Probabilities of Large Earthquakes 

in the San Francisco Bay Region, 

California 

Total 30-year probability 

of one or more large earthquakes 

for entire region is 67 percent 

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Probabilities of Large Earthquakes 

in the San Francisco. Bay. Region, 

California 

By WORKING GROUP ON CALIFORNIA 

EARTHQUAKE PROBABILITIES 

U.S. GEOLOGICAL SURVEY CIRCULAR 1053 
DEPARTMENT OF THE INTERIOR 

MANUEL LUJAN, JR., Secretary 

U.S. GEOLOGICAL SURVEY 

Dallas L. Peck, Director 

Any use of trade, product, or firm names 

in this publication is for descriptive purposes only 

and does not imply endorsement by the U.S. Government 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1990 

Free on application to the 

Books and Open-File Reports Section 

U.S. Geological Survey 

Federal Center, Box 25425 

Denver, CO 80225 
WORKING GROUP ON CALIFORNIA EARTHQUAKE PROBABILITIES 

James H. Dieterich, Chainnan 

Clarence R. Allen 

Lloyd S. Cluff 

C. Allin Cornell 

William L. Ellsworth 

Lane R. Johnson 

Allan G. Lindh 

Stuart P. Nishenko 

Chris H. Scholz 

David P. Schwartz 

Wayne Thatcher 

Patrick L. Williams 

,, 

U.S. Geological Survey 

California Institute of Technology 

Pacific Gas & Electric Co. 

Stanford University 

U.S. Geological Survey 

University of California, Berkeley 

U.S. Geological Survey 

U.S. Geological Survey 

Lamont-Doherty Geological Observatory, 

Columbia University 

U.S. Geological Survey 

U.S. Geological Survey 

Lawrence Berkeley Laboratory 
PREFACE 

In 1987 a Working Group on California Earthquake Probabilities was organized by the U.S. Geological 

Survey at the recommendation of the National Earthquake Prediction Evaluation Council (NEPEC). The 

membership included representatives from private industry, academia, and the U.S. Geological Survey. The 

Working Group computed long-term probabilities of earthquakes along the major faults of the San Andreas 

fault system on the basis of consensus interpretations of information then available. Faults considered by the 

Working Group included the San Andreas fault proper, the San Jacinto and Imperial-faUlts of southern 

California, and the Hayward fault of northern California. The Working Group issued a final report of its 

findings in 1988 (Working Group, 1988) that was reviewed and endorsed by NEPEC. 

As a consequence of the magnitude 7.1 Lorna Prieta, California, earthquake of October 17, 1989, a 

second Working Group on California Earthquake Probabilities was organized under the auspices of NEPEC. 

Its charge was to review and, as necessary, revise the findings of the 1988 report on the probability of large 

earthquakes in the San Francisco Bay region. In particular, the Working Group was requested to examine the 

probabilities of large earthquakes in the context of new interpretations or physical changes resulting from the 

Lorna Prieta earthquake. In addition, it was to consider new information pertaining to the San Andreas and other 

faults in the region obtained subsequent to the release of the 1988 report. Insofar as modified techniques and 

improved data have been used in this study, the same approach might also, of course, modify the probabilities 

for southern California. This reevaluation has, however, been specifically limited to the San Francisco Bay 

region. 

This report is intended to summarize the collective knowledge and judgments of a diverse group of 

earthquake scientists to assist in formulation of rational earthquake policies. A considerable body of information 

about active faults in the San Francisco Bay region leads to the conclusion that major earthquakes are likely 

within the next tens of years. Several techniques can be used to compute probabilities of future earthquakes, 

although there are uncertainties about the validity of specific assumptions or models that must be made when 

applying these techniques. The body of this report describes the data and detailed assumptions that lead to 

specific probabilities for different fault segments. Additional data and future advances in our understanding of 

earthquake physics may alter the way that these probabilities are estimated. Even though this uncertainty must 

be acknowledged, we emphasize that the fmdings of this report are supported by other lines of argument and 

are consistent with our best understanding of the likelihood for the occurrence of earthquakes in the San 

Francisco Bay region. 

Ill 
/ 

CONTENTS 

Executive summary 1 

Introduction 4 

Method 5 

San Andreas fault 8 

Lorna Prieta earthquake 8 

Implications of the Lorna Prieta earthquake 11 

1906 earthquake slip distribution 12 

San Andreas fault slip rate 14 

Segmentation 16 

Recurrence times 18 

Southern Santa Cruz Mountains segment 20 

Northern Santa Cruz Mountains segment 20 

Mid-Peninsula segment 20 

San Francisco Peninsula segment 20 

North Coast segment 21 

Lorna Prieta earthquake stresses 21 

Summary of probabilities for the San Andreas fault 21 

Hayward and Rodgers Creek faults 22 

Hayward fault zone 22 

Segmentation 24 

Slip rate 24 

Slip per event 27 

Recurrence interval 27 

Probabilities 27 

Rodgers Creek fault segment 27 

Slip rate 27 

Slip per event and recurrence interval 27 

Probabilities 28 

Summary and discussion 28 

Acknowledgments 32 

References 32 

Appendix A-Recurrence models 37 

Renewal model 37 

Parametric uncertainty 38 

Time-predictable model 40 

Appendix B-Logic-tree analysis of San Andreas fault probabilities 42 

Segmentation 42 

Recurrence time 42 

Effect of Lorna Prieta stress changes 44 

Hypothesis tests 45 

Logic tree for model 2 displacements 45 

Probabilities 46 

Appendix C-Tabulations of probabilities 48 

Discussion of uncertainties 48 

v 
VI 

FIGURES 

1. Graph showing probability density function for earthquake recurrence 7 

2. Map of major faults of San Francisco Bay region 9 

3. Cross sections showing seismicity along San Andreas fault, 1969-1989 10 

4. Graph showing geodetically estimated 1906 coseismic slip and surface 

fault offsets along San Andreas fault 13 

5. Map of San Andreas fault segments 17 

6. Map of Hayward and Rodgers Creek fault segments 25 

7. Cross section showing seismicity along Hayward and Rodgers Creek 

faults, 1/1/69 to 1/31/90 26 

8. Graph of slip rate along Hayward fault determined from offset cultural 

features and small-scale geodetic surveys 26 

9. Schematic map showing conditional probabilities of earthquakes (M'2.7) 

in San Francisco Bay region 29 

A -1. Graphical interpretation of conditional probability, C ro 39 

A-2. Graph showing conditional probability, era, of an earthquake in the 

next 30 years 39 

B-1. Diagram of logic trees for San Francisco Peninsula, southern Santa 

Cruz Mountains, and North Coast segments of San Andreas fault 43 

C-1. Graph showing sensitivity of quartile probabilities and conditional 

probability to intrinsic uncertainty 51 

TABLES 

1. San Andreas and southern Calaveras fault slip rate information 15 

2. San Andreas fault segments 18 

3. Summary of San Andreas fault segment parameters 19 

4. Change of recurrence time resulting from simulated Lorna Prieta 

earthquake studies 22 

5. Probabilities of earthquakes along San Andreas fault 23 

6. Hayward and Rodgers Creek fault segments 23 

7. Hayward and Rodgers Creek fault segment parameters 24 

8. Probabilities of earthquakes along Hayward and Rodgers Creek faults 28 

9. Probabilities of one or more large earthquakes in San Francisco Bay 

regioo 31 ~ 

B-1. Weighted means of recurrence time, T, and net uncertainty, O'N, of San 

Andreas fault segments 46 

B-2. Displacement weights for recurrence time 47 

C-1. Probabilities of logic-tree branch tips 48 

C-2. Final probabilities 49 
Probabilities of Large Earthquakes in the 

San Francisco Bay Region, California 

By Working Group on California Earthquake Probabilities 

EXECUTIVE SUMMARY 

In 1988 a Working Group convened by the National Earthquake Prediction Evaluation Council 

(NEPEC) issued a report (Working Group. 1988) assessing the long-term probabilities of large 

earthquakes (magnitude 7 or greater) along the San Andreas fault system. NEPEC organized the 

present Working Group to reexamine the probabilities of large earthquakes in the San Francisco Bay 

region. in light of new interpretations or physical changes resulting from the Lorna Prieta earthquake 

of October 17. 1989. and new data developed since the 1988 report. 

We now estimate the chance of one or more large earthquakes in the San Francisco Bay region 

in the coming 30 years to be about 67 percent. A magnitude 7 or larger earthquake along any of the 

segments considered by the Working Group will have a major impact on the entire San Francisco Bay 

region. 

The first step in the evaluation procedure is to identify fault segments expected to produce large 

earthquakes. and then to estimate the time to the next earthquake on each identifi~d segment. The 

recurrence times for earthquakes on a segment are based on the records of historic earthquakes, 

the long-term slip rate. and the displacement in the previous earthquake. The approach followed 

for calculation of probabilities employs the estimated recurrence times with a model that assumes 

that probability increases with elapsed time from the last large earthquake on a fault segment. The 

minimum information required for this analysis of the San Francisco Bay region is available only for the 

San Andreas. Hayward. and Rodgers Creek faults. Other potentially important faults in the region will 

require more study before they can be evaluated. Hence. the calculated probabilities are necessarily a 

minimum estimate of the hazard. 

Principal changes from the 1988 report and new factors considered by the Working Group that 

affect the estimates of probabilities are 

• Addition of the Rodgers Creek fault segment. Data on the Rodgers Creek fault (see map of 30-

year probabilities on following page) collected since 1988 permit probabilistic assessment of that 

fault for the first time. 

• Faster fault-slip rates. Estimates of the long-term rates of slip on the San Andreas and Hayward 

faults are revised upward relative to the previous estimates. A higher slip rate shortens the 

expected time to the next earthquake and increases the likelihood of an earthquake. The Working 

Group estimates the slip rate on the San Andreas fault within the San Francisco Bay region to 

be 19 mm/yr compared to the previous (1988) Working Group estimate of 16 mmfyr. The slip 

rate on the Hayward fault is now estimated at 9 mm/yr compared to the previous estimate of 

7.5 mm/yr. 

Manuscript approved for publication, July 19, 1990. 

1 
Rodgers Creek fault 

M-7, P=0.22 Total30-year probability of one or 

more major earthquakes = 0.67 

Northern East Bay 

segment: M-7, P=0.28 

Southern East Bay 

ent: M-7, P=0.23 

~~- V(,?~ 

30-YEAR PROBABILITIES (P) OF LARGE EARTHQUAKES (M~7) IN THE SAN FRANCISCO BAY REGION 

Column heights are proportional to 30-year probability of earthquake rupture 

• Effects of the Lorna Prieta earthquake on the San Andreas fault. The probability of an earthquake 

on the segment where the Lorna Prieta earthquake occurred (southern Santa Cruz Mountains 

segment) is low following that earthquake. Models of crustal deformation indicate that stress 

increased on nearby segments of the San Andreas fault as a result of the Lorna Prieta earthquake. 

The stress increase shortens the time to the next earthquake on these segments. However. it is 

not known if the magnitude of this effect is large enough to be significant. 

Because the quality of the data . the uncertainties relating to segmentation . and the uncertainties 

in application of the model vary from segment to segment. the Working Group has assigned letter 

grades to indicate its judgment of the reliability of the calculated probabilities. The reliability scale 

extends from A to E with A being the most reliable. Probabilities are expressed as numbers that range 

between 0 and 1. Differences of probability of less than 0.10 are not considered meaningful. A 30-year 

probability of 0.20 means there is a 20-percent chance of an earthquake in the coming 30 years. The 

probabilities for the seven segments considered in this report are summarized in the following table. 

2 
Probabilities of earthquakes on fault segments in the San Francisco Bay region 

Level of 

reliability 

Previous Expected Probability (scaled A toE; 

Segment event magnitude 1990-2020 A most reliable) 

San Andreas fault 

S. Santa Crus Mountains 1989 7 <0.01 B 

San Francisco Peninsula 1906 7 .28 c 

North Coast 1906 8 .02 B 

Hayward fault 

Southern East Bay 1868 7 .28 c 

Northern East Bay 1886 7 .28 D 

Rodgers Creek fault 1808 7 .22 D 

(or earlier) 

• Four fault segments have been identified that have a probability in the range 0.20 to 0.30 of 

producing a large earthquake (magnitude about 7) in the coming 30 years. . 

• The probability of a magnitude 7 earthquake along the southern Santa Cruz Mountains segment 

that produced the 1989 Lorna Prieta earthquake is now less than 0.01. The previous study 

(Working Group. 1988) had assigned a probability of 0.3 to this segment prior to the earthquake. 

Although the potential for damage from an earthquake generally decreases as distance from the 

epicentral region increases. the pattern of losses at rather large distances from the magnitude 7.1 Lorna 

Prie.ta earthquake clearly demonstrates that an earthquake on any of the fault segments considered by 

the Working Group could seriously affect the entire San Francisco Bay region. Indeed, the most densely 

populated parts of the area lie atop of. or adjacent to, fault segments having the greatest potential for 

large earthquakes. 

The probability that the San Francisco Bay region will experience at least one large earthquake on 

the segments considered is given by the following table. 

Probabilities of one or more large earthquakes in the San Francisco Bay region 

Segments 

Probability for intervals 

beginning 1/1/90 

5 yr 10 yr 20 yr 30 yr 

Level of 

reliability 

(A toE; 

A most reliable) 

North Coast, San Francisco 0.15 0.88 0.50 0.67 B 

Peninsula, N. East Bay, S. East Bay, 

and Rodgers Creek 

The probability of one or more large earthquakes in the San Francisco Bay region in the coming 

30 years is now estimated to be 0.67. The previous NEPEC Working Group (Working Group. 1988) 

found the probability to be about 0.5. but that aggregate probability did not include either the southern 

Santa Cruz Mountains segment or the Rodgers Creek fault. About half of the increase of probability 

from the previous report can be ascribed to adding the Rodgers Creek fault segment to the list of 

major earthquake sources. The remaining increase is due to smaller increases of the probabilities of 

earthquakes on the previously recognized fault segments. resulting primarily from new estimates of 

fault-slip rate. We consider these aggregate probabilities to be significantly more reliable than the 

probabilities of earthquakes on individual segments. 

3 
These cumulative probabilities for large earthquakes in the San Francisco Bay region are consistent 

with the observed rate of occurrence of such events during the 19th century. The average (Poisson) 

30-year probability of earthquakes greater than magnitude 7 since 1836 is 0.5. and the somewhat higher 

value of about 0.7 estimated here reflects the higher rate of activity that is expected as the post-1906 

earthquake quiescence ends and the 19th-century activity level resumes. 

This study was limited to evaluating the probabilities of large earthquakes on the San Andreas. 

Hayward. and Rodgers Creek faults. In the present assessment. these faults account for only 28 mm/yr 

of the 33 to 40 mmjyr of deformation that takes place across the entire San Andreas fault system in 

the region. Some or all of this unaccounted-for deformation may represent a potential for earthquakes 

on other important faults in the San Francisco Bay region. such as the Calaveras. Concord. Greenville. 

Green Valley, and San Gregorio faults. At present. however. there is not sufficient information to 

specifically address the time-dependent probability of earthquakes originating along these other faults. 

Hence, the probabilities reported here should be regarded as minimum values. 

The assessment of long-term seismic hazard on California's major faults continues to be a rapidly 

developing field. Models for the determination of probabilities and the data employed in those models 

are subject to uncertainty and alternate interpretations. In the future. new data and more refined models 

will undoubtedly lead to somewhat different probabilities for specific fault segments. However. the total 

aggregated probabilities are less sensitive to the detailed recurrence characteristics of the individual 

segments. This characteristic of the aggregated probabilities supports the principal conclusion of this 

study: There is a high likelihood of a major earthquake in the San Francisco Bay region within 

the next 30 years. 

INTRODUCTION 

The October 17, 1989, Lorna Prieta earthquake caused 62 deaths, 3, 757 injuries, and more than 

$6 billion in property damage (Plafker and Galloway, 1989). Earthquakes of comparable or larger 

size will certainly occur along other, more densely populated segments of the San Andreas and 

Hayward faults. Such earthquakes will result in far greater losses than experienced from the 1989 

earthquake. For example, about 1,260,000 people live within the epicentral region1 of an expected 

magnitude 7 earthquake along the northern East Bay segment of the Hayward fault. That is about 

10 times as many people as the 130,000 who live within the epicentral region of the Lorna Prieta 

earthquake (Brian Kilgore, written commun., 1989). 

The record of past earthquakes, along with related geodetic, geologic, and seismic observations, 

provides the principal means for evaluating the potential for future earthquakes. With the 

occurrence of the 1989 Lorna Prieta earthquake, California has now experienced at least 12 large 

earthquakes of magnitude 7 or greater since 1812. Five of these earthquakes affected the greater 

San Francisco Bay region. The San Andreas fault on the San Francisco Peninsula produced the 

earthquake of 1838 (probable magnitude 7) and the great earthquake of 1906 (magnitude about 

8). Additionally there was the earthquake of 1865 that appears similar to the recent Lorna Prieta 

earthquake and possibly affected the same segment of the San Andreas fault south of the San 

Francisco Peninsula. Along the eastern side of San Francisco Bay, earthquakes of about magnitude 7 

originated on the Hayward fault in 1836 and 1868. 

