling of some mainshock
magnitude intervals. An alternate solution that only considers 2.5 < M < 3.5 events is
presented in (a) where α = 0.67. In both regions, α values are significantly lower than
those determined by Helmstetter et al.[2005] (grey band) for all southern California
aftershocks spanning the interval 1980–2004. Likewise, the productivity of small, near-
fault events is significantly higher than the southern California regional average. Direct
comparison is made possible by using similar sampling parameters.
73
occur near faults. However, off-fault productivity in both SoCal (α ≈ 0.85) and NoCal (α
≈ 1.0) is closer to the southern California average. The observed on-fault productivity
gain is consistent with clustering and swarm behavior commonly observed with smaller
magnitude mainshocks [Vidale and Shearer, 2006]. These data suggest the phenomena is
associated with faults, however, closer inspection of the data compiled by Helmstetter et
al.[2005] shows that small magnitude events are consistently more productive across
southern California, and that lower α values are to be expected. When m
0
= 0, α ≈ 0.45 in
both NoCal and SoCal (Fig. 27). Although lower, this α-value is supported by a smoother
distribution of productivity values.
The radially averaged distribution of selected aftershocks is ~

(1+r
2
/h
2
)
!
!
"/2
where

!
!
is the linear decay of aftershocks with distance r from a mainshock and h prevents a near-
mainshock singularity (Fig. 28). Maximum likelihood estimates of

!
! for on-fault
aftershocks (T = 1.5 days) are 2.6 in SoCal and 2.3 in NoCal, varying only marginally
from values of Felzer and Brodsky [2006] who found that

!
! = 2.4 in SoCal and

!
! = 2.8
in NoCal. The low NoCal value is likely due to the greater along fault elongation of
aftershock sequences that would smooth a radially averaged distribution, consistent with
a higher off-fault value of 1.4 where there is no fault effect. As aftershock duration T
increases,

!
! -values fall in response to the addition of background events. Inner scale h is
largely invariant with respect to T and tends to decrease (e.g. h = 0.14 off-fault vs. h =
0.26 on-fault in SoCal) for off-fault events, also in response to the absence of a fault
effect there.
74

Figure 27. Aftershock productivity as a function of mainshock magnitude for aftershocks
where m
0
= 0. Symbols are the same as in Fig. 26. Lowering the magnitude threshold
results in better event sampling across different mainshock magnitude ranges but values
of α that are lower still. The results of Helmstetter et al.[2005] (grey band) can only be
used for comparison with α given different m
0
.
75

Figure 28. Aftershock productivity as a function of distance from SoCal mainshocks.
Open circles represent a nearest-neighbor binned distribution of stacked mainshock-
aftershock Euclidean distances with q events per bin. B is the linear decay exponent
(aftershock rate in events/km consistent with Felzer and Brodsky [2006]) whereas β is the
aerial decay exponent (aftershock rate in events/km
2
).
76
Aftershock Model
The initial survey of aftershocks of small earthquakes near strike-slip faults in
California suggests that for a mainshock of magnitude m
!
at location (x
!
,y
!
), the
aftershock rate is given by the spatial kernel
!(x,y |m
"
,x
"
,y
"
) = !
0
(m
"
)#(x) 1 +$
2
(x,y) /h
2
%
&
'
(
)*/2
, (14)
where ! describes the decay rate of aftershocks with distance from a mainshock and an
inner-scale h prevents an infinite number of events near the source (Fig. 29). The
mainshock-aftershock relative distance is given by
!
2
(x,y)= (x" x
*
)
2
+ (y" y
*
)
2
/A
2
(x
*
) , (15)
where the aspect ratio is
A(x
!
) = A
0
"1 ( ) 1 + x
!
2
/d
2
#
$
%
&
"' /2
+1. (16)
In this expression, the aspect ratio is a constant value A
0
on a fault and decays with
distance to an isotropic value of 1 according to the decay-rate of near-fault seismicity.
The relative excitation rate of the kernel has the standard form
!
0
(m
"
)=K
0
10
#(m
"
$m
0
)
, (17)
where K
0
and α are constants and m
0
is the minimum mainshock magnitude. To
accommodate the observed bias of aftershocks towards a fault, the near-fault rate, as
defined in the preceding seismicity analysis,
!(x) =!
0
(1 + x
2
/d
2
)
"# /2
, (18)
77

Figure 29. Contours of the p.d.f. of near-fault aftershock distribution for different values
of x
0
(mainshock distance from a fault). These contours are for the 95
th
, 90
th
, 75
th
and 50
th

(light to dark) percentiles for the preferred model parameters [γ = 1.2, d = 0.2, A
0
= 4, β =
2.7, h = 0.03] in SoCal.
78

is also included. Note that this term also contributes to the strike-parallel elongation of
the aftershock kernel.
Although ! and h are known to vary with distance from a fault and could be defined
in terms of x
!
, the variations are relatively small and so they are treated as constants.
Likewise, the on- and off-fault values of !
0
are known to be somewhat different, but
there are so few off-fault events that K
0
and α may also be considered constants. Because
the sampled aftershock sequences are sourced from numerous faults, it is difficult to
constrain the on-fault seismicity rate ν
0
and instead allow it to be subsumed into K
0
.
Parameter estimation
A non-stationary Poisson process, such as an aftershock sequence, may be completely
characterized by an intensity function !(x) for which the explicit likelihood function is
[Ogata, 1983; 1998]
L(!)= "(x
i
)
i
#
$
%
&
'
(
)
exp * "(x)dx
D
++
,
-
.
/
0
1
2
/
(19)
where { x
i
; i=1, 2,…,N} are the locations of events in a spatial domain D. The likelihood
function is a product of the probabilities !(x
i
)dx
i
of the individual events in infinitesimal
intervals and the probability exp ! "(x)dx
##
$
%
&
'
of no events in the gaps. For M
mainshock-aftershock sequences, where the spatial intensity function at each aftershock
!(x,y |m
"
,x
"
,y
"
) is conditional on the corresponding mainshock magnitude and location,
the log-likelihood is
79
!(K
0
,",# ,d,A
0
,$,h)=
ln%(x
i
,y
i
|m
j
,x
j
,y
j
)
i=1
N
&
' %(x,y |m
j
,x
j
,y
j
)dxdy
D
((
)
*
+
,
-
.
j=1
M
&
. (20)
Model parameters ! = [K
0
,",# ,d,A
0
,$,h] may be estimated by maximizing equation 20
for any number of mainshock-aftershock sequences.
Ultimately, a model is sought that improves upon the homogeneous and isotropic
form r
2
(x,y)= (x! x
*
)
2
+ (y! y
*
)
2
of aftershock distribution that does not include any
near-fault effect !(x) . To simplify the search for a set of valid model parameters, well-
established values, such as γ and d were held fixed (NoCal: γ = 1.6 d = 0.08; SoCal: γ =
1.2, d = 0.2). Initial experimentation estimating the remaining five parameters, using
mainshock-aftershock sets with the least background contamination (T = 1.5 days),
showed that α-values consistently matched those determined in the prior statistical
analysis and was therefore held fixed at 0.45 moving forward. Maximum likelihood
solutions of the remaining three parameters that govern the spatial distribution of
aftershocks are β = 3.5, h = 0.13 km, and A
0
= 12 for SoCal, and β = 3.6, h = 0.14 km,
and A
0
= 19 for NoCal. Although these values seem reasonable, β in both regions is
significantly higher than observed values

!
! . To verify that the parameter estimation
algorithms work as expected, experiments were conducted to recover model parameters
from synthetic catalogs. To generate synthetic catalogs, the source mainshock-aftershock
sequences were recreated, relocating aftershocks using a 2D p.d.f of a prescribed model.
80
These checks typically recovered β-values to within ± 0.5, h to within ± 0.1 km, and A
0

to within ± 1.
To better constrain β, h, and A
0
, the model parameters were subjected to the
additional constraint that

!
! and

!
h be recovered from synthetic catalogs using the same
procedure as for the statistical analysis. For the solutions listed above, resulting values of

!
! and

!
h are too high. Independently reducing β or A
0
drives both

!
! and

!
h higher still.
Independently reducing h only reduces

!
h .

!
! and

!
h are recovered only when β, h, and A
0

are reduced simultaneously. A
0
must be reduced by a factor of 3 in both SoCal (A
0
= 4)
and NoCal (A
0
= 7); β must be reduced by about 1 to 2.7 in SoCal and 2.3 in NoCal. As
with

!
! , the lower β -value in SoCal likely reflects the near-fault elongation of aftershock
distributions. The inner-scale of aftershock decay has the most significant impact on
values of

!
! and

!
h and very small model values (h ≈ 0.02 km) are required.
As a further check on estimates of β, h , and A
0
, the simple case of on-fault events
alone is also considered. Mainshocks located within d km of a fault were selected in
SoCal and NoCal and stacked on the fault (at x = 0). The aspect ratios of equal event
density contours (Fig. 30) are consistent with values for A
0
determined by maximum
likelihood (3:1 in SoCal; 9:1 in NoCal). Maximum likelihood estimates of β and h for the
on-fault stack and tradeoffs between β, h , and A
0
are also consistent with values and
behavior determined from the analysis of the full mainshock-aftershock dataset.
81

Figure 30. On-fault aftershock distributions. In each figure, aftershocks corresponding to
all mainshocks falling within d km of a fault (0.2 in SoCal; 0.1 in NoCal) were stacked at
the origin. The black ellipse is an event density contour that gives an estimate of the on-
fault aspect ratio constant A
0
for each region. A
0
≈ 3 in SoCal; A
0
≈ 9 in NoCal.

82
Synthetic catalogs generated using the parameter values [γ = 1.2, d = 0.2, A
0
= 4, β =
2.7, h = 0.03] in SoCal and [γ = 1.6, d = 0.1, A
0
= 7, β = 2.3, h = 0.03] in NoCal are in
good visual agreement with the original source catalogs (Fig. 31). The model of near-
fault aftershock distributions of small earthquakes described by equation (14) could lead
to improvements in earthquake forecasts by providing a better description of earthquake
triggering. However, it requires further improvement through the inclusion of full
renormalization, time dependence (Omori Law), and a spatially varying background rate.

83

Figure 31. Synthetic aftershocks sequences derived using the preferred model parameters
for (a) SoCal and (b) NoCal. In each figure, aftershocks are plotted relative to their
corresponding mainshock, each of which has been shifted to a fault parallel position of y
= 0 km.
84
Conclusions

The foregoing analysis of seismicity in the vicinity of strike-clip faults in California has
quantified, for the first time, the relationships between small earthquakes and faults. The
results presented here have important implications for a broad range of disciplines
including statistical seismology, structural geology, earthquake physics and rock
mechanics and will permit the development of refined models of earthquake triggering
that my prove improve earthquake forecasting. The primary results of this study are as
follows:
1. Out to a fault-normal distance x of 3-6 km, seismicity obeys a power-law
~ (1+ x
2
/d
2
)
!" /2
, where γ is the asymptotic roll-off rate and d is a near-fault
inner scale.
2. This scaling relation is compatible with a ‘rough fault loading’ model in which
the inner scale d measures the half-width of a volumetric damage zone and the
roll-off rate γ is governed by stress variations due to fault roughness.
3. Near-fault seismicity is more localized on faults in Northern California
(NoCal:d = 50±20m , ! =1.51±.05 ) than in Southern California (SoCal:
d = 210±40m , ! = 0.97±.05 ). The Parkfield region has a damage-zone half-
width (d =120±30m ) consistent with the SAFOD drilling estimate and its high
roll-off rate (! = 2.30±.25 ) indicates a relatively flat roughness spectrum:

~ k
!1

vs.

k
!2
for NoCal and

k
!3
for SoCal. Fault surfaces in SoCal are therefore nearly
self-similar, and their roughness spectra are redder than in NoCal, consistent with
the macroscopic complexity of the observed fault traces.
85
4. Damage-zone widths—the first direct estimates averaged over the seismogenic
layer—can be interpreted in terms of an across-strike ‘fault-core multiplicity’ that
is ~1 in NoCal, ~2 at Parkfield, and ~3 in SoCal.
5. The localization of seismicity near individual faults correlates with cumulative
offset, seismic productivity, and aseismic slip, consistent with a model in which
faults originate as branched networks with broad, multi-core damage zones and
evolve towards more localized, lineated features with low fault-core multiplicity,
thinner damage zones, and less seismic coupling.
6. The spatial distribution of aftershocks is modified by the presence of faults and is
well described by an elliptical kernel that includes a near-fault effect and an
aspect parameter that scales with distance from a fault.

