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Probabilistic Seismic Hazard Assessment - California Geological Survey
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Open-File Report 96-08
Open-File Report 96-706
PROBABILISTIC SEISMIC HAZARD ASSESSMENT FOR THE STATE OF CALIFORNIA
Mark D. Petersen, William A. Bryant, Chris H. Cramer, Tianqing Cao, and Michael Reichle
James J. Lienkaemper, Patricia A. McCrory, and David P. Schwartz
801 K Street, MA 12-31
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Seismicity in California
Faults in California
Comparison with Historical Damage
Comparison with Historical Seismicity
Deaggregation of the Hazard Model
Comparison of Hazard Across California
Appendix A: Fault Source Parameters (Index to Tabular Data)
A Faults
B Faults, Part 1
B Faults, Part 2
B Faults, Part 3
B Faults, Part 4
B Faults, Part 5
C Zones
Appendix B: References to Fault Source Parameters
Table 1. Class A faults with both independent and multi-segment ruptures.
Figure 1. Index map showing names of major faults with slip rates greater than about 5 mm/yr and feature names referred to in the text.
Figure 2. Seismicity M>6 in California between about 1800 and 1994 (DMG catalog).
Figure 3(a). Fault geometry applied in the source model. Weight of line is proportional to the slip rate. Faults and attributes are listed in Table 1. The individual fault names could not be shown on these figures but may be found on maps such as Jennings (1994). Blind thrusts are indicated by small boxes and are for the most part described in Dolan et al. (1995) and WGNCEP (1996). Large boxes located in the northeast portion of the state indicate area sources described in the text. Faults shown: BT—Bartlett Springs; DV—Death Valley; GA—Garlock; GV—Great Valley; HL—Honey Lake; HM—Hat Creek-McArthur-Mayfield; IP—Imperial; MA—Maacama; OV—Owens Valley; PM—Panamint Valley; PV—Palos Verdes; RN—Rinconada; SA—San Andreas; SG—San Gregorio; SJ—San Jacinto; SV—Surprise Valley; WE—Whittier-Elsinore.
Figure 3(b). Detail of San Francisco Bay area. Selected faults include: CA—Calaveras; CG—Concord-Green Valley; GL—Greenville; GV—Great Valley blind thrusts; HY—Hayward; OT—Ortigalita; PR—Point Reyes; QS—Quien Sabe; RC—Rodgers Creek; SA—San Andreas; SG—San Gregorio; SR—Sargent; WN—West Napa.
Figure 3(c). Detail of Los Angeles area. Selected faults include: CI—Channel Islands blind thrust; CT—Compton blind thrust; CU—Cucamonga; EP—Elysian Park blind thrust; GA—Garlock; MO—Montalvo-Oakridge blind thrust; NC—Nor Channel Slope blind thrust; NI—Newport-Inglewood; NR—Northridge blind thrust; OB—Oakridge blind thrust; PV—Palos Verdes; SA—San Andreas; SJ—San Jacinto; SM—Sierra Madre; SY—Santa Ynez; WE—Whittier Elsinore
Figure 4. Comparison of the slip rates to the NUVEL I plate tectonic rates. Lines numbered 1-13 indicate profiles along which slip rate vectors were summed (from east to west) to compare with the NUVEL I model. Boxes labeled 1-13 correspond with numbered lines and indicate the slip rate in mm/yr for the resultant north and east directions of the slip rate vectors and the overall NUVEL I model for California. NUVEL I vector appears in all plots and is the more clockwise vector in Line 1.
Figure 5. Probabilistic seismic hazard map for peak horizontal acceleration on firm-rock site conditions and for 10% probability of exceedance in 50 years. Contours are based on grided hazard values with spacing of 0.05 longitude and latitude. Colors indicate peak acceleration in %g units.
Figure 6. Areas that are thought to have experienced (or would have experienced if the area were developed) MMI VII or greater between 1800 and 1996. San Andreas and Eastern California Shear zones are noted. Boxes indicate epicenters of M>6 earthquakes for which we do not have damage data.
Figure 7. Comparison of the number of historic California earthquakes and the earthquakes used to calculate the seismic hazard. The historic earthquake numbers were normalized by the length of catalog which we used (e.g., since 1932 - 64 years; 1901 - 95 years; 1850 - 146 years) to show the variability in the historic earthquake rate.
Figure 8. Contour map of the magnitude of the earthquake that causes the dominant hazard for peak ground acceleration at 10% probability of exceedance in 50 years and alluvial site conditions. County boundaries are also shown.
Figure 9. Contour map of the distance of the earthquake that causes the dominant hazard for peak ground acceleration at 10% probability of exceedance in 50 years and alluvial site conditions. County boundaries are also shown.
Figure 10. Hazard curves for peak ground acceleration and alluvial site conditions at various cities located across California. The curves indicate the probability of exceeding the given peak ground acceleration levels on alluvial site conditions.