The 1988 Working Group estimated the 30-year probability of one or more magnitude 7 

earthquakes in the San Francisco Bay region to be 0.5. This probability was aggregated from the 

probabilities computed for individual fault segments, which included the San Francisco Peninsula 

segment of the San Andreas fault and two segments of the Hayward fault (the northern East Bay 

segment and the southern East Bay segment). An additional segment, the southern Santa Cruz 

1 The epicentral region is the area of most intense ground motion on bedrock sites and is, for this example, 

defined as the area lying within 10 km of the earthquake fault rupture. 

4 
Mountains segment at the southern end of the San Francisco Peninsula segment, was not included 

in this aggregation, because the reliability of the forecast was considered to be low and because 

the earthquake was expected to have a magnitude less than 7. However, this segment had a higher 

30-year probability (0.3) than any other segment in the region. Within the uncertainty associated 

with the definition offault segments, the October 17, 1989, magnitude 7.1 Lorna Prieta earthquake 

occurred on the southern Santa Cruz Mountains segment. 

The principal reason for undertaki~g this review of San Francisco Bay region probabilities 

was the occurrence of the Lorna Prieta earthquake. The Lorna Prieta earthquake could affect 

probabilistic assessments in two ways. First, the earthquake provides an added source of data that 

may alter interpretations of earlier observations that served as the basis for probability calculations. 

Second, slip on the Lorna Prieta earthquake segment altered the stress state on other fault segments; 

as a consequence of the Lorna Prieta earthquake, segments may now be closer or farther from failure 

than they were before the earthquake. 

Two additional factors provided impetus for this review. The first is new information on 

slip rate and earthquake recurrence for the Hayward and Rodgers Creek faults. The second is 

consideration of several features of the regional seismicity that may indicate an increased potential 

for large earthquakes. These include an apparent return to the higher rates of earthquake activity 

of the 1800's following a post-1906 lull in earthquake rates, migration of moderate earthquakes 

northward along the Calaveras fault to the southern end of the Hayward fault, and possible pairing 

of large earthquakes on the San Andreas fault with large earthquakes on the Hayward fault. 

Methods and models for estimation of earthquake probabilities are at an early stage of 

development, and we expect future research to provide more refined approaches. Input parameters 

for the calculation of probabilities are by their nature subject to alternative interpretations that 

may affect specific assessments of hazard. An important emphasis of this Working Group study was 

to explore and weigh alternate interpretations relevant to assessing the potential for earthquakes. 

The development of improved methods, the acquisition of new data, and the inevitable occurrence 

of earthquakes in the San Francisco Bay region will necessitate future revisions of this report. 

However, other lines of argument, which are not dependent on the details of the probabilistic 

model we have employed, also lead to the conclusion that there is a significant chance of one 

or more large earthquakes in the region in the coming decades. Those arguments are based on 

historical frequency of large earthquakes and a consensus that strain energy is accumulating that 

will be released in future large earthquakes. 

METHOD 

For this report, probabilities of earthquake recurrence have been calculated following the 

approach described in the 1988 Working Group report. We briefly outline the method here and 

refer the interested reader to appendix A for additional explanation. The approach used in this 

study is based upon a model of earthquake occurrence that assumes that the probability of an 

earthquake along a fault segment is initially low following a large segment-rupturing earthquake 

and increases with time as stress on the segment recovers the stress drop of the prior earthquake 

(Rikitake, 1974; Hagiwara, 1974). Fault segments expected to rupture in coming earthquakes are 

delineated using a variety of observations and judgments. We have reviewed the fault segmentation 

employed for the 1988 report and in some cases revised segment boundaries. 

Probabilities of the occurrence of the next segment-rupturing earthquake in some time interval 

are obtained from a probability density function for the random time of recurrence, T. We have 

followed the practice of the 1988 Working Group and employed the lognormal distribution. The 

current San Francisco Bay region forecasts are not sensitive to this particular choice of distribution 

function. Input parameters for the calculation of the pro_bability of recurrence alon~ a particular 

fault segment are Te, the elapsed time since the last segment-rupturing earthquake; T, the median 

5 
recurrence interval of the next segment-rupturing event; and u, a measure of the dispersion or 

spread in the recurrence· time distribution. Time is set to zero at the occurrence of the most recent 

earthquake. 

The fraction of all earthquake recurrence times in an interval (t, t + ~T) is obtained from the 

lognormal probability density function by integration: 

l

t+AT 1 [In ujf'j2 P(t ~ T ~ t+ ~T) = Vf,rexp{- 2 }du. 

t uu 21r 2u (1) 

The probabilities we report below employ the additional knowledge that the earthquake has not 

occurred prior to time Te. The probability conditional on the earthquake not having occurred prior 

toTe is 

P(T < T < T + ~TIT > T ) = P(Te ~ T ~ Te + ~T) e - - e e 1 - P(O ~ T ~ Te) (2) 

Figure 1 illustrates a lognormal probability density function and the graphical interpretation 

of the probabilities appearing in equation (2). All probabilities reported below are conditional 

probabilities and employ Te corresponding to January 1, 1990. 

For every fault segment considered in this report, an estimation of the median recurrence time, 

T, has been obtained using the time-predictable method (Reid, 1910; Shimazaki and Nakata, 1980). 

According to the time-predictable method, the most likely elapsed time to the next earthquake 

equals the slip in the last event divided by the average slip rate: 

(3) 

where D is the best (median) estimate of displacement in the previous segment-rupturing 

earthquake and V is the best (median) estimate of the long-term slip rate. 

For a lognormal distribution, u represents the standard deviation2 of the natural logarithm 

of the recurrence time. We have taken as u the total or net standard deviation, u N, which is the 

square root of the sum of the squares of two components: (1) uP, a parametric uncertainty in 

T arising from the uncertainties in D and V, and (2) u t' an intrinsic uncertainty which reflects 

the event-to-event variability in recurrence times when T is perfectly known. From the Nishenko 

and Buland (1987) study of the intrinsic variability of characteristic recurrence times for circumPacific earthquakes, an estimate of the (marginal) intrinsic uncertainty is 0.21. Because recurrence 

data are limited, the value of u1 may not be well defined, particularly for strike-slip earthquakes 

(Savage, 1990; J.C. Savage, written commun., 1990). Uncertainty in u1 strongly affects attempts 

to estimate uncertainties in the calculated probabilities (see appendix C). However, the total value 

of u N (parametric and intrinsic uncertainties combined) and consequently calculated probabilities 

are not very sensitive to this intrinsic value in our present application due to the larger values of 

the parametric uncertainty, uP. 

Below, we review the data and interpretations that affect the determination of earthquake 

probabilities in the San Francisco Bay region. A method for quantitative treatment of alternate 

interpretations of the data for San Andreas fault segments is outlined below and presented in 

greater detail in appendix B. 

Following the convention established by the previous Working Group report (1988), we have 

assigned letter grades to the consensus probabilities to indicate our judgment of the quality and 

completeness of the data used to estimate those probabilities. The segments are ranked from A to 

E. The segments judged to have the most reliable data are ranked A; E indicates the least .reliable 

2 Throughout this report u is used to indicate the standard deviation of the log of an estimate. Where it is 

necessary to indicate the standard deviation of an estimate, the symbol S is employed. ± values give the numerical 

value of the standard deviation of the estimate. 

6 
~ C/) 

z 

w 

Cl 

~ ::J 

m 

<( 

m 

0 

a: 

a.. 

0 

0 

TIME 

Figure 1. Probability density function for earthquake recurrence. 

Conditional probability in interval (Te ~ T ~ Te + ~T}. given elapsed 

time Te. is ratio of area of dark shading to sum of areas with dark and 

light shading. 

data. For levels of reliability C, D, and E, both the evaluation of segment length (and the related 

magnitude} and the probability value may change significantly with additional data. 

Consensus probabilities reported below are reported to two decimal places, but we emphasize 

that differences of less than a tenth are not considered meaningful. In appendix C we tabulate 

the probabilities for time intervals of 5, 10, 20, and 30 years. Appendix C includes tabulations of 

probabilities resulting from the different alternatives for the San Andreas fault. The probabilities 

based on the alternatives were combined following established procedures (appendix B) to arrive 

at the final consensus probabilities. In appendix C, we also report quantitative confidence limits 

to provide a measure of the range of probabilities permitted by the parametric uncertainty. 

The probabilities of large-magnitude earthquakes considered in this report constitute a 

hypothesis that will either prove to be viable or will be rejected in the coming years. Parameters 

relevant to the success or failure of these forecasts principally relate to the timing, location, and 

length of rupture. Secondary parameters such as the amount of fault slip and derivative parameters 

such as earthquake magnitude are inherently less well defined in these forecasts. 

Segment boundaries have been chosen on the basis of whatever seismic, geologic, and geodetic 

evidence is available. Different pieces of evidence usually agree to within 5-10 km, and on this basis 

we estimate an uncertainty of rupture boundaries of about ±10 km (± values represent estimates 

of one standard deviation}. We would consider a segment forecast to be successful if more than 

50 percent of the segment ruptured during an earthquake. 

The relation between the surface expression of a fault and the actual fault surface at depth may 

be complex. An example of this is given by evidence of the complex three-dimensional structure of 

the aftershock zone and the diversity of aftershock focal mechanisms of the Lorna Prieta earthquake 

(Dietz and Ellsworth, 1990). Experience from the Lorna Prieta earthquake and mismatch between 

the 1984 Morgan Hill earthquake and the surface trace of the Calaveras fault lead us to estimate 

the horizontal uncertainty of a segment, measured perpendicular to the fault trace, to be about 

7 
±2.5 km. Extreme variations of ±5 km may occur in mountainous regions where complex fault 

zones that include nonvertical faults with significant dip-slip components of motion are common. 

Uncertainties in segmentation also apply to the depth interval that produces the earthquake. 

On those segments with microearthquakes, the maximum depth of significant microseismicity marks 

the probable lower depth limit of earthquake rupture (Sibson, 1984). For the San Andreas fault 

segments considered here, we estimate the maximum depth of rupture to be 17 ± 3 km, and for 

the Hayward and Rodgers Creek faults, we estimate it to be about 12 ± 3 km. The upper limit 

of rupture is problematical. Where the fault shows no evidence of surface creep, an upper limit 

of 2 ± 2 km is suggested. For fault segments that are creeping at the surface, the upper limit of 

earthquake rupture may vary from the surface to the maximum depth of creep. 

The amount of slip has not beE:n explicitly considered. Rather we assign moment magnitudes 

based on segment length and the empirical length-displacement relation (D = 2.8 x 10-6 L) 

employed by the previous 1988 Working Group. We emphasize that the slip values used to 

establish T are not predictive values for the next earthquake. When we combine the uncertainties 

estimated above with a So-percent uncertainty in slip in the next event, we obtain an estimate 

of the uncertainty of about ±0.3 moment magnitude units. Because the forecasts in this report 

are for strike-slip earthquakes and because significant dip-slip motion may sometimes occur (as 

in the case of the Lorna Prieta earthquake), the displacement estimates and resulting magnitude 

estimates apply only to the strike-slip component of faulting. 

SAN ANDREAS FAULT 

Data relating to the assessment of earthquake probabilities for the San Andreas fault from 

San Juan Bautista to San Francisco permit a number of alternate interpretations that affect the 

calculation of earthquake probabilities. Although the Lorna Prieta earthquake of October 17, 1989, 

has provided important new information for this section of the fault, it has not narrowed the number 

of permissible interpretations. Below, we review the interpretations employed in the 1988 Working 

Group report in the context of the Lorna Prieta earthquake. Following this we discuss the different 

possibilities that arise in evaluating the segmentation of the fault and in the estimation of median 

recurrence times. 

Depending upon choices made at each step in the evaluation, these alternate interpretations 

result in different outcomes for earthquake probabilities. Because the Working Group considered 

several alternatives to have significant merit, we have employed a "logic tree." A logic tree is 

a formalism that permits quantitative incorporation of the principal uncertainties into our final 

consensus evaluation of the San Andreas fault. At each decision point in the analysis, branches are 

added representing the principal alternatives. The analysis continues in parallel along each branch 

which in turn repeatedly branches as additional decision points are encountered. A probability is 

associated with the tip of each branch of the tree. The probability results from the series of choices 

leading to that particular tip. To arrive at a final consensus probability, the branchings at every 

decision point are assigned weights (that add up to 1.0) based on 'the judgment of the Working 

Group. The weight of a probability at a tip is the product of the branch weights leading to that 

tip. The final probability is the sum of the individual weighted probabilities. At the end of this 

section on the San Andreas fault, we summarize the consensus probabilities resulting from the logic 

tree analysis. Details of the logic tree analysis are presented in appendix B. 

LOMA PRIETA EARTHQUAKE 

The Lorna Prieta earthquake of October 17, 1989, was located along the southern portion of the 

1906 earthquake break in the southern Santa Cruz Mountains (fig. 2). The earthquake rupture, as 

deduced from the aftershock distribution and geodetic measurements of the coseismic deformation, 

initiated at a point 18 km beneath the surface and broke upward to within 4 to 6 km of the surface 

8 
Hollister 

0 

122 B' 

Figure 2. Major faults of San Francisco Bay region (dotted where inferred). Shaded area shows 

approximate aftershock area of October 17, 1989, Lorna Prieta earthquake. A-A', B-B'. C-C'. and 

D-D' are endpoints of cross sections shown in figures 3, 4, 7, and 8, respectively. 

{fig. 3). It did .not produce a surface break. The rupture extended along strike for 35 to 40 km and 

involved right-reverse slip on a plane dipping 70° to the southwest. Preliminary dislocation models 

of the source based upon geodetic data indicate 1.6± 0.3 m ofright-lateral strike-slip displacement 

and 1.2 ± 0.4 m of reverse slip (Lisowski and others, 1990). Details of the distribution of slip with 

depth and along strike are not available at this time. 

A number of studies have considered the long-term seismic potential for the part of the 

San Andreas fault assumed to have ruptured in the Lorna Prieta earthquake {Lindh and others, 

1982; Lindh, 1983, 1988; Sykes and Nishenko, 1984; Scholz, 1985; Thatcher and Lisowski, 1987). 

These studies assumed slip rates varying from 12 to 20 mm/yr and also differed significantly in 

9 
A. 01 /01/69 to 10/17/89 

San Francisco 

A 

~ 0 

~ 

I -10 1- 0 0 

c... 

w 

0 -20 

B. Lama Prieta mainshock and aftershocks 

~ 

~ 

~ -1 0 

c... 

w 

0 -20 

A 

160 140 120 

Crystal Springs 

Reservoir 

t 

Portola Valley 

t 

Lama Prieta 

San Juan 

Bautista 

t A' 

S.F. PENINSULA SEGMENT, WORKING GROUP (1988) ) 

SSCM SEGMENT, 

\.. WORKING GROUP (1988) ) 

SYKES AND NISHENKO (1984) ) 

I.. ____ LI_ND_H_:.(_19_83-'- ) _ ___..) 

A' 

8> 0 

a. 

100 80 60 40 20 0 

DISTANCE (KM) 

Figure 3. Seismicity along San Andreas fault. 1969-1989. A. seismicity before lorna Prieta earthquake. 

and B. aftershocks of lorna Prieta earthquake. Size of symbols increases with increasing magnitude. 

Bars below section A indicate location of fault segment forecasts discussed in text: southern Santa 

Cruz Mountains segment of Working Group (1988) is indicated by initials SSCM. Rectangles in section 

B give location of lorna Prieta earthquake rupture inferred from geodetic data (Lisowski and others. 

1990). locations of section endpoints. A-A'. are shown in figure 2. 

estimates of the amount of slip at seismogenic depths in the great earthquake of 1906. Lindh (1983, 

1988) obtained a 30-year probability of 0.47, and Sykes and Nishenko (1984) obtained a 20-year 

probability of 0.19 to 0.95. 

In 1988 the Working Group on California Earthquake Probabilities reassessed these probability 

estimates. Geodetic estimates of the 1906 earthquake slip distribution were relied on to divide the 

fault into segments and to constrain 1906 slip values used in the calculation of expected recurrence 

time. Two segments considered by the 1988 Working Group are relevant to the Lorna Prieta 

earthquake. They are the San Francisco Peninsula segment (30-year probability of 0.2) and the 

southern Santa Cruz Mountains segment (30-year probability of0.3). Although the southern Santa 

Cruz Mountains segment was assigned the highest probability in the region, a low level of reliability 

(Eon the A-to-E scale used in the 1988 report) was attached to the probability estimate for that 

segment because seismic history and slip were not well defined. 

