The probability distribution model for principal displacement accommodated on the surface main trace is a critical input to the fault displacement hazard analysis. This article presents a new model for strike-slip ruptures in the moment magnitude (M) range of 6 to 8.3. The new model is the outcome of a multi-year research effort to update the widely used model developed by Petersen and others in 2011. Updates include the adoption of the Fault Displacement Hazard Initiative database and enhancements to rupture and displacement data preparation. Statistical formulation and estimation have also been updated substantially. A three-parameter modified normal distribution that we refer to as the negative Exponentially Modified Gaussian distribution is adopted to model the probability distribution of the natural logarithm of principal displacement. Formulation for the mean parameter of the modified normal includes a random earthquake term, a nonlinear scaling relation with M, and an ellipse function for along-main-trace variation. The aleatory variability of the updated model now depends on M as well as site’s along-main-trace position. These updates not only significantly improve the fit to the distribution of the observed displacements but also yield reasonable 95th percentile predictions for M > 7.5 events. Alternative models representing the estimation uncertainty of the M-scaling relation are also developed. These new models are compared to the previous model in terms of percentile predictions and the calculated hazard curves. The steeper hazard curves from the new models yield a lower exceedance rate than the normal-distribution based model developed previously by Petersen and others.
AbrahamsonNAYoungsRR (1992) A stable algorithm for regression analyses using the random effects model. Bulletin of the Seismological Society of America82(1): 505–510.
2.
AMEC Geomatrix (2010) Geotechnical and Engineering Geological Investigation: California Memorial Stadium—Phase 1 Seismic and Program Improvements.
3.
AndersonJGBiasiGPAngsterSWesnouskySG (2021) Improved scaling relationships for seismic moment and average slip of strike-slip earthquakes incorporating fault-slip rate, fault width, and stress drop. Bulletin of the Seismological Society of America111(5): 2379–2392.
4.
BozorgniaYAbrahamsonNArcosBBaizeSBoncioPChaoSHChenRChiouBDawsonTDonahueJGouletCHansonKKottkeAKuehnNKuoCHLavrentiadisGMadugoDMazzoniSMillinerCMossRNurminenFPaceBPetersenMSarmientoAShenAThomasKThompsonSVisiniFWangYYoungsRR (2021) An overview of the fault displacement hazard initiative research program. Seismological Research Letters92(2B): 1360–1361.
ChenRPetersenMD (2011) Mapping fault displacement hazards for the ShakeOut scenario using semi-probabilistic and probabilistic approaches. Earthquake Spectra27(2): 293–313.
8.
ChenRPetersenMD (2019) Improved implementation of rupture location uncertainty in fault displacement hazard assessment. Bulletin of the Seismological Society of America109(5): 2132–2137.
9.
ChiouBSJYoungsRR (2008) An NGA model for the average horizontal component of peak ground motion and response spectra. Earthquake Spectra24(1): 173–215.
10.
ChiouBSJYoungsRR (2014) Update of the Chiou and Youngs NGA model for the average horizontal component of peak ground motion and response spectra. Earthquake Spectra30(3): 1117–1153.
11.
ChiouBSJChenRThomasKMillinerCWDDawsonTEPetersenMD (2023a) Surface fault displacement models for strike-slip faults. Report GIRS-2022-07, University of California, Los Angeles. DOI: 10.34948/N3RG6X.
12.
ChiouBSJChenRThomasKMillinerCWDDawsonTEPetersenMD (2023b) Surface fault displacement models for strike-slip faults [Data set and FORTRAN subroutines]. Zenodo. DOI: 10.5281/zenodo.15059461.
13.
CluffLSPageRASlemmonsDBCrouseCB (2003) Seismic hazard exposure for the Trans-Alaska pipeline. In: Proceedings of the sixth U.S. conference and workshop on lifeline earthquake engineering, ASCE Technical Council on Lifeline Earthquake Engineering, August, p. 12. DOI: 10.1061/40687(2003)55.
14.
CoppersmithKJYoungsRR (2000) Data needs for probabilistic fault displacement hazard analysis. Journal of Geodynamics29(3–5): 329–343.
15.
DunnPLSmythGK (1996) Randomized quantile residuals. Journal of Computational and Graphical Statistics5(3): 236–244.
