Stress drop heterogeneity within tectonically …tgoebel/preprints/stress...107 of the San Andreas Fault in June 2005 (see Figure 2). 108 [Figure 1 about here.] 109 2.2 Tectonic complexity

Stress drop heterogeneity within tectonically complexregions: A case study of the San Gorgonio Pass region,

southern California

T. H. W. Goebel1,*, E. Hauksson1, P. M. Shearer2, and J. P. Ampuero1

1Caltech Seismological Laboratory, Pasadena, California, USA.2Scripps Institution of Oceanography, University of California, San Diego,

California, USA.*Corresponding Author: [email protected]

Key words

spatial stress drop variations, corner frequency, source spectra, Brune-type spectral model, slip

rates, restraining bend, transpressional tectonics

Abstract1

In general, seismic slip along faults reduces the average shear-stress within earthquake source re-2

gions, but individual stress drops during earthquakes are observed to vary widely in size. The3

details of how crustal and fault properties influence variations in stress drop are poorly under-4

stood. To advance our understanding of variations in stress drop, we analyze source parameters of5

small and intermediate magnitude events within the greater San Gorgonio Pass region, southern6

California. The tectonics within the region are controlled by a restraining bend of the San Andreas7

fault system, which results in distributed deformation, and heterogeneous slip along numerous8

strike-slip and thrust faults.9

Stress drops are computed by fitting a Brune-type spectral model to individual event spectra10

obtained through separating the observed spectra into site, path and source contributions. The lat-11

ter are obtained by iteratively removing stacked site and path terms and correcting high frequency12

contributions using a regional empirical Green’s function. The stress drop estimates show strong13

1

regional variations from ∼1 to ∼25 MPa with a median of 4.8 MPa. We observed anomalously14

high stress drops (>20 MPa) in a small region between the traces of the San Gorgonio and Mission15

Creek segments of the San Andreas fault. Detailed analyses of focal mechanisms reveal that stress16

drops are slightly higher for thrust faulting events (∼6 MPa) than for normal events (∼3.5 MPa).17

The estimated stress drops also increase below depths of ∼10 km and along the San Andreas fault18

segments, both from north and south, towards San Gorgonio Pass (SGP), showing a negative corre-19

lation with geologic slip rates. To test the stability of our results, we conducted a sensitivity analysis20

of input parameters and event selection criteria, confirming the robustness of the observations. We21

identified crustal conditions and fault properties that contribute to local variations in stress drop22

estimates including the style of faulting, changes in average tectonic slip rates, mineralogical com-23

position of the host rocks, as well as the hypocentral depths of seismic events. A detailed spatial24

mapping of stress drop variations can thus advance the assessment of expected earthquake ground25

motions.26

1 Introduction27

The relative motion of tectonic plates generally causes stress to build up along systems of faults.28

These stresses are released during earthquakes. The spatial variations in absolute stresses during29

earthquakes can generally not be determined directly, however, the relative decrease in shear-stress30

can be estimated from the radiated seismic spectrum. Stress drop estimates are based on a decon-31

volution of the seismic record into source, site and path effects. The seismic moment and corner32

frequency of the source spectrum can be used to determine rupture dimensions and stress drops33

if the aspect ratio and propagation speed of the rupture are assumed to be constant (e.g. Eshelby,34

1957; Knopoff , 1958; Brune, 1970; Madariaga, 1976; Boatwright et al., 1991).35

1.1 Earthquake scaling relations and self-similarity36

A detailed description of source parameter variations fundamentally influences our understand-37

ing of earthquake physics including expected ground motions (e.g. Hanks and McGuire, 1981) and38

scaling relations (e.g. Hanks and Thatcher, 1972; Prieto et al., 2004; Walter et al., 2006). Self-similar39

earthquake scaling requires that stress drops remain constant and fault slip increases as a function40

of rupture area (e.g. Prieto et al., 2004; Shearer, 2009). As a consequence, physical processes involved41

2

in small and large magnitude earthquakes are inherently similar (e.g. Aki, 1981).42

If the corner frequency of the source spectrum increases with magnitude, the energy radiation43

is partitioned differently over the earthquake frequency spectrum, causing large stress drop events44

to contain a relatively higher proportion of high-frequency energy. This has large implications45

for the expected ground motion of a particular size earthquake, i.e., seismic events with relatively46

high stress drops radiate more high frequency energy than low stress drop events (e.g. Hanks, 1979;47

Hanks and McGuire, 1981; Heaton et al., 1986).48

Some studies of source parameter scaling relations indicate self-similar scaling between corner49

frequencies and moments for regional data sets and mining induced seismicity (e.g. Abercrombie,50

1995; Ide and Beroza, 2001; Prieto et al., 2004; Baltay et al., 2010; Kwiatek et al., 2011) whereas other51

studies highlight deviation from self-similarity on regional and global scales (e.g. Kanamori et al.,52

1993; Harrington and Brodsky, 2009; Lin et al., 2012). The assessment of earthquake stress drops over53

a range of magnitudes is further complicated by near-surface attenuation. Attenuation is especially54

problematic for small events and high-frequencies, which can cause an artificial break-down of self-55

similar scaling (Abercrombie, 1995). High frequency attenuation, limited recording bandwidths and56

low quality records add to the controversy of self-similar source parameter scaling which has not57

been resolved at present.58

1.2 Fault properties, crustal parameters and stress drop variations59

In addition to magnitudes, stress drops are influenced by local crustal conditions. For example near60

Parkfield, seismic off-fault events show largely self-similar scaling whereas some events on the San61

Andreas fault exhibit the same source pulse width, independent of event magnitudes (Harrington62

and Brodsky, 2009). The independence of pulse width and earthquake magnitude results in stress63

drops between 0.18 and 63 MPa. High stress drops for on-fault events were also suggested by64