This report documents a probabilistic seismic hazard assessment for the state of California and represents an extensive effort to obtain consensus within the scientific community regarding earthquake parameters that contribute to the seismic hazard. The parameters displayed in this report are not the work of any individual scientist, but denote the effort of many scientists, engineers, and public policy officials that participated in developing the statistical distributions used in the analysis. Consensus in the earth-science community is essential for developing useful public policy that may influence land-use planning, building regulation, insurance rate assessment, and emergency preparedness. This consensus is imperative because our results indicate that roughly three-fourths of the population of California live in counties that have significant hazard due to earthquake ground shaking.
The primary purpose of this report is to present the earthquake source information; a general outline of the methodology and equations used to generate the seismic hazard map; and the seismic hazard map for peak horizontal acceleration on a uniform site condition of firm rock (average shear wave velocity of about 760 m/s) at a hazard level of 10% probability of exceedance in 50 years. Independent geologic, geodetic, and historical damage data are also presented as well as a comparison of the seismic hazard for several populated regions across the state. Further information regarding the hazard model, sensitivity studies, and uncertainty analyses may also be found in papers by Frankel (1995), Frankel et al. (1996), Petersen et al. (1996a,b), Cao et al. (1996), Cramer et al. (1996), Cramer and Petersen (1996), Working Group on Northern California Earthquake Potential (WGNCEP, 1996), McCrory (1996), and a text on probabilistic seismic hazard analysis by Reiter (1990).
We chose to describe the hazard using a probabilistic seismic hazard assessment that takes into account the recurrence rates of potential earthquakes on each fault and the potential ground motion that may result from each of those earthquakes. The hazard analysis incorporates both a) historical seismicity and b) geologic information within fault zones that display evidence of displacement during late Pleistocene and Holocene times.
a) Seismicity in California
Seismic hazard in California is high in many areas, as manifested by the number of large earthquakes that have occurred during historic time (Figures 1 and 2). Many of these earthquakes occurred in a belt of seismicity located within about 50 km of the San Andreas Fault Zone. Large earthquakes with moment magnitude M >7 have ruptured on or near the San Andreas Fault Zone (Figures 1 and 2) in the 1812 Wrightwood earthquake, M~7-71/2; 1838 San Francisco peninsula earthquake, M ~ 7-71/2; 1857 Fort Tejon earthquake, M ~ 7.9; 1868 Hayward earthquake, M ~ 7; 1906 San Francisco earthquake, M ~ 7.9; and the 1989 Loma Prieta earthquake, M 7.0. However, a number of moderate (M >51/2) to large earthquakes have also occurred on faults situated well away from the San Andreas Fault (e.g., the 1872 Owens Valley earthquake, M~7.6; 1952 Kern County earthquake, M ~ 7.5; 1971 San Fernando earthquake, M 6.7; 1992 Landers earthquake, M 7.4; and the 1994 Northridge earthquake, M 6.7). Moderate to large earthquakes have not only occurred on strike-slip faults associated with the broad San Andreas Fault System, but also along reverse faults that either rupture the surface (e.g., 1971 San Fernando and 1952 Kern County earthquakes) or to some depth beneath the surface as "blind thrusts" (e.g., 1983 Coalinga earthquake, M 6.5; 1987 Whittier Narrows earthquake, M 5.9; and the 1994 Northridge earthquake). The 1992 Petrolia earthquake (M 7.0) is thought to have occurred on the Cascadia subduction zone and demonstrates the potential hazard of this compressional zone (Figure 1). California has had an average of about one M > 6 event every 2 to 3 years and losses from many of this century’s large earthquakes have resulted in several billions of dollars in damage (e.g., 1906 San Francisco earthquake, 1933 Long Beach earthquake- M6.2, 1971 San Fernando earthquake, 1989 Loma Prieta earthquake, and 1994 Northridge earthquake).
Figure 1. Index map showing names of major fault systems with slip rates greater than about 5 mm/yr and feature names referred to in text.
b) Faults in California
The earthquake catalog for California includes only earthquakes for approximately the past 200 years or so, whereas the return times for large earthquakes on many faults are at least an order of magnitude longer. Therefore, when it was available we have relied on paleoseismic data for faults in order to develop as complete an inventory of paleo-earthquakes as possible for our seismic source model. Rather than consider whether faults are "active" or "inactive," we have attempted to quantify the degree of activity of faults based on their reported slip rates and recurrence intervals. We have incorporated average recurrence times and displacement per event (when known) from paleoseismic investigations. Paleoseismic data for the majority of faults considered in this study, however, are restricted to slip-rate data of variable quality; recurrence intervals are rarely documented. Thus the majority of earthquake recurrence rates for faults has been derived from slip rate data. For this hazard assessment we have evaluated fault length, geometry, and slip rates for about 180 faults statewide with reported displacements during latest Pleistocene and Holocene times (Appendix A).