16.
FieldEHBiasiGPBirdPDawsonTEFelzerKRJacksonDDJohnsonKMJordanTHMaddenCMichaelAJMilnerKRPageMTParsonsTPowersPMShawBEThatcherWRWeldonRJIIZengY (2013) Uniform California earthquake rupture forecast, version 3 (UCERF3)—The time-independent model. U.S. Geological Survey Open-File Report 2013–1165, California Geological Survey Special Report 228, and Southern California Earthquake Center Publication1792. DOI: 10.3133/ofr20131165.
KneibTSilbersdorffASäfkenB (2021) Rage against the mean—A review of distributional regression approaches. Econometrics and Statistics26: 99–123.
19.
KuehnNMKottkeARSarmientoACMadugoCMBozorgniaY (this volume) A fault displacement model based on the FDHI database. Earthquake Spectra. DOI: 10.1177/87552930241291077.
20.
LavrentiadisGAbrahamsonNA (2019) Generation of surface-slip profiles in the wavenumber domain. Bulletin of the Seismological Society of America109(3): 888–907.
21.
LavrentiadisGAbrahamsonNA (this volume) Fault-displacement models for aggregate and principal displacements. Earthquake Spectra. DOI: 10.1177/87552930231201531.
22.
MartelSJShacatC (2006) Mechanics and interpretations of fault slip. In: AbercrombieRMcGarrAKanamoriHDi ToroG (eds) Earthquakes: Radiated Energy and the Physics of Faulting, Geophysical Monograph Series, Volume 170. Washington, DC: American Geophysical Union, pp. 207–215.
23.
MossRESRossZE (2011) Probabilistic fault displacement hazard analysis for reverse faults. Bulletin of the Seismological Society of America101(4): 1542–1553.
24.
MossRESThompsonSCKuoC-HYounesiKBaumontD (this volume) New probabilistic fault displacement hazard models for reverse faulting. Earthquake Spectra. DOI: 10.1177/87552930241288560.
25.
NurminenFBoncioPVisiniFPaceBValentiniABaizeSScottiO (2020) Probability of occurrence and displacement regression of distributed surface rupturing for reverse earthquakes. Frontiers in Earth Science8: 581605.
26.
PetersenMDDawsonTEChenRCaoTWillsCJSchwartzDPFrankelAD (2011) Fault displacement hazard for strike-slip faults. Bulletin of the Seismological Society of America101(2): 805–825.
27.
PetersenMDShumwayAMPowersPMFieldEHMoschettiMPJaiswalKSMilnerKSRezaeianSFrankelADLlenosALMichaelAJAltekruseJMAhdiSKWithersKBMuellerCSZengYChaseRESalditchLMLucoN, Rukstales KS, Herrick JA, Girot DL, Aagaard BT, Bender AM, Blanpied ML, Briggs RW, Boyd OS, Clayton BS, DuRoss CB, Evans EL, Haeussler PJ, Hatem AE, Haynie KL, Hearn EH, Johnson KM, Kortum ZA, Kwong NS, Makdisi AJ, Mason HB, McNamara DE, McPhillips DF, Okubo PG, Page MT, Pollitz FF, Rubinstein JL, Shaw BE, Shen Z-K, Shiro BR, Smith JA, Stephenson WJ, Thompson EM, Jobe JAT, Wirth EAWitterRC (2024) The 2023 U.S. 50-state national seismic hazard model: Overview and implications. Earthquak Spectra40(1): 5–88.
28.
PinheiroJCBatesDM (2000) Mixed-effects Models in S and S-PLUS. New York: Springer.
29.
R Core Team (2023) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. https://www.R-project.org.
30.
RodgersDWLittleTA (2006) World’s largest coseismic strike-slip offset: The 1855 rupture of the Wairarapa Fault, New Zealand, and implications for displacement/length scaling of continental earthquakes. Journal of Geophysical Research: Solid Earth111(B12): B12408.
31.
SarmientoALavrentiadisGBozorgniaTChenRChiouBSJDawsonTEKottkeAKuehnNKuoCHMadugoCMossRThompsonSZandiehA (this volume) Comparisons of FDHI fault displacement models for principal and aggregate displacement. Earthquake Spectra. DOI:10.1177/87552930251327894
32.
