Distribution of seismicity across strike slip faults in California

Transcription

1 Click Here for Full Article JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2008jb006234, 2010 Distribution of seismicity across strike slip faults in California Peter M. Powers 1 and Thomas H. Jordan 2 Received 1 December 2008; revised 5 November 2009; accepted 16 December 2009; published 11 May [1] The distribution of seismicity about strike slip faults provides measurements of fault roughness and damage zone width. In California, seismicity decays with distance from strike slip faults according to a power law (1 + x 2 /d 2 ) g/2. This scaling relation holds out to a fault normal distance x of 3 6 km and is compatible with a rough fault loading model in which the inner scale d measures the half width of a volumetric damage zone and the roll off rate g is governed by stress variations due to fault roughness. According to Dieterich and Smith s 2 D simulations, g approximates the fractal dimension of alongstrike roughness. Near fault seismicity is more localized on faults in northern California (NoCal, d = 60 ± 20 m, g = 1.65 ±.05) than in southern California (SoCal, d = 220 ± 40 m, g = 1.16 ±.05). The Parkfield region has a damage zone half width (d = 120 ± 30 m) consistent with the SAFOD drilling estimate; its high roll off rate (g = 2.30 ±.25) indicates a relatively flat roughness spectrum: k 1 versus k 2 for NoCal, k 3 for SoCal. Our damage zone widths (the first direct estimates averaged over the seismogenic layer) can be interpreted in terms of an across strike fault core multiplicity that is 1 in NoCal, 2 at Parkfield, and 3 in SoCal. The localization of seismicity near individual faults correlates with cumulative offset, seismic productivity, and aseismic slip, consistent with a model in which faults originate as branched networks with broad, multicore damage zones and evolve toward more localized, lineated features with low fault core multiplicity, thinner damage zones, and less seismic coupling. Our results suggest how earthquake triggering statistics might be modified by the presence of faults. Citation: Powers, P. M., and T. H. Jordan (2010), Distribution of seismicity across strike slip faults in California, J. Geophys. Res., 115,, doi: /2008jb Introduction [2] California, with its dense, well mapped network of faults and high quality earthquake catalogs, is an excellent setting to investigate seismicity variations in space and time. Earthquake catalogs constructed using improved hypocenter relocation techniques [Ellsworth et al., 2000; Hauksson and Shearer, 2005; Shearer et al., 2005; Thurber et al., 2006] are revealing new details about the 3 D geometry of fault networks [Yule and Sieh, 2003; Carena et al., 2004] and ruptures of large earthquakes [Liu et al., 2003], properties of nascent faults [Bawden et al., 1999], earthquake streaks observed on creeping sections [Rubin et al., 1999; Waldhauser et al., 1999, 2004; Shearer et al., 2005; Thurber et al., 2006], and the space time behavior of earthquake swarms [Vidale and Shearer, 2006]. These studies, as well as extensive research on the fractal character of fault systems [Tchalenko, 1970; King, 1983; Okubo and Aki, 1987; Hirata, 1989; Robertson et al., 1995; Ouillon et al., 1996; Kagan, 2007], have raised a number of interesting 1 Department of Earth Sciences, University of Southern California, Los Angeles, California, USA. 2 Southern California Earthquake Center, University of Southern California, Los Angeles, California, USA. Copyright 2010 by the American Geophysical Union /10/2008JB issues regarding the relationship of small earthquakes to major faults. For instance: Are physical properties of a fault zone such as the distribution of secondary faults and fractures, damage zone width, and fault roughness captured in near fault earthquake rates? Does the rate of small earthquakes in the vicinity of a major fault zone reflect the longterm fault slip rate or cumulative offset of the fault? Do other factors such as heat flow and lithology modulate earthquake rate? How might spatial models of near fault seismicity improve subsurface fault maps or models of earthquake triggering? [3] To address these issues, we analyze the variation of seismicity rate normal to near vertical strike slip faults in California and examine its relation to stress heterogeneity, damage zones, and degree of seismic coupling. Strike slip faults were chosen because their locations are constrained by mapped surface traces and their approximate bilateral symmetry of seismicity makes their earthquake distributions simpler to interpret than those of normal and reverse faults. To reveal systematic scaling relationships, we aggregated data from fault segments in a common class, as defined by geographic region, fault length, and aftershock activity. We restricted our analysis to small earthquakes (M w < 5), which we treated as point sources. Examined this way, the nearfault seismicity shows a power law decay away from the 1of25

2 Figure 1. Map of northern California showing locations of seismicity samples (gray boxes with reference numbers; see Table 3). Black lines delineate large faults, and the heavy black line marks the San Andreas fault. Dark gray dots mark the locations of 1.5 < M 2.5 earthquakes ( ). Reference x label background colors reflect the fault normal intercatalog location uncertainty of each segment: s TN for x the Parkfield segments (51 and 52); s UN for all others. fault surface [Powers and Jordan, 2005, 2007a; Hauksson, 2010]. [4] We examined regional variations in this fault normal distribution of seismicity by comparing the results from selected fault segments in northern California, between Parkfield and the San Francisco Bay (Figure 1), and a more extensive distribution of faults in southern California (Figure 2). In the northern California region, the fault segments are on or subparallel to the San Andreas master fault, a larger percentage of the faults are creeping [Irwin, 1990], and little seismicity extends below 10 km [Hill et al., 1990] (Figure 3). In contrast, the southern California segments have deeper seismicity [Hauksson, 2000], show little or no creep [Bodin et al., 1994; Lyons and Sandwell, 2003; Shearer et al., 2005], and often intersect at high angles. In southern California, we also investigated the spatial distribution of seismicity near smaller faults (e.g., splays of large faults and unmapped secondary faults) to see how fault length and along fault variations affect the scaling relations. We declustered each data set and incorporated fault segments that ruptured during large (M w > 6) earthquakes to constrain how the scaling relations are modified by after- 2of25

