Fault setbacks - LA City Planning · Length, Rupture Width, Rupture Area, and Surface Displacement”, Bulletin of the Seismological Society of America , 1994, v. 84 no. 4, p. 974-1002

10/.20/2016 City of Los Angeles Mail - Fault setbacks

LA r:, GEECS

Dani el Sch neidereit <dan i [email protected]>

Fault setbacks 2 messages

Dani el Sch nei dereit <daniel. s [email protected]> To: [email protected]

Hi Alan. Thanks again for talking with me about fault setbacks and any new methods of determining off fault deformations

Daniel Schneidereit Engineering Geologist I ;~ ···-·-· ·-

(213) 482-0430

Hult, Alan <[email protected]> To: Daniel Schneidereit <[email protected]>

Dan:

Wed, Apr 29, 2015 at 1:12 PM

Wed, Apr 29, 2015 at 2: 16 PM

Here are three papers on probabilistic fault displacement, including the Caltrans guidelines. These papers do not cover the off-fault issues, just assessing the

probability on CA faults (Caltrans), reverse faults (Moss and Ross) and selection of fault-earthquake magnitude scaling relationships (Stirling et al.). I've also attached our in press paper on a simplified study for the Seattle fault.

I checked, and as yet, Caltrans seems to have no formal guideline for off-fault deformation calculations. The papers we sent seem to be it for now in the

formal literature. But check out the Caltrans fault rupture site for other resources.

http://www. dot. ca .gov/hq/esc/geotech/geo _support/gee _instrumentation/fa ult_rupture/

https:l/mail.google.comfmailnui=2&ik=l2cb7e2ea7&view=pt&q=Alan%20Hull&qs=true&search=query&th= 14d06cf7202cdac1&siml=14d06cf7202cdac1&sim1=140070ab43df10f1 1/3

10/20/2016 City of Los Angeles Mail - Fault set.backs

. Regards

Alan Hull, Ph.D, C.E.G. I Principal, Seismic Hazard Practice Leader I Golder Associates Inc. 18300 NE Union Hill Road, Suite 200, Redmond, Washington, USA 98052 T: +1 (425) 883-0777 I D: +1 (206) 316-5576 I F: +1 (425) 882-5498 1 C: +1 (949) 283-2253 I E: [email protected]

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From: Daniel Schneidereit [mailto:[email protected]] Sent: Wednesday, April 29, 2015 1: 13 PM To: Hull, Alan Subject: Fault setbacks

Hi Alan.

Thanks again for talking with me about fault setbacks and any new methods of determining off fault deformations

Daniel Schneidereit

Engineering Geologist I IA._ htlps://mail.google.oom/mall/?ui=2&ik=f2cb7e2ea7&view=pt&q=Alan%20Hull&qs=true&search=query&th=14cl06cf7202cdac1&siml=14d06cf7202c.dac1&siml=14d070ab43df10f1 213

10/20/2016

{213) 482-0430

2 attachments

Vj PFHDA Attachments.pdf 1440K

lfii':i 61CEGE_PFDHA.pdf ll'.:l 554K

City of Los Angeles Mai l - Fault setbacks

https://mail.google.com/mailnui=2&ik=f2cb7e2ea7&vifiN.f=pt&q=Alan%20Hull&qs=true&search=query&th=14d06cf7202cdac1&siml=14d06cf7202cdac1&simf=14d070ab43df10f1 313

ATTACHMENT 1 CALTRANS PROCEDURES FOR CALCULATION OF FAULT RUPTURE HAZARD

Caltrans Procedures for Calculation of Fault Rupture Hazard

Tom Shantz, Division of Research and Innovation

February 2013 The development of the hazard curve for fault offset follows simplified procedures described in Abrahamson (2008) with some enhancement on the calculation of the recurrence interval based on personal communication. The method relies on the assumption that the fault in question ruptures predominately within a narrow range of magnitudes, the center of this range being defined as the characteristic magnitude, Mc. A relation by Hanks and Bakun (2008) given in (A1) can be used to estimate the characteristic magnitude from fault dimensions.

��

��

� � ��

�

��

For application to faults with aseismic creep, such as the Hayward fault, a reduced fault area ��, defined in (A2), is used to account for the reduced seismogenic area.

��

As an example, for the Hayward fault an aseismic factor of 0.4 is used resulting in a characteristic magnitude of 7.0. The recurrence interval, Tr, for a characteristic earthquake can be estimated as

��

��

where the seismic moment is given by (A4), (Hanks and Kanamori, 1979) and moment rate is given by (A5).

��

��

In (A4), Mw represents the moment magnitude. In (A5), μ is the rigidity and is typically taken as 3x1011 dyne/cm2. � is the fault slip rate. �� is the modified fault plane area as given in (A2). The 0.8 in the denominator of (A3) is a combined adjustment factor that addresses (1) a presumption that approximately 5% of the seismic moment is expended in small, non-characteristic events, and (2) the seismic moment associated with a characteristic magnitude, Mc, at the center of a uniform distribution ranging from Mc-Δm to Mc+Δm,

(A3)

(A4)

(A5)

(A1)

(A2)

Δm typically assumed to be about 0.2 magnitude units, will underestimate the seismic moment when averaged across the uniform distribution. Fault rupture hazard is typically defined in terms of the rate of exceeding a particular fault displacement, D. As shown in (A6), the hazard value is calculated as the product of two terms. The first term is the rate at which characteristic events occur and is simply the inverse of the recurrence period calculated in (A3). The second term is the probability, conditioned on the occurrence of the characteristic event, that the fault displacement is larger than D.

��

��

��

��

��

��

��

��

��

��

This probability is represented by the hatched area in Figure A1. The curve describes the lognormal probability distribution of the fault displacement for the characteristic earthquake.

Figure A1: Lognormal probability distribution for fault displacement resulting from a characteristic earthquake. The center of the distribution is the logarithm of the average displacement, AD, and is given by a relation by Wells and Coppersmith (199x) for strike slip faults.

�� -6.32 (meters) The hatched area in Figure A1 can be calculated as

��

where � represents the cumulative distribution function (CDF) of a standard normal variate (i.e. mean=0, standard deviation=1) and � is given as

� ��

�

where σ is the standard deviation of the fault displacement (in log space) and is typically estimated as 0.39 unless fault offset measurements are available from previous events.

��

(A6)

(A7)

(A8)

(A9)

In application, an inverse CDF is used to determine the ε that corresponds to the desired rate of exceedence. (In Excel, the function NORMINV can be used to perform the inverse CDF calculation.) Once ε has been determined, the corresponding displacement D can be calculated as

� � �� Sample calculation For the Hayward fault we assume a fault plane of approximately 1400 km2, a slip rate of 9 mm/yr, and an aseismic factor of 0.4. Calculate the displacement corresponding to a � �� rate of exceedence: Using (A2) we get

��

� � ��

The corresponding magnitude is estimated using (A1):

��

��

� �� The recurrence period is calculated using (A3):

��

��

��

��

��

��

� ��

Using (A6) and (A8), we determine that for our target � �� rate of exceedence, the conditional rate of exceedence (which is represented by the hatched area in Fig. A1) is given by

��

��

��

� �� Using an inverse CDF function we determine that 0.2 corresponds to an ε of 0.84. The mean fault offset, AD, corresponding to a Mw7 event is given by (A7):

��

� �� Finally, we calculate D using (A10):

(A10)

� � ��

� ��

This calculation is repeated for different rates of exceedence to establish the hazard curve. References Abrahamson, N., 2008, Appendix C, Probabilistic Fault Rupture Hazard Analysis, San Francisco PUC, General Seismic Requirements for the Design on New Facilities and Upgrade of Existing Facilities Hanks, T. C., Bakun, W. H., “M-logA Observations for Recnt Large Earthquakes”, Bulletin of the Seismological Society of America, February 2008, v. 98 no. 1, p. 490-494 Hanks, Thomas C.; Kanamori, Hiroo (May 1979). "Moment magnitude scale". Journal of Geophysical Research 84 (B5): 2348–50 Wells, D. L.,Coppersmith, K. J., “New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement”, Bulletin of the Seismological Society of America, 1994, v. 84 no. 4, p. 974-1002 �

ATTACHMENT 2 SELECTION OF EARTHQUAKE SCALING RELATIONSHIPS FOR SEISMIC‐HAZARD

ANALYSIS

Selection of Earthquake Scaling Relationships

for Seismic-Hazard Analysis

by Mark Stirling, Tatiana Goded, Kelvin Berryman, and Nicola Litchfield

Abstract A fundamentally important but typically abbreviated component ofseismic-hazard analysis is the selection of earthquake scaling relationships. These aretypically regressions of historical earthquake datasets, in which magnitude is esti-mated from parameters such as fault rupture length and area. The mix of historicaldata from different tectonic environments and the different forms of the regressionequations can result in large differences in magnitude estimates for a given fault rup-ture length or area. We compile a worldwide set of regressions and make a first-ordershortlisting of regressions according to their relevance to a range of tectonic regimes(plate tectonic setting and fault slip type) in existence around the world. Regressionrelevance is based largely on the geographical distribution, age, and quantity/qualityof earthquake data used to develop them. Our compilation is limited to regressions ofmagnitude (or seismic moment) on fault rupture area or length, and our shortlistedregressions show a large magnitude range (up to a full magnitude unit) for a givenrupture length or area across the various tectonic regimes. These large differences inmagnitude estimates underline the importance of choosing regressions carefully forseismic-hazard application in different tectonic environments.

Introduction

Prior to this study, limited attention has been paid to theappropriate use of magnitude-area or magnitude-length scal-ing relationships (hereafter referred to simply as regressions)in seismic-hazard analysis, despite the considerable bodyof literature on the topic (e.g., Kanamori and Allen, 1986;Scholz et al., 1986). Well-known regressions, such as thoseof Wells and Coppersmith (1994) and Hanks and Bakun(2008) are applied the world over, often with limited consid-eration as to their applicability to a particular tectonic envi-ronment. A poignant example is that the above regressionsunderestimate the 4 September 2010 Mw 7.1 Darfield, NewZealand, earthquake by about 0.3 magnitude units when ap-plied to the length or area of the earthquake source (e.g.,Quigley et al., 2012; Fig. 1). The development of a GlobalEarthquake Model (GEM) active fault source database (seeData and Resources) has highlighted the need for compila-tion and assessment of global regressions and for recommen-dations for their use in different tectonic regimes. GEMis developing global models and tools for seismic-hazardand risk analysis. Our study is also timely for providing guid-ance to seismic-hazard analysis in general.

The purpose of this paper is to provide a compilation ofregressions from around the world. Part of this effort is thedevelopment of a simplistic framework for grouping regres-sions according to tectonic regime and a brief evaluation ofthe regressions according to quality and quantity of regres-

sion data. We also provide a tabulation and description ofwhat we consider to be the highest quality (shortlisted) re-gressions, along with recommendations on their applicationin the various tectonic regimes. While there remains consid-erable debate in the seismological community regarding thecontrols on/most appropriate way to model magnitude scal-ing, our compilation does not attempt to address these fun-damental issues. We instead simply report regressions thatalready exist in the literature and provide first-order guidancefor application to seismic-hazard assessment based on ob-vious differences between the regressions and underlyingdatasets. Finally, we do not include regressions specific foroceanic earthquakes in this compilation, aside from those rel-evant to subduction interface and intraslab environments.

Methodology

Regression Compilation and Assessment

The compilation and documentation of regressions fromaround the world is provided in Appendices A and B. Ourcompilation was achieved by searching the literature and islimited to regressions of magnitude (or seismic moment) onfault rupture area or length. These are the most readily-measurable/estimated parameters that are commonly appliedto seismic-hazard modeling and can be derived from eithergeologic (surface rupture) or geophysical (aftershocks or

BSSA Early Edition / 1

Bulletin of the Seismological Society of America, Vol. 103, No. 6, pp. 1–19, December 2013, doi: 10.1785/0120130052

geodetic data) constraints. We also mainly focus our study onregressions most useful for constraining the magnitudes ofground-rupturing earthquakes (around Mw >6:5–7) or blindearthquakes with similar source dimensions. At these magni-tudes, the differences between surface and subsurface lengthestimations are minimal in terms of magnitude estimation.

The regression equations are accompanied by a descrip-tion of the regression and the underlying earthquake datasetand recommendations from the authors (if available) and uson the use of the regression for specific tectonic regimes (seeTectonic Regime Framework). The regressions are alsoassigned a quality score (1, best available; 2, good; 3, fair)according to the quality and quantity of the regression data-set. This is a very arbitrary (and therefore readily debatable)score and is based largely on the size of the regression dataset

and age of publication. Logically a regression that does notinclude the last 10–20 years of data and/or has a small dataset(unless focused on a specific environment) will not score ashighly as one that is more data-rich and recent. To someextent, the prior frequency of regression usage is a criteriontaken into consideration, although we are aware of wide-spread misuse of some regressions (e.g., Wells and Copper-smith [1994] applied to intraplate areas of Europe). Weattempted to consider the scientific aspects of regressionformulation (e.g., inclusion of bilinear scaling) in our assign-ment of a quality score but decided this was too subjectiveand contentious to serve as a basis for evaluation. Appen-dix A comprises regressions that are generally of a higherquality score (with some exceptions; see Classification ofRegressions According to Tectonic Regime section), and Ap-pendix B comprises the remainder of the regressions.

Finally, it is important to note that this regression com-pilation is not comprehensive, in that it may not havecaptured all regressions available, particularly if these regres-sions are older and not published in journal papers or books(e.g., Mason and Smith, 1993). However, we are confidentthat our large compilation captures the range of regressionsfrom around the world, particularly those developed in thelast decade.

Tectonic Regime Framework

The definition of tectonic regimes and grouping of regres-sions into these regimes are the results of our own assessment,using any guidelines or recommendations we can glean fromthe regression publications. However, the common absence ofrecommendations in the regression publications requires us tomake our own assignment of regressions to specific tectonicregimes based upon where the regression data were collected.Some regression datasets are restricted to specific tectonic re-gimes, whereas others span multiple regimes or have a globalcoverage. In the latter cases, we assign these regressions to thetectonic regime responsible for most of the regression dataset.Our tectonic regime categories (plate tectonic setting and faultslip type) are shown in Table 1. These categories are based onour understanding of the broad differences in fault parameterssuch as slip rate, slip type, stress drop, recurrence interval,seismogenic thickness, heat flow, and lithology between thedifferent tectonic regimes.

Classification of Regressions Accordingto Tectonic Regime

In Table 2 we provide the regressions most applicable tothe categories of tectonic regime listed in Table 1. The regres-sions are shown in the published form, and this is typicallyin terms of Mw on area or length, consistent with the mostfrequent application in seismic-hazard analysis (i.e., Mw

estimated from source length or area). A subset of regres-sions (bold in Table 2) is shortlisted as our recommendedregressions for use in each tectonic regime. Examples ofthese shortlisted regressions are also plotted in Figure 1.

Figure 1 Moment magnitude on rupture length for the short-listed regressions for crustal earthquakes (underlined in Table 2).For regressions involving seismic moment and rupture area,moment magnitude is derived from the equation M0 � 16:05�1:5Mw (Hanks and Kanamori, 1979), in which M0 is seismicmoment and Mw is moment magnitude. Rupture length is derivedfrom area, assuming a constant fault width of 15 km. The exceptionis the width of 8 km used for the Villamor et al. (2001) regression(VL), which is developed from earthquakes within the thin crust ofthe Taupo volcanic zone backarc rift zone. The use of length for allregressions allows them to be plotted on one graph. We limit ourlength to 100 km for simplicity and because most faults are less than100 km (i.e., a meaningful comparison). Where possible, one-standard-deviation error bounds are shown on the regression curves(i.e., if standard deviations are provided in the relevant documen-tation). Subduction zone regressions (class C in Tables 1 and 2) arenot shown on this figure, as the assumption of a constant width for arange of lengths is inappropriate for subduction sources. Identifiersin the legend correspond to the tectonic regime classifications inTable 1; for example, A11(HB) signifies plate boundary crustal(“A”), fast slip rate (“1”), and strike-slip dominated (“1”). Abbre-viations in parentheses refer to authors of the regressions: HB,Hanks and Bakun (2008); YM, Yen and Ma (2011); ST, Stirlinget al. (2008); WS, Wesnousky (2008); NT, Nuttli (1983); JST,Johnston (1994); and VL, Villamor et al. (2001). Slip types: all, allslip types; n, normal; ds, dip-slip. The solid black circle on the graphshows the position of the magnitude and source length of the 2 Sep-tember 2010 Mw 7.1 Darfield, New Zealand, earthquake.

2 M. Stirling, T. Goded, K. Berryman, and N. Litchfield

BSSA Early Edition

Shortlisted regressions are generally those with a qualityscore of 1 and are described in more detail in Appendix A.Some regressions of lower quality scores (2 and 3) are alsoshown in Table 2, Figure 1, and Appendix A, if the relevanttectonic regimes are poorly represented in the regression lit-erature (e.g., stable continental B1 and B2). Regressionsfrom Appendix B are not included in Table 2 as they do notsatisfy our selection criteria to the same degree as our short-listed regressions.

Notable omissions from the above shortlisting processare the regressions of Wells and Coppersmith (1994). Despitebeing long-time industry standard regressions, they are notincluded due to being relatively old and, in our view, havebeen superseded by the more modern regressions listed inTable 2.

Results and Discussion

The shortlisted regressions in Figure 1 and Table 2 arealmost entirely assigned a quality score of 1. This is to beexpected, as our intention is to identify recent and relevantregressions for each of the tectonic regimes in Table 1. Theexceptions are the stable continental (B) regimes (qualityscore � 3), for which the most suitable regressions are basedon a combination of old and small datasets (Nuttli, 1983;Johnston, 1994; Anderson et al., 1996). In contrast, severalregressions with small datasets score highly due to recency ofdevelopment (e.g., Wesnousky, 2008). The lack of more re-cently developed regressions for stable continental regimesmeans that these older regressions default to being the mostsuitable for these environments. The Nuttli (1983) andJohnston (1994) regressions are specifically developed fromstable continental earthquake data, whereas the Anderson

et al. (1996) regression combines a mixed interplate/intra-plate earthquake dataset but includes a negative dependenceon slip rate in the regression equation (i.e., larger magnitudesfor faults with slower slip rates).

