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 The relationship between small-magnitude seismicity and large-scale crustal faulting along the Hayward Fault, California, is investigated using a double-difference (DD) earthquake location algorithm. We used the DD method to determine high-resolution hypocenter locations of the seismicity that occurred between 1967 and 1998. The DD technique incorporates catalog travel time data and relative P and S wave arrival time measurements from waveform cross correlation to solve for the hypocentral separation between events. The relocated seismicity reveals a narrow, near-vertical fault zone at most locations. This zone follows the Hayward Fault along its northern half and then diverges from it to the east near San Leandro, forming the Mission trend. The relocated seismicity is consistent with the idea that slip from the Calaveras Fault is transferred over the Mission trend onto the northern Hayward Fault. The Mission trend is not clearly associated with any mapped active fault as it continues to the south and joins the Calaveras Fault at Calaveras Reservoir. In some locations, discrete structures adjacent to the main trace are seen, features that were previously hidden in the uncertainty of the network locations. The fine structure of the seismicity suggests that the fault surface on the northern Hayward Fault is curved or that the events occur on several substructures. Near San Leandro, where the more westerly striking trend of the Mission seismicity intersects with the surface trace of the (aseismic) southern Hayward Fault, the seismicity remains diffuse after relocation, with strong variation in focal mechanisms between adjacent events indicating a highly fractured zone of deformation. The seismicity is highly organized in space, especially on the northern Hayward Fault, where it forms horizontal, slip-parallel streaks of hypocenters of only a few tens of meters width, bounded by areas almost absent of seismic activity. During the interval from 1984 to 1998, when digital waveforms are available, we find that fewer than 6.5% of the earthquakes can be classified as repeating earthquakes, events that rupture the same fault patch more than one time. These most commonly are located in the shallow creeping part of the fault, or within the streaks at greater depth. The slow repeat rate of 2–3 times within the 15-year observation period for events with magnitudes around M = 1.5 is indicative of a low slip rate or a high stress drop. The absence of microearthquakes over large, contiguous areas of the northern Hayward Fault plane in the depth interval from ∼5 to 10 km and the concentrations of seismicity at these depths suggest that the aseismic regions are either locked or retarded and are storing strain energy for release in future large-magnitude earthquakes.
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 The Hayward Fault is located on the eastern side of San Francisco Bay, California, and forms one branch of the San Andreas Fault system that accommodates the relative motion between the North American and Pacific plates. It extends for 85 km from south of Fremont on the south to San Pablo Bay on the north and traverses densely populated urban areas [Lienkaemper et al., 1991; Graymer et al., 1995] (Figure 1). The fault is considered the most probable source of a future major earthquake in the area [Working Group on California Earthquake Probabilities (WGCEP), 1999] and is arguably one of the most hazardous faults in the United States.
 The potential of the fault to rupture in large earthquakes is well documented by an M6.8 earthquake that occurred in 1868 and ruptured the surface at least 30 km from Fremont to somewhere north of San Leandro [Lawson, 1908; Radbruch-Hall, 1974; Bakun, 1999]. Recent studies suggest that the rupture may have extended as far north as Oakland [Lienkaemper and Borchardt, 1992] or Berkeley [Yu and Segall, 1996]. No other large historic earthquake has been unequivocally assigned to the Hayward Fault. An 1836 earthquake, long assumed to have ruptured the northern Hayward Fault, is now believed to have occurred ∼100 km to the SE, implying that the northernmost Hayward Fault has not ruptured since the region was settled beginning in 1776 [Bakun and Wentworth, 1997; Toppozada and Borchardt, 1998]. Paleoseismic observations from El Cerrito and the historical record suggest that the most recent large event on the northern Hayward Fault occurred between 1640 and 1776 [Hayward Fault Paleoearthquake Group, 1999]. Williams  documented at least six Hayward Fault ruptures during the past 2100 years in a trenching study on the southern Hayward Fault near Fremont.
 At the surface the fault is creeping along its entire length [Lienkaemper et al., 1991], although the rate of creep varies spatially along the fault trace. A current average creep rate near the surface of 5 mm/yr and an estimated long-term slip rate of ∼9 mm/yr suggest that >1 m of slip has accumulated since the 1868 event, and thus M > 6.5 events are now capable of occurring on the Hayward Fault [Lienkaemper et al., 1991; Savage and Lisowski, 1993].
 About 2000 events with coda duration magnitudes up to M = 4.6 have been recorded since 1967 by the Northern California Seismic Network (NCSN) along the Hayward Fault (Figure 1, small box). Slip produced by these earthquakes and fault creep are not enough to accommodate the strain accumulation on the fault due to relative plate movement. The estimated 30-year probability for rupture of the northern Hayward Fault by a M6.7 event is 16% and of the southern Hayward Fault is 17% [WGCEP, 1999]. Estimated cost and loss of life from such an event approach tens of billions dollars and several thousand deaths, respectively.