Several major fault systems accommodate high slip rates and significantly contribute to the hazard in California including: the San Andreas Fault, the Cascadia subduction zone, the Eastern California Shear Zone, and compressional faults associated with the western Transverse Ranges (Figures 1 and 3). Blind thrusts have recently been identified beneath the Los Angeles and San Fernando basins, the western Transverse Ranges, Santa Barbara Channel, and along the western flank of the Central Valley. In addition, several offshore faults have been identified and contribute significantly to the seismic hazard in coastal areas. Many late Quaternary faults are near a complex triple junction intersection of the Mendocino fracture zone, the San Andreas Fault, and the Cascadia subduction zone. Other significant faults are found in the eastern portion of California along a broad zone of portion of the state (Eastern California Shear Zone in Figure 1). Additional faults with Quaternary offsets are scattered over almost every strike-slip and normal faults distributed across the Mojave Desert, the Owens Valley, eastern Nevada, and across the northeastern region of California.
Figure 3a: Fault geometry applied in the source model. Weight of line is proportional to the slip rate. Faults and attributes are listed in Table 1. The individual fault names could not be shown on these figures but may be found on maps such as Jennings (1994). Blind thrusts are indicated by small boxes and are for the most part described in Dolan et al. (1995) and WGNCEP (1996).Large boxes located in the northeast portion of the state indicate area sources described in the text.
Figure 3b: Same as in Figure 3a but enlarged to show detail in the San Francisco Bay area.
Figure 3c: Same as in Figure 3a but enlarged to show detail in the Los Angeles area.
Development of the hazard model consists of three steps: a) delineating earthquake sources, b) defining the potential distribution of seismicity for each of these sources (magnitude frequency distributions), and c) calculating the potential ground motions from attenuation relations for all the model earthquakes.
a) Earthquake sources
For delineating the fault sources shown in Figure 3, we digitized the 1:750,000 scale fault activity map of Jennings (1994). Only a few points were digitized along faults of the Jennings map to approximate the location of each fault trace. The uncertainty in the location of the fault is approximately 1 to 2 kilometers. We digitized simplified fault traces from this map and calculated the length of each fault from these traces using Geographic Information System (GIS) analysis tools. For our uncertainty analysis, we assume a + 10% uncertainty in the length. This uncertainty reflects the range of values obtained by measuring the length of faults depicted on several different fault maps (Ziony and Yerkes, 1985, Ziony and Jones, 1989; and Jennings, 1994). When possible, the depth of the seismogenic rupture zone was obtained from the hypocentral locations of earthquakes surrounding the faults. We used the work of WGNCEP (1996), Hill et al. (1990), McCrory (1996), and Petersen and Wesnousky (1994) to assess the depth dimension of the seismogenic zone. For many of the faults with limited historical seismicity, the depths are simply an average of all earthquake depths located in the vicinity of the fault.
We conducted a comprehensive survey of the available slip rate information through literature searches and many discussions, meetings, and written correspondence with the authors of the fault studies to assign earthquake activity rates and slip rates along faults (Appendix A). As part of the survey, we evaluated published compilations of slip rates given by Bird and Rosenstock (1984), Clark et al. (1984), Wesnousky (1986), Ziony and Yerkes (1985), Thenhouse (personal communication), Petersen and Wesnousky, (1994), Petersen et al., (1996a), WGNCEP (1996) and McCrory (1996). We reviewed the original sources of slip rates whenever possible for constraints on the direction, amount, and timing of displacement. Mean slip rates and their uncertainties are based on these studies (see references in Appendices A and B). Slip rates are considered well constrained if the direction, amount, and timing of displacement have been demonstrated. Moderately constrained slip rates generally have significant uncertainty for one of these components. Poorly constrained slip rates have either significant uncertainty with respect to both amount and timing of displacement or else the reported slip rate is a long-term (late Cenozoic) average rate. Many of the faults in California are poorly to moderately constrained because they have not been studied sufficiently or because no available site has been found that contains appropriate stratigraphic relationships and dateable material needed to infer details of the paleoseismic history.
Figures 3a-c show the faults that were incorporated into the source model and Appendix A indicates the associated length, slip rate, quality of slip rate (Rank), maximum magnitude (moment magnitude), characteristic earthquake rate and recurrence interval (R.I.) for the maximum magnitude, down dip width of the seismogenic zone, the top and bottom of the rupture surface, as well as the rake, dip, and dip azimuth of the rupture surface, the endpoints of the fault or fault segment, and comments and references regarding the basis for these parameter values. The slip-rate table (Appendix A) reflects our "best estimate" of the mean and range of possible slip rates along a fault. We consider the range of slip rates to encompass about 95% of the observations and represent 2 in uncertainty. The range in slip rates is symmetrical about the mean for simplicity and because we found it difficult to assign more detailed uncertainty estimates based on sparse slip rate information. We assumed an uncertainty of + 2 km for the depth of the seismogenic zone. These values and quality assessments will be updated as new geologic and seismic investigations are completed.