3 Figure 2. Map of southern California showing locations of seismicity samples (with reference numbers; see Table 3). Black lines delineate large faults, and the heavy black line marks the San Andreas fault. Grey boxes with reference numbers in circles (1 15) indicate the limits of seismicity samples about large strike slip faults; reference numbers in squares indicate the locations of samples about small (16 29) and aftershock dominated (30 41) fault segments. Dark gray dots mark the locations of 1.5 < M 2.5 earthquakes ( ). Reference label background colors reflect the fault normal intercatalog location uncertainty, s x PS, of each segment. shock activity. To assess the bias and variance in the scaling parameters caused by event mislocation, we supplemented the errors estimated by the hypocenter location algorithms with constraints from intercatalog comparisons and statistical simulations. [5] Our results provide measures of shear localization on faults and indirect evidence that fault damage zones extend through the seismogenic crust. We present a model of fault behavior that incorporates slip on a fractal fault, and discuss the implications of the model on fault evolution using data on fault width, on fault earthquake density, cumulative offset, and aseismic slip rate. Through comparisons with studies of exhumed faults and drilling results, we relate the structure of a fault damage zone at depth, as defined by seismicity, to near surface observations. 2. Fault Referenced Seismicity Catalogs [6] Hypocenters from six earthquake catalogs (three in southern, two in northern California, and one for the Parkfield region (Table 1)) were used to constrain near fault seismicity distributions and their uncertainties. The Southern California Seismic Network (SCSN) is the southern part of the California Integrated Seismic Network (CISN), a region within the Advanced National Seismic System (ANSS). The SCSN catalog (here abbreviated as S ; available at 3of25

4 Figure 3. Depth distributions of relocated earthquakes in the fault segment catalogs. Events from (a) catalog H and (b) catalog P in southern California and (c) catalogs U and T in northern California. The darker shaded bars mark the medial 90% of all events in the catalogs. Note that seismicity is generally shallower in northern California (Figure 3c). The downward bias in catalog H (Figure 3a) is likely an artifact of the 3 D velocity model used for earthquake relocation. is the standard catalog for southern California and contains events reported by all networks in the region. It includes some estimates of hypocentral errors, but all events have a quality designation indicative of maximum horizontal and vertical location uncertainties. [7] Hauksson and Shearer [2005] relocated events (catalog H ; available at from the SCSN using the double difference algorithm of Waldhauser and Ellsworth [2000]. They cross correlated waveforms to measure traveltime differences and relocated seismicity in a three dimensional (3 D) velocity model. For events lacking sufficient data for double differencing (<10%), they determined hypocenters using Hauksson s [2000] relocation method. They also evaluated errors using this method, because the double difference code does not compute hypocentral location errors for large data sets. [8] Shearer et al. [2005] relocated events (catalog P ; available at using a sourcespecific station term algorithm [Richards Dinger and Shearer, 2000] that employs a layered (1 D) velocity model. Using event similarity data from a waveform cross correlation analysis, they further refined the locations of spatially related events ( 60%) via a cluster analysis. Hypocentral errors reported by Shearer et al. [2005] correspond to the relative locations of events in each cluster. [9] The catalog of the Northern California Seismic Network (NCSN, abbreviated N ; available at ncedc.org/ncsn) is the standard catalog for the northern part of the CISN. Ellsworth et al. [2000] relocated a subset of the NCSN events in the San Francisco Bay area (catalog U ; available at using the double difference algorithm of Waldhauser and Ellsworth [2000]. The catalog does not include hypocentral location errors, but Ellsworth et al. [2000] report average horizontal and vertical location uncertainties of 0.1 and 0.5 km, respectively. [10] On the creeping section of the San Andreas fault in the vicinity of Parkfield, relocated events (denoted catalog T ; available at BSSA_html/bssa_96 4b/05825 esupp/) were taken from Thurber et al. [2006]. They constructed an improved 3 D wave speed model to first determine station corrections and then relocated events via double difference using a combination of event cross correlation differential times and traveltime differences from NCSN phase picks. The catalog does not include any hypocentral error information. [11] For each of the six catalogs, we limited our analysis to events that occurred from the beginning of 1984 until the end of To allow for intercatalog comparisons, the events were required to have hypocenters in both northern California catalogs (N and U or T and U) or in all three southern California catalogs (S, P, and H). The northern California catalogs, T and U, do not overlap geographically and may only be compared independently to catalog N, whereas the southern California catalogs span the entire lower half of the state and may be compared collectively. Events identified as quarry blasts or ones with intercatalog separations greater than 10 km were discarded. [12] We constructed catalogs of earthquakes for five classes of near vertical strike slip faults (Tables 2 and 3 and Table 1. Earthquake Catalog Sources Sources by Region ID a Type Southern California SCSN S standard Shearer et al. [2005] P relocated Hauksson and Shearer [2005] H relocated Northern California NCSN N standard Ellsworth et al. [2000] U relocated Thurber et al. [2006], Parkfield T relocated a Used to reference catalog in equations and text. 4of25