Nadeau and Johnson (1998). While the Parkfield studies show locally higher stress drops, a study65

of earthquakes in southern California found no correlation between stress drop and distance from66

major faults (Shearer et al., 2006), and a study of global earthquakes with M>5 revealed higher stress67

drops for intraplate compared to plate boundary events (Allmann and Shearer, 2009). Elevated stress68

drops for intraplate events may be due to higher crustal strength and stresses far from active faults.69

Stress drops may also be sensitive to the type of tectonic regime. For example in southern Cali-70

3

fornia, Shearer et al. (2006) identified higher-than-average stress drops in some regions containing a71

relatively high fraction of normal-faulting events whereas the mainly reverse-faulting aftershocks72

of the Northridge earthquake have lower-than-average stress drops. In contrast, the global study73

of Allmann and Shearer (2009) found higher-than-average stress drops for strike-slip events. Fur-74

thermore, stress drops are observed to be lower for regions of relatively high heat flow in Japan75

(Oth, 2013) and increase with depth, for example, in southern California (Shearer et al., 2006; Yang76

and Hauksson, 2011) and Japan (Oth, 2013). In addition to fault proximity, tectonic regime, heat77

flow and depth, stress drops have also been observed to vary as a function of recurrence intervals78

and loading rates in the laboratory and nature (e.g. Kanamori et al., 1993; He et al., 2003). Slower79

loading rates and longer healing periods within interseismic periods lead to an increase in asperity80

strengths and stress drops (Beeler et al., 2001).81

In this study, we investigate stress drop variations close to the San Andreas fault in Gorgonio82

Pass. This region provides an ideal natural laboratory to study stress drop variations because83

of its high seismic activity, station density and well-studied tectonic setting. We first review the84

tectonic setting (Section 2), then introduce the method for estimating source spectra and stress85

drops largely following Shearer et al. (2006) (Section 3). We determine spatial variations in stress86

drops and assess their reliability (Section 4.1–4.2). We then perform a detailed analysis of crustal87

parameters that may influence stress drop variations (Section 4.3–4.5). More details about the stress88

drop computations can be found online in the supplementary material.89

2 Seismic data and tectonic setting90

2.1 Seismicity catalogs and waveform data91

We analyzed seismicity data and seismic waveforms within the greater SGP area (Figure 1). Our92

analysis was based on three different types of data: (1) A relocated earthquake catalog that im-93

proved single event location by using a 3D velocity structure, source-specific station terms and94

relative travel-time differences from waveform cross-correlations of event clusters (Shearer et al.,95

2005; Hauksson et al., 2012); (2) focal mechanisms, estimated from first-motion polarities and ampli-96

tude ratios of P- and S-waves (Yang et al., 2012); (3) seismic waveforms, obtained from the SCEC97

data center which we used to determine source spectra and source parameters. We limited our98

4

analysis to events that were recorded at broadband stations. These stations show a largely con-99

sistent frequency response from ∼0.2–50 Hz with a sampling frequency of 100 Hz. This wide100

frequency band is helpful for improving the resolution of corner frequencies and high-frequency101

fall-offs compared to previous studies. The broadband data are available for a dense array of sta-102

tions in southern California starting in 2000. We selected a period from 2000 to 2013 because of the103

availability of relatively homogeneous waveform records, station instrumentation and seismicity104

catalogs. During this period over ∼ 11,300 seismic events with magnitudes in the range of ML=0–105

4.88 occurred within the study region. The largest event occurred near the San Bernardino segment106

of the San Andreas Fault in June 2005 (see Figure 2).107

[Figure 1 about here.]108

2.2 Tectonic complexity within the SGP region109

The study area is crosscut by several faults that comprise the San Andreas fault system. The San110

Andreas fault system is characterized by relative structural simplicity within the Coachella seg-111

ment to the southeast and the Mojave segment to the northwest of SGP (Figure 1). The SGP region112

itself is marked by complex, distributed crustal deformation. Tectonic slip within this region is ac-113

commodated by systems of strike-slip and thrust faults (Allen, 1957). These fault segments include114

the Garnet Hill and Banning segments to the northwest of the Coachella segment, followed by the115

San Gorgonio thrust fault (SGF), Wilson Creek and San Bernardino segments and the Mill and Mis-116

sion Creek segments north of SGP (Figure 2). The Banning segment became seismically less active117

about 5 Myr ago (e.g. Yule and Sieh, 2003). Consequently, the slip on the San Andreas fault system118

partially by-passes the SGP region, for example, via the San Jacinto fault to the west (Allen, 1957;119

Yule and Sieh, 2003; Langenheim et al., 2005; McGill et al., 2013).120

The San Andreas fault within the SGP region lacks continuity because the regional deformation121

is strongly influenced by a restraining step within the Mission Creek section (Figure 2a). As a result,122

several secondary fault strands exist, which are oriented unfavorably with respect to the tectonic123

plate motion, leading to large-scale transpressional tectonics (Carena et al., 2004; Langenheim et al.,124

2005; Cooke and Dair, 2011). This tectonic complexity is also articulated in the distribution of seismic125

events, which occur preferably off the main fault strands of the San Andreas fault (e.g. Yule and126

Sieh, 2003). Similarly, the tectonic complexity can be observed in the diversity of focal mechanisms127

5

which show predominant oblique sinistral slip above 10 km. In contrast, below 10 km depth,128

oblique strike-slip, normal and thrust faulting accommodate east-west extension and north-south129

compression (Nicholson et al., 1986). The thrust faulting within the SGP region resulted in a high130

magnetic anomaly, likely caused by the wedging of Peninsular range rocks underneath Transverse131

range material and the presence of deep, magnetic rocks of San Bernardino or San Gabriel basement132

types (Langenheim et al., 2005). The convergence rates within this area are estimated at 1–11 mm/yr133