Continuing Work
Further attention is being given to asymmetries in the fault-normal seismicity
distribution. Across-fault material contrasts [e.g. Weertman, 1980; Cochard and Rice,
2000; Shi and Ben-Zion, 2006] and asymmetric fault damage [e.g. Dor, et al., 2006] may
be important in controlling rupture directivity. Material contrasts are known to cause
asymmetric fault-parallel distributions of aftershocks [Rubin and Gillard, 2000; Rubin
and Ampuero, 2007] and may therefore be reflected in fault-normal earthquake rates.
The fault-normal distribution of seismicity is also likely correlated with depth. In this
thesis, the analyses were restricted to the central part of the seismogenic crust and it was
verified that there is little variability in the results when the truncation depths were
86
varied. The distribution parameters d and γ were found to correlate with fault width W
(Fig. 18c,d), indicating that the fault-normal seismicity distributions depend on the
vertical structure of the fault zones, particularly the geothermal gradient. The near-fault
seismicity of some segments is also highly localized in depth, more often than not
towards the base of the seismogenic zone [Boutwell, et al., 2008]. Depth localization of
seismicity might have implications for the RFL model.

87
References

Aki, K. (1965), Maximum likelihood estimate of b in the fourmula log N = a – bM and its
confidence limits, Bull. Earthquake Res. Inst., Tokyo Univ., 43, 237–239.
Bawden, G. W., A. J. Michael, and L. H. Kellogg (1999), Birth of a fault: Connecting the
Kern County and Walker Pass, California, earthquakes, Geology, 27(7), 601-604.
Bedrosian, P. A., M. J. Unsworth, G. D. Egbert, and C. H. Thurber (2004), Geophysical
images of the creeping segment of the San Andreas fault: implications for the role of
crustal fluids in the earthquake process, Tectonophysics, 385(1–4), 137–158.
Ben-Zion, Y., Z. Peng, D. Okaya, L. Seeber, J. G. Armbruster, N. Ozer, A. J. Michael, S.
Baris, and M. Aktar (2003), A shallow fault-zone structure illuminated by trapped
waves in the Karadere–Duzce branch of the North Anatolian Fault, western Turkey,
Geophys. J. Int., 152(3), 699–717, doi: 10.1046/j.1365-246X.2003.01870.x.
Ben-Zion, Y., and C. G. Sammis (2003), Characterization of fault zones, Pure Appl.
Geophys., 160, 677–715.
Bilham, R., and J. Behr (1992), A two-layer model for aseismic slip on the Superstition
Hills Fault, California, Bull. Seismol. Soc. Am., 82(3), 1223–1235.
Bodin, P., R. Bilham, J. Behr, J. S. Gomberg, and K. W. Hudnut (1994), Slip triggered on
southern California faults by the 1992 Joshua Tree, Landers, and big bear
earthquakes, Bull. Seismol. Soc. Am., 84(3), 806–816.
Boettcher, M. S., and T. H. Jordan (2004), Earthquake scaling relations for mid-ocean
ridge transform faults, J. Geophys. Res., 109, B12302, doi: 10.1029/2004JB003110.
Boutwell, C., P. M. Powers, and T. H. Jordan (2008), Depth Localization of Seismicity
on Strike-Slip Faults in California, Eos Trans. AGU, 89(53), Fall Meet. Suppl.,
Abstract S21B-1832.
Brown, S. R. (1995), Simple mathematical model of a rough fracture, J. Geophys. Res.,
100(B4), 5941–5952.
Brown, S. R., and C. H. Scholz (1985), Broad bandwidth study of the topography of
natural rock surfaces, J. Geophys. Res., 90(B14), 12575–12582.
Buland, R. (1986), Uniform reduction error analysis, Bull. Seismol. Soc. Am., 76(1), 217–
230.
Carena, S., J. Suppe, and H. Kao (2004), Lack of continuity of the San Andreas fault in
southern California: Three dimensional fault models and earthquake scenarios, J.
Geophys. Res., 109(B04313), 1-17.
88
Chester, F. M., and J. S. Chester (2000), Stress and deformation along wavy frictional
faults, J. Geophys. Res., 105(B10), 23421–23430.
Chester, F. M., J. S. Chester, D. L. Kirschner, S. E. Schulz, and J. P. Evans (2004),
Structure of large-displacement, strike-slip fault zones in the brittle crust, in Rheology
and Deformation in the Lithosphere at Continental Margins, edited by G. D. Karner,
et al., pp. 223–260, Columbia University Press, New York.
Chester, F. M., J. P. Evans, and R. L. Biegel (1993), Internal structure and weakening
mechanisms of the San Andreas fault, J. Geophys. Res., 98(B1), 771–786.
Chester, F. M., and J. M. Logan (1986), Implications for mechanical properties of brittle
faults from observations of the Punchbowl fault zone, California, Pageoph, 124(1-2),
79–106.
Chester, J. S., F. M. Chester, D. L. Kirschner, R. Almeida, J. P. Evans, R. N. Guillemette,
S. Hickman, M. D. Zoback, and W. L. Ellsworth (2007), Deformation of sedimentary
rock across the San Andreas fault zone: Mesoscale and microscale structures
displayed in core from SAFOD, Eos Trans. AGU, 88(52), Fall Meet. Suppl., Abstract
T42C-05.
Chester, J. S., F. M. Chester, and A. K. Kronenberg (2005), Fracture surface energy of
the Punchbowl fault, San Andreas system, Nature, 437, 133–136, doi:
10.1038/nature03942.
Cochard, A., and J. R. Rice (2000), Fault rupture between dissimilar materials: Ill-
posedness, regularization, and slip-pulse response, J. Geophys. Res., 105(B11),
25,891–25,907.
Dieterich, J. H. (1994), A constitutive law for rate of earthquake production and its
application to earthquake clustering, J. Geophys. Res., 99, 2601–2618.
Dieterich, J. H., and D. E. Smith (2006), Stress Relaxation on Geometrically Complex
Faults, Eos Trans. AGU, 87(52), Fall Meet. Suppl., Abstract S34A-06.
Dor, O., T. K. Rockwell, and Y. Ben-Zion (2006), Geological observations of damage
asymmetry in the structure of the San Jacinto, San Andreas and Punchbowl faults in
southern California: A possible indicator for preferred rupture propagation direction,
Pure Appl. Geophys., 163(2–3), 301–349, doi: 10.1007/s00024-005-0023-9.
Efron, B. (1979), Bootstrap methods: Another look at the jackknife, Ann. Stat., 7(1), 1–
26.
Ellsworth, W. L., et al. (2000), Seismicity of the San Andreas Fault system in central
California: Application of the double-difference location algorithm on a regional
scale, Eos Trans. AGU, 81(48), Fall Meet. Suppl., Abstract S21D-01.
89
Faulkner, D. R., A. C. Lewis, and E. H. Rutter (2003), On the internal structure and
mechanics of large strike-slip fault zones: field observations of the Carboneras fault
in southeastern Spain, Tectonophysics, 367, 235–251, doi: 10.1016/S0040-
1951(03)00134-3.
Feder, J. (1988), Fractals, 283 pp., Plenum Press, New York.
Felzer, K. R., and E. E. Brodsky (2006), Decay of aftershock density with distance
indicates triggereing by dynamic stress, Nature, 441, 735-738.
Fialko, Y., D. T. Sandwell, D. C. Agnew, M. Simons, P. M. Shearer, and B. Minster
(2002), Deformation on nearby faults induced by the 1999 Hector Mine earthquake,
Science, 297(5588), 1858–1862, doi: 10.1126/science.1074671.
Finzi, Y., E. H. Hearn, Y. Ben-Zion, and V. Lyakhovsky (in press), Structural properties
and deformation patterns of evolving strike-slip faults: Numerical simulations
incorporating damage rheology, Pure Appl. Geophys.
Goff, J. A., and T. H. Jordan (1988), Stochastic modeling of seafloor morphology:
Inversion of sea beam data for second-order statistics, J. Geophys. Res., 93(B11),
13,589–13,608.
Gutenberg, B., and C. Richter (1944), Frequency of earthquakes in California, Bull.
Seismol. Soc. Am., 34, 185–188.
Hauksson, E. (2000), Crustal structure and seismicity distribution adjacent to the Pacific
and North America plate boundary in southern California, J. Geophys. Res., 105(B6),
13,875–13,903.
Hauksson, E., L. M. Jones, K. Hutton, and D. Eberhart-Phillips (1993), The 1992 Landers
earthquake sequence: Seimological observations, J. Geophys. Res., 98(B11), 19,835–
19,858.
Hauksson, E., and P. M. Shearer (2005), Southern California hypocenter relocation with
waveform cross-correlation, Part 1: Results using the double-difference method, Bull.
Seismol. Soc. Am., 95(3), 896–903.
Helmstetter, A. (2003), Is earthquake triggering driven by small earthquakes?, Physical
Review Letters, 91(5), 058501.
Helmstetter, A., Y. Y. Kagan, and D. D. Jackson (2005), Importance of small earthquakes
for stress transfers and earthquake triggering, J. Geophys. Res., 110, B05S08, doi:
10.1029/2004JB003286.
Helmstetter, A., Y. Y. Kagan, and D. D. Jackson (2006), Comparison of short-term and
time-independent earthquake forecast models for southern California, Bull. Seismol.
Soc. Am., 96(1), 90–106.
90
Helmstetter, A., G. Ouillon, and D. Sornette (2003), Are aftershocks of large Californian
earthquakes diffusing?, J. Geophys. Res., 108(B10), 2483, doi:
10.1029/2003JB002503.
Helmstetter, A., and D. Sornette (2002), Subcritical and supercritical regimes in epidemic
models of earthquake aftershocks, J. Geophys. Res., 107(B10), 2237, doi:
10.1029/2001JB001580.
Helmstetter, A., and D. Sornette (2003), Predictability in the Epidemic-Type Aftershock
Sequence model of interacting triggered seismicity, J. Geophys. Res., 108(B10),
2482, doi: 10.1029/2003JB002485.
Hill, D. P., J. P. Eaton, and L. M. Jones (1990), The San-Andreas fault system,
California, in U.S. Geol. Surv. Profess. Pap. 1515, edited by R. E. Wallace, pp. 115–
152.
Hirata, T. (1989), Fractal dimension of fault systems in Japan: Fractal structure in rock
fracture geometry at various scales, Pure Appl. Geophys., 131(1–2), 157–170.
Irwin, W. P. (1990), The San-Andreas fault system, California, in U.S. Geol. Surv.
Profess. Pap. 1515, edited by R. E. Wallace, pp. 61–80.
Irwin, W. P., and I. Barnes (1975), Effect of geologic structure and metamorphic fluids
on seismic behavior of the San Andreas fault system in central and northern
California, Geology, 3(12), 713–716.
Jeffreys, H. (1932), An alternative to the rejection of observations, Proc. Roy. Soc.
London, 187, 78–87.
Kagan, Y. Y. (2007), Earthquake spatial distribution: the correlation dimension, Geophys.
J. Int., 168(3), 1175–1194, doi: 10.1111/j.1365-246X.2006.03251.x.
King, G. C. P. (1983), The accommodation of large strains in the upper lithosphere of the
earth and other solids by self-similar fault systems: The geometrical origin of b-value,
Pageoph, 121(5–6), 761–815.
Korneev, V. A., R. M. Nadeau, and T. V. McEvilly (2003), Seismological studies at
Parkfield IX: Fault-zone imaging using guided wave attenuation, Bull. Seismol. Soc.
Am., 93(4), 1415–1426, doi: 10.1785/0120020114.
Lee, J.-J., and R. L. Bruhn (1996), Structural anisotropy of normal fault surfaces, J.
Struct. Geol., 18(8), 1043–1059, doi: 10.1016/0191-8141(96)00022-3.
Lewis, M. A., Z. Peng, Y. Ben-Zion, and F. L. Vernon (2005), Shallow seismic trapping
structure in the San Jacinto fault zone near Anza, California, Geophys. J. Int., 162(3),
867–881, doi: 10.1111/j.1365-246X.2005.02684.x.
91
Li, Y. G., P. Leary, K. Aki, and P. E. Malin (1990), Seismic trapped modes in the
Oroville and San Andreas faults, Science, 249(4970), 763–766.
Li, Y. G., J. E. Vidale, K. Aki, and X. Fei (2000), Depth-dependent structure of the
Landers fault zone from trapped waves generated by aftershocks, J. Geophys. Res.,
105(B3), 6237–6254.
Li, Y. G., J. E. Vidale, K. Aki, F. Xu, and T. Burdette (1998), Evidence of shallow fault