5 Table 2. Earthquake Catalog Statisitics N T a (events) b M c Southern California (SoCal) SCSN catalog 291, Fault classes Large 11, Small 8, Aftershock dominated 19, Northern California (NoCal) NCSN catalog 47, Fault classes Large 16, Parkfield 3, a All events common to regional and relocated catalogs in Table 1. Figures 1 and 2): large faults of northern California, the San Andreas fault at Parkfield, large faults of southern California, small faults of southern California, and fault segments with abundant aftershocks of major southern California earthquakes. For large faults, we chose relatively straight segments of named, throughgoing faults (e.g., Figure 4), eliminated fault segments with earthquake density of less than one event per km, and avoided fault junctions and zones of structural complexity. In southern California the SCEC Community Fault Model (CFM, available at [Plesch et al., 2007] was our guide for fault selection; in northern California, where faults are well defined by near vertical seismicity distributions, we used surface traces. Where the surface trace or seismicity along a particular fault indicates significant changes in strike or fault strand overlap, we restricted our selection to smaller fault segments; e.g., the Hayward fault (Figure 1; segments 42 43) and Garlock fault (Figure 2; segments 1 3). Large fault lengths, L k in Table 3, average 21 km in northern California and 47 km in southern. [13] We identified small and aftershock dominated faults by sets of earthquakes that define linear structural features of shorter length (average 9 km). The small fault class comprises splays off larger faults and unmapped secondary faults. Aftershock dominated segments were selected from faults activated by the 1992 Joshua Tree (M w 6.1), 1992 Landers (M w 7.3), or 1999 Hector Mine (M w 7.1) earthquakes. Although the seismicity in the aftershock dominated class spans the entire 19 year length of the source catalogs, it is dominated by aftershocks from these large events. The seismicity of the small fault class is more uniformly distributed in time. [14] We used the most recently updated magnitude data from catalogs S and N; these were generally reported as local magnitude, although there are a few events for which magnitudes were computed using other means. The maximum likelihood Gutenberg Richter b values [Aki, 1965] for the northern and southern California catalogs are 0.8 and 0.9, respectively (Table 2). Northern California has a lower magnitude of completeness (M c = 1.2) than southern California (M c = 2.0), reflecting its smaller area and higher station density. Notes to Table 3: a Down weighted level N 0, Fitting distance x max. b From relocated catalogs P, U, and T as described in text. Table 3. Fault Segment Catalogs a Segment Segment Name Size N k (events) L k (km) W k b (km) SoCal Large (N 0 = 1000, x max = 6 km) 1 Garlock (East) Garlock (Central) Garlock (West) Lenwood Lockhart San Andreas (Mojave) Santa Cruz Catalina Ridge Palos Verdes Newport Inglewood (North) Newport Inglewood (South) Elsinore Temecula San Jacinto (Anza) 5, Elsinore Coyote Mt Cerro Prieto Imperial 1, San Andreas (Coachella) Total (N T ) 11, Length weighted average 13.2 SoCal Small (N 0 = 700, x max = 2.5 km) 16 Scodie Lineament 1, San Jacinto (Anza) 1, San Jacinto (Anza) 1, San Jacinto (Anza) San Jacinto (Coyote Creek) San Jacinto (Anza) San Jacinto (Coyote Creek) San Jacinto (Anza) San Jacinto (Borrego) Superstition Mt Elmore Ranch Elmore Ranch (western ext.) Elmore Ranch (western ext.) Elsinore Total (N T ) 8, Length weighted average 9.2 SoCal Aftershock Dominated (N 0 = 1500, x max = 3 km) 30 Joshua Tree 1, Joshua Tree 2, Joshua Tree 1, Joshua Tree Landers Landers Landers 1, Landers 2, Landers 1, Hector Mine Hector Mine 2, Hector Mine 2, Total (N T ) 19, Length weighted average 8.2 NoCal Large (N 0 = 1500, x max = 3 km) 42 Hayward (North) Hayward (South) Calaveras (North) 2, Calaveras (Central) Calaveras (South) 1, Sargent 1, San Andreas Creeping (North) 1, San Andreas Creeping (Central) 3, San Andreas Creeping (South) 5, Total (N T ) 16, Length weighted average 7.9 NoCal Parkfield (No Down Weight, x max = 3 km) 51 San Andreas Parkfield (North) 3, San Andreas Parkfield (South) Total (N T ) 3, Length weighted average 8.4 5of25

6 Figure 4. Example of intercatalog earthquake location variation. (a) Map of the Elsinore fault (segment 10, Figure 2) showing relocated seismicity of catalog P and historic (heavy black lines), Holocene (thin black lines), and late Quaternary (thin gray lines) faults. (b) Depth section across the map showing locations of events in the standard catalog S relative to an initial, 3 D fault model based estimate of the fault trace (heavy dashed line); earthquakes are the same magnitude ranges as on the map. (c) Fault normal distribution of events. (d) Depth section across the map for relocated catalog P. (e) Fault normal seismicity distribution of relocated events. Note the difference in horizontal bias (black arrow in Figures 4c and 4e) of peak seismicity between the standard and relocated catalog. [15] We filtered the hypocentral depths in each fault catalog to focus on the central part of the seismogenic crust. Averaged across all fault segments, 90% of seismicity falls between 2 and 10 km for catalogs U and T and 2.5 and 17 km for catalog P (Figure 3). The upper 5% of events tend to occur within 2 km of the free surface, and so we set 2 km as an upper truncation depth. The lower cutoff shows significant variation reflecting regional differences in seismogenic thickness [Hauksson, 2000; Magistrale, 2002]. We therefore set the lower truncation depth to exclude the deepest 5% of hypocenters in each fault catalog. The differences between the lower and upper truncation depths for the kth fault segment determined the segment width W k ; values for each fault segment catalog are listed with the fault lengths L k in Table 3. [16] For each fault segment, we established a fault oriented coordinate system by fitting a plane to the seismicity. An initial estimate of the fault plane was derived from the CFM or, in the absence of a fault model, from a vertical plane that approximated the mapped surface or epicenter trace. All parameters of the plane were perturbed to obtain a least squares fit to relocated hypocenters from catalogs P, U or T within 2 km of this initial fault plane. For all fault segments considered, a 4 km wide swath captures most 6of25

