446 Seismological Research Letters Volume 80, Number 3 May/June 2009 doi: 10.1785/gssrl.80.3.446

INTRODUCTION

To construct and test certain hypotheses of earthquake occur-rence, we’ve compiled a new catalog covering the whole of California, which lists all known earthquakes at magnitude 4.7 and above and provides focal mechanism information for each earthquake. Accounting for magnitude errors, the catalog should be complete at magnitude 5.0 and above for most of California after 1940 and at specified higher thresholds oth-erwise.

Earthquake magnitudes play an important role in earth-quake forecasting and prediction, but their use is complicated by the fact that there are many magnitude types, measured in different ways with different uncertainties. Even a single cata-log may include moment magnitude, local magnitude, surface wave magnitude, and so on. Here we adopt moment magnitude as the standard and convert other types into moment magni-tude using regression relationships.

Catalog data have errors in location, magnitude, and focal mechanism that can influence the results of earthquake studies. Neglecting these errors, or estimating them poorly, could cause valid hypotheses to be rejected or invalid ones to be accepted. The uncertainties decrease with time, except that they increase temporarily after large earthquakes. Therefore we’ve conducted an extensive uncertainty study.

Many studies assume a distinction between mainshocks, aftershocks, and foreshocks, and some catalogs are “declus-tered” using somewhat arbitrary definitions (e.g., Gardner and Knopoff 1974; Reasenberg and Oppenheimer 1985). Here we take a somewhat different approach. Using a stochastic epidemic-type aftershock (ETAS) model (Zhuang et al. 2002, 2004; Zhuang et al. 2005), we assigned to each event a prob-ability that it occurred independently. The independence prob-ability for each earthquake can then be employed by any user to decluster the catalog to fit his or her needs. Our method is still arbitrary, but we feel it is more transparent and flexible than other methods.

Kagan, Jackson, and Rong (2006) compiled an earth-quake catalog covering southern California with lower magni-tude threshold 4.7 from 1800 to 2005. This catalog was used

to forecast long-term seismicity in southern California (Kagan, Jackson, and Rong 2007). Here, we extend the region to the whole of California and update through 2007. In addition we used more original catalog sources, estimated moment magni-tude for each event, calculated focal mechanism uncertainties, recalculated data uncertainties by different methods, and recal-culated the independence probability using an ETAS model.

Felzer and Cao (2008) created an earthquake catalog cov-ering California from 1800 through 2007 with lower magni-tude threshold 4.0. How is ours different? We included more existing catalogs that enabled us to provide more accurate mag-nitude and location estimation; we converted different types of magnitude to moment magnitude; we estimated focal mecha-nisms for small earthquakes; we estimated magnitude and focal mechanism uncertainties; and we assigned independence probability to each event in our catalog.

Our catalog contains two parts: 1) a point source catalog, in which every earthquake is represented as a point at its hypo-center, and 2) an extended source catalog in which some of the large earthquakes (M ≥ 6.5) are represented by multiple rectan-gular dislocations. Since our forecast program requires earth-quake focal mechanisms to calculate future seismicity rate, we need our new catalog to extend the forecast to all of California.

BASIC INFORMATION

Our catalog covers “greater California,” which we define as the region bounded by the polygon

43.5 N, 125.7 W; 43.5 N, 118.5 W; 39.7 N, 118 − − − ..5 W;

36.1 N, 113.6 W; 34.6 N, 112.6 W; 3

− − 44.3 N, 112.6 W;

32.7 N, 113.1 W; 31.8 N, 113.2

−

− −

W; 31.2 N, 114.5 W;

31.0 N, 117.1 W; 31.1 N,

−

− −− −

−

117.4 W; 31.5 N, 118.3 W;

32.4 N, 118.8 W; 3

33.3 N, 121.3 W; 34.0 N, 122.0 W;

37.5 N, 124.3

− −

−

W; 40.0 N, 125.9 W; 40.5 N, 125.9 W;

43.0 N,

− −

−− −125.7 W; 43.5 N, 125.7 W.

california earthquakes, 1800–2007: a unified catalog with moment magnitudes, uncertainties, and focal mechanismsQi Wang, David D. Jackson, and Yan Y. Kagan

Qi Wang, David D. Jackson, and Yan Y. KaganUniversity of California, Los Angeles

Seismological Research Letters Volume 80, Number 3 May/June 2009 447

As shown in Figure 1, it includes the region within the politi-cal boundaries as well as a surrounding region, because earth-quakes in the neighborhood of California can also influence the seismicity within California proper. Below, “California” without any modifiers means “greater California.”

Because different catalogs have different accuracies in different regions, we divided California into three regions: 1) southern California (SC), 2) a small part of Mexico, and 3) northern California and part of Nevada (NC). Southern California (SC), shown by the small polygon in Figure 1, is bounded by the vertices

35 8000. N, 116.4000 W; 34.0815 N, 114.4717 W;

3

− −

22.000 N, 114.3333 W; 32.0000 N, 120.5000 W;

34

− −

..5000 N, 121.2500 W; 37.2167 N, 118.0167 W;

36

− −

..6847 N, 117.7930 W; 35.8000 N, 116.4000 W. − −

This polygon coincides with the southern California region of authority assumed by the Advanced National Seismic System (ANSS). The region south of 32.0° N is a small part of Mexico, and the rest of the region is northern California and part of Nevada (NC).