(Yule et al., 2001; Langenheim et al., 2005). The long term fault slip rates decrease systematically134

when approaching the SGP region from the North and South from 24.5±3.5 and 14–17 mm/yr135

respectively down to 5.7±0.8 mm/yr (Dair and Cooke, 2009; Cooke and Dair, 2011; McGill et al., 2013).136

Since the 1940s, three mainshocks close to and above M = 5.0 have been recorded within the study137

area: 1) the 1986 M = 5.6 North Palm Springs, 2) the 1992 M = 6.4 Big Bear, and 3) the 2005 M = 4.9138

Yucaipa earthquake (Figure 2a). In addition, three large earthquakes were recorded nearby, i.e., the139

1948 M = 6.0 Desert Hot Springs and 1992 M = 6.1 Joshua Tree earthquakes to the east and the 1992140

M = 7.3 Landers earthquake to the northeast.141

Seismicity becomes deeper north of the SGF, which dips at about ∼ 55° underneath the San142

Bernardino mountains (Figure 2b). The base of the seismicity beneath the San Jacinto mountains143

dips gently to the north (Figure 2b). This is followed by an abrupt step in the seismicity base from144

∼21 to 13 km below the Mission Creek segment. This step marks the boundary between Peninsular145

and Transverse range rocks (see also Nicholson et al., 1986; Yule and Sieh, 2003). The depth profile of146

the relocated seismicity catalog suggests that the seismicity step may be slightly disturbed by the147

presence of the San Gorgonio thrust, leading to seismically active under-thrusting of Peninsular148

range rocks beneath the Transverse ranges. Based on mapped surface traces and approximate fault149

dip angles (Fuis et al., 2012), we connected fault surface expression with deep seismicity clusters at150

depth (Figure 2). The SGF is approximately co-located with the transition between deep seismicity151

to the south and shallower seismicity to the north. Faults to the South generally lack seismicity152

above ∼5 km whereas faults to the North (e.g. Mission and Mills Creek) produce seismic events153

from shallow depths down to 14–15 km.154


6

3 Method: Source spectra inversions and stress drop estimates156

Instead of estimating source parameters from individual spectra, we inverted the entire data set157

for average event, path and station terms thus diminishing the influence of high-frequency fluc-158

tuations, radiation patterns and source directivity (e.g. Andrews, 1986). Amplitude spectra were159

computed for tapered waveforms within a 1.28 s time window after the P-wave arrival. For the160

spectral inversions, we required a signal-to-noise ratio (SNR) above 5 within three different fre-161

quency bands (5–10, 10–15, 15–20 Hz) as well as at least 5 station picks per event. The observed162

waveforms are a convolution of source, path and site contributions. The convolution changes to a163

multiplication in the frequency domain and to a summation in the log-frequency domain:164

dij = ei + tij + sj , (1)

where dij is the logarithm of the recorded amplitude spectrum, ei and sj are the event and station165

terms and tij is the travel time term between the i th event and station j th (see also Suppl. Fig. S1).166

All of these terms are frequency-dependent.167

The path term was discretized by binning at 1-s intervals according to the corresponding P-168

wave travel times. This system of equations was then solved iteratively by estimating event, sta-169

tion and path terms as the average of the misfit to the observed spectra minus the other terms (e.g.170

Andrews, 1986; Warren and Shearer, 2000; Shearer et al., 2006; Yang et al., 2009). For robustness, we171

suppressed outliers by assigning L1 norm weights to large misfit residuals. The robustness of the172

spectral inversion method was also verified previously by comparing path terms with expectations173

from a frequency-independent attenuation model (Shearer et al., 2006) and by analyzing a synthetic174

data set (Allmann and Shearer, 2007). The spectral-stacking does not take differences in focal mecha-175

nisms into account which are a potential source of uncertainty within the source spectra estimates176

(e.g. Kaneko and Shearer, 2014). However, the differences in corresponding radiation patterns were177

diminished by stacking spectra from many stations thus averaging over the focal sphere.178

We estimated the relative seismic moment, Ω0, for individual source spectra from the corre-179

sponding low-frequency contributions by averaging the spectral amplitudes from ∼2–4 Hz. This180

frequency range is above the smallest corner frequencies. We then calibrated the relative moments181

using the catalog magnitudes, assuming that the low-frequency amplitudes are proportional to182

7

moment, and that the catalog magnitude is equal to the moment magnitude at ML = 3 (see Shearer183

et al., 2006, for details). The source spectra were then binned according to estimated local magni-184

tude using a 0.2 spacing and corrected using a regional Empirical Green’s Function (EGF) approach.185

The EGF is estimated by simultaneously fitting a constant stress-drop Brune-type spectral model to186

the magnitude-binned spectra between 2–20 Hz (Figure S2). The spectral model has the following187

form (Brune, 1970):188

u(f ) =Ω0

1 + (f /fc )2 (2)

where u(f ) is the source spectra, Ω0 is the low frequency spectral amplitude, and fc is the corner189

frequency. For a circular, isotropic rupture and constant rupture velocity, the stress drop (∆σ) and190

corner frequency are related by (Eshelby, 1957; Madariaga, 1976):191

∆σ = M0

(fc

0.42β

)3(3)

where M0 is the seismic moment and β is the shear wave velocity. Initially, we assumed a con-192

stant reference shear velocity of 3.5 km/s. We then tested the sensitivity of stress drop variations193

to changes in β, which is discussed in detail in Section 4.3. Changes in rupture velocities and in194

the scaling between corner-frequency and rupture extent affect stress-drop estimates strongly due195

to the cubed dependency on corner-frequencies. For example, Brune (1970) assumed that corner-196

frequency (fc ) and rupture dimension (r ) are related over fc = kβ/r , with k = 0.37, whereas here197

we assume a value of k = 0.32 for far-field P-wave radiation, based on Madariaga (1976). Nev-198

ertheless, these changes in scaling constants alter only the absolute value of stress drops whereas199

relative changes remain constant so that the in the following described spatial variations in stress200

drop estimates are not affected.201

The source parameters of individual events are determined by fitting a Brune-type spectral202

model to the source spectra after correcting the high-frequency contributions using the regional203