7 Figure 5. Example of how a fault seismicity based coordinate system localizes events on a fault and minimizes artificial fault normal dispersion. (a) Map of the southern Hayward fault (segment 43, Figure 1) showing relocated seismicity of catalog U; fault age representations are the same as in Figure 4. The fault strand cutting across the lower right corner of the map is the northern Calaveras fault. (b) Fault normal depth section across the fault trace prior to aligning coordinate system to relocated seismicity; earthquakes are the same magnitude ranges as in the map, and the heavy dashed line marks the depth projection of the fault surface trace. (c) Fault normal distribution of events. (d) Fault normal depth section across the fault trace after aligning coordinate system to a best fit plane to relocated seismicity. (e) Realigned fault normal distribution. Note that the fault seismicity based coordinate system yields a narrower event distribution in Figure 5e. near fault earthquakes while ignoring off fault clusters that would contribute to misalignment of the coordinate system with the fault plane. Narrower swaths fail to include nearfault events for fault segments where seismicity exhibits a significant horizontal shift from the initial estimate, as in the case of the Elsinore fault (Figure 4). Rotations permitted by the fitting process further localize events on final, seismicity based fault planes, as is observed on the Hayward fault (Figure 5). [17] The hypocenters from the relevant relocated catalog were transformed into a local Cartesian system defined by an origin at one end of the surface trace of the best fit fault plane, a near vertical z axis, a y axis along the fault strike, and an x axis perpendicular to the fault plane. A final, faultreferenced catalog was then constructed by eliminating events with relocated x coordinates greater than ±15 km, relocated y coordinates beyond the ends of the fault segment, and relocated z coordinates outside the depth limits 7of25

8 Table 4. Intercatalog Error Estimates Catalog Pair (AB) Bias (km) a Standard Deviation (km) b x AB b y AB b z AB s x AB s x AB b s y AB s z AB SoCal Large HS PS HP SoCal Small HS PS HP SoCal Aftershock Dominated HS PS HP NoCal UN (Large) TN (Parkfield) See the auxiliary material for individual fault values. a Event weighted mean absolute values. b The s x AB estimated by uniform reduction. described above. The fault segment catalogs are summarized in Table Intercatalog Analysis [18] A proper description of near fault seismicity distributions requires careful attention to mislocation errors. Information about such errors can be determined from comparisons of hypocenters determined by different methods [e.g., Shearer et al., 2005]. In the present study, we have quantified the intercatalog comparisons on a fault segment basis. For the kth fault segment with N k events common to the catalog pair A and B, we define the intercatalog faultnormal bias by b kx AB ¼ 1 X ðx i A N xi B Þ; k i2k and the fault normal variance by ð kx AB Þ2 ¼ 1 X ðx i A N k 1 xi B i2k bkx AB Þ2 : i Here, x A is the fault normal coordinate of the ith event, and the summation implied by i 2 k is over all N k events associated with the kth fault segment. Similar expressions can be written for the fault parallel and near vertical directions. The intercatalog bias and variance computed for each catalog pair (UN and TN in northern California and HS, PS, and HP in southern California) are listed by individual fault segment in Tables S1 S3 in the auxiliary material. 1 [19] For each coordinate of the fault oriented reference frame, the mean intercatalog bias for a fault class was computed by taking the absolute values of the segment biases, weighting them by the number of events for each segment, and averaging over all segments. Likewise, the 1 Auxiliary materials are available in the HTML. doi: / 2008JB ð1þ ð2þ mean standard deviation was calculated as the square root of the event weighted segment variances. These averages are given in Table 4. For all classes, the intercatalog biases and standard deviations are largest for the z coordinate, reflecting the uncertainty in estimating hypocentral depth. No systematic differences are observed between the two horizontal coordinate statistics, x and y. In southern California, the z coordinate statistics are especially large, in part because shallow events in the early part of Catalog S were often assigned a default depth of 6 km, and also because the velocity model used to relocate events in Catalog H tends to bias events downward (Figure 3). Because we are interested in the fault normal distribution of seismicity, we focus our x discussion on b AB and s x AB. [20] The intercatalog statistics for well instrumented Parkfield region are higher than those of the northern California fault class, particularly the fault normal values x x (e.g., s TN = 0.62 km versus s UN = 0.31 km). These differences are primarily due to more stations and a greater number of earthquakes being used in the relocation procedure, as well as a strong velocity contrast across the San Andreas fault near Parkfield, which is modeled in the Thurber et al. [2006] relocations but not in the standard catalog. [21] The intercatalog statistics for the large faults in x southern California (e.g., s PS = 1.04 km) are also substantially higher than for the northern California fault class, which we ascribe to several factors. The southern region has a more heterogeneous crustal structure than the northern region, such as larger and deeper sedimentary basins, increasing the location errors. Moreover, the faults sampled in northern California were restricted to well instrumented regions of the San Andreas system near the center of the NCSN. In southern California, a number of the large faults are peripheral to the SCSN, and they invariably show bigger intercatalog variations (Figure 2). For instance, s PS for the coastal Newport Inglewood fault (segments 8 9) is 2.1 km, and it reaches 2.7 km for the Cerro Prieto fault (segment 13), which is located in Mexico outside the SCSN. In contrast, the values for the more centrally located San Jacinto fault (segments 17 24) are less than 1 km. [22] In southern California, the large fault class has a higher intercatalog standard deviation than either the smallfault or aftershock classes (e.g., s PS = 1.04, 0.75, 0.55 km, respectively). The fault normal biases show a similar ordering (e.g., b PS = 0.54 km, 0.43 km, 0.23 km). The network x geometry again plays a role, because the latter two classes comprise segments that tend to be more centrally located within the SCSN. In addition, the estimator given by equation (1) accounts only for a constant translational bias; for long segments, other parameters, such as a rotational bias, may be needed to represent the catalog differences, especially for faults on the periphery of the network. The inadequacy of the bias model acts to increase the apparent intercatalog variance. [23] The standard deviations between the two relocated southern California catalogs (HP) are consistently lower than those involving the standard catalog (HS and PS), satisfying the expectation that relocation reduces the hypocentral variance (Table 4). However, histograms of the faultnormal differences for all three catalog combinations show heavy tailed distributions with outliers that dominate the variance estimates. Most of these outliers can be explained x x 8of25