 The epicentral alignment of the recorded seismicity correlates well with the mapped surface trace of the fault especially north of San Leandro [Ellsworth et al., 1982; Oppenheimer et al., 1992; Castillo and Ellsworth, 1993] (Figure 1). The seismic activity takes place in almost equally spaced clusters along the fault with a separation distance of 10 km on average. Gravity and magnetic anomalies suggest that the locations of some of these clusters may correlate with the presence of mafic and ultramafic rocks within the fault zone [Ponce et al., 1998]. The clusters are from 2 to 8 km in length and are separated by quiet regions in which there is very little seismicity.
 The seismicity diverges from the mapped surface trace of the Hayward Fault south of San Leandro to follow a more easterly trend down to Fremont. This diverging strand of seismicity lies partly under the more northwesterly trending Mission Fault, although there is no throughgoing structure at the surface that follows the seismicity trend from the Hayward to the Calaveras Faults [Wong and Hemphill-Haley, 1992; Andrews et al., 1993; Graymer et al., 1995]. In this article we will refer to the diverging trend of seismicity as the “Mission trend.” The adjacent principal surface trace of the Hayward Fault is nearly aseismic, although the most southern part of this portion of the fault exhibits the highest surface creep rate (10 mm/yr) observed anywhere along the fault [Lienkaemper et al., 1991]. The cumulative seismic moment is significantly lower on the Mission trend than on the northern Hayward Fault for the time period 1984–1998. The Mission Fault has been hypothesized to accommodate the compressive strain in the left step over configuration between the Calaveras and the Hayward Faults [Andrews et al., 1993]. On the other hand, because of the lack of definite evidence of Holocene surface rupture, Wong and Hemphill-Haley  associated the Mission seismicity to a seismically active buried trace of the Hayward Fault located east of its mapped surface trace.
 The factor of ∼2 difference between the long-term slip rate and the observed surface creep rate, the sparse seismicity that is organized in patches on the fault plane, and the paleoseismic rupture history lead to the broadly accepted view that the Hayward Fault is accumulating strain at depth. For the northern Hayward Fault this view has recently been challenged as geodetic data indicate that the northern Hayward Fault north of Berkeley may be creeping at seismogenic depths [Bürgmann et al., 2000; Simpson, 2000].
 A major limitation in investigating the behavior of the Hayward Fault is the sparse seismicity and the lack of accurate information on the rupture process of the one large historical event. In a collection of papers published by the California Department of Conservation [Borchardt et al., 1992] the instrumental seismicity has been studied on the basis of earthquake locations routinely determined by the Northern California Seismic Network (NCSN). Although in some cases the events were relocated, it was not possible to observe any fine structure within the clusters or to discriminate between on-fault and off-fault seismicity. Recently, Waldhauser et al.  imaged with high resolution the seismicity on the northern Hayward Fault using a double-difference earthquake location technique [Waldhauser and Ellsworth, 2000], revealing the surprising existence of horizontal streaks of hypocenters in the fault plane near Berkeley and El Cerrito.
 In this study we relocate the seismicity recorded between 1967 and 1998 by the NCSN along the Hayward and Mission Faults using hypoDD [Waldhauser, 2001], a program that implements the double-difference (DD) algorithm by Waldhauser and Ellsworth . We obtain relative location uncertainties that are in many cases smaller than the size of individual earthquakes (for M > ∼1.5), which enables us to image the fine-scale structure of the seismically slipping surface. We use the new locations together with high-resolution focal mechanisms to find a wide range of complex seismicity patterns and style of faulting, which we analyze in terms of the structure and mechanics of the Hayward Fault system.
2. Data Analysis
 The DD earthquake relocation algorithm takes advantage of the fact that if the hypocentral separation between two earthquakes is small compared to the event-station distance and the scale length of velocity heterogeneity, then the ray paths between the source region and a common station are similar along almost the entire ray path [Fréchet, 1985; Got et al., 1994]. In this case, the difference in travel times for two events observed at one station can be attributed to the spatial offset between the events by differencing Geiger's equation for earthquake location [Waldhauser and Ellsworth, 2000]:
where the right-hand side is the difference between observed and calculated travel time difference between two events, i and j, at station k (a double difference), and Δm are the changes required in the hypocentral parameters to make the model better fit the data. The partial derivatives of the travel times t for events i and j, with respect to their locations (x,y,z) and origin times (t), respectively, are calculated from a one-dimensional (1-D) layered velocity model for the current hypocenters and the location of the station where the kth phase was recorded. We use the velocity model used for routine location by the NCSN for events on the Hayward Fault (Table 1). The S velocity model is obtained by scaling the P velocity model by a factor The use of a 1-D model is appropriate since the DD algorithm cancels errors due to unmodeled velocity structure.