zone strengthening after the 1992 M7.5 Landers, California, earthquake, Science,
279(5348), 217–219, doi: 10.1126/science.279.5348.217.
Li, Y. G., J. E. Vidale, and E. S. Cochran (2004), Low-velocity damaged structure of the
San Andreas Fault at Parkfield from fault zone trapped waves, Geophys. Res. Lett.,
31, L12S06, doi: 10.1029/2003GL019044.
Li, Y. G., J. E. Vidale, S. M. Day, D. D. Oglesby, and E. S. Cochran (2003), Postseismic
fault healing on the rupture zone of the 1999 M 7.1 Hector Mine, California,
earthquake, Bull. Seismol. Soc. Am., 93(2), 854–869, doi: 10.1785/0120020131.
Lienkaemper, J. J., J. S. Galehouse, and R. W. Simpson (1997), Creep response of the
Hayward fault to stress changes caused by the Loma Prieta earthquake, Science,
276(5321), 2014–2016.
Liu, J., K. E. Sieh, and E. Hauksson (2003), A structural interpretation of the aftershock
"cloud" of the 1992 Mw 7.3 Landers earthquake, Bull. Seismol. Soc. Am., 93(3),
1333-1344.
Lockner, D. A., H. Naka, H. Tanaka, H. Ito, and R. Ikeda (1999), Permeability and
strength of core samples from the Nojima fault of the 1995 Kobe earthquake, in
Proceedings of the international workshop on the Nojima fault core and borehole
data analysis, Nov 22–23, 1999, USGS Open File Report 00-129, edited by H. Ito, et
al., Tsukuba, Japan.
Lyons, S., Y. Bock, and D. T. Sandwell (2002), Creep along the Imperial Fault, southern
California, from GPS measurements, J. Geophys. Res., 107(B10), 2249, doi:
10.1029/2001JB000763.
Lyons, S., and D. T. Sandwell (2003), Fault creep along the southern San Andreas from
interferometric synthetic aperture radar, permanent scatterers, and stacking J.
Geophys. Res., 108(B1), 2047, doi: 10.1029/2002JB001831.
Magistrale, H. (2002), Relative contributions of crustal temperature and composition to
controlling the depth of earthquakes in Southern California, Geophys. Res. Lett.,
29(10), 1447, doi: 10.1029/2001GL014375.
92
McGill, S. F., C. R. Allen, K. W. Hudnut, D. C. Johnson, W. F. Miller, and K. E. Sieh
(1989), Slip on the Superstition Hills Fault and on nearby faults associated with the
24 November 1987 Elmore Ranch and Superstition Hills earthquakes, Southern
California, Bull. Seismol. Soc. Am., 79(2), 362–375.
Moore, D. E., and M. J. Rymer (2007), Talc-bearing serpentinite and the creeping section
of the San Andreas fault, Nature, 448, 795–797, doi: 10.1038/nature06064.
Morrow, C. A., D. E. Moore, and D. A. Lockner (2000), The effect of mineral bond
strength and adsorbed water on fault gouge frictional strength, Geophys. Res. Lett.,
27(6), 815–818.
Ogata, Y. (1983), Estimation of the parameters in the modified Omori formula for
aftershock frequencies by the maximum likelihood procedure, Journal of the Physics
of the Earth, 31, 115-124.
Ogata, Y. (1988), Statistical models for earthquake occurrences and residual analysis for
point processes, J Am. Stat. Assoc., 83(401), 9–27.
Ogata, Y. (1998), Space-time point process models for earthquake occurrences, Ann. Inst.
Stat. Math., 50(2), 379–402.
Okubo, P. G., and K. Aki (1987), Fractal goemetry in the San Andreas fault system, J.
Geophys. Res., 92(B1), 345–355.
Ouillon, G., C. Castaing, and D. Sornette (1996), Hierarchical geometry of faulting, J.
Geophys. Res., 101(B3), 5477–5487.
Peng, Z., Y. Ben-Zion, A. J. Michael, and L. Zhu (2003), Quantitative analysis of seismic
fault zone waves in the rupture zone of the 1992 Landers, California, earthquake:
evidence for a shallow trapping structure, Geophys. J. Int., 155(3), 1021–1041, doi:
10.1111/j.1365-246X.2003.02109.x.
Plesch, A., et al. (2007), Community Fault Model (CFM) for Southern California, Bull.
Seismol. Soc. Am., 97(2), 1793–1802, doi: 10.1785/0120050211.
Power, W. L., and T. E. Tullis (1995), A review of the fractal character of natural fault
surfaces with implications for friction and the evolution of fault zones, in Fractals in
the Earth Sciences, edited by P. Lapointe and C. Barton, pp. 89–105, Plenum Press,
New York.
Powers, P. M., and T. H. Jordan (2005), Seismicity rate vs. distance from strike-slip
faults in southern California, Eos Trans. AGU, 86(52), Fall Meet. Suppl., Abstract
S13B-0199.
93
Powers, P. M., and T. H. Jordan (2007), On the spatial predictability of earthquakes and
aftershocks, paper presented at Seismological Society of America Annual Meeting,
Waikoloa, HI, 11-13 April.
Reasenberg, P. A. (1985), Second-Order Moment of Central California Seismicity, 1969-
1982, J. Geophys. Res., 90(B7), 5479–5495.
Renard, F., C. Voisin, D. Marsan, and J. Schmittbuhl (2006), High resolution 3D laser
scanner measurements of a strike-slip fault quantify its morphological anisotropy at
all scales, Geophys. Res. Lett., 33, L04305, doi: 10.1029/2005GL025038.
Richards-Dinger, K. B., and P. M. Shearer (2000), Earthquake locations in southern
California obtained using source-specific station terms, J. Geophys. Res., 105(B5),
10,939–10,960.
Robertson, M. C., C. G. Sammis, M. Sahimi, and A. Martin (1995), The 3-D spatial
distribution of earthquakes in southern California with a percolation theory
interpretation, J. Geophys. Res., 100, 609–620.
Rockwell, T. K., and Y. Ben-Zion (2007), High localization of primary slip zones in large
earthquakes from paleoseismic trenches: Observations and implications for
earthquake physics, J. Geophys. Res., 112, B10304, doi: 10.1029/2006JB004764.
Rubin, A. M., and J.-P. Ampuero (2007), Aftershock asymmetry on a bimaterial
interface, J. Geophys. Res., 112, B05307, doi: 10.1029/2006JB004337.
Rubin, A. M., and D. Gillard (2000), Aftershock asymmetry/rupture directivity among
central San Andreas fault microearthquakes, J. Geophys. Res., 105(B8), 19,095–
19,109, doi: 10.1029/2000JB900129.
Rubin, A. M., D. Gillard, and J.-L. Got (1999), Streaks of microearthquakes along
creeping faults, Nature, 400, 635–641.
Rymer, M. J. (2000), Triggered surface slips in the Coachella valley area associated with
the 1992 Joshua Tree and Landers, California, earthquakes, Bull. Seismol. Soc. Am.,
90(4), 832–848.
Rymer, M. J., J. Boatwright, L. C. Seekins, D. Yule, and J. Liu (2002), Triggered surface
slips in the Salton trough associated with the 1999 Hector Mine, California,
earthquake, Bull. Seismol. Soc. Am., 92(4), 1300–1317.
Sagy, A., E. E. Brodsky, and G. J. Axen (2007), Evolution of fault-surface roughness
with slip, Geology, 35(3), 283–286, doi: 10.1130/G23235A.1.
Saucier, F., E. D. Humphreys, and R. J. Weldon (1992), Stress near geometrically
complex strike-slip faults: Application to the San Andreas fault at Cajon Pass,
California, J. Geophys. Res., 97(B4), 5081–5094.
94
Shearer, P. M. (2002), Parallel fault strands at 9-km depth resolved on the Imperial Fault,
Southern California, Geophys. Res. Lett., 29(14), 1674, doi: 10.1029/2002GL015302.
Shearer, P. M., E. Hauksson, and G. Lin (2005), Southern California hypocenter
relocation with waveform cross-correlation, Part 2: Results using source-specific
station terms and cluster analysis, Bull. Seismol. Soc. Am., 95(3), 904–915.
Shi, Z., and Y. Ben-Zion (2006), Dynamic rupture on a bimaterial interface governed by
slip-weakening friction, Geophys. J. Int., 165(2), 469–484, doi: 10.1111/j.1365-
246x.2006.02853.x.
Silverman, B. W. (1986), Density Estimation for Statistics and Data Analysis, Chapman
and Hall, New York.
Stirling, M. W., S. G. Wesnousky, and K. Shimazaki (1996), Fault trace complexity,
cumulative slip, and the shape of the magnitude-frequency distribution for strike-slip
faults: a global survey, Geophys. J. Int., 124, 833–868.
Tchalenko, J. S. (1970), Similarities between shear zones of different magnitudes,
Geological Society of America Bulletin, 81, 1625–1640.
Thurber, C., H. Zhang, F. Waldhauser, J. L. Hardebeck, A. J. Michael, and D. Eberhart-
Phillips (2006), Three-Dimensional Compressional Wavespeed Model, Earthquake
Relocations, and Focal Mechanisms for the Parkfield, California, Region, Bull.
Seismol. Soc. Am., 96(4B), S38–S49, doi: 10.1785/0120050825.
Turcotte, D. L. (1997), Fractals and Chaos in Geology and Geophysics, 398 pp.,
Cambridge University Press, Cambridge.
Unsworth, M. J., P. E. Malin, G. D. Egbert, and J. R. Booker (1997), Internal structure of
the San Andreas fault at Parkfield, California, Geology, 25(4), 359–362.
Utsu, T., Y. Ogata, and R. S. Matsu'ura (1995), The centenary of the Omori Formula for
a decay law of aftershock activity, Journal of the Physics of the Earth, 43, 1–33.
Vidale, J. E., and P. M. Shearer (2006), A survey of 71 earthquake bursts across southern
California: Exploring the role of pore fluid pressure fluctuations and aseismic slip as
drivers, J. Geophys. Res., 111, B05312, doi: 10.1029/2005JB004034.
Waldhauser, F., and W. L. Ellsworth (2000), A double-difference earthquake location
algorithm: Method and application to the northern Hayward fault, Bull. Seismol. Soc.
Am., 90, 1353–1368.
Waldhauser, F., W. L. Ellsworth, and A. Cole (1999), Slip-parallel seismic lineations on
the northern Hayward fault, California, Geophys. Res. Lett., 26(23), 3525–3528.
95
Waldhauser, F., W. L. Ellsworth, D. P. Schaff, and A. Cole (2004), Streaks, multiplets,
and holes: High resolution spatio-temporal behavior of Parkfield seismicity, Geophys.
Res. Lett., 31, L18608, doi: 10.1029/2004GL020649.
Wallace, R. E., and H. T. Morris (1986), Characteristics of faults and shear zones in deep
mines, Pure Appl. Geophys., 124(1-2), 107–125.
Weertman, J. (1980), Unstable slippage across a fault that separates elastic media of
different elastic constants, J. Geophys. Res., 85(B3), 1455–1461.
Wesnousky, S. G. (1988), Seismological and structural evolution of strike-slip faults,
Nature, 335, 340–343.
Wesnousky, S. G. (1990), Seismicity as a function of cumulative geologic offset: Some
observations from southern California, Bull. Seismol. Soc. Am., 80(5), 1374–1381.
Wisely, B. A., D. A. Schmidt, and R. J. Weldon (2007), The Uniform California
Earthquake Rupture Forecast, Version 2 (UCERF 2) Appendix P: Compilation of
surface creep on California faults and comparison of WG–07 deformation model to
Pacific-North America plate motion, U.S. Geol. Surv. Open-File Rept., 2007-1437, 43
pp.
Working Group on California Earthquake Probabilities (WGCEP) and the USGS
National Seismic Hazard Mapping Program (NSHMP) (2007), The Uniform
California Earthquake Rupture Forecast, Version 2 (UCERF 2), U.S. Geol. Surv.
Open-File Rept., 2007-1437, 70 pp.
Wu, J., J. A. Hole, A. Snoke, and M. G. Imhof (2008), Depth extent of the fault-zone
seismic waveguide: effects of increasing velocity with depth, Geophys. J. Int., 173(2),
611–622, doi: 10.1111/j.1365-246X.2008.03755.x.
Yule, D., and K. E. Sieh (2003), Complexities of the San Andreas fault near San
Gorgonio Pass: Implications for large earthquake, J. Geophys. Res., 108(B11), 2548.
Zhuang, J., Y. Ogata, and D. Vere-Jones (2004), Analyzing earthquake clustering
features by using stochastic reconstruction, J. Geophys. Res., 109, B05301, doi:
10.1029/2003JB0027879.
Zoback, M. D., S. Hickman, and W. L. Ellsworth (2008), In-situ fault zone observations
from SAFOD, EarthScope Onsite Newsletter (winter).

