DCL-10-019, Requested Documents from the NRC - PG&E Shoreline Fault Zone Meeting

Requested Documents from the NRC - PG&E Shoreline Fault Zone Meeting

ML100680564
Person / Time
Site:	Diablo Canyon
Issue date:	02/26/2010
From:	Becker J Pacific Gas & Electric Co
To:	Document Control Desk, Office of Nuclear Reactor Regulation
References
DCL-10-019
Download: ML100680564 (68)

Text

Pacific Gas and Electric Company James R. Becker Diablo Canyon Power Plant Site Vice President Mail Code 104/5/601 P R Box 56 Avila Beach, CA 93424 805.545.3462 February 26, 2010 Internal: 691.3462 Fax: 805.545.6445 PG&E Letter No. DCL-10-019 U.S. Nuclear Regulatory Commission ATTN: Document Control Desk Washington, DC 20555-0001 Docket No. 50-275, OL-DPR-80 Docket No. 50-323, OL-DPR-82 Diablo-Canyon Units I and 2 Requested Documents From The NRC - PG&E Shoreline Fault Zone Meeting

Dear Commissioners and Staff:

On January 5, 2010, representatives from Pacific Gas and Electric Company (PG&E) met with the NRC to discuss the analysis of the California Central Coast Shoreline Fault Zone that is in close proximity to the Diablo Canyon Power Plant (DCPP).

During this meeting PG&E agreed to provide the following for the NRC staff:

• Calculation: Evaluation of Secondary Fault Rupture Hazard From The Shoreline Fault Zone A copy of a paper by Lloyd Cluff dated 1985 regarding techniques for assessment of fault activity slip rates and 2 provide the above requested documents. Enclosure 2 supports the previously communicated conclusion that secondary deformation due to the shoreline fault zone results in negligible change in the DCPP seismic core damage frequency.

PG&E makes no regulatory commitments as a part of this submittal.

swh/50086062/018 A member of the STARS (Strategic Teaming and Resource Sharing) Alliance Callaway

• Comanche Peak

• Diablo Canyon e Palo Verde *San Onofre e South Texas Project e Wolf Creek A00 I

Document Control Desk PG&E Letter DCL-10-019 February 26, 2010 Page 2 Enclosures cc: Norman A. Abrahamson Lloyd S. Cluff Elmo C. Collins, NRC Region IV Annie M. Kammerer, NRC Marcia K. McLaren Michael S. Peck, DCPP NRC Resident Alan B. Wang, NRR A member of the STARS (Strategic Teaming and Resource Sharing) Alliance Callaway

• Comanche Peak

• Diablo Canyon

• Palo Verde

• South Texas Project

• Wolf Creek

Enclosure 1 PG&E Letter DCL-10-019 Evaluation of Secondary Fault Rupture Hazard From The Shoreline Fault Zone

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Page 2 of 21 GEO.DCPP.10.01, Rev 0

3. RECORD OF REVISIONS:

Rev. Reason for Revision Revision No. Date 0 Initial Calc.

Reference:

Notification 50086062 Task 12 02/25/10

.4 4

Page 3 of 21 GEO.DCPP.10.01, Rev 0

4. PURPOSE:

The Shoreline fault zone is being characterized as part of a two-year study that will be completed in December 2010. During the first year of the study, an offshore fault that may be the surface expression of the Shoreline fault zone was identified through offshore geophysical surveys. This fault is located 0.6 km from the DCPP power block. Additional work during 2010 is needed to complete the characterization of the Shoreline fault zone and, in particular, to constrain the activity rate of the fault; however, given that the distance to the identified offshore fault is less than 1 kin, the potential for secondary rupture, on the order of a few cm, is considered. The only safety related structures that would be impacted by small secondary displacements resulting from the secondary fault rupture are eight Dresser couplings along the Auxiliary Salt Water (ASW) pipes that are located in the weaker rock unit called Unit c of the Obispo Formation (Tofc) (PG&E, 2009). Per Notification 50086062 Task 12, the purpose of this calculation is to estimate the probability that secondary surface rupture will occur at any one of the eight Dresser couplings along the ASW pipes from an earthquake along the Shoreline fault zone.

5. ASSUMPTIONS:

5.1. STYLE OF FAULTING It is assumed that the Shoreline fault zone is a strike-slip feature. The basis for this assumption is the characterization in the Action Plan that describes the Shoreline fault zone as a vertical strike-slip fault zone.

5.2. SEISMOGENIC THICKNESS A seismogenic thickness of 12 kilometers is assumed for the Central and Southern sections of the Shoreline fault zone. The basis for this assumption is that it is the thickness of the other faults in the region (LTSP, PGE 1988) 5.3. MINIMUM EARTHQUAKE MAGNITUDE FOR MOMENT BALANCE (Mm=0)

It is assumed that the minimum earthquake magnitude for balancing moment on the fault is magnitude 0. The basis for this assumption is that it is a commonly assumed value for calculating the activity rate based on moment balancing used in seismic hazard studies.

5.4. MINIMUM EARTHQUAKE MAGNITUDE FOR FAULT RUPTURE (Mmin)

Page 4 of 21 GEO.DCPP.10.01, Rev 0 It is assumed that the minimum earthquake magnitude for fault rupture is M5.0.

The basis for this assumption is that, given a model fit to the empirical data in Wells and Coppersmith (1994), no surface rupture is expected on a fault for earthquakes below M5.0.

5.5. FAULT b-VALUE It is assumed that the b-value for the Shoreline fault zone is 0.8. This assumption is based on the average b-value for California published by the USGS.

5.6. SHEAR MODULUS OF THE CRUST The shear modulus of the crust is assumed to be 3.Oel 1 dyne/cm 2. This is a commonly assumed value for this parameter.

5.7. YOUNGS AND COPPERSMITH CHARACTERISTIC EARTHQUAKE MODEL The Youngs and Coppersmith (1985) characteristic earthquake model is commonly assumed to represent the best model for describing the magnitude-frequency distribution of earthquakes on a fault.

5.8. WELLS AND COPPERSMITH RELATION FOR MAXIMUM DISPLACEMENT GIVEN MAGNITUDE The Wells and Coppersmith (1994) relationship for maximum displacement given magnitude is used to calculate the mean maximum displacement in meters given a moment magnitude. The basis for this assumption is that this relationship represents the state of the practice.

5.9. PRIMARY FAULT RUPTURE This calculation assumes uniform rupture of the Shoreline fault zone along the entire rupture area. It is therefore assumed that the primary surface rupture includes the section of the fault closest to DCPP. This is a conservative assumption made to simplify the calculation.

5.10. PROBABILITY OF SECONDARY FAULT RUPTURE

Page 5 of 21 GEO.DCPP. 10.01, Rev 0 The probability of secondary fault rupture within a 50 m x 50 m zone is assumed to follow the lower range of the Petersen et al (2004) data set as shown by the curve in Figure 5-1. The basis for this assumption is that the Shoreline fault zone is a straight strike-slip fault zone in the region offshore DCPP (PG&E, 2010), whereas, the data used by Petersen et al (2004) included secondary ruptures from strike-slip faults with more complex traces and stepovers.

O uor~grllO MOUmn~l a Wnpeftat Vaflay

~PG&E Assumption ASuperUdon Hill- Ehnor 01 Ranch sequence XLanders

,*l _ X Hector Mne o00i A I -. *4* jk rc25 m San Fernando SfrmPnpI

• Instances of no 0 0t_ý01 01 distrlbutdd rupture 0 200 4000 6=0 em0 10000 Distance from Pdrwnce Trace (mn)

FIG 4: Frequency of earthquake displacements within 50 m cells as a function distance from principal trace Figure 5-1. Frequency of earthquake displacements within 50 m cells as a function of distance from principal trace (Petersen et al, 2004). The red line shows the PG&E assumption.

5.11. GEOMETRY OF SECONDARY SURFACE RUPTURES

" It is assumed that if there is secondary rupture within the 50 m x 50 m zone that contains one or more of the Dresser Couplings, the secondary rupture will have a length that covers the full 50 m width of the zone. The basis for this assumption is that many secondary ruptures observed in past earthquakes have lengths of 50 m or more and it is conservative in terms of the hazard.

" It is also assumed that the secondary rupture is concentrated into a single knife edge rupture within the zone. The basis for this assumption is that it is consistent with the engineering analysis of the capacity of the Dresser couplings and is conservative in terms of the potential damage to the Dresser couplings (PG&E, 2009).

5.12. ASPECT RATIO OF STRIKE SLIP FAULTS

Page 6 of 21 GEO.DCPP.10.01, Rev 0 It is assumed that all ruptures on the Shoreline fault have an aspect ratio of 1.2 based on the fault dimension (14km/12km). Typical strike-slip faults have an aspect ratio of 2, but the aspect ratio, in this case, is limited by the fault dimension.

Page 7 of 21 GEO.DCPP.10.01, Rev 0

6. INPUTS:

6. 1. FAULT SEGMENTATION:

6.2. SEISMOGENIC THICKNESS SEISMOGENIC Segment THICKNESS (km) SOURCE Central 10 PG&E, 2010, Section 4.2 p.10 Central & 12 Assumption 5.2 Southern 6.3. CHARACTERISTIC MAGNITUDE CHARACTERISTIC Segment MAGNITUDE (Mw) SOURCE Central 6.00 PG&E, 2010, Section 5.2 p. 14 Central & 6.25 PG&E, 2010, Section 5.2 p. 1 4 Southern 6.4. FAULT DIP

Page 8 of 21 GEO.DCPP.10.01, Rev 0 6.5. DISTANCE TO DCPP RUPTURE DIST. (kin) SOURCE 0.6 PG&E, 2010, Section 4.3 p. 1 0 (Distance from Shoreline fault to DCPP power block) 6.6. SHORELINE FAULT b-VALUE:

6.7. SHEAR MODULUS OF THE CRUST (g):

6.8. SLIP RATE (S):

(mm/yr) SOURCE Lower bound 0.01 PG&E, 2010, Section 4.4 p.11, 12 Upper bound 0.3 PG&E, 2010 Section 4.4 p.12

Page 9 of 21 GEO.DCPP.10.01, Rev 0

7. METHOD AND EQUATION

SUMMARY

7.1 METHODOLOGY

The calculation of secondary rupture hazard follows the probabilistic method of Petersen et al. (2004). In this method, the probability of a displacement d that is larger than do occurring at a site location (x,y) with a square footprint that is z by z is given by Equation 2 of Petersen et al. (2004):

(d > do), a JfM (i) jfs(s) jf,(r)P[sr#O* Im]P[d Oj1l,r,m,z,s,sr 0]P[d -do I Ir;m,d # O]drdsdm (7-1)

M s r The individual terms are described below:

" fM(m): a probability density function that describes the magnitude-frequency distribution along a fault. Based on Assumption 5.7, the Youngs and Coppersmith (1985) characteristic model is used for fM(m).

" ct: a rate parameter that describes how often the earthquakes occur in the model above some minimum magnitude. This parameter is commonly called the activity rate, and it is defined based on a moment balance of the total accumulated seismic moment over the mean moment released per earthquake.

• fs(s): a probability density function that describes the probability of a rupture at a specific place along a fault. Based on Assumption 5-9, the fault rupture always passes through the point on the fault plane nearest to DCPP.

" P[sr#0lm]: the probability of surface rupture given magnitude. This probability term accounts for the possibility that an earthquake rupture on a fault will not reach the surface.

• P[d*0li,r,m,z,s,sr-:01: the probability of having non-zero displacement at a location (1,r) for a foundation size z given magnitude and an event with surface rupture.

• P[d!d011,r,m,d#0]: the probability of the secondary displacement d greater than or equal to a given value do at a location (1, r) given the magnitude of the earthquake on the Shoreline fault zone.

fR(r): a probability density function to define the distance from the main fault rupture to the site.

Based on Assumption 5.9, if there is surface rupture, it is assumed that the surface rupture includes the section of the fault closest to DCPP. With this assumption, the P[sr#0] terms are not dependent on location of the rupture (s). In addition, the closest distance from the rupture to the site is a constant (rmin), so f(r) becomes a delta function. Equation (7-1) becomes:

Page 10 of 21 GEO.DCPP.10.01, Rev 0 (do)= a "M AI~f()Jfjs~ss JS(r- rm)P[sr

• 0m,s]P[d

• 0r,z,sr *0]

nS r (7-2)

P[d Ž d0 IM,d o]dM dr Equation (7-2) simplifies to the following:

Ž(>do)=a Tfm(M)P[sr

• OlM]P[d* Olrmin,z,sr

• O]P[dŽ-dolM,d

• O]dM (7-3) m=Mm '

The Petersen et al (2004) paper gives a model for the probability of secondary rupture occurring within a 50 m x 50 m region at a distance r from the main trace.

For this application, the area for the eight Dresser couplings is smaller than 50m x, 50 m. The P[dL0[rmin,z,sr-A0] term can be written in terms of the probability that there is secondary rupture in a 50 m x 50 m region that contains the eight Dresser couplings and the probability that the secondary rupture is through one of the 8 Dresser couplings given that there is secondary rupture in the 50 m x 50 m region containing the Dresser couplings:

P[d # Olrrmin,z,sr # 0]= P[dI # 0jrminZ1 = 50mx _50msr # 0]P[d # 01z,dt

• 0] (7-4) where z is the combined area of the small region containing the eight Dresser couplings. The P[dl:i01rmin,Zi=50m x 50m,sr-*0] term is 0.004. It is read from Figure 5-1 (Petersen et al., 2004) Based on Assumption 5-11, the secondary rupture is assumed to have a length of at least 50 m, so the P[d:A0lz,di:A0] term is 0.048768 (see Section 8. Body of Calculations).

7.2 EQUATIONS 7.2.1. Youngs and Coppersmith Characteristic Earthquake Model (fM(m))

The Youngs and Coppersmith (1985) characteristic earthquake model is used to calculate the probability density function for the magnitude-frequency distribution along a fault.

for Mchar - 0.25 < M < Mchar + 0.25 1 83exp(-fJ(Mchar -Mmin -1.25))

f.mC Wm- I+c 2 1-exp(- /3(Mchar -Mmin -0.25))

for Mmin < M < Mchar - 0.25 1 8 exp(- f(M - Mmin))

frC W)I +c2 1-exp(- I(Mchar- Min -0.25)) (7-5b)

/

Page I1 of 21 GEO.DCPP.10.01, Rev 0 where: c2 = 0.5, exp(-/(Mchar - Mmi. -1.25)) (7-6) 1- exp(-/3(MChar -Mmin - 0.25))

/3 = ln(10)* (b - value) (7-7) 7.2.2. Activity Rate (a)

The rate of earthquakes on the fault above M=0 is computed by balancing the annual rate of moment accumulation on the' fault, AYo, with the long term rate of moment release in earthquakes. The following equations (7-8 to 7-12) for computing the activity rate based on fault slip-rates are given in Abrahamson (2009):

A-f0 = a(M >0)H 0 (7-8) where W0 is the mean moment per event .for earthquakes above M=0. The moment rate is given by:

A,0 = MS (7-9) and the mean moment per event is given by:

7o (M)= . fm(M)MO(M)dM (7-10) where the moment for a is given by:

Mo(M)= 1o1"5m+16"05 (7-11)

The activity rate is found by solving equation (7-8) for a:

AY a(M > 0)= -o MWo (7-12) 7.2.3. Probability of Surface Rupture on the Main Trace (P[sr-*0m])

Based on Assumption 5-4, a model fit to the empirical data in Wells and Coppersmith (1994) for the probability of surface rupture is used. This model is given by a histogram and parameterized by the following equations:

Log(RA) = -3.42 + 0.90M (7-13a)

Page 12 of 21 GEO.DCPP.10.01, Rev 0 (7=0.22 loglO units (7-13b)

For M > 5.0 P[sr-ýOjm] = 0.5 * (tanh(2.5 * (M - 5.9)) + 1) (7-13c)

For M < 5.0 P[sr-#Ojm] = 0 (7-13d) 7.2.4. Conditional Hazard from Secondary Rupture (P[d_>dOm,d:L0])

The conditional hazard from secondary rupture is given by:

P[i,*] log(d°)- log(D max(m))+ og Dm (714)

P[d>__do jm, d #O]=1-(l .tO.2o 2--- (7.1og---4)--

where (D is the cumulative normal distribution.

