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1 Department of Geology
University
of California, Davis
1 Shields Avenue
Davis, California
95616
manaker{at}geology.ucdavis.edu
(D.M.M.)
2 Western Earthquake Hazards
Team
U.S. Geological Survey
345 Middlefield Road, M/S 977
Menlo Park,
California
94025-3591
michael{at}usgs.gov
(A.J.M.)
3 Department of Earth and Planetary
Science
University of California, Berkeley
385 McCone Hall
Berkeley,
California
94720
burgmann{at}seismo.berkeley.edu
(R.B.)
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Abstract |
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 Top Abstract IntroductionModeling MethodologyInversion ResultsDiscussionConclusionsAcknowledgmentsReferences |
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We perform a joint inversion for hypocenters and the 3D P-wave velocity structure of the stepover region using 477 earthquakes. We find strong velocity contrasts across the Calaveras and Hayward faults, corroborated by geologic, gravity, and aeromagnetic data. Detailed examination of two seismic lineaments in conjunction with the velocity model and independent geologic and geophysical evidence suggests that they represent the southern extension of a northeasterly dipping Hayward fault that splays off the Calaveras fault, directly accounting for the deep slip transfer. The Mission fault appears to be accommodating deformation within the block between the Hayward and Calaveras faults. Thus, the Calaveras and Hayward faults need to be considered as a single system for developing rupture scenarios for seismic hazard assessments.
Online material: 3D interactive visualizations of the Mission and Alum Rock hypocenters.
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Introduction |
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TopAbstractIntroductionModeling MethodologyInversion ResultsDiscussionConclusionsAcknowledgmentsReferences |
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The Calaveras and Hayward faults overlap for a length of 
60 km, bounding
the East Bay Hills in a restraining stepover region
(Aydin and Page,
1984) (Figs. 1 and
2). The southeast 20 km of the
overlap between these two strike-slip faults bound the Mission Hills that border
the eastern San Francisco Bay alluvial plain
(Fig. 1). Here the surface
traces of the two faults are 3–5 km apart and the interaction between the
faults produces contractional structures
(Aydin and Page,
1984; Kelson
et al., 1993). The contraction in the Mission Hills due to
local fault interaction is accommodated by folding and reverse faulting
(Jones et al.,
1994).
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Although the most significant seismic threat in the San Francisco Bay region is due to earthquakes occurring on right-lateral, strike-slip faults, an additional hazard exists because of reverse faulting in the California Coast Ranges. Several recent damaging earthquakes in California involve a significant component of dip slip. Examples include the 1983 (MW 6.7) Coalinga (Sipkin and Needham, 1990), 1987 (ML 5.9) Whittier Narrows (Hauksson et al., 1988), 1989 (MW 6.9) Loma Prieta (Ellsworth, 1990), 1994 (MW 6.7) Northridge (Hauksson et al., 1995), and 2003 (MW 6.5) San Simeon earthquakes (Hardebeck et al., 2004). These events illustrate the seismic threat from reverse faulting in contractional regions along transform plate boundaries.
Recognizing the potential seismic hazard due to reverse faulting in the San Francisco Bay region, Andrews et al. (1993) evaluated such a hazard for the Calaveras-Hayward fault stepover region. Through an analysis of fault geometries and slip rates, they calculated a hypothetical dip-slip event in the region from the accumulated dip-slip deficit. Based on a seismogenic depth of 10 km, the horizontal shortening accumulated over 150 years would produce a MW 6.3 event if the entire slip deficit was released in a single event. Additionally, they hypothesize that a dip-slip event may trigger strike-slip events on the Hayward fault (Andrews et al., 1993). However, the lack of dip-slip earthquakes in the area led Andrews et al. (1993) to express a need for further investigation and characterization of the region.
A seismic lineament through the Mission Hills appears to link the seismicity on the southern and central Calaveras fault and the Hayward fault (Fig. 1). It originates on the Calaveras fault where the surface trace begins a more northerly strike (Jennings, 1994). The lineament exhibits weak seismicity (M <4) confined to depths of 3 to 8 km and is predominantly dextral strike-slip with little dip-slip movement (Andrews et al., 1993; Wong and Hemphill-Haley, 1992). Transfer of slip between the Calaveras and Hayward faults has been attributed to this lineament (Ellsworth et al., 1982; Wong and Hemphill-Haley, 1992; Andrews et al., 1993), based on the alignment of catalog hypocenter locations from the U.S. Geological Survey (USGS) Northern California Seismic Network (NCSN) with the mapped trace of the Mission fault (Fig. 1). The Calaveras fault south of this juncture is believed to have a long-term slip rate of 15 ± 3 mm/yr (Working Group on California Earthquake Probabilities, 1999). North of the juncture, the long-term slip rate decreases to 6 ± 2 mm/yr (Kelson et al., 1996), with the remaining slip (9 ± 2 mm/yr) presumably transferred to the Hayward fault (Working Group on California Earthquake Probabilities, 1999, 2003).
Despite the apparent alignment, evidence suggests that the Mission fault is not accomodating deep slip transfer. First, the highest rates of surface creep (8–9 mm/yr observed for several decades before the 1989 Loma Prieta earthquake) on the Hayward fault occur more than 11 km south of the mapped surface expression of the Mission-Hayward fault junction (Lienkaemper et al., 1991; Lienkaemper and Galehouse, 1997) in the Fremont area. Microseismicity is absent vertically below the southernmost Hayward fault where the maximum surface creep rate has been observed (Fig. 1). Another trend of shallow microseismicity diverges from the Calaveras fault south of the Calaveras Reservoir near the town of Alum Rock (Fig. 1) and projects to the southern Hayward fault south of the region of maximum creep. This trend (hereafter called the Alum Rock seismic trend) parallels the Mission seismic trend across the Mission Hills stepover region. The Alum Rock trend is less prominent and has a lower rate of seismicity than the Mission trend. However, no microseismicity occurs directly below the southern Hayward fault north of this trend (Fig. 1). Although this trend projects toward the southern Hayward fault, it is shallow (<5 km depth) and does not connect seismicity on the Hayward fault. Microseismicity is typically associated with creeping faults (i.e., Parkfield segment of the San Andreas fault, southern Calaveras fault, central and northern Hayward fault [Hill et al., 1990]), and aseismic areas are associated with locked fault zones (Oppenheimer et al., 1990; Kafka and Levin, 2001). Therefore, the southern Hayward fault should exhibit microseismicity where it is creeping at 9 mm/yr.