EGF. Variations in spectra, corner frequencies and stress drops are shown in Figure S3 for events204

with similar relative moments. The described method enables us to analyze large seismic data sets205

in a uniform way to obtain reliable estimates of relative differences in source parameters, e.g. stress206

drops. The absolute stress drop values may be sensitive to some of the modeling assumptions207

(e.g. constant rupture velocities in Equation 3, and fixed rupture aspect ratio) which has to be208

considered when comparing our results to other studies. Furthermore, uncertainties in corner-209

8

frequency estimates, or differences in the assumed relationship between rupture extent and corner-210

frequencies have a large influence on stress-drop estimates because of the cubed dependency on fc .211

Nevertheless, overall stress drop variations can be interpreted with greater confidence compared212

to the analysis of individual spectra or event pairs.213

4 Results214

The average stress drop of the stacked source spectra for the entire region was ∆σ = 6.1 MPa (Fig-215

ure S2b), and the median value of individual events was ∆σ = 4.8± 0.1 MPa (Figure S5) assuming216

log-normal-distributed data. The approximate agreement between these two values is one indi-217

cation of the robustness of our spectral inversion method. Stress drop estimates based on source218

spectra of small-magnitude earthquake are generally subject to large scatter. This scatter maybe re-219

lated to different sources, for example, uncertainties in the spectral inversion, deviations from the220

applied, simplistic source model, as well as uncertainties in corner-frequency and seismic moments221

estimates. Nevertheless, part of the variations in stress drops may also have underlying, physical222

causes which will be investigated in the following. For a more detailed presentation of uncertain-223

ties and misfits between observed and modeled spectral shapes see the supporting information in224

the online version of this article. In the following section, we show spatial variations in stress drop225

estimates and analyze their robustness.226

4.1 Spatial variations in stress-drops227

To assess the spatial variations of individual earthquake stress drops, we smooth the results using228

a spatial median filter for the closest 60 epicenters to a 2-D uniform grid within a maximum area229

of r = 5 km. The maximum kernel width is chosen to avoid associating median stress drops230

with distant events. The resulting map displays gradual variations in stress drop estimates from231

values of ∼2 MPa up to ∼25 MPa (Figure 3). The most striking feature in Figure 3 is the region232

of anomalously high stress drops between the SGF and Mill Creek fault traces. Within this area,233

stress drops change rapidly (from north to south along longitude = 116.8°W) from ∼5 MPa up to234

>20 MPa and back to <5 MPa. In addition, we observe several regions of increased stress drop235

estimates, for example, located close to the San Jacinto fault [-117.08, 33.9] and south of the San236

Bernardino segment [-117.05 34.07]. The dark red to orange regions highlight areas with stress237

9

drops between 2 to 8 MPa (see legend in Figure 3).238


Before probing different mechanisms that could explain the observed variations in stress drop240

estimates, we tested the robustness of our results. We started by investigating the difference be-241

tween the high and low stress drop regions (green and red circle in Figure 3) focusing on the rela-242

tion between corner frequencies and moment. We created a subset of data containing events within243

the two regions and performed a separate inversion for source spectra and source parameters. This244

inversion incorporates the estimation of a local EGF, which accounts for possibly unmodeled lateral245

variations in attenuation using the regional EGF for the entire study area. In case of systematic dif-246

ferences in source spectra, we expect to observe also systematic differences in corner frequency and247

stress drops for different magnitude events. Our tests confirmed this expectation so that seismic248

moment and corner frequency exhibit consistently higher ratios for high compared to low stress249

drop regions in log-log space (Figure 4). Based on the corresponding stress drop distributions, we250

compute median values of ∆σ = 1.4 MPa and 18.7 MPa assuming log-normal distributed data for251

low and high stress drop regions. These values are comparable to the values for the same regions252

in Figure 3.253


Following the analysis of corner frequency and moment, we compared the relative frequency255

content of seismic event waveforms within the low and high stress drop regions. To this aim, we256

juxtaposed low and high stress drop source spectra after normalizing spectral amplitudes by mo-257

ment and frequencies by the corner frequency derived from equation 3 based on the regional me-258

dian stress drop (Figure 5). This re-scaling corrects for differences in moment within the individual259

regions but also shows the differences in frequency content of individual events, thus providing260

a qualitative estimate of variations in corner frequency. In the case of constant, estimated stress261

drops, as observed for the regional source stacks (see Figure S2), the shifted source spectra collapse262

on the same curve. However, the present data subsets display strong variations within the two263

different regions: Low stress-drop events have lower corner frequencies and plot further to the left264

(Figure 5a), whereas high stress drop events exhibit relatively higher corner frequencies and plot265

further to the right (Figure 5b). Consequently, the relative difference between spectra within the266

low and high stress drop region further supports the reliability of observed spatial variations in267

10

stress drops. (More details about differences in spectra for events with different stress drops are268

shown in Figure S3).269


4.2 Sensitivity analysis of stress-drop computations271

To investigate the dependence of source inversion results on input parameters, we conducted a272

sensitivity analysis of selection criteria for the input spectra. The details of the sensitivity analysis273

can be found in the supplementary material. The analysis generally confirmed the relative differ-274

ences between low and high stress drop regions but also showed that the absolute stress drops may275

vary as a function of input parameters and connected data selection criteria. Limiting the analysis276

to records with many station picks had a larger influence on stress drops then choosing only high277