9 Table 5. Catalog Specific Error Estimates a Catalog (A) Bias (km) b,c Standard Deviation b (km) Catalog Error (km) b x A b y A b z A s x A s x A d s y A s z A Horizontal Vertical SoCal Large S (standard) P (relocated) H (relocated) SoCal Small S (standard) P (relocated) H (relocated) SoCal Aftershock Dominated S (standard) P (relocated) H (relocated) NoCal Large N (standard) U (relocated) e NoCal Parkfield N (standard) T (relocated) NR NR a See the auxiliary material for individual fault values. NR, not reported. b Computed assuming statistical independence. c Event weighted mean absolute values. d The s x A estimated by uniform reduction. e Catalog averages as reported by Ellsworth et al. [2000]. by the way the different location algorithms respond to anomalous travel times (e.g., picking blunders, large path anomalies). To account for outliers, we applied a method of uniform reduction [Jeffreys, 1932; Buland, 1986] in which we modeled the differences as the superposition of a Gaussian distribution and a nearly uniform distribution. The standard deviations of the best fit Gaussians are listed in Table 4. The largest reductions, more than 80% in variance, are obtained for the HP intercatalog differences. The reduced standard deviations were used to characterize the event mislocations in our subsequent analysis of the errors in the fault normal scaling parameters. [24] If the event location errors from the three southern California catalogs are assumed to be statistically independent (possibly a poor assumption) then we can determine catalog specific biases, b A kx, and standard deviations, s A kx,by solving the three equations for intercatalog bias: b kx AB ¼ bkx A bkx B ; and the three for intercatalog variance: kx AB 2¼ kx A ð3þ 2þ kx 2; B ð4þ where AB = {PS, HS, HP}. Equations (3) are not linearly independent, and we therefore included the additional constraint that the biases of the individual catalogs should sum to zero, which minimizes the overall bias. Similar sets of equations can be solved for the fault parallel and depth directions. We averaged the event weighted absolute values of the fault segment biases to obtain the values in Table 5 (see the auxiliary material for individual fault segment data). [25] The s values for the relocated catalogs are substantially smaller than those for the standard SCSN catalog, as expected from the intercatalog comparisons, and the s values for the Shearer et al. [2005] catalog are in all cases smaller than those for the Hauksson and Shearer [2005] catalog. In x particular, the values of s P obtained from the reduced intercatalog standard deviations are only about half the size of s x H, which is consistent with the qualitative observation that the cluster analysis relocation method used to develop the P catalog provides significantly better localization of hypocenters into fault like structures [Shearer et al., 2005]. For this preferred southern California catalog, the faultnormal standard deviations are less than 0.1 km for all three fault classes. As noted above, our linear removal of bias did not consider possible intercatalog rotations, which could skew the intercatalog variance to higher values, whereas possible correlations in the hypocenter errors between different catalogs would skew them to lower values. On the balance, s x P 0.1 km appears to be a good estimate. [26] In Table 5, we compare the results of the intercatalog error analysis with formal location errors listed in the individual catalogs. The standard deviations in depth from the latter sources are always larger than the corresponding mean horizontal standard deviation, in rough agreement with the intercatalog analysis, but the magnitudes are rather different. The mislocation errors included in the standard network catalogs are substantially larger than our computed values. The reverse is generally true for the relocated catalogs, though the agreement is much better. The confidence region of fault normal hypocentral error for the relocated catalogs is km with the high end of the range represented by a few fault segments at the periphery of the southern 9of25

10 California network. For the most part, location error is <0.1 km, consistent with the intercatalog analysis. Further checks on the mislocation errors from seismicity modeling, described below, support the intercatalog analysis. 4. Fault Normal Seismicity Distributions [27] Because strike slip faults in California are nearly vertical, we developed our scaling relations using the faultnormal distance x as the independent variable, ignoring bilateral asymmetry in seismicity. We stacked the seismicity data in each fault group and computed earthquake density as a function of distance x using a nearest neighbor method [Silverman, 1986] in which the bins are adjusted to contain q neighboring events. For each data set we experimented with a range of q values and selected one that yielded an adequate point density for deriving fault normal scaling relations (10 q 50). [28] Logarithmic plots of earthquake density versus x for each regional catalog indicate fault normal distributions that have flat peaks within a few hundred meters of the fault, rolloff as an inverse power law for about an order of magnitude in distance, and merge with irregular backgrounds at distances less than 10 km (Figures 6 9). Near the fault, the Figure 6. Fault normal earthquake density distributions for large faults in southern California. Distributions for (a) relocated catalog P, (b) relocated catalog H, and (c) standard catalog S using a nearest neighbor bin interval of q =50 events. The heavy dashed line marks the limit to which we fit data, x max ; beyond this limit, background seismicity dominates. The black line is a maximum likelihood fit of an inverse power law, with asymptotic slope ~, to observations within that limit. The inner scale of the distribution is described by d. ~ Figure 7. Fault normal earthquake density distributions for (a) small faults and (b) aftershock dominated fault segments in southern California. Both Figures 7a and 7b use events from relocated catalog P with a bin interval of q = 50 events. Features are the same as in Figure of 25