Second, geologic investigations indicate that the Mission fault is a reverse fault (Jones et al., 1994; Graymer et al., 1994, 1995), based on the placement of the older strata over younger strata. Third, Wong and Hemphill-Haley (1992) relocated hypocenters using a 1D velocity model with station corrections and found that the linear trend of seismicity was relocated 1 to 1.5 km southwest of the mapped trace of the Mission fault, dipping steeply to the northeast. Additionally, Wong and Hemphill-Haley (1992) observed that landslide material obscures much of the presumed Mission fault trace and found no evidence of the fault as mapped by Hall (1958) and Dibblee (1980). Wong and Hemphill-Haley (1992) also cite reports of fault trenching by consulting geologists who were unable to identify Holocene activity on the mapped Mission fault. Therefore, they consider the mapped trace of the Mission fault not to be the surface expression of the seismically active structure at depth. They suggest that the observed seismicity is attributable to a Hayward fault with multiple strands: an aseismic trace exposed at the surface along the creeping section and another seismic trace that is not exposed at the surface (Wong and Hemphill-Haley, 1992). Kelson et al. (1993) excavated across a tonal lineament and topographic swale that coincides with the surface projection of the relocated seismicity of Wong and Hemphill-Haley (1992) near the Hayward fault but found no evidence for such a structure.
To account for uncertainties in fault location and segmentation, an extension of the southern Hayward fault that projects beyond the Mission trend to the Alum Rock trend has been included as a possible source in earthquake probability studies for the San Francisco Bay area (California Division of Mines and Geology, 1996; Working Group on Northern California Earthquake Probabilities, 1996; Working Group on California Earthquake Probabilities, 1999, 2003). It is critical to understand how slip transfer occurs between the Calaveras and Hayward faults, because understanding the fault connectivity and the mechanism of slip transfer will allow us to better assess the potential seismic hazard, not only from reverse faulting in the stepover region, but from triggered strike-slip faulting on the Hayward fault.
In this article, we attempt to elucidate the subsurface structures that may contribute to the seismic hazard in the Mission Hills. Our investigation uses existing geophysical and geologic data to illuminate the subsurface structure. We develop a 3D P-wave velocity (Vp) model for the stepover region from catalog seismicity data of the Northern California Seismic Network (NCSN). Previous studies addressed the crustal velocity and its relation to subsurface structure along the Calaveras fault south of the stepover (Thurber, 1983; Michael, 1988; Dorbath et al., 1996) and the Hayward fault to the north of the stepover (Zhang and Thurber, 2003). Additionally, precise hypocenter relocations using double-difference and waveform cross-correlation techniques have produced more detailed hypocenter relocations, again south of the stepover region (Schaff et al., 2002; Rubin, 2002). Zhang and Thurber (2003) also performed a joint inversion for hypocenters and Vp structure utilizing a double-differencing technique on the Hayward fault, with some overlap with the northern portion of our study area.
We take a broader approach here, combining a 3D Vp model, hypocenter relocations, and focal mechanisms with independent geologic, seismologic, gravity, and aeromagnetic data to develop a structural and kinematic model of the Calaveras-Hayward fault stepover region. Our interpretation suggests a mode of direct slip transfer between the Calaveras and Hayward faults as the Hayward fault splays from the Calaveras fault near the intersection of the Alum Rock seismic trend with the Calaveras fault. A northeasterly dipping Hayward fault diverges from the Calaveras fault, becoming steeper as the fault progresses further north. The Hayward fault separates the San Francisco Bay and Mission Hills blocks, with the San Francisco block wedging under the Mission Hills, causing contraction across the Mission Hills. The Mission fault is internal to the zone of contraction within the Mission Hills. This suggests that the Calaveras and Hayward faults are a single system at seismogenic depths, and this has implications for rupture scenarios used in seismic hazard assessment.
Geologic Setting
Understanding the geologic setting of the region is critical for developing a
structural and kinematic model of the region. The Mission Hills rise from the
near sea level surface of the East Bay alluvial plain to an altitude of more
than 750 m in less than 4 km
(Andrews et al.,
1993). Uplift of the Mission Hills was coeval with the regional
uplift of the California Coast Ranges and is estimated to have commenced
3.5 Ma (Harbert and
Cox, 1989), although
Page et al.
(1998) suggest the present ranges were uplifted after a tectonic
pulse about 0.4 Ma. The East Bay Hills and Mission Hills are located between the
Calaveras and Hayward faults, and contain numerous contractional structures
(reverse faults and folds) in an en echelon arrangement between the major
bounding faults (Graymer
et al., 1994,
1996;
Aydin and Page,
1984). Jones
et al. (1994) suggest a significant component of vertical
displacement on the Mission fault based on a minimum vertical displacement of
520 m of late-Miocene to early-Pliocene rocks.
The surface bedrock geology of the stepover region is representative of fault-bounded, crustal blocks with lithologic assemblages that are largely distinct and easily distinguishable (Fig. 2). The Mission Hills block is composed of Cretaceous and Tertiary marine sedimentary rocks. Also present in the southern part of the stepover region are Franciscan Complex rocks, a subduction zone complex consisting of a mélange of marine sedimentary rocks and ultramafic bodies. These ultramafic bodies include serpentinite blocks of the Coast Range Ophiolite (Graymer et al., 1995, 1996). Alluvial deposits result from erosion of mainly the Franciscan Complex (Graymer et al., 1994, 1995). The northern-most part of the stepover region contains Cretaceous and Tertiary sedimentary rocks of the Great Valley sequence, with blocks of Franciscan Complex concentrated along the Hayward fault zone (Wagner et al., 1990). Mapping of fluvial terraces suggest the Mission Hills is being uplifted at a rate of 1.5 ± 0.5 mm/yr (Kelson et al., 1993).