SNR records. Nevertheless, the sensitivity analysis demonstrated that relative variations in stress278

drops can be identified reliably if the input parameters are chosen consistently though absolute279

values may vary.280

4.3 Stress drop variations with depth281

To test the influence of hypocentral depths and to examine possible lateral variations as a function282

of depth, we constructed smoothed stress-drop maps for three different depth ranges (Figure 6).283

Because there are few events above 5 km depth, we chose the first depth layer from 0–10 km, the284

second from 10–15 km and the third for events from 15–25 km. We observed a systematic difference285

in stress drops between the depth layers. The shallow events (0–10 km) were dominated by low286

stress drops, the intermediate depth layer includes some of the high stress drops and the deepest287

events clearly highlight the area of anomalously high stress drops between the San Gorgonio and288

Mission Creek fault traces. As expected, the intermediate and the bottom depth layers do not show289

the low stress drop region towards the north edge of the study region, which was dominated by290

relatively shallow events (see Figure 2b).291


Motivated by the observation of stress drop variations for different depth layers, we probed for293

a general correlation between focal depths and stress drops. Stress drops for events shallower than294

11

10 km are low, with average values from 2.6–3.0 MPa. At ∼10 km the average stress drops increase295

abruptly to ∼4.8 MPa. At depths from ∼ 10–17 km, average stress drops continue to increase296

gradually up to ∼ 5.5 MPa before decreasing to 5.3 MPa at 20 km depth. We tested whether these297

observations could be explained by variations in rupture velocity, assuming that rupture velocity298

is proportional to S velocity changes with depth. We used a regional velocity model (Langenheim299

et al., 2005), which has a high velocity anomaly just beneath the SGP region. We corrected our initial300

stress-drop estimates using two different depth profiles that capture the average seismic velocity301

changes beneath and outside of the SGP region, including a relatively high velocity zone at about302

7–13 km depth (Figure 7b). The results are shown by the round markers in Figure 7a. Including a303

depth-dependent change in rupture velocity affected the variations in stress drops only marginally.304

This is expected because most of the variations in seismic velocities are located close to the surface305

from 0–6 km whereas the largest changes in stress drops are at greater depths. The rupture velocity306

(Vr ) would have to change abruptly by a factor of 1.2 near 10 km to compensate the observed307

increase in stress drop with depth, but the inferred increase in Vr at this depth is only about 3%.308


The analysis of stress drop variations with depth revealed large values for relatively deep events310

(below 10 km). To put this finding into the seismo-tectonic context of the SGP region, we mapped311

stress drops of individual events along the depth cross-section highlighted in Figure 3. The previ-312

ous results of lower stress drops above 10 km are supported by the overall stress drop distribution313

(Figure 8a). However, we also observed a relatively dense cluster of high stress drop events in314

immediate proximity to the seismicity step extending from the base of the seismicity up to the SGF.315

This region marks the location of the deepest earthquakes within the study area. The transition316

to the hanging wall of the SGF is characterized by a noticeable decrease in stress drops. Similarly317

stress drop decreases to the southwest at greater distances to the seismicity step.318

The position of the seismicity step itself is likely connected to relatively strong transpressional319

tectonics, which can be derived from the motion along the SGF and predominant thrust-type focal320

mechanisms within the same region (Figure 8b). Although there is an apparent dominance of321

under-thrusting within this area, we also observed a cluster of normal faulting events (at [38, 16]322

in Figure 8b) which is in contrast to the overall tectonic regime in this area. Motivated by the323

observation of both thrust and normal faulting, we searched for a possible correlation between324

12

dominant faulting mechanisms and stress drops in the following section.325


4.4 Stress drop variations as function of faulting mechanism327

We correlated average faulting mechanisms expressed by their differences in rake angle (Figure 9).328

These differences can be quantified by normalizing the observed rake angles so that the spectrum329

of faulting mechanisms can be expressed on a continuous scale from -1 to 1 with normal faulting330

at -1, strike-slip at 0 and thrust faulting at a value of 1 (Shearer et al., 2006). Stress drops and focal331

mechanisms show a weak, positive correlation so that normal faulting has relatively lower average332

stress drops (∆σ = 3.5± 0.5 MPa) whereas thrust faulting has higher average stress drops (∆σ =333

6.0± 0.6 MPa). Strike-slip events represent the predominant type of faulting. Consequently, their334

median value (∆σ = 5.1 ± 0.6 MPa) is similar to the one observed for the whole region (∆σ =335

4.8± 0.1 MPa).336


4.5 Stress drop variations along the San Andreas fault system338

One of the fundamental questions concerning the SGP region is the possibility of large penetrat-339

ing ruptures that could propagate through the entire region, e.g., from Cajon Pass to the Salton340

Sea. Using the average fault orientation within the Mojave segment (see Figure 1), we determined341

variations of stress drop in the proximity of a possible path of such a rupture between the San342

Bernardino and Garnet hill segment (Figure 10). The stress drops decrease to the southeast of343

SGP within the area of the Banning and Garnet Hill segments which eventually merge with the344

Coachella segment of the San Andreas fault. The stress drops also decrease to the northwest of345

SGP and show consistently lower values outside of the San Gorgonio fault segment.346

The stress drop traverse through the SGP passes in immediate proximity to local estimations of347

geologic slip rates (highlighted by blue squares in Figure 3). Slip rates were previously compiled348

from many different studies and summarized by Dair and Cooke (2009); Cooke and Dair (2011) as well349

as by McGill et al. (2013) highlighting a systematic decrease from Cajon Creek (slip rates = 24.5 ±350

3.5 mm/yr) to Cabezon (5.7 ± 0.8 mm/yr), which is close to SGP. To the southeast, the slip rates351

increase again within the Coachella region (14–17 mm/yr) of the San Andreas fault. The average352

13

geologic slip rate on the SGF itself is estimated to be as low as 1.0–1.3 mm/yr (Matti et al., 1992).353