The location and dimensions of the 1989 earthquake most closely correspond to the forecast 

of Lindh and others (1982) and Lindh (1983, 1988), but the magnitude was larger than anticipated 

(fig. 3). At M 7.1, it was close to the magnitude forecast by Sykes and Nishenko (1984) for a 

75-km-long segment. The Lorna Prieta earthquake occurred on parts of two segments defined 

by the 1988 Working Group: the southern Santa Cruz Mountains segment and the San Francisco 

10 
Peninsula segment. The Lorna Prieta earthquake rupture is about the same length as the segment 

defined by the 1988 Working Group as the southern Santa Cruz Mountains segment, but the center 

of that segment is about 15 km to the south of the center of the earthquake rupture. 

IMPLICATIONS OF THE LOMA PRIETA EARTHQUAKE 

An important question is the extent to which slip in the 1989 earthquake represents recurrence 

of slip on this part of the 1906 rupture. If the 1906 slip observations apply to the source region of the 

Lorna Prieta earthquake, then we may take 1906 as the appropriate previous event for interpreting 

the Lorna Prieta earthquake and the various means of forecasting its occurrence. If, on the other 

hand, the 1989 earthquake source region moved little or not at all in 1906, then we may draw 

incorrect conclusions when 1906 is taken to be the prior rupture. 

Present information is insufficient to definitively resolve this issue. The 1906 earthquake 

rupture extended at least as far south as the Lorna Prieta earthquake rupture zone, as evidenced 

by the large displacement of the Lorna Prieta triangulation bench mark and by faulting in the 

Wright-Laurel tunnel. However, we do not know how the 1906 fault displacement varied along 

strike, whether it reached the surface, where it terminated, if there was a reverse-slip component, 

or how it varied with depth. The geodetic observations of the 1906 earthquake only indicate that 

there were large ( ""2.5 m) right-lateral displacements from near the surface to a depth of 5 to 10 km 

at Lorna Prieta (Thatcher and Lisowski, 1987). The data cannot be used to resolve the amount 

of slip at greater depths. Thus, the 1989 earthquake rupture probably overlaps at least some of 

the 1906 rupture below a depth of about 5 km, but could have significant differences in the depth 

distribution of slip. 

It is also possible that the 1989 and 1906 slip occurred on different but closely spaced fault 

planes. Certainly the prominent thrust faulting component of the 1989 earthquake is unlikely to 

occur in every event. Along this part of the San Andreas fault zone there are other narrowly spaced 

fault strands, in particular the Sargent fault. However, the stress drop produced by the Lorna Prieta 

earthquake is likely to have affected a sufficient volume of crust such that it makes little difference 

which of several closely spaced fault planes slipped. Acknowledging all of the uncertainties, the 

Working Group judges the currently available evidence to favor the interpretation that, for the 

purposes of this study, the 1989 earthquake represents recurrence of slip along the 1906 fault 

break. 

The occurrence of the 1989 Lorna Prieta earthquake, within two years of the publication of 

the 1988 Working Group's report, provides a test of prior interpretations and assumptions for 

this part of the San Andreas fault. Earlier estimates of recurrence time (Lindh and others, 1982; 

Lindh, 1983; Sykes and Nishenko, 1984; Scholz, 1985; Thatcher and Lisowski, 1987; Lindh, 1988; 

Working Group, 1988) differed significantly because of differences in assumed slip rate and 1906 

displacement. The southern half of the Lorna Prieta earthquake rupture was within the southern 

Santa Cruz Mountains segment, which was assigned a 1906 fault slip of 200±50 em by the Working 

Group (1988). The northern half of the Lorna Prieta earthquake rupture was within the San 

Francisco Peninsula segment, which was assigned a 1906 slip of 250 ± 60 em based on displacement 

of the Lorna Prieta triangulation benchmark. These displacements divided by the assumed slip 

rate of 16 ± 2.5 mm/yr yield estimates of median recurrence time, T, of 125 years for the southern 

Santa Cruz Mountains segment and 156 years for the San Francisco Peninsula segment. Does the 

occurrence of the Lorna Prieta earthquake only 83.5 years (1906.3-1989.8) after the most recent 

earthquake "disprove" the Working Group (1988) recurrence estimates? 

A statistical hypothesis test can be constructed. The Working Group {1988) not only estimated 

recurrence time intervals, they also stated their then-current uncertainty in recurrence time through 

the parameter uP and included the effect of uP in their probability estimates. Therefore, a 

hypothesis test of their stated position should be based on the {log) observed recurrence time 

{83.5 years), {log) median recurrence time estimate, T, (125 or 156 years), and their total 

11 
uncertainty,3 uN (=0.36). Specifically, one should reject the 1988 committee's hypothesis if 

In (83.5) <In T- ~ uN, (4) 

in which ~ characterizes the significance level of the test (1.96 and 1.65 for a significance level of 

1 percent and 5 percent, respectively). The conclusion is that we can accept either the 125-year 

or 156-year hypothesis for T at the 1-percent significance level, whereas at the 5-percent level one 

may accept the 125-year estimate but should reject the 156-year estimate. In short, the observed 

83.5-year recurrence interval is consistent with the 1988 Working Group's statements, although only 

marginally so with respect t9 the segmentation interpretation that yielded the 156-year estimate. 

On the other hand, after the event, given the "closed interval" of 83.5 years, the uncertainty 

of the log of the hypothesized median is no more than4 u/Vfi, where n is the sample size (here, 

n = 1). In this case, one can reject any mean that might be hypothesized whose (log) median is 

In T < In (83.5) + ~u.Jii. (5) 

For u = 0.21, n = 1, and ~ = 1.65 (or 1.96), this value ofT is 118 years (or 126 years). 

In this sense, the 1988 Working Group estimates ofT were somewhat large. The method 

of estimating T for segments of the San Andreas fault north of San Juan Bautista relied on 

interpretations of 1906 displacements and fault slip rate similar to those employed for the Lorna 

Prieta section of the fault. Consequently, if the 1988 Working Group overestimated the recurrence 

time for the section of the San Andreas fault that ruptured in the Lorna Prieta earthquake, then 

recurrence times for other segments of the San Andreas fault north of San Juan Bautista may also 

have been overestimated. 

1906 EARTHQUAKE SLIP DISTRIBUTION 

Figure 4 summarizes fault slip information for the great M,..,8 earthquake of 1906 from San 

Juan Bautista to Mussel Rock. These data are from observations of surface fault offsets (Lawson, 

1908) and modeling of geodetic observations (Thatcher and Lisowski, 1987) based on triangulation 

measurements made prior to and following the earthquake (Hayford and Baldwin, 1908). Surface 

fault offsets provide point observations of slippage. Because offset features seldom span the entire 

zone of earthquake slip and because distributed deformation is possible in near-surface materials, 

surface offsets often represent lower bounds to the total slip at depth. In principle, the geodetic 

observations reflect the total earthquake slip at depth, over large areas of the fault surface and 

across the full width of the fault zone. However, slip distribution from the geodetic observations 

must be inferred from modeling, which introduces its own uncertainties. Geodetic slip on the 

segment centered near Mussel Rock is estimated from observations at Mt. Tamalpais (not shown 

in fig. 4), which is about 20 km northwest of Mussel Rock. 

Northwest of Crystal Springs Reservoir (109 km on fig. 4) the surface fault offset values show 

considerable scatter, but their maximum values of 4 to 5 m are consistent with the geodetic 

estimates. For this segment (part of the North Coast segment) the previous Working Group used 

a slip value of 4.5 ± 0.5 m. Farther to the southeast the surface offset data are sparser and give 

maximum values that are considerably less than those determined geodetically. Between Crystal 

Springs and Woodville (now Woodside) the two available surface offset values are about 2.3 m, 

whereas the geodetic estimates are between 3.1 and 3.4 m. Southeast of Page Mill Road the lowest 

geodetic slip estimate is 2.3 ± 0.2 m and the largest surface offset is 1.5 m. The previous Working 

3 The net uncertainty values given in table 1 of the 1988 report are erroneously stated. However, the correct 

values were used in the calculation of probabilities stated in that report. 

4 See equation 8. 

12 
Figure 4. Geodetically estimated 1906 coseismic slip (lines) and surface fault 

offsets (dots) along San Andreas fault. Endpoints of plot. B-B'. are shown in 

figure 2. Triangles at top of figure project location of three important benchmarks. 

Solid line shows fault-slip model from Thatcher (1975). with one-standard-deviation 

error (stippled areas). Dotted line shows model calculation in which all observations 

made prior to about 1880 have been deleted . Dashed line plots slip distribution 

obtained when additional fault segment centered near Black Mountain is included 

in fault model (Thatcher and Lisowski. 1987). Dotted and dashed vertical bars show 

one-standard-deviation error. Horizontal arrow shows inferred extent of rupture in 

the 1989 Lorna Prieta earthquake. 

13 
Group used slip values of 2.5 ± 0.6 for the San Francisco Peninsula segment and 2.0 ± 0.5 for the 

southern Santa Cruz Mountains segment at the south end of the 1906 rupture. 

SAN ANDREAS FAULT SLIP RATE 

Sources of information for estimating the slip rate along the San Andreas fault include the 

record of large historical earthquakes, ages of offset geological features, and geodetic observations 

of displacement rates near the San Andreas fault. Interpretation of each data set is currently 

subject to uncertainty. Slip rate estimates are summarized in table 1. 

Geological studies give slip rates generally in the range of 10 to 25 mm/yr. These rates tend 

to be lower than some other estimates, but it should be noted that geologic slip rates are subject 

to the same limitations as the geologic observations of 1906 slip and tend to underestimate the full 

slip rate. On the San Francisco Peninsula, a 28-km offset of the 1- to 3-million-year-old gravels 

of the Santa Clara Formation gives a slip rate of 10 to 30 mm/yr (Cummings, 1968). A later study 

by Cummings (1983), of another facies of the Santa Clara Formation, found roughly 3-km offset 

of 0.45--million-year-old gravels indicating a slip rate of about 8 mm/yr. Offset of units 1.8 to 5 

million years old gives a slip rate of 6 to 22 mm/yr (Addicott, 1969). Near Lake San Andreas, 

Hall (1984) dated a Holocene offset of a stream channel, which yielded a minimum slip rate of 

12 mm/yr. The trench at this site was recently reopened (N.T. Hall, written commun., 1990) in 

hope of obtaining better constraints on the slip rate. Seven charcoal samples from the horizon used 

to develop the original slip rate were dated and gave a range of 1,800 to 2,800 14C years before 

present. This age range results in a reduction of the minimum geologic slip rate to 7.5 mm/yr for 

the past 1,800 years. Finally, at Point Arena, 200 km to the north of San Francisco, a study of 

offset terraces by Prentice (1989) yielded an upper limit for. slip rate of about 25 mm/yr for the 

San Andreas fault. 

Geodetic measurements provide detailed data on the short-term strain rates in the vicinity 

of the San Andreas fault, but interpretations of those observations to infer slip rates currently 

have considerable uncertainty. Prescott and others (1981) report a lower-bound slip rate of 

12.2±4 mm/yr (the net displacement rate across a 40-km-wide zone centered on the San Andreas 

fault). Dislocation model inversions of the data by Prescott and others (1981), assuming deep slip 

at a constant long-term rate with the upper 10 km of the fault locked, yield 21.5 mm/yr. Prescott 

and others (1981) do not report a preferred value, but W.H. Prescott (written commun., 1990) 

prefers a slip rate of about 15 mm/yr. Block motion inversion for San Andreas slip in the vicinity 

of San Juan Bautista gives a rate of 13 mm/yr (Savage and others, 1979). However, simultaneous 

dislocation inversions for slip rate on the Hayward, Calaveras, and San Andreas faults yield slip 

rates of 22 to 26 mm/yr (Savage and others, 1979; Matsu'ura and others, 1986) for the San Andreas 

fault at San Juan Bautista and to the north. Geodetic estimates based on rigid block inversion 

are uncertain because the models are incapable ofrepresenting internal (elastic) deformation of the 

crust, while dislocation inversions are uncertain because of tradeoffs between deep slip rate and 

depth distribution of slip. 

The occurrence of four large earthquakes in historical time (1838, 1865, 1906, 1989) suggests 

relatively large slip rates for the San Francisco Peninsula part of the San Andreas fault. The 

section of the fault affected by the 1989 Lorna Prieta earthquake (D = 1.6 ± 0.3 m) may have 

slipped previously in the earthquakes of 1906 and 1865. Estimates of 1906 slip vary from 1.5 to 

2.6 m (fig. 4). The earthquake of October 8, 1865, may constitute an earlier rupture along this 

segment, but information pertaining to that earthquake is very limited. Isoseismals center the 1865 

earthquake on the San Andreas fault at a location corresponding to the Lorna Prieta earthquake 

and have been used to give an assigned magnitude of 6.3 (Toppozada and others, 1981) and 6.5 

(Moths and others, 1981; Ellsworth, in press). Both magnitude and location are subject to great 

uncertainty, and it must be recognized that this earthquake may have occurred on an altogether 

different fault. Slip in 1865 is unknown, but the estimated magnitude of this event and the similarity 

14 
Table 1 •. San Andreas and southern Calaveras fault slip rate information 

Source 

Addicot (1969) 

Cummings (1968) 

Cummings (1981) 

Hall (1984, 1990) 

Prescott and others 

(1981) 

Matsu'ura and others 

(1986) 

Savage, written commun. 

(1990) 

Savage and others 

(1979) 

Mats'ura and others 

(1986) 

Thatcher (1979) 

Matsu'ura and others 

(1986) 

Nason (1971) 

Savage and others 

(1979) 

Matsu'ura and others 

(1986} 

Slip rate 

(mm/yr) Description 

San Andreas fault slip rate, San Francisco Peninsula 

6-22 

10-80 

8 

>12, >7.5 

12.2±4 

21.5±1.8 

26±8 

26-82 

Geologic-Offset of 1.8 to 5.0 million-year old units. 

Geologic-Offset of 1.0 to 8.0 million-year-old units. 

Geologic-Offset of 0.45 million-year-old unit. 

Geologic-Holocene offset of stream channel. 

Geodetic-Net rate across a zone 40 km wide. Not an inversion. 

Geodetic-2D dislocation inversion for deep slip rate, with fault 

locked to 10 km. 

Locking to 5 km and 20 km gives slip rates of 18.8±0.8 and 

85.9±2.2, respectively. 

Geodetic-Simultaneous inversion, deep slip rate on Hayward, 

Calaveras, and San Andreas faults. 

Geodetic-Deep slip rate with fault locked to depths of 18-16 km 

from 2D dislocation fit to observed 0.3 p.strain/yr of 

small-aperture geodetic networks. 

San Andreas fault slip rate, San Juan Bautista area 

18±2 

22.2±8.1 

25±3 

Geodetic-Inversion assuming rigid block motion of San Andreas 

and Calaveras faults. 

Geodetic-Simultaneous inversion, deep slip rate on Hayward, 

Calaveras, and San Andreas faults. 

Geodetic-Simultaneous inversion, deep slip rate on Hayward, 

Calaveras, and San Andreas faults. 

San Andreas fault slip rate, central creeping zone 

33±1 

38±3 

37±2 

Inversion assuming rigid block motion. 

Deep slip for slip below 15 km. Inversion for deep slip below 

10 km gives 33±2. 

Geodetic-Simultaneous inversion, deep slip rate on Hayward, 

Calaveras, and San Andreas faults. 

Southern Calaveras fault slip rate 

15 

17±2 

14.4±2.2 

13±2 

Observed surface creep rate. 

Inversion-assuming rigid block motion of San Andreas and 

Calaveras faults. 

Geodetic-Simultaneous inversion, deep slip rate on Hayward, 

Calaveras, and San Andreas faults. 

Solution for shallow creep rate is 14.9±1.8. 

Geodetic-Simultaneous inversion, deep slip rate on Hayward, 

Calaveras, and San Andreas faults. 

between its effects and those of the 1989 Lorna Prieta earthquake, including liquefaction in San 

Francisco (Townley and Allen, 1939), are consistent with displacements of 1 to 2 m. Dividing the 

average displacement in these three earthquakes by the average interval between them yields a 

rough estimate of slip rate of about 25 mm/yr. Ignoring the 1865 event and assuming that the 

1906 earthquake ruptured the same part of the fault plane that slipped in 1989, 1.6 ± 0.3 m of 

lateral slip was accumulated and released in 83 years. This yields a slip rate of 19 mm/yr. 

15 
Finally, constraints on slip rate may be derived by partitioning the total slip rate across 

the San Andreas system among the major faults of the San Francisco Bay region. The southern 

Monterey Bay geodetic profile spans most of the deformation zone and gives a net displacement 

rate of 38 ± 3 mm/yr (W.H. Prescott and M. Lisowski, written commun., 1990). Allowing for the 

possibility of some additional deformation beyond the ends of the profile, the total displacement 

rate could be as much as 40 mm/yr. Other estimates of total slip rate in the creeping section of 

the San Andreas fault south of Hollister vary from 33 to 37 mm/yr (table 1). North of Hollister, 

the total slip appears to be partitioned between the southern Calaveras and San Andreas faults. 