The Mission Hills block is bounded on the west by the Hayward fault and the
adjoining San Francisco Bay block. The San Francisco Bay block is composed of
Cretaceous-to-Jurassic Franciscan Complex which is covered by 250 m of
Quaternary alluvium derived from the hills of the stepover region and in most
places overlain by two types of interlayered bay deposits
(Koltermann and Gorelick,
1992). The base of the Franciscan Complex west of the Hayward fault
is estimated at a depth of 15 km and the depth of the Moho below San Francisco
Bay is estimated at 25 km
(Holbrook et al.,
1996). Exposures of Tertiary marine rocks west of the Hayward fault
are limited to the western margin of the San Francisco Bay block near the San
Andreas fault (Wagner
et al., 1990).
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Modeling Methodology |
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P-wave travel times to local stations from earthquakes, quarry
blasts, and seismic refraction shots were inverted for Vp,
hypocenter location, and station corrections as described by
Thurber (1983)
and Eberhart-Phillips and
Michael (1998). We use the program SIMULPS12, an algorithm developed
by Thurber, Eberhart-Phillips and others
(Evans et al.,
1994). The data consist of 29,826 P-wave arrival times for
576 events from 1984 to 1998, including 477 earthquakes of
MD 
1.5 in the study region, 49 well-located earthquakes
outside the study area, and 61 seismic refraction shots from the BASIX
(Brocher et al.,
1992) and Morgan Hill studies
(Blumling et al.,
1985). These events were recorded by 325 seismic stations, including
permanent stations of the NCSN and portable stations deployed during
seismic refraction studies (Fig.
3). All catalog locations, arrival times, and station information
used in the inversion were obtained from the data repository at the Northern
California Earthquake Data Center (NCEDC) and the
USGS.
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The velocity model is defined for nodes in a 3D grid with the x axis oriented at an azimuth of 55° (approximately perpendicular to the Mission fault) and the y axis oriented at an azimuth of 325° (Fig. 4). The depth spacing of the 3D grid was set at 3-km intervals, whereas horizontal grid spacing varies as shown in Figure 4, to concentrate nodes near the seismic lineaments. We calculate velocity values and hypocenter locations through an iterative, damped, least-squares inversion. Each iteration defines new ray paths, new hypocenter locations, and new Vp values at each grid node. Travel-time residuals showed a linearly increasing positive bias as the source-to-receiver distance increased over 30 km and were significantly positively biased past 70 km. This indicates the model is too coarse beyond the ±15 km from the y axis, which affects the travel times for larger source-to-receiver distances. Therefore, we apply distance weighting to each observation, with a source-to-receiver distance less than 30 km given a weight of unity, decreasing linearly to zero from 30 km to 70 km.
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We begin with a coarse 3D grid (node spacing >15 km) with a priori velocity values at each node from an initial 1D velocity model. The 1D a priori Vp model was created with the program VELEST (Kissling, 1995) using P-wave arrival times at local stations for 315 earthquakes of MD 1.5 or greater in the Mission Hills area. These earthquakes occurred between July 1984 and April 1997. We used three different starting velocity models, based on USGS 1D models routinely used for creating earthquake hypocenter catalogs. All three models converged to a similar velocity profile. A combined model based on the average convergence model was then used as a starting model to obtain a final, 1D Vp model that was expanded onto a coarse 3D grid for the starting model in the 3D Vp model inversion. The Vp values for the coarse grid were modeled using a series of damping parameters to obtain values for the outer grid nodes of the study area. We gradually increase the model complexity by densifying the grid to the fine model.
Each inversion uses an empirically selected damping parameter that optimizes the trade-off between the data variance and solution variance. The damping parameter is a weighting factor that determines the relative importance given to minimizing the prediction error (or model misfit) or the solution length (or model roughness) (Menke, 1989, pp. 52, 59, 76–79). If the damping parameter is too high, the model is too smooth and details in the structure will be lost. If the damping parameter is too low, the model becomes artificially complex without significantly reducing the data variance. Because the greatest change in the calculated 3D velocity model will occur in the first iteration, we performed a series of single-iteration inversions using different damping values to measure the effect of the damping parameter on the data misfit and solution variance (Fig. 5). For the final model, we selected a damping parameter of 1000, although damping values as low as 400 could be considered acceptable. Because we are attempting to elucidate gross subsurface features, the higher damping value provides sufficient model detail while ensuring a stable inversion.
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An inspection of the diagonal elements of the resolution matrix is insufficient to evaluate the model resolution of our damped inversion. The model resolution matrix includes contributions from neighboring nodes, and the off-diagonal elements of the resolution matrix are nonzero. The preferred resolution for a node is represented by a peaked distribution at that node without significant contributions from adjacent nodes. We use the spread function of Michelini and McEvilly (1991) to evaluate the distribution of the resolution matrix. The spread function is calculated for each node from the diagonal element of the resolution matrix and the elements of the corresponding row, weighted by the distance from the node (Michelini and McEvilly, 1991).
Figure 6 shows the model resolution matrix as described by the spread function. This serves two purposes: to evaluate the amount of information in each node and to evaluate the contribution from neighboring nodes. Higher diagonal values of the resolution matrix cause the spread function to be small for the corresponding node. Contributions from neighboring nodes, particularly distant nodes, cause a larger spread function value. As expected, the best resolution occurs in areas where seismicity is more frequent and where the stations are located. The best resolution is in the southern end of the model (spread functions less than 4) between y = 10 and y = 30 km and is associated with higher rates of seismicity. Although many nodes from 3 to 12 km in depth have a spread function more than 4, the number of modeled ray paths traveling through these nodes typically exceeds 1000. However, the velocities at these nodes have relatively greater contributions from neighboring nodes, reflecting the greater spread function values using the damping value of 1000 and the nonuniform distribution of earthquakes.