The most obvious aspect of our compilation is that thedifferences between many of the regressions are large(Fig. 1). Differences as large as one magnitude unit areevident for rupture lengths of about 60–80 km. These arelengths commonly associated with fault sources in seismic-hazard models, so highlights the importance of choosingregressions carefully with respect to tectonic regime. Obser-vations from Figure 1 specific to tectonic regimes are asfollows:

• Shortlisted regressions for A11 (plate boundary fast strike-slip faults) and A21 (plate boundary all faults) tend to showsome of the smallest magnitudes for a given fault length orarea. This is consistent with plate boundary faults generallybeing thought to produce smaller magnitude scaling thanfaults away from the plate boundary (e.g., Scholzet al., 1986).

• The shortlisted regression for A22 (plate boundary strike-slip faults) is developed from New Zealand oblique-slipearthquake data away from the main plate boundary zoneand produces larger magnitudes than A11 and A21. We areuncertain as to why New Zealand oblique-slip earthquakesscale in this distinctive way. It may be due to them beingdominantly oblique-slip earthquakes away from the mainplate boundary zone.

• The shortlisted regression for A23 (plate boundary slownormal faults) is developed from normal-slip earthquakesin the Basin and Range province and elsewhere. The result-ing magnitudes are lower for a given rupture length or areathan A22, which is consistent with expectation that nor-mal-slip produce smaller magnitudes than other slip types(e.g., Schorlemmer et al., 2005).

• The shortlisted regression for A24 (plate boundary slowreverse faults) produces magnitudes intermediate betweenA11/A21 and A22. This may be due to the mix of sliptypes contained in the earthquake dataset for the Yen andMa (2011) regression for dip-slip events.

• The shortlisted regression for B1 and B2 (stablecontinental reverse and strike-slip faults) produce a largespread of magnitudes for a given rupture length, reflectingthe large uncertainties in earthquake scaling for stablecontinental environments. The Nuttli (1983) regressionproduces the largest magnitudes in this context, which isagain consistent with earthquakes in stable continentalregions being thought to produce larger magnitudes fora given rupture length or area than earthquakes in plateboundary areas (e.g., Kanamori and Allen, 1986; Scholzet al., 1986). This is not, however, reflected in the Johnston(1994) regression, which shows similar scaling to some ofthe regressions representative of plate boundary settings. Itis therefore important to consider both scaling behaviors inthe relevant seismic-hazard applications.

Table 1Tectonic Regime Classification Scheme, Comprising Plate

Tectonic Settings, Subclasses, and Slip Types

Plate TectonicSetting Subclass Slip Type*

A. Plateboundarycrustal

A1: Fast plate boundaryfaults (>10 mm=yr)

A2: Slow plate boundaryfaults (<10 mm=yr)

Strike-slipdominated(A11)

All faults (A21)Strike-slip (A22)Normal (A23)Reverse (A24)

B. Stablecontinental

Reverse (B1)Strike-slip (B2)

C. Subduction Continental megathrustMarineIntraslab

Thrust (C1)Thrust (C2)Normal (C3)

D. Volcanic Thin crust (<10 km)Thick crust (>10 km)

Normal (D1)Normal (D2)

*The identifiers in parentheses allow cross referencing to Table 2 and havethe following derivation: first character (A–D), primary tectonic regime;second character (1–2), tectonic subregime; and third character (1–4),mechanism or slip-type. For example, A11 indicates a plate boundarycrustal setting (A), fast subclass (1), and strike-slip mechanism (1).

Selection of Earthquake Scaling Relationships for Seismic-Hazard Analysis 3

BSSA Early Edition

Table2

Shortlisted

Regressions

forEachCom

binatio

nof

Tectonic

Setting,Su

bclasses

andSlip

Type

Given

inTable1

Tectonic

Regim

e*Reference

forRegression†

RegressionEquations

‡Units

Quality

Score§

Com

ments||

A11

Han

ksan

dBak

un(2008);

A≤5

37km

2

Mw�

logA�

�3:98�

0:03�

A:area

(km

2)

1Bestrepresentedby

Hanks

andBakun

regressions.Regression

datasets

aredominated

byfast-slip

ping

plateboundary

faults.

Regressions

should

bechosen

accordingto

therelevant

faultarea

range.

Han

ksan

dBak

un(2008);

A>

537km

2

Mw�

4=3

logA�

�3:07�

0:04�

||1

Wesnousky

(2008);strike-slip

Mw�

5:56�

0:87logL

σ�

0:24(inM

w)

L:surface

rupturelength

(km)

1

Leonard

(2010)

Mw�

3:99�

logA

A:area

(km

2)

1A21

Yen

andMa(2011);all

logAe�

−13:79�

0:87logM

0

σ�

0:41(inAe)

logM

0�

16:05�

1:5M

Ae:effectivearea

(m2)

1Bestrepresented

byYen

andMaregression

asdatasetscontainamix

ofplateboundary

earthquakesof

strike-slip

anddip-slip

mechanism

s.A22

Hanks

andBakun

(2008);

A≤5

37km

2

Mw�

logA�

�3:98�

0:03�

A:area

(km

2)

1Largermagnitudesproduced

byStirlin

getal.(2008)than

byothers

(largerD–L

scaling)

Stirlin

get

al.(2008);New

Zealand

;ob

lique-slip

Mw�

4:18�

2=3

logW

�4=3

logL

σ�

0:18(inM

w)

L:subsurface

rupturelength

(km)

W:width

(km)

1

Wesnousky

(2008);strike-slip

Mw�

5:56�

0:87logL

σ�

0:24(inM

w)

L:surface

rupturelength

(km)

1

Yen

andMa(2011);strike-slip

logAe�

−14:77�

0:92logM

0

σ�

0:40(inAe)

logM

0�

16:05�

1:5M

w

Ae:effectivearea

(m2)

1

A23

Wesno

usky

(2008);no

rmal

Mw�

6:12�

0:47logL

σ�

0:27(inM

w)

L:surface

rupturelength

(km)

1Basin

andrange-rich

norm

al-slip

earthquake

dataset.

A24

Stirlin

get

al.(2008);New

Zealand;obliq

ueslip

Mw�

4:18�

2=3

logW

�4=3

logL

σ�

0:18(inM

w)

W:width

(km)

L:subsurface

rupturelength

(km)

1Yen

andMa(2011)

dip-slipdatasetd

ominated

byreverseandthrust-

slip

earthquakesfrom

widearea

(Taiwan

andeast

Asia).

Wesnousky

(2008);reverse

Mw�

4:11�

1:88logL

σ�

0:24(inM

w)

L:surface

rupturelength

(km)

1

Yen

andMa(2011);dip-slip

logAe�

−12:45�

0:80logM

0

σ�

0:43(inAe)

logM

0�

16:05�

1:5M

w

Ae:effectivearea

(m2)

1

B1

Andersonet

al.(1996)

Mw�

5:12�

1:16logL−0:20logS

σ�

0:26(inM

w)

L:surfacefaultlength

(km)

S:slip

rate

(mm/yr)

2Equal

priority

tothethreeregressions.Nuttli

(1983)

andJohnston

(1994)

regressionsaredevelopedexclusivelyforstablecontinental

regions(>

500km

from

plateboundaries),butdatasetis

old.

Andersonet

al.(1996)

datasetincludes

stable

continental

earthquakes,andnegativ

ecoefficienton

slip

rate

hasamajor

influenceon

Mw.Johnston

(1994)

database

dominantly

reverse

events.

(contin

ued)


BSSA Early Edition

Table2(Con

tinued)

Tectonic

Regim

e*Reference

forRegression†

RegressionEquations

‡Units

Quality

Score§

Com

ments||

Nuttli(1983)

logM

0�

3:65logL�

21:0

logM

0�

16:05�

1:5M

w

M0:seismic

mom

ent

(dyn

·cm)

L:subsurface

faultlength

(km)

3

John

ston

(1994)

Mw�

1:36*logL�

4:67

L:surfacerupturelength

(km)

3B2

And

ersonet

al.(1996)

Mw�

5:12�

1:16logL−0:20logS

σ�

0:26(inM

w)


(km)

S:slip

rate

(mm/yr)

2AsforB1

Nuttli(1983)

logM

0�

3:65

logL�

21:0

logM

0�

16:05�

1:5M

w

M0:seismic

mom

ent

(dyn

·cm)

L:subsurface

faultlength

(km)

3

C1

Strasser

etal.(2010);

interfaceevents

Mw�

4:441�

0:846log 1

0�A

�σ�

0:286(inM

w)

A:rupturearea

(km

2)

1Diverse

datasetandM

wdependence

oninterfacearea

makes

the

Strasser

etal.(2010)

regression

themostsuitableforusingon

awidevarietyof

subductio

nmegathrusts.

C2

Strasser

etal.(2010);

interfaceevents

Mw�

4:441�

0:846log 1

0�A

�σ�

0:286(inM

w)

A:rupturearea

(km

2)

1AsforC1

Blaseret

al.(2010);oceanic/

subductio

nreverse

log 1

0L�

−2:81�

0:62M

w

Sxy�

0:16(orthogonalstandarddeviation)

L:subsurface

faultlength

(km)

1

C3

Ichino

seet

al.(2006)

log 1

0�A

a��

0:57��

0:06�M

0−13:5��

1:5�

σ�

16:1

(inAa)

Aa:combinedarea

ofasperities(km

2)

M0�

seismic

mom

ent

(dyn

·cm)

1Onlyregression

ofrelevanceto

intraslabearthquakes.

D1

Villam

oret

al.(2001);New

Zealand

;no

rmal

Mw�

3:39�

1:33logA

σ�

0:195(inM

w)

A:area

(km

2)

1Onlyregression

ofrelevanceto

volcanic-normalearthquakesin

thin

crust(riftenvironm

ents).

D2

Wesno

usky

(2008);no

rmal

Mason

(1996)

Mw�

6:12�

0:47logL

σ�

0:27(inM

w)

Mw�

4:86�

1:32logL

σ�

0:34(inM

w)


(km)

L:surfacerupturelength

1 2Basin

andrange-rich

norm

al-slip

dataset.

Interm

ountainwest-dominated

norm

al-slip

dataset.

*The

“TectonicRegim

e”identifiers

relate

totheID

sgivenin

parenthesesin

Table1.

Forexam

ple,

A11

signifies“Plate

BoundaryCrustal/Plate

BoundaryFast

Slipping/Strike-Slip

Dom

inated.”

† Primaryreferenceforregression.B

oldregression

inform

ationcorrespondsto

theshortlisted

regressions(those

having

thehighestq

ualityscoreand/or

mostsuitableregressionsforthegiventectonicregimes).

Regressioninform

ationnotin

bold

provides

closealternatives

totheshortlisted

regressionsforthegiventectonic

regimes.

‡ Regressionequatio

nsandstandard

deviations

orstandard

errors(ifavailable).A

pplicableparametersarein

parentheses;forexam

ple,“inM

w”means

thestandard

deviationisforM

w.T

hestandard

Hanks

and

Kanam

ori(1979)equationisalso

provided

incasesforw

hich

seismicmom

entneeds

tobe

convertedtomom

entm

agnitude.U

seof

Aa(com

binedasperityarea

onfaultplane)ispossibleforw

ell-modeled

sourcesand

correlates

with

M0.

§ Qualityscores:1,

bestavailable;

2,good;3,

fair.

|| Justificationforshortlistingof

regression

into

this

table.


BSSA Early Edition

• The shortlisted regression for D1 (rift within thin crust) andD2 (rift within thicker crust) tend to show smaller magni-tudes for a given rupture length than the majority of theshortlisted regressions, so is again consistent with theexpectation that normal slip types produce smaller magni-tudes than other slip types (e.g., Wells and Copper-smith, 1994).

A synthesis of the above observations is that regressionsdominated by plate boundary earthquakes show tendency toproduce smaller magnitudes for a given rupture length orarea than do stable continental areas and produce similar-or-larger magnitudes than earthquakes in rift environments.The differences in scaling for these regressions make sensefrom physical grounds. Previous studies (e.g., Scholz et al.,1986; Schorlemmer et al., 2005) suggest that earthquakescaling should vary according to slip type and plate tectonicsetting, so our study is at least partially consistent with theprevious work.

Conclusions and Recommendations

We provided a large compilation of magnitude-area andmagnitude-length scaling relationships and shortlisted somefor application in seismic-hazard applications such as GEM.The equations are provided, as well as relevant dialog andguidelines to assist with the use of regressions in seismic-hazard modeling. The shortlisted regressions generally havebeen chosen as the best representatives of specific tectonicregimes (defined according to plate tectonic setting and sliptype). Graphical comparison of the regressions generallyreveals obvious differences in regressions for the differenttectonic regimes, and the majority of these differences makesense according to a tectonic regionalization of magnitudescaling. Specifically, the categories of tectonic regime(Table 1) are based on our understanding of the broaddifferences in fault parameters such as slip rate, slip type,stress drop, recurrence interval, seismogenic thickness, heatflow, and lithology between the different tectonic regimes.However, in some cases large differences exist betweenregressions for particular tectonic regimes (e.g., one of theregressions for stable continental regimes). It is importantfor seismic-hazard models to adequately represent thisimportant source of epistemic uncertainty.

Our study has been motivated by a need to assist scien-tists and practitioners in making the appropriate choice ofregressions for seismic-source modeling. We have tackled atopic area that is the focus of considerable debate in the lit-erature, with fundamental issues surrounding whether or notearthquake scaling is regionalized and what physical factorscontrol earthquake scaling. We therefore offer the followingrecommendations for future development and selection ofregressions for seismic-hazard application, in which the firstrecommendation seeks to push the boundaries of the under-standing of earthquake scaling, and the rest address the mostappropriate use of our compilation:

• We recommend that a large funded project akin to the NextGeneration Attenuation (NGA) project be initiated todevelop an up-to-date quality-assuredmaster regression da-tabase (like the NGA quality-assured strong-motiondatabase, or flatfile). The NGA project involved keyground-motion prediction modelers using the flatfile todevelop updated regressions and then comparing the result-ing ground-motion predictions as a cross-validation exer-cise. In the NGA context, regression developers wouldproduce a set of regressions for international applicationfrom the same master database and then undertake a cross-validation exercise. This effort would focus attention on thescientific basis for regression development and eliminateuncertainties due to data quality and quantity. Clearly theepistemic uncertainty in regression formulation is verylarge, and preferred methods have not yet been definedin the international seismological community.

• Regression users should ensure that their choice of regres-sion is as compatible as possible with the tectonic regimeof interest.

• Regressions should not be used beyond the magnituderange of data used to develop the regression. Exceptionsto this recommendation should be justified, as regressionsare often used incorrectly in this respect.

• Where possible, regression users should use a selection ofregressions (e.g., by way of a logic tree framework)according to the tectonic regime framework given inTable 2 and carefully evaluate the consequences of the par-ticular selection of regressions.

• Regression users should aim to use regressions of qualityscore � 1 whenever possible, although we acknowledgethis may not be possible for some tectonic regimes (e.g.,stable continental).

• Regression developers should strive to develop regressionsfor specific tectonic regimes, rather than combining allavailable earthquake data from an ensemble of tectonicregimes.

• Regression developers should provide clear recommenda-tions regarding the tectonic regimes relevant to theirregressions.

• Regression developers should always provide standarddeviations and/or standard errors for their regression equa-tions. Many of the regressions are not accompanied by anyindication of statistical uncertainty in the relevant docu-mentation.

Data and Resources

Regression equations are available from published liter-ature and from unpublished documents that are availablefrom the authors on request. The SRCMOD database offinite-source rupture models is available online at http://www.seismo.ethz.ch/srcmod (last accessed July 2012), andthe GEM Faulted Earth website can be viewed online athttp://www.nexus.globalquakemodel.org/gem-faulted-earth/posts (last accessed September 2013).


BSSA Early Edition

http://www.seismo.ethz.ch/srcmod





http://www.nexus.globalquakemodel.org/gem-faulted-earth/posts

http://www.nexus.globalquakemodel.org/gem-faulted-earth/posts

Acknowledgments

We thank John Shaw, Edward (Ned) Field, and Tom Hanks for usefuldiscussions and the GEM Foundation for their financial support of the study.An anonymous reviewer and Tom Hanks also provided very useful and in-sightful comments on the manuscript.

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BSSA Early Edition

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Appendix A

Documentation of RegressionsShown in Table 2

The regressions are ordered as in Table 2. Some regres-sion datasets include a mix of different types of magnitude.The regression developers have either converted these magni-tudes toMw or assumed that they approximateMw, unless theregression magnitude type is shown as being different toMw.

Hanks and Bakun (2008) Relationships

Mw � logA� �3:98� 0:03� for A < 537 km2;

Mw � �4=3� logA� �3:07� 0:04� for A > 537 km2;

in which A is the fault area in square kilometers.

Description. The regression is developed for continentalstrike-slip earthquakes. Based on a relatively small datasetof large earthquakes and mainly suitable for large to greatstrike-slip earthquakes in plate boundary settings (e.g.,San Andreas, Alpine, North Anatolian).

Data. Eighty-eight continental strike-slip earthquakes. In-cludes historical earthquakes since 1857 and 12 newMw >7

events added to the Wells and Coppersmith (1994) dataset.Regions for the seven newMw >7 events are Japan (1), Tur-key (2), California (1), China (2), and Alaska (1). Magnituderange: 5–8 (Mw).

Application. Major plate boundary strike-slip faults. Notsuitable for use on faults with slip rates less than ~1 mm/yr.Widely used in major seismic-hazard models around theworld. Should be given significant weighting in logic treeframework for application to plate boundary strike-slip faultswith high slip rates.

Tectonic Regime and Mechanism. A11, A22.

Quality Score. 1.

References. Wells and Coppersmith (1994) and Hanks andBakun (2008).

Wesnousky (2008) Relationships

Mw � 5:30� 1:02 logL; all events �37 events used�;


BSSA Early Edition

Mw�5:56�0:87 logL; strike-slip events�22events used�;

Mw � 6:12� 0:47 logL; normal events �7 events used�;and

Mw � 4:11� 1:88 logL; reverse events �8 events used�;

in which L is the surface rupture length in kilometers.

Description. The regressions have been developed fromearthquakes associated with rupture lengths greater than about15 km, encompassing three slip types from both interplate andintraplate tectonic environments. The regression is applicableto earthquake sources of lengths greater than 15 km.