If a catalog lists seismic moment we calculated moment magnitude from the formula

M Mw = × −( / ) (log . )2 3 16 110 0

where Mw is the moment magnitude and M0 is the moment in units of dyne-cm. This formula is the same one used in the Global Centroid Moment Tensor (CMT) catalog and is consis-tent with that of Kanamori (1977).

Table 1 shows generic uncertainty information for greater California. This Table is based on Table 1 in Kagan, Jackson, and Rong (2006) with magnitude and location uncertainties

−126˚−125˚−124˚−123˚−122˚−121˚−120˚−119˚−118˚−117˚−116˚−115˚−114˚−113˚31˚

32˚

33˚

34˚

35˚

36˚

37˚

38˚

39˚

40˚

41˚

42˚

43˚

0 50100

km

▲ Figure 1. Epicenter distribution of earthquakes in California study area, 1800–2007. Black beach balls are known focal mechanism solutions; gray beach balls are events whose focal mechanisms are inferred solutions from known focal mechanisms. Symbol size is proportional to earthquake magnitude.

448 Seismological Research Letters Volume 80, Number 3 May/June 2009

after 1980 added. As described below, we use the generic uncer-tainties only when more specific values are not available.

POINT SOURCE CATALOG

Original Catalogs There are many earthquake catalogs, covering all or part of California, reporting different values of location, magnitude, focal mechanism, etc., with different accuracies for the same earthquakes. To make our catalog more accurate and complete we selected the most reliable data from 23 such catalogs. Table 2 lists these catalogs with references and/or Web site links where available.

Toppozada’s catalog (see Table 2 for catalog details) lists large historical earthquakes, and we only included the part cov-ering the earthquakes before 1940. The California Division of Mines and Geology (CDMG) (now the California Geological Survey, CGS) catalog, which also lists historical events, has been updated recently. We only used it for earthquakes before 1974, because after that time more reliable instrumental data are avail-able. The ANSS catalog was built by combining the Northern California Seismic Network (NCSN) catalog, Southern California Seismic Network (SCSN) catalog, the Berkeley or BDSN catalog, Nevada seismic network catalog, and the National Earthquake Information Center (NEIC) catalog. When multiple solutions are provided from different catalogs for one event, ANSS gives priority to the most local seismic cata-log. Both catalog 6 and catalog 20 in Table 2 are NCSN catalogs. Catalog 6 provides fault plane solutions while catalog 20 does not but includes more events. The BDSN catalog (catalog 17 in Table 2) created by the Berkeley seismic lab and is not currently being updated after August 27, 2003. There are two Berkeley moment tensor catalogs: one is based on surface wave solution (catalog 11 in Table 2), and the other is based on time domain solution (catalog 12 in Table 2). Both these catalogs are listed in the same Web site provided in Table 2 and the format descrip-tion is listed at http://seismo.berkeley.edu/~dreger/mtcatexpl.html. The SCSN moment tensor (MT) catalog (catalog 19 in Table 2) provides moment tensor solutions for recent events; we included only events with variance reduction larger than 60.

Generally, different catalogs may report different coor-dinates for the same earthquake. Like the ANSS (see Table 2 for catalog details), we used the following criteria to decide whether two or more reports represent the same earthquake:

1. The various reports must be given by different catalogs. We assume that each catalog has eliminated duplicate solutions of the same event.

2. Any two reports must be within 100 km and 16 seconds.Any two or more solutions that satisfy the above criteria are considered duplicates, and only one of them will be retained in the final catalog. However, we made the preliminary compos-ite catalog available on our Web site (http://jumpy.igpp.ucla.edu/~kagan/cal_sortcat.dat), in which all available reports of each earthquake are listed in common format. There are some blasts reported as earthquakes in some particular cata-logs. We listed them on our Web site at http://jumpy.igpp.ucla.edu/~kagan/cal_explosions.dat.

Estimating Moment MagnitudeOne catalog may use different types of magnitudes for different earthquakes, but using a uniform magnitude type in one cata-log is preferable in statistical studies. Therefore we used regres-sion to estimate moment magnitude and uncertainty from all other types. Following Castellaro et al. (2006), we used general orthogonal regression because it accounts for random errors in both variables. We first created a standard moment-magnitude catalog by combining the Global CMT, SCSN moment, U.S. Geological Survey (USGS) moment, Berkeley MT surface wave (SW), and Berkeley MT time domain (TD) catalogs (Nos. 9, 19, 10, 11, and 12 in Table 2; see Table 2 for catalog details). Then we separated the different types of mag-nitude in each catalog, and if for each type there were at least 10 events with corresponding moment magnitudes we devel-oped a regression relationship. If there were fewer than 10 appropriate events for a given magnitude type in a given cata-log (for example, there were few events with surface wave mag-nitude in the ANSS catalog), we used the regression function between local magnitude in the ANSS catalog and moment magnitude. Our studies show that the procedure above pro-vides more reliable results than trying to carry out regression with too few data. Figure 2 shows the relationship between ANSS magnitudes and the available moment magnitudes. Table 3 shows selected regression results for the ANSS cata-log. For earthquakes before 1932, we used Toppozada’s catalog as the standard catalog, because Toppozada et al. (2002) had calibrated intensity magnitude to be approximately equal to moment magnitude.