This shows, that stress drops and slip rates are mostly inversely correlated within the study area.354


5 Discussion356

5.1 Seismicity and fault orientation357

The most prominent feature in the seismicity is a lack of shallow events south of the Mission and358

Mill Creek segment and a seismicity step close to the down-dip end of the SGF. To the north, we359

observed more shallow seismicity that extends down to about 14–15 km depth. The latter conforms360

to the commonly observed depth-extent of the seismogenic zone within southern California. The361

variations in the maximum depth of seismicity may be related to both topographic and lithologic362

effects, supported by the sharpness of the transition and the approximate, inverse relationship be-363

tween surface relief and seismicity base-depth (Magistrale and Sanders, 1996; Yule and Sieh, 2003).364

The juxtaposition of different lithologies due to the large displacement along the San Andreas fault365

system, seems to contribute to the creation of the observed difference in the maximum seismic-366

ity depths, moving the brittle-ductile transition to greater depths. The latter may be caused by367

a difference in plasticity temperature between feldspar-dominated Peninsular range and quartz-368

dominated Transverse range rocks (e.g. Scholz, 1988; Magistrale and Sanders, 1996). In addition,369

down-thrusting along the SGF may perturb the geotherm downward which can explain the locally370

deep earthquakes and base of seismicity. We will explore this question in more detail below within371

the context of the observed changes in stress drops.372

Stress drops within the present study show regional variations between ∼1 to ∼20 MPa. Sim-373

ilar variations are observed in laboratory earthquake-analog experiments and seismic events at374

shallow depth in mines. The latter exhibited relatively high displacements and locally-high stress375

drops of up to 70 MPa (McGarr et al., 1979). Shear stress drops during laboratory stick-slip ex-376

periments range from ∼1 to more than 160 MPa (e.g. Thompson et al., 2005; Goebel et al., 2012). The377

laboratory studies also highlight a connection between fault heterogeneity, aftershock duration and378

stress drop magnitudes so that stress release is higher and aftershock duration shorter for smooth,379

homogeneous faults in the laboratory (e.g. Goebel et al., 2013b,a).380

14

5.2 Stress drop variations381

5.2.1 Focal mechanisms and ambient stress level382

Previous investigations of the influence of focal mechanism types on stress drop variations pro-383

duced mixed results, supporting higher stress drops for both normal (Shearer et al., 2006), and384

strike-slip events (Allmann and Shearer, 2009) or no dependence on focal mechanisms (e.g. Oth,385

2013). The southern Californian data set was strongly influenced by the 1994 Northridge sequence386

which showed predominant thrust-type events with low stress-drops (Shearer et al., 2006). Our re-387

sults, on the other hand, revealed higher stress drops for thrust events compared to strike-slip and388

normal faulting, which can be understood in the context of large compressive stresses and higher389

ambient stress level. A possible reason for the difference between our results and other studies may390

be related to the observational scales and the mixture of vastly different tectonic regimes. While our391

study concentrated on a small crustal region, others investigated stress drops for all of Southern392

California (Shearer et al., 2006), Japan (Oth, 2013) and a global data set Allmann and Shearer (2009),393

inevitably mixing seismic events from volcanic activity, off-shore events, induced seismicity, and394

other sources. Over these large scales, stress level and faulting mechanics are bound to vary sub-395

stantially, which may contribute more extensively to variations in stress drops than the differences396

in faulting mechanisms. Furthermore, the rather weak correlation between focal mechanisms and397

stress drops within the present study, indicates that the type of faulting is not the only contributing398

factor to stress drops variations.399

5.2.2 Lithological variations400

The large cumulative displacement along the San Andreas fault system results in a juxtaposition of401

different lithology in many areas. Within the SGP area, feldspar-dominated Peninsular range rocks402

have been moved next to quartz-rich Transverse range rocks (Magistrale and Sanders, 1996) with403

very different brittle-ductile transition temperatures (e.g. Scholz, 1988). The difference in lithology404

and transition temperatures across the San Andreas fault system (or more precisely across the Mis-405

sion Creek segment of the San Andreas fault) not only controls the thickness of the seismogenic406

zone but also influences the stress drops within the SGP region. We observed an abrupt variation407

in determined stress drops across the Mission Creek segment so that feldspar-dominated rocks to408

the south are connected to substantially larger stress drops compared to quartz-rich material to409

15

the north of the Mission Creek segment. Similar observations have been made for mining induced410

seismicity, for which stress drops are higher in feldspar-dominated diorite dikes compared the sur-411

rounding quartzite host rocks (Kwiatek et al., 2011). Kwiatek et al. observed a maximum difference412

in stress drop estimates of about one order of magnitude whereas seismic velocities varied by only413

∼3%. Differences in ’rock-brittleness’ as a function of temperature also influence frictional proper-414

ties, specifically, frictional strengths and slip stability (e.g. Tse and Rice, 1986; Blanpied et al., 1995).415

Furthermore, the frictional stability, i.e., the degree of velocity strengthening or weakening of ma-416

terial interfaces, is directly connected to stress drop (e.g. Gu and Wong, 1991; He et al., 2003; Rubin417

and Ampuero, 2005). As a consequence, more ductile material, which favors velocity strengthening418

behavior, also exhibits relatively lower stress drops compared to more brittle material. This behav-419

ior appears to be observable for rocks at varying temperatures (e.g. Blanpied et al., 1995), but also, as420

in our case, for different rock types (quartz- vs. feldspar dominated) with different brittle/ductile421

transition temperatures.422

5.2.3 Asperity strengths and fault slip rates423

The present study revealed a correlation between geologically inferred fault slip rates and stress424

drops so that the areas of highest stress drops coincide with the lowest slip rates (see Figure 10).425