From Wells and Coppersmith (1994), Table 2B, the median value for the MD for strike-slip earthquakes is given by:

log(Dma,(m)) = -7.03 + 1.03m (7-15) and the standard deviation is given by:

C-ogDm, = 0.34 (7-16)

Peterson et al (2004), gives a histogram for the distribution of the ratio of the secondary displacement to the maximum displacement on the main trace (Ds/Dmax). This histogram was digitized and a mean and standard deviation were computed:

log(Ds/Dmax) =-1.587 (7-17) o- o*(DS/1D_.) = 0.537 (7-18)

The log-normal distribution based on the parameters in equations 7-17 and 7-18 is compared to the histogram in Figure 7-1. The log-normal distribution is a reasonable approximation to the histogram.

Page 13 of 21 GEO.DCPP.10.01, Rev 0 16 Figure 7-1. Histogram showing the frequency of logl0 normalized displacements (Petersen et al., 2004)

Page 14 of 21 GEO.DCPP.10.01, Rev 0

8. SOFTWARE:

All calculations were made using a script written in MatLab v7.4.0 (R2007a). An independent verification of the MatLab script was preformed in excel. The agreement between the MatLab and Excel values indicate that MatLab is operating correctly.

9. BODY OF CALCULATIONS:

9.1 CONDITIONAL PROBABILITY OF SECONDARY RUPTURE INTERSECTING A DRESSER COUPLING Based on Assumption 5-11, the conditional probability that rupture occurs through any one of the eight 1-ft long Dresser couplings, given that there is secondary rupture in the 50m x 50 m zone containing one or more Dresser couplings is:

P[d # 0z,d 1 # 0] = 8 ft / 50 meters = 2.4384 meters / 50 meters = 0.048768 9.2 CALCULATION FOR PROBABILITY OF SURFACE RUPTURE The Wells and coppersmith (1994) data (Table 1) lists earthquakes with surface rupture and without surface rupture. The ratio of the number of earthquakes with surface rupture to the total number of earthquakes within a magnitude bin provides an estimate of the probability of surface rupture for the magnitude range. The values are listed in Table 9-1 Table 9-1. Earthquakes used by Wells & Coppersmith (1 94), Table 1.

Mag Bin Total Number of Number of Fraction of Earthquakes Earthquakes Earthquakes with Surface with Surface Rupture Rupture 5.0-5.5 28 3 0.107 5.5-6.0 44 14 0.318 6.0-6.5 43 20 0.465 6.5-7.0 59 45 0.763 7.0-7.5 40 35 0.875 7.5-8.0 15 14 0.933 8.0-8.5 2 2 1.000 The fraction of surface rupturing earthquakes is shown in Figure 9-1 as a function of magnitude. The Wells and Coppersmith (1994) data set is a global data set with varying crustal thickness. For the Shoreline fault, the thickness is 10 km for the central segment and 12 km for the Central & Southern Segments (Input 6.2). The widths of the two rupture scenarios restricts the magnitude for which the rupture can be buried (e.g. no surface rupture).

Page 15 of 21 GEO.DCPP.10.01, Rev 0 Using the Wells and Coppersmith (1994) model (see Table 2A) for rupture area as a function of magnitude for strike slip earthquake (Equation 7-13a),

Log(RA) = -3.42 + 0.90M with a standard deviation of a=0.22 logl 0 units.

For a given magnitude, there is a 2.5% chance of the rupture area being less than the median minus 2 (Y. The 2 . 5th percentile rupture area as a function of magnitude is listed in Table 9-2.

Width = sqrt(area/AspectRatio)

The rupture width is the full 10 km fault width for the central segment rupture scenario for M>=6.6. The rupture width is the full 12 km width for the central &

southern rupture scenario for M>=6.8. Therefore, the probability of surface rupture is 97.5% for M6.6 for the 10 km width case. Similarly, it is 97.5% for M6.8 for the 12 km width case. These two points are shown on Figure 9-1.

U Wells and Coppersmith (1994)

- Modle I Constraint for 1Okm fault width m Constraint for 12km fault width 0O.9 0,I.

0.7.-

I.0.6 0.4.;

0 5 5.5 6.5

& 7 7.5 a 8.5 Magnitude Figure 9-1. Surface Rupture Probability Histogram Next, a smooth functional form was developed to fit the constraint on the probability of surface rupture for the two rupture scenarios for the Shoreline fault.

Page 16 of 21 GEO.DCPP. 10.01, Rev 0 A hyperbolic arctangent function was used. The model parameters were selected so that the resulting probability was close to the constrained values for M6.6 to 6.8 and close to the Wells and Coppersmith values (from Table 9-1) for M5.75. The resulting fit is shown in Figure 9-1 For M _>5.0 P[sr-AOm] = 0.5 * (tanh(2.5 * (M - 5.9)) + 1) (7-13c)

For M < 5.0 P[sr-AOjm] = 0 (7-13d)

Table 9-2. 2 .5 th Percentile Rupture Area as a Function of Magnitude Mag 2 .5 th percentile rupture area Width for aspect ratio of 1.2 6.5 98 9.0 6.6 120 10.0 6.7 148 11.1 6.8 182 12.3 6.9 224 13.7 9.3 HAZARD CALCULATION The MatLab computer code used to carry out the calculations is listed below:

Prohab-i I is Li c Ruptutre Haze rd: s cIi pt fo(U Ca I ý'ul t iuI Q adary ruptire di sp] acements Wr itLten By: Kat-hrtyn Woa)dd(el 12/01/2009 Modi fied 02/23/2020 Note: This scr ipt r ons t-he case for t he Cent ra 1 t Soul iethern Shorel ine fault zone with a slip rate of 0.3min/yr and 2.0 cm of secondary rupture. The j np)ts are: M6.25, L=] 4km, W] 2km, S-0 . 3mm/yr, and Zin=2 . 0cm.

INPUITS FOR ALL, CASES RUN IN GEO. DCPP. 10.01, Rev 0:

CENTRAL SEG (s] ip rate 0.0trirm/yr and 1.0 cm of seco nalar y rupture)

INPUTS: M6.0, L-8k , W- 10krl, S=-0.01mr-/yr, Zin =1.c CENTRAL SEG (s] ip rate=0.0]mc!/yr and 2.0 cU or ndary rupture)

INPUTS: M6.0, L-8kri, Wk B 0kmn, S-0 .)nTi/yr , Zir--2 . :0M CENTRALiSO SEC (slip rate (".01rimm/yr and .0 ct-v o! s acotirlary rupture)

INPUTS: M6. 25, L- 4kri, WI 12 2km, S (.0 mu, yr , 7Z I . Hr.rn

(,'ENTRALfSO SEG (slip) rate .OSE1rci s r and 2.(,, cc o3 secc )nalary rupture)

I N P -'TrS : M6 . 25, L-- 1 4 kn[, VJý 2kmi, S= 0. 01mv/yr, Zin-2. .(r=

Page 17 of 21 GEO.DCPP.10.01, Rev 0 CENTRAL SEG (slip rate=0.3rui/yr ard 1.0 cEn of secondary rupture):

INPUTS: MW.0, L=8km, W=10km, Sý0. 31im/yr, Zin=1 .0cm CENTRAL SEG (slip rate=0.3rmm/yr and 2.0 cm cf secondary rupture):

INPUTS: M6.0, L=8km, W=10km, S=0.3mm/yi, Zin=2.0cm CENTRAL-SO SEG (slip rate=0.3mm/yr and 1.0 cm of secondary rupture):

INPUTS: M6. 25, L=14km, W=2km, S=0. 3mm/yr, Zin-1 .0cm CENTRAL4SO SEG (slip rate=0.3mm/yr and 2.0 cm of secondary rupture):

INPUTS: M6.25, L=1 4km, W=]2km, S-0.3!mm/yr, Zirn:2.0cm INPUT VALUES:

Mchar = 6.25; Mean char. EQ mag (2 Cases: M6.0, M6.25) (Input6.2 Mmin = 5.0; Min. EQ mag for fault. rupture (Assumption 5.4)

Mmo = 0.0; Min. EQ mag for moment balance (Assumption 5.3) delM 0.01; Magnitude increment (step size) b = 0.8; Fault b-value (Assumptior 5.5) mumod = 3.00e+ll; Shear Modulus of crust (dyne/cm^2) (Assumption 5.6 L = 1400000; Fault length (cm) (2 Cases: 8km, 14km) (Input 6.1)

W = 1200000; Fault width (cm) (2 Cases: 10km, 12kmi) (Input 6.2)

S = 0.03; Slip rate (cm/yr) (2 Cases: 0.01mm/yr, 0.3rrmt/yr)

(Input 6.8)

Zin = 0.02 'ý Miniimum amoujnt of secotndary rupture (m)

DEFINE PARAMETERS USED IN SUBSEQUENT CALCULATIONS:

B = log(10)*b; Equation (7-7)

% Note: In MatLab log(x)==in(x), logl0(x)..log(x)

Parameter used in Y&C characteristic EQ model: Equation (7-6)

NOTE: c2 uses a min mag (M5.5) for the nain EQ mag expected to cause surface rupture and c2 0 uses a mtj EQ may (MO) that is used to comput 9 the moment balance.

c2 = (0.5*(B)*exp(-l*B*(Mchar-Mmin-1.25)))/(1-exp(-!*B*(Mchar-Mmin-0.25)));

c2 0 = (0.5"(B)*exp(-l*B* (Mchar-Mmo-l.25))/(l-exp(-l*B*(Mchar-Mmo-0.25)));

MoACC = mumod*L*W*S; Accumulated Seism Moment: Equation (7-9)

Define mag vectors for Y&C char FQ nau catculation M = Mmin+(delM/2):delM:Mchar+0.25; Mag for YC calc N (for fault rupture)

M_0 = Mmo+(delM/2):deiM:Mchar+0.25; Nau for YC calc (moment balance) sInitialize arrays for Y&C mag caics YC = zeros(l,length(M));

YC 0 = zeros(1,1ength(M 0));

, YOUNGS AND COPPERSMITH CHARACTERISTIC EQ MODEL (For moment balance) for k = l:length(M_0)

M_0(k)

Page 18 of 21 GEO.DCPP.10.01, Rev 0 Mo2(k) = 10^((l.5*M 0(k))+16.05); SeisIic Momnrtit: Equation (P-11) if M 0(k) > Mchar - 0.25; Ma-ig pdt - Y&C Char. EQ YC_0(k) = (1/(l+c2 0))*... 'Model: Equatioýn (7-5a)

(B*exp(-I*B*(Mchar-Mmo-i.25) ) )/ ...

(1-exp(-l*B*(Mchar-Mmo-0.25) )  ;

else YC_0(k) = (I/(l+c2 0))*... FAg pdf - Y&C Chai. EQ (B*exp(-l*B* (M 0(k)-Mmo) ) )/ ... M ]Eqs irn (7-51) l1-exp -I'B* (Mchar-Mmo-0.25)) )) ;

end Pm 0(k) = YC 0(k)*delM; P)hirbatility j~ t F r tO hcu MjNgri t ii I MoEQ(k) = Pm 0(k)*Mo2(k); @.riSrfdi Mrr Per FQ end MeanMoEQ = sum(MoEQ); iso] sr . rfvciiirt F

[.,r. Eby: Eq -ltdI0].I-lU NMmo = MoACC/MeanMoEQ A-t ivit s, Rot r EQs aoh ve I-1: Eqo<a iorn ( -, YUONGS AND) COPPEFSUIIl CHARPKA( ERIS'! C Ei MODEL f C)I f ýýu I r rup 'Lu rf7-for i = l:length(M)

M(i)

Mo(i) = I0^((1.5"M(i))+16.05); Seismn(i C Mo- ,c ent: Eq iiil~ 7-li) if M(i) > Mchar - 0.25; FUl'Jg d - ',]7 Cr~r EQ YC(i) = (l/(l+c2))*...

((B*exp(-l*B*(Mchar-Mmin-l.25) ))/...

(l-exp(-l*B*(Mchar-Mmin-0.25))  ;

else YC(i) = (I/(l+c2))*...

MO -ý 1l-:l irt: t/ Ky1)

((B*exp(-l*B*(M(i)-Mmin)))/ ...

(l-exp(-l*B*(Mchar-Mmin-0.25))))

end Pm(i) YC(i)*delM; Pr ic-UI')jI j1 i t' y f , FyprfIIJ i: , gTI i r uI PROBABILITY OF SUIRFACE R1P'T R1F U GIVEN MAGN]IU F if M(i) >= 5.0; Psurf (i) = 0.5* (tanh(2.5* (M(i)-5.9))+1);

else Psurf(i) = 0; Lid) end MA4iXIMUIM DISPI ACEHcMFNI 1IVFN VA0]) MVIDE:

loglODmax(i) = -7.03 + 1.03*M(i); Equaticn ,/

sigma = 0.34; Fquatio ( I ý,

mu = loglODmax(i);

PRATIO OF MINIMUM 'I( PAXrIt i I]Di' :

h II-A EIEI)1 OFF mu2 -1.587; sig2 = 0.537; logd0 = (loglO(Zin)); l aq 1r ii ii apE l-]' V,,i U P denom = (sigma^2 + sig2"2)"(l/2); clcirca'if .r Etq ý-2l' ( /-14)

Page 19 of 21 GEO.DCPP.10.01, Rev 0 A = ((logdO-(mu+mu2))/denom); 'e1m for calculating trie cc.

n~orm dist. in Equartion (7-14) eps i onl )

Pd(i) = 1 - normcdf(A,0,1) E`qat ion (/-14)

PFROBABTLI TY OF SECYONDIAPY SURFACE F IITUIRF -- for valies 0.04 and 0.04K76F see "Body of Calculations" integrand of FquaLtion (7-3)

Pl(i) = Pd(i)*Pm(i)*Psurf(i)*0.004*0.048768;

'integoand scalerd by ati Ivity rate Haz(i) = NMmo.*(10^((-l*b)*Mmin)).*Pl(i);

end Hazard = sum(Haz);

Page 20 of 21 GEO.DCPP.10.01, Rev 0

10. RESULTS AND CONCLUSIONS:

RESULTS The results of the secondary rupture hazard are given in Table 9-1 in terms of the probability of exceeding 1 cm and 2 cm at any one of the eight Dresser couplings. This table gives the results for a range of assumptions on the segmentation of the Shoreline fault zone (Input 6-1) and on the slip-rate oflthe Shoreline fault zone (Input 6-8).