To the north, closer to San Francisco Bay, the southern Calaveras fault slip is believed to feed 

onto the Hayward, northern Calaveras, and possibly other faults to the east. If the total slip is 

partitioned among the Hayward, Calaveras, and San Andreas faults, then we may use the data 

from the southern Calaveras fault, which is creeping, to bound the slip rates on the east and west 

San Francisco Bay faults. One estimate of creep rate on the southern Calaveras fault, 15 mm/yr, 

comes from Nason (1971) for a location 13 km north of Hollister. This is consistent with southern 

Calaveras slip rates inferred from inversions of geodetic data that give 13-17 mm/yr (table 1). 

Subtracting the 15 ± 2 mmjyr southern Calaveras rate from the 38 ± 3 mm/yr total rate of slip 

across the San Andreas system leaves an upper-bound estimate of 23 ± 4 mm/yr for the rate of 

slip on the San Andreas fault. However, some unknown portion of this deformation rate may be 

taken up by slip on faults to the west of the San Andreas, such as the San Gregorio fault, or by 

bulk shear across the San Francisco Bay region. 

In light of these considerations, the current Working Group concluded that the previous 

estimate of 16 ± 2.5 mm/yr was probably too small. The Working Group has adopted a slip 

rate of 19 ± 4 mm/yr for estimation of revised recurrence times. 

SEGMENTATION 

The southern Santa Cruz Mountains segment has been redefined to coincide with the primary 

rupture zone of the 1989 Lorna Prieta earthquake. This moves the segment boundaries about 15 km 

north from the locations used in the 1988 report. On the basis of the aftershock distribution in 

the first 3 hours following the mainshock and the results of analyses of geodetic data (Lisowski and 

others, 1990), the segment length is taken as 39 km. The segment extends from just north of the 

intersection of the San Andreas fault and Highway 17, between San Jose and Santa Cruz, south to 

Pajaro Gap, 15 km northwest of San Juan Bautista. 

Two alternatives for segmentation of the San Francisco Peninsula part of the San Andreas 

fault have been considered (fig. 5). The first is a single segment (San Francisco Peninsula) that 

extends 60 km from the vicinity of Lower Crystal Springs Reservoir to the northern end of the 

redefined southern Santa Cruz Mountains segment. This segment may correspond to the location 

of the M-7 earthquake of 1838 (Lindh, 1983). The second alternative divides the San Francisco 

Peninsula segment into two segments: the northern Santa Cruz Mountains segment and the midPeninsula segment. The mid-Peninsula segment extends from Lower Crystal Springs Reservoir 

about 40 km south to the intersection of Page Mill Road and the San Andreas fault. The northern 

Santa Cruz Mountains segment extends 20 km from Page Mill Road to the northern end of the 

southern Santa Cruz Mountains segment. North of the San Francisco Peninsula segment, the North 

Coast segment of the 1988 Working Group has been retained. 

Segment boundaries of the southern Santa Cruz Mountains segment are fixed by the Lorna 

Prieta· earthquake rupture. For the remaining two segment boundaries, the evidence of fault 

geometry, seismicity, and 1906 slip distribution, summarized below and in figures 3, 4, and 5, 

was considered. Coordinates of the segment boundaries are listed in table 2. 

Several notable changes in fault strike occur along the 120-km-long section of the San Andreas 

fault from Mussel Rock to San Juan Bautista (fig. 5). The most prominent feature is a go change 

m strike located at Black Mountain that was noted by Scholz {1985). This bend marks the 

16 
0 10KM 

San Jose 

122° 30' 

Figure 5. San Andreas fault segments. Stippled rectangles are segment boundary zones. Star marks 

epicenter of 1989 Lorna Prieta earthquake. 

approximate location of the north end of the northern Santa Cruz Mountains segment and the 

southern end of the mid-Peninsula segment. There are two additional changes in fault trend of 

about 8° (see also Nishenko and Williams, 1985). A smaller, approximately 5° change in trend 

occurs near Lower Crystal Springs Reservoir, where the reverse-slip Canada fault intersects the San 

Andreas. 

17 
Table 2. San Andreas fault segments 

Coordinates of 

segment boundaries 1 

Northwest end Southeast end 

Lat. Long. Lat. Long. Length 

Segment (N.) (W.) (N.) (W.) (km) 

Southern Santa Cruz 37°121 122°011 36°581 121°44' 39 

Mountains 

Northern Santa Cruz2 37°201 122°111 87°121 122°011 20 

Mountains 

Mid-Peninsula 2 37°341 122°24' 87°20' 122°111 41 

San Francisco Peninsula 87°341 122°24' 37°121 122°01' 61 

North Coast 40°171 124°80' 87°38' 122°011 340 

1 Coordinates correspond to midpoints of stippled rectangles in figure 5. 

2 Subsegments of the San Francisco Peninsula segment. 

Expected 

magnitude 

7 

6.5 

7 

7 

8 

A seismicity gap on the San Andreas fault extends from the 1989 aftershock zone northwest to 

the vicinity of Crystal Springs Reservoir, interrupted only by small clusters of activity near Portola 

Valley (Olson, 1986; fig. 3). The northern end of the San Francisco Peninsula and mid-Peninsula 

segments corresponds approximately to the clear discontinuity in 1906 slip that is evident from 

both the geologic and geodetic observations (fig. 4). 

RECURRENCE TIMES 

Prior to the Lorna Prieta earthquake the median recurrence times, T, could only be estimated 

for San Andreas fault segments from the ratios of the estimated 1906 slip to the estimated slip 

rate. The Lorna Prieta earthquake brings new information to the assessment of the San Andreas 

fault along the San Francisco Peninsula that may modify earlier estimates of T. Now that this 

segment has ruptured, the single datum we know best is the inter-event time of 83 years, assuming 

of course, that this segment ruptured in the 1906 earthquake. How then does this new information 

change our perception of the earthquake potential of this segment and of the other segments? 

The Working Group has considered three alternatives for estimation of recurrence times. In the 

following, we refer to these alternatives as recurrence time models 1, 2, and 3. Recurrence time 

estimates and earthquake probabilities from these three models have been incorporated into the 

logic-tree analysis. Results of the estimation of recurrence time using the three approaches are 

summarized in table 3. 

Model 1 retains the conclusions of the 1988 Working Group report with modifications based 

only on changes in segmentation. This alternative holds that no revision of the parameters is 

warranted by the occurrence of the Lorna Prieta earthquake. It is based on the postulate that 

the Lorna Prieta earthquake represents an example of vertical segmentation, in which slip on a 

shallow 1906 rupture has not recurred. Recurrence time is obtained from the time-predictable 

model (equation 3) using V = 16 ± 2.5 mm/yr. 

Model 2 combines the revised estimate of fault slip rate (V = 19 ± 4 mm/yr) with revised 

displacement estimates in the time-predictable model to determine T for the San Andreas fault 

segments. The procedure for obtaining revised estimates of segment displacement employed a 

separate logic tree that is described in appendix B. 

Model 3 asserts that the observed 83-year interval on the southern Santa Cruz Mountains 

segment is the most certain information we have and that it should therefore receive more weight 

18 
Table 3. Summary of San Andreas fault segment parameters 

(T, recurrence time; up, parametric uncertainty; n.a., not applicable] 

Model 

Accept 

stress effect 

t 

(years} Weight 

Southern Santa Cruz Mountains segment (previous event=1989} 

1 n.a. 100±24 0.24 0.13 

2 n.a. 84±24 .28 .47 

s n.a. 96±16 .17 .40 

Northern Santa Cruz Mountains segment (previous event=1906) 

1 no 156±45 .28 .09 

1 yes 127±45 .34 .04 

2 no 95±44 .44 .31 

2 yes 70±43 .56 .16 

s no 96±36 .37 .27 

s yes 71±43 .56 .13 

Mid-Peninsula segment (previous event=1906} 

1 no 213±60 .27 .09 

1 yes 210±60 .27 .04 

2 no 129±49 .37 .31 

2 yes 127±49 .38 .16 

3 no 149±31 .21 .27 

s yes 147±30 .20 .13 

San Francisco Peninsula segment (previous event=1906} 

1 no 188±54 .28 .02 

1 yes 176±53 .29 .11 

2 no 138±40 .28 .08 

2 yes 128±38 .29 .39 

s no 138±29 .21 .06 

s yes 129±28 .21 .34 

North Coast segment (previous event=1906} 

1 n.a. 281±76 .27 .13 

2 n.a. 237±73 .so .47 

s n.a. 201±49 .24 .40 

in the revised estimation of T on San Andreas fault segments. Under this approach, all San 

Andreas fault recurrence-time estimates are obtained by reference to an updated estimate of the 

median recurrence time, TLP, for the southern Santa Cruz Mountains segment following 1906. 

The update is based on the Lorna Prieta earthquake. The procedure compares the observations of 

1906 displacement along the southern Santa Cruz Mountains segment with the 1906 displacement 

observations on the segment of interest. The recurrence time for a San Andreas segment (other 

than the southern Santa Cruz Mountains segment itself) is then 

A A t:l.D 

T=TLP+--, v (6) 

where t:l.D is the difference between the 1906 displacement on the segment in question and the 1906 

displacement on the Lorna Prieta rupture, and Vis the revised slip rate of 19 ± 4 mm/yr. 

The updated estimate, TLP, appearing in equation (6) is found by application of Bayes theorem. 

Using the 1906 slip estimate of 2.5 ± 0.6 m (Working Group, 1988) and the revised slip rate of 

19 ± 4 mm/yr gives the a priori expected recurrence time of 132 ± 42 years. Using Bayes theorem 

19 
with the observed interval of 83 years gives 

A 

{[ ~+~]} .312 .212 

TLP = exp [-1

- _ 1

_] = 96 ± 16, 

.312 + .21 2 

in which the standard deviation, 16, is based on the revised parametric uncertainty in TLp: 

(Tp =.I 1 1 1 = o.17. v .312 + .212 

(7) 

(8) 

The calculation of uP, the parametric uncertainty of log T from equation (6) is summarized in 

appendix B. 

Southern Santa Cruz Mountains Segment 

The prior event for this segment is now the 1989 Lorna Prieta earthquake. Strike-slip 

displacement in the Lorna Prieta earthquake is well constrained by the geodetic models to be 

1.6 ± 0.3 m (Lisowski and others, 1990). Model 1 retains the earlier 16 mm/yr estimate of slip 

rate and ~ives T = 100 ± 24 years. The estiml!'ted San Andreas slip rate for model 2 is 19 mm/yr 

yielding T = 84 ± 24 years. With model 3, T for the post-1989 interval is taken as the revised 

estimate of 96 ± 16 years. 

Northern Santa Cruz Mountains Segment 

Between the northern end of the Lorna Prieta earthquake rupture and Alpine Road, surface 

ruptures due to the 1906 earthquake were highly discontinuous, and right-lateral displacements 

nowhere exceeded the 1.5-m offset in the Wright-Laurel tunnel (Lawson, 1908). Similarly, although 

they are larger than the surface offsets, the geodetic estimates of displacement during the 1906 

earthquake do not distinguish this segment from the southern Santa Cruz Mountains segment. 

Hence, model 1 assumes D=2.5±0.6 m on the basis of geodetic observations and V =16±2.5 mm/yr 

to obtain T = 156 ± 46 years. The consensus D for ·model 2 is 1.8 ± 0.7 m, which with 

V = 19 ± 4 mm/yr gives T = 95 ± 44 years. &cause 1906 displacements on this segment cannot 

be distinguished from those on the southern Santa Cruz Mountains segment, tl.D = 0.0 ± 0.6 m for 

model 3, and equation (6) gives T = 96 ± 36 years. 

Mid-Peninsula Segment 

This segment is about 40 km long and lies north of the northern Santa Cruz Mountains segment. 

From analysis of the geodetic observations, Thatcher and Lisowski (1987) gave their preferred slip 

of 3.4 ± 0.3 m for this section of the San Andreas fault. Surface offsets of 2.3 m or more were found 

at two sites, where it was noted that the fault trace was more continuous than farther to the south. 

For model1, Dis taken to be 3.4±0.8 m, giving an estimated recurrence time, 'i', of 213±60 years. 

For model 2, D is taken as 2.46 ± 0.78 m, giving an expected recurrence time of 129 ± 49 years. 

In model 3, tl.D has been estimated to be 1.0 ± 0.3 m on the basis of the observation that 1906 

slip (both surface and geodetic slip) on this segment was about 1.0 m greater than the slip on the 

southern Santa Cruz Mountains segment. This value results in an estimate forT of 149± 31 years. 

San Francisco Peninsula Segment 

This segment consists of the northern Santa Cruz Mountains segment and the mid-Peninsula 

segment combined. For this segment, model 1 uses a prior displacement, D, of 3.0 ± 0.7 m and 

model 2 uses D = 2.62 ± 0.52 m. These values give expected recurrence times of 188 ± 54 years 

20 
for model 1 and 138 ± 40 years for model 2. In the case of model 3, tiD has an assigned value of 

0.8 ± 0.3, which results in an expected recurrence time of 138 ± 29 years. 

North Coast Segment 

This segment extends about 340 km north from the end of the San Francisco Peninsula segment. 

Maximum 1906 surface slip and geodetic displacements along this segment are in good agreement, 

and models 1 and 2 retain the previous Working Group estimate of 4.5 ± 0.5 m. This value gives 

expected recurrence times of 281 ± 76 years and 237 ± 73 years for models 1 and 2, respectively. 

Model 3 uses tiD = 2.0 ± 0.6, giving T = 201 ± 49 years. 

LOMA PRIETA EARTHQUAKE STRESSES 

In addition to altering our perceptions of conditions along the San Andreas fault, the Lorna 

Prieta earthquake may have caused a change of physical conditions that is sufficient to affect the 

time of earthquake rupture. In particular, slip on the Lorna Prieta earthquake rupture surface has 

altered the stress on nearby fault segments. This stress change will bring a segment closer to the 

time of failure if the appropriate component of stress increased at the time of the earthquake or, 

conversely, will increase the time to failure if the stress decreased. As a consequence of the Lorna 

Prieta earthquake we considered the possibility that the expected recurrence time was altered by 

tiT, representing the equivalent change in recurrence time resulting from the Lorna Prieta stress 

changes (Dieterich, 1988). We have incorporated this alternative into the logic-tree analysis so as 

to include an estimate of the physical effect of the Lorna Prieta earthquake on recurrence times. 

This contrasts with the conventional approach, which does not provide for segment interactions. 

The method assumes that the change of stress on a fault segment, Ar, resulting from slip on 

the Lorna Prieta rupture surface is equivalent to the change of stress that would have occurred due 

to tectonic stressing at rate i in the interval AT: 

AT= -Arfi. (9) 

Hence, an increase of stress reduces the expected recurrence time. Three-dimensional elastic 

dislocation models of the San Andreas fault have been employed by R. W. Simpson and J .H. 

Dieterich (written commun., 1990) to estimate Ar and f resulting from imposition of the 

geodetically determined Lorna Prieta earthquake dislocation. 

Because stressing rate is proportional to the slip rate (f = kV), equation 9 is equivalent to 

-Ar -D' 

AT= kV =y-, (10) 

where D' = (Ar/k) is an equivalent reduction of the segment displacement, D, in the previous 

earthquake. Table 4 summarizes the results of R. W. Simpson and J .H. Dieterich (written commun., 

1990) for D' and AT resulting from the Lorna Prieta earthquake for San Andreas fault segments. 

The values in table 4 are based on the average change of stress over the entire segment. The 

Lorna Prieta earthquake also changed the stresses along the Hayward fault, but because of the 

greater distances from the Lorna Prieta earthquake, the stress effects are considered insignificant. 

The range of values for AT given in table 4 reflects the variation in tiT resulting from different 

model assumptions and from the uncertainty of the Lorna Prieta slip. Because of the rapid falloff 

of stresses with distance, the changes in recurrence time are greatest for the northern Santa Cruz 

Mountains segment, which is adjacent to the Lorna Prieta earthquake rupture. 

