Southern California seismicity is distributed across a diffuse plate boundary on a mosaic of strike-slip and thrust faults. In a significant advance of the science of seismic hazard analysis, WGCEP (1995) incorporated seismic, geologic, and geodetic data to determine the expected rate of occurrence and distribution of M>6 earthquakes in southern California, reaching the following provocative conclusions:

M> 6 shocks are ten times more abundant than M>7 shocks, so the catalog seismicity rate depends almost exclusively on the smallest earthquakes included, and thus on whether all M=6 shocks that occurred are in the catalog (whether the 'catalog is complete' at M=6). But because M>7 earthquakes release about 85% of the seismic moment, the seismic moment rate depends almost exclusively on accurate moment estimates of the largest shocks in the catalog. Thus the earthquake rate and seismic moment rate are nearly independent, and one can weigh the WGCEP (1995) findings separately.

Attempts to validate arguments that the rate of earthquakes is increasing through analysis of the more abundant M<6 earthquakes have been equivocal. Hutton and Jones (1993) studied M_L>5 events since 1932, finding no significant region-wide rate changes. Sykes (1996), in contrast, argued that the rate of both M>5 and M>6 shocks was higher in 1985-1994 than during the previous 9-year period, suggesting that this could be a long-term precursor to a great earthquake. Examining still smaller shocks, Jones and Hauksson (1997) found a high rate of M_L>3 events during 1945-52 and 1969-92, and a low rate in 1952-69 and 1992-96. But because nearly all of Jones and Hauksson's significant rate changes are associated with large earthquakes, these results are sensitive to the algorithm used to remove aftershocks (or to 'decluster the catalog').

We thus re-examined the M>6 southern California catalog, focusing on its completeness, the spatial and temporal variability of seismicity, and estimates of the seismic loading imposed by plate motions and released by earthquakes. We sought answers to four questions: Is there an earthquake deficit at any magnitude from 6 on up? Is there a deficit in the release of seismic moment? Is the rate of M>6 earthquakes increasing? And is there evidence for huge but rare earthquakes off the San Andreas fault? We find the answer to all four questions to be no.

Our principal goal is for a catalog complete for M>6. Following Richter (1958), we start our catalog in 1903 because instrumental records are available for all of the listed earthquakes. Table 2 lists events excluded from our catalog; Richter (1958) assigned M=6-61/4 to the first eight events in Table 2, but more recent analyses indicate they are M<6. We examine the region bounded by 32°00'-36°15'N and 114°00'-122°00'W. WGCEP (1995) cited latitude limits of 32°00'-36°00'N, but since they included the Coalinga earthquake at 36°14'N, we moved our northern boundary to include this event as well. For their seismotectonic zone map, WGCEP (1995) used a polygon with extremities bounded by 32°30'-36°10'N and 114°00'-122°00'W, so we have extended their zones south to 32°00'N to make it consistent with their study area (Fig. 2).

Frequency-Magnitude Relationship

Frequency-magnitude curves describe the number of earthquakes expected as a function of magnitude, and enable an assessment of catalog completeness. The curves for our 1903-97 catalog and the WGCEP 1850-1994 catalogs are shown in Fig. 3. The best fit line for each catalog is of the form

log N = a - bM (1)

the standard Gutenberg-Richter representation. For the M>6.0 1903-97 catalog, maximum likelihood estimation (Aki, 1965) yields b=0.97±0.15; least squares yields 1.04±0.04 (Table 3). Maximum likelihood is most sensitive to the completeness of the smallest magnitude included; least squares gives the same weight to all magnitudes, and thus provides a better extrapolation for the rate of the largest earthquakes. For M>6.2, b=1.04±0.20 by maximum likelihood and 1.11±0.04 by least squares, suggesting our catalog is not complete at M=6.0 from 1903. If we assume, for example, that the catalog is missing just two M=6.0 earthquakes (a rate of 0.44 yr^-1), the M>6.0 catalog would yield b=1.01±0.16 by maximum likelihood. We thus find that b=1.0 to be the best estimate for our catalog. Such a b-value is the theoretical value if earthquakes have a constant stress drop independent of magnitude (Hanks, 1992). Our catalog b-value is indistinguishable from the b-value of 0.968±0.023 for the same region for M>4.0 earthquakes by Cao et al (1996), and the b-value of 0.98 for nearly the same region during 1932-1971 by Hileman et al (1973). It is also consistent with global crustal earthquakes in the Harvard CMT catalog (5.6<M<7.4), for which b=1.07±0.01 (Pacheco et al., 1992). (Note that all cited b values are all for total-rather than declustered-catalogs, and all are computed by maximum likelihood unless otherwise stated).