Error Analysis and Data SelectionDifferent catalogs often provide different locations, magni-tudes, focal mechanisms, and error estimates for the same event. We addressed the problem of combining these earth-quake data in one catalog by establishing a list of priorities for each parameter and reporting the highest priority estimate as the favored one. We established the priorities by considering relative uncertainties in the various catalogs.

TABLE 1Assumed Default Value of Uncertainties of Location and

Magnitude in California

Date RangeLocation

Uncertainty (km)MagnitudeUncertainty

1800 < date ≤ 1850 100 0.71850 < date ≤ 1870 75 0.61870 < date ≤ 1880 50 0.51880 < date ≤ 1890 40 0.51890 < date ≤ 1925 30 0.41925 < date ≤ 1932 20 0.41932 < date ≤ 1980 15 0.31980 < date ≤ 2007 10 0.2

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To estimate magnitude uncertainties, we first divided the 23 catalogs into three groups. The first group contains five moment tensor catalogs, the second group contains nine com-prehensive instrumental catalogs, and the third group contains all other catalogs. The first group includes the Global CMT, Sipkin (USGS), Berkeley MT SW, Berkeley MT TD, and SCSN moment catalogs (Nos. 9, 10, 11, 12, and 19 in Table 2; see Table 2 for catalog details); the second group includes

Deng & Sykes A, Deng & Sykes B, NCSN, Hauksson B, Zhu, ANSS, Berkeley, NCSN without focal mechanism, and NEIC (Nos. 2, 5, 6, 8, 13, 16, 17, and 21 in Table 2; see Table 2 for catalog details). Then we used the comparison method described by Kagan (2002, 2003) to estimate the magnitude errors. Kagan assumed that catalogs are independent and the variance of the magnitude difference between catalogs equals to the sum of the variances of these catalogs. If n catalogs are

TABLE 2The 23 Catalogs Used to Combine and Their Original Sources

No Nickname DatesMinimum

Magnitude Sources

1 Toppozada 1800–1939 5.5 http://www.consrv.ca.gov/cgs/rghm/quakes/ms49epicenters.txtToppozada et al. (2000, 2004)

2 Deng & Sykes A 1812–1994 5.5 Deng and Sykes (1997a)3 CDMG (CGS) 1800–1968 4.7 http://www.consrv.ca.gov/cgs/rghm/quakes/index.htm

4 SCSN 1932–2007 4.7 http://www.data.scec.org/catalog_search/date_mag_loc.phpHutton et al. (1993)

5 Deng & Sykes B 1933–1995 5.0 Deng and Sykes (1997b)6 NCSN 1967–2007 4.7 http://www.ncedc.org/ncedc/catalog-search.html

choose “Fault Plane solutions in Fpfit format”Bolt et al. (1977)

7 Hauksson A 1975–1999 4.9 Hauksson (2000)8 Hauksson B 1970–2003 4.7 Hauksson et al. (2004)9 Global CMT 1977–2007 5.5 http://www.globalcmt.org/CMTsearch.html

Ekström et al. (2005)10 USGS (Sipkin) 1980–2003 4.7 http://neic.usgs.gov/neis/sopar/

Sipkin et al. (2002)11 Berkeley MT SW 1988–2001 4.7 http://www.ncedc.org/ncedc/mt.catalog.txt

Pasyanos et al. (1996)12 Berkeley MT TD 1988–2007 4.7 http://www.ncedc.org/ncedc/mt.catalog.txt

Pasyanos et al. (1996)13 Zhu 1991–1999 4.7 http://www.eas.slu.edu/People/LZhu/research/scal/sc_mech.updated

Zhu et al. (1996)14 Harris & Simon 1963–1993 5.0 Harris (1996) (personal communication with Yan Kagan) 15 Jones 1986–1993 4.7 Jones et al. (1998)16 ANSS 1920–2006 4.7 http://www.ncedc.org/anss/catalog-search.html

Sipkin et al. (2006)17 Berkeley 1932–2003 4.7 http://www.ncedc.org/ncedc/catalog-search.html

18 Dinger-Shearer 1975–1998 4.7 http://www.data.scec.org/ftp/catalogs/dinger-shearer/dinger-shearer.catalogRichards-Dinger et al. (2000)