Data. Dataset limited to the larger surface rupture earth-quakes of length dimension greater than 15 km and for whichboth maps and measurements of coseismic offset areavailable. A total of 37 events have been used, all continentalearthquakes. These include 22 strike-slip, 7 normal, and 8reverse-slip events. Regions: California (8), Turkey (7), Japan(5), Nevada (3), Australia (3), Iran (2), China (2), Mexico (1),Algeria (1), Philippines (1), Taiwan (1), Idaho (1), Montana(1), and Alaska (1). Magnitude range: 5.9–7.9 (Mw).

Application. All regions for the relevant slip types butacknowledging that the regression dataset will be dominatedby plate boundary earthquakes. Should be given significantweighting in logic trees. The author indicates the relationshipis most relevant to strike-slip sources.

Tectonic Regime and Mechanism. A11 (strike-slip), A22(strike-slip), A23 (normal), A24 (reverse), and D2 (normal).

Quality Score. 1.

Reference. Wesnousky (2008).

Leonard (2010) Relationships

Mw � 3:99� logA; strike-slip;

Mw � 4:00� logA; dip-slip;

Mw � 4:19� logA; stable continental regions;


Description. Three regressions for seismic moment M0.Regressions are developed by solving for widthW, displace-ment D as a function of area A, and seismic momentM0 (M0

can then be used to solve for Mw). The regressions aredeveloped using worldwide data and are provided in termsof fault area, fault rupture length, surface rupture length, andaverage surface displacement, for strike-slip, dip-slip, andstable continental regions (SCRs).

Data. Predominantly plate boundary earthquakes. Dividedinto two categories: (a) interplate and plate boundary (classesI and II; Scholz et al., 1986) and (b) SCR (i.e., intraplatecontinental crust that has not been extended by continentalrifting), which includes midcontinental (class III; Scholzet al., 1986). Several datasets were used: Wells and Copper-smith (1994), Henry and Das (2001), Hanks and Bakun(2002), Romanowicz and Ruff (2002), and Manighetti et al.(2007). The database of Johnston (1994) was also used. The2004 Sumatra–Andaman earthquake is included, as well as12 surface rupturing earthquakes. Data are separated intostrike-slip and dip-slip mechanisms.

Origin of Each Dataset

• Wells and Coppersmith (1994): Two hundred and forty-four continental crustal (h < 40 km) earthquakes of allmechanism types, both interplate and intraplate.

• Henry and Das (2001): Sixty-four shallow dip-slip andeight strike-slip events in the period 1977–1996, plus threerecent earthquakes: 1998 Antarctic plate, 1999 Izmit(Turkey), 2000 Wharton Basin. Twenty-seven strike-slipearthquakes from Pegler and Das (1996) also included(large earthquakes in the period 1977–1992 based on re-located 30-day aftershock zones). Wells and Coppersmith(1994) dataset were also used but augmented with largerdip-slip events and subduction zone events.

• Hanks andBakun (2002): Strike-slip subset of theWells andCoppersmith (1994) database, containing 83 continentalearthquakes of which 82 have magnitudes Mw ≥7:5.

• Romanowicz and Ruff (2002): The following datasets areused: reliable M0 − L database of large strike-slip earth-quakes since 1900 (Pegler and Das, 1996); data for greatcentral Asian events since the 1920s (Molnar and Denq,1984; Romanowicz, 1992); and data for recent large strike-slip events (e.g., Balleny Islands 1998; Izmit, Turkey 1999;and Hector Mines, California, 1999) that have been studiedusing a combination of modern techniques (i.e., field ob-servations, waveform modeling, aftershock relocation).

• Manighetti et al. (2007): Two hundred and fifty large(Mw ≥∼6), shallow (rupture width ≤40 km, with an aver-age value of width of 18 km), continental earthquakes ofmixed focal mechanisms (strike-slip, reverse, and normal),that have occurred in four of the most seismically activeregions worldwide: Asia, Turkey, Western United States,and Japan.

• Johnston (1994): SCR database of 870 earthquakes wheremoment could be estimated from waveform or isoseismaldata. Surface rupturing earthquakes are included (e.g., three1988 Tennant Creek events. Magnitude range: 4.2–8.5).


BSSA Early Edition

Application. Wide application, including low seismicity/intraplate regions but excluding normal faults regions (e.g.,Great Sumatra fault). The author suggests using this relation-ship for all types of faults. Nevertheless, the author makes thecomment that the relations were primarily developed fromdip-slip data and assumes it also applies to strike-slip earth-quakes out to fault lengths of 45 km and possibly 100 km, asit fits non-width-limited strike-slip earthquakes as well asother previous models.

Tectonic Regime and Mechanism. A11.

Quality Score. 1.

References. Molnar and Denq (1984), Scholz et al. (1986),Romanowicz (1992), Johnston (1994), Wells and Copper-smith (1994), Pegler and Das (1996), Henry and Das (2001),Hanks and Bakun (2002), Romanowicz and Ruff (2002),Manighetti et al. (2007), and Leonard (2010).

Yen and Ma (2011) Relationships

In terms of area:

logAe � −13:79� 0:87 logM0; all slip types �σ � 0:41�;

logAe � −12:45� 0:80 logM0; dip-slip types �σ � 0:43�;

logAe�−14:77�0:92 logM0; strike-slip types�σ�0:40�:In terms of length:

logLe � −7:46� 0:47 logM0; all slip types �σ � 0:19�;

logLe � −6:66� 0:42 logM0; dip-slip types �σ � 0:19�;

logLe �−8:11�0:50 logM0; strike-slip types �σ� 0:20�;

in which Ae is the effective area in square meters, Le is theeffective fault length in kilometers, and M0 is the seismicmoment in dyne centimeters. (Convert M0 to Mw with theequation logM0 � 16:05� 1:5Mw.)

Description. Developed exclusively from earthquakes in acollisional tectonic environment. Equation has a bilinear form.

Data. Twenty-nine events used: 12 dip-slip and 7 strike-slip events in Taiwan, plus 7 large events worldwide (Wen-chuan, China, 2008; Kunlun, Tibet, 2001; Sumatra 2004;Bhuj, India, 2001); and 3 large thrust earthquakes from Maiand Beroza (2000) dataset. Magnitude range: 4.6–8.9 (Mw).

Application. Applicable to reverse-to-reverse-obliquefaults in collisional environments. Use with significant

weighting in a logic tree framework relevant to collisionalenvironments.

Tectonic Regime and Mechanism. A21 (all types), A22(strike-slip), A24 (dip-slip).

Quality Score. 1.

References. Mai andBeroza (2000) andYen andMa (2011).

Stirling et al. (2008) Relationship (New ZealandOblique Slip)

Mw � 4:18� �2=3� logW � �4=3� logL;in whichW is the width in kilometers and L is the subsurfacerupture length in kilometers.

Description. This regression has been developed for NewZealand strike-slip to reverse-slip earthquakes. It producesmagnitudes that are larger than those of Wells and Copper-smith (1994) and Hanks and Bakun (2008), and magnitudesthat are appropriate for New Zealand fault sources based onexpert judgment. The regression has been applied to numer-ous studies in New Zealand and Australia in recent years.The regression is documented in a consulting report butwas first published in the reference below.

Data. Twenty-eight New Zealand strike-slip to reverseearthquakes on low slip rate faults. The data were obtainedfrom body-wave modeling studies of historical and contem-porary earthquakes where fault mechanism, depth, sourceduration, and seismic moment were obtained (Berrymanet al., 2002). Magnitude range: 5.6–7.8 (Mw).

Application. The authors recommend that the regressionshould be used for strike-slip–to–convergent-dip-slip faults,not for major plate boundary faults. Performs well for strike-slip to oblique-slip faults other than the primary plate boun-dary faults (e.g., Alpine fault, San Andreas fault) and forstrike-slip to oblique-slip faults in low seismicity regions,that is, larger magnitudes for given fault rupture lengths.

Tectonic Regime and Mechanism. A22, A24.

Quality Score. 1.

References. Berryman et al. (2002) andStirling et al. (2008).

Anderson et al. (1996) Relationship

Mw � 5:12� 1:16 logL − 0:20 log S;

in which L is the surface fault length in kilometers and S isthe slip rate in millimeters per year.


BSSA Early Edition

Description. Least-squares regression for a dataset of 43earthquakes on faults with known slip rates. The authors dem-onstrate a negative dependence of magnitude on slip rate.

Data. Worldwide dataset, although most from California.Other regions include Nevada (2), Missouri (1), Montana(1), Mexico (1), Philippines (1), Turkey (5), Japan (5), China(2), andNewZealand (3). Limited to regionswith seismogenicdepth from 15 to 20 km. Magnitude range: 5.8–8.2 (Mw).

Application. Interplate to intraplate environments whereearthquake magnitude and fault slip rate data are available.Although based on a relatively small earthquake dataset, thenegative dependence of magnitude on slip rate makes this apotentially suitable regression for use in a wide variety ofenvironments. However, the small size and age of the earth-quake dataset should limit the weight placed on this regres-sion in a logic tree framework.

Tectonic Regime and Mechanism. B1, B2.

Quality Score. 2.

Reference. Anderson et al. (1996).

Nuttli (1983) Relationship

logM0 � 3:65 logL� 21:0;

in which M0 is the seismic moment in dyne centimeters andL is the subsurface fault length in kilometers. (ConvertM0 toMw with the equation logM0 � 16:05� 1:5Mw.)

Description. Developed for midplate earthquakes(>500 km from plate margins), both continental andoceanic. Magnitude-length relationships are obtained fromderived fault lengths, not direct length measurements (empir-ical data are M0 and magnitudes mb and Ms).

Data. Published data for 143 midplate earthquakes.Magnitude range: 0.4–7.3 (Ms).

Application. Intraplate settings. The regression is 30 yearsold, so some key intraplate earthquakes are not included in re-gression database. However, being one of only two intraplateregressions in this compilation makes it a valuable inclusion.

Tectonic Regime and Mechanism. B1, B2.

Quality Score. 3.

Reference. Nuttli (1983).

Johnston (1994) Relationship

Mw � 1:36 logL� 4:67;


Description. A regression developed for SCRs. The authorsconsider this regression to be statistically indistinguishablefrom regressions for interplate and active continental plate inte-rior regions. They conclude that SCR earthquakes have com-parable stress drops and source scaling to events in activetectonic regions. It uses 10 stable continental surface ruptureearthquakes from Australia, Africa, India, and Canada. The da-taset is dominated by thrust events, most of them fromAustralia.The authors indicate that the regressions are not very robust, andtheir conclusions cannot be considered definitive until more dataare available, especially for the larger magnitudes.

Data. Ten earthquakes in SCRs and with surface rupture.Events include five earthquakes in west (3) and central (2)Australia, two in west Africa, one in northeast Africa, one inIndia, and one in Canada. The database is dominated bythrust events (seven events), with two strike-slip events andone oblique. Surface rupture lengths range from 3 to 140 km.Magnitude range: 5.46–7.79 (Mw).

Application. SCRs. As the relationship is based on only 10earthquakes and has been referred to as “purely empirical” and“not well constrained” (Leonard, 2010), it should therefore beused in seismic-hazard analyses with other relevant regressions.

Quality Score. 3.

References. Johnston (1994) and Leonard (2010).

Strasser et al. (2010) Relationships

In terms of length:

Mw � 4:868

� 1:392 log10�L�; interface events �95 events used�;

Mw � 4:725

� 1:445 log10�L�; intraslab events �20 events used�:

In terms of area:

Mw � 4:441

� 0:846 log10�A�; interface events �85 events used�;Mw � 4:054

� 0:981 log10�A�; intraslab events �18 events used�;


BSSA Early Edition

in which L is the surface rupture length in kilometers, and Ais the rupture area in square kilometers.

Description. Regressions for worldwide subduction inter-face and intraslab events. Relationship parameters are alsoavailable for width and length parameters as well as for areain terms of magnitude (instead of magnitudes in terms ofarea). Interface relationships show stress drop to be a de-creasing function of magnitude, which may be due to largermagnitudes involving a greater proportion of nonasperityareas than smaller magnitudes.

Data. Subduction interface and intraslab events takenprimarily from the SRCMOD database (Mai, 2004; see alsoData and Resources). Ninety-five interface events (magni-tude range Mw � 6:3–9:4) and 20 intraslab events (magni-tude range Mw � 5:9–7:8).

Application. Subduction interface and intraslab sources.

Tectonic Regime and Mechanism. C1, C2.

Quality Score. 1.

References. Mai (2004) and Strasser et al. (2010).

Blaser et al. (2010) Relationships

Relationships for Oceanic and Subduction Events. In termsof length:

log10 L � −2:81� 0:62Mw; reverse-slip �26 events used�:Magnitude range : 6:1–9:5�Mw��Sxy � 0:16�:L range : 13–1400 km:

log10 L � −2:56� 0:62Mw; strike-slip �16 events used�:Magnitude range : 5:3–8:1�Mw��Sxy � 0:19�:L range : 7:0–350 km:

log10 L � −2:07� 0:54Mw; all slip types�47events used�:Magnitude range : 5:3–9:5�Mw��Sxy � 0:18�:Lrange : 7:0–1400 km:

In terms of width:

log10 W � −1:79� 0:45Mw; reverse-slip �23 events used�:Magnitude range : 6:1–9:5�Mw��Sxy � 0:14�:W range : 12–240 km:

log10 W � −0:66� 0:27Mw; strike-slip �14 events used�:Magnitude range : 5:3–7:8�Mw��Sxy � 0:21�:W range : 4–30 km:

log10W � −1:76� 0:44Mw; all slip types �40 events used�:Magnitude range : 5:3–9:5�Mw��Sxy � 0:17�:W range : 4–240 km;

in which L is the subsurface fault length in kilometers, W isthe rupture width in kilometers, and Sxy is the orthogonalstandard deviation. (Note: only the relationships foroceanic/subduction events are shown.)

Description. Developed for subduction zones. Based on alarge dataset of 283 earthquakes. Most of the focal mecha-nisms are represented, but the analysis is focused on largesubduction zones. The authors recommend the relationshipsbe used by applying orthogonal regression methods. Exclu-sion of events prior to 1964 (when the World Wide StandardSeismograph Network [WWSSN], was established) showsno saturation on rupture width for strike-slip earthquakes.Thrust relationships for pure continental and pure subductionzone rupture areas are almost identical. The authors recom-mend different scaling relationships be used according tofocal mechanism.

Data. Published data for 283 earthquakes. Database com-posed of 196 source estimates by Wells and Coppersmith(1994), 40 by Geller (1976), 25 by Scholz (1982), 31 by Maiand Beroza (2000), 36 by Konstantinou et al. (2005), and 31by several other authors analyzing single large events. Mag-nitude range (for oceanic/subduction zones): 5.3–9.5 (Mw).

Application. Subduction zones (especially oceanic).

Tectonic Regime and Mechanism. C2.

Quality Score. 1.

References. Geller (1976), Scholz (1982), Wells andCoppersmith (1994), Mai and Beroza (2000), Konstantinouet al. (2005), and Blaser et al. (2010).

Ichinose et al. (2006) Relationship

log10�Aa� � 0:57��0:06�M0 − 13:5��1:5�;

in which Aa is the combined area of asperities in squarekilometers and M0 is the seismic moment in dynecentimeters. (Convert M0 to Mw with the equationlogM0 � 16:05� 1:5Mw.)


BSSA Early Edition

Description. Developed for intraslab earthquakes at globalscale.

Data. Data from the 3 events in Cascadia (1949 Olympia,Washington; 1965 Seattle-Tacoma; and 2001 Nisqually) andseveral Japan (9 events taken from Asano et al. [2003] andMorikawa and Sasatani [2004]) and Mexico (14 events takenfrom Hernandez et al. [2001], Iglesias et al. [2002], Yama-moto et al. [2002], and Garcia et al., [2004]) intraslab earth-quakes (26 events in total). Magnitude range: 5.4–8.0 (Mw).

Application. Intraslab earthquake source modeling.

Tectonic Regime and Mechanism. C3.

Quality Score. 1.

References. Hernandez et al. (2001), Iglesias et al. (2002),Yamamoto et al. (2002), Asano et al. (2003), Garcia et al.(2004), Morikawa and Sasatani (2004), and Ichinoseet al. (2006).

Villamor et al. (2001) Relationship (New Zealand;Normal Slip)

Mw � 3:39� 1:33 logA;

in which A is the area in square kilometers.

Description. This New Zealand-based regression has beendeveloped from Taupo volcanic zone earthquakes for appli-cation to normal faults in volcanic and rift environments. Itwas developed for a consulting project but first published inthe reference below.

Data. Seven large earthquakes in the Taupo volcanic zone(three strike-slip and four normal events), including theMw 6.5Edgecumbe 1987 earthquake. Magnitude range: 5.9–7.1 (Mw).

Application. Only for use with normal faults in thin weakcrust (e.g., New Zealand’s Taupo volcanic zone). Use in riftenvironments but with careful examination of the results.

Tectonic Regime and Mechanism. D1.

Quality Score. 1.

Reference. Villamor et al. (2001).

Mason (1996) Relationship

Mw � 4:86� 1:32 logL:

For which σ � 0:34 (in Mw), Mw is the moment mag-nitude, and L is the subsurface fault length in kilometers.

Description. Developed from the Wells and Coppersmith(1994) regression for normal fault earthquakes, but coeffi-cients adjusted for normal fault earthquakes in the inter-mountain west.

Data. Normal-slip earthquakes drawn from a dataset of 65intermountain historical and prehistoric earthquakes. Magni-tude range: 6.5–7.2 (Mw).

Application. Normal faulting settings such as the Basinand Range.

Tectonic Regime and Mechanism. D2.

Quality Score. 2.

Reference. Mason (1996).

Appendix B

Other Regressions

The following is a documentation of the regressions thathave not been shortlisted for reasons provided in the Introduc-tion. The purpose of including these regressions in the paper isto demonstrate that our compilation and evaluation has been athorough procedure, in that it has captured all of the readilyavailable published regressions in the literature. Furthermore,it allows access to all available regressions if so desired. Someregression datasets include a mix of different types of magni-tude. The regression developers have either converted thesemagnitudes toMw or assumed that they approximateMw, un-less the regression magnitude type is shown as being differentto Mw. The regressions are ordered alphabetically by source.