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Areas with spread function values greater than 8 indicate that the model is poorly resolved in these regions. This typically occurs at shallow depths where station coverage is poor. At shallow depths the rays travel nearly vertically, and the nodes are modeled only where there are stations directly above them. The number of ray paths per node is typically below 50. Similarly, the number of ray paths per node at depths below 12 km is 100 to 500. At depths greater than 10 km, the model also has poor resolution because of limited nodal offsets, and any velocity variations are small because of the higher damping parameter. Below 12 km, the velocity model remains essentially unchanged from the initial 1D model.
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Inversion Results |
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TopAbstractIntroductionModeling MethodologyInversion ResultsDiscussionConclusionsAcknowledgmentsReferences |
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Crustal Velocity Distribution
The final 3D Vp model is shown in
Figures 7 and
8. Model contours were obtained
from Delauney triangulation of the velocity model nodes. The model reveals
lateral velocity variations across the major faults, including a sharp
Vp contrast across the Calaveras fault below 3 km depth
(Fig. 8B,C,D). The velocity at
3 km depth reaches a relative high near the crest of the Mission Hills in the
stepover region (Fig. 7B),
conincident with the Mission fault surface trace. High velocities are apparent
at depths of 6–9 km in association with the Hayward fault
(Fig. 8A–H). North of the
Calaveras Reservoir, the velocities are lower to the east of the Calaveras fault
(Fig. 8A–E). At the
Calaveras Reservoir (Fig. 8F),
a relative velocity high is observed at the Calaveras fault. South of profile
FF', the Vp values east of the Calaveras fault are
markedly increased over velocities further northward
(Fig. 8G,H).
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Relocated Hypocenters
The final 3D Vp model with station corrections was used
in a simultaneous inversion to relocate the 477 model earthquakes
(Fig. 3). For these events, the
relative hypocentral relocation errors were 0.015 km (x), 0.220 km
(y), and 0.032 km (z). To better characterize the seismicity
of the region, we expanded our dataset and relocated 576 events
(MD >2) from January 1978 to July 1998
(Fig. 9). The relative
hypocentral relocation errors for these were 0.013 km (x),
0.012 km (y), and 0.032 km (z). The most obvious
difference between the NCSN catalog and relocated events appears on
the Calaveras fault in the southern portion of the study area. Most of the
events used to create the Vp model (all with
MD >2) are located below 6 km. Cross-fault seismicity
profiles of this area (Fig.
8G,H) suggest a steep, near-vertical Calaveras fault, in agreement
with studies by Michael
(1988), Schaff
et al. (2002), and
Rubin (2002)
for the Calaveras fault south of our study area. Our relocations are shifted
eastward from the surface expression of the Calaveras fault. This may be due to
the proximity of these profiles to the fine model boundary.
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Separately, we relocate 255 events of MD >1.5 (some of which were included in the previously mentioned 576 events) for the Mission and Alum Rock seismic trends for 1978–1998 to provide additional information about shallow seismicity, possible sources, and source geometry (Fig. 10). The relative relocation errors for the Mission seismic trend were 0.018 km (x), 0.015 km (y), and 0.044 km (z). The relative relocation errors for the Alum Rock seismic trend were 0.019 km (x), 0.018 km (y), and 0.051 km (z). The relocated Mission trend are shifted southwest of the mapped surface trace of the Mission fault and the NCSN catalog locations by 0.5 to 1.0 km, similar to the relocated trends of Wong and Hemphill-Haley (1992) and Zhang and Thurber (2003).
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Seismicity profiles of these trends suggest multiple fault planes as sources.
(3D plots of seismic trends created using LiveGraphics 3D
[Kraus,
2003] are available as an electronic supplement to this
article.) Coordinate axes and hypocenter locations
are referenced to the model grid axes shown in
Figure 4. Seismicity is
typically confined to depths of 3 to 11 km. For the Mission trend, most of the
seismicity appears to lie on a single fault plane (Plot is available
as an electronic supplement to this article). The source has a near-vertical dip,
with the southern portion of the trend exhibiting a steep northeasterly dip of
approximately 70°, with the dip rotating as the trend progresses
northwesterly to vertical. The northern end of the Mission trend
(Fig. 10B) exhibits clustering
at 5 km and 7 km depth. The central region
(Fig. 10C) shows clusters of
seismicity at depths of 7 to 11 km. Along the southern end near the junction
with the Calaveras fault seismicity (Fig.
10D), the seismicity becomes diffuse, suggesting multiple faults
accommodating motion at the junction.
The Alum Rock trend shows two to three clusters of seismicity (Plot
is available as an electronic supplement to this article). This shallow trend
(<5 km depth) diverges from the deeper seismicity (>5 km depth) associated
with the Calaveras fault. The seismicity
(Fig.
10E,F) associated with the Alum Rock seismic trend is more diffuse
than the Mission trend. The northern cluster of seismicity
(Fig. 10E) forms a distinct
linear trend in profile view, with a steep northeasterly dip of 70°.
The southern cluster of the Alum Rock trend
(Fig. 10F) shows subset of
hypocenters that defines a possible low-angle, eastern-dipping fault. These
multiple clusters suggest several fault planes may be responsible for the
seismicity of the Alum Rock trend.
Best-Fit Fault Plane, First-Motion Solutions, and Kostrov Summations
To better understand the seismotectonics of the Mission and Alum Rock seismic
trends, we calculate both the best-fit fault plane to the hypocenters and
first-motion, fault-plane solutions (assuming double-couple) for events on the
Mission and Alum Rock seismic trends from 1978 to 1998. We also calculate the
Kostrov sum of the moment tensors
(Kostrov,
1974). Because the time-span of the data includes the 1984
MW 6.2 Morgan Hill and 1988 MW 5.9 Alum
Rock earthquakes on the Calaveras fault, there may be concern that these events
might not represent the long-term strain mode. However,
Oppenheimer et al.
(1988) found no change in the focal mechanisms near the mainshock
rupture before and after the Morgan Hill event, and the orientations of the
aftershock slip planes were consistent with orientations predicted by the
Coulomb failure criterion due to stress changes from the main shock. Therefore,
we believe that the data are representative of the long-term strain orientation
in the region.