SarmientoAMadugoDShenADawsonTMadugoCThompsonSBozorgniaYBaizeSBoncioPKottkeALavrentiadisGMazzoniSMillinerCNurminenFVisiniF (this volume) Database for the fault displacement hazard initiative project. Earthquake Spectra. DOI: 10.1177/87552930241262766.
33.
ScholzCHLawlerTM (2004) Slip tapers at the tips of faults and earthquake ruptures. Geophysical Research Letters31(21): L21609.
34.
SpudichPChiouB (2015) Strike-parallel and strike-normal coordinate system around geometrically complicated rupture traces: Use by NGA-West2 and further improvements. U.S. Geological Survey Open File Report 2015-1028. DOI: 10.3133/ofr20151028.
35.
StasinopoulosMDRigbyRAHellerGZVoudourisVBastianiFD (2017) Flexible Regression and Smoothing: Using GAMLSS in R. New York: Chapman & Hall/CRC.
36.
SteppJCWongIWhitneyJWQuittmeyerRAbrahamsonNToroGYoungSRCoppersmithKSavyJSullivanT (2001) Probabilistic seismic hazard analyses for ground motions and fault displacement at Yucca Mountain, Nevada. Earthquake Spectra17(1): 113–151.
37.
TakaoMTsuchiyamaJAnnakaTKuritaT (2013) Application of probabilistic fault displacement hazard analysis in Japan. Journal of the Japanese Association of Earthquake Engineering13(1): 17–36.
38.
ThomasKMillinerCChenRChiouBDawsonTPetersenM (this volume) Least cost path analysis as an objective and automatic method to define the main fault trace for probabilistic fault displacement hazard analyses. Earthquake Spectra. DOI: 10.1177/87552930231205878.
39.
US Nuclear Regulatory Commission (NRC) (2012). Confirmatory Analysis of Seismic Hazard at Diablo Canyon Power Plant from the Shoreline Fault Zone. Research Information Letter (RIL) 12-01, September, ML 121230035. https://www.nrc.gov/docs/ml1212/ml121230035.pdf
40.
ValentiniAFukushimaYContriPGülerceZ (2025) The IAEA exercise on probabilistic fault displacement hazard assessment. Earthquake Spectra. DOI: 10.1177/87552930241306450.
41.
ValentiniAFukushimaYContriPOnoMSakaiTThompsonSCVialletEAnnakaTChenRMossREPetersenMD (2021) Probabilistic fault displacement hazard assessment (PFDHA) for nuclear installations according to IAEA safety standards. Bulletin of the Seismological Society of America111(5): 2661–2672.
42.
WangYGouletC (2022) Constraining fault displacements for strike-slip events using physics-based simulations. In: Proceedings of the 12th national conference on earthquake engineering, Salt Lake City, UT. https://www.eeri.org/what-we-offer/digital-library/?lid=12791.
43.
WellsDLCoppersmithKJ (1993) Likelihood of surface rupture as a function of magnitude. Seismological Research Letters64(1): 54.
44.
WellsDLYoungsB (2015) Improved regression relations for earthquake source parameters. Seismological Research Letters86(2B): 623.
45.
WesnouskySG (2008) 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 America98(4): 1609–1632.
46.
YadavRKKunduBGahalautKCatherineJGahalautVKAmbikapthyANaiduMS (2013) Coseismic offsets due to the 11 April 2012 Indian Ocean earthquakes (Mw 8.6 and 8.2) derived from GPS measurements. Geophysical Research Letters40(13): 3389–3393.
47.
YoungsRRAbrahamsonNMakdisiFISadighK (1995) Magnitude-dependent variance of peak ground acceleration. Bulletin of the Seismological Society of America85(4): 1161–1176.
48.
YoungsRRArabaszWJAndersonRERamelliARAkeJPSlemmonsDBMcCalpinJPDoserDIFridrichCJSwanFHIIIRogersAMYountJCAndersonLWSmithKDBruhnRLKnuepferLKSmithRBdePoloCMO’LearyKWCoppersmithKJPezzopaneSKSchwartzDPWhitneyJWOligSSToroGR (2003) A methodology for probabilistic fault displacement hazard analysis (PFDHA). Earthquake Spectra19(1): 191–219.
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