In addition to fault studies, geodetic, magnetic, and earthquake source mechanism data provide insights constraining the stress and strain rates on faults in California. These strain measurements have not been incorporated explicitly in this model because of lack of uniform spatial coverage and availability. This strain data, however, provide independent constraints on the slip rate information independent of the geological data. The Working Group on California Earthquake Probabilities (WGCEP, 1995) indicated that the geodetically determined moment rates obtained from Global Positioning Satellite data are similar to the geologically determined moment rates from known faults in southern California. For this report we compared the modern plate tectonic rate from NUVEL I (DeMets et al., 1990), obtained using global seismic, geodetic, and fault and fracture orientation information, with the slip rates that we have compiled from fault studies in California (Figure 4). For this comparison slip rate vectors are summed across profiles oriented nearly perpendicular to the Pacific-North American plate boundary. We find that the cumulative slip rates that we used are consistent with the NUVEL I model in amplitude (about 48 mm/yr) and generally consistent in azimuth. In southern California, however, there is a systematic discrepancy in slip rate direction between our model and the NUVEL I model. Part of this discrepancy may be related to the fact that the NUVEL I model does not take into account the bend in the southern San Andreas Fault and is only based on a concentric circle about an Euler pole. The sum of fault slip rates across the plate boundary is generally slightly less than the NUVEL I model predicts, but we assume that a relatively small amount of strain also occurs east of California.
Figure 4: Comparison of the slip rates to the NUVEL I plate tectonic rates. Lines numbered 1-13 indicate profiles along which slip rate vectors were summed (from east to west) to compare with the NUVEL I model. Boxes labeled 1-13 correspond with numbered lines and indicate the slip rate in mm/yr for the resultant north and east directions of the slip rate vectors and the overall NUVEL I model for California.
b) Magnitude-frequency distributions
The annual number of earthquakes of various sizes that are assigned to each fault is based on the slip rate information and is defined using a combination of two statistical distributions: (1) the characteristic earthquake model that implies that a typical size of earthquake ruptures repeatedly along a particular segment of the fault (Schwartz and Coppersmith, 1984), and (2) the exponential model that implies that earthquakes on a given fault follow the Gutenberg-Richter relationship: n(m) = 10a-bm where n is the incremental number of earthquakes, a is the incremental number of earthquakes of m>0, b is the slope of the distribution, and m is moment magnitude (Richter, 1958). These two distributions have been discussed at length in the scientific literature and are both considered to be reasonable models either for specific faults or for larger areas of California. A combination of the two distributions is also thought to characterize the behavior of many fault systems. This composite model allows for more large earthquakes than predicted by the exponential distribution, and also for earthquakes of sizes different than the characteristic event.
The recurrence time of the characteristic earthquake is obtained using the methodology described in Wesnousky (1986):
where is the seismic moment of the characteristic earthquake and is the rate that the fault accumulates moment. The rigidity or shear modulus of the crust is represented by and for this study is taken as 3.0 x 1011 dyne/cm2s. The value l represents the length of the fault, w is the downdip width (or depth) of the seismogenic zone, is the slip rate for the fault, and is the average displacement on the fault. The relation 1/ gives the rate of earthquakes on a fault of the characteristic size.
The exponential distribution is used to partition the moment rate of the fault into events between a minimum and maximum magnitude. The geologic moment rate can be related to the exponential distribution by the following relation:
where (m) is the annual number of events of moment magnitude m, M0 is the moment of each of those events, a is the incremental rate of earthquakes with magnitude m, b is the slope of the distribution, c and d are constants defined by Hanks and Kanamori (1979) as 1.5 and 9.1, mu and m0 are the upper and lower bound magnitude truncations of the magnitude-frequency distribution. Equation 2 is used to solve for the incremental a-value.
This formulation assumes that all the moment rate from a fault is released seismically by earthquakes between the upper and lower bound magnitudes.
We categorize the faults into two classes and apply different magnitude-frequency statistical distributions for each class. The class A faults generally have slip rates greater than 5 mm/yr and well constrained paleoseismic data (i.e., the San Andreas, San Jacinto, Elsinore, Imperial, Hayward, and Rodgers Creek faults). The class B faults include all the other faults lacking paleoseismic data necessary to constrain the recurrence intervals of large events (Appendix A).
For class A faults we use characteristic earthquakes to describe the magnitude-frequency distribution along the faults. In addition to independent fault segment ruptures, we allow multiple contiguous segments to rupture together in larger events, comparable to large historical events on the San Andreas Fault System (Table 1). We use slip rate, displacement, and individual segment recurrence information provided by the WGCEP (1988, 1990, 1995) to account for multiple segment ruptures on the class A faults, except for the northernmost 1906 segment of the San Andreas Fault segment that is based on WGNCEP (1996). All the probabilities that we calculate incorporate a Poissonian model and do not consider the time since the last large earthquake.
The source model accounts for all large earthquakes including the 1857 and 1906 earthquakes along the southern and northern San Andreas Fault, respectively. We assign the paleoseismically derived recurrence rate of earthquakes along the Carrizo and North Coast segments of the San Andreas Fault as the rate of the large multi-segment ruptures (similar to the 1857 and 1906 sized earthquakes). We assign the rate of the Coachella Valley segment to that of the the multi-segment earthquake that ruptures the southernmost San Andreas Fault south of the 1857 rupture (Table 1). We subtract the annual rupture rates assigned to the multi-segment rupture from each of the other individual segment rates (from WGCEP reports) to obtain the revised rates for individual segment ruptures along the San Andreas Fault. This means that the Carrizo, North Coast, and Coachella segments are only allowed to rupture as large events and not in individual segment ruptures while the other segments may rupture as an individual segment or in conjunction with other contiguous segments in a multi-segment rupture.