A potential problem with 3D tomography is the effect that lateral variations in the crustal velocity can have on the modeled ray paths. The velocity contrast across faults at depth may produce lateral refractions, resulting in a systematic bias in the azimuth of the first arrivals. The resulting incorrectly modeled velocity contrasts will thus introduce bias into the hypocenters. Additionally, ray parameters near the recording stations will be incorrect, resulting in bias in the focal mechanisms. This would be especially true for our modeling, where the use of microseismicity in the modeling places a strong reliance on events with few first motions.
If lateral refractions have introduced a systematic bias, we should observe an abnormally high number of discrepant data close to the fault plane on the "slow" material side. Specifically, higher numbers of discrepant compressive first motions in the slow material’s dilation quadrant and discrepant dilations in the slow material’s compressive quadrant in a double-couple focal mechanism should be apparent (Dorbath et al., 1996).
To test for lateral refractions, we analyze the distribution of first-motion arrivals by looking at the angle between the ray path and the fault plane. To do this, we calculate the angle between the fault plane and the first arrival ray path, looking at the distribution of discrepant motions from the fault plane for each focal mechanism. We analyzed the distribution of angles between the discrepant motions and the fault plane divided using 15° and 30° bins (Fig. 11). If bias exists, then the distribution of discrepant compressive first motions should peak within 15° to 30° of the azimuth of the fault plane on the "slow" side, and discrepant dilatory first motions should similarly peak near 180° from the fault-strike azimuth. Our analysis of the distributions indicates no such peak in the distribution for both the Mission and Alum Rock seismic trends. Therefore, there is no apparent bias of the relocated hypocenters and focal mechanisms due to lateral refractions.
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We calculate the best-fit fault plane for subsets of the relocated hypocenters, using 152 events on the Mission trend and 101 events on the Alum Rock trend. The best-fit fault plane was calculated by taking a sample of the hypocenters and performing a least-squares minimization of the distance from each hypocenter to a plane. We perform 1000 bootstrap samplings for each data set to calculate the 95% confidence level. The best-fit fault plane for the Mission seismic trend is oriented N43°W dipping 82° to the northeast. The 95% confidence range for the dip angle is 78°–86°, which suggests faulting on a steep northeasterly dipping plane. Although this dip might be due to unmodeled velocity contrasts across the fault, it is in agreement with the dip suggested by the seismicity profiles for the Mission trend (Fig. 10). The best-fit fault plane for the Alum Rock seismic trend is oriented N54°W with a southwest dip of 89°, essentially a vertical fault plane within the uncertainty at the 95% confidence level. However, profiles of the Alum Rock trend suggest that the seismicity is due to multiple fault planes, and therefore the best-fit plane is not fully representative of structures within the trend.
We use the program FPFIT (Reasenberg and Oppenheimer, 1985) to calculate the focal mechanisms for earthquakes relocated with the 3D velocity model. After removing events with less than 20 recorded first arrivals, focal mechanisms for 138 earthquakes from the Mission fault trend and 56 earthquakes from the Alum Rock trends were calculated. An examination of the focal mechanisms shows that the Mission seismic trend is composed of largely strike-slip events, although events with a component of reverse dip-slip motion occur (Figs. 12 and 13). Although seismicity profiles suggest that the northern portion of the Mission trend is likely confined to a single, near-vertical fault plane, the diffuse nature of the seismicity to the south suggests more complexity, with the possibility of multiple, northeasterly dipping structures in a broader fault zone as the seismic source. This is in agreement with the analysis of focal mechanisms by Wong and Hemphill-Haley (1992), who found 19 right-lateral, strike-slip events, 12 reverse events, and 2 normal events in 33 focal mechanisms analyzed. Focal mechanisms for the Alum Rock seismic trend show a combination of strike-slip and oblique-slip events with a significant component of reverse motion (Figs. 12 and 14). Again, the multiple sources suggested by seismicity profiles are evident in the focal mechanisms. The easterly dipping faulting suggested by seismicity profiles and focal mechanisms is in agreement with the general trend of reverse faulting present in this part of the stepover region (Jones et al., 1994).
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We determined the average focal mechanism for the Mission and Alum Rock seismic trends with Kostrov moment tensor sums (Fig. 15). Each individual fault plane solution has sufficient uncertainty so that most could be either pure strike-slip events or have a component of dip-slip. This was noted by Andrews et al. (1993), who started with the null hypothesis that the events on the Mission seismic trend should be pure strike-slip. By examining each mechanism separately they were unable to void this null hypothesis and concluded that the earthquakes on the Mission trend are pure strike-slip. However, the inability to void the null hypothesis could simply be a result of statistical uncertainty in the focal mechanisms. Additionally, inspection of seismicity profiles indicates that the Mission trend sources may define a more complex zone of faulting. By using the Kostrov sums for the best focal mechanisms, we determine the average mechanism that will have smaller uncertainties to determine whether a statistically significant component of dip-slip occurs in these seismic trends. We can then evaluate the strain release within the volume and determine the dominant style of deformation.
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The uncertainty in the Kostrov sum is determined with nonparametric bootstrap statistics, with each data set resampled 1000 times to produce 95% confidence regions. We select the "best" focal mechanisms for Kostrov summation calculations based on the following criteria, presented in the order of selection process: (1) minimum of 20 first arrivals; (2) reject events with misfit greater than 0.15 for the Mission trend and 0.20 for the Alum Rock trend (different misfit levels were applied to the different trends to ensure a sufficient number of events were available for analysis); (3) reject events which, by inspection, have poor coverage of the focal sphere; (4) for multiple solutions, select solution with lowest misfit; and, if the misfit is equal, select solution with fewest discrepant observations. Events with multiple minima that had equal misfit and number of discrepant observations were discarded entirely to prevent bias in the selection process. After reducing the data set, 98 focal mechanisms remained from the Mission trend and 33 focal mechanisms remained from the Alum Rock trend.