SUMMARY OF PROBABILITIES FOR THE SAN ANDREAS FAULT 

Consensus probabilities, obtained from the logic-tree weights, are given in table 5. The low 

probability of an earthquake on the southern Santa Cruz Mountains segment, essentially zero in the 

21 
Table 4. Change of recurrence time resulting from simulated lorna Prieta earthquake 

studies 

[See text for explanation of variables] 

Segment 

Mid-Peninsula 

Northern Santa Cruz Mountains 

San Francisco Peninsula 

D' = ll.T/k 

(mm) 

40±20 

470±280 

180±90 

ll.T = D' /V (years) 

V = 16 mm/yr V = 19 mm/yr 

-2.5±1.8 -2.1±1.1 

-29.4±158 -24.7±13.8 

-11.8±6.9 -9.5±5.1 

next 30 years, is based on our assumption that the earthquake of 1989 relieved stresses throughout 

the seismogenic depth along this section of the San Andreas fault zone. Because the 1989 Lorna 

Prieta earthquake appears not to have slipped to as shallow a depth as apparently occurred in 1906, 

the possibility remains that the Lorna Prieta earthquake did not relieve the stresses in the upper 

part of the seismogenic zone that have accumulated since 1906. This hypothesis is considered under 

model 1, which was given a low weight by the Working Group. If this hypothesis is correct, there 

may be a possibility for a shallow earthquake occurring above the 1989 Lorna Prieta earthquake 

rupture. However, the maximum expected magnitude, 6 to 6.5, is below the magnitude range 

considered in this study. 

The low probability of a M,....8 earthquake on the North Coast segment {0.02) is the result of 

the large displacements, averaging about 4.5 m, that occurred along this segment in the great 

earthquake of 1906. The method we have employed considers only earthquakes that rupture 

the entire segment. However, slip information for the 1906 earthquake is somewhat sparse and 

subsegments of shorter length that had less than 4.5 m of slip in 1906 could have escaped detection. 

This possibility could not be evaluated, but it means that the North Coast segment, particularly 

north of Point Arena, could have a higher probability of producing smaller earthquakes of M $.1. 

We considered two alternatives for the San Francisco Peninsula segment .. The first, given a 

weight of 0.56, is that the entire segment will slip in an earthquake of about magnitude 7. The 

second scenario, given a weight of 0.44, is that separate earthquakes will rupture the northern 

Santa Cruz Mountains and mid-Peninsula subsegments of the San Francisco Peninsula segment. 

The expected magnitudes are 6.5 for the northern Santa Cruz Mountains segment and 7.0 for 

the longer mid-Peninsula segment. The sum of the San Francisco Peninsula segment probability 

multiplied by the segment weight (0.56), plus the mid-Peninsula segment probability times its 

weight (0.44), gives a 30-year probability of 0.23 for a magnitude 7 earthquake on this part of the 

San Andreas fault. The probability of a magnitude 6.5 earthquake on the northern Santa Cruz 

segment is the segment probability times the segment weight (0.44) and gives a 30-year probability 

of 0.18. Finally, considering both segmentation scenarios, the aggregate probability of a M 6.5 or 

M 1.0 event is 0.37 for the entire San Francisco Peninsula segment. 

HAYWARD AND RODGERS CREEK FAULTS 

HAYWARD FAULT ZONE 

The previous Working Group identified and computed probabilities for two 50-km-long 

segments of the Hayward fault. New information on geologic slip rate, rates of historical surface 

creep, and segmentation provides a basis for revising the Hayward fault probabilities. Table 6 

gives segmentation data, and table 7 summarizes parameters for calculations of probabilities for 

the Hayward and Rodgers Creek faults. Inputs for calculation of the probabilities in the 1988 

Working Group report were (a) a 7.5 ± 2 mm/yr slip rate based on limited trenching data and 

regional geodetic interpretations, (b) a 1.4 ± 0.4 m slip per event, which was based on an empirical 

22 
Table 5. Probabilities of earthquakes along San Andreas fault 

Level of 

relia hili ty 

Previous Expected Probability1 (scale of A toE; 

Segment event magnitude 1990-2020 A most reliable) 

S. Santa Cruz Mountains 1989 7 "'0.00 B 

N. Santa Cruz Mountains2 1906 6.5 .18 c 

San Francisco Peninsula3 1906 7 .28 c 

San Francisco Peninsula4 1906 6.5 or 7 .87 c 

North Coast 1906 8 .02 B 

1 Differences in probability of less than 0.10 are not considered meaningful. 2 Subsegment of San Francisco Peninsula segment. Probability incorporates weight for 

this segmentation scenario. 

3 Weighted average of San Francisco Peninsula segment and mid-Peninsula segment 

probabilities. 4 Aggregated probability of M 6.5 or M 7 on San Francisco Peninsula segment. 

Table 6. Hayward and Rodgers Creek fault segments 

Coordinates of 

segment boundaries1 

Southeast end Northwest end 

Lat. Long. Lat. Long. Length Expected 

Segment (N.) (W.) (N.) (W.) (km) magnitude 

Southern East Bay 87°80' 121°551 87°44' 122°07.7' 82 7 

segment 

Northern East Bay 87°44' 122°07.7' 88°07' 122°251 50 7 

segment 

Rodgers Creek fault 88°071 122°251 38°801 122°451 50 7 

1 Coordinates correspond to midpoints of stippled rectangles in figure 6. 

relation between fault length and displacement, and (c) elapsed times of 120 and 162 years since the 

last earthquake for the south and north segments, respectively. The 30-year probability of a M 7 

earthquake on each segment was previously calculated to be 0.2. Considering the uncertainties in 

the input parameters, the south segment (southern East Bay segment) probability was rated C and 

the north segment (northern East Bay segment) probability was rated D (Working Group, 1988). 

The mode of strain accumulation along the Hayward fault presents a dilemma that cannot be 

resolved given our present state of knowledge. Two end-member hypotheses have been considered: 

(1) The fault is locked at depth (.....,5 to ...... 10 km) and accumulating strain at a rate appropriate to its 

long-term geologic slip rate, or (2) the fault is creeping and accumulating little or no elastic strain 

at present. The two alternatives clearly lead to divergent views of the earthquake hazard. The first 

hypothesis is consistent with the two major earthquakes on the fault in 1836 and 1868. The second· 

is consistent with the high rate of surface creep. The committee carefully weighed both alternatives 

and various lines of evidence supporting them. The occurrence of surface creep in conjunction with 

documented M 6 to 7 earthquakes elsewhere on the San Andreas fault system (1979 Coyote Lake, 

1966 Parkfield, 1979 Imperial Valley) argues for the locked-fault hypothesis. However, more data 

23 
Table 7. Hayward and Rodgers Creek fault segment parameters 

[D, displacement in previous event; T, recurrence time; uP, parametric uncertainty) 

Slip rate V = 9±2 mm/yr 

Previous Expected D 1 

Segment event magnitude (m) (years) Up 

Southern East Bay 1868 7 1.5±0.5 167±67 0.89 

Northern East Bay 1886 7 1.5±0.5 167±67 .89 

Rodgers Creek fault 1808 7 2.0±0.5 ~222±74 .88 

(or earlier) 

are needed to critically test this hypothesis, and new observations on the Hayward fault could well 

lead to significant revision (upward or downward) of the probabilities developed below. 

Segmentation 

The Hayward fault segmentation adopted for the present report is shown in figure 6. 

The stippled rectangles are segment boundary zones, and their along-fault width suggests the 

uncertainty in defining potential rupture endpoints. Coordinates of segment endpoints listed in 

table 6 correspond to the midpoints of the stippled zones. 

We consider the fault to be composed of two fault segments. However, both segments appear 

to be well advanced in the earthquake cycle, and we recognize the possibility of both rupturing at 

the same time. 

The extent of the southern East Bay segment is based on reports of the 1868 surface faulting 

(Lawson, 1908). In 1868, surface faulting was apparently well defined from Warm Springs to San 

Leandro and may have occurred discontinuously as far north as Mills College. This gives a segment 

length of 28 to 36 km. The south end of the segment coincides with increasing structural complexity 

of the fault zone and a change in the observed historical surface creep. Creep, which characterizes 

much of the Hayward fault as far north as San Pablo Bay, is not recognized south of Warm Springs. 

The north end of the segment is associated with an approximately 700- to 800-m-wide, 4-kmlong right-stepping bend (a releasing bend), which is the most prominent geometric irregularity 

along this section of the fault. Coincident with the surface bend is an approximate doubling of 

the width of the zone of epicenters associated with the Hayward fault to a depth of about 10 km 

(D.H. Oppenheimer, written commun., 1989), suggesting that the releasing bend extends through 

the seismogenic zone. A cross section of seismicity along the Hayward and Rodgers Creek faults 

is shown in figure 7. 

The northern East Bay segment is the section of fault between the 1868 rupture zone and 

the Rodgers Creek fault. It is a plausible location of the 1836 earthquake (Louderback, 1947; 

Toppozada and others, 1981). This segment has a length of 45 to 50 km. The south boundary is 

placed at the north end of the 1868 rupture zone (San Leandro-Mills College area). The north 

boundary is placed at the north side of San Pablo Bay where (a) there is a 6-km right (releasing) 

step to the Rodgers Creek fault at the surface (fig. 6), and (b) a well-defined 35-milligal negative 

Bouguer gravity gradient that characterizes this part of the Hayward-Rodgers Creek structural trend 

bends sharply northeast in the step-over area (Chapman and Bishop, 1988). 

Slip Rate 

An important change from the 1988 report is the Hayward fault slip rate. We have increased it 

from the previous value of 7.5± 2.0 mm/yr to 9± 2 mm/yr. This revision reflects new geologic data 

and new information on rates of historical surface creep. Trenching investigations near Union City 

24 
Santa Rosa 

San 

Francisco 

122° 30' 

0 10KM 

San Jose 

Figure 6. Hayward and Rodgers Creek fault segments. Faults dotted where inferred . Stippled 

rectangles are segment boundary zones: their along-fault width indicates relative uncertainty in defining 

segment endpoints. 

(Lienkaemper and others, 1989) provide a preliminary estimate of 8 mm/yr for the past 8,000 years 

and permit a range of7 to 10 mm/yr for periods between 4,000 and 14,000 years ago. Measurements 

of surface creep (fig. 8) (Lienkaemper and others, 1989) show that the Hayward fault has been 

25 
Santa Rosa 

0 c ' ~ ~.,, ... :~ ~~;~ri:oa- - • • •• ~:.O='t~~~ :c -1o-· · . .:·~~·~ -~ 

IC.. 

UJ 

0 -20-

I 

120 

I I 

100 

I I 

80 

I I 

60 

DISTANCE (KM) 

I I 

40 

I I 

20 

I 

-

0 

Figure 7. Seismicity along Hayward and Rodgers Creek faults. 1/1/69 to 1/31/90. Size of symbols 

increases with increasing magnitude. Locations of section endpoints. C-C'. are shown in figure 2. 

:>. 

co "'~ 

0 g :0 .9 a: "' ·;:: 

a.. E Qj 

c: u 

"' ·a 

rn a.. w 

10 

~ 8 ~ 

~ 

~ 6 w 

I-

< 

c: 4 

a.. 

::J 

rn 2 

0 

90 80 70 

D 

60 50 40 

DISTANCE (KM) 

e 

"E 

"' Q) 

...J 

c: 

rn "' 

"E 

"' 

~ 

I "' 

MIN 

30 

:>. 

~ 

u E c: 0 

.Q E c: 

::::> ~ 

1868 RUPTURE 

20 10 0 

D' 

Figure 8. Slip rate along Hayward fault determined from offset cultural features and small-scale 

geodetic surveys (solid squares with ±1 standard deviation error bars). Curve represents polynomial 

fit to data. Also shown are slip rates (open triangles) corresponding to change of distance between 

geodetic monuments. with nearest benchmark located at a perpendicular distance of 2 to 4 km from 

fault trace. Horizontal bar indicates length of network projected onto section . open triangle marks 

center of line. and vertical bar shows ±1 standard deviation error. Horizontal arrows at bottom of 

figure show extent of 1868 rupture: "MAX" and "MIN" refer. respectively. to maximum and minimum 

estimates of northwest extent of rupture. Endpoints of plot. 0-D'. are shown in figure 2. Figure after 

J.J. Lienkaemper and others (written commun .. 1990). 

creeping at a rate of 5 to 6 mm/yr. An exception is the southern 5 km, which has been creeping 

at 8 to 91/2 mmjyr and at times has had creep rates as fast as 10.2 ± 0.5 mm/yr. The creep rates 

are comparable to the new geologic estimates, and both the geologic and creep observations may 

represent the minimum total rate of slip for the Hayward fault. The increase of our estimated slip 

rate to 9±2 mm/yr reflects these new observations and their associated uncertainties. The relation 

26 
between surface creep and crustal stress accumulation is not well understood for the Hayward 

fault. For the calculation of probabilities we have assumed that the fault is locked at depth and is 

accumulating stress at a rate appropriate to 9 ± 2 mm/yr. 

Slip Per Event 

No new information has been obtained on the amount of coseismic slip that occurs during 

large-magnitude Hayward fault earthquakes. In the 1988 report a slip per event of 1.4 ± 0.4 m was 

used for both segments, on the basis of an empirical relation between fault length and displacement. 

The current Working Group felt that the 1988 value suggested a degree of precision that was too 

high. For the present report the displacements for both segments have been revised to 1.5 ± 0.5 m. 

This value, and its uncertainty, are based on both the empirical relationship between length and 

displacement and the amount of slip often associated with earthquakes comparable to the historical 

earthquakes (M ...... 7) on these segments. 

Recurrence Interval 

The mean recurrence interval for each Hayward fault segment derived from the slip rate and 

slip per event values is 167 ± 67 years. 

Probabilities 

Based on the input parameters above, the 3Q-year probabilities for the southern East Bay 

segment and northern East Bay segment are 0.23 and 0.28, respectively (table 8). 

RODGERS CREEK FAULT SEGMENT 

The Rodgers Creek fault is a major segment of the Hayward fault zone (fig. 6). It extends 

from about San Pablo Bay to at least as far north as Santa Rosa. The Rodgers Creek fault has 

long been recognized as an active fault. It appears on the 1975 State of California map (Jennings, 

1975) as a Holocene fault and has an Alquist-Priolo Special Studies Zone along it (Hart, 1988). 

The Rodgers Creek fault was not included in the 1988 Working Group report because of an absence 

of information on slip rate, recurrence interval, and slip per event. New paleoseismic data, along 

with preliminary geodetic observations and microseismic data (fig. 7), indicate that the Rodgers 

Creek fault zone has a rate of activity comparable to that estimated for the Hayward fault and has 

the capability of causing large earthquakes. 

Slip Rate 

Trenches excavated where the fault offsets alluvial fan deposits, 18 km north of San Pablo Bay, 

have exposed buried channels offset by the fault (Budding and others, 1989). These channels have 

been offset 5 to 7 m and yield a slip rate of 3.9 to 5.5 mm/yr for the past 1,270 years (D.P. Schwartz, 

unpub. data, 1990). This is a minimum rate because the offset channel deposits were dated with 

detrital charcoal and are therefore younger, by an unknown amount, than the radiocarbon age. 

Unpublished geodetic data can be interpreted as placing 6 to 10 mm/yr of slip on the Rodgers 

Creek fault (Lisowski, written commun., 1990). These data are consistent with the 9 ± 2 mm/yr 

slip rate employed for the Hayward fault, and we have adopted the same rate for the Rogers Creek 

fault segment. 

Slip Per Event and Recurrence Interval 

At present there is no information on the timing of past large earthquakes on the Rodgers 

Creek fault. Preliminary estimates of recurrence can be made using two methods. First, slip per 

event can be divided by slip rate. A gully and adjacent surface debris flow at the trench site were 
Table 8. Probabilities of earthquakes along Hayward and Rodgers Creek faults 

Level of 

Probability1 reliability Previous Expected (scale of A toE; 

Segment event magnitude 1990-2020 A most reliable) 

Southern East Bay 1868 7 0.28 c 

Northern East Bay 1886 7 .28 D 

Rodgers Creek fault 1808 7 .22 D 

(or earlier) 

1 Differences in probabilities of less than 0.10 are not considered meaningful. 

offset 2.0 (+0.3, -0.2) m during the most recent event (Budding and others, 1989). Using this offset 

-value with an uncertainty of ±0.5 m and the 9 mm/yr slip rate adopted for this segment yields an 

expected recurrence interval of 222 ± 7 4 years. Second, the number of events that occurred during 

the interval represented by the channel deposits can be used to calculate average recurrence. If the 

2 m offset is a characteristic value, the 5 to 7 m represents 3 to 4 paleoearthquakes in a 1,270-year 

period. This gives a range of intervals from 254 to 635 years. These would be maximum values. 

For calculation of probabilities for this segment, we have used the 222 ± 7 4 year result. 

Probabilities 

It is uncertain how much time has elapsed since the most recent event capable of producing 

2 m of surface offset. The 1898 Mare Island M 61/2 earthquake is the largest historical event that 

could have occurred on the fault, but it appears to have been too small to produce the 2-m offset. 

Available descriptions of the Sonoma Mission do not indicate that it was damaged in 1836, although 

damage was reported from the 1868 Hayward event. An earthquake of 1808 caused damage in the 

Presidio in San Francisco. It is unknown what the source of this earthquake was, but the Rodgers 

Creek fault cannot be excluded. Therefore, the minimum elapsed time is set at 181 years. The 

30-year probability (table 8) derived using this elapsed time and the previously discussed input 

parameters is 0.22. This should be considered a minimum value. 