For the Hayward Fault, we allow both individual segments to rupture separately as well as together in a larger event, as defined by the WGCEP (1990). We allow only single segment ruptures on the San Jacinto and Elsinore faults as defined by WGCEP (1995) and the Rodgers Creek Fault as defined by WGCEP (1990), because the single segment rupture model yielded nearly the same hazard as the multiple segment rupture model in southern California (Petersen et al., 1996a; Cramer et al., 1996).
Table 1: Class A faults with both independent and multi-segment ruptures.
independent segment recurrence (yr), 1/
multi-segment recurrence (yr), 1/
San Andreas: 1906 rupture
210 / 0.00476
138 / 0.00726
400 / 0.00250
San Andreas: 1857 rupture
206 / 0.00485
22 / 0.04545
25 / 0.04060
140 / 0.00714
437 0.00229
150 / 0.00667
550 / 0.00182
San Andreas: Southern
220 / 0.00454
146 / 0.00685
433 / 0.00231
330 / 0.00299
167 / 0.00599
500 / 0.00200
335 / 0.00298
In this report the Cascadia subduction zone is treated as a class A fault. We have assumed that large earthquakes occur every few hundred to 1000 years as inferred from paleoseismic information (e.g., McCrory, 1996; Frankel et al.,1996). The entire Cascadia subduction zone was modeled as a combination of a M 9 characteristic rupture along the entire subduction zone from California to Washington every 500 years and a M 8.3 rupture along the California portion of the zone about every 335 years. The recurrence of the M 8.3 event reflects the time for the entire Cascadia to rupture all the segments in 500 years (Frankel et al., 1996). We assign a one-third weight to the M 9 event and a two-thirds weight to the M 8.3 event.
For class B faults we have chosen to use both characteristic and exponential earthquake magnitude-frequency distributions with each weighted 50%. This composite model allows for a greater number of large earthquakes than predicted by a simple exponential distribution while still accounting for the smaller earthquakes that may occur on the fault. In addition, this model also accounts for the diversity of opinion regarding these distributions within the science and engineering communities. Blind thrusts were treated as B class faults for this analysis. Some of the blind thrusts and offshore faults in the Santa Barbara Channel were weighted (Appendix A) to account for alternative scientific models after the work of Treiman (1996, written communication) that accounts for rotation of the western Transverse Ranges and Foxall (1996, written communication). In the source model presented here, earthquakes on fault sources generally have a minimum magnitude of 6.5 and a maximum magnitude consistent with the fault rupture area or displacement per event (Wells and Coppersmith, 1994). The shorter faults that have calculated magnitude less than 6.5 are described by a characteristic earthquake magnitude rather than a Gutenberg-Richter magnitude-frequency distribution.
Maximum magnitudes are an important variable in calculating the seismic hazard because they determine how much strain is released in larger earthquakes. The displacements per event were generally obtained from the WGCEP (1988, 1990, 1995) and were used to calculate maximum magnitudes and average recurrence intervals for earthquakes on class A faults. For class B faults we use a historical earthquake magnitude on a particular fault, if available, or the relation of Wells and Coppersmith (1994) between area of the fault rupture and magnitude of the event to calculate the maximum magnitude (or characteristic earthquake magnitude):
M=a+ b x log10(rupture area) (4)
where a and b are constants of 4.07 and 0.98 and the standard deviation of the magnitude is 0.24. The length, dip, and the top and bottom of the rupture of the fault are used to calculate the rupture area.
In general, alternate segmentation models were not considered in this version of the map. However, multiple segment earthquake ruptures were considered for modeling earthquakes on many of the class A faults (Table 1). In addition, alternative weighted models were considered for the blind thrusts and other faults in the Los Angeles basin and Santa Barbara Channel. These weighted models account for the lack of consensus in the earth-science community regarding these structures and their activity rates. Future versions of the map will most likely include additional alternatives for models of rupture.
Modeling the sources for faults that have known creep is not straightforward because some of the strain along these faults may not be released in earthquakes. Future seismic hazard research should focus on better ways to model such faults (e.g., creeping section of the San Andreas Fault, the Hayward Fault, the Calaveras Fault, the Brawley seismic zone, and the Maacama Fault). For constructing the source model along the creeping section of the San Andreas Fault and the creeping section of the southern Calaveras Fault we have varied the general methodology for calculating hazard. We have not added a separate source to account for the seismicity along the creeping segment of the San Andreas Fault, although we tested the sensitivity of various source models to the hazard results. The historical seismicity along the creeping segment of the San Andreas alone is quite high and contributes to a significant hazard. We modeled the earthquakes along the southern Calaveras Fault by allowing a M 6.2 event to occur anywhere along the fault. We constrained the maximum magnitude to 6.2 because several earthquakes about that size have occurred historically.