19 SCSN MT 1999–2007 4.7 http://www.data.scec.org/catalog_search/CMTsearch.phpClinton et al. (2006)

20 NCSN “nofm” 1969–2007 4.7 http://www.ncedc.org/ncedc/catalog-search.htmlchoose “Catalog in readable format”Bolt et al. (1977)

21 NEIC 1973–2007 4.7 http://neic.usgs.gov/neis/epic/epic_rect.html

22 Prejean 1980–1999 5.1 Prejean et al. (2002)23 LSH 1981–2005 4.7 http://igpphome.ucsd.edu/~glin/LSH/

Lin et al. (2007)

450 Seismological Research Letters Volume 80, Number 3 May/June 2009

being compared, there are n  ×  (n  –  1)/2 difference variances that can be inverted to solve for the n unknown single-catalog variances. We used this procedure only in the first and second groups. If no moment magnitude was reported for a particular event in a given catalog, we converted whatever magnitude was available into moment magnitude by regression before estimat-ing the variances. Our result clearly shows that the magnitude errors in the first group are much smaller than those in the second group. The magnitude errors of catalogs in the third group were chosen from Table 1. To assign magnitude priority order, the following criteria are used: (1) The magnitude from a global catalog is more accurate than that from a local cata-log; (2) The ANSS catalog has higher priority than other local catalogs such as SCSN, NCSN, and BDSN (Berkeley) due to its effort in selecting data and removing duplicate events; (3) Higher priority is assigned to the most local catalog, for exam-ple, in northern California the northern California catalog has higher priority than the southern California catalog; (4) A catalog with lower magnitude uncertainty has higher priority

For location errors, we used the values directly from the catalogs themselves if they were available; otherwise we adopted the generic values in Table 1. The LSH and Dinger-Shearer cat-alogs (see Table 2 for catalog details) present the most accurate location information for earthquakes in southern California, and the Prejean catalog presents the most accurate in northern California. Thus we gave these three catalogs the highest prior-ity in location selection in their covered regions. A similar inter-comparison method was used for location as magnitude to help

us decide the location priority order. To assign location priority order, the following criteria were used: 1) The location from a local catalog is more accurate than that from global catalog; 2) The ANSS catalog has higher priority for location than other local catalogs such as SCSN, NCSN, and BDSN (Berkeley) due to its effort in selecting data and removing duplicate events; 3) Higher priority is assigned to the most local catalog, for exam-ple, the northern California catalog has higher priority than southern California catalog in northern California; 4) A cata-log with lower location uncertainty has higher priority.

We estimated focal mechanism errors based on the mech-anism discrepancy. Kagan (1992) wrote that the mechanism discrepancy can be described by a 3D rotation angle, which is used to transform one double-couple mechanism to another one. The pair-wise catalog differences show that the focal mechanism errors of moment tensor catalogs are from 18 to 23 degrees and smaller than those of first-motion catalogs, which are at least 27 degrees. Above all, we gave higher priority to global catalogs, among which the highest priority was given to the Global CMT catalog. Then the next higher priority was given to a catalog with lower focal mechanism uncertainty.

Using the priority order shown in Table 4 we selected the relatively more accurate data to be included in our new catalog. Table 4 also shows the proportions of location, magnitude, and focal mechanism values selected from different catalogs. Many location and magnitude data are selected from the ANSS, SCSN, Toppozada, and CDMG catalogs (see Table 2 for cata-log details), although they do not necessarily provide the most accurate estimates. The reason is simply that these catalogs report many events that are not in the more accurate catalogs. Even though we gave higher priority to the ANSS catalog than to the SCSN and NCSN catalogs for both magnitude and location in all regions, some magnitudes and locations from the SCSN and NCSN catalogs still end up in final catalog because some early earthquakes (generally before 1973) were reported in these catalogs but not by ANSS.

In the small part of Mexico in our catalog, we used the same priority order to choose data as we did in southern California except that we gave higher priority to the NEIC catalog (see Table 2 for catalog details) than to the SCSN catalog.

Independence Probability

For some studies aftershocks are just an annoyance, and declus-tering methods have been much discussed. In traditional declustering methods, people choose “mainshocks” (Gardner and Knopoff 1974, Reasenberg and Oppenheimer 1985) some-what arbitrarily, then use different space-time windows around the mainshocks to identify foreshocks and aftershocks. The size

5 6 7

5

6

7

Mw

Magnitude regressionM

w

5 6 7

5

6

7

Ml

Magnitude regression

Mw

5 6 7

5

6

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Mc

Magnitude regression

Mw

5 6 7

5

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Md

Magnitude regression

Mw

▲ Figure 2. Regression relations between ANSS catalog and the combination of moment tensor catalogs.