Table 10-1. Results of the Secondary R pture Hazard Segment Slip-rate Annual Probability of (mm/yr) Exceedance 1 cm 2 cm Central 0.01 2.6e- 10 1.4e- 10 Central & 0.01 6.0e- 10 3.5e-10 Southern Central 0.3 7.8e-9 4.le-9 Central & 0.3 1.8e-8 1.le-8 Southern CONCLUSIONS The chance of secondary rupture from the nearby Shoreline fault zone damaging one of the eight Dresser couplings in the ASW pipes in the Tofc formation is very unlikely. With the current uncertainties in the characterization of the Shoreline fault zone, the annual probability of secondary rupture of I to 2 cm at any of the eight Dresser couplings is between 2e-08 and le-10. This large uncertainty is mainly due to the large uncertainty in the slip-rate on the Shoreline fault zone.

11. LIMITATIONS:

This calculation uses arange of estimates of the slip-rate for the Shoreline fault zone that were between 0.01 and 0.3 mm/yr. This leads to the large uncertainty in the computed secondary rupture hazard. There is an ongoing study to improve the constraints on the slip-rate of the Shoreline fault zone. Although not expected, if the new slip-rate from the ongoing work is much larger than 0.3 mm/yr, then this evaluation will need to be repeated.

12. IMPACT EVALUATION:

The impacts are evaluated in terms of the increase to the seismic core damage frequency (CDF) for DCPP. The seismic CDF at DCPP is 3.7e-5 (LTSP, 1988). The chance of secondary rupture occurring at any of the eight Dresser couplings in the ASW pipes is very

Page 21 of 21 GEO.DCPP. 10.01, Rev 0 unlikely: in the range, of 2e-08 and le-10 for I to 2 cm of secondary rupture. Even if we assume that failure of one of the Dresser couplings lead to core damage, the increase in the seismic CDF is between 0.0001% and 0.01%. Therefore, secondary rupture hazard has a negligible impact on the seismic CDF for DCPP.

13.

REFERENCES:

Abrahamson, Norman (2009). UC Berkeley Class Notes: Chapter 6.

Pacific Gas and Electric Company (1988). Final Report of the Diablo Canyon Long-Term-Seismic Program: U.S. Nuclear Regulatory Commission Docket Nos. 50-275 and 50-323.

Pacific Gas and Electric Company (2009). Calculation 17-107,Rev 0, Postulated ground deformation shoreline fault auxiliary salt water buried piping stress analysis, August 3, 2009.

Pacific Gas and Electric Company (2010). Progress Report: Shoreline fault zone, central coastal California: U.S. Nuclear Regulatory Commission Docket Nos. 50-275 and 50-323, PG&E Letter No. DCL- 10-003, January 13, 2010.

Petersen, M., Tianqing, C., Dawson, T., Frankel, A., Wills, C., and Schwartz, D. (2004).

Evaluating fault rupture hazard for strike-slip earthquakes, Geotechnical Engineering for Transportation Projects (GSP 126), ASCE Proceedingsof GeoTrans 2004, 787-796.

Wells, D.L., and Coppersmith, K.J. (1994). New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement.

Bulletin of the Seismological Society ofAmerica, 84, 974-1002.

Youngs, R. and Coppersmith, K. (1985). Implications of fault slip rates and earthquake recurrence models to probabilistic seismic hazard estimates. Bulletin of the Seismological Society ofAmerica, 75, 939-964.

14. ATTACHMENTS:

Attachment 1 Petersen et al. (2004)

Atta~chment 2 Abrahamson, Norman (2009)

Page I of 10

.GEO.DCPP.10.01, Rev 0 Attachment 1 EVALUATING FAULT RUPTURE HAZARD FOR STRIKE-SLIP EARTHQUAKES Mark Petersenl, Tianqing Cao2, Tim Dawson3 , Arthur Frankel 4, Chris Wills5 , and David Schwartz' ABSTRACT: We present fault displacement data, regressions, and a methodology to calculate in both a probabilistic and deterministic framework the fault rupture hazard for strike-slip faults. To assess this hazard we consider. (1) the size of the earthquake and probability that it will rupture to the surface, (2) the rate of all potential earthquakes on the fault (3) the distance of the site along and from the mapped fault, (4) the complexity of the fault and quality of the fault mapping, (5) the size of the structure that will be placed at the site, and (6) the potential and size of displacements along or near the fault. Probabilistic fault rupture hazard analysis should be an important consideration in design of structures or lifelines that are located within about 50m of well-mapped active faults.

INTRODUCTION Earthquake displacements can cause significant damage to structures and lifelines located on or near the causative fault. Recent fault ruptures from earthquakes have caused failure or near-failure on bridges (Japan, 1995; Taiwan, 1999; Turkey, 1999),

dams (Taiwan, 1999) and buildings (California, 1971). Earthquake ruptures in the '

1971 San Fernando, California earthquake (M 6.7) caused extensive structural damage and resulted in to prevent construction of habitable buildings on the surface trace of an active fault. However, it xmay not be possible to relocate many structures and lifelines away from an active fault and loss of these facilities can significantly impact society.

Therefore, it is essential to consider the effects of fault rupture displacements when designing structures near fault sources. The 2002 Denali earthquake showed that major I U.S. Geological Survey, Golden, CO. USA. E-maih: mnetersenftus1.woy 2 California Geological Survey, Sacramento, CA. USA. E-mail: tcao(akcomrv.cawov 3

U.S. Geological Survey, Menlo Park, CA,'USA. E-mail: tdawsonahusguov 4U.S. Geological Survey, Golden, CO, USA. E-mail: afrnkelftsgj.goV 3Califomia Geological Survey, Sacramento, CA, USA. E-mail: cwills(@consrv.ca.uov 6

U.S. Geological Survey, Menlo Park, CA, USA. E-mail: h 787 Copyright ASCE 2004 GeoTrans 2004 Downloaded 18 Nov 2008 to 131.89.192.111. Redistribution subject to ASCE Ilconse or copyright; see http)lwww.ascellbrary.org

Page 2 of 10 GEO.DCPP.10.01, Rev 0 Attachment 1 788 GEOTECHNICAL ENGINEERING FOR TRANSPORTATION PROJECTS lifeline structures can be designed to accommodate fault displacement if the potcntial for location and size ofdisplacement is known.

The methodology presented here is an extension of the probabilistic fault displacement hazard assessments of Stepp et al. (2001) and Youngs et al. (2002) for the proposed Yucca Mountain high-level nuclear waste repository in Nevada and of Braun (2000) for the Wasatch Fault in central Utah. We present fault rupture data and a methodology to assess fault rupture hazard. The overall goal of the project is the development of improved design-oriented conditional probability models needed for estimating fault rupture hazard within either a deterministic or probabilistic framework.

METHODOLOGY Several parameters are important in determining the fault rupture hazard at a site: (I) the size of the earthquake and probability that it will rupture to the surface, (2) the rate of all potential earthquakes on the fault (3) the distance of the site along and from the mapped fault, (4) the complexity of the fault and quality of the fault mapping, (5) the size of the structure that will be placed at the site, and (6) the potential and size of displacements along or near the fault. To develop the methodology, we consider a fault and site (xfy) as shown in Figure 1. The structure has a footprint with dimension z that is located a distance r from the fault and a distance I, measured from the nearest point on the fault to the end of the rupture, point P. The rupture in this case does not extend along the entire fault length and ruptures a section located a distances from the end of the fault. The displacement on the fault has as intensity D and the displacement at a site off the fault has intensity d.

S

ýT FIG. 1: Definition of variables used in the fault rupture hazard analysis For assessing the fault rupture hazard we construct five probability density functions that describe parameters that influence the displacement on or near a fault rupture. The first two probability density functions characterize the magnitude and location of ruptures on a fault (fj(m),fi(s)), the next density function characterizes the distance from the site to all potential ruptures (fr(r)) and the last two probability density functions define the displacements at that site (fvzM(P),fD(D(D,.,.I))).-

Copyright ASCE 2004 GeoTmns 2004 Downloaded 18 Nov 2008 to 131.89.192.111. Redistribution subject to ASCE license or copyright; see hItp'./www.ascollbrary.org

Page 3 of 10 GEO.DCPP.10.01, Rev 0 Attachment 1 GEOTECHNICAL ENGINEERING FOR TRANSPORTATION PROJECTS 789 The first probability density function*m(m), describes the magnitude-fequency distribution along a fault. Typically, in hazard analysis it is assumed that a fault has a preferred size of rupture, that can be determined from consideration of the physical constraints on the length or area of the fault, complexity of the fault along strike, crustal rheological properties along the fault, or rupture history. The size of the earthquake given the fault dimensions is-also uncertain (Wells and Coppersmith, 1993; 1994). From all known potential rupture scenarios, we develop a probability density function for the various sizes of earthquakes along the fault.

Once we determine the potential sizes of the earthquakes, we need to assess how often these ruptures occur. We define a rate parameter, a., that constrains how often the earthquakes occur in the model. This rate parameter is based on the long-term fault slip-rate, paleoseismic rate of large earthquakes, or the rate of historical earthquakes.

The density function for the magnitude frequency in conjunction with the annualized rate parameter defines the frequency of each earthquake rupture along the fault.

The second probability density function describes the probability of a rupture at a specific place along a fault, f,(s). We consider the potential for the partial rupture occurring over various portions of the fault. The range of s is from zero to the fault length minus the rupture length. If the rupture is distributed uniformly along the fault, thenfi(s) is a constant, which is equal to one over the fault length minus the rupture length.

If we simply consider magnitude and rupture variability, the probability that displacement d is greater than or equal to do at a location (xfy) and with a foundation size z is given by-S(dd),,. =a~fM(m)Jf,(s)PIsr=OIm]Fld*eOl,r,n;zsreOjfldadol,r,rnd*OYsdn, (I) m S where P[sr4)/m] is the probability of having surface rupture given a magnitude m event This term accounts for the possibility that an earthquake rupture on a fault will not reach the surface. For example, the 1989 Loma Prieta (M 6.9) and 1994 Northridge (M 6.7) earthquakes did not extend up to the surface and would not present a fault rupture hazard. We obtain this probability from regressions of global earthquake ruptures as published by Wells and Coppersmith (1993,1994). The term P[d**OV,r,m,z,sr4J] represents the probability of having non-zero displacement at a location (lQr) for a foundation size z given magnitude m event with surface rupture, and P[dŽdoI l,r,m,d'O3 is theprobability of the non-zero displacement d greater than or equal to a given value do at a location (ro.When the site is located on the main fault (r=0)we use D to denote the displacement at (r-0,) and then (1) becomes:

A(d > do) =

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Page 4 of 10 GEO.DCPP.10.01, Rev 0 Attachment 1 790 GEOTECHMICAL ENGINEERING FOR TRANSPORTATION PROJECTS a If(m) f, (s)P[sr, ' ImJ]P[D#0 1I, r =om,z,sr 0o]P[D do I1,r = Om, D O]dsdm The data indicate a discontinuity between P[d 01 1,r O,m,z, sr

• 0] and P(D 0.1 l,r = O,m,z, sr 0] ,as well as a discontinuity between P[D do I1,r = 0,m,D* 0] and P[d :,doI 1,r -+O,m,d

• 0].

The third probability density function defines the distance perpendicular to the fault.

If the fault has multiple strands that could rupture in an earthquake, this aleatory variability should be considered in the fault rupture hazard model. This is not due to the fault mapping quality, which is epistemic and treated in a logic tree. We define a density functionfR(r) to denote the variability, the expected rate (I) becomes:

Ad* =a~fu(m)*(s), JII,ti d#*0fl(r)drdsd. (2)

U S r We need to take into account the size of the structure that will be placed at the site.

We define a probability density function for the surface displacement given the structural footprint size, the distance from the fault, and the magnitude of the earthquake that ruptures the surface. The Probability P[ddJ/lor,rmzssr.O] is not a constant for a given distance r and grid size z. It should also depend on I and m. Our data do not allow us to derive these relations for 1, therefore, for this analysis we have ignored the dependences on L From these data we can derive a density function fza,(P) for the above probability to have value p for a given grid size z, distance r, and magnitude.

,A(d>do)z,, =atf(m)ffs(s)lisrt Oj m] JA(r)Jfz.i(p)pId>:d0 I ,,r~~d*Odpdrdsdn, (3)

Finally, we develop a probability density function for displacements along the main fault f 0(D(D.f,,)). The magnitude m is related to the probability of d >do through the displacement D on the main fault at a point nearest to the site (xfy) that is a function of the maximum displacement (usually at middle of the fault rupture) Dn and the location of this point on the rupture (1)orD=D(DI). The displacement on the fault D has aleatory variability also. Therefore, we have:

P[d >: do Ii,r,m,d

• 0] JP[d > do ID(D,=,I),d

• Olfz>(D(D,,n,,))dD (4)

D where fD(D(D,,l)) is the density function forD= D(DI)given magnitude m and location L. If formula (4) is inserted into (3), we get the final formula with aleatory variability of rupture distribution on the fault, multiple fault rupture traces, displacement variability on the main fault, and probability variability of having non-zero displacement. The final formula for the probabilistic fault rupture hazard is:

A(d > do), = a ff, (m) ffs ($)P[sr* 0Oi 1 If. (r) ff,..(p)p X U 5 5* p jfD(D(D., i))P[d> do ID(D.,,,),d

• O]dDdpdrdsdm (5)

This formula is used to assess the probabilistic fault rupture hazard at a site. Ifone desires to calculate the deterministic fault rupture hazard the formula would be Copyright ASCE 2004 GeoTrans 2004 Downloaded 18 Nov 2008 to 131.89.192.111. Redistribution subject to ASCE license or copyright; see htlpd/www.ascelibrary.org

Page 5 of 10.

GEO.DCPP.10.01, Rev 0 Attachment 1 GEOTECHNICAL ENGINEERING FOR TRANSPORTATION PROJECTS 791 modified by eliminating the rate parameter, a., from the equation. Alternatively, one could calculate the median displacement for a particular earthquake using the empirical data and relations that-are described below.

DATA AND REGRESSIONS Following earthquakes that rupture the ground surface, geologists have prepared detailed maps and measured displacement along the surface trace. We collected displacement data from published measurements obtained from studies of several large strike-slip earthquakes: 1968 Borrego Mountain (M6.6), 1979 Imperial Valley (M6.5),

1987 Elmore Ranch (M6.2), 1987 Superstition Hills (M 6.6), 1995 Kobe (M6.9), 1992 Landers (M7.3), 1999 lzmit (M7.4), and the 1999 Hector Mine (M7.1) (Figure 2).

This fault displacement data is used with earthquake recurrence information provided by the National Seismic Hazard maps (Petersen et al., 1996; Frankel et al., 2002). To evaluate the fault hazard at a site we need to answer three questions: 1).Where will future fault displacements occur? 2).How often do surface displacements occur? 3).