Table 1. One-Dimensional P Velocity Model
Top of Layer, km
 DD equations are built to link each event to several neighboring events, so that all events are connected and the solution for the adjustment to each hypocenter can be determined simultaneously. The DD vector is minimized by weighted least squares using the conjugate gradient method (LSQR) [Paige and Saunders, 1982]. Solutions are found by iteratively adjusting the vector difference between hypocentral pairs [Waldhauser, 2001]. When the earthquake location problem is linearized using the DD equations, the common mode errors cancel, principally those related to the receiver-side structure. Thus we avoid the need for station corrections or high-accuracy predicted travel times for the portion of the ray path that lies outside the focal volume. Details of the DD algorithm are given by Waldhauser and Ellsworth .
 We use ordinary phase picks from the NCSN earthquake catalog together with high-precision differential travel times from phase correlation of P and S waves. The former are expressed as differential travel times so that the same equation is used for all data. The combined use of both catalog and cross-correlation data permits the simultaneous relocation of all events, with interevent distances within clusters of correlated events (multiplets) determined to the accuracy of the cross-correlation data, whereas relative locations between the multiplets and uncorrelated events are determined to the accuracy of the absolute data.
2.1. Catalog Travel Time Differences
 Travel times routinely computed from P wave arrival times of ∼13,800 events recorded by the NCSN between 1967 and 1998 near the Hayward/Mission Faults (see large box in Figure 1) are differenced for pairs of earthquakes at each station that observed both events. The travel time differences are selected to build a network of pair-wise connected events in which any event is linked to a maximum of 10 neighboring events by at least eight pair-wise observations, so that all events are simultaneously relocated relative to each other. An NCSN pick quality of 0, 1, or 2 is used. Only event pairs with hypocentral separation <10 km are considered to keep the effect of ray path differences outside the source region small [Waldhauser and Ellsworth, 2000].
Figure 2a shows ∼250,000 selected catalog travel time differences as a function of separation distance obtained from events on the Hayward and Mission Faults for the time period 1984–1998 using 260 stations; 99.7% of the catalog travel-time differences are smaller than the maximum travel time difference expected for a given event pair offset when the station lies on the line connecting both events. Travel time differences are close to 0 s at zero event pair offset and generally smaller than ∼2 s at offsets of 10 km, indicating an average source region velocity of ∼5 km/s. Data above the indicated straight line in Figure 2a are considered to be outliers and are removed before relocation. The concentration of outliers near the zero offset (Figure 2b) is due to the increased number of observations for nearby events in our sampling scheme. Outliers that occur within the triangular area below the line, however, cannot be detected by this approach. Theoretically, we could detect these outliers by predicting travel time differences based on the offset of an event pair and its relative orientation to a specific station. For a horizontally aligned event pair, for example, delay times plotted against observation azimuth describe a sine curve with the amplitude scaled by the length of the offset. However, the uncertainty in the catalog locations, and thus the uncertainty in the orientation of the event pair, is too large to detect such outliers efficiently. We remove these outliers during relocation.
2.2. Cross-Correlation Travel Time Differentials
 In addition to the catalog travel time differences for events that are on or close to the Hayward/Mission Faults (small box in Figure 1a) we measure travel time differentials for each event pair with waveforms that correlated at a common station using the cross-spectral method described by Poupinet et al. . Identical waveforms occur when the sources have a common slip surface (i.e., a repeating earthquake). Waveform similarity decreases with event pair separation because of increasingly different wave propagation paths and/or focal mechanisms and generally breaks down after the separation distance exceeds roughly the first Fresnel zone (∼300 m for 5-Hz P waves). We use the digital waveforms recorded on vertical component seismometers and archived since 1984 by the NCSN. Stations at distances of up to 200 km from the event pair centroid are used. Two waveforms recorded at a specific station are considered similar when half of the squared coherency values, in the frequency range 2–10 Hz, of a tapered 2.56-s (256 samples) window containing the P wave (S wave) train, exceed 0.9. For two similar waveforms the time difference is proportional to the slope of the phase of the cross spectrum [Poupinet et al., 1984]. For sufficiently similar signals a precision of 1 ms can be achieved for the measurement of time differences in the energy of P and S arrivals from data digitized at 10-ms intervals [Poupinet et al., 1984; Fréchet, 1985].
 The distributions of coherency values for 56,000 measured P and S wave differential travel times are shown in Figure 3a. Both distributions feature a peak at 0.9 coherency, indicating the high quality of the data. Outliers are difficult to detect prior to relocation, but we can assess the consistency between the P and S wave data. For a given event pair and station we expect P and S wave delay times to be either negative or positive, i.e., exhibiting either a delay or an advance of the travel time of one event with respect to the other. In 3.2% of the data with both P and S wave measurements, however, we observe sign changes between P and S delay times. The distribution of the differences between P and S delay times of these inconsistent data (Figure 3b) shows that 20% of the data have a difference between P and S delay times <5 ms, reflecting measurement uncertainties for close-by events rather than outliers. Data in the tails of Figure 3b represent outliers (e.g., misaligned phases), either in the P wave or the S wave data, or both. Coherency values of these data, however, are typically low, and the measurements will therefore be downweighted during relocation.