TABLE 3Magnitude Regression Relationship in ANSS Catalog

Original Magnitude Type Mc Md Ml Mc Md Ml Mc Md Ml

Original Magnitude 5.0 5.0 5.0 5.5 5.5 5.5 6.0 6.0 6.0Estimated Moment Magnitude 5.110 5.299 4.968 5.619 5.784 5.493 6.129 6.270 6.018

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of the space-time windows varies from one study to another. Here we take a different approach. Using a stochastic cluster-ing model, we identify earthquakes that were likely triggered by previous earthquakes and link them in clusters, without having to first choose a mainshock. Specifically, we used the epidemic-type aftershock sequence (ETAS) model (Zhuang et al. 2002, 2004; Zhuang et al. 2005). With this model we can assign to each earthquake the probability that it was triggered by each previous earthquake. The “independence” probability that we report here is the complementary probability that any earthquake occurred spontaneously, that is, without being trig-gered. While most events with a low independence probability would be identified as aftershocks in a traditional declustering procedure, there is an important difference: dependent events may be larger than the ones that triggered them. Thus a large earthquake with low independence might be identified as a mainshock in a traditional declustering procedure. An inde-pendent earthquake will be the first in a sequence, not neces-sarily the largest. Our criteria for assessing the independence of any earthquake do not depend on its magnitude; they depend only on the conditions existing just before the earthquake. We made the selection criteria independent of the event’s proper-

ties, because otherwise any study of the properties of spontane-ous vs. triggered events would be subject to selection bias.

We have optimized the parameters in the ETAS model using maximum likelihood estimation. Most independence probabilities in our catalog are either less than 0.1 (506 out of 1,355 events) or greater than 0.9 (576 events).

In any seismicity study, it is important to know the lowest magnitude, as a function of location and time, above which a catalog is complete. We adopted the results of Felzer (2008), who divided California into eight different regions and estimated the completeness magnitude for each as a function of time. Her regions are Northeast, North, San Francisco, Central Coast, Los Angeles, Mojave, Mid, and the rest of the state (see Table 4 in Felzer 2008). Her results imply that the catalog is complete at magnitude 4.7 after 1940 for a combined area including the San Francisco, Central Coast, Los Angeles, Mojave, and Mid regions.

Focal Mechanism Estimation and Fault Plane SelectionOne goal of earthquake forecasting is to estimate seismic haz-ard, best represented by ensembles of seismograms. To calcu-late those, we need tensor focal mechanisms. Although focal

TABLE 4 Priority Order and Contributed Values (i.e., How Many Values Are Chosen from Each Original Catalog)

No NicknameFocal

Priority Order Contributed Values

Magnitude Location

Focal Magnitude Location Focal SC NC SC NC

1 Toppozada no 12 16 21 21 — 198 163 02 Deng & Sykes A yes 13 17 10 16 12 0 35 533 CDMG (CGS) no 14 18 23 23 — 113 112 04 SCSN no 7 12 4 11 — 85 84 05 Deng & Sykes B yes 8 13 9 15 13 2 2 226 NCSN yes 20 7 16 5 9 2 5 897 Hauksson A yes 10 15 7 14 7 0 288 Hauksson B yes 9 14 6 13 8 7 1 409 Global CMT yes 1 1 22 22 1 135 0 135

10 USGS (Sipkin) yes 3 3 20 20 2 1 0 111 Berkeley MT SW yes 5 4 15 9 4 12 2 1212 Berkeley MT TD yes 4 2 14 8 3 39 2 4113 Zhu yes 18 22 12 18 6 0 0 714 Harris & Simon yes 16 20 13 19 11 0 0 1115 Jones yes 17 21 11 17 10 3 3 816 ANSS no 6 6 3 4 — 692 713 017 Berkeley no 22 9 18 7 — 24 30 018 Shearer no 15 19 2 3 — 2 16 019 SCSN MT yes 2 5 5 12 5 10 1 820 NCSN “nofm” no 21 8 17 6 — 2 2 021 NEIC no 11 11 8 10 — 28 28 022 Prejean no 23 10 3 1 — 0 14 023 LSH no 19 23 1 2 — 0 142 0

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mechanisms are now available for some recent large earth-quakes, they are not available for some historical earthquakes and some small recent earthquakes. It is useful to estimate the unmeasured focal mechanisms from the measured ones. In our catalog, we provided focal mechanism solutions if available and our own estimates otherwise.

We estimated the unknown focal mechanisms using a weighted average from the nearby earthquakes with known focal mechanisms. The weighting algorithm is similar to that used in smoothing seismicity in long-term forecasts of seis-mic hazard (Kagan and Jackson 1994). The process has been described by Kagan, Jackson, and Rong (2006). We did not estimate the uncertainty of these estimated focal mechanisms. Hardebeck (2006) finds that focal mechanisms become more diverse with increasing distance and indicates that focal mech-anisms differ substantially for earthquakes more than 50 km apart. For each event with an estimated focal mechanism, we give the distance to the nearest measured focal mechanism in column 28 of our point source catalog. If this distance is larger than 50 km, the uncertainty of this estimated focal mechanism is large, based on Hardebeck (2006).

We also calculated the correlation coefficients of both nodal planes of each earthquake to the known fault planes of large earthquakes. Instead of deciding which nodal plane is the fault plane, we provided a probability that the first nodal plane is the fault plane. This probability is estimated from the cor-relation coefficients. The process has been described by Kagan, Jackson, and Rong (2006).