Ambraseys and Jackson (1998) Relationships

Ms � 5:13� 1:14 logL; for historical and instrumental

data �σ � 0:15; inMS�;and

Ms � 5:27� 1:04 logL;

for instrumental data �σ � 0:22; inMS�;in which L is the surface fault length in kilometers.

Description. The regression has been developed fromstrike-slip, normal, and thrust events in the Eastern Mediter-ranean region.

Data. Collected from a variety of published and unpublishedsources and from field investigations, with 25% collected bythe first author. Uses both historical and instrumental data in


BSSA Early Edition

the Eastern Mediterranean region and the Middle East. Onehundred and fifty events used to obtain the scaling relationship,all of them associated with coseismic surface faulting. Only 35events are common to the Wells and Coppersmith (1994) data-base; 55% of the data are strike-slip events, 30% normalevents, and 15% thrust faults. Magnitude range: Ms ≥5:1.

Application. Eastern Mediterranean, Middle East, and sim-ilar environments (i.e., plate boundary transpressional totranstensional environments). Regression dataset is reason-ably large and therefore makes the regressions suitable forapplication in Eastern Mediterranean/Middle East.

Quality Score. 1.

Reference. Ambraseys and Jackson (1998).

Bonilla et al. (1984) Relationships

Ms � 6:04� 0:708 logL;

all types of faults �45 events used�;

Ms � 5:71� 0:916 logL;

reverse and reverse-oblique faults �12 events used�;

Ms � 6:24� 0:619 logL; strike-slip �23 events used�;

Ms � 5:58� 0:888 logL; plate margins �9 events used�;

Ms � 6:02� 0:729 logL; plate interiors �36 events used�;

Ms � 4:94� 1:296 logL; United States and China k

� 1:75 attenuation region �9 events used�;

Ms � 4:88� 1:286 logL; United States k

� 1:75 attenuation region �5 events used�;

Ms � 6:18� 0:606 logL; Turkey �9 events used�;

Ms � 5:17� 1:237 logL;

Western North America �12 events used�;


Description. Magnitude-length and/or displacement rela-tionships obtained for five types of mechanisms: normal, re-verse, normal oblique, reverse oblique, and strike-slip. One

hundred published and unpublished events analyzed, 48 ofthem used to obtain the equation, which correspond to theones with error estimations in reported length or displace-ment. Tests made for ordinary and weighted least-squaresregression methods (ordinary least squares found to be theappropriate approach).

Data. Forty-eight worldwide earthquakes, taken from pub-lished and unpublished data. No subduction events included.Fault length 3–450 km. Magnitude range: 6.5–8.3 (Ms).

Application. Worldwide application, although some rela-tionships are specific for certain regions (United States k �1:75 attenuation region, United States and China k � 1:75attenuation region, Turkey, Western North America). Nomagnitude-length equations are available for normal mech-anisms, but magnitude-displacement or displacement-lengthrelations are also available for these events (not shown here).Age and size of the earthquake dataset limit the applicabilityof these regressions, and they therefore should be given verylow weighting if used in a logic tree framework. An addi-tional recommendation from the author is that the equationsshould not be extrapolated beyond the range of the dataset orapplied to subduction zone sources.

Quality Score. 3.

Reference. Bonilla et al. (1984).

Dowrick and Rhoades (2004) Relationships

Mw � 4:39� 2:0 logL; L < 6:0 km;

Mw � 4:76� 1:53 logL; L ≥ 6:0 km;

in which L is the subsurface rupture length in kilometers.

Description. Developed for New Zealand events. When re-sults were compared to multiregional relationships, significantdifferences were found to regressions for California, Japan,and China. Authors consider multiregional relationships tobe a poor estimation for New Zealand data, as they under-estimate New Zealand magnitudes (by 0.4 magnitude unitswhen compared to Wells and Coppersmith, 1994, Somervilleet al., 1999 and the lower part of the bilinear regression byHanks and Bakun, 2002 relationships). The relations are in-fluenced by structural restrictions placed on rupture width.

Data. Eighteen events in New Zealand. Magnitude range:5.9–8.2 (Mw).

Application. New Zealand interplate. Use only in a logictree framework with low weighting relative to other more


BSSA Early Edition

widely used New Zealand-based regressions (e.g., Villamoret al., 2001; Stirling et al., 2008).

Quality Score. 3.

Reference. Dowrick and Rhoades (2004).

Ellsworth-B Relationship

Mw � logA� 4:2;


Description. Simple magnitude-area scaling relationshipapplicable to all slip types in plate boundary areas. Nostand-alone reference exists for this relationship, but it isdocumented in Working Group on California EarthquakeProbabilities (WGCEP; 2003, 2008) and has been developedfrom worldwide earthquakes.

Data. Continental strike-slip events from Wells andCoppersmith (1994) dataset with areas A > 500 km2 corre-sponding to Mw >6:5. Magnitude range: 6.5–8.5 (severaltypes of magnitudes: mainly Ms but also some ML and mb).

Application. Best applied to continental strike-slip faults butcan also be used in intraplate areas. Used by the WGCEP in the2002 U.S. National Seismic HazardMapping Project with equalweight to the Hanks and Bakun (2008) relationship, indicatingthat it can be used with confidence in logic tree frameworks.

Quality Score. 1.

References. Wells and Coppersmith (1994), WGCEP(2003, 2008).

Mai and Beroza (2000) Relationships

In terms of area:

logA � −11:18 − 0:72 logM0;

all events �18 events used��σ � 0:26; in area�;

logA � −8:49 − 0:57 logM0; strike-slip events

�8 events used��σ � 0:19; in area�;

logA � −11:90 − 0:75 logM0; dip � slip events

�10 events used��σ � 0:31; in area�:

In terms of length:

logL � −6:13 − 0:39 logM0; all events

�18 events used��σ � 0:16; in length�;

logL � −6:31 − 0:40 logM0; strike-slip events


logL � −6:39 − 0:40 logM0; dip-slip events


in which A is the area in square kilometers, L is the subsur-face length in kilometers, and M0 is the seismic moment innewton meters. (Convert M0 to Mw with the equa-tion logM0 � 16:05� 1:5Mw.)

Description. Developed from finite-fault rupture models.The dataset lacks very large strike-slip events. The scalinglaws produce very similar results to those of Wells andCoppersmith (1994).

Data. Eighteen earthquakes, of which eight are largecrustal strike-slip and 10 dip-slip earthquakes; regions: mostof them in California (13), other regions: Idaho (1), Japan(2), Iran (1), Mexico (1). Magnitude range: 5.6–8.1 (Mw).

Application. To plate boundary environments. The smallregression dataset potentially limits the stability of theseregressions.

Quality Score. 2.

Reference. Mai and Beroza (2000).

Romanowicz and Ruff (2002) Relationships

logM0 � n logL� log�M0�min;

�M0�min � 0:5 × 1020 N·m;

n � 1:20� 1:4; continental=interplate

strike-slip events �25 events used�;

�M0�min � 1:0 × 1020 N·m;

n � 1:09� 2:4; continental=interplate

strike-slip events �16 events used�;in which L is the rupture length in kilometers.

Description. Moment-length scaling laws developed for largecontinental strike-slip earthquakes. The regressions are devel-oped according to a bimodal distribution of earthquake scaling.

Data. Several datasets have been combined to developthese regressions: Pegler and Das (1996); M0 − L data forlarge strike-slip earthquakes since 1900 (Romanowicz,1992); great central Asian events since 1920 (Molnar and


BSSA Early Edition

Denq, 1984); and data from recent large strike-slip events.Continental strike-slip earthquakes from California (includ-ing San Francisco, 1906; Loma Prieta, 1989; and HectorMines, 1999 events), Turkey (including Izmit, 1999), Japan,Tibet, Fiji, India, Papua, Honduras, Sudan, and Iran are in-cluded in the database.

Magnitude Range. Mw ≥5:5 for the full dataset. Subsets ofthe data have been used to develop the various scaling laws.

Application. Interplate strike-slip (two regressions) andoceanic intraplate environments (two regressions).

Quality Score. 1.

References. Molnar and Denq (1984), Romanowicz (1992),Pegler and Das (1996), Romanowicz and Ruff (2002).

Shaw (2009) Relationship

M � logA� 2

3log

max�1;

��AH2

q �h1�max

�1; A

H2β

�i=2

� const:;

in which A is the rupture area in square kilometers, H is theseismogenic thickness in kilometers, β � 2χ, in whichχ � 3, and const. is the constant.

Description. Developed for worldwide earthquakes, bothsmall and large. The regression has been developed to ad-dress the hypothesis that earthquake stress drops are constantfrom the smallest to the largest events (most other regressionsassume nonconstant stress-drop scaling), combined with athorough treatment of the geometrical effects of the finiteseismogenic layer depth. The relationship has been testedfor strike-slip events, because they are the ones with the larg-est aspect ratio L=W. For these events (see Data below) thebest fitting corresponds to H � 15:6 km and β � 6:9.

Data. Strike-slip events taken from Hanks and Bakun(2008) data as well as Wells and Coppersmith (1994), Hanksand Bakun (2002), and WGCEP (2003). These datasets donot have error bars. Magnitude range: 4.2–8.5 (several typesof magnitudes: mainly Ms but also some ML and mb).

Origin of Each Dataset

• Wells and Coppersmith (1994): Two hundred and forty-four continental crustal (h < 40 km) earthquakes of allmechanism types, both interplate and intraplate.

• Hanks and Bakun (2002): Strike-slip subset of theWells andCoppersmith (1994) database, which contains 83 continentalearthquakes of which 82 have magnitudes Mw ≥7:5.

• Hanks and Bakun (2008): Eighty-eight continental strike-slip earthquakes. Includes historical earthquakes since

1857 and 12 new Mw >7 events added to the Wells andCoppersmith (1994) dataset.

Application. Applicable to all types of faults in all regionsaround the world. Has not been used greatly in seismic haz-ard studies, so careful examination of regression results isrecommended. The author states that the scaling law fitsthe whole range of magnitude-area data.

Quality Score. 2.

References. Hanks and Bakun (2002, 2008), WGCEP(2003), Shaw (2009)

P. G. Somerville, personal comm. (2006) Relationship

Mw � 3:87� 1:05 log�A�;


Description. Uses a uniform dataset of recent worldwidecrustal earthquakes for which seismic inversions are avail-able. Makes extensive use of teleseismic and strong-motioninversions of coseismic slip. The relationship provides nearidentical estimates of Mw to self-similar models.

Data. Sixteen large strike-slip events worldwide (UnitedStates, Japan, Tibet, and Turkey). Magnitude range: 5.7–7.9 (Mw).

Application. For use on all fault types in interplatetectonic settings, that is, western North America, Indonesia,Caribbean/central America, northern South America, NewZealand, Middle East, and southeast Asia. Paucity of docu-mentation for this relationship makes it difficult to assess thequality of this regression, so recommended usage in a logictree framework is with relatively low weighting. Use in intra-plate settings after verifying results make sense (e.g., com-parison of predicted to observed earthquake magnitudes andrupture areas). Use with low weighting in logic tree frame-work on account of small regression dataset.

Quality Score. 2.

References. WGCEP (2002), P. G. Somerville, personalcomm. (2006), Somerville et al. (2006).

Somerville et al. (1999) Relationship

Mw � logA� 3:95;

in which A is the rupture area in square kilometers.


BSSA Early Edition

Description. Developed from crustal earthquakes. Therelationships are constrained to be self-similar and producevery similar results to those of Wells and Copper-smith (1994).

Data. Fifteen inland crustal earthquakes worldwide, mostof them in California. Other regions are Canada (2), Iran (1),Idaho (1), and Japan (1). Mechanisms: one normal, six thrustevents, six strike-slip events, two oblique earthquakes.Magnitude range: 5.7–7.2 (Mw).

Application. Crustal earthquakes worldwide. Can be usedwith greatest confidence at moderate-to-large magnitudes.Departure from self-similar scaling may occur for very largecrustal strike-slip earthquakes at very large magnitudes.Use with significant logic tree weighting when focus is onmoderate-to-large magnitude earthquake sources.

Quality Score. 2.

Reference. Somerville et al. (1999).

Stirling et al. (1996) Relationships

M0 � 1:22�1018�L5:0; strike-slip faults worldwide;

L < 50 km;

M0 � 2:37�1024�L1:3; strike-slip faults worldwide;

L > 50 km;

M0 � 2�1023�L2:1; large intraplate earthquakes in Japan;

in which M0 is the seismic moment in dyne centimeters andL is the surface or subsurface rupture length in kilometers.(Convert M0 to Mw with the equation logM0 � 16:05�1:5Mw.)

Description. Scaling laws for worldwide plate boundaryearthquakes and intraplate events in Japan.

Data. Strike-slips events worldwide recorded in regionalnetworks located in California, Mexico, New Zealand,Japan, China, and Turkey. Data taken from published papers(Wesnousky et al., 1983; Romanowicz, 1992). Magnituderange: 5.7–7.8 (Mw).

Application. The authors recommend use of this regressionfor strike-slip faults worldwide and intraplate faults in Japan.Regression databases will now be significantly lacking withrespect to the more modern earthquakes. Use only if logictree framework requires a large number of regressions.

Quality Score. 3.

References. Wesnousky et al. (1983), Romanowicz (1992),and Stirling et al. (1996).

Stirling et al. (2002) Relationship

Mw � 5:88� 0:80 logL�50 events used�;in which L is the surface rupture length in kilometers.

Description. Magnitude-length, magnitude-area, and dis-placement-length relationships developed to compare preinstru-mental (pre-1900) and instrumental events in order to understandwhy Wells and Coppersmith (1994) regressions underestimatethe magnitudes of many large worldwide earthquakes. Resultsshow that these regressions produce significantly larger magni-tudes than Wells and Coppersmith (1994) relationships.

Data. Three hundred and eighty-nine worldwide events,305 instrumental (post-1900), and 84 preinstrumental (pre-1900). Expanded and updated dataset fromWells andCopper-smith (1994). Magnitude range: 4.6–8.7 (Ms, ML, and Mw).

Application. The authors did not intend this regression tobe used in seismic-hazard studies, so it should only be used ifa large number of regressions are required for a logic treeframework. They further recommend that the regression onlybe used for the range of magnitudes, displacements, and rup-ture lengths contained in the regression dataset.

Quality Score. 2.

References. Wells and Coppersmith (1994) and Stirlinget al. (2002).

Stock and Smith (2000) Relationships

logM0�3:1 logL; small normal faults�32events used�;

logM0 � 4:1 logL; large normal faults �6 events used�;

logM0 � 2:9 logL; small reverse faults �77 events used�;

logM0 � 2:9 logL; large reverse faults �9 events used�;

logM0�3:2 logL; dip-slip faults in Japan�21events used�;

logM0 � 2:9 logL; dip-slip events in eastern Russia

�16 events used�;


BSSA Early Edition

logM0 � 2:8 logL; small strike-slip faults in California


logM0 � 2:1 logL; large strike-slip faults in California


logM0 � 2:9 logL; small strike-slip faults outside

California �33 events used�;

logM0 � 2:3 logL; large strike-slip faults outside

California �25 events used�;

in which M0 is the seismic moment in dyne centimetersand L is the average dislocation (rupture) subsurface lengthin kilometers. (Convert M0 to Mw with the equationlogM0 � 16:05� 1:5Mw.) Large earthquakes ruptured thewhole seismogenic layer; small earthquakes did not rupturethe whole seismogenic layer.

Description. Scaling relationships obtained from a largedataset of more than 550 worldwide events. The influenceof the mechanism and the size in the scaling relationshipshas been analyzed. No differences in the scaling behaviorhave been found between normal and reverse events or be-tween events from different regions for this type of mech-anisms.

Data. Database of more than 550 events obtained fromseveral published papers (Kanamori and Anderson, 1975;Geller, 1976; Purcaru and Berckhemer, 1982; Scholz, 1982;Bonilla et al., 1984; Kanamori and Allen, 1986; Scholz et al.,1986; Shimazaki, 1986; Romanowicz, 1992; Wells andCoppersmith, 1994; Anderson et al., 1996; Yeats et al.,1997; Margaris and Boore, 1998). Magnitude range: 4.2–8.5 (several types of magnitudes: mainly Ms but also someML and mb).

Application. Worldwide, although specific relationshipshave been developed from data in specific regions (Califor-nia, Japan, and Eastern Russia). Regressions have not beenwidely used to date.

Quality Score. 2.

References. Kanamori and Anderson (1975), Geller (1976),Purcaru and Berckhemer (1982), Scholz (1982), Bonilla et al.(1984), Kanamori andAllen (1986), Scholz et al. (1986), Shi-mazaki (1986), Romanowicz (1992), Wells and Coppersmith(1994), Anderson et al. (1996), Yeats et al. (1997), Margarisand Boore (1998), and Stock and Smith (2000).

Vakov (1996) Relationships

Ms � 4:442� 1:448 logL; slip faults �31 events used�;Ms � 3:862� 1:988 logL; normal

� reverse-strike faults �13 events used�;

Ms � 4:171� 1:949 logL; strike-normal

� strike-reverse faults �20 events used�;

Ms � 3:161� 3:034 logL; normal� reverse faults


Ms � 4:524� 1:454 logL; strike-slip faults


Ms � 4:323� 1:784 logL; oblique faults


Ms � 4:270� 1:947 logL; dip-slip faults


Ms � 4:805� 1:348 logL; strike-slip

� oblique-slip faults �64 events used�;

Ms � 4:525� 1:697 logL; oblique

� dip-slip faults �51 events used�;

Ms � 4:973� 1:273 logL; all faults �82 eventsused�;


Description. Magnitude versus area/length/width analyzedfor worldwide events and different types of mechanisms. Theauthors have found dependence of the scaling relationshipson the source mechanism but not on the regional setting. Ac-cording to the authors, these relationships can also be usedfor the evaluation of earthquake mechanism types.

Data. Database of 400 events worldwide taken fromexisting sources. Subduction events from Japan, NewZealand, Taiwan, and Philippines have been excluded, aswell as normal and thrust events with fault planes dippingless than 45°. A total of 137 events have been finally usedin the scaling laws. Magnitude range: 4.5–8.5 (Ms).

Application. Worldwide. Not widely used to date.