11 parameter, we found that the maximum likelihood fits to the observed fault normal distributions were obtained for m 2. We also experimented with exponential and Gaussian distributions but found they were a poor fit to the data. [29] Assuming m = 2, we obtained a maximum likelihood fit of equation (5) to the binned data for each fault group out to a maximum fault normal distance x max, chosen such that the relative contributions from background seismicity were small; the values of x max for each fault class are listed in Figure 8. Fault normal earthquake density distributions for large faults in northern California. Distributions for (a) relocated catalog U and (b) standard catalog N using a nearestneighbor bin interval of q = 20 events. The heavy dashed line marks the limit to which we fit data, x max ; beyond this limit, background seismicity dominates. As in Figures 6 and 7, the black line is a maximum likelihood fit of an inverse power law to observations within that limit. observed distributions can be described by the functional form: ðxþ ¼ 0 d m =m : ð5þ jj x m þ d m In expression (5), d is an inner scale that removes the power law singularity on the fault, g is the asymptotic roll off of seismicity away from the fault, and the exponent m controls the shape of the distribution for x d, i.e., the sharpness of the corner on a logarithmic plot. By varying the latter Figure 9. Fault normal earthquake density distributions for the Parkfield fault segments. Distributions for (a) relocated catalog T and (b) standard catalog N using a nearest neighbor bin interval of q = 10 events. Features are the same as in Figure of 25

12 We assume the observed value, n j, in each bin is Poisson distributed, which yields the log likelihood function [e.g., Boettcher and Jordan, 2004]: XJbins ð 0 ;;dþ ¼ n j ln n j ðxþ nj ðxþ lnðnj!þ ; ð7þ j¼1 Maximizing (7) using a linear approximation to n(x) over each binning interval (adequate for the small intervals used here) yields the estimates ~ 0, ~, and d. ~ These estimates have correlated errors. However, we note that the maximum likelihood estimator for ~ 0 is N max / R x max (1 + x 2 /d 2 ) g/2 dx, 0 where N max is the cumulative number of events out to x max. If N max is large, its relative error is small ( N 1/2 max, the standard population error) and uncorrelated with the errors in ~ and d. ~ The latter are positively correlated, as shown in Figure 10, which plots the maximum likelihood estimates and confidence intervals for the various fault groups in the ~ d ~ plane. [30] We checked the error estimates from the maximum likelihood procedure with those derived from jackknife resampling [Efron, 1979]. Generally speaking, the two were in agreement, but where they differed, we used the larger estimate. We experimented with the lower magnitude cutoff and depth ranges and found the results to be robust. We also tested a range of bin widths, q, and found little variation in our results. [31] An important issue is the weighting of individual fault segments in the seismicity stacking. Owing to the variability in seismicity rates, the number of earthquakes per fault segment ranges from a hundred to several thousand (Table 3), and our results will depend on how each is weighted. In our stacking procedure, we applied a positive weighting factor w k to each event in the kth fault segment catalog, which we computed by w k ¼ min½1; N 0 =N k Š; ð8þ Figure 10. Maximum likelihood solutions and errors for ~ and d. ~ Values for (a) southern California large faults, (b) northern California large faults, and (c) Parkfield showing the positive correlation between scaling parameters. Light gray and black ovals mark the 68% and 95% confidence bounds, respectively. Table 3. The expected number of events in the jth bin of width Dx is the integral: n j ¼ Z jxjj jx jj x ðxþdx: ð6þ where N 0 is a down weighted level that was held constant for each fault group. We varied N 0 from N min, the minimum of all catalog sizes N k in each fault group, to N max, the maximum in each group. The latter bound corresponds to one event one vote (w k = 1), whereas the former corresponds to one catalog one vote (w k 1/N k ). For intermediate values, events from catalogs larger than N 0 were down weighted by the ratio N 0 /N k, while those from smaller catalogs received unit weight. We experimented with a range of down weight levels for each structural group and found that the maximum likelihood estimates for most of the parameters were stable across a wide range between N min and N max (Figure 11). Table 3 lists the actual values used in deriving the parameter values discussed below. [32] For all structural groups, there is a well defined scaling region of at least an order of magnitude in faultnormal distance where the earthquake density shows a power law roll off before it merges with the background seismicity (Figures 6 9). In Table 6, we list by fault group the maximum likelihood estimates of ~ and ~ d. To assess the effects of earthquake clustering, we declustered the fault segment catalogs using the algorithm of Reasenberg [1985] with default parameters (r fact = 10, x k = 0.5, x meff = 1.5, t 0 = 2 days, t max = 10 days, p 1 = 0.99) and obtained the distri- 12 of 25