Point Source and Extended Source CatalogsTo estimate ground motion and stress perturbations from earthquakes, to associate earthquakes with faults, and for vari-ous other endeavors, it is very useful to know the extent and orientation of the rupture surface. We have made an attempt to characterize the rupture planes, but unfortunately data are generally lacking, and for small earthquakes the uncertainty in locations is comparable to the extent of the rupture zone. In our point source catalog we described 1,355 earthquakes as point sources at their hypocenters, no matter how large their magnitudes. Table 5 gives a sample of the point sources catalog. The complete point sources catalog is available online at http://jumpy.igpp.ucla.edu/~kagan/cal.dat.

The rupture dimensions of large earthquakes cannot be ignored in most studies, and an extended catalog that pro-vides the rupture extent and the details of large earthquakes is needed. Kagan, Jackson, and Rong (2006) created one for southern California. They represented rupture surfaces of larger earthquakes as collections of subevents associated with rectangular slip patches, whose orientation possibly varies along strike. The geometry of the slip patches was taken from published geological or geodetic studies if available; otherwise it was estimated using standard scaling relationships (Wells and Coppersmith 1994). Each subevent was also given a mag-nitude, such that the sum of the implied moments adds up to the reported moment of the earthquake. We used the same approach to include northern California earthquakes in the

new extended source catalog. The multiple dislocation mod-els are available for most earthquakes over magnitude 6.5. If an earthquake is larger than 6.75 and there were no published papers describing its rupture details, we divided it into several equal patches along its fault plane. The extended sources cata-log is available online at http://jumpy.igpp.ucla.edu/~kagan/cal_extended.dat. Figure 3 shows a map of the extended earth-quakes, with the focal mechanism of each subevent represented by a “beach ball” in the customary way.

The extended catalog file contains the following parts: year, month, day, hour, minute, latitude, longitude, depth, magnitude (original estimate, not converted to moment mag-nitude), moment, strike, dip, rake, width, code1, and code2. All data are numerical, with the following properties:

1–5. Year, month, day, hour, and minute as integers6–7. Latitude and longitude8. Depth in km: 9.9 means that the depth is unknown9. Moment in units of Nm10–12. Strike, dip, rake of nodal plane presumably corre-

sponding to the fault plane13. Half rupture width in km: 5.0 means the width is

unknown14. Code1: 0—point source 1—distributed source15. Code2, source of focal mechanism: 0—guessed focal

mechanism solution, 1—fault direction, strike-slip mecha-nism, 2—waveform inversion, 3—waveform inversion and geodetic studies

DISCUSSION

Both location and magnitude errors can affect the complete-ness of a catalog. To avoid the rejection of a valid hypothesis or acceptance of an invalid one, it is very important to analyze the data errors in one integrated catalog.

The locations of historical earthquakes are determined by old records in newspapers and from individuals, or in some cases still cannot be determined, so the location errors of histor-ical earthquakes are larger than those of modern earthquakes.

Magnitude observation errors depend on time and loca-tion. We estimated the errors by assuming that they are inde-pendent between catalogs. In our pair-wise comparison, we did not include every possible pair. Instead, we separated the cata-logs into groups of similar type, because the properties reported in moment tensor catalogs are inherently different from those in first-motion catalogs, for example.

After using general orthogonal regression, the estimated moment magnitudes of 159 earthquakes are smaller than 4.7. We left them in our catalog, but we claim no completeness below magnitude 4.7.

California earthquakes, like those in most other places on the Earth, appear to follow the Gutenberg-Richter magnitude distribution

N a bM= −10

Seismological Research Letters Volume 80, Number 3 May/June 2009 453

TABLE 5Sample of Point Source Catalog

Index 1 2 3 4 5 6 7 8

Year 1800 1800 1803 1803 1806 1808 1812 1812Month 10 11 4 5 3 6 12 12Day 11 22 0 25 25 21 8 21Hour 0 21 0 0 8 0 15 19Minute 0 30 0 0 0 0 0 0Second 99.99 99.99 99.99 99.99 99.99 99.99 99.99 99.99Latitude 36.8 32.9 34.2 32.8 34.4 37.8 34.37 34.2Longitude –121.5 –117.8 –118.1 –117.1 –119.7 –122.6 –117.65 –119.9LC 1 1 1 1 1 1 2 2LU 100 100 100 100 100 100 100 100LUC 1 1 1 1 1 1 1 1Depth 9.9 9.9 9.9 9.9 9.9 9.9 9.9 9.9Magnitude 5.5 6.3 5.5 5.5 5.5 5.5 7.5 7.1Mag type 1 1 1 1 1 1 1 1Moment mag 5.5 6.3 5.5 5.5 5.5 5.5 7.5 7.1MC 1 1 1 1 1 1 1 1MU 0.7 0.7 0.7 0.7 0.7 0.7 0.7 0.7MUC 1 1 1 1 1 1 1 1Strike1 141 234 136 137 122 144 295 280Dip1 88 84 81 89 57 90 90 26Rake1 176 12 167 179 120 175 180 57Strike2 231 142 228 227 255 234 25 136Dip2 86 78 77 89 44 85 90 68Rake2 2 173 10 1 52 0 0 105FW 81 32 89 91 74 99 95 74FMC 0 0 0 0 0 0 2 2FMU 0 0 0 0 0 0 37 37FMUC 0 0 0 0 0 0 2 2Independce 100 100 100 99 100 100 100 89region 2 0 4 4 4 2 4 0Comment 0 0 0 0 0 0 0 0