BSSA Early Edition

Quality Score. 2.

Reference. Vakov (1996).

Wells and Coppersmith (1994) Relationships

Mw�4:07�0:98 logA; all slip types�148events used�;

Mw � 3:98� 1:02 logA; strike-slip faults �83events used�;

Mw � 4:33� 0:90 logA; reverse faults �43 events used�;

Mw � 3:93� 1:02 logA; normal faults �22 events used�;


Description. These regressions are developed for world-wide earthquakes. Are still considered by many to be indus-try standards but in reality are out of date in terms of data.Magnitudes tend to be less than those estimated from themore modern regressions.

Data. Two hundred and forty-four continental crustal(h < 40 km) earthquakes of all mechanism types, both inter-plate and intraplate, 127 are surface ruptures, and 117 calcu-lated subsurface ruptures. Taken from published results.Magnitude range: 4.2–8.5 (several types of magnitudes:mainly Ms but also some ML and mb).

Application. The regressions should only be used in plateboundary regimes and in general should not be used if moremodern regressions are available. Use with low weighting ifit has to be used in a logic tree framework. The authors rec-ommend that the all slip type regression be used for mostsituations; the use of subsurface rupture length and area re-gressions may be appropriate where it is difficult to estimate

the near-surface behavior of faults, such as for buried or blindfaults.

Quality Score. 2.

Reference. Wells and Coppersmith (1994).

Wyss (1979) Relationship

Mw � logA� 4:15;


Description. Maximum magnitude values are found to bemore reliably obtained from magnitude-area relationshipsthan magnitude-length relationships.

Data. Worldwide events obtained from published data-bases. Some of the best data were collected by Kanamoriand Anderson (1975). Magnitude range: 5.8–8.5 (Ms) (forthe best data published in Kanamori and Anderson, 1975).

Application. Mw >5:6 earthquakes worldwide. Age of re-gression is such that database will be significantly lackingwith respect to more modern earthquakes. Only use if logictree framework requires consideration of a large number ofregressions.

Quality Score. 3.

References. Kanamori and Anderson (1975) andWyss (1979).

GNS ScienceP.O. Box 30368Lower Hutt 5011, New Zealand

Manuscript received 26 February 2013;Published Online 15 October 2013


BSSA Early Edition

ATTACHMENT 3 PROBABILISTIC FAULT DISPLACEMENT HAZARD ANALYSIS FOR REVERSE FAULTS

Probabilistic Fault Displacement Hazard Analysis for Reverse Faults

by Robb Eric S. Moss and Zachary E. Ross

Abstract We present a methodology for evaluating potential surface fault displace-ment due to reverse faulting events in a probabilistic manner. This methodology,called probabilistic fault displacement hazard analysis (PFDHA) follows proceduresthat were originally applied to normal faulting. We present empirical distributions forsurface rupture, maximum and average displacement, spatial variability of slip, andother random variables that are central to performing PFDHA for reverse faults.Additionally, a sensitivity analysis is conducted on all independent variables in thePFDHA procedure. The Los Osos fault zone of central California is used as the testcase, and results are presented in the form of a hazard curve. The influence each of thevariables has on a hazard curve is quantified to provide direction for future research inPFDHA. It is seen that a distribution for slip spatial variability is the least influentialterm in the procedure, and a term for the probability of surface rupture has the mostinfluence.

Introduction

Fault displacement hazard is a critical issue for infrastruc-ture in tectonically active regions. Unlike the hazard fromstrong ground motion, the primary method of mitigating faultdisplacement hazard is usually avoidance. For some projects,however, crossing a fault is inevitable and providing a reliableestimate of surface fault rupture and its associated displace-ment is crucial for these projects. For example, the Trans-Alaska Pipeline has sections that were designed with theanticipation of surface rupture from the Denali fault, whichmost recently occurred in the 2002 event. Currently, standardengineeringmethods for predicting the levels of potential faultdisplacement are based on deterministic scenarios and thusare susceptible to overestimation and inefficiency in projectdesign. Over the last several decades, probabilistic seismichazard analysis (PSHA) has become one of the most valuabletools available for ground-motion prediction and seismic-code construction. As a result, methods have been proposed(Youngs et al., 2003; Todorovska et al., 2007) to estimate faultdisplacement in a similarly probabilisticmanner. Probabilisticfault displacement hazard analysis (PFDHA), is one such pro-cedure that provides an estimate of expected levels of slip on afault due to surface rupture.

One of the best known uses for PFDHAwas in the YuccaMountain project (Stepp et al., 2001), where the tectonicenvironment is primarily extensional, producing normalfaulting. The distributions developed for the Yucca Mountainproject were derived from empirical normal-faulting data andtherefore are only applicable to this type of faulting. To beused for other types of faulting, they must be reformulatedusing data from other slip types. We present a completePFDHA methodology for faults with reverse mechanisms

and provide new empirical equations for the necessary prob-ability terms.

Additionally, in recent years, the methods used in PSHAhave been scrutinized, and consensus is building on how bestto deal with the various forms of functional and computa-tional uncertainty (e.g., Thomas et al., 2010). PFDHA, incomparison, is a relatively new field with much of thisunaddressed, and therefore quantifying the functional uncer-tainty underlying the components of a PFDHA will helpimprove the accuracy of the procedure. We conduct a sensi-tivity analysis of all independent variables involved to deter-mine how they influence the resulting hazard curve.

Methodology

The PSHA methodology forms the basis for our PFDHAand thus follows the general procedures outlined by Cornell(1968). PSHA uses empirical probability distributions tomodel the estimated ground motion levels at a given site.It does so by accounting for all possible events from all loca-tions on every fault in a region. The result is an annual rate ofevents that exceed a specified level of ground motion and canbe computed using the following integral:

ν�z� � αZ

mmax

m0

Z ∞0

f�m�f�r�P�Z > zjm; r�drdm: (1)

Here, f�m� is a distribution for magnitude occurrencethat is based on a range of magnitude values that a faultis believed capable of producing. The truncated exponentialor characteristic models are the most commonly used.The distribution f�rjm� estimates the source-to-site distances

1542

Bulletin of the Seismological Society of America, Vol. 101, No. 4, pp. 1542–1553, August 2011, doi: 10.1785/0120100248

Table 1Database of Reverse Events without Surface Rupture

Date (mm/dd/yyyy) Event MW Reference

04/04/1905 Kangra, India 7.8 Lettis et al. (1997)03/01/1925 Charlevoix, Canada 7.0 Lettis et al. (1997)05/22/1927 Gansu, China 7.7 Lettis et al. (1997)11/04/1927 Lompoc, California 6.6 Lettis et al. (1997)01/15/1934 Bihar, Nepal 8.2 Lettis et al. (1997)11/01/1935 Temiskaming, Canada 6.4 Lettis et al. (1997)04/29/1941 Imaichi, Japan 6.3 Lettis et al. (1997)09/09/1954 Orleansville, Algeria 6.91 Lettis et al. (1997)01/31/1955 Serra do Tombador, Brazil 6.79 Lettis et al. (1997)05/07/1961 Hyogo, Japan 5.88 Lettis et al. (1997)08/19/1961 Kita-Mino, Japan 7.23 Lettis et al. (1997)04/30/1962 Miyagi Prefecture, Japan 6.5 Lettis et al. (1997)01/18/1964 Southwest Taiwan 6.55 Lettis et al. (1997)06/16/1964 Niigata, Japan 7.6 Lettis et al. (1997)11/13/1965 Urumchi, China 6.5 Lettis et al. (1997)03/24/1970 Lake Mackay, Australia 6.0 Lettis et al. (1997)10/16/1970 Akita, Japan 6.1 Lettis et al. (1997)04/24/1972 Taiwan 7.0 Lettis et al. (1997)08/28/1972 Simpson Desert, Australia 6.0 Lettis et al. (1997)09/03/1972 Hamran, Pakistan 6.2 Lettis et al. (1997)02/21/1973 Point Mugu, California 5.7 Lettis et al. (1997)08/11/1974 Markansu Valley, Tajikistan 7.1 Lettis et al. (1997)08/11/1974 Markansu Valley, Tajikistan 5.58 Lettis et al. (1997)08/11/1974 Markansu Valley, Tajikistan 6.16 Lettis et al. (1997)03/07/1975 Sarkun, Iran 6.16 Lettis et al. (1997)04/08/1976 Gazli, Uzbekistan 6.9 Lettis et al. (1997)05/17/1976 Gazli, Uzbekistan 6.8 Lettis et al. (1997)05/06/1976 Friuli, Italy 6.5 Lettis et al. (1997)03/21/1977 Khurgu, Iran 6.7 Lettis et al. (1997)04/01/1977 Khurgu, Iran 6.0 Lettis et al. (1997)04/06/1977 Naghan, Iran 6.0 Lettis et al. (1997)11/23/1977 Caucete, Argentina 7.5 Lettis et al. (1997)08/13/1978 Santa Barbara, California 5.9 Lettis et al. (1997)04/15/1979 Montenegro 7.0 Lettis et al. (1997)01/09/1979 Miramichi, Canada 5.6 Lettis et al. (1997)12/16/1982 Tadjik, Afghanistan 6.5 Lettis et al. (1997)05/02/1983 Coalinga, California 6.4 Lettis et al. (1997)03/19/1984 Gazli, Uzbekistan 7.0 Lettis et al. (1997)01/26/1985 Mendoza, Argentina 6.0 Lettis et al. (1997)07/03/1985 New Ireland, Papua New Guinea 7.2 Lettis et al. (1997)08/04/1985 Kettleman Hills, California 6.1 Lettis et al. (1997)08/23/1985 Wuquai, China 6.9 Lettis et al. (1997)10/05/1985 Nahanni, Canada 6.7 Lettis et al. (1997)12/23/1985 Nahanni, Canada 6.8 Lettis et al. (1997)03/25/1988 Nahanni, Canada 6.2 Lettis et al. (1997)05/20/1986 Hualien, Taiwan 6.4 Lettis et al. (1997)11/14/1986 Hualien, Taiwan 7.3 Lettis et al. (1997)03/06/1987 Northeast Ecuador 7.1 Lettis et al. (1997)10/01/1987 Whittier Narrows, California 6.0 Lettis et al. (1997)11/25/1988 Saguenay, Canada 5.9 Lettis et al. (1997)01/14/1990 Mangyai-Lenghu, China 6.0 Lettis et al. (1997)03/04/1990 Kalat, Pakistan 6.0 Lettis et al. (1997)04/26/1990 Gonghe-Xinghai, China 6.4 Lettis et al. (1997)11/06/1990 Darab, Iran 6.6 Lettis et al. (1997)12/13/1990 Hualien, Taiwan 6.6 Lettis et al. (1997)01/28/1991 Hawks Crag, New Zealand 6.0 Lettis et al. (1997)02/25/1991 Kalpin, China 6.0 Lettis et al. (1997)03/08/1991 Eastern Siberia, Russia 6.79 Lettis et al. (1997)04/04/1991 Rioja, Peru 6.4 Lettis et al. (1997)04/29/1991 Georgia 7.1 Lettis et al. (1997)06/15/1991 Dzhava-Tzkinvali, Georgia 6.3 Lettis et al. (1997)

(continued)

Probabilistic Fault Displacement Hazard Analysis for Reverse Faults 1543

for all events possible in a region; α is defined as the meanrate of all earthquakes per year from a specific source and isgenerally given as an annual rate; ν�z� is therefore the meanannual rate of events exceeding the level of ground motion, z.Lastly, the term P�Z > zjm; r� is often called a ground-motion prediction equation and defines how a parametersuch as peak ground acceleration varies as a function ofdistance and magnitude.

In a similar manner, Youngs et al. (2003) developed amethodology which estimates the potential levels of fault dis-placement due to surface rupture. In this formulation, PFDHAfollows straight from PSHA but now produces an annual rateof events that exceeds a given level of fault displacement:

ν�d� � αZ

mmax

m0

f�m�P�D > djm; r�dm: (2)

For PFDHA, the equations are the same except theground motion attenuation relationship has been replacedwith a distribution to model the probability of exceeding agiven level of slip. This distribution is based on empiricalfault displacement measurements and incorporates the spa-tial variability of slip along a fault at the ground surface. Asthe Youngs et al. (2003) PFDHA methodology was createdfor normal faulting, the probability distributions involvedwere created using empirical normal faulting data. ForPFDHA to work with reverse mechanisms, these distributionsmust be determined from reverse slip data.

The slip exceedance term, P�D > djm; r�, is whatdistinguishes the results of a PFDHA from a PSHA. It is aninverted cumulative distribution function that is both locationand magnitude dependent and is chosen to correspond with aspecific focal mechanism. The slip exceedance is written asthe product of two terms:

P�D > djm; r� � P�Slipjm� � P�D > djm; r; slip�: (3)

The first term, P�Slipjm�, is an empirical probabilitydistribution of surface rupture, yielding the probability of slip

occurrence at the ground surface as a function of magnitude.The second term is a cumulative distribution of displacementand is conditional on the occurrence of surface rupture. Adistance term, r, can be included in equation 2 to accountfor off-fault displacement:

ν�d� � αZ

mmax

m0

Z ∞0

f�m�f�rjm�P�D > djm; r�drdm:

(4)

Qualitatively it has been observed that the hangingwall can have fault-related displacements on the order ofhundreds of meters back from the primary surface expressionof the fault plane (Bonilla, 1970). We have been collectingdata for off-fault displacement on reverse faults and antici-pate presenting these results along with other complimentaryanalyses in a future study.

Probability of Surface Rupture

The probability of fault rupture propagating to thesurface, P�Slipjm�, is central to the PFDHA procedure. It isdifferent from a PSHA, where the probability of some levelof ground shaking is one within a reasonable distance fromthe event. As slip can only occur when a fault ruptures theground surface, there is a probability that an event will notyield any fault displacement at all. Wells and Coppersmith(1993) showed that because the outcome of surface ruptureis binary, it can be represented through a logistic regression.They created surface rupture probability terms using severalhundred events of all slip types with M > 4. Youngs et al.(2003) used the same procedure for purely normal faultingevents from Pezzopane and Dawson (1996). We have createda similar distribution for the probability of fault rupture onreverse faults using reverse events from Lettis et al. (1997)and six additional events. The events without surface ruptureare found in Table 1, and those reported with surface ruptureare found in Table 2.All events fromLettis et al. (1997) exceptthose reported with MI were used. The events that were

Table 1 (Continued)Date (mm/dd/yyyy) Event MW Reference

06/28/1991 Sierra Madre, California 5.43 Lettis et al. (1997)10/19/1991 Northern India 7.0 Lettis et al. (1997)05/20/1992 Peshawar-Kohat, Pakistan 6.2 Lettis et al. (1997)10/17/1992 Murindo, Columbia 6.7 Lettis et al. (1997)10/23/1992 Barisakho-Kazbegi, Georgia 6.5 Lettis et al. (1997)10/02/1993 Xinjiang, China 6.1 Lettis et al. (1997)01/17/1994 Northridge, California 6.7 Lettis et al. (1997)02/23/1994 Sedabeh, Iran 6.1 Lettis et al. (1997)02/24/1994 Sedabeh, Iran 6.3 Lettis et al. (1997)02/26/1994 Sedabeh, Iran 6.0 Lettis et al. (1997)05/01/1994 Hindu Kush, Afghanistan 6.1 Lettis et al. (1997)05/31/1994 Western Venezuela 6.0 Lettis et al. (1997)06/18/1994 New Zealand 6.8 Lettis et al. (1997)01/19/1995 Tauramena, Columbia 6.6 Lettis et al. (1997)01/26/2001 Bhuj, India 7.9 Rajendran et al. (2001)

1544 R. E. S. Moss and Z. E. Ross

reported withML orMS were converted toMW using Heatonet al. (1986). The catalog of events was separated intocategories of slip and no slip. These two datasets were thenused in a logistic regression to obtain an equation for the prob-ability of surface rupture occurrence. This probability is repre-sented in the form of the logistic function:

P�Slipjm� � 1

1� ea�b�m a � 7:30; b � �1:03:(5)

We find that the probability of surface rupture for all sliptypes is significantly greater than that of purely reverse

Table 2Database of Reverse Events with Surface Rupture

Date (mm/dd/yyyy) Event MW Reference

08/31/1896 Rikuu, Japan 7.42 Lettis et al. (1997)12/23/1906 Manas, China 7.95 Lettis et al. (1997)01/23/1909 Silakhar, Iran 7.23 Lettis et al. (1997)01/23/1911 Kirgizia, Russia 7.89 Lettis et al. (1997)04/18/1911 Raver, Iran 6.29 Lettis et al. (1997)05/01/1929 Baghan, Iran 7.51 Lettis et al. (1997)06/17/1929 White Creek, New Zealand 7.89 Lettis et al. (1997)05/06/1930 Salmas, Iran 7.6 Lettis et al. (1997)02/02/1931 Hawkes Bay, New Zealand 7.89 Lettis et al. (1997)12/25/1932 Changma, China 7.82 Lettis et al. (1997)11/28/1933 Behabad, Iran 6.29 Lettis et al. (1997)04/21/1935 Taiwan 7.23 Lettis et al. (1997)01/15/1944 San Juan, Argentina 7.6 Lettis et al. (1997)01/13/1945 Mikawa-Fukozu, Japan 7.02 Lettis et al. (1997)03/17/1947 Dari, China 7.89 Lettis et al. (1997)07/10/1949 Tajikistan 7.75 Lettis et al. (1997)07/21/1952 Kern County, California 7.4 Lettis et al. (1997)02/12/1953 Torud, Iran 6.67 Lettis et al. (1997)12/13/1957 Farsinaj, Iran 6.91 Lettis et al. (1997)09/01/1962 Ipak, Iran 7.42 Lettis et al. (1997)05/24/1968 Inangahua, New Zealand 7.1 Lettis et al. (1997)10/01/1967 Meckering, Australia 6.6 Lettis et al. (1997)07/24/1969 Pariahuanca, Peru 6.1 Lettis et al. (1997)10/01/1969 Pariahuanca, Peru 6.6 Lettis et al. (1997)03/10/1970 Calingiri, Australia 5.97 Lettis et al. (1997)02/09/1971 San Fernando, California 6.6 Lettis et al. (1997)04/10/1972 Qir, Iran 6.8 Lettis et al. (1997)09/06/1975 Lice, Turkey 6.6 Lettis et al. (1997)08/16/1976 Songpan, China 6.90 Lettis et al. (1997)08/21/1976 Songpan, China 6.4 Lettis et al. (1997)08/23/1976 Songpan, China 6.7 Lettis et al. (1997)01/01/1977 Mangya, China 6.1 Lettis et al. (1997)09/16/1978 Tabas, Iran 7.4 Lettis et al. (1997)06/02/1979 Cadoux, Australia 6.1 Lettis et al. (1997)10/10/1980 El Asnam, Algeria 7.1 Lettis et al. (1997)06/11/1981 Golbaf, Iran 6.6 Lettis et al. (1997)07/27/1981 Sirch, Iran 7.1 Lettis et al. (1997)06/11/1983 Coalinga, California 5.4 Lettis et al. (1997)03/30/1986 Marryat Creek, Australia 5.8 Lettis et al. (1997)01/22/1988 Tennant Creek, Australia 6.3 Lettis et al. (1997)01/22/1988 Tennant Creek, Australia 6.4 Lettis et al. (1997)01/22/1988 Tennant Creek, Australia 6.6 Lettis et al. (1997)12/07/1988 Armenia 6.8 Lettis et al. (1997)10/29/1989 Chenoua, Algeria 6.0 Lettis et al. (1997)12/25/1989 Ungava, Canada 6.0 Lettis et al. (1997)06/20/1990 Rudbar-Tarom, Iran 7.4 Lettis et al. (1997)08/19/1992 Kyrgyzstan 7.2 Lettis et al. (1997)09/29/1993 Killari-Latur, India 6.2 Lettis et al. (1997)09/29/1999 Chi-Chi, Taiwan 7.6 Lee et al. (2002)06/22/2002 Avaj, Iran 6.5 Walker et al. (2005)02/22/2005 Zarand, Iran 6.4 Talebian et al. (2006)10/08/2005 Kashmir, Pakistan 7.6 Kaneda et al. (2008)05/12/2008 Sichuan Province, China 7.9 Lin et al. (2009)


events, as shown in Figure 1. The disparity is greatestwhen the comparison is between normal faulting and reversefaulting. Sediment and rock can sustain compression muchmore than tension, and it can be seen that the reversemechanism does not reach a 100% probability of rupturingthe surface even at large magnitudes. The probability of sur-face rupture for all slip types increases rapidly withMW > 5,while reverse faults alone do not exhibit a similar trend.