We compute the principal strain axes based on the average of 1000 bootstrap samples. The average focal mechanism will have P, T, and B axes that coincide with the eigenvectors of the summed moment tensors. The bootstrap sampling ensures that the random errors in each mechanism are not propagated through to the calculation of the principal strains, because they are averaged before the eigenvectors are calculated. In the original form, the Kostrov sum is computed by weighting each focal mechanism according to its seismic moment. We performed two sets of calculations for the Kostrov sum. The first calculations weighted the events by a factor of 101.5M (where M is the coda magnitude). As expected, the results were strongly influenced whenever the largest magnitude events were included in the random bootstrap resamplings. Therefore, we also performed a second set of calculations where each mechanism was given equal weight. This reduces the effect of the largest events, whose contribution is heavily dependent on the period studied.
Figure 15 shows the results of the Kostrov sum calculations for the Mission and Alum Rock seismic trends. The Kostrov sum for the Mission seismic trend is indicative of primarily strike-slip motion. The magnitude-weighted solution suggests that the presumed right-lateral component of slip dominates the moment release with almost no reverse motion as a percentage of the total moment released. The equal-weighted solution is right-lateral with a component of dip-slip with reverse motion (northeast side up). Although the Mission trend shows a component of contraction occurring across the region, it is a negligible amount of the total moment released. The Alum Rock seismic trend differs in style from the Mission trend. The magnitude-weighted sum exhibited a consistent trend for the P axis. However there was a considerable range between the T and B axes, due to spread in the focal mechanisms for the largest events in the Alum Rock seismic trend, especially the largest reverse focal mechanism (Fig. 14). Because the first test is weighted by magnitude, the larger events exert more influence on the final P-, B-, and T-axis locations. The resulting orientation for the magnitude-weighted solution indicates primarily reverse-style deformation on a northwest or southerly dipping fault (Fig. 15). The equal-weight solution exhibits a more consistent mechanism of oblique right-lateral slip on a northwest trending, northeast dipping fault. These solutions suggest a strong component of contraction across the region in addition to strike-slip motion. This is consistent with the style of faulting observed in the stepover region (Graymer et al., 1995). Based on magnitude-weighted solutions, the Mission seismic trend accommodates mainly strike-slip motion, and the Alum Rock trend is dominated by contraction.
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Discussion |
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TopAbstractIntroductionModeling MethodologyInversion ResultsDiscussionConclusionsAcknowledgmentsReferences |
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Certain features of the model that are relatively well resolved based on the model resolution are corroborated by other data (Figs. 7 and 8). A Vp high is visible in sections AA' and BB' (Fig. 8A,B) west of the Hayward fault, corresponding to the location of the Coyote Hills. The Coyote Hills define a prominent ridge of low hills, composed of metasedimentary rocks and greenstone of the Franciscan Complex, that project out of the bay alluvial plain west of the Silver Creek fault (Wagner et al., 1990; Graymer et al., 1996). This linear ridge appears as a prominent aeromagnetic low (Jachens and Roberts, 1993) and corresponding local gravity high (Roberts and Jachens, 1993). A relative velocity high on the GG' section (Fig. 8G) at x = 7.5 km corresponds to a magnetic high (Jachens and Roberts, 1993) associated with surface exposure of ultramafic rocks of the Franciscan Complex (Wagner et al., 1990).
Other general features, although not well resolved based on the resolution spread, are also corroborated. The shallow Vp structure at z = 0 and 3 km (Fig. 7A,B) shows Vp highs along the Calaveras fault corresponding to the start of a significant negative gradient in the isostatic residual gravity westward toward the San Francisco Bay block (Roberts and Jachens, 1993). Two local Vp lows at z = 0 and 3 km correspond with this low-gravity anomaly of the Santa Clara basin (Fig. 7A,B). The gravity low is represented in the velocity profile HH' (Fig. 8H) between the Evergreen and Silver Creek faults. Additionally, low Vp east of the Calaveras fault at z = 0 and 3 km (Figs. 7A,B and 8A–D) correspond with the Livermore Valley basin and the related local isostatic residual gravity low (Roberts and Jachens, 1993). South of the Calaveras Reservoir and east of the Calaveras fault (Figs. 7B and 8G,H), the elevated Vp corresponds to the rocks of the Franciscan Complex in the Diablo Range (Wagner et al., 1990; Graymer et al., 1996), and a relative gravity "plateau" (Roberts and Jachens, 1993).
Although the 3D Vp model is weakly resolved in some areas, there is evidence of discrete blocks of high-velocity material. The profiles of the velocity model with relocated hypocenters show the seismicity clustering around high-velocity regions, suggesting that the material properties of the rock in the fault zone are controlling the distribution of seismicity (Fig. 8G,H). Michael and Eberhart-Phillips (1991) suggested a general relation between increasing Vp and the ability of rocks to accumulate elastic strain energy. They also suggest that if the material properties of the fault zone and the surrounding rocks control how the fault generates earthquakes, then Vp models could be used in fault segmentation models to estimate future seismic moment release (Michael and Eberhart-Phillips, 1991). Regions of relatively high velocity correspond to local aeromagnetic highs (Jachens and Roberts, 1993) and suggest the presence of ultramafic rocks in the fault zone. Ultramafic rocks are exposed at the surface along the Calaveras and Hayward faults (Wagner et al., 1990; Graymer et al., 1994). Control of seismicity by these ultramafic bodies has been observed further northward on the Hayward fault, where seismicity is concentrated on the western side of the San Leandro gabbro body (Ponce et al., 2003).
Development of Structural Model
The uplift in the Mission Hills region has been attributed to local fault
geometry or the partitioning of the contractional strain from the oblique motion
along the Pacific-North American Plate boundary.
Aydin and Page
(1984) examined the East Bay and Mission Hills and concluded that
the left stepover geometry of the right-lateral Calaveras and Hayward faults
resulted in contractional strain in the region between them.
Jones et al.