Second: 99.99 means unknown; LC is Location code indicating the catalog used to determine location; see the catalog list (Table 4); LU is Location uncertainty (km); Location uncertainty code: 1—from Table 2, 2—from original catalog; Depth: 9.9 means unknown. Original magnitude type: 0-unknown, 1-Mw, 2-Ms, 3-Mb, 4-ML, 5-Mi, 6-Me, 7-Mc, 8-Mh, 9-Md, 10-Mlg, 11-Mln, 12-BM, 13-Mz, 14-Mx; Moment magnitude is estimated moment magnitude; MC is Magnitude code is the label of the catalog from which magnitude was determined. See catalog list (Table 4). MU is Magnitude uncertainty; MUC is Magnitude uncertainty code: 1—from table 1, 2—from intercomparison, 3—from specific estimation; FW is Fault plane normalized weight, which indicates the probability that the plane 1 is fault plane; FMC is Focal mechanism code is the label of the catalog from which focal mechanism is taken. Code 0 means that focal mechanism was estimated using a weighted average of those from nearby earthquakes with known focal mechanisms; FMU is Uncertainty of focal mechanisms: rotation degrees for known focal mechanism and distance to the nearest event with known focal mechanism for estimated focal mechanism; FMUC is Focal mechanism uncertainty code: 0—estimated focal mechanism, 1—from intercomparison; Independence is independence probability; region is geographic code: 1—Northeast region, 2—North region, 3—San Francisco region, 4—Central Coast region, 5—Los Angeles region, 6—Mojave region, 7—Mid region described in Felzer (2008); Comment: 0 means point source, 1 means that the rupture surface for this event has been extended in the combined catalog.

454 Seismological Research Letters Volume 80, Number 3 May/June 2009

where N is the cumulative rate of earthquakes at or above magni-tude M and a and b are constants. The b-value is very important because it is critical for both hazard analysis and physical under-standing of earthquakes: a small change in the b-value can lead to a large change in the implied number of large earthquakes.

Aki (1965) derived the maximum likelihood estimate of the b-value,

b M M=< > −

110log( )( )min

,

assuming that the catalog is complete above Mmin , that mag-nitudes are known precisely, that the catalog contains enough events to overcome random sampling errors, and that any upper limit on earthquake size is much larger than the largest magnitude in the catalog. Under those conditions, the maxi-mum likelihood a-value is that for which N in the formula above equals the rate of events at or above Mmin , when the maximum likelihood b-value is used.

The completeness level of a particular catalog is itself a subject of research (e.g., Schorlemmer et al. 2006; Felzer 2008). For this reason many investigators estimate the b-value using the Aki formula above for a range of assumed completeness thresholds Mmin . When Mmin is too small, the catalog will be incomplete; when it is too large, there will be too few quakes to estimate the b-value. The hope is that there will be a com-fortable range in the middle where the catalog is both complete and adequate, so that the estimated b-value will not depend strongly on Mmin . We employed this technique for the earth-quakes after 1957 (Figure 4). The minimum magnitude thresh-old runs from 4.7 to 6.8, although we believe the catalog could be incomplete below about magnitude 5.3 for the earthquakes after 1957 as suggested by Felzer (2008).

In Figure 4, covering the instrumental period, the curve is relatively flat out to about magnitude 5.8, and the estimated b-value around magnitude 5.3 is close to the global average b-value of 1.0 (Felzer 2008). Figure 4 is consistent with the results of Felzer (2008).

−126˚−125˚−124˚−123˚−122˚−121˚−120˚−119˚−118˚−117˚−116˚−115˚−114˚−113˚31˚

32˚

33˚

34˚

35˚

36˚

37˚

38˚

39˚

40˚

41˚

42˚

43˚

0 50100

km

▲ Figure 3. Extended earthquakes catalog in all of California, 1800–2006. Beach balls are focal mechanisms.

Seismological Research Letters Volume 80, Number 3 May/June 2009 455

Several modifications are required when the assumptions above (completeness, adequacy, precise magnitudes, and lack of upper magnitude limit) do not hold. Aki (1965) did treat the case with an upper magnitude limit, but he kept the other assumptions. Tinti and Mulargia (1985) showed that when magnitude observations are subject to uniform uncertainties σ , then the apparent a-value will be inflated by a bias equal to

b elnlog ( )

102

2 2

10( )( ) σ

where σ is the standard deviation of the magnitude errors.Felzer (2008) showed that round-off error can also cause

a bias. Because of the exponentially decreasing rate of events with increasing magnitude, the average magnitude within a range (bin) will be less than the rate estimated at the center of the bin. In her catalog she estimated completeness vs. time for several regions in California and made corrections to indi-vidual magnitudes to remove biases caused by magnitude errors and rounding off. Using only values in California from 1997 to 2006, she estimated the completeness threshold to be 4.0. She estimated a b-value of 1 02 0 11. .± for all earthquakes. After declustering with the Gardner and Knopoff (1974) method, she estimated a b-value for mainshocks of 0 85 0 13. .± .