At Mo = 1 x 1018 Nm, the best fit line suggests the 95-year southern California sample is missing about 3±3 M>6 shocks. Some of these 'missing' earthquakes may be among the 8 events in Table 2 that we judged to be M<6.0; two were assigned M>6 by WGCEP. Because any missed earthquakes probably occurred during the first part of the 20th century in the least populated southeastern part of the region, and because these events can contribute at most 10 x 10¹⁸ Nm or 2% of the 95-year sum, neither the earthquake nor moment rate would change much for their inclusion, with the possible exception of the decade, 1903-1912.

The 1903-97 catalog gives higher rates of seismicity than the WGCEP 1850-1994 catalog for all magnitudes less than 7, with the difference most pronounced for M<6.3. The principal reason for the higher rates of seismicity in our catalog, as we argue below, is insufficient reporting before the turn of the century. A second reason is that WGCEP (1995) omitted all earthquakes south of 32°30'N, despite stating that the catalog extended to 32°00'N. Thus four 6.2<M<7.0 shocks occurring during 1915-1980 are missing, including two events at 32°00' and two at 32°15' (Fig. 1 and Table 1). Recent analyses of these events by Doser (1994) demonstrates that they lie within the WGCEP study area defined by WGCEP. A third reason is that we re-evaluated and document the seismic moment, location, and focal mechanism of all shocks in our catalog (Appendix), leading to differences in moment assignments. In contrast, WGCEP (1995) cites only Ellsworth (1990) for all pre-1992 shocks.

The rate of M>6.0 shocks from the WGCEP catalog is 0.32 yr-1; the observed rate for the 1903-97 catalog is 0.42 yr-1, and the rate extrapolated from the 1903-97 catalog using the best-fit b=1.0 is 0.49 yr-1 (Fig. 4a). If instead we count earthquakes from 1915, the date when Richter (1958) considered the catalog to be complete, the rate becomes 0.46 yr-1, suggesting that our catalog yields a M>6 earthquake rate 44% higher than suggested by WGCEP (1995). Stirling and Wesnousky (1997a) showed that the statistics of a Poisson process are alone sufficient to nullify the WGCEP (1995) claim of a seismicity deficit. This is an important result, but we believe that the deterministic solution to this problem-catalog incompleteness-is even more important, because the observations used by both WGCEP (1995) and Stirling and Wesnousky (1997) were biased by catalog incompleteness before the turn of the century.
 

The rate of M>7.0 shocks from the WGCEP catalog is 0.033 yr-1; the observed rate for the 1903-97 catalog is 0.052 yr-1, 58% higher (Fig. 4b). The difference in the rates of M>7 shocks arises because WGCEP omitted the 1934 M=7.0 Colorado River delta shock, and identified the 1940 Imperial Valley earthquake as M=6.9 rather than M=7.0 (Table 1 and Appendix). The WGCEP catalog for 1850-1994 includes five M>7.0 events, a rate of 0.033 yr-1 (Fig. 4b). In contrast, we count five M>7.0 events since 1903 (Table 1), and seven since 1850 (Table 2), a rate for both time periods of 0.053 yr-1. (Because the M=7.4 1872 Owens Valley earthquake lies north of the WGCEP boundary, it is not included in these rates.) Note that for M>7.3, the annual rate of earthquakes extrapolated from our catalog and that measured by WGCEP converge.

Catalog Completeness

Inadequate to nonexistent reporting of moderate earthquakes in southern California before the turn of the 20th century has been widely studied, and we argue here that this is the principal reason why the WGCEP catalog shows a lower rate of M>6 shock than does ours. Richter (1958) commented that "for the years before 1915 [his M>6 catalog] is almost certainly incomplete." Toppozada et al (1981) found that in several inland southern California counties (San Bernardino, Riverside, and Imperial), M=7 shocks could have been inadequately reported for proper identification until about 1870, and M=6.5 events could have been improperly identified until the late 1880's. Agnew (1991) concluded that M>6.5 events would have gone unidentified along the southernmost San Andreas and central San Jacinto faults as late as 1870-1880. The reason for these conclusions is simple: while northern California experienced dramatic population growth after the discovery of gold in 1849, immigration to southern California occurred much later (Fig. 5a), with a corresponding delay in the adequate reporting of small earthquakes (Fig. 5b). Before 1875, there were almost ten times more people living in northern than southern California; the population of northern California in 1880 was not attained in southern California until 1910.