-How much displacement can occur at the site? In this section we will discuss the data and model regressions that are used to evaluate each of these questions in a probabilistic sense.

Where will future fault displacements occur?

The primary method of assessing where future ruptures will occur is to identify sites of past earthquakes. We can identify these potential rupture sources by studying historic earthquake ruptures, defining seismicity patterns, and identifying active faults.

Historical ruptures are an important dataset to interpret future fault ruptures. Figure 2 shows examples of historic strike-slip earthquake rupture traces that have been used in this hazard assessment. These traces show a wide variety of rupture patterns. The largest fault displacements are along the principal fault, but significant displacements may also occur on distributed ruptures located several meters to kilometers away from the main fault. The displacement values are not shown, but have been compiled in ARC (IS files. The rupture patterns for a single earthquake may be fairly simple in some regions but quite complex in others, characterized by discontinuous faulting that occurs over a broad zone.

m,,. RUM. Active faults are J&U"0,WftLft*L 119319 places where the likelihood is greatest

• that we will have future earthquakes. in tm "

)4.r,. ,

• California, legislation requires that the State FIG. 2: Traces of faults used in analysis Copyright ASCE 2004 GeoTrans 2004 Downloaded 18 Nov 2008 to 131.89.192.111. Redistribution subject to ASCE license or copyright; see http./hvww.ascollbrary.org

Page 6 of 10 GEO:DCPP.10.01, Rev 0 Attachment 1 792 GEOTECHNICAL ENGINEERING FOR TRANSPORTATION PROJECTS Geologist .identify those faults that are "sufficiently active and well-defined" to represent a surface rupture hazard. In ordcr to K do this, the Cali fornia Geological Survey has

• "examined the majority of the potentially active

- , "faults in the state and prepared detailed maps

. of those that can be shown to have ruptured to

"-,the ground surface in Holocene time. These faults are included in "Alquist-Priolo Earthquake Fault Zones" (A-P zones), which

',. regulate development near active fault traces.

. '*j.. In our analysis we have compared the maps of

. ,0 . faults within A-P zones prepared before surface-rupturing earthquakes with maps of the 0, "actual surface rupture mapped following the

- ' "event. This type of analysis provides a measure

'\ N of the uncertainty in accurately locating future

____ ____ ____ ruptures.

FIG 3: Comparison of previously The 1999 Hector Mine earthquake is an apped A-P fault (white) and 1999 example of an event that ruptured along a fault ector Mine earthquake surface that had been mapped prior to the earthquake Ipture (black) rupture. CGS had evaluated the Bullion fault and established A-P zones in 1988 (Hart. 1987). The 1999 event ruptured part of the Bullion fault (Figure 3). Much of the rupture occurred close to the previously mapped fault. Much of the northern part of the rupture occurred on a fault east of the Bullion fault that had been previously mapped, but not evaluated for A-P zones because it lies in such a remote area. The event also ruptured secondary faults over a wide area at the south end of the rupture. In evaluating the potential for surface fault displacements, we need to account for the potential that significant displacement can occur on previously unmapped faults and that secondary displacement can occur over a broad area.

The accuracy of mapping and complexity of the fault trace parameters are handled in a logic tree to account for our uncertainty in estimating the location of the fault traces.

Faults mapped for A-P zones show the surface traces of the faults in four categories based on how clearly and precisely they can be located. We compared the fault traces mapped in each of these categories with later surface rupture. In general, the regressions show faults where a geologist is more confident of the location more accurately predict the surface rupture location, although these distinctions are not as clear as one might expect. We also examined the A-P fault traces and characterized them as "simple" or "complex". We expect that surface rupture will be more distributed and not as accurately predicted at "complex" fault bends, stopovers, branch points, and ends than on "simple" straight traces. The regressions comparing the A-P fault traces with the later surface rupture will allow us to determine if and how much the fault complexity influences our ability to predict the location of fault rupture.

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Page 7 of 10 GEO.DCPP.10.01, Rev 0 Attachment 1 GEOTECIINICAL ENGINEERING FOR TRANSPORTATION PROJECTS 793

• gorreao'Mountain wImperial Valley

.01 i a SupersUtlon Hills. Elmorm 01* Ranch sequence x Landers 0 0' " x Hector Mine

• L* #t, -,*._eaa,*

• *,-x z

• Kob 0 ( )01 ~aeIM~-

-T... . .. . - 4 San Fernando Instance& of no 00001 distributd rupture 0 2000 4000 6(000 BO 10000

,Distance from Pdncipal Trace (ml FIG 4: Frequency of earthquake displacements within 50 m cells as a function listance from principal trace How often do surface displacements occur?

To answer the question of how often surface fault displacements occur, requires assessing the magnitudes of earthquakes that may rupture a fault, the rate of occurrence of these earthquakes, the potential for ruptures on a fault to pass by the site, and the potential for the modeled earthquakes to rupture the surface. CGS amd USGS have developed earthquake source models for earthquake ground shaking hazard assessment (Petersen ct al.( 1996); Frankel et al. (2002). These models identify earthquake magnitudes, rates, and ruptures that can be used in a fault displacement hazard analysis for the United States. We calculate the number of ruptures that will pass by the site by considering the total fault length and the rupture length for each magnitude.

Assessing the rates of occurrence of earthquakes is pertinent to probabilistic fault displacement hazard analysis but not necessary for the deterministic analysis. A deterministic analysis simply gives a median (or some other fractile) displacement assuming that the event occurs.

I YJL G 5: Displacement data on the How much displacement can occur at the It. The y-axis indicates the site?

asured displacement divided b) To assess probabilistic displacement hazard at average displacement and the x. a site, it is necessary to understand the potential s indicates the distance from the for rupture at that site and the distribution of I of the fault x divided by the displacements. The probability of experiencing il length of the rupture. displacements on a fault, given that a large earthquake occurs, is typically greater than 50%

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Page 8 of 10 GEO.DCPP.1 0.01, Rev 0 Attachment 1 794 GEOTECHNICAL ENGINEERING FOR TRANSPORTATION PROJECTS and the displacements can be measured in meters. In contrast, the probability of experiencing displacements at a site located a few hundred meters away is typically much CL.

!)~.  :,

a 121. 6S5 lower (usually less than 30%) and the a.

4Jo displacements will probably be measured in centimeters rather than meters. Most of the 50

,m cells located away from the fault do not

-experience distributed displacements unless there is complexity in the fault truce.

• se 00.0" 90.

,10 Following the method of Youngs at al (2002) 10O Distance from Fault (km) we analyzed the potential for distributed fault Histogram displacement to pass through an area as a function of distance from the principal trace.

We performed regressions on the displacement data to analyze the rupture potential in different footprint areas. Figure 4 shows the frequency of occurrence of a rupture in a 50 m footprint for each of the different earthquakes.

.1I .26 .1l0 .16 .1s.0 +.0. '

Log(dl))

FIG 6: Displacement data for The footprint size is critical in calculating the sites located off the fault. (A) A probability of rupture at a site. Typically the plot of normalized displacements smaller footprints have lower probability of (displacement divided by the containing a rupture. The frequency is very maximum displacement on the high for distances very close to the fault.

fault) as a function of distance However, this frequency drops off quickly and (with Superstition Hills data there is only about a 1 in 100 chance of having removed) and (B) a histogram rupture within a 50 m footprint if the distance showing the frequency of logo is more than about 2 kilometers. The normalized displacements for all displacement data indicate that most of the the data shown in A. displacements occur on or within a few hundred meters of the principal fault Once we have calculated the likelihood for having displacements pass through a given area, we need to define a distribution of the displacements. We separate the data into on-fault and off-fault displacements. Figure 5 shows the displacements along the strike of the fault. We performed a polynomial regression on the on-fault data to obtain the typical distribution of displacements along a fault. In general the displacements are

'largest near the middle of the fault and falls off rapidly within about 10% of the end of the rupture. The displacement data indicate that most of the displacements occur on or within a few hundred meters of the principal fault. Figure 6 shows of the normalized off-fault displacements as a function of distance. The data indicates almost no correlation of displacements with distance. Displacements are typically quite small.

The histogram indicates that the mode of the data is centered at about 10-- = 0.03, or Copyright ASCE 2004 GeoTrans 2004 Downloaded 18 Nov 2008 to 131.89.192.111. Redistribution subject to ASCE license or copyright, see http:/Iwww.asceJbrary.org

Page 9 of 10 GEO.DCPP.10.01, Rev 0 Attachment 1 GEOTECHNICAL ENGINEERING FOR TRANSPORTATION PROJECTS 795 about 3%of the displacements observed on the principal fault. Displacements range from less than 1%to about 32% of the values observed on the -fault.

xv DISCUSSION S"N"M We -haveassembled data on world-wide strike-

]z= slip earthquake surface rupture and compared it

• o """ with pre-mpture ault-maps faultformapping.

prepared In California, the the Alquist-Priolo aEarthquake Fault Zones Act provide a uniform,

°.M .410. -,*0 . 0 .

V 40 .

0 0 9= detailed set of pre-rupture fault maps that are the

'Cltarm from Fault (m) basisfor comparison for most of our data. We Figure 8: Example of fault have analyzed the distribution of fault ilacementhazard on a transect displacement about previously mapped fault at crosses thefault. traces and used that analysis to construct a system for evaluating the hazard of fault displacement.

In order to consider the probability for surface fault displacement at a site, one must consider the rates of earthquakes on significant active nearby faults. For California, most of the activity rates for faults have been compiled and used in the National Seismic Hazard Maps. For earthquakes that rupture to the ground surface, we can obtain probabilistic estimates of displacement from the regressions for this study.

We developed regressions for fault displacement considering that most earthquakes do not rupture entire faults, that the fault displacement tends to die-out rapidly near the ends of a rupture and that fault rupture does not always follow previously mapped faults. Maps of faults prepared before the rupture show faults with varying levels of perceived accuracy. Our regressions show that more accurately mapped faults correlate better with subsequent fault rupture, but the differences are not great. Surface displacements also tend to show greater complexity in areas where the fault geometry is complicated. Later regressions will include the potential for more broadly distributed displacement at fault bends, stopovers, branches and ends.

To illustrate the methodology and datasets, we assume a fault that has which has a characteristic magnitude 7.26 and with a recurrence of 167 years. This recurrence leads to an annual rate of 0.006 earthquakes per year. Figure 7 shows the calculated displacement hazard on a lineperpendicular to the fault. For this illustration, the fault trace location is assumed to be well located, with a standard deviation of 10 meters.

The amplitude of the displacement hazards is controlled by the characteristic magnitude, recurrence rate, and the duration of the exposure for the hazards.

Using the formulation and data developed in this study, one can estimate the potential for surface fault displacement within an area of a lifeline or other project.

The input required for this analysis includes the rate of earthquakes of various Copyright ASCE 2004 GeoTrans 2004 Downloaded 18 Nov 2008 to 131.89.192.111. Rodistributlon subject to ASCE license or copyright: see http://www.ascotibrary.org

Page 10 of 10 GEO.DCPP.10.01, Rev 0 Attachment 1 796 GEOTECHNICAL ENGINEERING FOR TRANSPORTATION PROJECTS magnitudes on a nearby fault or faults; the distance from the active fault; the accuracy of the nearest fault trace on the detailed map; and the size of the site to be considered.

Output of the analysis is the amount of displacement with a specified probability or corresponding to a particular deterministic earthquake. The potential displacement.

considers the potential displacement along the fault, the potential that the location of the fault varies from where it was mapped and the potential for distributed displacement around the trace of the fault.

ACKNOWLEDGEMENTS We would like to especially thank the Pacific Earthquake Engineering Research Center (PEER Lifelines project# 1J02,IJ02,1J03) advisory groups that assisted us in the formulation and implementation of these results. These members include: Norm Abrahamson, Lloyd Cluff, Brian Chiou, Cliff Roblee, Bill Bryant, Jon Bray, Tom Rockwell, Donald Wells, Bob Youngs, and Clarence Allen.

REFERENCES Braun, J.B. 2000 "Probabilistic fault displacement hazards of the Wasatch fault, Utah." Dept. of Geology and Geophysics, The University of Utah (Masters thesis).

Frankel, A.D., Petersen, M.D., Mueller, C.S., Hailer, K.M., Wheeler, R.L.,

Leyendecker, E.V., Wesson, I.L., Harmsen, S.C., Cramer, C.H., and Perkins, D.M.

(2002) "Documentation for the 2002 update of the National Seismic Hazard Map" U.S. G. S. Open-file Report 02-420.

Hart, E.W., 1987, "Pisgah, Bullion and related faults" California Division of Mines and Geology Fault Evaluation Report FER-l188, 14 p.

Petersen, M.D., Bryant, W.A., Cramer, C.H., Cao, T., Reichle, M.S., Frankel, A.D.,

Lienkaemper, J.J., McCrory, PA., and Schwartz, D.P. (1996) "Probabilistic seismic hazard assessment for the state of California." California Div. of Mines and Geology Open-file Report 96-08 and U.S. G. S. Open-file Report 96-706.

Stepp, J.C., Wong, I., Whitney, J., Quittmeyer, R., Abrahamson, N., Tom, G., Youngs, R., Coppersmith, K., Savy, J., Sullivan, T., and Yucca Mountain PSHA Project Members. 2001 "Probabilistic seismic hazard analyses for ground motions and fault displacement at Yucca Mountain, Nevada." EarthquakeSpectra; 17(1): 113-150.

Wells, D.L and Coppersmith, KJ.. 1993 "Likelihood of surface rupture as a function of magnitude (abs.)." SeismologicalResearch Letters; 64(1): p54.

Wells, D.L and Coppersmith, KJ. 1994 "New empirical relationships among magnitude, rupture length, rupture width, rupture area, and surface displacement."

Bulletin of the Seismological Society ofAmerica; 84: 974-1002.

Youngs, R.R., Arabasz, WJ., Anderson, R.E., Ramelli, A.R., Ake, J.P., Slemmons, D.B., MeCalpin, J.P., Doser, D.I., Fridrich, CJ., Swan, F.H. RI, Rogers, A.M.,

Yount, J.C., Anderson, L.W., Smith, KID., Bruhn, R.L, Knuepfer, LK. Smith, R.B., dePolo, C.M., O'Leary, KLW., Coppersmith, I-., Pezzopane, S.K., Schwartz, D.P., Whitney, J.W., Olig, S.S., and Toro, G.R. 2002 "A methodology for probabilistic fault displacement hazard analysis (PFDHA)." EarthquakeSpectra; Copyright ASCE 2004 GeoTrans 2004 Downloaded 18 Nov 2008 to 131.89.192.111. Redistribution subject to ASCE license or copyright; see http'J/www.ascelibrary.org

Page 1 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 UC Berkeley seismic hazard lecture notes by Dr. Norm Abrahamson, 2009 6 Source Characterization Source characterization describes the rate at which earthquakes of a given magnitude, and dimensions (length and width) occur at a given location. For each seismic source, the source characterization develops a suite of credible and relevant earthquake scenarios (magnitude, dimension, and location) and computes the rate at which each earthquake scenario occurs.

The first step in the source characterization is to develop a model of the geometry of the sources. There are two basic approaches used to model geometries of seismic sources in hazard analyses: areal source zone and faults sources.