There is another valuable approach to estimate the uncer-tainty of the b-value considering magnitude errors and round-off. That method is to assume hypothetical knowledge of the system, generate theoretical data, allow for measurement errors, and ask if the observed data are consistent with predic-tions. We will use the second method to estimate the range of b-values consistent with the data in the future.

In Figure 5, the dash-dot line shows the magnitude dis-tribution of all data in our catalog, considering catalog incom-pleteness. This magnitude distribution appears consistent with the Gutenberg-Richter law. It has an approximately uniform

slope from magnitude 4.9 to 6.4, in agreement with Felzer’s (2008) observation. There are also some “knees” in this plot at magnitudes 6.5, 6.7, 7, 7.2, and 7.5, which may have been caused by round-off. This is reasonable because the magnitudes of some large historical earthquakes were rounded to half-integer or quarter-integer values.

In Figure 5, we also compare the empirical magnitude distributions of spontaneous and triggered earthquakes. The solid line shows the magnitude distribution of independent earthquakes and the dotted line shows the magnitude dis-tribution of triggered earthquakes. In this analysis, we used a weighted average of numbers for each event, such that an earthquake with a 60% independence estimate would con-tribute 60% toward the count of spontaneous events, and 40% toward the count of triggered events. Statistically, the separate distributions cannot be caused by random sampling of a single distribution at the 95% confidence level. We’ve tried to avoid two common biases. First, we defined the independence of each event using information independent of the magnitude of that event. The traditional definition of aftershocks prefer-entially treats large events as mainshocks, biasing the assign-ment. Second, the ETAS model we used to assess independence assumes at the outset that all events have the same magnitude distribution. Nevertheless, the results imply that independent and dependent events have different distributions. We can at least be assured that this result was not built into our analysis by a hidden assumption. If true, the result that independent and dependent results have different magnitude distributions would be profound, as it implies that temporal stress variations affect the magnitude distribution. However, we consider the independence estimates to be somewhat arbitrary, depending on the assumed functional form of the distance and magnitude dependence in the ETAS model, the way that unmeasured

▲ Figure 4. Gutenberg-Richter b-value estimation for California using data after 1957.

4.5 5 5.5 6 6.5 7 7.5 8−2.5

−2

−1.5

−1

−0.5

0

0.5

1

1.5California earthquakes,1800−2007,converted magnitudes

Magnitude

Log 10

(Cum

ulat

ive

Freq

uenc

y)

▲ Figure 5. Gutenberg-Richter plot for all earthquakes using estimated moment magnitude after considering catalog incom-pleteness. Dash-dot line represents all earthquakes, dotted line represents triggered ones, and solid line represents indepen-dent ones.

456 Seismological Research Letters Volume 80, Number 3 May/June 2009

immediate aftershocks are allowed for, and the lower magni-tude threshold of the catalog. Thus we are not ready to accept the apparent magnitude distributions as fact, reserving judg-ment pending further study

CONCLUSIONS

We compiled a new catalog of earthquakes with M ≥ 4.7 from 1800 to 2007 for greater California from known catalogs. Estimation of unknown focal mechanisms can help people to explore more unknown earthquake behaviors. More accurate estimation of location and magnitude errors can help people to estimate the confidence level of hypothesis test results. Magnitude regression provides useful estimated moment magnitude. Independence probability provides cluster infor-mation of our catalog. The Gutenberg-Richer b-value of our catalog after 1957 is around 1, which is consistent with other researchers’ estimation, e.g. Felzer (2008). Bird and Kagan (2004) obtained a similar b-value ( b = ±0 98 0 18. . ) for the continental transform fault-type of plate boundary appropriate for California (95% confidence limits are indicated). Our cata-log data fit the Gutenberg-Richer law well, especially when we use the estimated moment magnitude instead of the original magnitude.

ACKNOWLEDGMENTS

The authors appreciate support from the National Science Foundation through grant EAR-0711515, as well as from the Southern California Earthquake Center (SCEC). SCEC is funded by NSF Cooperative Agreement EAR-0529922 and the U.S. Geological Survey (USGS) Cooperative Agreement 07HQAG0008. Comments by an anonymous reviewer have been helpful in revising the manuscript. Publication 1269, SCEC.

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Department of Earth and Space SciencesUniversity of California, Los Angeles

595 Charles Young Drive East3806 Geology Building

Box 951567Los Angeles, California 90095-1567 U.S.A.

qiwang@ucla.edu(Q. W.)