Relatively high stress drops are also inferred for large magnitude earthquakes (M = 5.5–8.5) for426

faults with long recurrence intervals and high fault strengths (Kanamori, 1986). Besides studies of427

large magnitude earthquakes, small-scale laboratory stick-slip experiments highlight a connection428

between loading rates, recurrence intervals and stress drops. In the laboratory, recurrence intervals429

of stick-slip events are correlated with fault strengths and stress drops so that longer recurrence430

intervals due to slower loading rates results in relatively high stress drops (Beeler et al., 2001). Sim-431

ilar results have been obtained for repeating earthquakes which show a higher proportion of high432

frequency energy radiation if the recurrence intervals between events are long (e.g. Beeler et al.,433

2001; McLaskey et al., 2012). The connection between earthquake recurrence and stress drops can be434

explained by increasing strength of load bearing asperities as a function of time. Asperities on a435

slowly loaded fault undergo relatively longer interseismic healing periods and exhibit higher resis-436

tance to shear before failure events occur, releasing a comparably high amount of stored stress. The437

amount of fault healing is, in addition to loading rates, also sensitive to pressure and temperature438

conditions at depth, which can significantly influence the distribution of radiated seismic energy439

16

as a function of frequency (McLaskey et al., 2012). Increased asperity strength due to longer healing440

periods may also influence the tendency of asperities to fail individually. For instance, ruptures441

on heterogeneous faults with strong asperities are more likely to be arrested before growing to442

large sizes (Sammonds and Ohnaka, 1998). The presence of strong asperities and fault heterogeneity443

may explain the relatively high stress drops of small and intermediate magnitude events that were444

observed here.445

Theoretical considerations of seismic slip on a fault that is governed by rate-and-state friction446

confirm the dependence of stress-drops on loading rates. In addition, the static stress drop (∆τs ) is447

sensitive to friction-parameters (e.g. Gu and Wong, 1991; He et al., 2003; Rubin and Ampuero, 2005):448

∆τs = σn(b− a) ln(Vdyn/Vl) (4)

where σn is the normal stress, b and a are material parameters that control the frictional behavior,449

and Vl and Vdyn are the loading and dynamic slip velocities. The latter occupies values close to450

1 m/s. Furthermore, if we assume approximately constant friction and normal stress across the451

fault, the stress drop changes as a function of loading velocity, Vl, so that a decrease in loading rate452

by a factor of 4–5, as observed in our study, corresponds to an increase in stress drop by factor of453

∼ 1.7. Our results show an increase in stress drop along the San Andreas fault by a factor of 2–3 (see454

Figure 10), which is slightly higher than predicted from this simple model. This difference can be455

explained by possible changes in material and frictional properties, which were not considered, but456

likely also contribute to variations in stress drop. In addition, spatial and temporal heterogeneity457

in stress-drops may be a result of variations in seismic coupling and transient slip processes before458

mainshocks, for example, expressed by differences in foreshock and aftershock source spectra in459

Southern California (Chen and Shearer, 2013).460

5.2.4 What is the major controlling parameter of stress drop variations?461

We identified four parameters that were connected to variations in stress drops within the SGP462

region, i.e., the type of faulting, hypocentral depths, geologic slip rates and mineralogical composi-463

tion of the regional rock types. Our analysis suggests that all four mechanisms contribute to some464

extent to the creation of the relatively high stress drops between the surface traces of the SGF and465

the Mission Creek segment. The largest variations in stress drops occurred along fault strike and466

17

in the proximity of the seismicity step at the down-dip end of the SGF. This suggests that average467

slip rates and the presence of abrupt lithologic changes exert the strongest control on stress drops.468

We hypothesize that relatively slow down-thrusting of feldspar-dominated material in connection469

with longer healing periods and increased asperity strengths generally promote high stress drops.470

5.3 Implications for seismic hazard and earthquake rupture dynamics471

The relatively high stress drops and slow geologic slip rates (e.g. McGill et al., 2013) within the San472

Gorgonio pass area suggest locally increased fault strength and long earthquake recurrence inter-473

vals. We hypothesize that areas of high stress drop are connected to the failure of individual small474

but strong fault patches. Consequently, rupture propagation may be stifled within the SGP area475

decreasing the probability of large earthquakes that extend through the SGP. The role of the SGP in476

hindering rupture propagation has been recognized previously based on the strongly segmented477

fault geometry within the area (Magistrale and Sanders, 1996). The overall deformation along the478

San Andreas fault system may increasingly by-pass the SGP region to the north and south-east, for479

example, via the San Jacinto fault (McGill et al., 2013).480

6 Conclusion481

We have analyzed the spatial variation in source parameters of small and intermediate magnitude482

earthquakes within the San Gorgonio Pass region. Our analysis revealed a localized region with483

relatively high stress drop estimates between the surface traces of the San Gorgonio thrust and484

Mission fault. Furthermore, stress drops show a weak correlation with focal mechanism types so485

that thrust faults are connected to higher median stress drops than strike-slip and normal faults.486

Stress drops increase abruptly below ∼10 km depth and at the interface between Peninsular range487

and Transverse range rocks. The latter is likely related to differences in lithology between the488

two geological formations, so that feldspar-dominated Peninsular range material favors relatively489

larger stress drops whereas quartz-dominated Transverse range rocks exhibit relatively lower stress490

drops. Stress drops vary systematically with geologically inferred slip rates along the San Andreas491

fault system. Consequently, more rapidly loaded fault segments are connected to lower stress492

drops whereas slowly loaded faults create events with higher stress drops. While several factors493

may contribute to stress drop variations, our results suggest that within the greater San Gorgonio494

18

area, variations in slip rates and lithology are the predominant mechanisms. Thus, they should495

also be considered for seismic hazard assessment and ground motion simulations.496

Acknowledgments497

T. Goebel and E. Hauksson were supported by NEHRP/USGS grant G13AP00047. This research498

was also supported by the Southern California Earthquake Center (SCEC) under contribution num-499

ber 12017. SCEC is funded by NSF Cooperative Agreement EAR-0529922 and USGS Cooperative500

Agreement 07HQAG0008. We would also like to thank the open-source community for many of the501

programs utilized here (GMT, python, python-basemap, Gimp and the Linux operating system).502

19

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25

Figure 1: Overview of the major faults and seismicity within the study region. The study region and connectedseismicity are highlighted in red. Seismic events within southern California are shown by blue dots. Thelocations and names of major faults are highlighted by black lines and white font respectively. The insetshows the map location with respect to the Californian state boundaries and the San Andreas fault (SAF).