2.3. Data Weighting
 The catalog data are downweighted by a factor of 100 relative to the cross-correlation data. Cross-correlation data are a priori weighted by the squared coherency catalog data by weights of 1, 0.75, and 0.25 for NCSN pick qualities 0, 1, and 2. Equal weights are used for P and S wave cross-correlation data. Residuals are reweighted after each iteration according to the misfit and the distance between events [Waldhauser and Ellsworth, 2000] (Figure 4). Catalog and cross-correlation data are removed/reweighted for event pairs with separation distances larger/smaller than 10 and 2 km, respectively. Weights are highest for close-by events and drop exponentially with increasing separation distance. Residuals larger than 6 times the median absolute deviation from the median of each data type are considered outliers and discarded. When using both data types simultaneously, one has to be aware that the first-motion arrival times image the point of rupture initiation (hypocenter), whereas cross-correlation data image the center of moment release (hypocentroid) as the cross spectra of entire P or S phases are used to estimate the time delays between the event arrivals.
3. Relocation Results
 While catalog P wave travel times are available for events that date back as far as 1967, digital waveforms were archived by the NCSN only from 1984. To account for the different time periods and data quality, we perform two sets of relocations. The first set includes catalog data of 13,764 well-located and well-connected events (84% of the events listed in the catalog) that occurred between 1967 and 1998 and are located within a larger area encompassing the Hayward/Mission Fault system (large box in Figure 1a). The epicenter distribution of the 13,598 relocated events is shown in Figure 1b. Events get deleted during relocation when they loose linkage to neighboring events due to outlier removal. The RMS residual decreased by ∼75% from 78 to 18 ms after relocation.
 The second set includes catalog and waveform data of events between 1984 and 1998 that are located on the Hayward/Mission Faults or are within ∼10 km of the surface trace of the Hayward Fault (Figure 5a). The combined data set of ∼300,000 delay time observations enables us to relocate 97% of the 1251 hypocenters listed in the NCSN catalog (Figure 5b). Most of the excluded events do not have waveforms and/or have only few and low-quality first-arrival picks. Sixty-two percent of the events have at least four cross-correlation measurements. In Figure 5b, groups of eight or more events with highly correlated waveforms are indicated in red and labeled. Routine locations for correlated events are dramatically improved by including the phase correlation measurements, with RMS error decreasing by 95% from 110 to 5 ms. The RMS error for catalog P wave data decreased by 50% to ∼54 ms. The mean shifts in horizontal and vertical direction during relocation are 250 and 520 m, respectively. In comparison, the average horizontal and vertical uncertainties in the routine locations are 370 and 680 m, respectively. In general, the error estimates in hypocenter location decreased by an order of magnitude. The resolution estimates reflect the relative location uncertainty, but the absolute location uncertainty might be larger.
 The improvement in relative hypocenter location is, to first order, due to the use of travel time differences as the data, which minimizes common model travel time errors [Waldhauser and Ellsworth, 2000]. The further improvement of the correlated events is due to the increased accuracy with which cross-correlation techniques measure P and S wave delay times (∼1 ms). This is particularly important for S waves for which absolute arrivals cannot be identified on the vertical component seismograms but for which the relative travel time for two similar events can easily be measured with cross correlation.
 In map view the relocated seismicity reveals a narrow fault zone at most locations along the Hayward and Mission trends. In some locations, discrete structures adjacent to the main trace are seen, features that were previously hidden in the uncertainty of the routine locations (Figures 1 and 5). Near San Leandro, where the more westerly striking Mission seismicity trend intersects the Hayward Fault, the seismicity remains diffuse, indicating a more volumetric zone of deformation to the northwest of the main trace of the Hayward Fault. Most of the on-fault seismicity collapses into narrow lines of epicenters that are oriented in the general direction of the trend of the seismicity (Figure 5b). Off-fault activity is notable near Berkeley where the seismicity forms tight clusters to the east of a well-defined Hayward Fault surface. The southern Hayward Fault as mapped at the surface is aseismic except for a small cluster of events slightly to the northeast of the fault near Alum Rock (AR, Figure 1). Few earthquakes are located southwest of the Hayward Fault.
 Fault-parallel cross-sectional views of the on-fault seismicity indicate that most of the events are located within a depth range of ∼3–13 km (Figure 5b). The maximum depths are more constant on the Hayward Fault than on the Mission trend. Most of the earthquakes cluster in patches on the fault surface, with large regions devoid of detectable earthquakes adjacent to the clusters. The aseismic regions at depths shallower than ∼4 km are believed to release stress primarily by creep [Savage and Lisowski, 1993]. Creep is likely to also occur in regions of the fault characterized by dense microseismicity.