SUMMARY AND DISCUSSION 

This report summarizes available information pertaining to large earthquakes in the San 

Francisco Bay region. By using the available information, reasonable assumptions, and simple 

models, it strives to make projections about the locations, sizes, and times of future earthquakes. 

The types of basic information used in this report include the following: 

(1) 

(2) 

(3) 

(4) 

Identification of fault segments judged to be capable of producing large earthquakes in 

the future. 

Estimates of the amount of displacement and thus the magnitude of future large 

earthquakes likely to occur during rupture of these fault segments. 

Estimates of the median recurrence intervals (and their uncertainties) for major earthquakes on the fault segments. 

Estimates of the date of the most recent large earthquake for each of the fault segments. 

There is considerable uncertainty associated with each of these types of basic earthquake 

information. One of the principal tasks of the current Working Group was to examine and explore 

alternative explanations and interpretations of the data. The information about earthquakes in 

28 
the San Francisco Bay region will improve with better means of analysis and with additional data. 

The Working Group sees an urgent need for additional studies to reduce the uncertainty of the 

fault segment assessments considered in this report and to permit evaluation of other faults that 

may have the potential for producing major earthquakes. In particular, knowledge of the average 

time interval between segment-rupturing earthquakes, which might be learned from paleoseismic 

studies, might permit major revisions of the consensus forecasts presented here. Studies aimed at 

providing dates of large earthquakes on the Hayward fault prior to 1836 are essential. 

In its present form, even with its inherent uncertainty, this basic information has something to 

say about future large earthquakes in the San Francisco Bay region. Several fault segments have a 

demonstrated capability of causing large earthquakes. Furthermore, for several of these segments 

the time interval that has elapsed since the last earthquake is approaching the estimated recurrence 

interval, which means that large earthquakes on these segments in the coming decades are not only 

possible, but likely. 

The method of using this basic information to develop probabilistic assessments followed the 

general procedures employed in the previous Working Group report (1988). Results of the current 

study are summarized in figure 9. 

Rodgers Creek fault 

M-7, P=0.22 

Total 30-year probability of one or 

more large earthquakes = 0.67 

Northern East Bay 

segment: M-7, P=0.28 

Concord and Green Valley faults 

Figure 9. Conditional probabilities of earthquakes (M~7} in San Francisco Bay region. Column heights 

are proportional to probabilities. Letters on columns indicate reliability of forecast. on a scale of A to 

E. with A being most reliable. M. magnitude: P. probability. 

29 
The principal revisions and additions to the previous report include the following: 

(1) Segment boundaries were revised on the San Francisco Peninsula as a consequence of the 

Lorna Prieta earthquake, and along the Hayward fault as a result of a review of geological, 

geophysical, and historical data. 

(2) The preferred San Andreas fault slip rate was revised upward from 16 ± 2.5 mm/yr to 

19 ± 4 mm/yr. This change shortens the expected earthquake recurrence times. 

(3) The effects of stress changes on the time of earthquake recurrence caused by the Lorna 

Prieta earthquake have been considered. The effect of the estimated stress changes is to 

decrease the recurrence time of the northern Santa Cruz Mountains segment possibly by 

as much as 25 to 30 years (table 4). This possible effect becomes less important with 

increasing distance from the Lorna Prieta earthquake rupture. 

(4) The slip rate on the Hayward fault was revised from 7.5 ± 2.0 mm/yr to 9.0 ± 2 mm/yr. 

This change also tends to reduce expected recurrence times. 

(5) Information on earthquake recurrence and slip per event has become available for the 

Rodgers Creek fault, permitting an assessment of its potential for generating a major 

earthquake. 

Although the potential for damage from an earthquake generally decreases as distance from 

the epicentral region increases, the pattern of losses at rather large distances from theM 7.1 Lorna 

Prieta earthquake clearly demonstrates that an earthquake on any of the fault segments considered 

by the Working Group could seriously affect the entire San Francisco Bay region. Indeed, the most 

densely populated parts of the area lie atop of or adjacent to fault segments having the greatest 

potential for large earthquakes. Table 9 gives the combined probabilities of one or more large 

earthquakes in the San Francisco Bay region. These combined probabilities, referred to here as 

total or aggregate probabilities, are obtained from aggregating the probabilities of the individual 

segments following the procedure employed in the 1988 report. Total probabilities for 5-, 1D-, 

2D-, and 30-year intervals beginning at the start of 1990 have been calculated. The aggregated 

probability, P, is obtained from 

P = 1- (1- Pa)(1- Pb}(1- Pc) · · ·, (11) 

where Pa, Pb, and Pc are the individual probabilities for earthquakes on segments a, b, and c, 

respectively, for the interval of interest. Application of equation (11) assumes independence of the 

individual events, which is not strictly true given that segments share uncertain slip rates. 

The revisions leading to the interpretation of higher slip rate on the San Andreas and Hayward 

faults and the calculations of increased fault stress due to the Lorna Prieta earthquake all tend to 

decrease the expected recurrence times and thereby increase the probability of major earthquakes 

along the San Andreas and Hayward faults. 

We now conclude that the total 3D-year probability of one or more major earthquakes in the 

San Francisco Bay region is 0.67 (table 9). This represents a significant increase from the value of 

0.5 of the previous Working Group report (1988). About half of this increase can be ascribed to 

the addition of the Rodgers Creek fault segment to the list of potential major earthquake sources. 

The remaining increase is due to the increases of earthquake probabilities on the individual fault 

segments described above. In the previous report the southern Santa Cruz Mountains segment was 

assigned a probability of 0.3, but that segment was not included in the 1988 aggregated probability. 

As these numbers make clear, the estimated probability of a major earthquake in the San 

Francisco Bay region has increased from the 1988 report. In addition, we emphasize that the 

estimate of total probability may represent a minimum value. This is because other faults, for 

which there is insufficient information to presently conduct an analysis of this type, particularly 

the San Gregorio, Calaveras, Greenville, Concord, Green Valley, and West Napa faults, may have 

30 
Table 9. Probabilities of one or more large earthquakes in San Francisco Bay region 

Segments 

North Coast, San Francisco Peninsula, 

N. East Bay, S. East Bay, and 

Rodgers Creek 

Probability for intervals 

beginning 1/1/90 

5 yr 10 yr 20 yr 80 yr 

0.15 0.88 0.50 0.67 

Level of 

reliability 

(scale of A toE; 

A most reliable) 

B 

the potential for producing major earthquakes in the San Francisco Bay region. Indeed, of the 

likely 33-40 mm/yr displacement rate that is believed to occur across the entire San Andreas fault 

system, only 28 mm/yr is accounted for in the present assessment of the San Andreas fault proper 

and the Hayward and Rodgers Creek faults. 

There is a consensus among all who have studied the large-scale motions across the San 

Andreas fault system at the latitude of San Francisco Bay that strain is currently accumulating 

and will be released in future large-magnitude earthquakes (Ellsworth and others, 1981; Prescott 

and Yu, 1986; Scholz, 1990). In view of this strong conclusion, the question of another earthquake 

reduces from "if" to "when" and "where." This report presents one approach to this problem. 

As a counterpart to this fault-specific approach, the aggregate probability of one or more M 7 

earthquakes during the next 30 years can also be determined using a more traditional, timeindependent method. 

The rate of occurrence of earthquakes in a region may be modelled as a Poisson process in 

which the probability of one or more events in a time interval t is P = 1 - e-.\t, where A is the 

average rate of earthquake occurrence. Two estimates of A for M?,7 earthquakes are available 

for the San Francisco Bay region. One is obtained by noting that four such events have occurred 

since the 1836 earthquake (in 1838, 1868, 1906, and 1989), giving A= 0.026/year. Over a 30-year 

period, P = 0.54. The other estimate derives from the Gutenberg-Richter frequency-magnitude 

distribution of smaller earthquakes in the region. The annual frequency of M?.7 earthquakes has 

been estimated as A = 0.017/year (Collins and others, 1989), leading to a 30-year estimate of 

P = 0.40. While each of these Poisson estimates is smaller than our preferred value of P = 0.67, 

they too suggest a serious possibility of damaging earthquakes in the coming decades. 

In addition, three other lines of argument, based on earthquakes prior to 1906, suggest that 

the likelihood of large earthquakes in the San Francisco Bay region in the coming decades is as 

great as or possibly greater than the above probabilities indicate. The first is the seismic cycle 

argument. It has long been noted (Tocher, 1959) that seismic activity in the San Francisco Bay 

region was much higher during the 70 years preceding 1906 than in the 70 years following. On the 

basis of an increase in activity in the late 1970's, Ellsworth and others (1981) suggested that the 

quiet portion of the cycle was over and that M 6-7 earthquakes might be expected at the rate of 

one per decade or more; subsequent events suggest that their estimate was too low. If the analogy 

with the 19th century is correct, then the 30-year Poisson probability of M?,7 earthquakes (based 

on the earthquakes of 1836, 1838, 1868, and 1906) is estimated to be 0.72. 

The second argument pertains to the pairing of large earthquakes in this region in the 

nineteenth century. In 1836, there was a M 7 event on the northern half of the Hayward fault, 

and two years later, a M 7 event on the San Francisco Peninsula. In 1865, there was a M 6.5 

earthquah, possibly on the same segment of the San Andreas fault that produced the recent Lorna 

Prieta earthquake, and it was followed three years later by a M 7 earthquake on the southern 

Hayward fault (Toppazada and others, 1981). Such pairing could be coincidence, of course, and 

we have no physical model that supports a causal connection. Conversely, we cannot confidently 

dismiss the pattern as coincidence. 

31 
The third argument is based on a comparison of earthquakes along the Calaveras faults since 

1979 with the earthquakes in the decade preceding the 1868 Hayward earthquake. The 10 years 

prior to the 1868 Hayward earthquake were characterized by a high rate of activity primarily along 

the northern Calaveras fault, including six events between M 5.5 and M 6.1 (Ellsworth and others, 

1981). Since 1979 there have been four events of M 5.5 toM 6.1 in the same general area, an area 

which had not had any events larger than M 5.5 since 1911. In addition, since 1979 there has been 

a clear progression of activity from south to north along the southern Calaveras fault; the most 

recent activity has been near Alum Rock, just south of the point where the Calaveras and Hayward 

fault systems intersect (Oppenheimer and others, 1990). H this propagation of activity continues 

to the northwest, it might well involve a transfer of stress to the Hayward fault, potentially raising 

the likelihood of a repeat of the 1868 Hayward event. It should also be noted that a sequence of 

M 5-6 earthquakes occurred on the same section of the Calaveras fault between 1897 and 1911. 

This was not followed by a large earthquake on the Hayward fault. However, the earthquake in 

1897 and the two events in 1903 occurred at a time of heightened regional activity that culminated 

in the 1906 earthquake. 

Finally, it is instructive to compare these revised results for the San Francisco Bay region with 

those of the 1988 report for other parts of California. The Parkfield segment of the San Andreas 

fault in central California, with an estimated 30-year probability of >0.9 for a moderate-size (M 6) 

earthquake, remains the segment with the highest probability of rupture in California, as well as 

one for which the level of reliability of the estimate is considered highest. In southern California, 

the highest 30-year probabilities for individual fault segments estimated in 1988 were 0.5 for the 

Imperial fault and 0.4 for the Coachella Valley segment of the San Andreas fault. For the entire 

southern San Andreas fault, the probability of one or more large earthquakes was estimated to be 

0.6, and for the San Jacinto fault, 0.5; the probability would be still greater if the two faults were 

considered together. Many cities such as San Bernardino are close to both faults. Thus, these 

total probabilities are similar to the revised estimates for the San Francisco Bay region, although 

it should be emphasized that numerous active faults were not included in the evaluations for either 

area because of the lack of data. Furthermore, we again point out that a reevaluation of the 1988 

estimates has not yet been carried out for southern California, where many new data have also 

been gathered recently, and the probability estimates could change there as in the San Francisco 

Bay region. 

ACKNOWLEDGMENTS 

The Working Group thanks the many individuals who cooperated in preparation of this report. 

We particularly wish to acknowledge the contributions of expertise and unpublished data from 

Karin Budding, Lynn Dietz, Timothy Hall, Brian Kilgore, James Lienkaemper, Michael Lisowski, 

Mark Matthews, David Oppenheimer, Carol Prentice, William Prescott, Paul Reasenberg, James 

Savage, and Robert Simpson. The National Earthquake Prediction Evaluation Council (chaired 

by Thomas McEvilly) and the California Earthquake Prediction Evaluation Council (chaired by 

James Davis) reviewed the report and offered numerous useful suggestions. William Bakun and 

Thomas Heaton provided additional detailed technical reviews. Helen Gibbons edited the report. 

The efforts of Nancy Arp in preparing this report and in arranging the meetings of the Working 

Group are especially appreciated. 

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32 
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33 
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Geological Survey Open-File Report 85-754, p. 351-366. 

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California, and prospects for future earthquakes: Journal of Geophysical Research, v. 95, 

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34 
earthquake of April 18, 1906, Report of the State Earthquake Investigation Commission 

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398,62 p. 

35 

APPENDIX A-RECURRENCE MODELS 

The earthquake probability estimates in this report are based on current stochastic recurrence 

models of characteristic earthquakes, including explicit consideration of the uncertainty in the 

values of the parameters of these models. By "characteristic earthquakes" we mean the relatively 

narrow range of large events associated with successive "complete" ruptures of a specific segment 

(for example, Schwartz and Coppersmith, 1984). The frequency of occurrence of such events 

is not necessarily predicted by extrapolation of the conventional (Gutenberg-Richter) linear 

(log) frequency-versus-magnitude relationship. Further, because characteristic earthquakes are 

associated with a "cycle" of major stress drop and stress recovery, it is believed that the interevent, or recurrence, times of these events may follow a temporal pattern associated with a relatively 

narrow probability distribution (relative in this case to the exponential distribution associated 

with the reference case, a Poissonian recurrence model). In contrast to the Gutenberg-Richter 

magnitude-frequency distribution and the familiar Poisson recurrence model, the two general 

characteristics of this report's models, that is, a relatively narrow magnitude (or slip per event) 

range and a relatively narrow recurrence time distribution, are consistent with the notions of nearconstant strain rate and a nearly deterministic characteristic earthquake cycle. Furthermore, in 

this mechanical context, these two characteristics are also consistent with each other. As long as 

some degree of proportionality exists between actual successive earthquake slips and recurrence 

times-for example, that proportionality associated with a. constant slip rate1-this narrowness of 

one distribution will imply the narrowness of the other. 

There are many probabilistic models that display these two basic characteristics. The 

discussion here is limited, first, to the simplest, the renewal model, because it has been widely 

studied, and second, to the time-predictable model favored by the current Working Group. The 

developments for the first are easily extended to the second. In both cases the recurrence time, 

T, follows a. probability distribution, fT(t), with (marginal) median value, i', and variability or 

dispersion measure, q. In this report the dispersion measure is defined to be the standard deviation 

of the (natural) logarithm ofT. In the range of our interest, this parameter is approximately equal 

to the coefficient of variation, that is, the standard deviation divided by the mean of the recurrence 

times. Various distribution types have been used in the literature for IT (t), including normal, 

lognormal, Weibull, and gamma. For any single segment there is insufficient data to distinguish 

among these distribution types; fortunately the majority of forecasts in this report are insensitive 

to the choice. The Working Group's general policy has been to retain the assumptions of the 1988 

Working Group unless more recent evidence compels us to do otherwise. Therefore the lognormal 

distribution has been used again in this report. Research by Nishenko and Buland (1987) supports 

this assumption: 

RENEWAL MODEL 

The renewal model for characteristic events on a segment is based on the assumption of 

(probabilistic) independence among the sequence of recurrence times (T1 , T2 , ••• ) and the sequence 

of slips per event (Dt, D2, ... ). Probability forecasts are based on conditional probability 

statements, the condition being that no event has occurred between the previous event and the day 

of the forecast, that is, that a time, Te, has elapsed since the last event. For the renewal model, 

the forecast for the next 30--year interval is written 

1 Note, however, that there is always proportionality between the mean (or median) of the slips per event and 

the mean (or median) of the recurrence times (by definition of the slip rate), even if, for example, the characteristic 

earthquakes occur in a Poisson fashion. 

37 
Cf0 = P[Te < T $ Te + 30 I T ~ Te] 

FT(Te + 30) - FT(Te) 

1- FT(Te) 

in which the cumulative distribution function, FT(t), is related to the density function by 

(A-1) 

(A- 2) 

A graphical interpretation of equation (A-1) is given in figure A-1. Equation (A-1) is equivalent 

to equation 2 in the main body of the report. Typical plots of the function Cia versus Te (for 

given parameter values, T and u) are shown in figure A-2. The value of u dictates the sensitivity 

of the forecast to the elapsed time; for u ~ 1.0, the probability is virtually independent of the 

elapsed time. (More precisely, for an exponential recurrence distribution, that is, for a Poissonian 

recurrence model, which has a coefficient of variation of 1.0, C~ is independent of Te. In other 

words, the Poisson process has no memory. Note that, in general, when Te is about two-thirds of 

T, the hazard is approximately equivalent to that of the Poisson model no matter what the value 

of u. See fig. A-2.) 