Population in southern California was very sparse along the San Andreas system and eastern California shear zone until about 1900 (Fig. 6). In the pre-instrumental era, newspaper reports are the principal source of isoseismal maps used to estimate the size and locations of earthquakes in California (Toppozada et al., 1981). Although earthquakes were mentioned in diaries and letters from sites which lacked newspaper coverage, newspapers are the principal source of data for the pre-instrumental record, and thus limitations in newspaper coverage is reflected in the catalogs. Newspaper coverage closely mirrored the population expansion, with inland population following railroad construction (Fig. 7).
 

The MMI (Modified Mercalli Intensity) VI isoseismal, which extends 50-60 km from a M=6 shock (Hanks et al., 1975; Toppozada, 1975), is generally needed to estimate a size and location (Fig. 7). Before 1880, no southern California newspapers were printed within 75 km of the San Andreas fault except at Cajon Pass. As late as 1890-99, newspapers were printed within 50 km of the San Andreas fault only near the Parkfield, Mojave, and San Bernardino Mountain fault segments (Fig. 7). Consistent with these reporting limitations, no 6.0<M<6.1 shocks are in the 1850-1994 catalog during the thirty-year period, 1863-1893. Until about 1895, the Elsinore, Garlock, Owens Valley, and Imperial Valley and most of the San Jacinto fault lacked newspapers printed within 100 km, and most of the western Transverse Ranges, the borderland faults, and the eastern California shear zones lacked any coverage at all. Further, many of the pre-1910 newspapers have not survived, and thus are not presently available for isoseismal analysis (Toppozada et al, 1981).

Could the low observed rate of southern California M>6 shocks during 1850-1900 (Fig. 5b) instead be a consequence of the 1857 M=7.9 earthquake? Harris and Simpson (1996) found that for 50 yr after 1857, at least 10 of the 13 known M>5.5 events were brought closer to failure by the 1857 earthquake, whereas during the succeeding 50 yr, only 13 to 15 of the 23 M>5.5 events were encouraged by the 1857 shock. They concluded that the earthquake-induced stress changes depressed earthquake rates for 50 yr after the 1857 event. However, the zone in which strike-slip faults were brought farther from failure (termed the stress shadow), and where few shocks were seen during 1857-1907, is centered on the San Andreas between Parkfield and Cajon Pass (Fig. 6). Until 1890, there was poor earthquake reporting in the shadow due to lack of population. For example, there are no recorded aftershocks of any magnitude within 40 km the M=7.8 1857 event for at least 27 years (Toppozada, 1995), suggesting that M>6 aftershocks went unidentified. The much smaller Kern County and Landers shocks (both M=7.3) had two M=6.3 aftershocks, and one M=6.5 aftershock, respectively. In addition, regions in which the 1857 event increased and decreased the stress should be roughly equal in extent, and thus the overall rate of shocks should have been little changed.

Given the reporting limitations within the stress shadow, only if it could be shown that the rate of shocks during 1807-1857 was higher than during 1857-1907 could the stress shadow be a tenable hypothesis to explain the low M>6 rate before 1900. The limited evidence does not support such an hypothesis: During the 50 yr before the Ft. Tejon earthquake there were four recorded M>6 and two M>6.5 shocks (Toppozada, 1995). During the succeeding 50 yr there were eleven M>6 shocks and three M>6.5 shocks (WGCEP, 1995). Thus even at a completeness level of M=6.5, there is no evidence to suggest that the rate of shocks in southern California was depressed by the 1857 event. We consider it highly unlikely that the 1857 earthquake can account for the difference in M>6 earthquake rate between southern and northern California during 1850-1900, or between 1850-1900 and 1900-1950 within southern California.

We thus conclude that the 1850-1995 catalog used by WGCEP (1995) is incomplete for M<6.5 before about 1880-1900 (Fig. 5b), rendering its observed M>6 earthquake rate 31-44% too low. This conclusion is far more likely than the possibility that the 1857 stress shadow depressed the rate of earthquakes until the turn of the Century. Our finding is bolstered by the observation that ten times more earthquakes are reported for northern than southern California during 1850-1890, whereas after 1895, the rates of reported shocks rates are about equal (Toppozada et al., 1981). We attribute this difference primarily to the ten-fold population difference between north and south during the same era (Fig. 5).
 