96
APPENDIX A:
FAULT SEGMENT CATALOG SUMMARIES
The following figures provide (a) detailed seismicity maps, (b) fault-normal depth-
sections, and (c) the fault-normal distribution of seismicity for each fault segment
included in this study . The figures are numbered according to the reference ID’ s listed
in T able 3 and displayed in Figs. 1 and 2. All events are from relocated catalogs and
are displayed in the local fault-referenced coordinate system for the fault segment. For
segments 1–41, events are from catalog P; for segments 42-50, events are from catalog U;
for segments 51-51, events are from catalog T . For clarity , the maps and depth-sections
only show events spanning a limited magnitude range; the histograms include all near -
fault events.
97
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
50
55
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−1. Summary of catalog data for Box 1, Garlock (East).
98
−10 −5 0 5 10
0
5
10
15
20
25
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−2. Summary of catalog data for Box 2, Garlock (Central).
99
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
50
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−3. Summary of catalog data for Box 3, Garlock (West).
100
−10 −5 0 5 10
0
5
10
15
20
25
30
35
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
5
10
15
20
25
30
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−4. Summary of catalog data for Box 4, Lenwood−Lockhart.
101
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
20
40
60
80
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−5. Summary of catalog data for Box 5, San Andreas (Mojave).
102
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
50
55
60
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
5
10
15
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−6. Summary of catalog data for Box 6, Santa Cruz − Catalina Ridge.
103
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
50
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
5
10
15
20
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−7. Summary of catalog data for Box 7, Palos Verdes.
104
−10 −5 0 5 10
0
5
10
15
20
25
30
35
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
10
20
30
40
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−8. Summary of catalog data for Box 8, Newport Inglewood (North).
105
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
10
20
30
40
50
60
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−9. Summary of catalog data for Box 9, Newport Inglewood (South).
106
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
50
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
20
40
60
80
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−10. Summary of catalog data for Box 10, Elsinore − Temecula.
107
−10 −5 0 5 10
0
5
10
15
20
25
30
35
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
500
1000
1500
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−11. Summary of catalog data for Box 11, San Jacinto (Anza).
108
−10 −5 0 5 10
0
5
10
15
20
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
10
20
30
40
50
60
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−12. Summary of catalog data for Box 12, Elsinore − Coyote Mtn..
109
−10 −5 0 5 10
0
5
10
15
20
25
30
35
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−13. Summary of catalog data for Box 13, Cerro Prieto.
1 10
−10 −5 0 5 10
0
5
10
15
20
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−14. Summary of catalog data for Box 14, Imperial.
111
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−15. Summary of catalog data for Box 15, San Andreas (Coachella).
1 12
−10 −5 0 5 10
0
5
10
15
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−16. Summary of catalog data for Box 16, Scodie Lineament.
1 13
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−17. Summary of catalog data for Box 17, San Jacinto (Anza).
1 14
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−18. Summary of catalog data for Box 18, San Jacinto (Anza).
1 15
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
600
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−19. Summary of catalog data for Box 19, San Jacinto (Anza).
1 16
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−20. Summary of catalog data for Box 20, San Jacinto (Coyote Ck.).
1 17
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
250
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−21. Summary of catalog data for Box 21, San Jacinto (Anza).
1 18
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
250
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−22. Summary of catalog data for Box 22, San Jacinto (Coyote Ck.).
1 19
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−23. Summary of catalog data for Box 23, San Jacinto (Anza).
120
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−24. Summary of catalog data for Box 24, San Jacinto (Borrego).
121
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−25. Summary of catalog data for Box 25, Superstition Mtn..
122
−10 −5 0 5 10
0
5
10
15
20
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−26. Summary of catalog data for Box 26, Elmore Ranch.
123
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−27. Summary of catalog data for Box 27, Elmore Ranch (western ext.).
124
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
250
300
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−28. Summary of catalog data for Box 28, Elmore Ranch (western ext.).
125
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
600
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−29. Summary of catalog data for Box 29, Elsinore.
126
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−30. Summary of catalog data for Box 30, Joshua Tree.
127
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−31. Summary of catalog data for Box 31, Joshua Tree.
128
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−32. Summary of catalog data for Box 32, Joshua Tree.
129
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
250
300
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−33. Summary of catalog data for Box 33, Joshua Tree.
130
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
600
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−34. Summary of catalog data for Box 34, Landers.
131
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−35. Summary of catalog data for Box 35, Landers.
132
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−36. Summary of catalog data for Box 36, Landers.
133
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
500
1000
1500
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−37. Summary of catalog data for Box 37, Landers.
134
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−38. Summary of catalog data for Box 38, Landers.
135
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−39. Summary of catalog data for Box 39, Hector Mine.
136
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
600
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−40. Summary of catalog data for Box 40, Hector Mine.
137
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
1000
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−41. Summary of catalog data for Box 41, Hector Mine.
138
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−42. Summary of catalog data for Box 42, Hayward (North).
139
−10 −5 0 5 10
0
5
10
15
20
25
30
35
40
45
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
50
100
150
200
250
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−43. Summary of catalog data for Box 43, Hayward (South).
140
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
1000
2000
3000
4000
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−44. Summary of catalog data for Box 44, Calaveras (North).
141
−10 −5 0 5 10
0
5
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−45. Summary of catalog data for Box 45, Calaveras (Central).
142
−10 −5 0 5 10
0
5
10
15
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−46. Summary of catalog data for Box 46, Calaveras (South).
143
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
200
400
600
800
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−47. Summary of catalog data for Box 47, Sargent.
144
−10 −5 0 5 10
0
5
10
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
500
1000
1500
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−48. Summary of catalog data for Box 48, San Andreas Creeping (North).
145
−10 −5 0 5 10
0
5
10
15
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
500
1000
1500
2000
2500
3000
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−49. Summary of catalog data for Box 49, San Andreas Creeping (Central).
146
−10 −5 0 5 10
0
5
10
15
20
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
1000
2000
3000
4000
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−50. Summary of catalog data for Box 50, San Andreas Creeping (South).