(1994) argue that the observed reverse faulting and folding in the
region is caused by an eastward translation of crustal blocks that move along a
midcrustal decollemont at 12–15 km depth, allowing tectonic wedges to
translate eastward and accounting for the compressive component of the oblique
motion of the Pacific plate. It has been proposed that the transfer of slip
between the Calaveras and Hayward faults occurs on this subhorizontal ductile
shear zone (Jones et
al., 1994). This is difficult to substantiate without
additional evidence of the subsurface geology and fault geometry at greater
depth. However, seismic reflection studies suggest that the northern Hayward and
San Andreas faults are dipping structures and continue below this speculated
detachment (Parsons and
Hart, 1999). Therefore, we do not believe that a detachment is
responsible for slip transfer, and we base our model on the stepover scenario of
Aydin and Page
(1984).
Fault stepover regions and similar fault discontinuities in strike-slip faults show that left-stepping, dextral-slip systems produce regions of convergence in the stepover region (McClay and Bonora, 2001; Westaway, 1995; Twiss and Moores, 1992, pp. 117–124; Woodcock and Fischer, 1986; Christie-Blick and Biddle, 1985). This geometry produces a strike-slip duplex, a region of deformation bounded by major faults containing horses separated by internal faults that accommodate strike-slip and vertical motion. The region bounded by the major faults experiences internal deformation through folding and faulting to accommodate the convergence. However, the Calaveras-Hayward fault stepover is not a "pure" stepover, because the Calaveras fault continues to slip north of the Mission Hills. Despite this, the fault geometry will produce a similar zone of convergence (Aydin and Page, 1984) and is structurally similar to a contractional duplex.
Based on the fault geometry, geologic and geophysical evidence, and the results of our velocity model with relocated hypocenters, we suggest that uplift in the Mission Hills region is caused by the San Francisco Bay block wedging under the Diablo Range, with relatively high-velocity material (and by inference, strong and difficult to deform) translating along the fault. As the wedge proceeds northwesterly along the Calaveras fault, the block boundary also moves northward. This tectonic "snow plow" of Franciscan Complex rocks west of the Calaveras fault is being driven under the Mission Hills as the block translates to the northwest. This hypothesis implies that the Hayward-Evergreen fault system is a bounding fault along the face of the contractional strike-slip stepover, because the block to the southwest of the fault is wedging under the Mission Hills. A corollary is that the Hayward fault may also be the site of reverse motion, with the Mission Hills representing the hanging wall. Koltermann and Gorelick (1992) and Jones et al. (1994) report 225 m and 300 m, respectively, of vertical displacement across the Hayward fault in the Mission Hills area. As a southern extension of the Hayward fault, the Evergreen fault serves as the direct interface between the leading edge of the wedge of the contractional stepover. A similar fault structure is observed further south, where the San Andreas fault makes a slight westerly jog and the Paicines-Calaveras faults diverge near San Juan Bautista (Dorbath et al., 1996).
In Figure 16, we compare our
model interpretation with analog models of restraining stepovers in strike-slip
fault systems from McClay
and Bonora (2001). The southern and central Calaveras fault exhibits
15 mm/yr, of which 9 mm/yr of slip is believed to be transferred to the
Hayward fault, leaving the northern Calaveras fault to slip at 6 mm/yr for
another 40 km further north from the where the Mission seismic trend diverges
from the Calaveras fault microseismicity
(Working Group on
California Earthquake Probabilities, 1999). Despite this added
complexity of incomplete slip transfer, similarities in structure are observed,
suggesting that the stepover analogy is suitable. In
Figure 16, the bounding fault
on the left side of the analog model of
McClay and Bonora
(2001) represents the Hayward-Evergreen fault system. The bounding
fault splays from the analog model’s main fault trace, which represents
the Calaveras fault (Fig. 16,
analog profile A). The bounding fault accommodates both strike-slip and dip-slip
movement (Fig. 16, analog
profiles A and B) and bounds an area of uplift within the Calaveras-Hayward
system. As the fault system progresses further north
(Fig. 16, from analog profiles
B to D), more strike-slip movement is accommodated by the bounding fault and the
faults within the analog model exhibit strike-slip and vertical slip. Our
interpretation of the Vp model and microseismicity places
the shallow seismicity of the Alum Rock trend on the dipping surface of the
bounding fault. However it is likely a broad fault zone with deformation
distributed among several faults. The Mission fault is represented in the analog
model as one of the prominent internal faults contained by the bounding faults.
Strike-slip movement is present on the Mission fault equivalent in the analog
model, due to shear within the duplex structure. Our Vp
model and microseismicity interpretation places the deeper seismicity of the
Mission trend on the bounding Hayward fault at the northern end, while the
shallow events occur on the Mission fault. Our model interpretation suggests a
steeper dip to the Hayward fault than the bounding fault of the analog model, as
well as a closer distance between the Hayward and Mission faults than the
corresponding faults in the analog model. These differences in the fault
geometry between the analog model and the Calaveras-Hayward system may be due to
the incomplete nature of the restraining stepover and continuation of slip on
the northern Calaveras fault. Slip transfer is completed to the left-bounding
fault and the faults internal to the contractional stepover merge with the
bounding fault (Fig. 16, analog
profile E), as represented by the convergence between the Mission and Hayward
faults.
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Model Implications
Our structural and kinematic model combines a 3D Vp
model, relocated hypocenters, and recomputed focal mechanisms with independent
geologic and geophysical data. In particular, our model provides for a mechanism
of slip transfer between the Calaveras and Hayward faults. The Mission and Alum
Rock seismic trends reflect the style of deformation and kinematics of the
region. These seismic lineaments exist in an area of active contraction,
exhibiting predominantly strike-slip motion but with a clear component of
vertical deformation. The seismic lineaments are arranged en echelon, parallel
to the en echelon arrangement of mapped reverse faults and folds in the area
(Graymer et al.,
1994,
1995;
Jones et al.,
1994). Andrews
et al. (1993) suggest that strike-slip and dip-slip motion
are partitioned onto two (or more) discrete fault surfaces, and that the
dip-slip surface is locked while the strike-slip surface exhibits
microseismicity. Our analyses suggest a single fault zone responsible for the
Mission trend, with the hypocenters on the northern part of the Mission trend
less dispersed than in the south near the Calaveras Reservoir (plot is
available as an electronic supplement to this article). The fault planes are near
vertical to steeply northeasterly dipping
(Figs.