We modeled four aerial source zones along the eastern border of the state that extend from about Mammoth Lakes up into northeastern California and incorporate much of northeastern California and small portions of eastern Nevada and southern Oregon (Figure 3). These zones account for faults with poorly constrained or unknown slip rates with multiple fault strands distributed over a wide area. These source zones are shown in Figure 3 and included in Table 1. The zones were modeled using linear sources, oriented along regional structural trends. They incorporate earthquakes modeled using an exponential magnitude-frequency distribution between M 6.5 and 7.3, except for the Foothills Fault System that incorporates exponentially distributed earthquakes between M 6.0 and 7.0.
In addition to the characteristic and exponential distributions for fault sources, we also allow for background seismicity that accounts for random earthquakes between M 5 and 7 based on the methodology described by Frankel et al. (1996). We note that an overlap occurs in our source model between M 6.5 and 7 because both the background as well as the fault magnitude distributions may contain that range of events. Frankel et al. (1996) and Cao et al. (1996), however, include sensitivity studies indicating that this overlap causes only small differences to the calculated hazard values. The inclusion of larger events in the background allows for sources such as the 1994 Northridge earthquake that occurred on a previously unknown fault. The background seismicity is based on the assumption and observation that large earthquakes occur where smaller earthquakes have occurred in the past. Therefore, the background seismicity is highest near locations of M>4 events and is based on the DMG California catalog of earthquakes (1800-1994; Petersen et al., written communication, 1996). The background hazard is based on the rate of M 4 events since 1933, M 5 events since 1900, and M 6 events since 1850. The seismicity is smoothed using a Gaussian operator with correlation distance of 50 km and then the smoothed seismicity value is summed at each grid point. The a-values are calculated using the method described in Weichert (1980) for all grid points across California (Frankel, 1995, Frankel et al., 1996). The hazard may then be calculated using this a-value, a b-value of 0.9, minimum magnitude of 5, maximum magnitude of 7, and applying an exponential distribution as described by Hermann (1977).
c) Attenuation relations
Once the earthquake distributions have been calculated for all the faults, attenuation relations are applied to estimate the ground motion distribution for each earthquake of a given magnitude, distance, and rupture mechanism. We have chosen to use three attenuation relations for crustal faults and two relations for subduction zone events. The peak ground acceleration (pga) relations that we chose for crustal earthquakes are from: Boore et al. (1993, with revisions given in written communication 1995); Geomatrix-Sadigh equation found in Geomatrix (1995); and Campbell and Bozorgnia, (1994). The relations that we use for subduction earthquakes are: the Geomatrix-Youngs subduction zone interface earthquake relation and the Geomatrix-Sadigh equation both described in Geomatrix (1995). For all faults and background seismicity, except for the Cascadia subduction events, we apply Boore et al., Campbell and Bozorgnia, and Geometrix-Sadigh et al. weighted equally. For earthquakes along the Cascadia subduction zone we apply the Geomatrix-Youngs equation and the Geomatrix-Sadigh equation weighted equally for the M 8.3 event and apply only the Geomatrix-Youngs equation for the M 9 event because the Geomatrix-Sadigh equation does not apply for that size earthquake.
The Boore, Joyner and Fumal relation for random horizontal component of peak ground acceleration (pga) is given by:
log10 (pga) = b1 + b2(m-6) + b3(M-6)2 + b4r + b5 log10r + b6Gb + b7Gc + (5)
with r=( d2 +h2 ) 1/2 and log10Y=0.226, lnY=0.520. In this equation b1(reverse)=-0.051, b1(strike-slip)=-0.136, b1(all)=-0.105, b2=0.229, b3=0, b4=0, b5=-0.778, b6=0.162, b7=0.251, Gb=0.5 Gc=0.5, and h=5.57, d is the closest distance to the surface projection of the rupture, is the random uncertainty term, and M is moment magnitude. The firm-rock equation is used to assess ground motion for a soil condition near the boundary between soil types b and c. Therefore, we use the relation with Gb and Gc each 0.5 to account for this firm-rock condition.
The Geomatrix - Sadigh pga for strike slip style of faulting and for rock site conditions is given by:
for M < 6.5: ln (pga) = -0.624 + 1.0M -2.1 ln[R + exp(1.29649+ 0.250M)] (6)
for M > 6.5: ln (pga) = -1.274 + 1.1M -2.1 ln[R + exp(-0.48451 + 0.524M)]
with dispersion relation: [ln (pga)] = 1.39 - 0.14M, or 0.38 for M >7.25
These values are increased by 20% for reverse faults. M is moment magnitude and R is the closest distance to the source in km.
The Campbell and Bozorgnia (geometric mean of two horizontal components of pga) is given by:
ln(pga) = -3.512 + 0.904M - 1.328 ln +
[1.125 - 0.112 ln(Rs) - 0.0957M]F + [0.440-0.171 ln(Rs )]Ssr +
[0.405-0.222 ln(Rs)]Shr+
ln(pga)= 0.889-0.0691M if M < 7.4 and
ln(pga) = 0.38 if M ³ 7.4 (7)
where Rs is the closest distance to the seismogenic rupture, F is 1 for reverse, thrust and oblique faulting events and 0 for strike-slip and normal faulting events, M is moment magnitude, Ssr=1 for firm-rock sites and zero otherwise, Shr = 1 for hard-rock sites and zero otherwise, and is the random error term with zero mean and standard deviation equal to ln(pga). The top of seismogenic rupture is assumed to be about 3 km depth.