Once the source geometry has been modelled, then models are then developed to describe the occurrence of earthquakes on the source. This includes models that describe the distribution of earthquake magnitudes, the distribution of rupture dimensions for each earthquake magnitude, the distribution of locations of the earthquakes for each rupture dimension, and the rate at which earthquakes occur on the source (above some minimum magnitude of interest).

-6.1 Geometrical Models Used for Seismic Sources in Hazard Analyses In the 1970s and early 1980s, the seismic source characterization was typically based on historical seismicity data using seismic zones (called areal' sources). In many parts of the world, particularly those without known -faults, this is still the standard of practice. In regions with geologic information on the faults (slip-rates or recurrence intervals), the geologic information can be used to define the activity rates of faults.

6.1.1. Areal Source Zones

Page 2 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 Areal source zones are used to model the spatial distribution of seismicity in regions with unknown fault locations. In general, -the areal source zone -is a volume; there is a range on the depths of the seismicity in addition -to the plot of the zone in map view.

Even for regions with known faults, background zones modeled as areal sources are commonly included in the source characterization to account for earthquakes that occur off of the known faults.

Gridded seismicity is another type of areal source. In this model the dimensions of the areal source zones are small. The seismicity rate for each small zone is not based solely on the historical seismicity that has occurred in the small zone, but rather it is based on the smoothed seismicity smoothed over a much larger region. This method of smoothed seismicity has been used by the USGS in the development of national hazard maps (e.g. Frankel et al, 1996).

6.1.2 Fault Sources Fault sources were initially modelled as multi-linear line sources. Now they are more commonly modelled as multi-planar features. The earthquake ruptures are distributed over the fault plane. Usually, the rupture are uniformly distributed along the fault strike, but may have a non-uniform distribution along strike.

6.2 Seismic moment, moment magnitude, and stress-drop We begin with some important equations in seismology that provide a theoretical

,basis for the source scaling relations. The seismic moment, Mo (in dyne-cm), of an earthquake is given by Mo= pAD (6.1) where p.is the shear modulus of the crust (in dyne/cm 2), A is the area of the fault rupture (in cm2 ), and D -is the average displacement (slip) over the rupture surface (in cm). For the crust, a typical value of g is 3 x 10"1 dyne/cm 2.

Page 3 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 The moment magnitude, M, defined by Hanks and Kanamori (1979) is M =21og,0 (Mo)-10.7 (6.2) 3 The relation for seismic moment as a function of magnitude is loglo Me = 1.5 M + 16.05 (6.3)

Note that since eq. (6.2) is a definition, the constant, 16.05, in eq. (6.3) should not be rounded to 16.1.

These equations are important because they allow us to relate the magnitude of the earthquake to physical properties of the earthquake. Substituting the eq.(6.2) into eq.

(6.1) shows that the magnitude is related to the rupture area and average slip.

Mw 2_- log(A) + 2--log(D) 2 + -2 log(p) -10.7 3 3 3 (6.4)

The rupture area, A, and the average rupture displacement, D, are related through the stress-drop. In general terms, the stress-drop of an earthquake describes the compactness of the seismic moment release in space and/or time. A high stress-drop indicates that the moment release is tightly compacted in space and/or time. A low stress-drop indicates that the moment release is spread out in space and/or time.

There are several different measures of stress-drop used in seismology. Typically, they are all just called "stress-drop". In this section, we will refer to the static stress-drop which is a measure of the compactness of the source in space only.

For a circular rupture, the static stress-drop at the center of the rupture is given by 7x10-61 D AU,= 16 (6.5)

Page 4 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 where AG is on bars (Kanamori and Anderson, 1979). The constants will change for other rupture geometries (e.g. rectangular faults) and depending on the how the stress-drop is defined (e.g. stress-drop at the center of the rupture, or average stress-drop over the rupture plane).

A circular rupture is reasonable for small and moderate magnitude earthquakes (e.g.

M<6), but -forlarge earthquakes a rectangular shape is more appropriate. For a finite

-rectangular fault, Sato (1972) showed that the stress-drop is dependent on the aspect ratio (Length / Width). Based on the results of Sato, -the stress-drop for a rectangular fault scales approximately as (L/W)-°' 5 . Using this scaling and assuming that L=W for a circular crack, eq. (6.5) can be generalized as 1ac7xO6 zl.5p L 01 (6.6) 16 TA~ W)

Note that eq. (6.6) is not directly from Sata (1972), since he computed the average stress-drop over the fault. Here, I have used constants such that rectangular fault with an aspect ratio of 1.0 is equal to the stress-drop for a circular crack. The absolute numerical value of the stress-drop is not critical for our purposes here. The key is that the stress-drop is proportional to D/sqrt(A) with a weak dependence on the aspect ratio. For an aspect ratio of 10, the stress-drop given by eq. (6.6) is 30% smaller than for a circular crack (eq. 6.5).

If the median value of D/sqrt(A) does not depend on earthquake magnitude and the dependence on the aspect ratio is ignored, then the stress-drop will independent of magnitude which simplifies the source scaling relation givenin eq. (6.4). Let D

C,=---A (6.7) and assuming g = 3 x 1011 dyne/cm 2, then eq (6-4) becomes 2

M! =log(A) + -log(c 1 ) -3.05(68 3(68 where M is the mean magnitude for a given rupture area.

-Page 5 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2

'For a constant median static stress-drop, magnitude is a linear function of the log(A) with a slope of 1.0. That is, M =log(A)+b (6.9) where b is a constant that depends on the median stress-drop. For individual earthquakes, there will be aleatory variability about the mean magnitude.

It has been suggested that the static stress-drop may be dependent on the slip-rate of the fault (Kanamori 1979). In this model, faults with low slip-rates have higher static stress-drops (e.g. smaller rupture area for the given magnitude) than faults with high slip-rates. This implies that the constant, b, in eq. (6-9) will be dependent on slip-rate.

6.2.1 Other magnitude scales While moment magnitude is the preferred magnitude scale, the moment magnitude is not available for many historical earthquakes. Other magnitude scales that are commonly available are body wave magnitude (mb), surface wave magnitude (Ms),

and local magnitude (ML). The mb and ML magnitudes typically are from periods of about 1 second and the Ms is from a period of about 20 seconds. These different magnitude scales all give about the same value in the magnitude 5 to 6 range (Figure 6-1). As the moment magnitude increases, the difference between the magniude scales increases. This is caused because the short period magnitude measures (mb and ML) saturate at about magnitude 7 and the long period magnitude measures (Ms) begin to saturate at about magnitude 8.0.

There are various -conversion equations that have been developed to convert the magnitudes of older earthquakes to moment magnitude. Figure 6-1 shows and example of these conversions. When developing an earthquake catalog for a PSHA, it is important to take these conversions into account.

6.3 "Maximum" Magnitude Once the source geometry is defined, the next step in the source characterization is to estimate the magnitude of largest earthquakes that could occur on a source.

, 'Page 6 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 For areal sources, the estimation of the maximum magnitude has traditionally been

,computed by considering the largest historical earthquake in the source zone and adding some additional value (e.g. halfmagnitude unit). For source zones with low

,historical seismicity rates, such as the Eastern United States, then the largest historical earthquake from regions with similar tectonic regimes are also used.

,For fault sources, the maximum magnitude is usually computed based on the fault dimensions (length or area). Prior to the 1980s, it was common to estimate the maximum magnitude of faults assuming that the ;largest earthquake will rupture 1/4 to 1/2 of the total fault length. In modem studies, fault segmentation is often used to constrain the rupture dimensions. Using the fault segmentation approach, geometric discontinuities in the fault are sometimes identified as features that may stop ruptures.

An example of a discontinuity would be a "step-over" in which the fault trace has a discontinuity. Fault step-overs of several km or more are often considered to be segmentation points. The segmentation point define the maximum dimension of the rupture, which in tern defines the characteristic magnitude for the segment. The magnitude'of the rupture of a segment is called the "characteristic magnitude".

The concept of fault segmenation has been called into question following the 1992 Landers earthquake which ruptured multiple segments, including rupturing through several apparent segmentation points. As a result of this event, multi-segment ruptures are also considered in defining the characteristic earthquakes, Before going on with this section, we need to deal with a terminology problem. The

,term "maxmimum" magnitude .is commonly used in seismic hazard analyses, but in many cases it is not a true maximum. The source scaling relations that are discussed below are empirically based models of the form shown in eq. 6.9). If the entire fault area ruptures, then the magnitude given by eq. (6.9) is the mean magnitude for full fault rupture. There is still significant aleatory variability about this mean magnitude.

For example, the using an aleatory variability of 0.25 magnitude units, the distribution of magnitudes for a mean magnitude of 7.0 is shown in Figure 6-2. The mean magnitude (point A) is computed from a magnitude area relation of the form of eq.

Page 7 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 (6.9). The true maximum magnitude is the magnitude at which the magnitude distribution is truncated. In Figure 6-2, the maximum magnitude shown as point B is based on 2 standard deviations above the mean. In practice, it -is common to see the mean magnitude listed as the "maximum magnitude". Some of the ideas for less*

confusing notation are awkward. For example, the term "mean maximum magnitude" could be used, but this is already used for describing the average "maximum magnitude" from alternative scaling relations (e.g. through logic .trees). In this report, the term "mean characteristic magnitude" will be used for the mean magnitude for full

,rupture of a fault.

The mean characteristic magnitude is estimated using source scaling relations based on either the fault area or the fault length. These two approaches are discussed below.

6.3.1 Magnitude-Area Relations Evaluations of empirical data have found that the constant stress-drop scaling (as in eq. 6.9) is consistent with observations. For example, the Wells and Coppersmith (1994) magnitude-area relation for all fault types is M=o.98Log(A)+ 4.07 (6.10) with a standard deviation of 0.24 magnitude units. The estimated slope of 0.98 has a standard error of 0.04, indicating that the slope is not significantly different from 1.0.

That is, the empirical data are consistent with a constant stress-drop model. The standard deviation of 0.24 magnitude units is the aleatory variability of the magnitude for a given rupture area. Part of this standard deviation may be due to measurement error in the magnitude or rupture area.

For large crustal earthquakes, the rupure reaches a maximum width due to the thickness of the crust. Once the maximum fault with is reached, the scaling relation may deviate from a simple 1.0 slope. In particular, how does the average fault slip, D, scale once the maximum width is reached? Two models commonly used in seismiology are the W-model and the L-model. In the W-model, D scales only with the rupture width and does not increase once the full rupture width is reached. In the

Page8 of 25 GEO.DCPP.10.01, Re6 0 Attachment 2 L-model, 1D is proportional to the rupture length. A third model is a constant stress-drop model in which the stress-drop remains constant even after the full fault width is reached.

Past studies have shown that for large earthquake that were depth limited (e.g. the rupture went through the full crustal thickness), the average displacement average continues to increase as a function of the fault length, indicating that the W-model is

,not appropriate. Using an L-model (D = axL), then A=L Wmax and eq. (6.4) becomes M41og( 2 2 +*2log(,)-107 (6.11) i3 mx 3 Combining all of the constants together leads to 4 4 (6.12)

M =log(L)+b +1 4=log(A) + b 2 3 ' . 3 So for an L-model, once the full fault width is reached, the slope on the log(L) or log(A) term is 4/3. Hanks and Bakun (2001) developed a magnitude-area model that incorporates an L-model for strike-slip earthquakes in California (Table 6-1). In their model, the transition from a constant stress-drop model to an L-model occurs for a, rupture area of 468 km 2 (Figure 6-3). For and aspect ratio of 2, this transition area corresponds to a fault width of 15 km.

Table 6-1. Examples of magnitude-area scaling relations for crustal faults Mean Magnitude Standard Deviation Wells and Coppersmith M = 0.98 Log (A) + 4.07 ym-0.24 (1994) all fault types Wells and Coppersmith M = 1.02 Log(A) + 3.98 CYm-0.23 (1994) strike-slip Wells and Coppersmith M - 0.90 Log(A) + 4.33 u.=0.25

.(1994) reverse th Ellsworth (2001) M log(A) + 4.1 (lower range: 2.5thm=0.12 strike-slip for A> 500 percentile) km2 M = log(A) + 4.2 (best estimate)

M = log(A) + 4.3 (upper range: 97.5th percentile)

Hanks and Bakun M = log(A) + 3.98 for A< 468 km2 dm=-0.12

Page 9 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 (2001) strike-slip M = 4/3 Log(A) + 3.09 for A> 468 km2)

Somerville t al (1999)1 M log(A) + 3.95 Examining the various models listed in Table 6-1. The mean magnitude as a function of the rupture area is close to M = log(A) + 4 (6.13)

This simplified relation will be used in some of the examples in later sections to keep the examples simple. Its use -is not meant to imply that the more precise models (such as those in Table 6-1) should not be used in practice.

Regional variations in the average stress-drop of earthquakes can be accommodated by different a constant in the scaling relation.

6.3.2 Magnitude-Length Relations The magnitude is also commonly estimated using fault length, L, rather than rupture area. One reason given for using the rupture length rather than the rupture area is that the down-dip width of the fault is not known. The seismic moment is related to the rupture area (eq. 6.1) and using empirical models of rupture length does not provide the missing information on the fault width. Rather, it simply assumes that the average fault width of the earthquakes in the empirical database used to develop the magnitude-length relation is appropriate for the site under study. Typically, this assumption is not reviewed. A better approach is to use rupture area relations and include epistemic uncertainty in the down-dip width of the fault. This forces the uncertainty in the down-dip width to be considered and acknowledged rather than hiding it in -unstated assumptions about the down-dip width implicit in the use of magnitude-length relations.

If the length-magnitude relations are developed based only on data from the region under study, and the faults have similar dips, then length-magnitude relations may be used.

6.4 Rupture Dimension Scaling Relations

Page 10 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 The magnitude-area and magnitude-length relations described above in section 6.3 are used to compute the mean characteristic magnitude for a given -fault dimension. The mean characteristic magnitude is used to define the magnitude pdf. In the hazard calculation, the scaling relations are also used to define the rupture dimensions of the scenario earthquakes. To estimate the mean characteristic magnitude, we used equations that gave the magnitude as a function of the rupture dimension (e.g. M(A)).

Here, we need to have equations that gives the -rupture dimensions as a function of magnitude (e.g. A(M)).

Typically, the rupture is assumed to be rectangular. Therefore, to describe the rupture dimension requires the rupture length and the rupture width. For a given magnitude, there will be aleatory variability in the rupture length and rupture width.

6.4.1 Area-Magnitude Relations The common practice is to use empirical relations for the A(M) model; however, the empirical models based on regression are not the same for a regression of magnitude given and area versus a regression of area given magnitude. In most hazard evaluations, different models are used for estimating M(A) versus A(M). As an example, the difference between the M(A) and A(M) based on the Wells and Coppersmith (1994) model for all ruptures simply due to the regression is shown in Figure 6-4, with A on the x-axis for most models. The two models are similar, but they differ at larger magnitudes. While the application of these different models is consistent with the statistical derivation of the models, there is a problem of inconsistency when both models are used in the hazard analysis. The median rupture area for the mean characteristic earthquake computed using the A(M) model will not, in general, be the same as the fault area.