Spatial Slip Variability

The second term on the right-hand side of equation 3,P�D > djm; slip�, represents the probability of exceedinga given level of displacement provided that surface rupturehas occurred. This is an inverse cumulative distribution func-tion (CDF) that is also based on empirical data. It is deter-mined from two probability distributions: a distributionfor the spatial variability of slip along a fault and a distribu-tion for the average or maximum displacement. The formercan be created from a set of earthquake events where slip hasbeen measured regularly along the fault.

Using data of nine reverse faulting events fromWesnousky (2008) and Kaneda et al. (2008), a distributionwas used to model the spatial variability of slip on reversefaults. Following Youngs et al. (2003), we treat slip along afault as symmetric about the center but note that this assump-tion adds additional uncertainty to the model. To account forvarying fault rupture lengths from one fault to another, theposition along a fault is normalized by the length of the rup-ture yielding x=L. The assumption here is that faulting isscale independent, which has been shown to hold in a varietyof different situations (e.g., Savage and Brodsky, 2010). Weplace the origin at the ends of the fault such that x=L � 0 andx=L � 0:5 at the center. These values are then normalized byeither the average displacement (AD) or the maximum dis-

placement (MD) along the entire rupture length. The choiceof proceeding with either AD or MD is analytically unimpor-tant as it will later be shown to cancel out, but MD tends to bea more statistically robust approach because of the largerempirical database.

All of the reverse slip measurements were normalizedfor both position x=L and displacement D=AD or D=MDand are plotted in Figure 2. The data were then binnedwith a bin width ofΔx=L � 0:05. TheD=AD values in eachbin were then subjected to a series of Anderson–Darlinggoodness-of-fit tests (D’Agostino and Stephens, 1986) fornormal, lognormal, gamma, and Weibull distributions. It wasfound that only 20% of the bins were rejected as Weibulldistributed, and 20% of the bins were rejected as gamma dis-tributed. However, for normal and lognormal distributions,60% of the bins were rejected in the Anderson–Darling tests.These goodness-of-fit tests used a confidence level of 99% tojudge which probability distributions relatively fit the best,with the Weibull and gamma distributions showing superiorfit. The D=MD values were tested with Kolmogorov–Smirnov tests for the beta distribution because of the upperand lower bounds. These tests used a 95% confidence level,and in this case, 20% of the bins were rejected.

Figure 1. Probability of surface rupture for reverse, normal, andall slip types. The normal and all slip types are from Youngs et al.(2003). Empirical distributions are fit using logistic regression for adichotomous outcome. The probability for reverse events is signif-icantly lower than that of normal and all slip types. These distribu-tions are only valid in the range of 5:5 ≤ MW ≤ 8.

(a)

(b)

Figure 2. Combined dataset for normalized slip measurementsfrom nine reverse faulting events plotted as a function of x=L;x=L � 0 is treated as the beginning (or end) of the fault rupture.(a) Displacement normalized by the average surface displacement.(b) Displacement normalized by the maximum surface displace-ment measured.


Based on these results, we proceed with only the gammaand Weibull distributions for modeling D=AD and beta forD=MD. The gamma and Weibull distribution parameters,shape and scale, were then fit to the data in each of the bins,including those that were rejected in the goodness-of-fit tests.The beta distribution shape parameters were fit in the samemanner. A 95% confidence level could have been used forthe D=AD goodness-of-fit tests, and while the results wouldbe slightly worse, nothing would change with respect to theestimated distribution parameters. This is because we still usethe data from bins that are rejected to estimate param-eters, and these remain the same no matter what confidencelevel used. The results are a pair of distribution parameters foreach normalized position bin. These parameters are plotted inFigure 3 and were regressed to obtain an equation for theirspatial dependence. The functional form used in the D=ADregression is a third-order polynomial in log space and waschosen solely based on its ability to fit the data. For theD=MD data, a simple linear regression was found to be ap-propriate. At the ends of the rupture x=L � 0, slip is requiredto be zero, which creates an issue when using binned data.

Because data at the ends fall into the outermost bins, this re-sults in a nonzero displacement associated with the very endsof a fault. This is treated as additional epistemic uncertaintyintroduced into the PFDHA as part of the modeling process.

The resulting probability distribution from treating thenormalized average displacement D=AD as Weibull distrib-uted is defined as

f�z� � k

λ

�z

λ

�k�1

e�z=λ�k

k � exp��31:8

�x

L

�3

� 21:5

�x

L

�2

� 3:32x

L� 0:431

�

λ � exp�17:2

�x

L

�3

� 12:8

�x

L

�2

� 3:99x

L� 0:38

�: (6)

Here, z � D=AD. The Weibull distribution parameters’shape, k, and scale, λ, are functions of x=L, as indicated ear-lier in this section. These parameters are specific to reversefaulting. If we instead treat D=AD as gamma distributed, thecorresponding probability distribution is

f�z� � zk�1e�z=θ

θkΓ�k�

k � exp��30:4

�x

L

�3

� 19:9

�x

L

�2

� 2:29x

L� 0:574

�

θ � exp�50:3

�x

L

�3

� 34:6

�x

L

�2

� 6:60x

L� 1:05

�: (7)

Again, z � D=AD, and this probability density function(PDF) is specific to reverse faulting; k is the gamma shapeparameter, and θ is the gamma scale parameter. Figure 4 con-tains a plot of both equations (5) and (6) for the full range ofD=AD and fixed values of x=L. It is clear that both thegamma and Weibull distributions’ fit are very similar for thesame values of x=L. If the normalized maximum displace-ment D=MD is used, the Beta distribution is defined as

f�z� � Γ�α� β�Γ�α�Γ�β� z

α�1�1 � z�β�1

α � 0:901x� 0:713 β � �1:86x� 1:74;

whereΓ is the gamma function, andα,β are shape parameters.

Average and Maximum Displacement

Wells and Coppersmith (1994) showed that both aver-age and maximum displacement have strong magnitudedependence. These variables, when presented in log space,vary linearly with magnitude. Wells and Coppersmith (1994)provided regression equations for strike-slip, normal, re-verse, and all slip types. The reverse slip equations, however,have low values for the coefficient of determination, R2, anddo not present a strong case for a magnitude dependence on

Figure 3. Example distribution parameters for spatial slipvariability P�D > djm; slip�. The regressions shown are valid fora Weibull distribution. Each point plotted here is a distributionparameter fit from data in the corresponding bin. The regressionsare third-order polynomials in log space. These parameters areinserted into a Weibull distribution to yield the correct shape neces-sary to represent D=AD anywhere along the surface rupture.


AD and MD. The eight events from Table 3 have been addedto the reverse events from Wells and Coppersmith (1994) toform new equations. In addition, six reverse events fromWells and Coppersmith (1994) were also discussed in Wes-nousky (2008), and therefore the average values were used.Two events, Golbaf, Iran, and Sirch, Iran, have been removedfor reasons discussed later. The regressions are shown inFigure 5 along with the original regression equations fromWells and Coppersmith (1994):

log�AD� � 0:3244 �M � 2:2192

σ � 0:17; R2 � 0:62; (8)

log�MD� � 0:5102 �M � 3:1971

σ � 0:31; R2 � 0:53: (9)

The R2 values have increased substantially, from 0.01and 0.13 to 0.62 and 0.53, respectively. Furthermore, the pre-viously reported standard deviations of 0.42 for MD and 0.38for AD have decreased to 0.31 and 0.17. If we assume that theresiduals of log�AD� and log�MD� are normally distributed,then AD and MD are said to be lognormally distributed.This lognormal distribution is a function of magnitude andvalid only in the range of regression equations (8) and(9): 5:5 ≤ MW ≤ 8.

Slip Exceedance Distribution

The final inverse CDF in equation 3 is obtained by com-bining the distribution for spatial slip variability with thelognormal distribution for AD or MD. As each of these PDFsrepresent a random variable, namely D=AD and AD, theproduct of these random variables yields a PDF for D. A pro-duct of random variables can be shown to be equivalent to alogarithmic convolution (Glen et al., 2004), and the resultingdistribution is

h�D� �Z ∞�∞

f

�D

AD

�g�AD� 1

ADdAD: (10)

Here, f� DAD� is either equation (6) or (7), and g�AD�

is the lognormal distribution using equation (8) or (9).Equation (10) must be integrated to obtain the cumulativedistribution H�D� and finally,

P�D > djm; r; slip� � 1 �H�d�: (11)

We found that numerically solving equation (10) was abit too computationally expensive for practical purposes.

Figure 4. Comparison of gamma and Weibull distributions forspatial variability at two values of position. These examples are forAD and are independent of magnitude. These distributions are usedto ultimately obtain a distribution for displacement.

Table 3Events Added for AD and MD Regressions

Date (mm/dd/yyyy) Event MW AD MD Reference

01/13/1945 Mikawa, Japan 7.02 1.35 2.05 Wesnousky (2008)08/19/1992 Kyrgyzstan 7.2 N/A 4.2 Lettis et al. (1997)09/29/1993 Killari-Latur, India 6.2 N/A 0.5 Lettis et al. (1997)09/29/1999 Chi-Chi, Taiwan 7.6 3.76 12.8 Wesnousky (2008)06/22/2002 Avaj, Iran 6.5 N/A 0.65 Walker et al. (2005)02/22/2005 Zarand, Iran 6.4 N/A 1.05 Talebian et al. (2006)10/08/2005 Kashmir, Pakistan 7.6 1.7 7.05 Kaneda et al. (2008)05/12/2008 Sichuan, China 7.9 2.09 6.5 Lin et al. (2009)


Therefore, in computing this integral, we use Monte Carlosimulations to obtain the cumulative distribution. This isdone by generating a random value from both the spatial-slipvariability distribution and the average (or maximum) dis-placement distribution, taking the product of the two, andrepeating on the order of five thousand times to achievestability in the solution. Figure 6 shows the inverse CDF forseveral magnitude values at x=L � 0:25. The increase of dis-placement with magnitude is expected, as average/maximumdisplacement also increases with magnitude.

Example: Los Osos Fault Zone

As a method of illustrating the PFDHA procedure and toprovide a basis for a sensitivity analysis, we have chosen touse the Los Osos fault zone in central California. TheLos Osos fault is reported to have a median slip rate of0.5 mm per year (Cao et al., 2003) with a maximum mag-nitude of MW 7. The fault area is approximately 44 km by14 km and has a b value of 0.8. A shear modulus of 3:75 ×1011 dynes=cm2 was used. For this example, the average dis-

placement method is chosen as a point of reference andpaired with the gamma distribution. The gamma distributionhas parameters as defined in equation 7. Additionally, it usesboth the empirical probability of surface rupture and lognor-mal distribution for purely reverse mechanisms. This exam-ple uses x=L � 0:25. It is assumed that events withMW < 5

have a negligible probability of rupturing the surface andthus do not contribute to the rates of exceedance.

The results of the PFDHA are presented in the form of ahazard curve, or a curve indicating the annual probability ofexceeding a given level of displacement, which is shown inFigure 7. Currently there are no generally accepted risk stan-dards for fault displacement, and the traditional standards forground shaking may or may not be applicable depending onthe problem at hand. In our example, there is no value of

Figure 5. Regression equations for AD and MD on reversefaults following the procedures by Wells and Coppersmith(1994). Additional events have been added to improve the accuracyof the regressions, which are shown along with previous relation-ships. The slope has increased for both equations as well as for thevalues for R2.

Figure 6. This is the complete inverse CDF for displacement,P�D > djm; slip�. Here it is shown for x=L � 0:25 and for varyingmagnitude. The CDF is formed by taking a product of the randomvariables D=AD (lognormally distributed) and AD (here gammadistributed as in equation 6).

Figure 7. PFDHA for the Los Osos fault zone near San LuisObispo, California. This is a Class B fault with a maximum mag-nitude ofMW 7 (Cao et al., 2003). The PFDHAwas computed usingthe AD method and a gamma distribution. The hazard curve indi-cates the annual probability that a given level of displacement willbe exceeded.


displacement corresponding to a 10% probability of excee-dance in 50 yr (0:0021 =yr). There is, however, a 2% prob-ability in 50 yr of exceeding 55 cm and 1% probability in50 yr of exceeding 105 cm. These risk parameters havereturn periods of 2475 yr and 4975 yr, respectively. We nowtreat this hazard curve as a reference curve to be used forcomparisons in a sensitivity analysis.

Sensitivity Analysis

As PFDHA is a relatively new tool for estimating fault-displacement hazard, the major sources of uncertainty inPFDHA are unexplored. Quantifying the uncertainty of theindependent variables and understanding the effect of thisuncertainty on the outcome is necessary for confidence inthe slip estimates. There are a number of opportunities in thePFDHA methodology for testing the sensitivity of the proce-dure, and all should be examined to determine the extent oftheir influence.

An independent variable involved in the spatial slipvariability is the choice of using either a gamma or Weibulldistribution to describe the random variables D=AD. Bothgamma and Weibull distributions for D=AD represent80% of the bins used in the curve fitting, as only 20% wererejected through the Anderson–Darling tests. Because bothdistributions passed the same number of tests, we cannotsay from the tests alone that one is more correct than theother. More data are required in a future study to assesswhether these results change. The differences betweenPFDHA’s using Weibull or gamma distributions are mostlyinsignificant. The percent difference between the Weibull-based hazard curve and the gamma-based hazard curve isplotted as a function of displacement in Figure 8, which alsocontains the results for the entire sensitivity analysis. Thedifferences are below 1% up to 2 m and slowly increaseup to a maximum of 32% by 10 m. The 2% and 1% in50-yr values are, in this case, both approximately 1% differ-ent from the reference hazard curve values.

Additional uncertainty is introduced into the PFDHAprocedure through the fitting of curves to distributionparameters, equations (6) and (7). The functional form of theregression was chosen to best fit the parameters because itwas necessary to obtain as close of a predictor equation aspossible. We used a logarithmic form for the regressions;however, other regression forms, such as nonlogarithmicpolynomials, could provide nearly the same goodness-of-fit. Therefore, testing the influence of the spatial dependenceof the distribution parameters on a hazard curve outcome isimportant. Figure 8 shows the percent difference betweentwo hazard curves using parameter regression form as an in-dependent variable. The curves are identical in both usingAD-based gamma distributions for slip variation, reverse sur-face rupture distributions, and a purely reverse lognormaldistribution. The reference hazard curve, however, uses alogarithmic form for the regression, and the comparisoncurve uses a simple third-order polynomial. It can be seen

that the sensitivity of this PFDHA due to the spatial distribu-tion fitting is low until approximately 0.5 m, where the per-cent difference then slowly begins to rise. It ultimately peaksat 43% for 10 m. The risk parameters for the comparisonhazard curve, 2% and 1% in 50 yr, are 71 cm and 113 cm,respectively. These values are ultimately just under 10%different from those of the reference curve.

Because both average displacement and maximum dis-placement methods are available for the PFDHA procedure, itis important that the differences between these two be quan-tified. Either is eventually canceled out through the productof random variables defined by equation (10); therefore, thetwo methods should ideally be equivalent. However, as aresult of natural variability in the faulting process and ourfitting and modeling of this phenomenon, differences areexpected. Computing a hazard curve via the maximum dis-placement method requires that the lognormal distributionfor AD be changed to one for MD in addition to using thebeta distribution for D=MD. Hazard curves for Los Ososwere computed using gamma-based AD and beta-based MDmethods, and they are shown in Figure 9. Both methods havea well-defined plateau region, which exists for D ≤ 0:1 m.The percent difference as a function of the displacementis shown in Figure 8. The MD method ultimately yields ahazard curve with a different curvature, and the probabilitiesfall off more quickly than the reference curve. The riskparameters here for the comparison curve are 52 cm for 2%in 50 yr and 85 cm for 1% in 50 yr. These are 20%different from those of the reference curve.