13 bution parameters for the declustered catalogs and the event clusters. [33] Table 6 shows interesting variations across the fault groups and catalog types. Comparing the relocated catalogs P and U, seismicity decays away from the large faults in southern California at a significantly lower rate (~ = 0.98 ± 0.04) than it decays in northern California (1.60 ± 0.04) or for the small faults in southern California (1.37 ± 0.08). In southern California, clustered events decay more rapidly than independent events, in agreement with the higher decay rate for aftershocks of large southern California earthquakes (~ = 1.50 ± 0.08). [34] For the larger faults, the apparent inner scale ~ d for relocated catalogs is smaller in northern California (0.08 ± 0.01 km) than in southern California (0.23 ± 0.03 km). The former is comparable to the relocation uncertainty. Significantly higher values are obtained for the standard catalogs ( km), consistent with more dispersion due to mislocation. Figure 11. Down weighted analysis results for small faults in southern California: (a) ~ and (b) d ~ vary with down weighted value across the different catalogs. The dashed gray line marks our selected value of N 0 = 700. Note that parameter estimates are largely stable within error for most down weighted values. Only at low values of N 0 do parameters start to vary as more box catalogs, including those with few events, are weighted equally. 5. Analysis of Bias [35] The results in Table 6 are biased by two factors: contributions from background seismicity and hypocentral error. The former is apparent when we relax the assumption of bilateral symmetry. We first identified which side of each fault segment had more events for x x max and then restacked the data for each of the five fault classes, preserving this asymmetry in seismic abundance (Figure 12 and the auxiliary material). The estimates of ~ obtained for the less abundant side were consistently higher than those on the more abundant side. The values of d ~ on the less abundant side of each fault class also increased slightly over those of the symmeterized distributions owing to the positive correlation between ~ and d. ~ We did find that, on the side with fewer events, the scaling region extended to greater distances from the fault, in some cases by an order of magni- Table 6. Apparent Fault Normal Scaling Parameters Catalog Whole Catalog Declustered Clusters ~d (km) ~ ~ d (km) ~ ~ d (km) ~ SoCal Large S (standard) 0.88 ± ± ± ± ± ± 0.12 P (relocated) 0.23 ± ± ± ± ± ± 0.05 H (relocated) 0.27 ± ± ± ± ± ± 0.05 SoCal Small S (standard) 0.79 ± ± ± ± ± ± 0.54 P (relocated) 0.19 ± ± ± ± ± ± 0.17 H (relocated) 0.23 ± ± ± ± ± ± 0.19 SoCal Aftershock Dominated S (standard) 0.55 ± ± 0.11 P (relocated) 0.33 ± ± 0.08 H (relocated) 0.31 ± ± 0.07 NoCal Large N (standard) 0.16 ± ± ± ± ± ± 0.07 U (relocated) 0.08 ± ± ± ± ± ± 0.05 NoCal Parkfield N (standard) 0.89 ± ± ± ± ± ± 1.60 T (relocated) 0.13 ± ± ± ± ± ± of 25

14 distribution close to x max. We show this by modeling the distribution in each fault class as the superposition of a fault normal decay of earthquake rate and a uniform background rate (Figures 12b and 13). Parkfield was excluded from the modeling because the background signal is weak and the scaling parameters therefore unbiased. We use the parameters of the low abundance side of the fault in each class because the contribution from background is significantly lower and the scaling only minimally biased. By varying the ratio of background to decaying events, we recovered the results reported in Table 6, as well as the distributions on the event heavy side of the fault for each fault class, suggesting that the fault normal decay of seismicity is similar across strike slip faults. Values for background corrected scaling parameters are reported in Table 7. [37] We investigated how the results are biased by hypocenter errors in two ways, theoretically and using Monte Carlo simulations. We assumed that the true fault normal Figure 12. Comparison of fault normal earthquake density for (a) low and (b) high productivity sides of a fault for catalog P about large, southern California faults using a nearest neighbor bin interval of q = 20 events. Features are the same as in Figures 6 9. Seismicity decays more rapidly on the low productivity side of a fault and spans almost 2 orders of magnitude. In Figure 12a, maximum likelihood fits of exponential (dashed) and Gaussian (dotted) distributions are shown for comparison. In Figure 12b, we additionally fit the data using the parameters from the lowproductivity side (Figure 12a) and include a uniform background rate, n bg. See the auxiliary material for distributions of other fault classes. tude, supporting our choice of power law model. Figure 12a shows that exponential and Gaussian distributions are a poor fit to the data. Fault maps show that the truncation of the scaling region on the abundant side can generally be explained by the seismicity increase from another fault branch or splay, proximate to the target fault segment, a common feature of the San Andreas system (e.g., Figure 5). [36] Uniform background seismicity associated with proximate faults significantly alters the shape of a density Figure 13. Comparison of fault normal earthquake density for (a) large faults in southern California (catalog P) with (b) that of a synthetic distribution using bin intervals of q = 50 events. Features are the same as in Figures 6 9. The synthetic distribution is one realization of a Monte Carlo simulation in which fault normal earthquake density is modeled as the superposition of an unbiased distribution (g = 1.3, d = 0.3 km; compare Figure 12a) that decays beyond x max (dashed gray line) and a uniform background. The maximum likelihood fit to the synthetic distribution out to x max recovers the scaling parameters determined in the initial analysis of symmeterized distributions. 14 of 25