As an alternative, if the empirical models are derived with constraints on the slopes (based on constant stress-drop, for example) then the M(A) and A(M) models will be consistent. That is, applying constraints to the slopes leads to models that can be applied in either direction. As noted above, the empirically derived slopes are close to unity, implying that a constant stress-drop constraint is consistent with the observations.

Page 11 of25 GEO.DCPP.10.01, Rev 0 Attachment 2 6.4.2 Width-Magnitude Relations It is common in .practice to use empirical models of the rupture width as a function of magnitude. For shallow crustal earthquakes, the available fault width is limited due -to the seismogenic tlhickness of the crust. The maximum rupture width is given by jseimo H

.Wmax =SHind)

(6.14) where Hseismo is the seismogenic thickness of the crustal (measured in the vertical direction). This maximum width will vary based on the crustal -thickness and the fault dip. The empirical rupture width models are truncated on fault-specific basis to reflect individual fault widths. For example, if the seismogenic crust has a thickness of 15 km and a fault has a dip of 45 degrees, then the maximum width is 21 km; however, if another fault in this same region has a dip of 90 degrees, then the maximum width is 15 km.

For moderate magnitudes (e.g. M5-6), the median width from the empirical model is consistent with the width based on an aspect ratio of 1.0. At larger magnitudes, the empirical model produces much smaller rupture widths, reflecting the limits on the rupture width for the faults in the empirical data base.

Rather than using a width-magnitude model in which the slope is estimated from a regression analysis, a fault-specific width limited model can be used in which the median aspect ratio is assumed to be unity until the maximum width is reached.

Using this model, the median rupture width is given by log(W(M))= O.5log(A(M)) for A(M) <W.x log(Wmax) for A(M) > Wm.x (6.15)

The aleatory variability of the 'log(W(M)) should be based on the empirical regressions for the moderate magnitude (M5.0 - 6.5) earthquakes because the widths from the larger magnitudes will tend to have less variability due to the width limitation

'In the application of this model, the rupture width pdf is not simply a truncated normal distribution, but rather the area of the pdf for rupture widths greater than

Page 12 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 Wmax is put at Wmax. Formally, the log rupture width model is a composite of a truncated normal distribution and a delta function. 'The weight .given to the delta function part of the model is given by the area of the normal distribution that is above Wmax. In practice, this composite distribution is implemented by simply setting W=Wmax for any widths greater than Wmax ,predicted from the log-normal distribution.

6.5 Magnitude Distributions

'In general, a seismic source will generate a range of earthquake magnitudes. That is, there is aleatory variability in the magnitude of earthquakes on a given source. If you were told that an earthquake with magnitude greater than 5.0 occurred on a fault, and then you were asked to give the magnitude, your answer would not be a single value, but rather it would be a pdf.

The magnitude pdf (often called the magnitude distribution) will be denoted fm(m). It describes the relative number of large magnitude, moderate, and small magnitude earthquakes that occur on the seismic source.

There are two general categories of magnitude density functions that are typically considered in seismic hazard analyses: the truncated exponential model and the characteristic model. These are described in detail below.

6.5.1 Truncated Exponential Model The truncated exponential model is based on the well known Gutenberg-Richter magnitude recurrence relation. The Gutenberg-Richter relation is given by Log N(M)=a-bM (6.16) where N(M) is the cumulative number of earthquakes with magnitude greater than M.

The a-value is the log of the rate of earthquakes above magnitude 0 and the b-value is the slope on a semi-log plot (Figure 6-5). Since N(M) is the cumulative rate, then the derivative of N(M) is the rate per unit magnitude. This derivative is proportional to the magnitude pdf.

Page 13 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 The density function for the truncated exponential model is given in Section 4. If the model is truncated a Mmin and Mmax, then the magnitude pdfis .given by fTE (m /Jexp(-fl(m 8 - Mmin) 1 - exp(-,8(Mmax - Mmin))

(6.17) where 03is ln(1O) times the b-value. Empirical estimates of the b-value are usually used with this model. An example of the truncated exponential distribution is shown in Figure 6-5.

6.5.2 Characteristic Earthquake Models The exponential distribution of earthquake magnitudes works well for large regions; however, in most cases is does not work well for fault sources (Youngs and Coppersmith, (1985). As an example, Figure 6-6 shows the recurrence of small earthquakes on the south central segment of the San Andreas fault. While the small earthquakes approximate an exponential distribution, the rate of large earthquakes found using geologic studies of the recurrence of large magnitude earthquakes is nuch higher than the extrapolated exponential model. This discrepancy lead to the development of the characteristic earthquake model.

Individual faults tend to generate earthquakes of a preferred magnitude due to the geometry of the fault. The basic idea is that once a fault begins to rupture in a large earthquake, it will tend to rupture the entire fault segment. As a result, there is a "characteristic"' size of earthquake that the fault tends to generate based on the dimension of the fault segment.

The fully characteristic model assumes that all of the seismic energy is released in characteristic earthquakes. This is also called the "maximum magnitude" model because it does not allow for moderate magnitude on the faults. The simplest form of this model uses a single magnitude for the characteristic earthquake (e.g. a delta

function).

Page 14 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 A more general form of the -fully characteristic model is a truncated normal distribution (see Section 4) that allows a range of magnitudes for the characteristic earthquake consistent with the aleatory variability in the magnitude-area or magnitude-length relation. The distribution may 'be truncated at nsigmax standard deviations above the mean characteristic magnitude. The magnitude density function for the truncated normal (TN) model is given by:

Ixn(M 2 or- M MA fm*V(M = ý (D*-*r (nSigmax) r* 2'. fo).

(6.18) 0 otherwise and Mchar is the mean magnitude of the characteristic earthquake. An example of this model is also shown in Figure 6-5.

6.5.3 Composite Models The fully characteristic earthquake model does not incorporate moderate magnitude earthquakes on the faults. This model is appropriate in many cases.

Alternative models are based on a combination of the truncated exponential model and the characteristic model. These composite models include a characteristic earthquake distribution for the large magnitude earthquakes and an exponential distribution for the smaller magnitide earthquakes. Although they contain an exponential tail, these models are usually called characteristic models One such composite model is the Youngs and Coppersmith (1985) characteristic model. The magnitude density function for this model is shown in Figure 6-5. This model has a uniform distribution for the large magnitudes and an exponential distribution for the smaller size earthquakes. The uniform distribution is centered on the mean characteristic magnitude and has a width of 0.5 magnitude. Since this model is a composite of two distributions, an additional constraint is needed to define the relative amplitudes of the two distributions. This is done by setting the height of the uniform distribution to be equal to the value of the exponential distribution at 1.0 magnitude units below the lower end of the characteristic part (1 magnitude unit less

Page 15 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 than the lower magnitude of the uniform distribution). This additional constraint sounds rather. arbitrary, but it has an empirical basis. The key feature is that this constraint results in about 94% of the total seismic moment being released in characteristic earthquakes and about 6% of the moment being released in the smaller earthquakes that fall on the exponential tail. Other forms of the model could be

,developed (e.g. a uniform distribution with a width of 0.3 magnitude units). As long as the fractional contribution of the total moment remains the same, then the hazard is not sensitive to there details.

The equations for the magnitude density function for the Youngs and Coppersmith characteristic model are given by 1 f/exp(-3(Mc*car - Mmin - 125) 1+c 2 1 - exp(--3(Mchar.- Mmin -0.25) rc()m (6.19) 1 Pi exp(-._(M- Mmin) for Mmin - m

• Mchar 0.25 exp(-/3(Mchar - mmin -0.25) 1+ c 2 1 -

where 0.5,6 exp(-,6(Mchar - Mmin -1.25)

C2 1 - exp(--3(Mchar - Mmin - 0.25)

(6.20) 6.6 Activity Rates The magnitude density functions described in section 6.5 above give the relative rate of different earthquake magnitudes on a source (above some given minimum magnitude). To compute the absolute rate of earthquakes of different magnitudes requires an estimate of rate of earthquakes above the -minimum magnitude, which is called the activity rate and is denoted N(Mmin).

There are two common approaches used for estimating the activity rates of seismic sources: historical seismicity and geologic (and geodetic) information.

6.6.1 Activity Rate Based on Historic Seismicity

Page 16 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 If historical seismicity catalogs are used to compute the activity rate, then the estimate of N(Mmin) is usually based on fitting the truncated exponential model to the historical data from an earthquake catalog. When working with earthquake catalogs, there are several important aspects to consider: magnitude scale, dependent events, and completeness.

The catalog needs to be for a single magnitude scale. Typically, historical.

earthquakes will be converted to moment magnitude as discussed previously.

Dependent events, aftershocks and foreshocks, need to be removed from the catalog.

The probability models that are used for earthquake ocurrence assume that the earthquakes are independent. Clearly, aftershocks and foreshocks are dependent and do not satisfy this assumption. The definition of what is an aftershock and what is a new earthquake sequence is not simple. It is most common for the dependent earthquakes to be idenified by a magnitude dependent time and space window. Any earthquake that fall with a specified time or distance from an earthquake (and has a smaller magnitude) is defined as an aftershock. The size of the time and space windows can vary from region to region, but in all cases the window lengths are greater for larger magnitude earthquakes.

Once the catalog has been converted to a common magnitude scale and the dependen evens have been removed, the catalog is then evaluated for completeness. Figure 6-7 shows an evaulation of the completeness for the Swiss earthquake catalog.

The model of the activity rate from historical catalogs assumes that all events the occurred in the time period covered by the catalog have been reported in the catalog.

In general, this is not the, case and the catalogs are incomplete for the smaller magnitudes. A method for evaluating catalog completeness was developed by Stepp (1972). In this method, the rate of earthquakes is plotted as a function of time, starting at the present and moving back toward the beginning of the catalog. If the occurrence of earthquakes is stationary (not changing with time), then this rate should be approximately constant with time. If the catalog is incomplete, then the rate should start to decline. This process is used to estimate the time periods of completeness for

Page 17 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 specific magnitude ranges. An example is shown in Figure 6-7 for the Swiss catalog.

In this example, the magnitude 6 and larger earthquakes are complete for about 400 years, but the magnitude 3 earthquakes are complete for about 150 years. The rate of each magnitude is computed over the time period for which it is complete.

Once the catalog has been corrected for completeness, the b-value and the activity rate are usually computed using the maximum likelihood method (Weicherdt, 1980) rather han least-squares fit to the cumulative -rate. The maximum likelihood estimate for the b-value is given -by b 1 (6-21) and the activity rate is simple the observed rate at the minimum magnitude.

The maximum likelihood method is generally preferred because the cumulative rate data are not independent and least-squares gives higher weight to rare large magnitude events that may not give a reliable long term rate. As an example, an artificial data set was generated using the truncated expontial distribution with a b-value of 1.0. This sample was then fit using maximum likelihood and using least-squares. As shown in Figure 6-8, the least-sqaures fit lead to a b-value much smaller than the population sampled (b=1.0). In this example, the maximum likelihood method gives a b-value of 0.97, but the least-squares model gives a b-value of 0.68. The use of the maximum likelihood method, depends on quality of the catalog at the smallest magnitudes used.

Typical b-values are between 0.8 and 1.2 for crustal sources. For subduction zones, lower b-values .(0.5 - 1.0) are common. If the b-value is outside of this range, then they should be reviewed for possible errors such as not removing dependent events, not accounting for catalog completeness, and the fitting method (e.g. use of odrinary least-squares to fit the cumulaive data).

6.6.2 Activity Rate based on SliD-Rate

Page 18 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 If fault slip-rate is used to compute the activity rate, -then the activity rate is usually computed by balancing the long-term accumulation of seismic moment with the long-

.term release of seismic moment in earthquakes.

The build up of seismic moment is computed from the long-term slip-rate and the

-fault area. The annual rate of build up of seismic moment is given by the time derivative of eq. (6.1):

dM pAdD=

dt =t (6.22) where S is the fault slip-rate in cm/year. The seismic moment released during an earthquake of magnitude M is given by eq. (6.3).

The slip-rate is converted to an earthquake activity rate by requiring the fault to be in equilibrium. The long-term rate of seismic moment accumulation is set equal to the long-term rate of the seismic moment release. The activity rate of the fault will depend on the distribution of magnitudes of earthquakes that release the seismic energy. For example, a fault could be in equilibrium by releasing the seismic moment in many moderate magnitude earthquakes or in a few large magnitude earthquakes. The relative rate of moderate to large magnitude

-earthquakes is described by the magnitude pdfs that were described in section 6.5.

As an example of the method, consider a case in which only one size earthquake occurs on the fault. Assume that the fault has a length of 100 km and a width of 12 km and a slip-rate of 5 mm/yr. The rate of moment accumulation is computed using eq. (6-21) etAS = (3x10 1 1 dyne/cm 2 ) (1000 x 1010 cm 2) (0.5 cm/yr)

= 1.5 x 1024 dyne-cm/yr Next, using the simplified magnitude-area relation (eq. 6-13), the mean magnitude is

Page 19 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 M =log(1000) + 4 = 7.0, and the moment for each earthquake is Mo/eqk = 10(1.5x7.+16.o5) 3.5 x 1026 'dyne-cm/eqk The rate of earthquakes, N, is the ratio of the moment accumulation rate to the moment released in each earthquake N/AS 1.5x1024 dyne -cm/yr N- M, / eqk- 3.5 x1027 dyne - cm/eqk =0.0043eqk/yr This approach can be easily generalized to an arbitrary form of the magnitude pdf.

The rate of earthquakes above some specified minimum -magnitude, N(Mmin), is given by the ratio of the rate of accumulation of seismic moment to the mean moment per earthquake with M>Mmin. From Chapter 4 (eq. 4.10), the mean moment per earthquake is given by M max Mean eqk - l OM"M+x6.0) fm(M)dM (6-23)

Leqkjm mmin and the activity rate is given by N(Mmin)= AS (6-24)

Mean[Mo / eqk]

6.7 Magnitude Recurrence Relations Together, the -magnitude distribution and the activity rate are used to define the magnitude recurrence relation. The magnitude recurrence relation, N(M), describes the rate at which earthquakes with magnitudes greater than or equal to M occur on a source (or a region). The recurrence relation is computed by integrating the magnitude density function and scaling by the activity rate:

mmax N(M)=N(Mmin) Jfm,(m)dm m=M

Page 20 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 (6-25)

Although the density -functions for the truncated exponential and Y&C characteristic models are similar at small magnitudes (Figure 6-5), if the geologic moment-rate is used to set the'annual rate of events, N(Mmin), then there is a large impact on the computed activity rate depending on the selection of the magnitude density function.

Figure 6-9 shows the comparison of the magnitude recurrence relations for the alternative magnitude density functions when they are constrained to have the same total moment rate. The characteristic model has many fewer moderate magnitude events than the truncated exponential model (about a factor of 5 difference). The maximum magnitude model does not include moderate magnitude earthquakes. With

• thismodel, moderate magnitude earthquakes are generally considered using areal source zones.