10 and 13). The
focal mechanisms for these relocated events suggest that most of the observed
dip-slip motion occurs during oblique strike-slip events. No seismicity is
associated with pure thrust faulting, so we cannot directly support or disprove
a large dip-slip fault of significant seismic potential in proximity to the
Mission fault. The focal mechanisms also suggest the possibility of multiple
sources, confined to a relatively narrow fault zone.
The Alum Rock trend is more dispersed than the Mission trend. Three discrete
groupings of seismicity are evident in hypocenter profiles (available
as an electronic supplement to this article). The northern part of the trend is
shallow and defines a northeasterly dipping plane. The southern part of the trend
contains two discrete clusters: one cluster that defines a northeasterly dipping
plane, and another that is a diffuse, globular cluster with no apparent fault
plane. Focal mechanisms for events MD 2 show primarily
strike-slip behavior, although some reverse and normal events are indicated
(Figs. 12 and
14). The wide range of behavior
observed in the focal mechanisms for the Alum Rock trend also suggests that
strain is distributed on multiple fault planes and in a manner that is more
widely dispersed than the Mission trend.
The Mission Fault, Mission Seismic Trend, and Slip Transfer.
We believe that the Mission fault is not the mechanism of deep slip transfer
between the Calaveras and Hayward faults. The primary evidence for this is that
the Hayward fault exhibits surface creep at 9 mm/yr, its highest rate observed
along its surface trace, 11 km south of the junction between the surface
traces of the Mission and Hayward faults
(Lienkaemper,
1992;
Lienkaemper and Galehouse,
1997; Graymer
et al., 1994). Therefore, slip transfer between the
Calaveras and Hayward faults likely occurs south of the Mission-Hayward fault
junction. Relocated hypocenters of the Mission trend lie southwest of the mapped
trace and show a steep dip to the northeast, in agreement with relocations
performed by Wong and
Hemphill-Haley (1992) and
Zhang and Thurber
(2003). If these relocations are accurate to <500 m, then the
seismicity would have to dip southwest for the seismicity to project back to the
surface trace of the Mission fault. Studies of convergent regions associated
with strike-slip faulting suggest that the Mission fault should be a steeply
northeasterly dipping reverse fault
(Aydin and Page,
1984; Woodcock
and Fischer, 1986). Therefore, we believe that the Mission fault is
not the source of the Mission seismic trend. However, the Mission fault likely
accommodates deformation within the contractional region.
The velocity model indicates a velocity contrast (Fig. 8B–F) across the Mission seismic trend, delineating a significant structure that bounds contrasting crustal blocks. Although our velocity model resolution is low and the exact boundaries imprecise using the velocity model alone, we can combine the seismicity and the velocity model to infer the subsurface structure. We interpret this structure as the Hayward fault, which is the eastern boundary of the San Francisco Bay block. Slip transfer is accommodated as the Hayward fault diverges from the Calaveras fault. Near the junction of their surface traces, the Mission fault may merge into the Hayward fault at depth and diverge southward until it reaches the Calaveras fault at the Calaveras Reservoir.
Figure 8 shows the proposed subsurface fault architecture of our model. We propose that the southern Hayward-Evergreen fault system is seismically active and that the southern Hayward fault is a steeply dipping fault that extends from the surface through the upper crust. The Hayward fault diverges from the Calaveras fault, providing a mechanism for the direct transfer of deep slip. As the Hayward fault begins to diverge, it deepens and steepens to the north, and the hypocenters diverge from the Calaveras fault onto the Mission trend. In this model, the Mission fault is an oblique-slip fault that accommodates some of the internal deformation in the stepover region. Although our interpretation places the Mission trend on the Hayward fault, the Mission fault is not precluded as a source of some of the events due to the hypocenter uncertainties. However, the full breadth of geologic and geophysical evidence suggests otherwise. It is unlikely that the Hayward fault, exhibiting surface creep at its maximum rate of 9 mm/yr, is slipping without microseismicity at depth, especially in an area of contraction. Although shallow slip and surface creep is observed where the Hayward fault is locked at depth further northward, the rate of slip is considerably less than the deeper loading rates (Lienkaemper and Galehouse, 1997; Bürgmann et al., 2000; Simpson et al., 2001). Additionally, the distribution of microseismicity on the Mission trend is suggestive of fault creep, yet no creep has been observed on the Mission fault (Wong and Hemphill-Haley, 1992).
Seismic, geodetic, and geologic data require that most of the strain release in the San Andreas fault system within the San Francisco Bay region occur on vertical strike-slip faults. However, strain release within the San Andreas fault system can also be accommodated by pure or oblique strike-slip motion on dipping planes, and a steeply dipping Hayward fault zone that splays off of the Calaveras fault can accommodate both strike slip and oblique slip (Fig. 8).
The Role of the Alum Rock Trend.
The Alum Rock seismic trend is more enigmatic and the role it plays in slip
transfer is unknown. Profile views of seismicity distribution show that the Alum
Rock trend is largely confined to depths of 5 km or less
(Fig. 14). A subset of the
seismicity in profile view suggests a shallowly dipping fault surface, perhaps
on fault splay (Fig. 14). For
all the events, the "best-fit" fault plane was nearly vertical. The
average focal mechanism, however, suggests that appreciable shortening is
occurring along the Alum Rock seismic trend
(Fig. 15). Because the
seismicity is largely shallow, these events are likely evidence of distributed
contractional strain through multiple smaller faults in a broad Hayward fault
transition zone.
Implications for Seismic Hazard.
Our structural model has implications for the seismic hazards in the southern
San Francisco Bay region. If the southern Hayward fault is continuous at depth,
extending southward below the Evergreen fault and connecting the Hayward fault
to the Calaveras fault, then this extension could possibly contribute additional
moment release to a rupture of the southern Hayward fault.
Andrews et al.
(1993) recognized that the dip-slip moment released is not
sufficient to account for all the accumulated contractional strain, and
therefore there is an additional threat from reverse faulting in the region.
They calculated a MW 6.3 earthquake on the Mission fault due
to dip slip alone. If c