147
−10 −5 0 5 10
0
5
10
15
20
25
30
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
500
1000
1500
2000
2500
3000
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−51. Summary of catalog data for Box 51, San Andreas Parkfield (North).
148
−10 −5 0 5 10
0
5
10
15
20
25
30
Fault−normal Distance (km)
Fault−parallel Distance (km)
(a) Map View
M < 2
M ≥ 2
−10 −5 0 5 10
−15
−10
−5
0
Fault−normal Distance (km)
Depth (km)
(b) Depth Section
M < 2
M ≥ 2
−10 −5 0 5 10
0
100
200
300
400
500
Fault−normal Distance (km)
Events / km
(c) Fault−normal Distribution
Figure A−52. Summary of catalog data for Box 52, San Andreas Parkfield (South).
149
APPENDIX B:
CATALOG ANALYSIS RESULTS
The following tables provide values of intercatalog and catalog-specific location bias
and variation for each fault segment. Catalog subscripts in column headers are identical
to those used in Tables 4 and 5.
150
Fault Class: σ
HS
σ
PS
σ
HP
Ref. Segment Name x y z x y z x y z
Southern California Large Faults:
1 Garlock (East) 0.53 0.72 1.56 0.50 0.61 1.49 0.49 0.50 1.33
2 Garlock (Central) 1.06 0.87 2.60 1.05 0.88 2.52 0.47 0.27 1.39
3 Garlock (West) 1.17 1.75 2.95 1.13 1.59 3.06 0.64 0.84 1.34
4 Lenwood - Lockhart 0.60 0.43 3.54 0.68 0.36 3.26 0.48 0.24 1.95
5 San Andreas (Mojave) 0.47 0.71 1.21 0.45 0.62 1.27 0.29 0.53 0.88
6 Santa Cruz - Catalina Ridge 1.64 1.24 4.08 1.67 1.26 4.30 1.97 1.14 3.81
7 Palos Verdes 1.19 2.06 4.75 1.09 1.69 3.70 1.27 1.74 5.09
8 Newport Inglewood (North) 1.96 1.45 4.75 1.83 1.26 4.71 1.36 1.01 3.67
9 Newport Inglewood (South) 1.81 1.09 4.09 1.90 1.02 4.08 1.46 0.66 3.08
10 Elsinore - Temecula 0.89 0.89 2.43 0.72 0.62 2.02 0.73 0.75 2.00
11 San Jacinto (Anza) 0.97 0.82 2.20 0.90 0.75 2.14 0.55 0.57 1.20
12 Elsinore - Coyote Mtn. 0.98 0.77 2.43 0.82 0.63 2.42 0.86 0.59 2.10
13 Cerro Prieto 2.09 2.14 4.07 1.92 2.14 4.72 1.18 1.48 4.01
14 Imperial 1.02 1.51 4.55 0.98 1.48 4.59 0.38 0.67 1.97
15 San Andreas (Coachella) 0.69 0.84 2.17 0.83 0.88 1.95 0.58 0.47 1.61
Weighted mean variation: 1.14 1.23 3.09 1.08 1.16 3.12 0.74 0.77 2.15
Southern California Small Faults:
16 Scodie Lineament 0.65 0.44 1.53 0.65 0.45 1.58 0.28 0.26 0.62
17 San Jacinto (Anza) 0.67 0.69 1.88 0.63 0.65 1.86 0.27 0.26 0.93
18 San Jacinto (Anza) 0.76 0.59 4.08 0.72 0.57 3.71 0.35 0.31 2.35
19 San Jacinto (Anza) 0.86 0.60 3.52 0.82 0.57 3.16 0.19 0.22 1.52
20 San Jacinto (Coyote Ck.) 0.73 0.94 3.05 0.68 0.85 2.58 0.34 0.35 1.81
21 San Jacinto (Anza) 0.69 0.80 2.64 0.64 0.79 2.28 0.29 0.26 1.15
22 San Jacinto (Coyote Ck.) 0.78 0.76 1.99 0.73 0.72 1.64 0.41 0.34 1.45
23 San Jacinto (Anza) 0.87 1.01 2.61 0.77 0.95 2.45 0.46 0.57 1.69
24 San Jacinto (Borrego) 1.02 0.92 2.08 0.98 0.88 1.64 0.51 0.51 1.19
25 Superstition Mtn. 1.11 1.05 2.56 1.10 0.99 2.62 0.39 0.46 1.19
26 Elmore Ranch 1.38 1.28 2.56 1.03 1.09 2.68 0.96 1.11 2.46
27 Elmore Ranch (western ext.) 0.51 0.97 2.17 0.50 0.83 2.01 0.30 0.65 1.60
28 Elmore Ranch (western ext.) 0.65 0.96 1.65 0.72 0.91 1.66 0.44 0.69 0.89
29 Elsinore 0.61 0.91 2.33 0.56 0.87 2.25 0.31 0.36 1.44
Weighted mean variation: 0.80 0.82 2.62 0.75 0.77 2.41 0.40 0.45 1.52
Southern California Aftershocks:
30 Joshua Tree 0.58 0.50 1.42 0.55 0.47 1.37 0.28 0.22 0.62
31 Joshua Tree 0.50 0.66 1.20 0.47 0.62 1.16 0.26 0.35 0.72
32 Joshua Tree 0.46 0.55 1.89 0.44 0.53 1.80 0.25 0.23 1.15
33 Joshua Tree 0.41 0.56 2.09 0.42 0.52 2.19 0.34 0.32 1.64
34 Landers 0.44 0.92 2.69 0.38 0.78 2.10 0.37 0.65 1.95
35 Landers 0.55 0.76 3.05 0.48 0.67 2.53 0.45 0.58 2.35
36 Landers 0.76 0.81 1.81 0.65 0.67 1.45 0.44 0.51 1.34
37 Landers 0.75 0.89 1.98 0.69 0.81 1.81 0.38 0.41 1.02
38 Landers 0.54 0.75 1.84 0.48 0.69 1.75 0.39 0.41 1.19
39 Hector Mine 0.81 0.68 2.28 0.66 0.59 1.89 0.60 0.58 1.53
40 Hector Mine 0.71 0.54 3.35 0.57 0.48 2.97 0.58 0.47 1.99
41 Hector Mine 0.64 0.66 2.80 0.56 0.60 2.20 0.48 0.46 1.96
Weighted mean variation: 0.62 0.70 2.25 0.55 0.63 1.97 0.41 0.44 1.49
Table B-1. Intercatalog event variation for southern California faults.
151
Fault Class σ
S
σ
P
σ
H
Ref. Segment Name x y z x y z x y z
Southern California Large Faults:
1 Garlock (East) 0.38 0.56 1.20 0.33 0.23 0.89 0.37 0.44 0.99
2 Garlock (Central) 1.00 0.86 2.36 0.31 0.21 0.88 0.35 0.17 1.07
3 Garlock (West) 1.06 1.56 2.85 0.39 0.28 1.12 0.51 0.79 0.73
4 Lenwood - Lockhart 0.55 0.36 3.11 0.41 0.03 0.98 0.25 0.24 1.69
5 San Andreas (Mojave) 0.41 0.55 1.07 0.18 0.28 0.68 0.23 0.45 0.56
6 Santa Cruz - Catalina Ridge 0.90 0.95 3.21 1.41 0.82 2.86 1.37 0.79 2.51
7 Palos Verdes 0.70 1.43 2.27 0.83 0.91 2.92 0.96 1.48 4.17
8 Newport Inglewood (North) 1.63 1.16 3.95 0.83 0.51 2.56 1.08 0.87 2.63
9 Newport Inglewood (South) 1.54 0.95 3.46 1.11 0.37 2.16 0.95 0.54 2.19
10 Elsinore - Temecula 0.62 0.55 1.73 0.37 0.28 1.04 0.63 0.69 1.71
11 San Jacinto (Anza) 0.86 0.68 2.00 0.29 0.33 0.76 0.46 0.47 0.93
12 Elsinore - Coyote Mtn. 0.67 0.57 1.91 0.48 0.28 1.47 0.71 0.52 1.49
13 Cerro Prieto 1.82 1.87 3.37 0.59 1.05 3.30 1.02 1.05 2.27
14 Imperial 0.96 1.42 4.35 0.19 0.41 1.45 0.33 0.53 1.34
15 San Andreas (Coachella) 0.64 0.79 1.72 0.53 0.38 0.92 0.24 0.28 1.32
Weighted mean variation: 0.98 1.07 2.71 0.45 0.45 1.55 0.58 0.62 1.50
Southern California Small Faults:
16 Scodie Lineament 0.62 0.41 1.49 0.18 0.19 0.52 0.21 0.17 0.34
17 San Jacinto (Anza) 0.62 0.64 1.75 0.12 0.08 0.62 0.24 0.25 0.69
18 San Jacinto (Anza) 0.70 0.54 3.53 0.19 0.20 1.14 0.30 0.24 2.05
19 San Jacinto (Anza) 0.82 0.56 3.17 0.12 0.10 0.22 0.23 0.19 1.54
20 San Jacinto (Coyote Ck.) 0.66 0.86 2.52 0.16 0.15 0.56 0.30 0.39 1.71
21 San Jacinto (Anza) 0.63 0.77 2.33 0.12 0.16 0.46 0.27 0.20 1.24
22 San Jacinto (Coyote Ck.) 0.70 0.70 1.51 0.21 0.14 0.64 0.35 0.30 1.29
23 San Jacinto (Anza) 0.76 0.89 2.23 0.16 0.32 1.02 0.44 0.47 1.36
24 San Jacinto (Borrego) 0.93 0.82 1.67 0.30 0.31 0.34 0.40 0.40 1.23
25 Superstition Mtn. 1.07 0.97 2.45 0.27 0.21 0.92 0.29 0.40 0.76
26 Elmore Ranch 1.01 0.89 1.96 0.20 0.63 1.83 0.94 0.91 1.65
27 Elmore Ranch (western ext.) 0.46 0.77 1.75 0.19 0.30 0.98 0.24 0.58 1.27
28 Elmore Ranch (western ext.) 0.61 0.80 1.53 0.38 0.44 0.64 0.22 0.53 0.61
29 Elsinore 0.54 0.85 2.05 0.15 0.16 0.93 0.28 0.32 1.11
Weighted mean variation: 0.72 0.73 2.28 0.19 0.24 0.78 0.35 0.38 1.30
Southern California Aftershocks:
30 Joshua Tree 0.53 0.46 1.32 0.15 0.09 0.35 0.24 0.20 0.52
31 Joshua Tree 0.44 0.59 1.06 0.15 0.18 0.46 0.22 0.29 0.55
32 Joshua Tree 0.42 0.52 1.65 0.16 0.12 0.70 0.19 0.20 0.91
33 Joshua Tree 0.34 0.49 1.80 0.25 0.18 1.25 0.24 0.27 1.06
34 Landers 0.32 0.72 1.98 0.21 0.31 0.71 0.30 0.57 1.82
35 Landers 0.41 0.59 2.25 0.25 0.33 1.15 0.38 0.48 2.05
36 Landers 0.63 0.65 1.34 0.15 0.18 0.57 0.41 0.47 1.22
37 Landers 0.67 0.80 1.76 0.17 0.12 0.43 0.34 0.39 0.92
38 Landers 0.43 0.66 1.58 0.22 0.22 0.75 0.33 0.35 0.93
39 Hector Mine 0.61 0.49 1.79 0.25 0.33 0.60 0.54 0.48 1.41
40 Hector Mine 0.49 0.39 2.83 0.28 0.29 0.89 0.50 0.37 1.78
41 Hector Mine 0.49 0.54 2.10 0.26 0.26 0.66 0.40 0.38 1.84
Weighted mean variation: 0.50 0.59 1.83 0.21 0.22 0.71 0.36 0.38 1.30
Table B-2. Catalog-specific event variation for southern California faults.
152
Fault Class b
HS
b
PS
b
HP
Ref. Segment Name x y z x y z x y z
Southern California Large Faults:
1 Garlock (East) -1.01 -0.21 1.22 -0.16 0.15 1.41 0.85 0.37 0.19
2 Garlock (Central) 0.62 0.39 1.34 1.16 0.24 0.18 0.53 -0.15 -1.15
3 Garlock (West) -0.82 -1.09 3.58 -1.10 -1.06 2.01 -0.28 0.03 -1.57
4 Lenwood - Lockhart -0.32 0.52 4.08 -0.46 0.06 4.36 -0.14 -0.46 0.29
5 San Andreas (Mojave) -0.14 0.07 0.55 0.22 0.09 0.54 0.36 0.02 -0.01
6 Santa Cruz - Catalina Ridge -1.91 -0.48 2.58 -0.64 -0.43 3.45 1.27 0.05 0.87
7 Palos Verdes 0.35 -2.24 2.22 -0.61 -0.51 1.90 -0.97 1.73 -0.31
8 Newport Inglewood (North) 0.12 -2.00 0.04 -0.90 -0.63 1.72 -1.01 1.37 1.68
9 Newport Inglewood (South) 1.52 -0.77 -2.32 0.43 -0.72 0.82 -1.10 0.05 3.13
10 Elsinore - Temecula 0.58 0.09 0.72 0.14 0.05 0.69 -0.45 -0.04 -0.03
11 San Jacinto (Anza) 0.50 0.33 0.93 0.40 -0.11 0.74 -0.10 -0.43 -0.19
12 Elsinore - Coyote Mtn. -0.33 -0.66 0.80 0.20 -0.09 0.64 0.53 0.57 -0.16
13 Cerro Prieto -2.91 -1.72 2.25 -1.73 -0.98 3.46 1.18 0.75 1.21
14 Imperial -0.45 -0.56 -1.20 0.39 -0.17 2.08 0.85 0.39 3.28
15 San Andreas (Coachella) 0.15 -0.42 0.87 -0.26 -0.56 -0.63 -0.41 -0.15 -1.50
Weighted mean absolute value: 0.74 0.61 1.36 0.57 0.33 1.36 0.59 0.35 1.06
Southern California Small Faults:
16 Scodie Lineament -0.11 0.01 0.60 0.22 0.09 0.28 0.33 0.09 -0.31
17 San Jacinto (Anza) -0.03 0.41 1.61 0.39 -0.08 0.46 0.42 -0.49 -1.15
18 San Jacinto (Anza) 0.92 0.16 1.13 0.70 -0.14 1.00 -0.22 -0.30 -0.13
19 San Jacinto (Anza) 0.37 0.49 1.86 0.57 0.16 1.35 0.20 -0.33 -0.51
20 San Jacinto (Coyote Ck.) 0.66 0.10 2.41 0.53 -0.27 0.95 -0.14 -0.37 -1.46
21 San Jacinto (Anza) 0.74 -0.06 2.72 0.50 -0.22 1.23 -0.24 -0.16 -1.49
22 San Jacinto (Coyote Ck.) 0.29 0.07 2.19 0.27 -0.32 0.60 -0.02 -0.39 -1.60
23 San Jacinto (Anza) -0.04 0.53 3.28 0.12 -0.03 1.36 0.16 -0.56 -1.92