Earthquake Time Series

While southern California was more active during some decades than others, no interval is statistically anomalous, with the possible exception of 1983-92 (Fig. 8). We bin from the third year of each decade, starting in 1903. The average rate of M>6 shocks is 4.2 per decade. For a Poisson process, the 2s confidence limit on the observed rate is ±2(4.2)^0.5 or 4.2±4.1. Thus 0-8 earthquakes per decade are consistent with a Poissonian process, and only one decade out of ten (9 events fall in 1983-92) exceeds this rate. If we had binned from 1900, the range would be 2-7 per decade and 5 since 1990, and thus no decade would be anomalous. Using the c² test (Evans, 1955), there is a 10% probability that still larger excursions from the mean rate would occur if this were associated with a Poisson distribution. Thus there is no evidence from the M>6 catalog that the rate of earthquakes has undergone a significant increase at any time since 1903.

Fig.8 (about 42 kb GIF). Seismic moment and the number of M>6 earthquakes per decade since 1903, with the contribution of M>7 earthquakes and their largest aftershocks distinguished. Large fluctuations of the number of earthquakes from one decade to the next are consistent with a Poisson process.

Seismic Moment Sums

Summing the effects of two or more earthquakes should proceed by addition of the seismic moment tensors. Because focal mechanisms for some events are unknown or poorly known (Fig. 1), we use scalar seismic moment sums as a gross measure of seismic strain release in southern California. Fig. 8 shows these sums for the nine 10-yr periods since 1903. The accuracy of the seismic moment estimates rests on the ten post-1903 earthquakes with Mo > 1019 Nm in Table 1, for these account for 86% of the moment. Apart from the 1927 Lompoc and the 1925 Santa Barbara shocks, we consider the estimates for the M_o > 10¹⁹ Nm earthquakes given in Table 1 to be accurate to ±50%, and somewhat better than this for the five most recent events. The uniform slope of the observations in Fig. 3 suggests that we are not likely to have missed even one earthquake of M_o > 10¹⁹ Nm by grossly underestimating M_o for an event. Apart from the dominance of M>7 shocks in the decade moment sums, it is intriguing that the earthquake moment rate rose steadily for 5 decades from 1903. As we have shown, however, this is based on very few earthquakes and is not statistically significant.

The size and frequency of occurrence of the 1857 Ft. Tejon-type earthquakes (Fig. 1) play a key role in estimating the rate of moment release in southern California. By including the full moment of the 1857 event in the 1850-1994 catalog, WGCEP (1995) implicitly assumed that its inter-event time is equal to the catalog duration, 148 yr. To compare the 1903-97 and 1850-1995 catalog rates to the moment-accumulation rate expected from plate motions, we augment the 1903-97 moment rate to include the effect of larger, less frequent events such as the Ft. Tejon earthquake. To do this we must estimate the seismic moment of the 1857 event (8 x 10²⁰ Nm; see Appendix) and its inter-event time.

Paleoseismic studies suggest that large earthquakes have occurred on the southern San Andreas fault with an average inter-event time of 125-250 yr (Grant and Sieh, 1994; Sieh, 1996). The available data suggest inter-event times of 160 yr at two sites in the Carrizo Plain, 125 yr at two sites along the edge of the Mojave desert, and about 250 yr in one site the Coachella Valley (sites shown in Fig. 7c). What, if any, correlation exists between events at these sites is unclear, but the paleoseismic record suggests that the 1857 earthquake is not characteristic: There is evidence for shorter rupture lengths and lower values of slip for several prehistoric events in both the Carrizo Plain and in the Mojave Desert, and for the possibility of events with ruptures longer than occurred in 1857 in about AD 1480 and AD 1000 (Sieh, 1996). The data thus suggest that an earthquake comparable in size to the Ft. Tejon event occurs every 125-250 yr somewhere along the southern San Andreas fault.

We estimate the seismic moment release rate in several ways. First, we sum the seismic moments of the eight M>7 shocks in Tables 1 and 2, divide this by the 148-yr period 1850-1997, and add to this the seismic moment release rate of the 6.0<M<6.9 shocks observed this century. This assumes a 148-yr repeat time (RT) for the 1857 Ft. Tejon shock. Alternative calculations assume a 125-250-yr repeat time for such M=7.9 events, calculated with and without the 1872 Owens Valley shock. This yields 7.9-1.1 x 10¹⁸ Nm yr-1, a broad range but indistinguishable from the WGCEP (1995) moment release rate of 8.3 x 10¹⁸ Nm yr-1 for 1850-1995 (Fig. 9). This agreement is not surprising, because the moment rate depends principally on the few largest earthquakes, while the earthquake rate depends on the smallest shocks and thus differs between the two catalogs by 44%. If we include the 1872 M=7.4 Owens Valley shock, the release rate rises to 9.2-1.24 x 10¹⁸ Nm yr-1. Although the 1872 shock struck just outside of the WGCEP border (Fig. 1), the earthquake lies athwart the North America-Pacific plate boundary in southern California, and thus is appropriate to include in the moment balance.

Moment Accumulation Rate

The rate of moment accumulation can be inferred from remote plate motions or from the geodetically measured shear strain rate. But estimating the moment rate is complicated by the unknown depth, H, over which the strain accumulates. The geodetically inferred locking depth on the southern San Andreas is 25 km, which could be interpreted to be H. Savage and Lisowski (1997) explain the apparent 25-km locking depth to be a consequence of viscoelastic coupling with an elastic crust extending to 15 km depth. H might thus be set to equal the depth extent of earthquakes (12-15 km), minus the upper ~2 km of the crust in which little elastic energy is believed to be stored, or 10-13 km. But H could be 7-10 km if inelastic strain release occurs during the time period between large earthquakes at the base of the rupture, as suggested by studies of the effective elastic thickness of the crust over hundreds of earthquake cycles (King et al., 1988; Stein et al., 1988). Here we assume that H=10-12 km; WGCEP (1995) used 11 km but considered this a lower bound.

The simplest estimate of the moment accumulation from plate motions, is made by resolving the plate motion across southern California.

= m LH

where is the plate motion rate, L is the length of the fault or trend within the study area parallel to the plate motion vector, 600 km. For at 36°N latitude, Argus and Gordon (1991) obtained 39 mm yr-1 oriented N37°W by removing the Basin and Range opening, DeMets (1995) found 49 mm yr-1 oriented N38°W (NUVEL-1A), and at latitude 33°30', Bennett et al (1996) found 49±3 mm yr-1. We thus use 49 mm yr-1 oriented N38°W. For m = 3.0 x 10¹⁰ Nm-2 and H = 11 km, = 1 x 10¹⁹ Nm yr-1, slightly higher than the value used by WGCEP (1995). This gives a lower bound because some of the seismic moment is associated with creation of compressional structures by slip on thrust faults (Fig. 9).

Ward (1997) integrated the horizontal velocities of 287 geodetic stations surveyed during 1970-1995 to obtain a southern California strain rate, , of 11.8±2.6 x 10^-8 yr-1. From Kostrov (1974), , the moment measured from elastic strains can be written

= 2mAH 

where m is the shear modulus, A is the area, and H is the thickness over which strain is accumulated and released. For m = 3.0 x 10¹⁰ Nm-2, and H = 11 km, Ward obtained = 1.23±0.17 x 10¹⁹ Nm yr-1 (Fig. 9), 30% higher than the value used by WGCEP (1995). Jackson et al (1997) have shown that the distribution of strain is highly concentrated where some of the large earthquakes most recently occurred, suggesting that transient postseismic strain may obscure the long-term strain accumulation.

Moment Release Rate From Fault Slip

A discrete summation of the moment release on all faults with known slip rates and lengths, , was carried out by WGCEP (1995) and Ward (1997). This method is subject to the uncertainty on the slip rate of the many minor faults. WGCEP (1995) reported = 0.93 x 10¹⁹ Nm yr-1; using H=11 km, Ward (1997) got = 1.00 x 10¹⁹ Nm yr-1 using the improved Petersen et al (1996) fault inventory, which we use here (Fig. 9).

Balance of Moment Accumulation and Release

When H is fixed at 11 km, the two estimates of the moment accumulation rate vary from 9 to 12 x 10¹⁸ Nm yr-1. For a minimal uncertainty on H of 10-12 km, the range expands to 8-13 x 10¹⁸ Nm yr-1. This can be compared to the moment release rate from fault slip of 8.0-11.5 x 10¹⁸ Nm yr-1 and a release rate measured by the catalog of 7.9-12.4 x 10¹⁸ Nm yr-1 (Fig. 9). We thus find no observable difference between the rates of moment accumulation by plate motions and moment release by earthquakes. Irrespective of the particular seismic model advanced by WGCEP (1995) or others, the absence of a significant difference between the rates of moment accumulation and release precludes any statement that there is a deficit in the rate of historical seismic moment.

Rate Predictions for Seismotectonic Zones

To understand why and where WGCEP (1995) predicted higher earthquake rates than observed during this century, we examine the distribution of the earthquakes in Table 1. WGCEP divided southern California into 65 seismotectonic zones, based on fault activity and the extent of knowledge in each region (Fig. 2). The A zones include major segments of the San Andreas, San Jacinto, and Elsinore faults (by area, 7% of southern California); the B zones include major faults with known slip rates, such as the Garlock and Newport-Inglewood (15%); the C zones include lesser or blind faults, and faults with unknown slip rates (78% by area).

The WGCEP (1995) predicted a rate of moment release in each of the 65 seismotectonic zones. WGCEP states that the rate of distributed earthquakes was assigned under the assumption that b=1.0 in equation (1) in all zones, but this is only true for the discrete magnitude distributions. For the cumulative distributions presented here and in their report, 0.4<b<4.0 in different magnitude bands (Fig. 10). Equation (1) was modified by WGCEP (1995) so that the rate of earthquakes approaches zero at a limiting magnitude, Mx, which they supplement with additional events of magnitude Mx (the 'characteristic' earthquakes) occurring at an assigned frequency, fc. In the A zones, fc was set to the rate of characteristic earthquakes determined from geologic data, and a in (1) was based on the rate of M>6 shocks with characteristic earthquakes removed. The characteristic earthquakes were instead represented by the moment associated with the fault slip in these zones. In the B zones, a was based on the rate of all M>6 shocks, and fc was set so that the predicted moment rate equaled the average of the geological (slip-rate based) and geodetic (shear-strain based) moment rates. In the C zones, fc was set to zero, and Mx was related to the mapped faults (or the total length of each zone) by the empirical relations of Wells and Coppersmith (1994). In the C zones, Mx was assigned values ranging from 6.4 to 7.3, and a was based on the average of the smoothed catalog seismicity and the geodetic moment rate.

We compare the 1903-97 catalog distribution of earthquakes with the WGCEP (1995) predictions in Fig. 10. As discussed previously (Fig. 4), our estimate of the rate of M>6 shocks is about 44% higher than the rate reported by WGCEP (1995). But the WGCEP (1995) model predicts a rate of 0.60 M>6 shocks yr-1, 33% higher than our maximum estimated rate of 0.46 yr-1 (Fig. 4a). Nearly all earthquake deficit predicted by the WGCEP model is in the C zones (Fig. 4c), the site of blind faults or those with low or unknown slip rates. WGCEP (1995) predicts nearly three times the number of earthquakes observed during the past 95 years, even though the past century has produced three large C zone events, the M=6.8 Santa Barbara, M=7.1 Lompoc and M=7.3 Landers shocks.

Source of WGCEP's M>6 Earthquake Rate Deficit

Despite the rough agreement between the WGCEP predicted and observed moment rate in the C zones (Fig. 4d), there is a large disparity between the predicted and observed earthquake rates (Fig. 4c). How can this be? The cumulative frequency-magnitude curve predicted by the WGCEP (1995) model and the curve observed during 1903-97 for all C zones is shown in Fig. 10c. In the WGCEP (1995) model, b=1 only for 6<M<6.1; b=2.5 for 6.5<M<6.9, and b=4 for M>6.9. In contrast, b=0.9 for the observed earthquakes in C zones over the full range of 6<M<7.3 (Fig. 10c and Table 3). Thus the observed rate of M>6 shocks in the C zones is one-third the rate predicted by the WGCEP model, while the observed rate of M>7 shocks is much higher than predicted by WGCEP. In fact the predicted rate of M>6 shocks in the C zones is close to the observed rate for zones A, B, and C combined (shown by the black arrow in Fig. 10c), a highly unlikely scenario. Both observed and predicted curves yield similar seismic moments, because for b-values greater than 1.5, smaller earthquakes contribute more moment than larger ones. Thus the WGCEP model for C zones bears no resemblance to the observed earthquake occurrence in this century; the evidence favors an inappropriate model b-value rather than an earthquake deficit on the minor and blind faults.

Source of WGCEP's Large-Earthquake Deficit

The frequency-magnitude relations assumed in the WGCEP model differ substantially from the observed catalog. In the A zones, the WGCEP model predicts an earthquake rate about three times higher than that observed this century for M>7 shocks, and five times higher than observed for M>6.8 shocks (Fig. 10a). This, we believe, is the origin of the M>7 earthquake deficit identified in the WGCEP report; it is a product of a model in which b=0.4 for M<7.3 and b=2.2 for M>7.4. In contrast, the observed b-values of 0.9-1.2 are similar in all zones and all magnitude bands, with b values perhaps declining slightly off the San Andreas system (Fig. 10 and Table 3).

The moment rate predicted for each of the three zones by WGCEP (1995) is in good agreement with the observed moment rate during this century (Fig. 4c); no deficit is evident. This agreement, in concert with the absence of a significant difference between the moment release and accumulation rates (Fig. 9), removes any basis for WGCEP's conclusion that there is a deficit in the rate of large earthquakes that must be made up by aseismic creep, rare huge earthquakes, or a higher rate of M>7 events.

WGCEP (1995) omitted several large earthquakes within its defined boundaries and used a minimum magnitude for which the catalog is incomplete, resulting in an underestimate of the rate of both M>6 and M>7 earthquakes. The more complete 1903-1996 M>6 catalog presented here yields an earthquake rate 44% higher than the rate cited by WGCEP. We find that southern California has sustained 4-5 M>6 shocks per decade and 4-5 M>7 shocks per century. Although the earthquake rate varied sharply from one decade to the next during the 20th century, we find that this behavior is consistent with a Poisson process; there is no evidence that the rate of M>6 earthquakes is increasing at the present time or at any other time during the 20th century.

The inferred rate of seismic moment release is dependent on the size and expected inter-event time of great earthquakes on the San Andreas fault, and the rate of moment accumulation rate is dependent on the depth extent over which seismic strain is stored. Though uncertain, we find that the rates of moment accumulation and release measured over both short and long time scales are not significantly different. There is no seismic moment deficit during the past 150 yr. We therefore find no evidence for a deficit in the rate of large earthquakes or seismic moment release.

In this paper we do not advocate a particular model for the distribution of earthquakes in space and time. Rather, it is our view that any model advanced must obey the observed frequency-magnitude relationship and earthquake production rate for the region (Fig. 3 and Table 3). This means that over 6.0<M<7.8, b=1.0 and a, the earthquake productivity rate, must lie between 5.5 and 6.0. This holds not only for the San Andreas fault but also for faults well off the major system (Fig. 10). We have thus sought to produce the most accurate and consistent catalog of earthquakes possible, and have used it to test a key model in use today.

Roughly half of the twentieth century M>6 earthquakes have struck on the San Andreas system and half on the myriad secondary faults, with most of the seismic moment contributed by the largest earthquakes on the San Andreas system. In contrast, WGCEP (1995) concluded that the rate of M>6 shocks on the lesser faults should be three times higher than what we have experienced during the past century. We suggest that the WGCEP distribution model suffered from insupportably high b-values for the minor faults. We thus find no evidence that huge (M~8), rare earthquakes strike southern California off the major faults. Nor do we see any need to invoke aseismic moment release to reconcile the observed rate of earthquakes with the driving motions of plate tectonics.

Acknowledgments. We thank James Savage, Susan Hough, Lucile Jones, Wayne Thatcher, Tousson Toppozada, Edward Field, Thomas Henyey, David Jackson, and Lind Gee for thoughtful reviews of this manuscript; Kerry Sieh for discussion on the San Andreas paleoseismic record; and Chuck Wicks for GMT expertise.

This appendix provides a brief discussion and references for the locations, seismic moments, and focal mechanisms of the earthquakes given in Tables 1 and 2 and Fig. 1. Unless otherwise specified, locations and seismic moments are those given by Hanks et al (1975), with conversion from Mo to M following Hanks and Kanamori (1979). Times are shown when more than one earthquake occurs in one year.

 
Table 2. What's Not in Table 1

Table 3. Frequency-Magnitude Relationships for the M>6.0 Southern California Catalog