15 Table 7. Bias Corrected Scaling Parameters Fault Class Catalog Hypocentral Error Correction Background Correction Simulated a d (km) g Theoretical a d (km) d (km) g SoCal large P 0.26 ± ± ± ± 0.05 SoCal small P 0.21 ± ± ± ± 0.10 SoCal aftershock dominated P 0.39 ± ± ± ± 0.10 NoCal large U 0.09 ± ± ± ± 0.05 NoCal Parkfield T 0.13 ± ± ± ± 0.25 a Bias corrections computed assuming s x A = 0.1 km. seismicity is governed by the distribution n(x) in equation (5), and that the catalogs have independent, identically distributed mislocation errors approximated by a zero mean Gaussian probability density function (pdf), g A ðxþ ¼ p 1 ffiffiffiffiffi 2 x A h i exp x 2 =2ð x A Þ2 ; ð9þ where s x A is the standard error for catalog A. The pdf for the observed seismicity can then be computed as the convolution of the two (normalized) distributions: p A ðxþ ¼ Z 1 1 ðx Þg A ðþd= Z 1 1 ðþd: ð10þ A little analysis shows that, if s A x /d is not too large (less than 5 or so), p A (x) can be approximated by equation (5) with an asymptotic slope ~ = g and an inner scale ~ d computed as the intersection of the small x probability density with the large x asymptote, d= d ~ ¼ pffiffiffiffiffiffiffiffi Z 1 2= 1 þð x =m A x=dþm e x 2 =2 dx: ð11þ 0 The bias correction d d ~ derived by solving (11) is only weakly dependent on the shape parameter m, so we fixed it at its best fit value (m = 2). We experimented with s x A values spanning the confidence region of km recorded in the relocated catalogs. Because low values have only a minimal effect and the large values are only applicable to a few fault segments in southern California, the conservative estimate of s x A = 0.1 km determined from our intercatalog analysis is appropriate for A = P, U, and T. Figure 14 plots d ~ versus d for s x A = 0.1 km and we see that the correction is small for d > s x A and decreases with g. [38] The bias corrected estimates of d obtained from (11) are listed in Table 7. The largest correction, for large fault seismicity in northern California, changes the estimated inner scale from 0.09 km to 0.06 km, a difference of only 30 m. Note that the magnitude of bias in this worst pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi case, 0.03 km, is smaller than the quadratic estimator d 2 þ 2 A d = 0.05 km. We verified the small size of the bias correction using a Monte Carlo method in which we generated synthetic catalogs that satisfied (12), perturbed them with Gaussian noise (0.05 s x A 0.2 km), and calculated a likelihood score of their fit to the distribution curves obtained from the actual data. The values of d and g that maximized the likelihood for many ( 50) catalog realizations for s x A = 0.1 km are listed in Table 7; an example of a single realization is presented in Figure 15. The estimates of d are nearly identical to the theoretically corrected values. Moreover, the simulations provided bias corrections for g, which are not zero (as the asymptotic theory predicts) owing to the positive correlation between the estimators of d and g arising from a finite range of x (see Figure 10). However, the corrections to g are also small, 10% (for catalog T) or less. 6. Rough Fault Loading Model [39] Our multicatalog analysis of earthquake hypocenters in California reveals that the seismicity in the vicinity of strike slip faults can be represented by a three parameter distribution: d 2 =2 ðxþ ¼ 0 x 2 þ d 2 ; jxj x max: ð12þ The constant n 0 describes the fault normal seismic intensity (in events/km) on the fault surface. Using the data in Table 3, the intensity n(x) can be normalized by the total fault length S L k, as plotted in Figures 6 9, or by the total fault area S L k W k, which yields a spatial seismic density for the catalog interval T = 19 years. The inner scale d measures the Figure 14. Theoretical relationship between an observed inner scale, d,andthetruevalueofd ~ plotted for various g. Theory assumes that an observed fault seismicity scaling distribution is the product of the true distribution convolved with a Gaussian noise function with standard deviation of 0.1 km. Only at d < 0.2 km do the observed and true values diverge significantly. 15 of 25

16 Figure 15. Sample result from simulation analysis of parameter bias. In each simulation, synthetic distributions were perturbed with Gaussian noise (s x A = 0.1 km) until a combination of g and d was found that maximized the likelihood score of the fit to the original distribution. The simulation result pictured is for large faults of southern California and illustrates a good correlation between a perturbed synthetic distribution (dots) and our observed distribution (dashed line) for catalog P. half width of a near fault region where the seismic intensity is flat ( n 0 ), and the exponent g specifies the power law roll off of seismic intensity in the scaling region d < x x max. [40] Figure 16 presents a conceptual rough faulting loading (RFL) model that we will use to explain the seismicity behavior. Our starting point is the observation that fault surfaces can be described by a self affine (fractal) complexity over a large range of spatial scales [Power and Tullis, 1995; Lee and Bruhn, 1996; Renard et al., 2006] and evolve in time toward surfaces that are less complex in the direction of slip [Wesnousky, 1988; Stirling et al., 1996; Sagy et al., 2007; Finzi et al., 2009]. Here complexity refers to the fractal branching of faults into multiple surfaces [e.g., King, 1983; Hirata, 1989] as well as the fractal roughness of individual fault surfaces [e.g., Lee and Bruhn, 1996; Renard et al., 2006; Sagy et al., 2007]. To build a simple model, we begin by considering a single fault surface whose deviations from the planar approximation x = 0 define a fault normal topography [Saucier et al., 1992; Chester and Chester, 2000; Dieterich and Smith, 2009]. We represent an along strike (constant z) profile of this topography as the realization of a stationary stochastic process X(y) that has zero expectation, hx(y)i = 0, and a variogram D E 1=2: 2 2 ðyþ ¼ ½X ðy þ yþ XðyÞŠ 2 ð13þ the surface is self affine, then x Dy H, where 0 H 1is the Hausdorff measure (sometimes referred to as the Hurst exponent) of the along strike profile [Feder, 1988; Turcotte, 1997]. Assume the self affine scaling of fault roughness breaks down above some outer scale Dy outer related to the Figure 16. Schematic representation of the RFL (rough fault loading) model that explains observations of near fault seismicity distribution. (a) Tectonic loading of a self affine fault generates a heterogeneous stress field that yields a power law decay of seismicity over a scaling region via stress relaxation [Dieterich and Smith, 2009, Figure 3]. (b) Toward the fault core, small scale stress heterogeneities of the rough fault are attenuated by low fracture strength across a damage zone of width 2d km. (c) Illustration of how observed seismicity rates vary with distance from a fault (solid black line). The scaling region likely extends beyond x max, as indicated by the dashed black line, but is masked by interference from proximal fault branches. 16 of 25