24 San Jacinto (Borrego) 0.72 0.11 1.42 0.67 -0.30 1.02 -0.04 -0.40 -0.40
25 Superstition Mtn. -1.35 -0.50 -3.55 -0.17 0.12 -1.34 1.19 0.62 2.21
26 Elmore Ranch 0.61 -0.08 2.12 0.72 0.09 4.18 0.10 0.17 2.06
27 Elmore Ranch (western ext.) 1.12 -0.94 -0.75 0.45 -0.08 0.28 -0.68 0.86 1.03
28 Elmore Ranch (western ext.) 0.78 -0.44 0.13 0.92 -1.04 0.55 0.13 -0.60 0.42
29 Elsinore 0.14 0.03 1.33 -0.06 0.39 0.47 -0.20 0.36 -0.87
Weighted mean absolute value: 0.47 0.23 1.69 0.43 0.24 0.96 0.24 0.37 0.98
Southern California Aftershocks:
30 Joshua Tree -0.52 0.11 1.41 -0.56 0.09 0.74 -0.05 -0.02 -0.67
31 Joshua Tree -0.41 0.12 1.63 -0.37 0.11 0.79 0.04 -0.01 -0.83
32 Joshua Tree 0.03 0.18 2.09 -0.13 0.11 0.74 -0.15 -0.07 -1.35
33 Joshua Tree -0.02 0.09 2.13 -0.29 0.01 1.84 -0.27 -0.08 -0.29
34 Landers 0.15 0.37 2.91 0.07 0.01 1.15 -0.08 -0.36 -1.75
35 Landers 0.21 0.39 3.84 0.41 0.45 1.99 0.20 0.06 -1.85
36 Landers 0.19 0.26 1.77 0.24 0.20 0.90 0.06 -0.05 -0.87
37 Landers -0.08 -0.44 2.60 0.29 -0.84 1.69 0.37 -0.40 -0.91
38 Landers -0.41 -0.43 2.24 -0.04 -0.77 0.95 0.36 -0.34 -1.29
39 Hector Mine -0.10 -0.11 1.53 -0.27 -0.05 0.95 -0.17 0.07 -0.58
40 Hector Mine -0.06 -0.07 1.51 -0.26 -0.15 1.24 -0.20 -0.08 -0.27
41 Hector Mine 0.01 -0.14 2.09 -0.10 -0.23 0.78 -0.11 -0.10 -1.30
Weighted mean absolute value: 0.18 0.22 2.06 0.24 0.27 1.09 0.17 0.14 0.97
Table B-3. Intercatalog event bias for southern California faults.
153
Fault Class b
S
b
P
b
H
Ref. Segment Name x y z x y z x y z
Southern California Large Faults:
1 Garlock (East) -0.39 -0.02 0.88 -0.23 -0.17 -0.54 0.62 0.19 -0.34
2 Garlock (Central) 0.59 0.21 0.51 -0.56 -0.03 0.32 -0.03 -0.18 -0.83
3 Garlock (West) -0.64 -0.71 1.86 0.46 0.34 -0.15 0.18 0.37 -1.72
4 Lenwood - Lockhart -0.26 0.19 2.81 0.20 0.14 -1.55 0.06 -0.33 -1.26
5 San Andreas (Mojave) 0.02 0.05 0.36 -0.19 -0.04 -0.18 0.17 -0.01 -0.19
6 Santa Cruz - Catalina Ridge -0.85 -0.31 2.01 -0.21 0.13 -1.44 1.06 0.18 -0.57
7 Palos Verdes -0.09 -0.92 1.37 0.53 -0.41 -0.53 -0.44 1.32 -0.84
8 Newport Inglewood (North) -0.26 -0.88 0.59 0.64 -0.25 -1.13 -0.38 1.12 0.55
9 Newport Inglewood (South) 0.65 -0.50 -0.50 0.22 0.22 -1.32 -0.87 0.27 1.82
10 Elsinore - Temecula 0.24 0.05 0.47 0.10 0.00 -0.22 -0.34 -0.04 -0.25
11 San Jacinto (Anza) 0.30 0.07 0.56 -0.10 0.18 -0.18 -0.20 -0.25 -0.37
12 Elsinore - Coyote Mtn. -0.04 -0.25 0.48 -0.24 -0.16 -0.16 0.28 0.41 -0.32
13 Cerro Prieto -1.55 -0.90 1.90 0.19 0.08 -1.56 1.36 0.82 -0.35
14 Imperial -0.02 -0.24 0.30 -0.41 -0.07 -1.79 0.43 0.31 1.49
15 San Andreas (Coachella) -0.04 -0.33 0.08 0.22 0.24 0.71 -0.18 0.09 -0.79
Weighted mean absolute value: 0.37 0.29 0.76 0.28 0.13 0.69 0.40 0.32 0.72
Southern California Small Faults:
16 Scodie Lineament 0.04 0.03 0.29 -0.18 -0.06 0.01 0.15 0.03 -0.30
17 San Jacinto (Anza) 0.12 0.11 0.69 -0.27 0.19 0.23 0.15 -0.30 -0.92
18 San Jacinto (Anza) 0.54 0.00 0.71 -0.16 0.15 -0.29 -0.38 -0.15 -0.42
19 San Jacinto (Anza) 0.31 0.22 1.07 -0.26 0.06 -0.28 -0.06 -0.27 -0.79
20 San Jacinto (Coyote Ck.) 0.40 -0.06 1.12 -0.13 0.21 0.17 -0.27 -0.15 -1.29
21 San Jacinto (Anza) 0.41 -0.10 1.32 -0.09 0.13 0.09 -0.33 -0.03 -1.40
22 San Jacinto (Coyote Ck.) 0.19 -0.08 0.93 -0.08 0.24 0.33 -0.10 -0.15 -1.26
23 San Jacinto (Anza) 0.03 0.17 1.55 -0.10 0.19 0.19 0.07 -0.36 -1.73
24 San Jacinto (Borrego) 0.46 -0.06 0.82 -0.21 0.23 -0.21 -0.25 -0.17 -0.61
25 Superstition Mtn. -0.51 -0.12 -1.63 -0.34 -0.25 -0.29 0.85 0.37 1.92
26 Elmore Ranch 0.44 0.00 2.10 -0.27 -0.09 -2.08 -0.17 0.08 -0.02
27 Elmore Ranch (western ext.) 0.52 -0.34 -0.16 0.08 -0.26 -0.44 -0.60 0.60 0.60
28 Elmore Ranch (western ext.) 0.57 -0.49 0.23 -0.35 0.55 -0.33 -0.22 -0.05 0.10
29 Elsinore 0.03 0.14 0.60 0.09 -0.25 0.13 -0.11 0.11 -0.73
Weighted mean absolute value: 0.28 0.12 0.88 0.18 0.19 0.30 0.22 0.18 0.82
Southern California Aftershocks:
30 Joshua Tree -0.36 0.07 0.72 0.20 -0.02 -0.02 0.16 -0.04 -0.69
31 Joshua Tree -0.26 0.08 0.81 0.11 -0.03 0.01 0.15 -0.04 -0.82
32 Joshua Tree -0.03 0.10 0.94 0.09 -0.01 0.21 -0.06 -0.08 -1.15
33 Joshua Tree -0.11 0.03 1.32 0.19 0.02 -0.51 -0.08 -0.06 -0.81
34 Landers 0.07 0.13 1.35 0.01 0.12 0.20 -0.08 -0.24 -1.55
35 Landers 0.20 0.28 1.94 -0.20 -0.17 -0.05 0.00 -0.11 -1.90
36 Landers 0.14 0.15 0.89 -0.10 -0.05 -0.01 -0.04 -0.10 -0.88
37 Landers 0.07 -0.42 1.43 -0.22 0.41 -0.26 0.15 0.01 -1.17
38 Landers -0.15 -0.40 1.07 -0.11 0.37 0.11 0.26 0.03 -1.18
39 Hector Mine -0.12 -0.05 0.83 0.14 -0.01 -0.12 -0.02 0.06 -0.70
40 Hector Mine -0.11 -0.08 0.92 0.15 0.08 -0.33 -0.05 0.00 -0.59
41 Hector Mine -0.03 -0.12 0.96 0.07 0.11 0.17 -0.04 0.01 -1.13
Weighted mean absolute value: 0.13 0.16 1.05 0.13 0.12 0.16 0.10 0.06 1.01
Table B-4. Catalog-specific event bias for southern California faults.
154
b
UN
σ
UN
Ref. Segment Name
x y z
x y
z
42 Hayward (North) 0.03 0.03 0.11 0.29 0.27 0.59
43 Hayward (South) 0.00 0.04 0.13 0.29 0.23 0.45
44 Calaveras (North) -0.02 0.01 0.14 0.16 0.17 0.48
45 Calaveras (Central) -0.16 -0.07 -0.06 0.37 0.35 0.74
46 Calaveras (South) 0.07 0.00 0.10 0.21 0.22 0.46
47 Sargent 0.09 -0.01 0.21 0.35 0.35 0.71
48 San Andreas Creeping (North) 0.17 0.05 0.02 0.56 0.34 0.63
49 San Andreas Creeping (Central) -0.02 0.02 0.06 0.22 0.14 0.34
50 San Andreas Creeping (South) -0.05 -0.01 0.10 0.17 0.16 0.37
Weighted mean absolute value: 0.10 0.03 0.15
Weighted mean variation: 0.30 0.24 0.52
b
UT
σ
UT
51 San Andreas Parkfield (North) 0.51 0.14 -0.74 0.70 0.31 0.84
52 San Andreas Parkfield (South) 0.30 0.13 0.08 0.45 0.39 0.66
Weighted mean absolute value: 0.47 0.13 0.60
Weighted mean variation: 0.68 0.32 0.82
Table B-5. Intercatalog event bias and variation for northern California faults.
155
APPENDIX C:
UNIFORM REDUCTION OF ERROR
(SUPPLEMENTARY FIGURES)
The following figures illustrate the corrections made to estimates of intercatalog
uncertainty for each fault class using a method of uniform reduction [Jeffreys, 1932;
Buland , 1986]. Each figure shows logarithmic and linear distributions of fault-normal
intercatalog location variation between matching events for dif ferent catalog pairs
(indicated by subscripts), less the intercatalog bias of the corresponding fault segment.
The dashed lines mark a Gaussian distribution with a standard deviation computed from
the intercatalog values. The solid lines are Gaussian fits to the observations that ignore
the outliers (heavy tails) of the observed distributions and provide an improved estimate
of fault-normal location uncertainty . The results of this analysis are summarized in T able
4.
156
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
∆x
HS
−b
HS
Distribution
log p(x)
(a)
σ
obs
= 1.14
σ
fit
= 0.75
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
∆x
HS
−b
HS
Distribution
p(x)
(b)
σ
obs
= 1.14
σ
fit
= 0.75
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
∆x
PS
−b
PS
Distribution
log p(x)
(c)
σ
obs
= 1.08
σ
fit
= 0.72
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
∆x
PS
−b
PS
Distribution
p(x)
(d)
σ
obs
= 1.08
σ
fit
= 0.72
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
10
1
∆x
HP
−b
HP
Distribution
log p(x)
(e)
σ
obs
= 0.74
σ
fit
= 0.25
−3 −2 −1 0 1 2 3
0
0.5
1
1.5
∆x
HP
−b
HP
Distribution
p(x)
(f)
σ
obs
= 0.74
σ
fit
= 0.25
Figure C–1 . Uniform reduction of error , lar ge SoCal lar ge faults.
157
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
∆x
HS
−b
HS
Distribution
log p(x)
(a)
σ
obs
= 0.8
σ
fit
= 0.6
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
∆x
HS
−b
HS
Distribution
p(x)
(b)
σ
obs
= 0.8
σ
fit
= 0.6
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
∆x
PS
−b
PS
Distribution
log p(x)
(c)
σ
obs
= 0.75
σ
fit
= 0.58
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
∆x
PS
−b
PS
Distribution
p(x)
(d)
σ
obs
= 0.75
σ
fit
= 0.58
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
10
1
∆x
HP
−b
HP
Distribution
log p(x)
(e)
σ
obs
= 0.4
σ
fit
= 0.15
−3 −2 −1 0 1 2 3
0
0.5
1
1.5
2
2.5
3
∆x
HP
−b
HP
Distribution
p(x)
(f)
σ
obs
= 0.4
σ
fit
= 0.15
Figure C–2 . Uniform reduction of error , small SoCal faults.
158
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
∆x
HS
−b
HS
Distribution
log p(x)
(a)
σ
obs
= 0.62
σ
fit
= 0.42
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
1
∆x
HS
−b
HS
Distribution
p(x)
(b)
σ
obs
= 0.62
σ
fit
= 0.42
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
∆x
PS
−b
PS
Distribution
log p(x)
(c)
σ
obs
= 0.55
σ
fit
= 0.39
−3 −2 −1 0 1 2 3
0
0.2
0.4
0.6
0.8
1
∆x
PS
−b
PS
Distribution
p(x)
(d)
σ
obs
= 0.55
σ
fit
= 0.39
−3 −2 −1 0 1 2 3
10
−2
10
−1
10
0
10
1
∆x
HP
−b
HP
Distribution
log p(x)
(e)
σ
obs
= 0.41
σ
fit
= 0.19
−3 −2 −1 0 1 2 3
0
0.5
1
1.5
2
2.5
∆x
HP
−b
HP
Distribution
p(x)
(f)
σ
obs
= 0.41
σ
fit
= 0.19
Figure C–3. Uniform reduction of error , aftershock-dominated segments.
159
−2 −1 0 1 2
10
−3
10
−2
10
−1
10
0
10
1
∆x
UN
−b
UN
Distribution
log p(x)
(a)
σ
obs
= 0.62
σ
fit
= 0.42
−2 −1 0 1 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
∆x
UN
−b
UN
Distribution
p(x)
(b)
σ
obs
= 0.62
σ
fit
= 0.42