 In fault-parallel cross section the relocated events reveal that only a small fraction of the fault plane slips seismically, compared to a much larger area that might be inferred from the catalog locations. This is mostly evident on the northern Hayward Fault between Point Pinole and Berkeley, where the relocated hypocenters form seismic streaks or lineations, alignments of hypocenters along one-dimensional horizontal structures (P1, E1, E2, B1, B2 in Figure 5b) [Waldhauser et al., 1999]. The streaks seem to bound holes, large areas where seismicity is sparse or absent. The seismicity on the Hayward Fault south of Berkeley and on the Mission trend is more scattered in depth, and fewer events correlate. Three small groups of correlated events in the San Leandro cluster form short southeast dipping streaks (S1, S2, S3 in Figure 5b) that parallel the Hayward Fault. These streaks, composed of ∼10 events each and extending over a few hundred meters, are many times smaller in size and length than the ones observed farther north (several tens of events along ∼2000 m). Although short, the horizontal alignment of the hypocenters is unambiguous. On the Mission Fault the distribution of correlated events is more diffuse. Near Hayward, the shallow multiplet H1 at ∼3 km depth seems to trend more westerly than the multiplet H2 at a depth of ∼6 km (Figure 5).
 Cross-sectional views perpendicular to the fault (Figure 5b) show that the general dip of the fault is near-vertical, although it dips slightly to the northeast near El Cerrito and Union City. While the seismicity on the northern Hayward Fault clearly underlies the surface trace of the fault, the association of seismicity and mapped fault trace south of San Leandro is less clear. The geometry of the seismically active fault is easily seen in a three-dimensional view of the hypocenters by means of stereoscopic plotting in Figure 6. At some locations, in particular, north of Oakland, the active fault zone is very narrow. The width of the streaks and presumably that of the active fault plane at these locations is generally <200 m. Along streak B1 at a depth of ∼10 km the width is as small as 25 m. Such narrow fault zones are consistent with geologic findings [Chester et al., 1993] and studies based on a comparison of plate rates to seismic moment release in the Bay area [King et al., 1994]. In contrast, the seismicity near San Leandro forms a large-scale inverted flower structure, with the width of the earthquake distribution at greater depth being many times larger than the mislocation accuracy. This implies that the seismicity is occurring on structures adjacent to the Hayward Fault or that the fault consists of several substructures at this location. The short, southeast dipping streaks S1, S2, and S3 (Figure 5b) may represent the slip direction on such secondary faults.
4. Focal Mechanisms
 We compute well-constrained P wave focal mechanisms having a minimum of 30 first-motion picks for selected M > 2.5 events with the newly computed takeoff angles (Figure 7, shaded mechanisms). The mechanisms and 95% confidence regions were determined using FPFIT, a least squares grid search procedure which minimizes the number of discrepant first motions [Reasenberg and Oppenheimer, 1985]. In addition to the single-event focal mechanisms we compute composite mechanisms (solid mechanisms in Figure 7) for events that belong to a multiplet. First motions of such correlated events are, in general, consistent, which is what we expect because of the high similarity of the waveforms. Hence variations in focal mechanisms of individual events within a multiplet are due to variations in the number of observations per event or errors in the reading and not due to variations in faulting. Thus we can enhance the solution of these events by computing composite mechanisms.
 The focal mechanisms displayed in Figure 7 show that the dominant style of deformation along the Hayward/Mission Faults is right-lateral strike slip on NW trending planes, with indication of convergent components near San Leandro and on the Mission Fault. Events on the northern Hayward Fault north of Oakland exhibit pure strike-slip motion, indicating a fault plane with a strike that is consistent with the trend of the seismicity and the surface trace. Small variations in the strike of the composite mechanisms for the streaks are consistent with the variation in streak orientation (Figure 8). We observe a trend of N45°W for streak E1 near El Cerrito, while the fault plane solution gives a strike of N41°W (±5°) (Figure 8a). Similarly, a trend of N55°W is observed for the deeper streaks E2 near El Cerrito (Figure 8b) and B1 near Berkeley (Figure 8c), consistent with the strike of N57°W (±3°) obtained from the fault plane solutions. Although streak P1 near Point Pinole is only ∼700 m in length, it exhibits a clear N55°W direction which agrees with the fault plane solution at the 95% confidence level (N50°E ± 5°) (Figure 8e). These results indicate that the trend of the deeper fault plane is ∼10° more northerly than the shallow trend (see 3-D view in Figure 6). The change in strike occurs across the almost aseismic depth interval from 5 to 9 km, indicating a curved fault surface or different structures on which the events occur. The streaks at shallow depths show a slight counterclockwise rotation in strike from southeast (Berkeley) to northwest (El Cerrito) (see mechanisms B2, E1, and 33 in Figure 7).
 The composite focal mechanism for the off-fault multiplet B3 near Berkeley as well as focal mechanisms from single events (6 and 48 in Figure 7) within that cluster all show shear parallel to the main trace of the Hayward Fault. This is different from what is observed, for example, on the creeping San Andreas Fault near Stone Canyon or along the Calaveras Fault [Zoback et al., 1987; Oppenheimer et al., 1988], where maximum stress orientations show fault normal compression off the fault, arguing for a weak rheology of these faults.