26

Figure 2: Seismicity within the SGP region in map view (a) and within a 2 km wide depth cross-sectionbetween A and A’ (b). Different fault segments that comprise the San Andreas fault system are labeled inblue. The beach balls in (a) mark the locations and focal mechanisms of the 1992, M6.4 Big Bear, the 1986,M5.6 North Palm Springs and the 2005, M4.9 Yucaipa earthquake. The fault orientations in (b) are constructedusing mapped fault traces, approximate dip angles and near-by seismicity clusters. Seismic events are broadlydistributed and can only partially be associated with mapped fault traces (e.g. for Banning and Mission Creekfault) highlighting the complexity of the deformation within the area.

27

Mission creek

Wilson creek

San Bernardinomountains

San Jacintomountains

Garnet hill

Pinto mount-

tain fault

San Bernardino Mill creek

San Gorgonio thrustBanning

San Jacinto fault

see Fig. 4

see Fig. 4

Pl

WC

BF

Cb

Figure 3: Map view of smoothed stress drop variations within the study region. Fault segments of the SanAndreas fault system are labeled in blue. The red line from A to A’ marks the location of the depth cross-sections in Figures 2b and 8. The blue squares show the sites of geologic slip rate estimates (see Figure 10 anddescription for details). Stress drops vary substantially from about 1 MPa to more than 20 MPa (see color-bar).

28

Low Stress Drop regionHigh Stress Drop region

0.1 MPa

1.0 MPa

10 MPa

100 MPa

1.4 MPa

18.7 MPa

Figure 4: Corner frequency and seismic moment for events within a high (green circle in Figure 3) and a lowstress drop region (red circle in Figure 3). The black, dashed lines highlight constant stress drops from ∼1 to∼20 MPa and the green and red lines mark the median stress drops for the two different regions. The two datasets show almost no overlap, which highlights a generic difference between the corresponding stress drops.

29

Figure 5: Source spectra for events within an area of low (left) and high stress drop corrected for differencesin moment by shifting along f −3 and colored according to stress drop. The solid, black line highlights a high-frequency fall-off slope of −2. High stress drop spectra are generally shifted further to the right due to highercorner frequencies and a smaller proportion of low-frequency contributions compared to the area of low stressdrop.

30

Figure 6: Smoothed spatial variations in stress drop for events within three different depth layers from 0–10,10–15 and 15–25 km.

31

Figure 7: Variations in stress drops as function of depth (a). Green dots show individual event stress drops andsquares show the binned, median stress drops and bootstrap errors. The latter are shown by horizontal error-bars which are of approximately same extent as the markers. The vertical error-bars highlight the extent ofindividual depth bins. The circles display stress drops after correcting for a depth dependent rupture velocityusing two different 1-D velocity profiles (b) for events beneath (green curve) and outside (red curve) of SGP.The dashed lines in b) show 10th and 90th percentiles.

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Figure 8: Same depth cross-section as in Figure 2 bottom, now with events colored and scaled according tostress drop. The background colors depict the spatial distribution of median stress drop, smoothed as in Figure3. The deep events southwest of the Mission Creek segment are connected to clusters of locally high stressdrops whereas events above 10 km seem to be marked by generally shallow stress drops. Focal mechanismsolutions for events within the area are shown in the inset. The beach-balls show strike-slip mechanisms inred, thrust in blue and normal faulting in green.

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Figure 9: Variations in average stress drops as function of faulting mechanism. The gray dots represent indi-vidual event stress drops and the solid line marks the median values for normal (green), strike-slip (red) andthrust (blue) faulting. Average values for these three faulting types are shown at the bottom of the figure. Thedashed lines show 10th and 90th percentiles. Normal faulting is generally connected to relatively lower stressdrops of ∼4 MPa whereas thrust faulting exhibits higher stress drops of ∼7 MPa.

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WC: 14-25 mm/yr

BF: 8+/-4 mm/yr

Cb: 5.7+/-0.8 mm/yr

San Bernardino Segment San Gorgonio Segment Banning &Garnett Hill Segments

Pl: 7-16 mm/yr

NW SE3

BC: 13 mm/yr

−2 +4

BP: 14-17 mm/yr

3

Figure 10: Changes in stress drop for seismic events along the San Andreas fault segments through the SGPregion from the northwest to the southeast within a ∼ 10 km wide zone. The x-axis shows the distance fromCajon pass in kilometers (see Figure 1 for Cajon pass location) for a transect that passes through the sites ofgeologic slip rate estimates (blue squares in Figure 3). Individual events are marked by gray dots and greenline marks the median. The dashed lines show 10th and 90th percentiles. Sites of geologic slip rate estimates:BC: Badger Canon (McGill et al., 2013), Pl: Plunge Creek (McGill et al., 2013), WC: Wilson Creek (Weldon andSieh, 1985), BF: Burro flats (Orozco and Yule, 2003), Cb: Cabezon (Yule et al., 2001), BP: Biskra Palms (Behr et al.,2010).

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Stress drop heterogeneity within tectonically …tgoebel/preprints/stress...107 of the San Andreas Fault in June 2005 (see Figure 2). 108 [Figure 1 about here.] 109 2.2 Tectonic complexity

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