The large difference in the recurrence rates of moderate magnitude earthquakes between the Y+C and truncated exponential models can be used to test the models against observations for some faults: The truncated exponential model significantly overestimates the number of moderate magnitude earthquakes. This discrepancy can be removed by increasing the maximum magnitude for the exponential model by about 1 magnitude unit. While this approach will satisfy the both the observed rates of moderate magnitude earthquakes and the geologically determined moment rate, it generally leads to unrealistically large maximum magnitudes for known fault segments (e.g. about 4-6 standard deviations above the mean from a magnitude-area scaling relation) or it requires combining segments of different faults into one huge rupture. Although the truncated exponential model does not work well for faults in which the geologic moment-rate is used to define the earthquake activity rate, in practice it is usually still included as a viable model in a logic tree because of it wide use -in the past. Including the truncated exponential model is generally conservative for high frequency ground motion (f>5 hz) and unconservative for long period ground motions (T>2 seconds).

6.8 Rupture Location Density Functions The final part of the source characterization is the distribution of the locations of the ruptures. For faults, a uniform distribution along the strike of the fault plane is

Page 21 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 commonly used and a triangle distribution or lognormal distribution is often used for the location down-dip.

For areal sources, the earthquakes are typically distributed uniformly with a zone (in map view) and a triangle distribution or lognormal distribution is often used for the

'location at depth. For the areal source zone that contains the site, it is important that a

.small integration step size for the location pdf be used so that the probability of an earthquake being located at a short distance from the site is accurately computed. The step size for the zone -containing the site should be no greater than 1 km.

Page 22 of 25 GEO.DCPP.10.01, Rev 0 Attachment 2 6.9 Earthquake Probabilities The activity rate and ,the magnitude pdf can be used to compute the rate of earthquake with a given magnitude range. To convert this rate of earthquakes to a probability of an earthquake requires an assumption of earthquake occurrence. Two common assumptions used in seismic hazard analysis are the Poisson assumption and the renewal model assumption.

6.9.1 Poisson Assumption A standard assumption is that the occurrence of earthquakes is a Poisson process. That is, there is no memory of past earthquakes, so the chance of an earthquake occurring in a given year does not depend on how long it has been since the last earthquake. For a Poisson process, the probability of at least one occurrence of an earthquake above Mmin in t years is given by eq. 4.28:

P(M>Mminlt) = 1 - exp( -v(M> Mmnu)t) (6.26)

In PSHA, we are concerned with the occurrence of ground motion at, a site, not the occurrence of earthquakes. If the occurrence of earthquakes is a Poisson process then the occurrence of peak ground motions is also a Poisson process.

6.9.2 Renewal Assumption While the most common assumption is that the occurrence of earthquakes is a Poisson process, an alternative model that is often used is the renewal model. In the renewal model, the occurrence of large earthquakes is assumed to have some periodicity. The conditional probability that an earthquake occurs in the next AT years given that it has not occurred in the last T years is given by (7)

T+A T jf(t)dt P(T,AT)= T

,f(t) dt T

where f(t) is the probability density function for the earthquake recurrence intervals.

Several difference forms of-the distribution of earthquake recurrence intervals have been used: normal, log-normal, Weibull, and.Gamma. In engineering practice, the

Page 23 of 25 GEO.DCPP.10.01, -Rev 0 Attachment 2 most commonly used distribution is the log-normal distribution. The lognormal distribution is given by (eq. 4-19):

1 -(ln(t) -In()) 2 (6.28) fL~yexp 22 T2 ýdjaln It 2 a2.

Although lognormal distributions are usually parameterized by the median and standard deviation, in renewal models, the usual approach is to parameterize -the distribution by the mean and the coefficient of variation (C.V.). For a log normal distribution, the relations between the mean and the median, and between the standard deviation and the C.V. are given in eq. 4.20 and 4.21:

P T (6.29) exp(o2',/2) rln, = 1(1 + CV 2 ) (6.30)

The conditional probability computed using the renewal model with a lognormal distribution is shown graphically in Figure 6-10. In this example, the mean recurrence interval is 200 years and the coefficient of variation (C.V.) is 0.5. The conditional probability is computed for an exposure time of 50 years assuming that it has been 200 years since the last earthquake. Graphically, the conditional probability is given by the ratio of the area labeled "A" to the sum of the areas labeled "A" and "B". That is, P(T=200,AT=50)=A/(A+B).

An important parameter in the renewal model is the C.V.. The C.V. is a measure of the periodicity of the earthquake recurrence intervals. A small C.V. (e.g. C.V. < 0.3) indicates that the earthquakes are very periodic, whereas a large C.V. (e.g. C.V>>I) indicates that the earthquakes are not periodic. Early estimates of the C.V. found small C.V. of about 0.2 (e.g. Nishenko, 1982); however, more recent estimates of the C.V. are much larger, with C.V. values ranging from 0.3 to 0.7. In practice, the typical C.V. used in seismic hazard analysis between 0.4 and 0.6. The sensitivity of the conditional probability to the C.V. is shown in Figures 6-11 and 6-12 for a 50 and 5

Page 24 of 25 -

GEO.DCPP.10.01, Rev 0 Attachment 2 year exposure periods, respectively. For comparison, the Poisson rate is also shown.

These figures shows that the renewal model leads to higher probabilities once the

,elapse time since the last earthquake is greater than about one-half of the mean recurrence interval. In addition, these figures show that as the C.V. becomes larger, the conditional probability becomes closer to the Poisson probability.

Figures 6-11 and 6-12 show one short-coming of the lognormal distribution when applied to the renewal model. As the time since the last earthquakes increases past about twice ,the mean recurrence interval, the computed probability begins to decrease, contrary to the basic concept of the renewal model that the probability goes up as the time since the last earthquake increases (e.g. strain continues to build on the fault).

To address this short-coming of the lognormal model, Mathews (1999) developed a new pdf for earthquake recurrence times called the Brownian Passsage Time (BPT) model. The pdf for this model is given by:

T) VZr exp ln(-) -

where r is the normalized time since the last event:

t T

The pdf for the lognormal and BPT model are compared in Figure 6-13 for a CV=0.5 and a mean recurrence interval of 200 years. These two pdfs are very similar. The difference is that the BPT -model puts more mass in the .pdf at large recurrence times

,that avoids the problem of the probability reducing for large recurrence times. This increase in mass at large recurrence times is shown in Figure 6-14 which is a blow-up of the pdf shown in Figure 6-13.

Another difference between the lognormal and BPT models is a very short recurrence times. At short recurrence times, the BPT model has less mass -thanthe lognormal

Page 25 of 25 GEO.DCPP.10.01,Rev 0 Attachment 2 model as shown in Figure 6-15. This will lead to lower earthquake probabilities shortly after a large earthquake occurs.

The probabilities computed using the lognormal and BPT models are shown in Figure 6-16 for a mean recurrence of 200 years and a CV of 0.5. This figure shows that the BPT model is very similar to the lognormal model, but does not have the undesirable feature or decreasing probabilities for long recurrence times. For this reason, the BPT model is preferred over the log-normal model.

6-25

Enclosure 2 PG&E Letter DCL-10-019 Importance of Assessing Degrees of Fault Activity for Engineering Decisions Cluff, L.S., and J.L.Cluff As published in "Proceedingof the 8th World Conference on Earthquake Engineering,"

Vol. 2, Prentice-Hall, Englewood Cliffs, N.J., pp. 629-636, (1984)

IMPORTANCE OF ASSESSING DEGREES OF FAULT ACTIVITY FOR ENGINEERING DECISIONS counting in a more esponse .of local L. S. Cluff (I) as well as to the J. L. Cluff (1) proaches are more Presenting Author:' L. S. Cluff of the various Its of systematic

SUMMARY

Classifying faults as either "active" or "inactive" is a scientific tion at Canyons of oversimplification that usually results in overconservatism in the grg. Strucl. Dyn., siting and design of structures. Because of the need to more accurately define the range in the degree of activity of faults, the behavioral Model of Use iln characteristics of more than 150 active faults worldwide were Central American compared. The faults were found to differ by several orders of ador, pp. 127-137, magnitude in many of their characteristics, especially in rates of slip and in size and frequency of earthquakes. A classification scheme has lode] for Infinite been developed using six different activity classifications to provide a more realistic framework for seismic hazard and risk assessments.

oundary for Finite 1977. INTRODUCTION Solution for the U e VI Nat. Conf. on Decisions with regard to seismic safety for many critical facilities have become legal battles in which opponents to the facility ions of Motion of grasp the earthquake issue as an excuse to invalidate the facility or 64, 1958. the chosen site, and, in defense, site advocates often tend to on in Mechanical understate the earthquake issues. In many cases, the seismic safety decision process has consumed years, has cost millions of dollars, and s o4 Earthquake has become a disservice to society.

s', North Holland, A major factor that has confused nontechnical decision makers is that earthquake hazards have been characterized by classifying faults as Ch. 8 in 'Seismic either "active" or "inactive" based soley on the recency of fault h E. (Eds.), Else- displacement. This has led to rigid legal definitions of fault activity based on a specified time criterion. For example, the U.S. Nuclear Regulatory Commission considers a fault active if it has evidence of multiple displacements in 500,000 years, or evidence of a single displacement in 35,000 years. For the purpose of classifying faults at sites of major dams, the U.S. Bureau of Reclamation has used 100,000 years, and the U.S. Army Corps of Engineers has used 35,000 years as their criteria for time intervals since the most recent fault displace-ment. Once a fault is classified as active by applying these criteria,

- -I it is considered equal to other active faults from a legal point of

-'I view. This is a scientific oversimplification and usually results in

- I unrealistic overconservatism in the siting and design of structures.

(I) Woodward-Clyde Consultants, Walnut Creek, California, USA 629

-- ~ ~ 4 Realistic earthquake hazard assessments and risk analyses must events can be ,

recognize the differences that exist in the degree to which faults are subsurface seit active. Because of the need to more accurately define the range in degree- of activity of faults to provide a more satisfactory framework It is oft, for seismic hazard' and risk assessments by decision-makers, a classifi- representative cation scheme that considers the different factors that cause variations in the literat in fault activity has been developed. Using this degree of fault apparent displ activity classification scheme should result in a more .realistic, events, scarp technical basis for seismic safety decisions. tectonic displ tectonic displ FAULT ACTIVITY CHARACTERISTICS graben formati of thrust fau)

Significant differences exist in the degree to which various faults the measure of are active. The differences in relative degree of activity are been underestJ manifested by several fault behavioral characteristics, including rate of strain release or fault slip, amount of fault displacement in each Rupture Lengd event, length of fault rupture, earthquake size, and earthquake recur-rence interval. These behavioral characteristics are a function of the The leng' tectonic environment, the -fault type and geometry, the rate of strain of the result:

accumulation, the direction of crustal stress, the stratigraphic large earthqS character and physical properties of the earth's crust, and the worldwide dat.

complexity and physical properties of the fault zone. between fault slip Rate Earthquake Si The geologic slip rate provides a measure of the average rate of The earl deformation across a fault. The slip rate is,calculated by dividing the intensity and amount of cumulative displacement, measured from displaced geologic or recordings of geomorphic features, by the age of the geologic material or feature. scale. Althc The geologic slip rate is an average value through the geologic time earthquake sl period being considered, and reliable to the extent that strain of seismic we accumulation and release over the time period has been uniform and terms of any responding to the same tectonic stress environment. In some tectonic seismic momet environments, the current stress conditions have only been in effect for meaningful m(

about 1.5 million yearsl in others, the stress conditions have been in related dire, force for 4 to 5 million years, or even for more than 10 million shear modulwr years. Many faults, particularly the highly active ones, displace multiple markers of different ages, allowing comparisons of slip rates The mag through time./ extent that duration of Slip Per Event 20- second-pe amplitudes o The amount of fault displacement for each fault rupture event with magnitu differs among faults and fault segments and provides another indication in earthquak of relative differences in degrees of fault activity. The differences by the Ms me in amounts of displacement are governed by the tectonic.environment, magnitude, I-fault type and geometry and pattern of faulting, and the amount of thus saturat accumulated strain being released.

Hanks i The amount of slip per event can be directly measured in the field M, in which during studies of historical faulting, and is usually reported in empirical f, maximum and average values. Displacements for prehistoric rupture because it 630

ies must events can be estimated for some faults from detailed surface and faults are subsurface seismic geologic investigation (for example, Ref. 1, 2).

range in framework It is often difficult to decide what value is most accurate and a classifi- representative of maximum or average displacements from data available 3e variations in the literature. Often, reported displacement values represent fault apparent dispiacement or separation across a fault. For normal faulting Lstic, events, scarp height has typically been reported as a measurement of the tectonic displacement. The scarp height, however, often exceeds the net tectonic displacement across a fault by as much as two times, due to graben formation and other effects near the fault (Ref. 2). In the case of thrust faults, the reported vertical displacement often is actually irious faults the measure of vertical separation, and the net slip on the fault has are been underestimated by a significant amount.

Luding rate it in each . Rupture Length iake recur-

,tion of the The length of the fault rupture significantly influences the size of strain of the resulting earthquakes. It is mechanically not possible for a iphic large earthquake to be released along a fault of short length, and, from the worldwide data of historical earthquakes, a rough correlation exists between fault rupture length and earthquake magnitude (Ref. 3).

Earthquake size le rate of The earliest measures of earthquake size were based on the maximum dividing the intensity and areal extent of perceptible ground shaking. Instrumental jeologic or recordings of ground shaking led to the development of the magnitude feature. scale. Although the scale permitted quantitative comparisons of gic time earthquake size, magnitude was defined empirically from the amplitudes

ain of seismic waves, and the "size" that it measured was not definable in

)rm and terms of any aspect of the physical process of faulting. In defining

! tectonic seismic moment, theoretical seismology has provided a physically Ln effect for meaningful measure of the size of a faulting event. seismic moment is ive been in related directly to the static parameters of an earthquake, including Llion shear modulus, average fault displacement, and the rupture area.

Lsplace slip rates The magnitude value is a good estimate of earthquake size to the extent that the period of the wave used is longer than the rupture duration of the earthquake. The surface-wave magnitude scale, Ms, uses 20-second-period surface waves, and saturates at M. = 7.5. That is, the amplitudes of 20-second-period surface waves stop increasing linearly event with magnitude at ms = 7.5, and become insensitive to further increases

indication in earthquake size. Thus, earthquake size is not accurately reflected lif ferences by the s measurement when earthquake size exceeds m. = 7.5. Local 1

Lronme nt, magnitude, At, and body wave magnitude, ob, use shorter period waves and

)unt of thus saturate at even lower magnitudes.

Hanks and Kanamori (Ref. 4) have proposed a moment-magnitude scale, Ln the field M, in which magnitude is calculated from seismic moment using an

ed in empirical formula. The moment-magnitude scale does not saturate, rupture because it is based on seismic moment, a true measure of the size of an 631

earthquake. Moment magnitude is well calibrated with the Mw scale of FAULT CLASSIFICA Kanamori (Ref. 5). which is a theoretically based moment-magnitude I1 scale, and with M. and M1.below their respective saturation levels. .CLASS Slip Rate ;P 10 t mm/Yr Slip pet Even *' I n The use of magnitude or seismic moment as a criterion for the Rupture Length > 100 s comparison of fault activity requires the choice of the magnitude or Swsmic Moment > 10 Magnitude > M, 1.5 moment value that is characteristic of the fault. Of course, in many Recurrence Interval C 50 instances it is not possible to ascertain whether historical seismic CLASS iA activity is characteristic of the fault through geologic time, unless a long historical seismic record is available or evidence of the sizes of Same as Class 1.