 The diffuse spatial distribution of the events and the strong variation in focal mechanisms between close-by events near Oakland and San Leandro argue for a highly fractured zone. Only 40% of the events in these clusters correlate, compared to ∼80% in clusters like El Cerrito or Fremont. The variation in faulting in the San Leandro–Oakland area persists to depth as shown by a reverse event (40) that occurred at a depth of ∼9 km. Some events (1, 7, 14, 59, 29 in Figure 7) indicate strike-slip motion on northwest trending planes, while others (11, 12, 13, 24, 38, S3 in Figure 7) exhibit right-lateral strike slip on a shallow northeast dipping plane. The M4.5 earthquake of 27 March 1984 appears to occur on the latter structure (large circle, located at 35 km distance and 6 km depth in the cross section of Figure 5b), although its focal mechanism (70 in Figure 7) indicates oblique right-lateral reverse motion.
 On the Mission Fault near Hayward the composite mechanisms for the two elongated multiplets H1 and H2 do not show evidence for a change in strike as observed in the relocated seismicity (Figures 5 and 8). This might indicate that the shallow seismicity occurs on en echelon structures (Figure 6). Near Union City one event (41 in Figure 7) indicates dip-slip motion. Near Fremont, composite focal mechanisms for multiplets F1 and F3 are consistent with a vertical fault plane. Events in multiplet F2 show compressional components, as does an event (53) that lies slightly to the east of the main fault (Figure 7).
5. Repeating Earthquakes
 Location uncertainties in the meter range for events that correlate permit us to investigate the existence of repeating earthquakes. Presumably, these earthquakes are caused by patches of brittle material (asperities) on the fault that fail repeatedly as they are loaded by creep on the surrounding surface [Vidale et al., 1994; Nadeau et al., 1995]. In theory, repeating events will have identical waveforms due to identical source mechanisms, ray paths, and receiver response. Real seismograms, however, may exhibit small variations in the shape of the signals that reflect changes in source, path, receiver characteristics, and/or noise. Although two events might be perfectly colocated, the signals may be incoherent due to noise in the data. On the other hand, two events that are separated in space, could produce highly coherent waveforms if they occur in a homogenous velocity field. Although the degree of similarity between two phases at a common station can be used as a rough measure of the closeness of two events [Nadeau et al., 1995; Menke, 1999], it does not translate directly into the distance between the events. In particular, relative location uncertainties cannot easily be estimated from waveform similarity alone.
 Given these problems, we search for repeating events in the 1984–1998 seismicity by investigating the separation distance between centroids determined from phase correlation measurements. We select events that have small relative location uncertainites, with probable overlap of their source areas (>50%), assuming a 3-MPa stress drop and magnitude differences smaller than 0.5. The time intervals between successive events show a broad distribution between 1 and 11 years with a peak around 5.5 years and a sharp peak for intervals <1 year (Figure 9). Thirty-four percent of the intervals are <1 month, and 27% are <1 day (Figure 9, inset). Time intervals of <1 month are approximately exponentially distributed, suggesting that they represent an aftershock process. Those events with short time separation may, in fact, have little or no overlap, given our lack of control on source dimension. To form sequences of repeating earthquakes, we only consider events with recurrence intervals >1 by removing the smaller-magnitude event that precedes or follows another event by <1 month in each sequence.
 The locations of these sequences on the fault surface are shown in Figure 10a. A detailed look at the relative location of the repeating events shows that some sequences are formed by events that lie virtually on top of each other (Figure 10b), whereas others include events that are possibly slightly separated in space (Figure 10c). Events of the latter type could be distinct if their stress drop is >30 bars. Unfortunately, not all of the hypocentroids are precise enough to test this possibility. Some repeating sequences occupy distinct, isolated areas on the fault plane (Figures 10b and 10c), others are located in close proximity to other events (Figure 10d, left part of streak). Some sequences may occur within groups of scattered hypocenters that include fore/aftershock sequences, mostly within clusters or streaks (Figure 10d, right part of the streak). The source parameters for the first two types of repeating earthquakes are listed in Table 2. There are 31 sequences that have two repeating events and five sequences that have three events. The sequences with three events typically show a larger variation in their magnitudes.