Figure C–4. Uniform reduction of error , lar ge NoCal faults.
160
−2 −1 0 1 2
10
−3
10
−2
10
−1
10
0
10
1
∆x
UN
−b
UN
Distribution
log p(x)
(a)
σ
obs
= 0.62
σ
fit
= 0.42
−2 −1 0 1 2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
∆x
UN
−b
UN
Distribution
p(x)
(b)
σ
obs
= 0.62
σ
fit
= 0.42
Figure C–5. Uniform reduction of error , Parkfield segments.
161
APPENDIX D:
SCALING ANALYSIS
(SUPPLEMENTARY FIGURES)
The following figures illustrate the fault-seismicity scaling analysis for all fault
classes using events from both regional and relocated catalogs. In addition to an analysis
of the entire catalog of events for a particular fault class, analyses of clustered (triggered)
and independent (background) events were also performed. Each figure gives the
maximum likelihood solutions for the scaling parameters ( γ , d, and ν
0
; see also equation
12) and includes the maximum likelihood error estimates for γ and d. For each fault-
normal earthquake density distribution, the nearest-neighbor bin interval is given by q.
The heavy dashed line marks x
max
, the fitting limit of the data, beyond which background
seismicity dominates. Results from this analysis are summarized in T able 6.
162
Figure D–1. Scaling analysis of lar ge SoCal faults (all events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 3 ± 0 .0 3
˜ γ = 0 .9 7 8 ± 0 .0 1 8
˜ ν
0
= 1 1
q = 5 0
(a) Catalog P
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 6 8 ± 0 .0 3 2
˜ γ = 0 .9 8 ± 0 .0 2
˜ ν
0
= 9
q = 5 0
(b) Catalog H
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .8 7 5 ± 0 .0 8 5
˜ γ = 1 .1 9 ± 0 .0 3
˜ ν
0
= 5
q = 5 0
(c) Catalog S
163
Figure D–1 (Continued). Maximum likelihood errors.
0.9 0.95 1 1.05 1.1 1.15 1.2 1.25
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
˜ γ
˜
d ( k m )
164
Figure D–2. Scaling analysis of lar ge SoCal faults (independent events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 3 6 ± 0 .0 3 4
˜ γ = 0 .9 2 6 ± 0 .0 1 6
˜ ν
0
= 8
q = 3 0
(a) Catalog P (declustered)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 7 8 ± 0 .0 4 2
˜ γ = 0 .9 3 6 ± 0 .0 1 6
˜ ν
0
= 7
q = 3 0
(b) Catalog H (declustered)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .8 6 ± 0 .0 9
˜ γ = 1 .1 2 ± 0 .0 3
˜ ν
0
= 4
q = 3 0
(c) Catalog S (declustered)
165
Figure D–2 (Continued). Maximum likelihood errors.
0.85 0.9 0.95 1 1.05 1.1 1.15 1.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
˜ γ
˜
d ( k m )
166
Figure D–3. Scaling analysis of lar ge SoCal faults (clustered events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 3 6 ± 0 .0 4 4
˜ γ = 1 .2 1 6 ± 0 .0 5 4
˜ ν
0
= 3
q = 1 0
(a) Catalog P (clusters)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 6 6 ± 0 .0 5 4
˜ γ = 1 .1 7 8 ± 0 .0 5 2
˜ ν
0
= 3
q = 1 0
(b) Catalog H (clusters)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .9 4 5 ± 0 .1 8 5
˜ γ = 1 .5 0 5 ± 0 .1 1 5
˜ ν
0
= 1
q = 1 0
(c) Catalog S (clusters)
167
Figure D–3 (Continued). Maximum likelihood errors.
1.1 1.2 1.3 1.4 1.5 1.6 1.7
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
˜ γ
˜
d ( k m )
168
Figure D–4. Scaling analysis of small SoCal faults (all events).
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .1 9 4 ± 0 .0 1 6
˜ γ = 1 .3 6 9 ± 0 .0 8 1
˜ ν
0
= 1 3 0
q = 4 0
(a) Catalog P
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 2 8 ± 0 .0 2 2
˜ γ = 1 .4 4 3 ± 0 .0 8 7
˜ ν
0
= 1 2 0
q = 4 0
(b) Catalog H
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .7 8 6 ± 0 .1 1 4
˜ γ = 1 .8 9 6 ± 0 .3 0 4
˜ ν
0
= 5 3
q = 4 0
(c) Catalog S
169
Figure D–4 (Continued). Maximum likelihood errors.
1.2 1.4 1.6 1.8 2 2.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
˜ γ
˜
d ( k m )
170
Figure D–5. Scaling analysis of small SoCal faults (independent events).
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .1 8 5 ± 0 .0 2 5
˜ γ = 1 .2 6 8 ± 0 .0 8 2
˜ ν
0
= 8 2
q = 2 0
(a) Catalog P (declustered)
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 1 7 ± 0 .0 2 7
˜ γ = 1 .3 5 4 ± 0 .0 9 6
˜ ν
0
= 7 7
q = 2 0
(b) Catalog H (declustered)
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .8 6 ± 0 .1 8
˜ γ = 1 .8 5 6 ± 0 .4 4 4
˜ ν
0
= 3 4
q = 2 0
(c) Catalog S (declustered)
171
Figure D–5 (Continued). Maximum likelihood errors.
1.2 1.4 1.6 1.8 2 2.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
˜ γ
˜
d ( k m )
172
Figure D–6. Scaling analysis of small SoCal faults (clustered events).
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 1 8 ± 0 .0 3 2
˜ γ = 1 .6 1 6 ± 0 .1 7 4
˜ ν
0
= 4 5
q = 1 0
(a) Catalog P (clusters)
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .2 6 6 ± 0 .0 4 4
˜ γ = 1 .7 0 6 ± 0 .1 9 4
˜ ν
0
= 4 0
q = 1 0
(b) Catalog H (clusters)
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .7 3 ± 0 .1 7
˜ γ = 2 .1 6 5 ± 0 .5 3 5
˜ ν
0
= 2 0
q = 1 0
(c) Catalog S (clusters)
173
Figure D–6 (Continued). Maximum likelihood errors.
1.4 1.6 1.8 2 2.2 2.4 2.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
˜ γ
˜
d ( k m )
174
Figure D–7. Scaling analysis of aftershock-dominated faults (all events).
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .3 2 8 ± 0 .0 2 2
˜ γ = 1 .5 0 4 ± 0 .0 6 6
˜ ν
0
= 2 3 0
q = 5 0
(a) Catalog P
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .3 0 8 ± 0 .0 2 2
˜ γ = 1 .4 4 ± 0 .0 6
˜ ν
0
= 2 3 0
q = 5 0
(b) Catalog H
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .5 5 2 ± 0 .0 4 2
˜ γ = 1 .6 2 8 ± 0 .1 0 2
˜ ν
0
= 1 6 0
q = 5 0
(c) Catalog S
175
Figure D–7 (Continued). Maximum likelihood errors.
1.35 1.4 1.45 1.5 1.55 1.6 1.65 1.7 1.75
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
˜ γ
˜
d ( k m )
176
Figure D–8. Scaling analysis of lar ge NoCal faults (all events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .0 8 1 ± 0 .0 0 9
˜ γ = 1 . 6 ± 0 .0 4
˜ ν
0
= 3 0 0
q = 4 0
(a) Catalog U
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .1 6 1 ± 0 .0 1 1
˜ γ = 1 .6 8 2 ± 0 .0 5 8
˜ ν
0
= 1 7 0
q = 4 0
(b) Catalog N
177
Figure D–8 (Continued). Maximum likelihood errors.
1.55 1.6 1.65 1.7 1.75
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
˜ γ
˜
d ( k m )
178
Figure D–9. Scaling analysis of lar ge NoCal faults (independent events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .0 9 8 ± 0 .0 1 2
˜ γ = 1 .6 2 2 ± 0 .0 6 8
˜ ν
0
= 1 2 0
q = 2 0
(a) Catalog U (declustered)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .1 8 ± 0 .0 2
˜ γ = 1 .7 3 4 ± 0 .0 9 6
˜ ν
0
= 7 1
q = 2 0
(b) Catalog N (declustered)
179
Figure D–9 (Continued). Maximum likelihood errors.
1.5 1.55 1.6 1.65 1.7 1.75 1.8 1.85 1.9
0.05
0.1
0.15
0.2
˜ γ
˜
d ( k m )
180
Figure D–10. Scaling analysis of lar ge NoCal faults (clustered events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .0 7 2 ± 0 .0 0 8
˜ γ = 1 .6 0 6 ± 0 .0 5 4
˜ ν
0
= 1 9 0
q = 2 0
(a) Catalog U (clusters)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .1 5 2 ± 0 .0 1 8
˜ γ = 1 .6 6 ± 0 .0 7
˜ ν
0
= 9 8
q = 2 0
(b) Catalog N (clusters)
181
Figure D–10 (Continued). Maximum likelihood errors.
1.5 1.55 1.6 1.65 1.7 1.75 1.8
0.05
0.1
0.15
0.2
˜ γ
˜
d ( k m )
182
Figure D–11. Scaling analysis of Parkfield segments (all events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .1 3 2 ± 0 .0 1 2
˜ γ = 2 .5 2 ± 0 .1 4
˜ ν
0
= 3 9 0
q = 1 0
(a) Catalog T
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .8 9 ± 0 .1 2
˜ γ = 4 .6 7 ± 0 .8 2
˜ ν
0
= 9 7
q = 1 0
(b) Catalog N
183
Figure D–11 (Continued). Maximum likelihood errors.
2 2.5 3 3.5 4 4.5 5 5.5 6
0
0.2
0.4
0.6
0.8
1
1.2
˜ γ
˜
d ( k m )
184
Figure D–12. Scaling analysis of Parkfield segments (independent events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .1 4 4 ± 0 .0 1 6
˜ γ = 2 .5 0 2 ± 0 .1 6 8
˜ ν
0
= 2 8 0
q = 1 0
(a) Catalog T (declustered)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .9 3 ± 0 .1 4
˜ γ = 4 .6 3 5 ± 0 .9 4 5
˜ ν
0
= 7 3
q = 1 0
(b) Catalog N (declustered)
185
Figure D–12 (Continued). Maximum likelihood errors.
2 2.5 3 3.5 4 4.5 5 5.5 6
0
0.2
0.4
0.6
0.8
1
1.2
˜ γ
˜
d ( k m )
186
Figure D–13. Scaling analysis of Parkfield segments (clustered events).
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .0 9 9 ± 0 .0 2 1
˜ γ = 2 .7 0 4 ± 0 .4 4 6
˜ ν
0
= 1 2 0
q = 5
(a) Catalog T (clusters)
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d = 0 .8 4 5 ± 0 .3 8 5
˜ γ = 5 .5 7 ± 4 .0 1
˜ ν
0
= 2 4
q = 5
(b) Catalog N (clusters)
187
Figure D–13 (Continued). Maximum likelihood errors.
2 3 4 5 6 7 8 9 10
0
0.2
0.4
0.6
0.8
1
1.2
˜ γ
˜
d ( k m )
188
APPENDIX E:
FAULT CATALOG WEIGHTING ANALYSIS
(SUPPLEMENTARY FIGURES)
The following figures illustrate the fault catalog downweight analysis that was
performed to ensure that the few fault segments with many events did not bias the results
of the scaling analysis. In each figure, the dashed gray line marks our the selected value
of N
0
. The Parkfield fault class was not included as it is composed of only two fault
segments.
189
0 1000 2000 3000 4000 5000
0.8
0.9
1
1.1
1.2
1.3
γ