Each of the major elements of uncertainty in the spatialvariation distribution have been discussed thus far; however,there still remain two other components that contribute to aPFDHA. The empirical probability of surface rupture hasbeen defined for reverse mechanisms in equation (5) andfor all slip types by Wells and Coppersmith (1993). While

Figure 8. The results of the entire sensitivity analysis. Percentdifference between the reference hazard curve and a specificcomparison curve is plotted as a function of displacement. Eachcomparison curve is one of the independent variables involved inPFDHA. The only variable that is capable of shifting the plateauregion is the probability of surface rupture.


the equation for all slip types has a significantly higher prob-ability of surface rupture, the overall impact of such a differ-ence was previously unknown. Additionally, it is importantto understand what controls the probability at which theplateau occurs in a PFDHA hazard curve. In Figure 10, wehave constructed hazard curves for two PFDHA scenarios.Both PFDHAs are the same, except for the different sur-face-rupture distributions used, P�Slipjm�. For the compar-ison curve, the 2%-and-1%-in-50-yr parameters are 95 cmand 142 cm, respectively. These are, in turn, 46% and 35%different from the reference curve values. The percent differ-ence between the two hazard curves is plotted as a functionof the associated displacement level in Figure 8. Contrary toprevious comparisons within the spatial variability distribu-tion, the probability at which the hazard curve plateaus hasincreased by nearly 45%. This is simply from using all sliptypes in the surface rupture probability instead of just reverse

mechanisms. The percent difference itself remains roughlyconstant until about 20 cm, where it then begins to steadilyincrease and reaches nearly 90% by 6 m.

One final source of potential uncertainty analyzed hereis the lognormal distribution for AD or MD. We chose tostudy the effect of the mean value of AD, μ, for all slip types(Wells and Coppersmith, 1994) on a PFDHA compared to μfor purely reverse faulting mechanisms. Both methods usepurely reverse surface rupture distributions and AD-basedgamma distributions for spatial-slip variability. The resultscan be seen in Figure 11. The displacement for 2% probabil-ity of exceedance in 50 yr is 24 cm and for 1% in 50 yr, it is49 cm. These values are 62% and 53% different from thoseof the reference hazard curve, respectively. The full range ofthe percent difference with respect to displacement is shownin Figure 8. The percent difference begins to increase untilapproximately D � 0:7 m, where it then begins to decrease.The two curves eventually become equal at approximately6.5 m, and then start to diverge rapidly.

Discussion

PSHA has had several decades of debate about on howbest to treat and model the uncertainty associated with themethodology. As the PFDHA methodology is relativelynew, the majority of this uncertainty is unaddressed with re-spect to both computational methods as well as empirical andprocedural choices. This uncertainty should be studied in amanner which is independent of the bounds and range of theproblem at hand, to sort out variability that is both naturallyinherent to the faulting process as well as variability that isdue to lack of knowledge. In PSHA, the conventional methodof naming these is aleatory and epistemic uncertainty. Stan-dard PSHA practice involves the use of logic trees, whichseparate out the various possible methods progressing tothe same result. Because of this inclusion of all possible

Figure 9. Comparison of computed hazard curve using MD op-tion to reference hazard curve using AD. Both curves use lognormaldistributions for reverse faults, but MD uses a beta distribution andAD uses a gamma distribution.

Figure 10. Comparison of computed hazard curve usingsurface rupture distribution for all slip types to reference hazardcurve using purely reverse distribution. Both curves use gammadistributions for spatial variability and lognormal distributionsfor reverse faults.

Figure 11. Comparison of computed hazard curve usingregression equation for all slip types to reference curve with purelyreverse events. Both curves use gamma distributions for spatialvariability and purely reverse surface rupture distributions.


methods, weights must be assigned to the different branchesin an effort to establish confidence levels on each branch.Therefore, the final PSHA is viewed as a weighted averageof all possible hazard curves in an attempt to deal with theepistemic uncertainty associated with the procedure.

A PFDHA has three primary terms within the methodol-ogy that act as major sources of uncertainty. These three arespecifically those that are not involved in a PSHA. They arethe empirical probability of surface rupture, the lognormaldistribution for AD or MD, and the spatial variability termfor D=AD or D=MD. All of these terms play a distinct rolein a PFDHA, and studying the uncertainty contributed byeach can explain their unique influence on a PFDHA hazardcurve. In addition, understanding how the uncertainty propa-gates through the PFDHA procedure can help to establishareas where the uncertainty is potentially negligible andwhere more research and data collection is necessary.

The spatial variability term for normalized displacementD=AD or D=MD has the greatest impact on the uncertaintyin a PFDHA, yet the least overall influence in a hazard curve.From Figure 8, it is clear that the percent difference curvesinvolving spatial variability distribution have a lower abso-lute maximum than any of the other independent variables.The most probable explanation for why the spatial variabilityterm has the least influence on the resulting hazard curve isthat its dependence is only on position. Because of this,whether the term uses AD or MD, gamma or Weibull, theresult is still normalized displacement. Another possibleexplanation is the finite range of the bounds on normalizeddisplacement, seen in Figure 2. MD especially is affected bythis, as it has a maximum possible value of 1.

The lognormal distribution for AD and MD has a sub-stantially greater degree of influence in a PFDHA hazardcurve than the spatial variability term, and in some cases,has the highest sensitivity of all. This distribution is basedaround the regression of a logarithmic form of displacementversus magnitude, and therefore, the characteristics of thisfunction are central to the behavior of the lognormal distri-bution itself. From the comparison made in Figure 8, whereall slip types and reverse mechanisms are used for the regres-sion equations, the hazard curves have, on average, a percentdifference of 50. This is significantly larger than the spatialvariability term, and after D � 3 m, the two curves comple-tely diverge from each other. This is because a plateau regiondoes not exist for the all-slip-types curve, and therefore, theannual probabilities begin to decrease at even small dis-placements. The annual probabilities decrease at a muchslower rate with displacement than the reference curve. Assuch, the two curves finally become equal by approximately6.5 m, and the divergence ultimately occurs due to the highdisparity in the rate that annual probability decreases. Themost probable explanation for why these two curves havesuch different behavior is the large change in the standarddeviation, σ, from the reverse-fault regression to the all-slip-type regression. As σ for all slip types is more than twicethat of reverse events, this is certainly possible.

In the process of determining our regression equationsfor reverse faults, we decided to omit the 1981 Golbaf, Iran,and Sirch, Iran, events in the dataset. These two eventsoccurred within two months of each other, and both tookplace on the Gowk fault system. These events are notablebecause they had extremely low levels of fault displacementcompared to other events of the same magnitude. Walker andJackson (2002) have shown that this fault system is extre-mely complicated with normal faults overlaying the larger,main thrust fault. We feel that due to the nature of this faultsystem, the energy available is partitioned among all of thedifferent parts and results in substantially lower levels of dis-placement than expected from the thrust fault.

The empirical probability of surface rupture has themost consistent overall influence on the results of a PFDHAand therefore is the most important term for quantifyinguncertainty. As the entire PFDHA procedure, with the excep-tion of magnitude, is conditional on the surface rupturing forslip to occur, it is obvious why this distribution is the mostinfluential. Figure 1 shows that the probability of surfacerupture is significantly lower for reverse faults than for otherslip types, and such a difference is expected to have a stronginfluence in the outcome of a PFDHA. Changing the surfacerupture probability type in a PFDHA tends to shift the entirecurve, especially the plateau region. This is importantbecause it is the only one of the three terms that is capableof altering the probability at which the plateau occurs. Theplateau portion is a region in which the annual probability ofexceedance is approximately the same for a range of dis-placement values. Therefore, it can be said that every valueof displacement within that range has an equal probability ofoccurring. Because the surface rupture probability controlsthe value at which the probability plateaus, identificationof the uncertainty underlying surface rupture is crucial to ob-taining the most accurate PFDHA results. From Figure 8, itcan be seen that the percent difference between the referenceand comparison hazard curves is nearly constant forD ≤ 0:2 m. This is essentially the full plateau region for bothhazard curves. We note that this results in a shift of the entireplateau region upward by 45%. Beyond the plateau region,the percent difference then rises steadily with approximatelyconstant slope for the remainder of the hazard curve.

Conclusion

We present a reverse fault methodology for estimatingthe levels of potential surface fault displacement at a givensite. The methodology is based on the PFDHA proceduredeveloped by Youngs et al. (2003) for normal faulting inthe Yucca Mountain project. In this methodology, a PFDHAis analogous to a PSHA for estimating strong ground motionand follows the same general procedure developed byCornell (1968). We have determined reverse-specific distri-butions for all of the terms involved in a PFDHA. This in-cludes a spatial variability distribution for normalized slip,a lognormal distribution for average (or maximum) slip,


and an empirical equation for estimating the probability ofsurface rupture. The Los Osos fault zone of central Californiawas used as a test case for a reverse-fault PFDHA. Each of theterms in PFDHA are then compared in a sensitivity analysis todetermine the full extent of their influence on a hazard curve.

As PFDHA is a relatively new procedure, quantifyinguncertainty and the influence it has on a PFDHA has not beenpreviously studied. The sensitivity analysis in this studyisolates the influence of the independent variables in aPFDHA and shows how these variables contribute to a hazardcurve. Understanding the uncertainty associated with theprocedure is critical to achieving relative accuracy and con-fidence in fault displacement estimates. In turn, this providesdirection for the future of uncertainty treatment in PFDHA.

Data and Resources

All data used in this paper came from published sourceslisted in the references.

Acknowledgments

We thank the reviewers for their constructive comments and sugges-tions on this paper. This material is based on work supported by the U.S.Department of Homeland Security under Grant Award Number 2008-ST-061-ND0001. Administration of this grant is conducted through the Depart-ment of Homeland Security Center of Excellence for Natural Disasters,Coastal Infrastructure, and Emergency Management (DIEM). The viewsand conclusions contained in this document are those of the authors andshould not be interpreted as necessarily representing the official policies,either expressed or implied, of the U.S. Department of Homeland Security.

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Dept. Civil and Environmental Engineering 13-259California Polytechnic State UniversitySan Luis Obispo, California 93407-0353

Manuscript received 14 September 2010


http://dx.doi.org/10.1029/2010JB007665

http://dx.doi.org/10.1029/2010JB007665

6th International Conference on Earthquake Geotechnical Engineering 1-4 November 2015 Christchurch, New Zealand

A Simplified Probabilistic Fault Displacement Hazard Analysis

Procedure: Application to the Seattle Fault Zone, Washington, USA

F. Li1, E. Hsiao2, Z. Lifton1, A. Hull1

ABSTRACT This paper extends a simplified probabilistic fault displacement hazard analysis (PFDHA)

procedure to estimate the probability of surface fault displacement for the relatively low slip rate Seattle fault zone in Washington, USA. The proposed procedure incorporates up-to-date research to estimate earthquake magnitude and fault displacement—two key inputs to any PFDHA. A parametric study is used to evaluate the sensitivity of the results to changes in the key PFDHA input parameters. Probabilistically-determined fault displacement hazard along the Seattle fault is most sensitive to fault type; and the choices of empirical models for maximum earthquake magnitude and average surface fault rupture scaling.

Introduction

Ever since the extensive damage that accompanied the 1971 Sylmar earthquake in California, policy makers, engineers and scientists have grappled with ways to mitigate surface rupture hazards to buildings and urban lifeline infrastructure. While the California Alquist-Priolo Earthquake Fault Zone Act mandates avoidance for structures for human occupancy, building across active faults can be unavoidable. The need to provide transportation, water, gas and electrical infrastructure to existing facilities often precludes avoidance as a viable active fault mitigation strategy. In the many situations structural design needs to accommodate surface fault displacement at a level of risk acceptable to infrastructure owners and the communities they serve. For many engineers, therefore, a major design consideration is their ability to use accepted, robust analytical procedures to accommodate coseismic ground deformation and/or differential displacements that can range from centimeters to up to 10 meters (m) in a single earthquake (ASCE 1984). The quantification of active fault or fault zone rupture amount becomes a critical input for seismic design of critical facilities that cross active faults. Existing guidelines for surface fault rupture assessment and mitigation typically suggest that displacement design be based on a deterministic evaluation. Deterministic evaluations use empirical earthquake magnitude-fault displacement scaling relations to predict the amount of fault rupture for a given earthquake magnitude and/or average fault slip rate. Deterministic analyses are often calibrated with detailed site investigations including shallow trenching where the facilities cross the active faults. Field determined values can then be adjusted to the known level of uncertainty and potential consequence of failure. The process, however, is generally not used for small- to medium-sized projects because of the substantial cost of site-specific investigations. Deterministic evaluations provide single-value estimates, but are limited because they do not account for any uncertainties associated with input parameters.

1Feng Li, Zachery Lifton, Alan Hull, Golder Associates Inc., Redmond, Washington USA. For correspondence, [email protected] 2Evan Hsiao, Partner, geoLyteca LLC, Irvine, USA, [email protected]

mailto:feng_li@

mailto:[email protected]

An alternative approach is probabilistic fault displacement hazard analysis (PFDHA). Youngs et al. (2003) describe two general methods for PFDHA—probabilistic-earthquake-based and displacement-based approaches. These approaches were developed for normal faults encountered at the proposed nuclear waste disposal facility at Yucca Mountain, Nevada, USA (Stepp et al. 2001). A similar probabilistic-earthquake-based approach was developed for the Wasatch fault in central Utah, USA by Braun (2000). Petersen et al. (2011) and Moss and Ross (2011) extended the probabilistic-earthquake approach and applied them to strike-slip and reverse faults in California, USA. More recently, Shantz (2013) presented simplified procedures developed by the California Department of Transportation (Caltrans)—the Caltrans procedures—to evaluate fault displacement on strike-slip faults in California. The Shantz (2013) procedures are based on the method developed by Abrahamson (2008). The underlying methodology for these methods/procedures is probabilistic-earthquake-based, and they are similar in approach to methods applied in probabilistic seismic hazard analysis (PSHA). The probabilistic-earthquake-based approach in PFDHA relates surface fault displacement to the occurrence of an earthquake; but unlike PSHA, the earthquake approach in PFDHA replaces the ground motion prediction equation with a fault displacement prediction equation. This paper presents a simplified PFDHA procedure that is an application and extension of the Caltrans procedures—originally developed for strike-slip faults in California—to estimate the probability of surface fault displacement for a low-slip reverse fault. The extended procedure reported in this paper incorporates up-to-date research on earthquake magnitude and fault displacement estimation. We applied the extended procedure to a known, active reverse fault—the Seattle Fault Zone (SFZ)—in Washington.

Simplified Fault Displacement Hazard Analysis Procedure Caltrans Procedures The Caltrans fault displacement hazard analysis procedures (Caltrans procedures) assume that the site of interest is located on a fault that ruptures to the surface during large earthquakes within a narrow range of magnitudes (characteristic earthquake). The Caltrans procedures have the following key steps:

• Estimate the characteristic earthquake magnitude (moment magnitude or MW) for the fault of interest using known or estimated fault parameters, e.g., fault length and/or area. Earthquake magnitudes are estimated using empirical earthquake magnitude scaling relations.

• Estimate the recurrence interval of the characteristic earthquake using the following equation:

Where is the moment rate and M0 is the seismic moment. The moment rate is estimated using the equation =µAS, where µ is the crustal rigidity; A is the effective fault area after taking into account any aseismic factor; S is the fault slip rate. The seismic moment is estimated using the relation developed by Hanks and Kanamori (1979).

• Estimate the lognormal distribution of the average surface rupture displacement value for the characteristic earthquake using an empirical average fault displacement prediction equation.

• Estimate the fault rupture hazard curve using the following equation:

v(d) = αP(D>d|MW) Where α is the mean annual rate of earthquakes with a minimum magnitude or greater from a specific source and d is a specific fault displacement level.

The Caltrans procedures, however, were developed to estimate the surface rupture probability for relatively high slip-rate faults located in the North America-Pacific plate boundary zone in California. The fault of interest, however, could be a reverse fault located away from the major plate boundary. To reflect the specific faulting style and regional tectonic setting, we extended the Caltrans procedures by selecting appropriate empirical magnitude scaling relation and empirical displacement prediction equations. Selection of these empirical relations is discussed below. Maximum Moment Magnitude Scaling Relation Similar to PSHA, a fundamentally important component in PFDHA is the need to estimate the earthquake magnitude from fault parameters such as fault rupture length/width and/or fault area. A wide range of empirical earthquake scaling relations have been developed based on different worldwide historical datasets and using varying regression forms. Different scaling relations can result in significant different earthquake magnitude estimates. We adopted the scheme of Stirling et al. (2013) to select empirical earthquake magnitude scaling relations according to their relevance to predefined tectonic regimes, such as plate boundary crustal regime and fault slip types. Caltrans procedures use the equations developed by Hanks and Bakun (2008) that, according to Stirling et al. (2013), are most suitable for strike-slip faults located on fast-moving plate boundaries. The Seattle fault studied in this paper, however, is a reverse fault located away from the major plate boundary. Stirling et al. (2013) recommended three regression equations for use in reverse fault setting, including Stirling et al. (2008), Wesnousky (2008) and Yen and Ma (2011), referred to as S08, W08 and YM11 hereafter. The magnitude scaling regressions of Wells and Coppersmith (1994), although being the long-term industry standard, were not recommended in Stirling et al. (2013) because they are relatively old and have been superseded by more modern regressions (Stirling et al. 2013). Among three recommended regressions, the Yen and Ma (2011) relation was considered to have the highest quality score and/or most suitable regression for the given tectonic regime (Stirling et al. 2013). Average Fault Displacement Prediction Equation Fault displacement prediction equations in PFDHA characterize the ground displacement along a fault ruptured under earthquakes with varying magnitude. Historical fault rupture data have been collected and global scaling relations developed to relate fault displacement amount and earthquake magnitude. Out of the available equations, three alternatives are considered and compared in this paper, including the equations presented in: 1) Wells and Coppersmith (1994) for all fault types, 2) Hecker et al. (2013) for all fault types, and 3) Moss and Ross (2011) for reverse faults. These equations are referred to as WC94, H13 and MR11, respectively. The variability of displacement at the site is defined in terms of the coefficient of variation (CV) about 0.5 as estimated in Hecker et al. (2013), instead of using the variability in the global scaling relations between average displacement and earthquake magnitude. The variability for the global relations, according to Hecker et al. (2013), is a likely

overestimation of the fault-specific variability in average displacement because it contains possible fault-to-fault and regional variations and also observational uncertainties.