Table 2. Repeating Earthquakes
4 Nov. 1992
31 May 1998
6 May 1985
31 July 1993
19 Oct. 1997
3 March 1986
12 June 1991
28 Dec. 1986
3 June 1996
19 Feb. 1989
13 Sept. 1993
4 Nov. 1991
4 June 1997
19 Nov. 1991
29 May 1998
14 May 1992
15 May 1996
16 Oct. 1986
14 Jan. 1987
7 June 1990
20 Nov. 1994
4 June 1997
7 April 1984
26 July 1989
27 Feb. 1986
6 Nov. 1994
27 Jan. 1986
29 Jan. 1995
24 May 1988
24 Jan. 1998
22 Dec. 1990
9 Dec. 1994
31 Jan. 1986
25 Dec. 1987
18 Feb. 1988
21 Sept. 1997
14 Aug. 1990
6 Aug. 1993
4 Feb. 1992
12 Aug. 1997
23 Nov. 1984
12 July 1988
18 May 1985
11 Feb. 1990
29 July 1985
21 Oct. 1987
19 July 1985
27 May 1988
28 Nov. 1985
3 April 1987
15 Aug. 1997
28 March 1989
4 March 1995
11 Oct. 1997
11 Nov. 1985
23 July 1993
11 Oct. 1996
26 Oct. 1986
3 March 1991
5 Nov. 1988
29 Aug. 1998
26 Dec. 1986
22 Jan. 1995
21 March 1992
7 March 1996
2 April 1985
8 Nov. 1996
14 Aug. 1985
10 Jan. 1992
21 Feb. 1986
17 Aug. 1997
5 Oct. 1986
12 May 1994
5 July 1991
9 Nov. 1996
29 Dec. 1991
9 Nov. 1996
8 March 1985
7 Jan. 1992
22 Jan. 1998
 From Figure 10a we see that repeating events are most common at shallow depth, between ∼2 and 7 km. Surface creep measurements [Lienkaemper et al., 2001] (Figure 10a) and geodetic surveys indicate that the fault is creeping to ∼5 km depth [Savage and Lisowski, 1993; Lienkaemper and Galehouse, 1998; Bürgmann et al., 1998]. The shallow repeating events can be interpreted to represent strong patches undergoing stick-slip failure as they are continuously loaded by creep on the surrounding fault plane. Multiplets with higher repeat rates (e.g., multiplet 7 with three events of M1.8, M1.8, and M1.5 in the 15-year observational period, Figure 10a and 10b) located at the shallowest depths, suggesting a positive creep rate gradient toward the surface.
 Repeating events at greater depth rarely occur as isolated sources. Instead, they predominantly occur within the streaks. A time-distance plot of the events along streak B1 (Figure 10e) shows a large variability of recurrence intervals and magnitude. Although there is no clear pattern emerging from Figure 10e, a possible progression of events along the streak can be observed that seems plausible from a triggering viewpoint since these events are all more or less in a line. Also, a clearer pattern may be hidden in a seismic gap observed between 1987 and 1992 that may be related to stress changes on the Hayward Fault caused by the 1989 M7.1 Loma Prieta earthquake [Reasenberg and Simpson, 1992; Lienkaemper et al., 1997].
 In contrast to creeping portions of the San Andreas and Calaveras Faults where repeating earthquakes are the norm and occur throughout the slipping fault surface [Nadeau et al., 1995; Schaff et al., 1998; Rubin et al., 1999], the Hayward Fault less frequently exhibits repeating behavior. On the Parkfield section of the San Andreas Fault, repeating events of M ∼ 1.4 have been found to occur at a rate of about once per year or two [Nadeau and Johnson, 1998], with a creep rate that is ∼4 times the average creep rate of the Hayward Fault. Thus the repeat rate for source 7 (Figure 10b), when scaled by creep rate, approximately agrees with San Andreas Fault recurrence rate. Comparisons, however, are hampered by the fact that repeat rates on the Hayward Fault appear to be less regular than on the San Andreas Fault and do not correlate with magnitude (Figure 11).
6. Discussion and Conclusion
 The seismicity rate of the Hayward Fault is substantially lower than that of the creeping central Calaveras Fault to its south, whether measured by the contemporary microearthquake rate or twentieth century moderate magnitude activity [Oppenheimer et al., 1990]. The difference in seismicity rates cannot be explained by the difference in creep rates (6 versus 15 mm/yr). This suggests to us that there is a more fundamental difference between them. We suggest that the large aseismic areas on the Hayward Fault plane between ∼5 and 10 km are either locked or retarded (areas A, B, C, D in Figure 10a). Studies on pre- and post-main shock seismicity on the Calaveras Fault [Bakun et al., 1986; Oppenheimer et al., 1990] and along the San Andreas Fault segment that ruptured during the 1989 Loma Prieta earthquake [Olson, 1990; Oppenheimer, 1990] have shown that sections of the fault that rupture during main shocks exhibit little on-fault earthquake activity in between the time of major events. The circular hole near Fremont (area D), for example, could produce a M ∼ 5.5 event (considering 3-MPa stress drop) or larger if it ruptured into the adjacent aseismic areas to the northwest near Union City and Hayward (area C). Although several large historic earthquakes have occurred near the Mission trend [Andrews et al., 1993; Bakun, 1999], uncertainties in their locations are too large to determine if one or more of them actually occurred on the Mission trend.
 On the northern Hayward Fault, creep rates may vary with depth. A relatively high rate of creep might encompass the shallow repeating events, while large aseismic areas (within area A) between the streaks suggest zones of locking. In this interpretation the streaks are close to the upper and lower boundaries of the proposed seismogenic zone. If correct, stress concentrations due to fault creep above and below the locked zone may explain the generation and localization of the streaks. Such stress concentrations are highest if the zone between the streaks is frictionally locked.