The Geomatrix-Youngs equation for pga from slab interface earthquakes on the Cascadia subduction zone is based on a fault depth of 20 km and is given by:
ln(pga) = 0.3633 + 1.414M - 2.556(R+1.782e0.554M) (8)
with standard deviation = 1.45 - 0.1M. M is moment magnitude and R is the closest distance to the source in kilometers. Standard deviation for magnitudes greater than M 8 are set equal to the standard deviation for M 8.
In addition, deep events (depth > 35 km) in northwestern California were considered for this map, but they do not contribute significantly to the hazard probabilities because about 25 or so M>4 events have been recorded in that region. Those deeper events mostly influence the hazard north of California and for further details see Frankel et al. (1996).
The hazard map shown in Figure 5 depicts the peak horizontal ground acceleration exceeded at a 10% probability in 50 years on a uniform firm-rock site condition. Acceleration at 10% in 50 years ranges from about 0.1 g to over 1 g. This map indicates high hazard in a belt about 50 km on either side of the San Andreas Fault Zone and along the Eastern California Shear Zone (Figure 1). The hazard is also quite high over the western Transverse Ranges, although no large earthquakes are known to have occurred in this region during the historical record. The northwest coastal portion of the state reflects high hazard from potential earthquakes on several onshore faults and the Cascadia subduction zone. The hazard is lower in the Central Valley and many portions of northeastern and southeastern California. More than three-fourths of the population of the state resides in counties that have seismic hazard above about 0.4 g, including counties near the San Francisco Bay and greater Los Angeles regions. This value is a rough estimate based on overall state population of about 32 million and county population as defined by the Governor’s Office of Planning and Research (1996).
Figure 5: Probabilistic seismic hazard map for peak horizontal acceleration on firm-rock site conditions and for 10% probability of exceedance in 50 years. Contours are based on grided hazard values with spacing of 0.05 longitude and latitude. Colors indicate peak acceleration in %g units.
The area of California where ground shaking during historical earthquakes has exceeded Modified Mercalli Intensity (MMI) VII is shown in Figure 6, revised after the work of Toppozada et al. (1986) to include the 1992 Landers sequence, the 1987 Superstition Hills events and the 1994 Markleeville earthquake. MMI is a scale that measures the effects of earthquake ground motion on people and structures. MMI VII effects are characterized by significant damage to weak structures. Therefore, the map depicts all areas that either experienced damage or would have experienced damage to structures if the area had been developed at the time of the earthquake. The damage pattern extends about 50 km on either side of the San Andreas Fault Zone and extends up through the Eastern California Shear Zone. This pattern is very similar to the hazard pattern shown in the hazard map of Figure 5. Differences between the historic damage and the map we produced can be observed near the Cascadia subduction zone and near the Transverse Ranges of southern California. In these areas, few large earthquakes have occurred historically but geologic and geodetic data indicate high strain rates.
Figure 6: Areas that are thought to have experienced (or would have experienced if the area were developed) MMI VII or greater between 1800 and 1996. San Andreas and Eastern California Shear zones are noted. Boxes indicate epicenters of M ~ 6 earthquakes for which we do not have damage data.
The seismic hazard was calculated by inferring a suite of representative earthquakes for each fault, calculating the ground motion from these events, and summing the hazard from all the earthquakes. An important constraint on the hazard model is a comparison of the model earthquakes with the historical rate of earthquakes. This comparison is shown in Figure 7. The hazard model matches very well from M 5 to M 6 and M 7 to M 8. However, there is an excess of events, on the order of a factor of 2, for M 6 to M 7 across the entire state. Overall the match between the model seismicity and the historical seismicity is fairly good. The mismatch between the historical and model seismicity indicates the discrepancy between the geologic fault information and the historic earthquake catalog. As mentioned earlier, the historic earthquake catalog covers only about 200 years, while recurrence of earthquakes on many faults are at least an order of magnitude longer. Therefore, we would not expect to have seen all the earthquakes during the past 200 years that would be expected in the future. We cannot say how much the rate of seismicity fluctuates over time scales of hundreds to thousands of years.
Figure 7: Comparison of the number of historic California earthquakes and the earthquakes used to calculate the seismic hazard. The historic earthquake numbers were normalized by the length of catalog which we used (e.g., since 1932 - 64 years; 1901 - 95 years; 1850 - 146 years) to show the variability in the historic earthquake rate.
We have deaggregated the hazard model to determine the size and distance of the earthquakes that contribute most to the hazard at specific sites throughout California. The deaggregation process compares the probabilities of exceeding a certain ground motion level from each event used in the model to determine the event(s) that contribute most to the hazard at each site. This should enable engineers, geologists, and public policy makers to identify the predominant hazardous earthquakes in any region and provide guidance in choosing strong motion records or scenario earthquakes in their design and planning.