PARAMETRIC UNCERTAINTY 

In practice it is difficult to know with precision the numerical values of parameters in this 

model for a specific fault. Following the practice of the 1988 Working Group (and practice in 

the engineering seismic hazard community), we treat the uncertain parameters in turn as random 

variables. The simplest model of parametric uncertainty considers only T, the median, as uncertain 

and ignores the uncertainty in the dispersion measure. For reasons that will become clear below, 

this Working Group concurs with the 1988 Working Group in adopting this parametric uncertainty 

model and, further, in using a common value of 0.21 for the measure of variability of recurrence 

times. (The basis for this particular numerical value is the report by Nishenko and Buland (1987), 

who found it to be a representative value for circum-Pacific segments.) It will be seen below that 

the precise value of this parameter estimate is not critical provided it is less than about 0.3. Again 

like the 1988 Working Group, we assume that the parametric uncertainty in the median, T, can 

be represented by a lognormal (prior) distribution with a specified best-estimate (median) value 

and a specified parametric uncertainty measure, denoted uP, which is the standard deviation of the 

(natural) log of the uncertain median. In this report, uP reflects the combined uncertainty in the 

slip per event and slip rate whose ratio is used to estimate the median T. Typical values are about 

0.4 (tables 3 and 7). 

The simplest way to deal with parametric uncertainty is to "fold it in" with the intrinsic, 

obtaining what is called a "predictive distribution" on the recurrence T. For the assumptions 

here it can be shown (for example, Benjamin and Cornell, 1970, Chapter 6) that the predictive 

distribution ofT is again lognormal with median T and net uncertainty, parameter, u N: 

(A- 3) 

in which o-1 is now used to denote the "intrinsic," random, or event-to-event recurrence-time 

variability observed on a given segment, the parameter which was set equal to 0.21 in the discussion 

above. With this approach, one can again use equation (A-1) to calculate "the" conditional 

probability of an event in the next 30 years given an elapsed time interval of Te years. The result is 

"the" value of this probability in that it has effectively considered each possible value of T and its 

relative likelihood (multiplied times the 30-year probability associated with that value ofT). As we 

shall see below, the result can also be interpreted as a mean estimate of this conditional probability, 

38 
~ (f) 

z 

w 

0 

~ :::::i 

Ill 

<( 

Ill 

0 

a: 

a.. 

0 

TIME 

Figure A-1. Graphical interpretation of cJo. the conditional probability of 

Te ~ T ~ Te + 30 given T > Te. See text for explanation of variables . 

._•g 

t) 

~ _J 

Ill 

<( 

Ill 

0 

a: 

a.. 

_J 

<( 

z 

0 

1-

0 

z 

0 

() 

I 

- --

ELAPSED TIME, Te 

a: 0.2 

I 

a::0.4 

a: 1.0 

f 

Figure A-2. Conditional probability. cJo. of an earthquake in the next 30 years 

given an elapsed time of Te since the last event. for several values of u. 

the degree of dispersion in the recurrence-time distribution. (Assumption: 

Recurrence interval. T. is much greater than 30 years.) 

39 
cJ0. Equation (A-3) explains why these estimates of cJ0 are insensitive to the intrinsic variability 

u1: if the parametric uncertainty, uP, is approximately 0.4 or more, then the net uncertainty, u N, 

is insensitive to un provided u1 is less than about 0.3. 

It has been found effective when dealing with technical probability assessments to report more 

than simply a best estimate; we can also make explicit the degree of uncertainty in the estimates. 

Here the parametric uncertainty in the median (represented by the value of uP) induces uncertainty 

in c[o. If we rewrite equation (A-1) as 

cT· (T) = FT(Te + 30; T) - ~T(Tei T) 

80 1 - .F (T · T) ' 

T '" 

(A- 4) 

it emphasizes the fact that c[o is a function of the uncertain parameter T. (It is understood in 

this paragraph that the distribution FT(t; T) has for its dispersion level only the intrinsic value, 

un that is, 0.21 in these calculations.) Assuming that C~(T) is monotonically decreasing in T 

in the range of interest, we can find the fractile, c', of CJ0 by calculating the probability that T 

is less than the corresponding value of the median, t'. (For a given value of c', the corresponding 

value oft' is found by solving equation (A-4) for T.) To calculate this probability we must use 

the distribution on the uncertain parameter T. This computation is complicated somewhat by the 

fact that the distribution on T must be "updated" to reflect the information that this particular, 

current recurrence time is greater than Te, the elapsed time since the last event (see, for example, 

Davis and others, 1989). The updating uses Bayes theorum: 

(A- 5) 

In this equation ff,(t) is the "prior" distribution on the uncertain median (here lognormal with 

dispersion uP), while f;(tiT>Te) is the "posterior" distribution (given the observation that 

T > Te)· Note that ff,(t) is modified by the "likelihood function" (that is, the likelihood of 

the observation given that the true median, T, has value t), which here is P[T > Te IT= t]. This 

probability is obtained from the (intrinsic; u = u 1 ) distribution on the recurrence time, T, but as a 

function of its median, T. In this application P[T>TelT=tJ varies from zero to one as t increases; for 

example, if the true median is very small, it is unlikely that one would have observed a recurrence 

interval as large as Te. Therefore, such small values ofT are "downweighted." Finally, the coefficient 

kin equation (A-4) is a normalizing factor that "ensures" that the posterior distribution on T has 

unit area. In practice these computations are conducted by numerical integration (or simulation). 

Making the calculations at a set of values, c', defines the probability distribution on the uncertain 

forecast cJo induced by the uncertainty in the parameter f. From this distribution one can 

read specified fractiles, for example, quantiles corresponding to probabilities of 0.25, 0.5, and 0. 75. 

Results of such calculations appear in appendix C. In addition to fractiles, one can calculate the 

mean of the distribution of C[0; it can be shown that it is equivalent to "the" probability calculated 

from equation (A-1) using the predictive distribution on T, that is, using the total uncertainty uN 

(equation (A-3)). Therefore this result, which was also used by the 1988 Working Group, implicitly 

includes the updating of the distribution on the median due to the "open interval" information, 

T > Te. 

TIME-PREDICTABLE MODEL 

In contrast to the renewal model, the time-predictable model of characteristic earthquake 

recurrence is based on the assumption that there is positive correlation between the slip, D,, in a 

particular event on a segment and the subsequent recurrence time, T;, to the next event. Further, 

some form of proportionality is assumed between the recurrence time and the slip. In this report 

40 
we adopt the probabilistic model 

(A- 6) 

in which D1 is the (random) slip in the ith. characteristic earthquake in a sequence, T, is the 

subsequent recurrence time to the next event, V is a constant (the constant slip rate), and Ei is 

an (independent) random deviation term (with unit median value). Then, as discussed above, the 

(marginal) median ofT is equal to the (marginal) median of D (that is, the median slip per event) 

divided by the slip rate, V. Conditional on knowing that the slip Di was, say, d, the conditional 

median ofT, is d/V. Further, noting that ln Ti = -ln V + ln D, + ln Ei, we see that u, the marginal 

standard deviation of the log of T, is J u1 + u~, in which u 0 is the marginal (event-to-event) 

standard deviation of log D and uE is the standard deviation of log E. In contrast, the conditional 

standard deviation of ln T (given D,) is only uE. (We retain the somewhat unusual notation of u 

for standard deviation of the log of the ·variable.) 

We need not repeat the results (equations (A-1) through (A-5)} for the time-predictable 

model. All the analysis developed above for the renewal model applies equally well to the timepredictable model, provided one interprets those distributions, parameters, and probabilities as 

conditional on the slip in the last event. For example, T and u in equation (A-1) are now the 

conditional median and (log) standard deviation given the slip. The probability distribution 

functions FT and IT in equation (A-1) and (A-2) are those of the conditional distribution of 

T given D, and so on. 

As stated, the Working Groups utilized the time-predictable model, and therefore the adoption 

of the lognormal type of distribution and the value u1 = 0.21 are both strictly applicable to the 

conditional distribution on T given the past slip. For notational and editorial simplicity in the 

main body of the report, the notion that all is conditional on D = dis normally deleted in the 

presentation. It is implicit. Note, as is clear in the model above, that the conditional (log) standard 

deviation ofT is less than (or equal to) the marginal value. Hence, using 0.21 for the conditional 

value may be an upper bound because the Nishenko and Buland (1987) analysis, upon which the 

value is based, was conducted on marginal distributions. In fact there is as yet little evidence to 

establish the relative values of the marginal and conditional values of these dispersion measures, 

or equivalently the correlation coefficient2 between ln D and the successive ln T. Preliminary 

investigations show negligible estimated correlation between (estimated) characteristic magnitudes 

and logs of the succeeding recurrence times on a given segment, but the implied measurement noise 

(in relation to log slips and log times) is severe. 

In the current application of these models to San Francisco Bay region forecasts there is little 

possibility to distinguish between the renewal and time-predictable model in any case. For virtually 

every segment there is only one past known earthquake. Therefore the best current estimate of the 

median slip per event, fJ, is simply the slip in the last event, D. In this case the current estimate 

of the marginal median of T (that is, iJ /V) is numerically equal to the conditional median of T 

given the past slip8 (that is, D/V). The former is used in the renewal model and the latter in the 

time-predictable model. Provided one continues to use 0.21 for both the marginal and conditional 

variability measure, the two models will then produce the same forecast probability. As more 

information becomes available it will be possible to distinguish between the two. 

2 For the model in equation (A-6), the correlation coefficient between lnT and lnD is ui:,f(ui:, + u~), that is, 

ui:,Ju;. The renewal model, incidently, is obtained by replacing D0 by its median, fJ, in equation (A-6). 

8 The slip in the last event, like the "constant" slip rate V, can only be estimated, of course, but that is a separate 

parameter-estimation problem discussed above and in the body of the report. 

41 
APPENDIX B-LOGIC-TREE ANALYSIS OF SAN ANDREAS FAULT PROBABILITIES 

The Working Group has employed a logic tree to incorporate alternative interpretations of data 

and modeling of processes into the evaluation of earthquake probabilities. A logic-tree analysis 

consists of specifying the alternatives for potential outcomes or interpretations of parameters. 

Relative weights or likelihoods that a specific alternative is the correct one are assigned at branch 

points in the analysis (nodes). The sum of the branch weights at each node totals 1.00. For this 

study, the weights are based on the judgments of the Working Group and consist of the simple 

averages of weights polled from Working Group members. 

Logic trees for earthquake probabilities on the southern Santa Cruz Mountains segment, the 

San Francisco Peninsula segment, and the North Coast segment are illustrated in figure B-1. Branch 

weights are indicated on the logic-tree diagrams. The logic-tree for the San Francisco Peninsula 

segment contains more branches than the others and serves as the basis for the following discussion. 

SEGMENTATION 

The first node of the San Francisco Peninsula segment logic tree arises from uncertainty over 

the segmentation of this part of the fault. The upper branch retains the single San Francisco 

Peninsula segment. The lower branch considers the possibility of earthquakes on two segments, the 

northern Santa Cruz Mountains segment and the mid-Peninsula segment. These alternatives are 

discussed in the report. We have assigned a likelihood of 0.56 to the single-segment branch and a 

likelihood of 0.44 to the two-segment branch. 

RECURRENCE TIME 

For each fault segment the next node represents the choice between models 1, 2, and 3 for 

estimating the median recurrence time, T, and its associated parametric uncertainty, uP. The 

logic trees for the southern Santa Cruz Mountains and North Coast segments have only this single 

branching point. In each logic tree, the assigned weights for recurrence time models 1, 2, and 3 are 

0.13, 0.47, and 0.40, respectively. 

For models 1 and 2 the basis for the best estimate (the median) of T and its uncertainty 

measure, uP, are 

(B- 1) 

where uP, u 0 , and uv are the standard deviations of the logs reflecting parametric uncertainty, 

respectively, of the uncertain median, T, slip in the last event, D, and slip rate, V. The value 

of u 0 was estimated by the coefficient of variation of D, that is, by the standard deviation of 

the estimate, 80 , divided by the best estimate of D. The segment displacements, D, used in the 

model 2 calculations were estimated using a separate logic tree described later in this appendix. 

For the case of model 3, Tis based on TLP, the updated estimate ofT for recurrence following 

the 1906 earthquake as given by equation (7) in the body of the report: 

(B- 2) 

The estimate TLP is equivalent to the weighted product (that is, a geometric mean): 

TLP = 83wl132w2 = 83wl ( ~) W:~' (B- 3) 

42 
Segmentation 

model 

Logic tree for San 

Francisco Peninsula 

Recurrence-time 

model 

Accept model for effect of 

stress on elapsed time 

Southern Santa Cruz Mts. 

Recurrence-time 

model 

Logic tree for southern Santa 

Cruz Mountains segment 

North Coast 

Logic tree for North 

Coast segment 

Figure B-1. logic trees for San Francisco Peninsula, southern Santa Cruz Mountains, and North Coast segments of San Andreas fault. SFP. 

NSCM. and MP indicate branches for San Francisco Peninsula. northern Santa Cruz Mountains. and mid-Peninsula segments. respectively. 

Quantities in parentheses give assigned weight for the hypothesis represented by the branch. 
in which 

W1 = 1- W2, W2 = ( 1 ~ 1 ) . (B- 4) 

:3'12 + .212 

Hence, from the definition of recurrence-time model 3 (equation (6) in the report), the estimated 

recurrence time is 

T = 83wl (D)w2 + tl.D 

v v ' (B- 5) 

where D is the estimated 1906 slip at Lorna Prieta (2.5 ± 0.6 m), and tl.D is the difference 

between the 1906 slip on the segment of interest and the 1906 slip on the southern Santa Cruz 

Mountains segment. The approximate squared standard deviation of logT can be found by firstorder expansion (Benjamin and Cornell, 1970, p. 180): 

(B- 6) 

in which the S's are the standard deviations of the estimates of the indicated parameters. 

EFFECT OF LOMA PRIETA STRESS CHANGES 

The final node for the San Francisco Peninsula segment represents the decision of whether to 

accept or reject the calculations based on stress changes resulting from the Lorna Prieta earthquake 

that reduce the expected recurrence time by an amount tl.T. The magnitude of tl.T is based on 

three-dimensional elastic dislocation calculations of the Lorna Prieta earthquake slip that give 

the change of shear stress averaged over the entire segment of interest (R. W. Simpson and J .H. 

Dieterich, written commun., 1990). The branches for this node were independently weighted for 

the side of the tree having a single segment and for the side of the tree consisting of the two 

subsegments. For the single San Francisco Peninsula segment, a weight of 0.84 was assigned to 

branches that use the stress calculation to modify the expected recurrence times, and a weight of 

0.16 was given to the branches that use the unmodified recurrence times. For the two-segment side 

of the tree, which considers the northern Santa Cruz Mountains segment and the mid-Peninsula 

segment, a weight of 0.33 was given to the branches that use the stress calculation to modify the 

expected ~ecurrence times, and a weight of 0.67 was given to the branches that use the recurrence 

times unmodified by the calculated stress. 

Details of the stress field in the zone of concentrated stresses near the edge of the Lorna Prieta 

rupture surface are sensitive to model assumptions. Consequently, the effect of Lorna Prieta stress 

changes is greatest but possibly most uncertain for the northern Santa Cruz Mountains segment, 

which is relatively small and is adjacent to the Lorna Prieta rupture. The low weight assigned to 

the stress calculation in the two-segment branch reflects this uncertainty. 

The best estimates of the median recurrence interval from models 1 and 2 and including the 

effect of Lorna Prieta stresses are 

A D-D' ./ 

T = V ,uP= yu1-v• +u~ (B- 7) 

where D' is the equivalent displacement reduction resulting from the stress effect given previously 

in table 4. For branches in which recurrence time is calculated using recurrence time model 3 and 

44 
including Lorna Prieta stresses, 

(B- 8) 

AB in the case of equation (B-6), the approximate squared standard deviation of logT can be found 

by first-order expansion. The result is the same as in (B-6) except that (Siv + SA,) is used in 

place of SXv and (~D- D') is used for ~D. 

HYPOTHESIS TESTS 

It is our intention that as future large earthquakes occur (or do not occur) on the San Andreas 

and Hayward faults in northern California,··our estimated recurrence times will form a quantitatively 

testable set of hypotheses. Such a test was performed above (see equation 4, in the body of the 

report) to test whether the time of occurrence of the Lorna Prieta earthquake was consistent with 

the projections of the previous Working Group (1988). 