Catalog S
Catalog P
Catalog H
0 1000 2000 3000 4000 5000
0.8
0.9
1
d

Catalog S
0 1000 2000 3000 4000 5000
0.2
0.3
0.4
Down−weight Level
d

Catalog P
Catalog H
Figure E–1. Downweight analysis results of lar ge SoCal faults.
190
200 400 600 800 1000 1200 1400
1.2
1.4
1.6
1.8
2
2.2
γ

Catalog S
Catalog P
Catalog H
200 400 600 800 1000 1200 1400
0.6
0.7
0.8
d

Catalog S
200 400 600 800 1000 1200 1400
0.1
0.2
0.3
Down−weight Level
d

Catalog P
Catalog H
Figure E–2. Downweight analysis results of small SoCal faults.
191
500 1000 1500 2000 2500 3000
1.3
1.4
1.5
1.6
1.7
1.8
γ

Catalog S
Catalog P
Catalog H
500 1000 1500 2000 2500 3000
0.4
0.5
0.6
d

Catalog S
500 1000 1500 2000 2500 3000
0.2
0.3
0.4
Down−weight Level
d

Catalog P
Catalog H
Figure E–3. Downweight analysis results of aftershock-dominated segments.
192
0 1000 2000 3000 4000 5000 6000
1.4
1.5
1.6
1.7
1.8
γ

Catalog N
Catalog U
0 1000 2000 3000 4000 5000 6000
0.05
0.1
0.15
0.2
0.25
Down−weight Level
d

Catalog N
Catalog U
Figure E–4. Downweight analysis results of lar ge NoCal faults.
193
APPENDIX F:
FAULT SEGMENT SUBSETS
Subsets of fault segments in each fault class were used to investigate the evolutionary
aspects of near-fault seismicity. The following figures present fault-normal seismicity
distributions and scaling parameter estimates for each subset, the results of which are
summarized in Table 9. The individual fault segments used in each subset analysis are
indicated in brackets in each caption.
194
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .2 8 8
˜ γ =1 .0 7 1
˜ ν
0
= 1 3
q = 1 0
Garlock
Figure F–1. Scaling analysis of the Garlock fault [1,2,3].
195
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .2 0 2
˜ γ =0 .8 4
˜ ν
0
=3
q =5
Newport Inglewood
Figure F–2. Scaling analysis of the Newport - Inglewood fault [8,9].
196
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .5 3
˜ γ =0 .9 3 3
˜ ν
0
=7
q = 1 0
Elsinore
Figure F–3. Scaling analysis of the Elsinore fault [10,12].
197
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .2 5 4
˜ γ =0 .9 5 9
˜ ν
0
= 1 3 0
q = 2 0
San Jacinto
Figure F–4. Scaling analysis of the San Jacinto fault [11].
198
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .3 2 3
˜ γ =2 .5 2 7
˜ ν
0
= 1 4 0
q = 2 0
Imperial
Figure F–5. Scaling analysis of the Imperial fault [14].
199
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .7 7 3
˜ γ =2 .9 5 4
˜ ν
0
=8
q =3
San Andreas Coachella
Figure F–6. Scaling analysis of the San Andreas fault at Coachella [15].
200
10
−2
10
−1
10
0
10
1
10
−1
10
0
10
1
10
2
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .2 1
˜ γ =1 .3 6 5
˜ ν
0
= 2 3
q = 1 0
Hayward
Figure F–7. Scaling analysis of the Hayward fault [42,43].
201
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .0 5 6
˜ γ =1 .7 2 9
˜ ν
0
= 1 1 2 0
q = 1 0
Calaveras
Figure F–8. Scaling analysis of the Calaveras fault [44,45,46].
202
10
−2
10
−1
10
0
10
1
10
0
10
1
10
2
10
3
Fault−normal distance |x| (km)
Events / km
2
˜
d =0 .0 8 5
˜ γ =1 .6 2 7
˜ ν
0
= 1 2 0 0
q = 3 0
San Andreas (Creeping)
Figure F–9. Scaling analysis of the creeping section of the San Andreas fault [48,49,50].

Abstract (if available)

Abstract Hypocenters of small, relocated earthquakes are used to constrain how seismicity rates vary with distance from strike-slip faults in California. Stacks of events in a fault-referenced coordinate system show that out to a fault-normal distance x of 3-6 km, seismicity obeys a power-law ~(1+x^2/d^2)^(-g/2), where g is the asymptotic roll-off rate and d is a near-fault inner scale. These results are compatible with a 'rough fault loading' model in which the inner scale d measures the half-width of a volumetric damage zone and the roll-off rate g is governed by stress variations due to fault roughness. Two-dimensional numerical simulations by J. Dieterich and D. Smith indicate that g is approximately equal to the fractal dimension of along-strike roughness. Results of a multi-catalog error analysis and catalog simulations are used to correct the estimates of g and d for mislocation bias. Near-fault seismicity is more localized on faults in Northern California (NoCal: d=50±20m, g=1.51±0.05) than in Southern California (SoCal: d=210±40m, g=0.97±0.05). The Parkfield region has a damage-zone half-width (d=120±30m) consistent with the SAFOD drilling estimate and its high roll-off rate (g=2.30±0.25) indicates a relatively flat roughness spectrum: ~k^-1 vs. ~k^-2 for NoCal and ~k^-3 for SoCal. Fault surfaces in SoCal are therefore nearly self-similar, and their roughness spectra are redder than in NoCal, consistent with the macroscopic complexity of the observed fault traces. The damage-zone widths -- the first direct estimates averaged over the seismogenic layer -- can be interpreted in terms of an across-strike 'fault-core multiplicity' that is ~1 in NoCal, ~2 at Parkfield, and ~3 in SoCal.

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Asset Metadata

Creator Powers, Peter Marion (author)

Core Title Seismicity distribution near strike-slip faults in California

School College of Letters, Arts and Sciences

Degree Doctor of Philosophy

Degree Program Geological Sciences

Publication Date 06/04/2009

Defense Date 04/17/2009

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

Tag earthquake forecasting,earthquake triggering,Earthquakes,fault evolution,fault models,microseismicity,OAI-PMH Harvest,statistical seismology,strike-slip faults

Place Name California (states)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Jordan, Thomas H. (committee chair), Dolan, James F. (committee member), Ghanem, Roger Georges (committee member), Sammis, Charles G. (committee member)

Creator Email geowerks@gmail.com,pmpowers@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2283

Unique identifier UC1429829

Identifier etd-Powers-2914 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-245465 (legacy record id),usctheses-m2283 (legacy record id)

Legacy Identifier etd-Powers-2914.pdf

Dmrecord 245465

Document Type Dissertation

Rights Powers, Peter Marion

Type texts

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

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu