During this year we completed our examination of the discrepancy between historical and predicted recurrence rates of moderate-to-large earthquakes reported by the Working Group on California Earthquake Probabilities (WGCEP, 1995). A report describing this work is now in press, and is briefly summarized below (Stirling and Wesnousky, BSSA 87, 1997). We also assessed the differences between seismic hazard maps of southern California recently produced by different groups and investigators, and have submitted a paper describing this work to the BSSA for consideration for publication. The results of the study are summarized in the latter part of this report.
The WGCEP reported a discrepancy between the historical rates of large earthquakes in southern California and rates predicted from interpretation of geological, geodetic and historical seismicity data. It was suggested that the discrepancy may be due to the assumption within their analysis that the magnitude of the largest earthquake on a fault is limited by the mapped fault length. Our approach to addressing this issue has been to reconstruct the WGCEP 'Preferred Model' using the same geologic, geodetic and historical seismicity data as the WGCEP, and essentially the same procedure, with an aim towards placing uncertainty bounds on size and rate distribution of earthquakes. Specifically, we examined the likelihood that a 145 year 'sample' from the 'Preferred Model' would yield the rate of seismicity observed in the last 145 years. This was done by converting the 'Total Predicted' curves to the equivalent minimum and maximum incremental recurrence rates (number of events per year of magnitude M), and then using a Monte Carlo method to choose a rate at random between these extremes for each magnitude interval. The rate was then multiplied by the sampling time (145 years) to give the expected number of events (n) of magnitude M for that time period. Finally, we assumed each n to be described by a Poisson distribution, and chose a final value at random from a Poisson distribution with mean equal to n. The final value of n was then converted back to the number of events per year. In Figure 1 we show the number of events per year versus magnitude observed in southern California (solid circles), and the number of events per year produced from 500 repetitions of the above procedure (dots). The numbers shown on the graph at M>6 represent the percentages of simulations that yield rates less than or equal to the rates observed historically. These percentages did not change for a greater number of repetitions. In Figure 1 we observe that the historical seismicity rates fall well within the rates calculated from the WGCEP data for the same period of time and for the entire range of magnitudes. Thus, our analysis of the data currently available do not support the presence of a historical deficit in the rate of seismicity, nor does it require that unusually large earthquakes which rupture beyond the lengths of mapped active faults in southern California, or that rupture numerous sub-parallel faults are needed to explain the historical distribution of seismicity.
We recently completed a survey of the differences in probabilistic seismic hazard (PSH) for the three PSH models of Ward (1994), WGCEP (1995), and USGS/CDMG (Petersen et al. 1996). In the Ward model, geodetic data were used to calculate earthquake recurrence rates for a gridwork of point sources inside each polygon, the earthquakes at each source were assumed to follow a magnitude-frequency distribution described by the Gutenberg-Richter relationship, and the maximum magnitude (Mmax) was estimated from the 'maximum linear dimension' of the polygon enclosing the source. The Joyner and Boore (1983) attenuation relationship was used to estimate peak ground accelerations as a function of magnitude and source-to-site distance. In the WGCEP model, earthquake recurrence rates were calculated from geodetic, geologic and historical seismicity data. The source of seismicity was taken to be the combination of characteristic earthquakes occurring on major fault zones and a component of distributed seismicity described by the Gutenberg-Richter relationship. The Mmax of earthquakes was estimated from 'the length of the surface traces of faults' inside each polygon, and the 'Geomatrix-Sadigh' attenuation relation (Geomatrix, 1995) was used to estimate peak accelerations for the WGCEP model. For the USGS/CDMG model, the source of seismicity was assumed to be the combination of characteristic and Gutenberg-Richter-distributed earthquakes occurring on the faults, and a component of Gutenberg-Richter distributed earthquakes in the areas between the faults (i.e. 'background' seismicity). The earthquake rates for the faults were calculated from geologic and historical seismicity data, and the Mmax for each fault or fault segment was estimated from the fault area. Peak ground accelerations were estimated for all fault and background earthquake sources by equally weighting the results of three attenuation relations; the Boore et al., (1994), Campbell and Bozorgnia, (1994), and 'Geomatrix-Sadigh' (Geomatrix, 1995) attenuation relations.
We used PSH maps produced from the 'Preferred' PSH model of the WGCEP (Mahdyiar, 1995) and hazard matrices supplied in digital form from the Ward and USGS/CDMG models in our analysis. Hazard matrices list the expected annual rate at which a suite of ground motion levels will be equaled or exceeded on rock at a gridwork of southern California sites, and were no longer available for the WGCEP model at the initiaton of the study. The gridwork of sites cover the area 32.5-36oN and 115-121oW at a grid spacing of 0.1o N and W. With the hazard matrices from the Ward and USGS/CDMG models we constructed and compared maps showing the levels of peak acceleration expected at 10% probability in 50 years (equivalent to a 475 year return time; Fig. 2a- c), and maps showing the 30 year probability of exceedance for 0.2g (Fig. 2d-f). Despite being limited to these two sets of maps by the availability of maps produced from the WGCEP model, the data were sufficient to make comparisons of PSH at two significantly different time scales. The highest peak accelerations in Figure 2a-c generally occur along the major mapped faults where M>7 earthquakes are predicted to occur at rates of greater than about 0.002 events per year, whereas the highest 30 year probabilities in Figure 2d-f are generally restricted to areas where M<7 earthquakes are predicted to occur at rates of greater than about 0.02 events per year, and to areas that are in close proximity to many faults. We followed the same approach used by Ward (1994) and Petersen et al. (1996) to construct the Ward and USGS/CDMG maps, in which the probability of exceeding a particular ground motion at each site in a certain time period is calculated according to a Poisson model. For convenience of discussion, the term 'hazard' is taken to be synonomous with 'peak ground acceleration' for the maps in Figure 2a-c and '30 year probability for 0.2g' for the maps in Figure 2d-f.
The Ward map (Fig. 2a) shows the lowest hazard of the three maps over much of southern California (typically 0.4 to 0.5g lower than the other maps). The relatively low hazard is attributed to the combined effect of distributing seismicity over a gridwork of point sources, and defining Mmaxes that are typically 0.5 to 0.7 units larger than the magnitudes defined in the other models. The main effect of distributing the seismicity of a fault over a series of line or point sources instead of placing it all on the fault is to reduce the hazard at the fault trace, and the effect of assuming larger values of Mmax is also to reduce hazard by allowing a slip rate budget to be accommodated by fewer earthquakes of Mmax. Some discrepancies between the USGS/CDMG and WGCEP maps can also be attributed to these same effects. For instance, the higher hazard along the Garlock fault on the USGS/CDMG map as compared to the WGCEP map (Figs. 2b and 2c) is due to the seismicity being distributed in a region around the faults in the WGCEP model rather than being limited to the fault trace. The USGS/CDMG map also shows higher hazard than the WGCEP map along the Elsinore and San Jacinto faults (up to 0.4g higher) because the WGCEP define larger Mmaxes and lower recurrence rates than the USGS/CDMG for these faults. Hence, large variations in hazard between the maps reflect different approaches to the manner in which seismicity is assumed to be distributed along fault zones and the values of Mmax assumed for those same fault zones.
Peak accelerations on the WGCEP map are consistently greater (up to 0.5g) in the periphery of the map area as compared to the Ward and USGS/CDMG maps (Fig. 2a-c), particularly at the western end of the Santa Barbara channel and north of the Santa Ynez fault. The high hazard in the peripheral regions of the WGCEP map (Fig. 2b) generally occur where geodetically-derived earthquake rates tend to dominate the hazard calculations, and where uncertainties in the geodetic rates are considered to be high (WGCEP, 1995). Although the peak accelerations shown on the Ward map are also derived from geodetic strain data, they are lower than the WGCEP accelerations across the entire map area because of the larger Mmaxes and lower recurrence rates of Mmax events defined in the Ward model. Understanding whether or not geodetic strains measured in areas absent of known active faults are ultimately released during nearby earthquakes or, rather, reflect strain changes associated with more distant faults is thus of importance to reducing uncertainties attendant to PSHA.
Some discrepancies between the maps in Figure 2a-c may also be attributed to the use of different attenuation relations, which each predict slightly different levels of peak acceleration at close distances to faults. The discrepancies can be observed along faults that have been treated similarly but for the attenuation relationship. Such is the case when comparing the USGS/CDMG and WGCEP maps along the San Andreas fault. The ground motion estimates on the USGS/CDMG map are slightly above those of the WGCEP map along the San Andreas (Figure 2b&c). The USGS/CDMG used three attenuation relations (i.e., Boore et al.,1994, Campbell and Bozorgnia, 1994, and 'Geomatrix-Sadigh') to obtain mean estimates of ground motion, whereas the WGCEP used the 'Geomatrix-Sadigh' attenuation relation alone. The PSH maps are therefore sensitive to these choices of attenuation relation at close distances to the faults.
Maps of the 30 year probability of exceedance for 0.2g for each PSH model (Figure 2d-f) also show some significant differences. The WGCEP map shows probabilities that are up to 50% higher than the other maps in the northwest of the map area. These high probabilities are in similar locations to anomalously high peak accelerations shown on the WGCEP map in Figure 2b, and are likewise attributed to the WGCEP's use of geodetic strain data to calculate earthquake recurrence rates in regions where the geodetically-derived earthquake rates dominate the hazard calculations. There are also discrepancies between the maps in the vicinity of the Imperial fault and Brawley Seismic Zone (southeast corner of the map area). The Ward map shows higher hazard than the other maps along the Imperial fault because it is assumed that the seismicity of the Imperial is described by the Gutenberg-Richter relationship, which produces a high predicted rate of M<7 earthquakes. The 30 year probabilities along the Brawley are highest on the USGS/CDMG map. This is due to the WGCEP and Ward assigning low and nil earthquake potential to the Brawley, respectively, as compared to the high earthquake rates defined by the USGS/CDMG (Petersen et al., 1996).
Significant discrepancies exist between PSH maps constructed from the Ward, USGS/CDMG, and WGCEP models for time spans of importance to engineers and planners. Assumptions bearing on (1) how seismicity is distributed on and around mapped fault traces, (2) the size of the Mmax assigned to a fault, (3) the ground motion attenuation relation most applicable to southern California, and (4) the relationship between geodetic strain rates and the locations and recurrence rates of large earthquakes are responsible for differences of up to 0.5g (Fig. 2a-c) and 50% (Fig. 2d-f) between the maps. The capture of more strong motion data at close distances to large earthquakes, where attenuation relations are poorly constrained by the existing strong motion datasets, and development of field criteria to test the predictions of the PSH models are avenues of research that could lead to more confident estimates of PSH in the future. We are now investigating the constraints that can be placed on ground motions by the distribution of precariously-balanced rocks around southern California (e.g. Brune, 1996) in order to test the various PSH models. All three PSH models predict ground motions that would topple the precarious rocks, and we have collected and analyzed weak motion data at three precarious rock sites to determine whether the rocks have remained standing because of anomalous site conditions. Our preliminary conclusion is that the site conditions at precarious rock sites are similar to the "average rock" conditions assumed in construction of the three PSH models, which appears to eliminate the possibility that anomalous site conditions have prevented the rocks from toppling.
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