Case Study Seattle Fault Zone We illustrate the simplified PFDHA procedure with the SFZ as a case study. The east-west striking SFZ presents a fault rupture hazard to the Puget Sound region with a metropolitan population of approximately 3.6 million people. The integrity of regional lifelines—transportation, energy, water, and other critical infrastructure—is an important factor in earthquake resilience for the wider Puget Sound community. Many major lifelines are oriented north-south along the eastern side of Puget Sound and are located perpendicular to the SFZ (Figure 1). These lifelines include three interstate freeways, at least one 500 kW electric transmission line, at least three natural gas or liquid fuel pipelines, and at least three major sewer lines (Haugerud et al. 2002; Ballantyne et al. 2005). Any future surface rupture of the SFZ can be expected to generate surface displacement across these lifelines. The SFZ is mapped as an approximately 5-kilometer (km)-wide, 70-km-long series of east-west striking, south- and north-dipping reverse-slip faults that separate the Seattle basin to the north (footwall) from the Seattle uplift in the south (hanging wall) (Johnson et al. 1999; Liberty and Pratt 2008). The SFZ juxtaposes Neogene-age (23 to 2.6 million years ago) rocks to the south with younger Quaternary-age (last 2.6 million years) basin fill to the north. The hanging wall of the SFZ includes a number of north-dipping backthrusts, such as the Toe Jam Hill (on Bainbridge Island) and Waterman Point faults (on Pt. Glover Peninsula). These faults dip northward into the main south-dipping faults and locally create “pop-up” structures (Blakely et al. 2002; Nelson et al. 2003). The backthrusts are not considered to be independent seismogenic sources that produce large earthquakes and associated surface fault rupture. Instead, the backthrusts accommodate slip on the main, south-dipping SFZ faults, and therefore, only experience displacement when the main SFZ ruptures. This PFDHA requires geological input parameters for fault length, fault dip, fault locking depth, average fault slip rate, rigidity and aseismic factor. Creep has not been observed for the SFZ and the aseismic factor is assumed to be zero. The crustal rigidity is assumed to be 3.0×1011 dynes/cm2. The other fault rupture parameters were taken or derived from the open literature. The following sections discuss each parameter briefly. Table 1 summarized the values selected for use in this PFDHA. Fault Length Published estimates of the total length of the SFZ range from 68 km (Johnson et al. 1999; Blakely et al. 2002) to 75 km (Brocher et al. 2000). We use a total fault length of 69 km, as preferred by the authors of the Seattle Fault section of the US Geological Survey (USGS) Quaternary Fault and Fold Database (Johnson et al. 2004). Fault Dip Estimates of the fault dip range from 25° to 80° (Johnson et al. 2004). We use an intermediate dip value of 55° south because it is the mean of Johnson et al.’s (1999) estimate range from 45° to 65°.

Figure 1. Location of Seattle fault zone (SFZ) and major lifelines. The SFZ (hatched area) intersects a 500kV electric line (red); major sewer lines (dark red); natural gas or liquid fuel pipelines (yellow); interstate and other major highways (black) (figure after Haugerud et al.

2002). Fault Locking Depth We estimate the hypocentral depth for the earthquake that generates slip on the SFZ to be about 18 km. This depth is the median depth of instrumental seismicity (M>2) in the Puget Sound region (n = 340). Nearly 99% of the located earthquake hypocenters have specified hypocentral depths above ~34 km. This depth, however, is probably deeper than most surface-rupturing events, and we favor the shallower depth of 18 km. This depth is in accordance with the result of Blakely et al. (2002) who reported that 60% of earthquake hypocenters in the region surrounding the SFZ occur at depth between 15 km and 25 km, with a mean depth of 17.6 km. Average Fault Slip Rate Estimates of the average fault slip rate for the SFZ range from 0.2 millimeters per year (mm/year) to 1.0 mm/year (Johnson et al. 2004; Johnson et al. 1999; Calvert et al. 2001; ten

Brink et al. 2002; Nelson et al. 2003). Nelson et al. (2003) estimated average slip rates as high as 2 mm/year based on paleoseismic trench data. They concluded, however, that this higher fault slip rate probably results from temporal clustering of earthquakes and is not representative of the long-term average slip rate. We use the preferred slip rate assigned by the USGS Quaternary Fault and Fold Database, 0.9 mm/year (Johnson et al. 2004).

Table 1. Fault parameters for the SFZ.

Parameter Preferred Value Lower Limit Upper Limit Fault Length (km) 69 68 75

Dip Angle (˚) 55 25 80 Fault Locking Depth (km) 18 15 25

Slip Rate (mm/year) 0.9 0.2 1.0 Results The main output of a PFDHA is a hazard curve showing the annual exceedance probability (AEP) of a fault displacement exceeding fault displacement levels. The hazard curve for SFZ displacement near Seattle, Washington is shown in Figure 2. Since the estimated characteristic MW 7.3 earthquake has a recurrence interval of about 3,300 years, the fault displacement for return periods less than 3,300 years, such as 150 years and 2,500 years, is negligible. The estimated fault displacement for 10,000-year return period is close to 1.6 m. Parametric Study of Fault Parameters A limited parametric study has been undertaken to assess the sensitivity of the analysis results to reasonable and possible variations in the “best estimate” fault parameters. The best-estimate analysis case that uses the preferred parameters listed in Table 1 is the “baseline” case. The parametric study results indicate that within the range of generally accepted SFZ fault activity parameters, the surface fault rupture hazard is most sensitive to the average fault slip rate and dip angle and is much less sensitive to the locking depth and fault length. For example, an increase in dip angle from 25˚ to 55˚ results in a 4% and 19% increase in fault displacement at 5,000-year and 10,000-year return periods, respectively. In comparison, the estimated fault displacement only increases by 1% and 2% at 5,000-year and 10,000-year return periods, respectively, when the fault length increases from 69 to 75 km. Parametric Study of Scaling Relations The results of a parametric study on maximum earthquake magnitude scaling relation and average fault displacement prediction equation are shown in Figure 3. Application of the empirical equations—YM11 and MR11 for reverse faults—is the baseline case. Compared to the baseline case, the cases using alternative moment magnitude scaling relations provided an appreciably lower fault displacement hazard at a 5,000-year return period. The cases using the average displacement prediction equations—WC94 and H13 for all faults—result in a much higher fault displacement at 5,000- and 10,000-year return periods.

Figure 2. Fault displacement hazard curve and its sensitivity to (upper-left) fault slip rate;

(upper-right) dip angle; (lower-left) locking depth; (lower-right) fault length.

Figure 3. Sensitivity of fault displacement hazard curve to (left) earthquake magnitude

scaling relations; (right) average displacement prediction equation.

Discussion The Caltrans procedures of Shantz (2013) have been applied and extended in this study to estimate fault rupture hazard for the relatively low slip rate SFZ in Washington, USA. The

extended procedure incorporates the most up-to-date research results on earthquake magnitude and fault displacement estimation. The SFZ fault rupture hazard curves can be used to support informed, risk-based decision making for lifeline owners and operators in the Puget Sound area. We note that both the original and extended Caltrans procedures have several assumptions that may limit their wider applicability. For example, both procedures assume that the surface fault rupture at any point is the average displacement occurring on the fault even though historic surface fault ruptures show asymmetric slip distributions (Wesnousky 2008; Petersen et al. 2011). Another assumption is that the SFZ is the only contributor to the fault displacement hazard at the site. That is, all fault slip occurs on the SFZ and the slip is from earthquakes occurring on the specific fault rather than triggered by large slip on other crustal faults. The off-fault displacement from other crustal faults is assumed to be negligible compared to the primary fault displacement. We recognize that in some design applications it will be necessary to estimate the amount and distribution of off-fault deformation as well as slip on the primary rupture surface. Unlike PSHA, PFDHA is a relatively new procedure and less mature in its practical applications. Nevertheless, this site-specific PFDHA procedure incorporates the best estimates of fault parameters, current understanding of the PFDHA methodology; and a range of established empirical magnitude and fault displacement scaling relations. Our results indicate that the fault displacement hazard is sensitive to the fault parameters and empirical relations used to estimate the maximum earthquake magnitude and average fault rupture along the fault. PFDHA is subject to significant uncertainties, and careful consideration is needed when characterizing the contributing faults and selecting empirical relations.

References Abrahamson N. Appendix C, Probabilistic Fault Rupture Hazard Analysis, San Francisco PUC, General

Seismic Requirements for the Design on New Facilities and Upgrade of Existing Facilities, 2008.

ASCE Technical Council on Lifeline Earthquake Engineering, Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, Committee on Gas and Liquid Fuel Lines, American Society of Civil Engineers, 1984.

Ballantyne D, Bartoletti S, Chang S, Graff B, MacRae G, Meszaros J, Weaver C. Scenario for a Magnitude 6.7 Earthquake on the Seattle Fault. Earthquake Engineering Research Institute, Oakland, California, 2005, https://www.eeri.org/wp-content/uploads/2011/05/seattscen_full_book.pdf, accessed 03/10/2015.

Blakely RJ, Wells RE, Weaver CS, Johnson SY. Location, structure, and seismicity of the Seattle fault zone, Washington: Evidence from aeromagnetic anomalies, geologic mapping, and seismic reflection data: Geological Society of America Bulletin 2002; 114(2): 169-177, http://dx.doi.org/10.1130/0016-7606(2002)114<0169%3ALSASOT>2.0.CO;2.

Braun JB. Probabilistic fault displacement hazards of the Wasatch fault. Master’s Thesis, Department of Geology and Geophysics, University of Utah, Salt Lake City, Utah, 2000.

Brocher TM, Pratt TL, Creager KC, Crosson RS, Steele WP, Weaver CS, Frankel AD, Trehu AM, Snelson CM., Miller KC, Harder SH, ten Brink US. Urban seismic experiments investigate Seattle fault and basin. EOS Transactions of the American Geophysical Union 2000; 81: 551-552.

Calvert AJ, Fisher MA, SHIPS Working Group. Imaging the Seattle fault zone with high-resolution seismic tomography. Geophysical Research Letters 2001; 28: 2337-2340.

Hanks TC, Bakun WH. M-logA Observations for Recent Large Earthquakes. Bulletin of the Seismological Society of America 2008; 98(1): 490-494.

Hanks TC, Kanamori H. Moment magnitude scale. Journal of Geophysical Research 1979; 84(B5): 2348–50.

Haugerud RA, Ballantyne DB, Weaver CS, Meagher KL, Barnett EA. Lifelines and earthquake hazards in the greater Seattle area, 2002, U.S. Geological Survey website, http://geomaps.wr.usgs.gov/pacnw/lifeline/ index.html, accessed 03/10/2015.

Hecker S, Abrahamson NA, Wooddell K E. Variability of Displacement at a Point: Implications for Earthquake‐Size Distribution and Rupture Hazard on Faults. Bulletin of the Seismological Society of America 2013; 103(2A): 651-674.

Johnson SY, Dadisman SV, Childs JR, Stanley WD. Active tectonics of the Seattle fault and central Puget Sound, Washington—Implications for earthquake hazards. Geological Society of America Bulletin 1999;111(7), 1042-1053.

Johnson SY, Blakely RJ, Brocher TM, Bucknam RC, Haeussler PJ, Pratt TL, Nelson AR, Sherrod BL, Wells RE, Lidke DJ, Harding DJ, Kelsey HM. compilers. 2004. Fault number 570, Seattle fault zone, in Quaternary fault and fold database of the United States: US Geological Survey website, http://earthquakes.usgs.gov/hazards/qfaults, accessed 11/13/2013.

Liberty LM, Pratt TL. Structure of the eastern Seattle fault zone, Washington State: New insights from seismic reflection data. Bulletin of the Seismological Society of America 2008; 98(4), 1681-1695.

Moss RS, Ross ZE. Probabilistic Fault Displacement Hazard Analysis for Reverse Faults. Bulletin of the Seismological Society of America 2011; 101(4): 1542-1553.

Nelson AR, Johnson SY, Kelsey HM, Wells RE, Sherrod BL, Pezzopane SK, Bradley LA, Koehler RD III. Late Holocene earthquakes on the Toe Jam Hill fault, Seattle fault zone, Bainbridge Island, Washington. Geological Society of America Bulletin 2003; 115(11): 1388-1403.

Petersen MD, Timothy ED, Chen R, Cao T, Wills CJ, Schwartz DP, Frankel AD. Fault displacement hazard for strike-slip faults. Bulletin of the Seismological Society of America 2011; 101(2): 805-825.

Shantz T. Caltrans Procedures for Calculation of Fault Rupture Hazard. 2013. http://www.dot.ca.gov/ newtech/structures/peer_lifeline_program/docs/Caltrans_Procedures_for_Fault_Rupture_Hazard_Calculation.pdf, accessed 03/10/2015.

Stepp JC, Wong I, Whitney J, Quittmeyer R, Abrahamson N, Toro G, Youngs SR, Coppersmith K, Savy J, Sullivan T. Probabilistic seismic hazard analyses for ground motions and fault displacement at Yucca Mountain, Nevada. Earthquake Spectra 2001; 17(1): 113-151.

Stirling M, Gerstenberger M, Litchfield N, McVerry G, Smith W, Pettinga J, Barnes P. Seismic hazard of the Canterbury region, New Zealand: New earthquake source model and methodology. Bulletin of the New Zealand Society for Earthquake Engineering 2008; 41(2): 51-67.

Stirling M, Goded T, Berryman K, Litchfield N. Selection of Earthquake Scaling Relationships for Seismic Hazard Analysis. Bulletin of the Seismological Society of America 2013; 103(6): 2993-3011.

ten Brink US, Molzer PC, Fisher MA, Blakely RJ, Bucknam RC, Parsons T, Crosson RS, Creagher KC. Subsurface geometry and evolution of the Seattle fault zone and the Seattle basin, Washington. Bulletin of the Seismological Society of America 2002; 92: 1737-1753.

Wells DL, Coppersmith KJ. New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement. Bulletin of the Seismological Society of America 1994; 84(4): 974-1002.

Wesnousky SG. Displacement and geometrical characteristics of earthquake surface ruptures: Issues and implications for seismic-hazard analysis and the process of earthquake rupture. Bulletin of the Seismological Society of America 2008; 98(4): 1609-1632.

Yen YT, Ma KF. Source-scaling relationship for M 4.6–8.9 earthquakes, specifically for earthquakes in the collision zone of Taiwan. Bulletin of the Seismological Society of America 2011; 101(2): 464-481.

Youngs RR, Arabasz WJ, Anderson RE, Ramelli AR, Ake JP, Slemmons DB, McCalpin JP, et al. A methodology for probabilistic fault displacement hazard analysis (PFDHA). Earthquake Spectra 2003; 19(1): 191-219.

1111412016

8150 Sunset 7 messages

Nytzen, Michael <[email protected]> To: Daniel Schneidereit <[email protected]>

Hi Dan - did you say you are available on Tuesday (8/25) morning?

City of Los Angeles Mail - 8150 Sunset

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Dani el Sch nei dereit < daniel. [email protected]> To: "Nytzen, Michael" <[email protected]>

I am but I have a meeting at 10 to 11

Daniel Schneidereit Engineering Geologist I

li (213) 482-0430 [Quoted text hidden)

Nytzen, Michael <[email protected]> To: Daniel Sch neidereit < daniel. sch nei [email protected]>

Hi Dan. How does Thursday (8/27) at 11 or in the afternoon look for you?

From: Daniel Schneidereit [mailtn: [email protected]] Sent: Friday, August 21, 2015 9:56 AM To: Nytzen, Michael Subject: Re: 8150 Sunset

Daniel Schneidereit <[email protected]>

Fri, Aug 21 , 2015 at 9:54 AM

Fri, Aug 21 , 2015 at 9:55 AM

Fri, Aug 21 , 2015 at 12:07 PM

https:f/mai I .google.com/mail/?ui=2&i k=t2cb7e2ea7&view= pt&qc8150&qs=true&search=query&th= 14f51211 Qabb5977 &sim I= 14f512f1 Oabb5977&simI=14f5130116f19f7c&sim I= 14f51a8a0b8435ec&sim I= 14f51ece119... 113

11/1412016

(Quoted text hidden]

(Quoted text hidden]

Daniel Sch neidereit <daniel. schneidereit@lac ity. org> To: "Nytzen, Michael" <[email protected]>

That should be fine

Sent on the new Sprint Network from my Samsung Galaxy S®4.

[Quoted text hidden]

Nytzen, Michael <[email protected]> To: "Daniel. Sc [email protected]" <Daniel. Sc [email protected]>

Ok. We'll see you Thursday at 11. Have a great weekend.

From: Daniel Schneidereit [mailto:[email protected]] Sent: Friday, August 21, 2015 01:21 PM To: Nytzen, Michael Subject: RE: 8150 Sunset

[Quoted text hidden]

Nytzen, Michael < m ichaelnytzen@paul hastings. com> To: "Daniel. Schneidereit@lac ity. org" <Daniel. [email protected]>

One last thing - we should meet in a conference room, if possible.

Thanks,

Michael

From: Nytzen, Michael Sent: Friday, August 21, 2015 1:29 PM To: 'Daniel. [email protected]' Subject: Re: 8150 Sunset

[Quoted text hidden) [Quoted text hidden)


Fri, Aug 21, 2015 at 1 :21 PM

Fri, Aug 21 , 2015 at 1 :28 PM

Fri, Aug 21, 2015 at 3:09 PM

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Daniel Sch nei dereit <daniel.schneidereit@lac ity. org> · To: "Nytzen, Michael" <[email protected]>

Yes. I'll try to sign up for one

Sent on the new Sprint Network from my Samsung Galaxy S®4.

--- Original message - From: "Nytzen, Michael" (Quoted text hidden!


Fri, Aug 21, 2015 at 4:01 PM

https://m ai 1.google.com/mai rnui"' 2&ik,.12cb7e2ea7&view"'pl&q=8150&qs=true&search=query&th= 14f512f1 ()abb5977&sim I= 14f512f10abb5977&sim I= 14f5130116f19f7c&si m I= 14f51a8a0b8435ec&siml=14f51ece119. . . 313

Documents

Fault setbacks - LA City Planning · Length, Rupture Width, Rupture Area, and Surface Displacement”, Bulletin of the Seismological Society of America , 1994, v. 84 no. 4, p. 974-1002