Slip Rate > 5 rm past earthquakes is available from seismic geology studies of paleoseis- Recurrence Inter micity. In a few cases, detailed seismic geology studies have yielded CLASS 10 data on the sizes of past surface faulting earthquakes (Ref. 1, 2). In general, these data involve measurements of prehistoric rupture length same as Clas s.

Slip Pe, Event and/or displacement, and a seismic moment or magnitude can be estimated MagnilUde < M.

probably within one-half magnitude. Recurrence Inte CLASS 2 Recurrence Interval Slip Rate. 1-10 mmlv' Slip per Event 1* m Faults having different degrees of activity differ by several Rupture Length. 50-201 Seismic Moment ) t0!

orders of magnitude in the average recurrence intervals of significant Magnitude

• Ms 7.0 earthquakes. Comparisons of recurrence provide a useful means of Recurrence Interval 10' assessing the relative activity of faults, because the recurrence 2A

_CLASS interval provides a direct link between slip rate and earthquake size. Same as Classt?

Recurrence intervals can be calculated directly from slip-rate and Slip per Event displacement-per-event data. In some cases, where the record of Magniturde <

Short 14100 Y' historical seismicity is sufficiently long compared to the average recurrence interval, seismicity data can be incorporated when estimating CLASS 28 recurrence. In many regions of the world, however, the historical Some as Clas.

seismicity record is too brief; some active faults have little or no Slip per Event Rupture Longt historical seismicity and the recurrence time between significant Recurrence Int earthquakes is longer than the available historical record along the CLASS 3 fault of interest. Plots of frequency of occurrence versus magnitude can be prepared for small to moderate earthquakes and extrapolations to Slip Rate. 0.5-S mmlv Slip per Event. 0.1-3 n larger magnitudes can provide estimates of the mean rate of occurrence Rupture Length 10-l'

,(b-values) of larger magnitude earthquakes. This technique has Seivnic Moment ; 10 Fagntude > Ms 6.5 limitations, however, because it is based on regional seismicity, and Recurrence Interval S cannot result in reliable recurrence intervals for specific faults.

CLASS_4 CLASSIFICATION SCHEME Slip Role: 0.1-1 mm1s Slip per Event: 0.01-1 Rupture Lenglth 1-5C The behavioral characteristics of more than 350 active faults Seismic Moment > 10 Magnitude > i16 1 55 worldwide were researched for analysis. Particular emphasis was placed Recurrence Interval I on examining data from faults that have experienced historical surface CLýASS4A displacement, because data were expected to be available for most fault Same as Cl031 activity characteristics. One hundred fifty faults were chosen to Slip per Even represent all styles of faulting within different tectonic environments Rupture LOO Seismic Mon around the world. Data were obtained on the various activity charac- Magnitude >

teristics of these faults, and order-of-magnitude differences were recognized. Cluff and others (Ref. 6) show classes of active faults CLASS 5 established based on patterns of combinations of characteristics Slip Rate < Imm]¥'

(Table 1). Recurrence Interval CLASS.6 Slip Rate < 0.1 mini Recurrence lrlerva .

632

FTABLE 1 F__AULT CLASSIFICATION CRITERIA 4w scale of Six general classes of active igni tude faults and five sub-clases have been i levels. identified. The sub-classes have most Slip Rate > 10 mm/yr of the same characteristics as the Slip per Event > I m for the Rupture Length ) 100 k1m larger classes, but important differ-

nitude or Seismic Moment ) 1023 dyne-Cm ences in fault behavior necessitated le, in many Magnitude > MS7.5 sub-class designations. A brief Recurrence Interval e 500 yrs tl seismic discussion of several faults will CLASS IA

.me, unless a illustrate the classification scheme.

the sizes of Some as Class 1, except:

Slip Rate > 5 mmlyr of paleoseis- Recurrence Interval r. 1000 yrs The south-central segment of the iave yielded San Andreas fault, from Cholame to San CLASS 18

". 1, 2). In Bernardino in southern California, can

>ture length Same as Class 1. except: be considered a Class I fault. A Slip pet Event e I m be estimated Magnitude < Ms 7.0 geologic slip rate of about 40 mm/yr Recurrence Interval generally < 100 Yff has been calculated for Holocene CLASS 2 displacement along the fault. Recur-rence intervals ranging from about 100 Slip Rate. 1-10 mm/yr Slip per Event >1 m to 330 years have been estimated for several Rupture Length: 50-200 km great earthquakes similar to the 1857 Seismic Moment > 102S dyne-cm significant Maghitude ;, Ms 7.0 event (K 8) that produced up to 9.5 m tans of Recurrence Interval: 100-1000 yrs of right slip. The Parkfield segment trrence CLASS 2A of the San Andreas fault is Class 1B iquake size. because, although the slip rate is Same as Clasn 2. except:

7ate and Slip per Event < 1 m similar to that of the south-central

)rd of Magnitude < M, 7.0 segment, the magnitude (less than K.

Short (<100 yrs) Recurrence Interval average 6.5), displacement (less than 0.5 to ten estimating CLASS 28 1.0 m), and recurrence interval (less

torical Same as Clasn 2. except than 30 years) of historical earth-

tle or no Slip per Event > 5 mt quakes are much different. Available Rupture Length > 100 km

.ficant Recurrence Interval > 1000 yrs evidence indicates that such behavior along the -- frequent small rupture events--is CLASS 3 I magnitude characteristic of this segment, tpolations to Slip Rate: 0.5-5 mmlyr whereas less frequent, large rupture Slip per Event: 0.1-3 m occurrence Rupture Length: 10-100 km events characterize the adjacent i has Seismic Moment > 102 5 dyne-eas south-central segment.

Magritude) MP 5.5 ticity, and Recurrence Interval: 500-5000 yrs

faults. The Motagua fault of Guatemala, CLASS 4 source of the 1976 H 7.5 earthquake, Slip Rate: 0.1-1 mm/yr Slip per Event: 0.01-1 m is typical of the larger faults of Rupture Length: 1-50 km Class 2. The late Quaternary slip I faults Seismic Moment :0 1024 dyne-Cm rate is about 6 mm/yr, typical rupture Magnitude ) M, 5.5

.s was placed Recurrence Interval: 1000-10.000 yrs events produce about I to 2 m of right

.cal surface CLASS 4A slip, and recurrence intervals of ir most fault around 200 years appear to be charac-rosen to Some as Class 4. except: teristic. Somewhat less active Slip per Event > 0.5 mn environments Rupture Length > 10 km strike-slip faults, such as the Seismic Momentm 1025dyne-Cm

.ty charac- Magnitude > Ms 6.6 calaveras and Hayward faults in

es were northern California, are also included

.ve faults CLASS 5 in Class 2. The Wasatch fault of Utah

.stics Slip Rate < Imm/yr is a good example of a Class 2 intra-Recurrence Interval > 10.000 yrs plate normal fault: slip rate is CLASS 6 Slip Rate < 0.1 mm/yr Recurrence Interval ) 100.000 yrs 633

about 1 .5 mm/yr, displacement per event is 1 to 3 m, recurrence inter- of fault activi vals along individual segments range from 500 to 2500 years, and are appropriate to probably less than 500 years for the entire fault.

The Elsinore fault in southern California is a typical Class 3 strike-slip fault: slip rate is about 3 mm/yr, slip events are Seismic ge relatively small, and recurrence intervals are moderately long, up to a electric projec few thousand years. The sierra Madre fault, source of the 1971 San seismic hazard Fernando earthquake, illustrates Class 3 reverse faulting: slip rate is can assist deci I to 2 mm/yr and recurrence intervals range from a few to several critical struct thousands of years. Many Basin and Range normal faults fall into where earthqua)

Class 3, including the Dixie Valley and Pleasant Valley faults. seismic hazard project planned Many class 4 faults have been recognized. The Greenville fault in interconexion I northern California is typical: slip rate is probably less than companies for (

0.5 mm/yr; minor surface faulting was associated with an earthquake of several of thai magnitude less than 6. Most of the reverse faults of the Transverse Range of California are in Class 4; their slip rates generally are 0.2 It was foo to 0.8 sm/yr. Class 4A is an important sub-class. It represents a Colombia could group of faults having relatively low slip rates, large-magnitude regional tecto, earthquakes, and relatively long recurrence intervals. For example, the sive investiga Zenkoji fault in Japan has a slip rate of less than 0.2 mm/yr, yet potential for produced an estimated M. 7.4 earthquake in 1847. considered 'toO Further detail.

Faults of Class 5, and especially class 6, generally behave slip rates and similarly to faults of Class 4A: low slip rates are accompanied by originally est large earthquakes having very long recurrence intervals. The most incorrectly 1o dramatic example is the Pitaycachi fault, source of the 1887 Sonora, activity to co Mexico, earthquake. The slip rate appears to be only about 0.02 mm/yr, into considera yet an estimated ML 7.5 earthquake in 1887 was accompanied by as much as reassessed as 4 m of normal fault displacement. Geomorphic studies of the fault zone made between a suggest a hiatus of several hundred thousand years between periods of in the design fault displacement. of the seismic The principal advantage of this degree of activity fault classi- The resul fication scheme is that all the characteristics that can be used to to quantitativ define fault behavioral activity are incorporated, thus, this scheme 'possible hazar incorporates the range of fault behavior. In using this classification, likelihood of if certain characteristics of a fault are known, then relatively to be 1000 to restricted values for other characteristics of the fault can be entering the I calculated or deduced. evaluation and During the analysis of fault activity data, it was quickly In Califc recognized that faults do not behave in simple order-of-magnitude became so enti classifications. Significant overlap is recognized among various rose to $400 1 characteristics. A fault that has a slip rate of 0.7 mm/yr.and a eventually rei recurrence interval of 2000 years of a 0.5 m displacement might fit scientific ant either Class 3 or Class 4. The Rose Canyon and the La Nacion faults the site-appr, near San Diego, California, would be Class 5 with regard to recurrence evaluated. T interval, and Class 6 with regard to slip rate. The choice of a and were deve particular classification will depend on the preponderance of evidence controversial 634

rence inter. of fault activity; where iwo options are available, it is generally s,. and are appropriate to choose the class having the higher degree of activity.

VALUE IN SEISMIC HAZARD ASSESSMENTS 1 Class 3 s are Seismic geology and seismicity studies for more than ten hydro-long, up to a electric projects in Colombia, South America provide examples of how 1971 San .seismic hazard evaluations using the degree of fault activity concept slip rate is can assist decision-makers in making assessments of relative risk to several. critical structures. Because Colombia is a tectonically active region 11 into where earthquakes are relatively common, prudence dictated that detailed alts. seismic hazard evaluations be performed for every major hydroelectric project planned. Many of these studies have been conducted by tile fault in -Interconexion Electrica S.A. (ISA), the central consortium of power s than companies for Colombia, and their consultants for the past 10 years, and arthquake of several of these projects are now being designed and constructed.

transverse ally are 0.2 It was found.that the degree of fault activity on faults in resents a Colombia could be reassessed based on the increased understanding of gnitude regional tectonics and Quaternary faulting rates gained during succes-r example, the sive investigations. Faults considered active because they have the

/yr, yet potential for slip in the current tectonic stress regime were first considered to have a moderate to high degree of activity (Class 1).

Further detailed seismic geologic and seismicity studies showed that the behave slip rates and amounts of displacement on some faults were less than panied by originally estimated, and several large historical earthquakes were rhe most incorrectly located. Not having a rigid, legal definition of fault 87 Sonora, activity to constrain decision-makers allowed this new data to be taken t 0.02 mm/yr, into consideration. The degree of fault activity on these faults was by as much as reassessed as low to moderate (Class 3). As a result, choices could be te fault zone made between alternate sites, and significant savings are being realized periods of in the design and construction of major projects where such assessments of the seismic hazard can be made with confidence.

• lit classi- The results of the seismic hazard studies also provided a mechanism e used to to quantitatively compare the hazard from faulting with the other his scheme possible hazards. For example, at one dam site in Colombia, the lassification, likelihood of surface fault rupture through the dam foundation was found tively to be 1000 to 10,000 times less than the likelihood of a large landslide in be entering the reservoir. This information aided decision-makers in the evaluation and selection of the type of dam for this site.

Lckly In California, the siting of a liquefied natural gas (LNG) terminal gni tude became so entangled in debates over seismic safety that the project cost various rose to $400 million prior to facility-design, and the extensive delays r and a eventually resulted in cancellation of the project. Although many night fit scientific and environmental issues were the subjects of debate during ion faults the site-approval phases of this project, most of. them could be easily 3 recurrence evaluated. The seismic safety issues, .however, were more complicated e of a and were developed into major obstacles to the siting of this of evidence controversial facility.

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Fault activity was defined in such a way that the seismic issues could be and were misused. One major stumbling block in the decision process was a legalistic definition of fault activity based on a specific time criterion: faults older than 100,000 to 140,000 years were "safe;" younger ones were not. The criteria also included the term "maximum credible earthquake." Use of this term invites controversy, because what it credible to one person may not be credible to another.

The LNG case was finally resolved by engaging a panel, of experts, who shunned the previously adopted criteria and terminology (Ref. 7). 4.7 The(

The panel addressed the "active fault" problem by describing the earth-quake sources important to the proposed LNG terminal site according to their degree of activity. This involved estimating earthquake mag-nitudes for various recurrence intervals for each earthquake source.

Instead of "maximum credible earthquake," the panel recommended that likely maximum earthquakes for different recurrence intervals be con-sidered when choosing design parameters. This approach allows choices to be made that are consistent with judgments about acceptable risk.

REFERENCES

1. Sieh, K.E., 1978, prehistoric large earthquakes produced by slip on the San Andreas fault at Pallett Creek, California: Journal of Geophysical Research, v. 83, no. B8, p. 3907-3939.

2. Swan, P.H., III, Schwartz, D.P., and Cluff, L.S., 1980, Recurrence of moderate to large magnitude earthquakes produced by surface faulting on the Wasatch fault zone, Utah: Bulletin of the Seismological Society of America, v. 70, no. 5, p. 1431-1462.

3. slemmons, D.B., 1977, State-of-the-art for assessing earthquake hazards in the united states; Report 6, faults and earthquake magnitude: U. S. Army Corps of Engineers, Waterways Experiment Station, Soils and Pavements Laboratory, Vicksburg, Mississippi, Miscellaneous Paper S-;.73-1, 129 p.

4. fanks, T.C., and Kanamori, H., 1979, A moment magnitude scale:

Journal of Geophysical Research, v. 84, no. 20, p. 2981-2987.

5. Kanamori, H., 1977, The energy release in great earthquakes:

Journal of Geophysical Research, v. 82, p. 2981-2987.

6. Cluff, L.S., Coppersmith, K.J., and Knuepfer, P.L., 1982, Assessing degrees of fault activity for seismic microzonation: Third International Earthquake Microzonation Conference Proceedings,

v. 1, p. 113-118.

7. Cluff, L.S., Chairman, LNG Seismic Review Panel, 1981, Seismic Safety Review of the Proposed Liquefied Natural Gas Facility, Little Cojo Bay, Santa Barbara County, California: unpublished report for the California Public Utilities Commission, 33 p.

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