To facilitate tests of our hypotheses in the future, we have attempted to state all relevant 

parameters relating to segmentation and recurrence time quantitatively and to place reasonable 

uncertainties on those parameters. However, because of the logic-tree analysis we. have used for 

the San Andreas fault segments, precisely how to test recurrence-time hypotheses against future 

earthquakes may not be obvious. Hence, for each San Andreas fault segment we have computed 

a. single median recurrence-time estimate, T, and a net standard deviation, u N, to summarize our 

results in a simple way and in a form that is amenable to simple hypothesis tests (table B-1). The 

approximate median recurrence time for each segment that is given in table B-1 has been obtained 

by taking the weighted mean of the individual hypothesis T estimates listed in table 3: 

(B- 9) 

where fi is the recurrence time for hypothesis i. The net uncertainty, u N, given in table B-1 is 

computed for each segment by use of the following approximate formula: 

(B- 10) 

where SN; and SN are the standard deviations of the median recurrence time for hypothesis i and 

the weighted mean of the recurrence time for all hypotheses, respectively. Then the net standard 

deviation of the log of the median, u N, is given by 

(B- 11) 

Although the recurrence parameters obtained from equations B-9, B-10, and B-11' and listed 

in table B-1 could be used to compute probabilities, those probabilities will differ slightly from 

the probabilities given in this report (the difference is 0.01 or less). This is because the reported 

probabilities are based on the weighted mean of the probabilities computed from the individual 

hypothesis parameters. 

LOGIC TREE FOR MODEL 2 DISPLACEMENTS 

Recurrence times for model2 are dependent on the displacement, D, assigned to each segment. 

As discussed in the report, the amount of displacement that best characterizes the behavior of each 

segment has been one of the most difficult parameters to constrain. This is a result of differences 

between the 1906 geologic and geodetic observations and the lack of slip data from the 1838 and 

1865 earthquakes. To ensure that all possible interpretations were accounted for, displacement 

logic trees were constructed for the three possible San Andreas fault segments (San Francisco 

45 
Table B-1. Weighted means of recurrence time. 1'. and net uncertainty. u N. of San Andreas fault segments 

Previous Exp~cted 

Segment event magnitude t UN 

S. Santa Cruz Mountains 1989 7 90.9 0.81 

N. Santa Cruz Mountains 1906 6.5 94.9 .51 

Mid-Peninsula 1906 7 147.2 .40 

San Francisco Peninsula 1906 7 186.8 .85 

North Coast 1906 8 228.8 .86 

Peninsula, northern Santa Cruz Mountains, and mid-Peninsula) (table B-2). The displacement 

alternatives contained in each logic tree represent values for which there was an observational basis 

or which could be derived from a segment length/displacement relationship or could be based on 

other geologic arguments. The length/displacement relationship employed here is D = 2.8 X 10-5 L 

(Working Group, 1988). Segment displacements and weights are given in table B-2. 

The northern Santa Cruz Mountains segment contains five branches. Values are 0.6 m, a direct 

calculation using the rupture length of 22 km and the length/ displacement relationship; 1.0 m, the 

maximum observed 1906 surface offset; 1.4 m, the 1906 Wright-Laurel tunnel offset, which, even 

though located just south of this segment, had a displacement similar to the 1989 displacement and 

might be representative of displacements for this part of the fault; 2.6 m, the average 1906 geodetic 

slip; and 3.3 m, the maximum allowable 1906 geodetic offset. 

The mid-Peninsula segment has three branches. Displacement values are 1.1 m, the calculated 

value using a 40-km length and the length/displacement relationship; 2.5 m, the maximum 

measured 1906 surface offset; and 3.4 m, the maximum 1906 geodetic offset. 

The single San Francisco Peninsula segment contains four branches. Displacement values are 

1.8 m, a direct calculation using a 60-km rupture length and the length/displacement relationship; 

2.5 m, the maximum 1906 surface offset; 3.0, an average of 1906 geologic and geodetic observations; 

and 3.5 m, the maximum 1906 geodetic offset. 

PROBABILITIES 

The final consensus probability or' an earthquake on a segment is based on the weighted 

probability of each tip of the logic tree for that segment. The probability of an earthquake is found 

using the parameters (T, u, and Te) appropriate to the branches leading to that tip. Probabilities 

for each segment tip are summarized in appendix C. The final probability of a segment-rupturing 

earthquake is the sum of the weighted probabilities. The weighting factor for a tip is the product 

of the branch weights leading to that tip. For a given segment the sum of the weights equals 1.00. 

For the San Francisco Peninsula segment, where two segmentation alternatives have been 

considered, segment probabilities are subject to additional weighting by the segmentation weights. 

For example, the 30-year probability of an earthquake affecting the entire San Francisco Peninsula 

segment is the segment probability of 0.25 multiplied by the weighting factor for that segmentation 

alternative (0.56) giving a probability of 0.14. Similarly, the 30-year probability of the alternate 

case, that of earthquakes affecting only the northern Santa Cruz Mountains and mid~Peninsula 

segments are 0.44 x 0.41 = 0.18 and 0.44 x 0.20 = 0.09, respectively. The expected magnitude 

of an earthquake on the northern Santa Cruz Mountains segment is about 6.5 compared to an 

expected magnitude of about 7.0 for both the San Francisco Peninsula and mid..,;.Peninsula segments. 

Consequently, the total probability of an earthquake of about 7.0 originating on either the entire 

segment or the longer subsegment is 0.14 + 0.09 = 0.23. 

46 
Table B-2. Displacement weights for recurrence time model 2 

Displacement 

(m) 

0.6 

1.0 

1.4 

2.6 

s.s 

1.1 

2.5 

8.4 

1.8 

2.5 

3.0 

3.5 

Weight 

Weighted 

displacement 

Northern Santa Cruz Mountains segment 

0.06 

.15 

.86 

.42 

.01 

0.04 

.15 

.50 

1.09 

.OS 

Final D=l.SO* 

Mid-Peninsula segment 

.20 

.54 

.26 

.20 

1.35 

.88 

Final 0=2.46* 

San Francisco Peninsula segment 

.21 

.37 

.82 

.10 

.38 

.93 

.96 

.85 

Final 0=2.62 

*Weighted displacements do not add up to the final displacement because 

of rounding error. 

47 
APPENDIX C-TABULATIONS OF PROBABILITIES 

This appendix presents tabulated results of probability calculations for intervals of 5, 10, 20, 

and 30 years. Although the Working Group regards these probabilities to be significant only to the 

nearest tenth, we report the probabilities to two decimal places to permit quantitative comparison 

of our results with other calculations. 

San Andreas fault segment probabilities for each of the logic-tree branches described in 

appendix B are shown in table C-1. The "final" segment probabilities are the weighted sums 

of the branch probabilities. 

The final segment probabilities for the San Andreas, Hayward, and Rodgers Creek faults are 

listed in table C-2. 

DISCUSSION OF UNCERTAINTIES 

Throughout this report the Working Group has acknowledged the uncertainties in both the 

data and the models upon which our calculations are based. The procedure for calculating the values 

Table C-1. Probabilities of logic-tree branch tips 

[f, recurrence time; uP, parametric uncertainty; M, magnitude; n.a., not applicable] 

Probability for intervals 

Accept t beginning 1/1/90 

Model stress effect (years) Up Weight 5yr 10 yr 20 yr so yr 

Southern Santa Cruz Mountains segment, M"'7 (previous event=1989) 

1 n.a. 100±24 0.24 0.1S o.oo 0.00 0.00 0.00 

2 n.a. 84±24 .28 .47 .00 .00 .00 .00 

s n.a. 96±16 .17 .40 .00 .00 .00 .00 

Northern Santa Cruz Mountains segment, M"'6.5 (previous event=1906) 

1 no 156±45 .28 .09 .02 .04 .09 .15 

1 yes 127±45 .84 .04 .04 .09 .19 .29 

2 no 95±44 .44 .S1 .08 .15 .29 .41 

2 yes 70±4S .56 .16 .10 .18 .ss .45 

s no 96±86 .S7 .27 .09 .17 .S2 .45 

s yes 71±4S .56 .18 .10 .18 .8S .45 

Mid-Peninsula segment, M"'7 (previous event=1906) 

1 no 21S±60 .27 .09 .00 .01 .02 .OS 

1 yes 210±60 .27 .04 .00 .01 .02 .04 

2 no 129±49 .S7 .S1 .04 .09 .18 .27 

2 yes 127±49 .S8 .16 .04 .09 .18 .28 

s no 149±S1 .21 .27 .02 .OS .09 .16 

s yes 147±SO .20 .1S .02 .04 .09 .17 

San Francisco Peninsula segment, M"'7 (previous event=1906) 

1 no 188±54 .28 .02 .01 .01 .04 .07 

1 yes 176±5S .29 .11 .01 .02 .05 .10 

2 no 1S8±40 .28 .08 .OS .06 .14 .2S 

2 yes 128±88 .29 .S9 .04 .09 .18 .29 

s no 1S8±29 .21 .06 .02 .05 .IS .22 

s yes 129±28 .21 .S4 .OS .07 .17 .29 

North Coast segment, M"'8 (previous event=1906) 

1 n.a. 281±76 .27 .IS .00 .00 .00 .00 

2 n.a. 2S7±7S .so .47 .00 .00 .01 .02 

s n.a. 201±49 .24 .40 .00 .00 .02 .OS 

48 
Table C-2. Final probabilities 

(M, magnitude. See text for explanation of P11

, and P%] 

Interval Conditional Quartile probabilities 

beginning 1/1/90 probability 

Segment (years) (mean) Pal• pll• 

S. Santa Cruz Mountains 5 0.00 0.00 0.00 

M"'7 10 .00 .00 .00 

20 .00 .oo .00 

so .00 .oo .00 

N. Santa Cruz Mountains 1 5 .OS .05 .00 

M .... 6.5 10 .07 .11 .00 

20 .1S .22 .02 

so .18 .S1 .04 

San Francisco Peninsula2 5 .OS .OS .00 

M"'7 10 .06 .08 .00 

20 .14 .21 .01 

so .2S .sa .02 

North Coast 5 .00 :oo .00 

M"'B 10 .00 .00 .00 

20 .01 .00 .00 

so .02 .01 .00 

S. East Bay 5 .04 .05 .00 

M"'7 10 .08 .12 .00 

20 .16 .25 .01 

so .28 .40 .02 

N. East Bay 5 .05 .08 .01 

M....,7 10 .10 .16 .01 

20 .19 .82 .08 

80 .28 .46 .06 

Rodgers Creek 5 .04 .05 .00 

M....,7 10 .07 .11 .01 

20 .14 .28 .02 

80 .22 .85 .04 

1 Subsegment of the San Francisco Peninsula segment. Probability includes segmentation 

weight. 

2 Weighted average of San Francisco Peninsula segment and mid-Peninsula subsegment 

probabilities. 

of probability takes into account the quantifiable aspects of these uncertainties. The Working Group 

believes that the presentation of the estimates of probability is consistent with current practice in 

decision theory. The conditional probability obtained using the net uncertainty, u N, and reported 

here corresponds to the mean of the probabilities one would obtain from a sufficiently large number 

of calculations using only the intrinsic uncertainty, u 1 , and values of T repeatedly drawn from 

the posterior distribution on the uncertain median given that T > Te (see appendix A, equation 

A-5). Hence, we emphasize that the conditional probability obtained using u N represents "the" 

probability because it has considered all possible values of T and their relative likelihoods. 

There is, however, a view as set forth by Savage (1990, and written commun., 1990) that 

a better presentation of the results of the calculations is to give the distribution of probabilities 

obtained from u 1 using values of T drawn from the distribution on the uncertain median. Thus, in 

addition to the mean probabilities, we report probabilities obtained using values of T at the first 

and third quartiles of the parametric distribution1 and calculated with u1 alone. These quartile 

1 The parametric distribution ofT needs to be updated to reflect the information (equation. 2) that T > Te. See 

appendix A. 

49 
probabilities provide a measure of the range of probabilities permitted by the parametric uncertainty 

-assuming fixed u1 =: 0.21. The probability at the first quartile, Pt14 , is the probability obtained 

using the value of T that is larger than 75 percent of the recurrence times in the distribution. 

Hence, there is a 25-percent likelihood that the actual probability (that is, the probability that 

would be obtained if T were perfectly known) is less than Pt;4 or a 75-percel!t likelihood that it is 

greater. Similarly, the probability of the third quartile, Ps14 , uses a value ofT that is greater than 

25 percent of the recurrence times in the distribution, and there is a 75-percent likelihood that the 

actual probability is less than Ps14 • There is a 50-percent chance that the actual probability lies 

between Pt;4 and Ps1

.

1• For the San Andreas fault segments the quartiles were found by numerical 

integration of the weighted sum of the posterior parametric distributions (given T > Te) employed 

in the logic-tree analysis. 

Unlike other computations in this report, these quartile probabilities are quite sensitive to the 

detailed model and specific parameter values adopted. In particular, it can be shown that the 

calculated quartiles are very sensitive to the ratio of the intrinsic uncertainty, u1 , to the parametric 

uncertainty, uP. In contrast, for a fixed net uncertainty, uN = Ju: + u;, and given T, the mean 

probability will remain unchanged. Because of limited data for estimation of u1 , particularly from 

strike-slip faults, the numerical value of u1 may be rather uncertain. In addition, Savage (1990, and 

written conimun., 1990) argues that u1 may be different for different fault segments. Consequently, 

we believe the quartiles or other measures of the distributions of probabilities may not be well 

defined. However, because the net uncertainty is rather insensitive to un the mean probability 

is not very sensitive to ul" Figure C-1 uses the northern East Bay segment as an example to 

illustrate these effects. Savage argues that a large spread in the distribution of probabilities (for 

example, a large difference between Ps14 and Pt14 ) indicates low reliability of the assigned (mean) 

probability. However, note in figure C-1 that the distribution becomes broader as the uncertainty 

decreases. In keeping with the Working Group's general position, which is not to rely on results 

that are specifically dependent on details of a particular model, we recommend that these quartile 

values be used only with caution. The qualitative letter grades (for example, tables 5, 8, and 9) and 

statements regarding first-digit accuracy represent the Working Group's preferred position with 

respect to uncertainties in the segment and aggregated probabilities. 

50 
~ _J 

co 

<( 

en 

0 

a: 

0... 

1.0 

I 

I 

0.8 I 

I 

I 

I 

\ 

\ 

\ 

\ 

0.6 \ 

\ 

' ' 

0.4 

Mean 

0.2 

-------------- ---- / 

.,.-' 

0~--~~~~--._--~--~~--~--_.----~--~--~ 

0.0 0.2 0.4 0.6 0.8 1.0 

INTRINSIC UNCERTAINTY, G1 

Figure C-1. Sensitivity of quartile probabilities (P114 and Ps14) and 

conditional probability (mean) to intrinsic uncertainty. u1 . Dotted vertical 

line indicates value of u 1 (0.21) used in this study. Other parameters 

(median recurrence time. elapsed time. and parametric uncertainty) are 

fixed and are set equal to parameters used for northern East Bay segment. 

Time interval is 30 years. 

51 

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·envirorunental studies or wilderness mineral investigations. 

Hydrologic Investigations Atlases are multicolored or black-andwhitemaps on topographic or planimetri<.. bases presenting a wide range 

of geohydrologic data of both regular and irregular areas; principal scale 

is 1:24,000 and regional studies are at 1:250,000 scale or smaller. 

Catalogs 

Permanent catalogs, as well as some others, giving comprehensive listings of U.S. Geological Survey publications are available under 

the conditions indicated below from the U.S. Geological Survey, Books 

and Open-File Reports Section, Federal Center, Box 25425, Denver, 

CO 80225. (See latest Price and Availability List) 

"Publications of the Geological Survey, 1879-1961" may be purchased by mail and over the counter in paperback book form and as a 

set ofmicrotiche. 

"Publications of the Geological Survey, 1962- 1970" may be purchased by mail and over the counter in paperback book form and as a 

set of microfiche. 

"Publications of the U.S. Geological Survey, 1971-1981" may be 

purchased by mail and over the counter in paperback book form (two 

volumes, publications listing and index) and as a set of microfiche. 

Supplements for 1982,1983,1984,1985,1986, and for subsequent 

years since the last permanent catalog may be purchased by mail and 

over the counter in paperback book form. 

State catalogs, "List of U.S. Geological Survey Geologic and 

Water-Supply Reports and Maps For(State)," may be purchased by mail 

and over the counter in paperback booklet form only. 

"Price and Availabillty List of U.S. Geological Survey Publications," issued armually, is available free of charge in paperback booklet form only. 

Selectedcoplesofamonthlycatalog "New Publications of the U.S. 

Geological Survey" available free of charge by mail or may be obtained 

over the counter in paperback booklet form only. Those wishing a free 

subscription to the monthly catalog ''New Publications of the U.S. 

Geological Survey" should write to the U.S. Geological Survey, 582 

National Center, Reston, VA 22092., 

Note.--Prices of Government publications listed in older catalogs, 

announcements, and publications may be incorrect Therefore, the 

prices charged may differ from the prices in catalogs, announcements, 

and publications.