 Interferometric synthetic aperture radar (InSAR) and GPS data analyzed by Bürgmann et al. , on the other hand, suggest a freely slipping northern Hayward Fault (NW of km 25 in Figure 10a). Their model favors fault creep of ∼7 mm/yr to depths >6 km. In their model, however, a locked fault below 6 km would decrease the creep rate only by ∼7%, which is less than the mean of the uncertainties of the creep rate measurements. Bürgmann et al.  supported their argument of a freely slipping fault by analyzing repeating earthquakes to infer the distribution of subsurface fault creep rates [Nadeau and McEvilly, 1999]. They determined a creep rate of 5–7 mm/yr from repeating earthquakes with catalog locations around 5.7 and 9.8 km depth near El Cerrito and Berkeley (one of their repeating earthquake locates at 7 km depth). The relocated hypocenters in Figure 10a show that there is no evidence for repeating earthquakes between 6 and 9 km depth. Thus the creep rate of Bürgmann et al.  might represent the creep rate at the upper and lower boundary of a locked zone (area A, Figure 10a).
 The Hayward Fault is one member of a series of linked strike-slip faults that parallels the San Andreas Fault from the Calaveras–San Andreas junction to near the Mendocino Triple Junction 400 km to the northwest. Castillo and Ellsworth  suggested that the Hayward Fault reflects a mature stage of fault development from the systematic evolution of seismically defined structures within this fault system from its northwest end (youngest) to its southeast end (oldest). This hypothesis is strengthened by the streaks described by Waldhauser et al. , who argued that the streaks on the northern Hayward Fault might represent long-lived structures created by a wear process. The absence of such streaks on the Mission trend may indicate that this structure is relatively young or that is has been reactivated. The fault-normal cross sections in Figure 5b show that the Mission trend seismicity near Union City and to the south does not underlie the surface trace of the Hayward Fault, suggesting an independent structure in this area. North of Union City to near San Leandro the seismicity seems to occur on the Chabot Fault, a feature that extends ∼1 km to the northeast and parallel to the Hayward Fault and is recognized by R. W. Graymer (Neogene development of the Hayward Fault zone: A different perspective on an active strike-slip fault, submitted to Tectonics, 2001, hereinafter referred to as Graymer, submitted manuscript, 2001) as part of a broadened zone of the Hayward Fault. Double-difference locations near Hayward, where the intersection between the Mission and the Chabot Fault takes place, show that the shallow seismicity strikes more westerly than the seismicity at greater depth (best seen in Figure 6), suggesting that the intersection of the Mission trend with the Hayward Fault may involve substructures such as the Chabot Fault. It is possible that we see a migration process in which new strands are generated, old strands are reactivated, or the Mission trend and the southern Hayward Fault interact in their activity.
Andrews et al.  placed the Mission trend in a left step over between the Calaveras and Hayward Faults, with a structure along the Mission trend transferring slip from the Calaveras Fault onto the northern Hayward Fault. Assuming pure strike-slip on the Hayward Fault and the Calaveras Fault, they argue for a blind dipping structure to satisfy the geometric constraint of convergence. They interpret the apparent absence of dip on the structure as defined by the Mission seismicity trend as indicating an accumulating dip-slip moment deficit that will eventually be released in a large earthquake, thus making the Mission step over more likely to rupture in large earthquakes than previously assumed. The relocated seismicity along the Mission trend, on the other hand, indicates that at least some compression is being accommodated. Fault-normal cross sections (Figure 5b) show that the dip changes from near vertical near Fremont to ∼75° southeast dipping near Hayward. A few thrust events are observed along the entire Mission trend, the most notable near San Leandro where we observe shallow dip-slip events (including five M > 3.0 events) that occur on a 10°, northwest dipping structure (Figure 7). The contemporary seismicity on the Mission trend, however, is not able accommodate enough slip to compensate the compressional forces evident in the topographic expression.
 The wide range of complex faulting associated with the intersection of the Mission trend and the Hayward Fault might represent stress accumulation that arises from slip transfer along the Mission trend between the Calaveras and the Hayward Faults. Similar complex patterns are observed in zones of fault bends where stress concentrations at the tip of the fault are relieved by complex faulting patterns [King and Nábelek, 1985]. In addition to geometric complexity, faulting in this area might be complicated or controlled by structural heterogeneities, in particular, by a gabbroic body near San Leandro that steeply dips into the fault zone from its western side [Ponce et al., 1998; Graymer, submitted manuscript, 2001]. The off-fault seismicity near Berkeley might also be an indication that the transfer of slip onto the northern Hayward Fault is not occurring in a smooth fashion, as irregularities on the surface of the northern Hayward Fault and possibly locked patches act as asperities and distribute slip away from the main trace.
 We thank Bob Simpson, David Oppenheimer, Andy Michael, Allan Rubin, and two anonymous reviewers for their constructive comments on the manuscript. We greatly benefited from fruitful discussions within the USGS Hayward Fault Working Group. Russ Graymer is thanked for leading a elucidating field trip to the Hayward Fault. We are grateful to the staff at the NCSN for making their data available. We thank Paul Reasenberg and Bruce Julian for providing the software to create Figure 6.