The modal (most probable) magnitude for earthquakes that dominate the hazard is contoured and displayed in Figure 8. The map indicates hazard in the northwest from great earthquakes along the Cascadia subduction zone, the hazard near the San Andreas and the Central Valley from large earthquakes along the San Andreas Fault, and the hazard in the east San Francisco Bay area and greater Los Angeles region from moderate to large events along local faults. The modal distance map indicates the distance to the earthquake that contributes most to the hazard at each site. This map is shown in Figure 9 and indicates that for most areas the fault that is nearest the site causes the highest hazard. For the Central Valley, few faults have been identified that contribute to the hazard and so the distances are considerably longer than for coastal areas and generally these longer distances correspond to the distance from the San Andreas Fault.
Figure 8: Contour map of the magnitude of the earthquake that causes the dominant hazard for peak ground acceleration at 10% probability of exceedance in 50 years and alluvial site conditions.
Figure 9: Contour map of the distance of the earthquake that causes the dominant hazard for peak ground acceleration at 10% probability of exceedance in 50 years and alluvial site conditions.
The hazard map in Figure 5 indicates the hazard at a 0.0021 annual probability level. Figure 10 shows the hazard curves at six sites across the state and indicates the annual probability of exceeding a given level of ground motion at each site (the 0.0021 probability is represented by a single point on each of the curves). Probabilities of exceeding low ground motions less than 0.1 g are the highest and the probabilities of exceeding high ground motions near 1 g are generally 2 or 3 orders of magnitude lower. The hazard is quite high near San Bernardino because of proximity to two very active geologic structures, the San Andreas and San Jacinto faults. Eureka is located near several moderately active crustal faults (e.g., the Little Salmon, Mad River, Trinadad, and Fickle Hill faults) and directly over the Cascadia subduction zone that is thought to be capable of great (M 8 to 9) earthquakes. San Francisco is situated about 10 km from the segment of the San Andreas Fault that has slip rate about 17 - 24 mm/yr and about 20 km from the Hayward fault that has slip rate of about 9 mm/yr. These high slip rate faults combine to produce a significant seismic hazard in the San Francisco Bay area. Los Angeles is located near several faults and blind thrusts that have slip rates between 1 and 3 mm/yr and about 50 km from the section of the San Andreas Fault System that has a slip rate between 25 and 35 mm/yr. San Diego is located about 30 km from the offshore Coronado Bank Fault with slip rate of about 3 mm/yr and adjacent to the Rose Canyon Fault that is characterized by a slip rate of about 1.5 mm/yr. Therefore, the hazard levels at San Diego are somewhat lower than at the Los Angeles site. Sacramento has the lowest hazard levels of the cities shown (i.e., the probability of all levels of ground motions is lower than in many other regions of the state). Few known faults and low historical seismicity have been observed in this region. However, we cannot preclude the possibility that future earthquakes will occur in any of these areas of low hazard. In fact, the possibility of earthquakes up to M 7 have been included in the random background seismicity that is distributed everywhere across this map. Thus, the probability of exceeding large ground motions in Sacramento or any other site in California is never zero.
Figure 10: Hazard curves for peak ground acceleration and alluvial site conditions at various cities located across California. The curves indicate the probability of exceeding the given peak ground acceleration levels on alluvial site conditions.
The seismic hazard map and model presented in this report indicate that the hazard is high in many regions across the state, especially within about 50 km of the San Andreas fault system, the Eastern California Shear Zone faults, the western Transverse Ranges, and the Cascadia subduction zone. Earthquakes in populated regions have already caused considerable losses during the past 2 centuries that span California’s recorded seismic history. The hazard map is consistent with this historical seismicity, the historical damage patterns, and with geologic information regarding the slip rate and pre-historic earthquakes.
This study indicates that about three-fourths of California’s population resides in counties that have significant seismic hazard. This level of hazard reaffirms the need to examine existing infrastructure and verify that it is adequate to withstand the expected seismic shaking to prevent loss of life from structural collapse during an earthquake. The seismic hazard maps and models presented in this report should be useful for assisting policy makers, engineers, and scientists to plan for strong earthquake ground shaking.
We wish to thank the hundred or so individuals who reviewed and provided input for the source model and hazard mapping methodology. In particular we would like to thank George Saucedo, Siang Tan, Gary Taylor, Jerry Treiman, and Chris Wills for reviewing and compiling the geologic information across the entire state and the Working Group on Northern California Earthquake Potential for compiling the fault information for northern California. The Southern California Earthquake Center group led by Jim Dolan provided important review and input of the geologic parameters for southern California. Many scientists, engineers and public policy officials participated in the U.S. Geological Survey review meetings and committees including the Applied Technology Council that gave guidance regarding what parameters should be mapped. We also thank staff at DMG for drafting figures, assisting in GIS analysis, and editing text. We especially thank Lena Dida at DMG and Bob Simpson at USGS for reviewing the text. In addition we thank the Office of Emergency Services and Federal Emergency Management Agency for their support of the mapping in portions of southern California.
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