Abstract
Seismic hazard analysis requires knowledge of the recurrence rates of large magnitude earthquakes that drive the hazard at low probabilities of interest for seismic design. Earthquake recurrence is usually determined through studies of the historic earthquake catalogue for a given region. Reliable historic catalogues generally span time periods of 100–200 years in North America, while large magnitude events (M ≥ 7) have recurrence rates on the order of hundreds or thousands of years in many areas, resulting in large uncertainty in recurrence rates for large events. Using Monte Carlo techniques and assuming typical recurrence parameters, we simulate earthquake catalogues that span long periods of time. We then split these catalogues into smaller catalogues spanning 100–200 years that mimic the length of historic catalogues. For each of these simulated “historic” catalogues, a recurrence rate for large magnitude events is determined. By comparing recurrence rates from one historic-length catalogue to another, we quantify the uncertainty associated with determining recurrence rates from short historic catalogues. The use of simulations to explore the uncertainty (rather than analytical solutions) allows us flexibility to consider issues such as the relative contributions of aleatory versus epistemic uncertainty, and the influence of fitting method, as well as lending insight into extreme-event statistics. The uncertainty in recurrence rates of large (M > 7) events is about a factor of two in regions of high seismicity, due to the shortness of historic catalogues. This uncertainty increases greatly with decreasing seismic activity. Uncertainty is dependent on the length of the catalogue as well as the fitting method used (least squares vs. maximum likelihood). Examination of 90th percentile recurrence rates reveals that epistemic uncertainty in the true parameters may cause recurrence rates determined from historic catalogues to be uncertain by a factor greater than 50.
References
Adams J, Halchuk S (2013) Draft documentation for Trial3 national seismic hazard maps, for use in 2015 NBCC. Geol. Surv. Canada, Ottawa
Aki K (1965) Maximum likelihood estimate of b in the formula log (N) = a − bM and its confidence limits. Bull Earthq Res Inst Tokyo Univ 43:237–239
Assatourians K, Atkinson G M (2012) EQHAZ - An open-source probabilistic seismic hazard code based on the Monte Carlo simulation approach, for submission to Seismological Research Letters
Bender B (1983) Maximum likelihood estimation of b values for magnitude grouped data. Bull Seismol Soc Am 73:831–851
Gutenberg B, Richter C (1954) Seismicity of the Earth and associated phenomena, 2nd edn. Princeton University Press, Princeton, p 310
Heffron JJA (1975) On fitting the ‘best’ line to enzyme kinetic data. Biochem Educ 3(4):70
Hong HP, Goda K (2006) A comparison of seismic-hazard and risk deaggregation. Bull Seismol Soc Am 96:2021–2039
Johnston A C, Coppersmith K J, Kanter L, Cornell A (1994) The earthquakes in stable continental regions, Volume 1: Assessment of Large Earthquake Potential, EPRI Report
Kramer S L (1996) Geotechnical Earthquake Engineering, Prentice Hall, Inc., Upper Saddle River, New Jersey, 653 pp. Chaptor 4, page 123
Marzocchi W, Sandri L (2003) A review and new insights on the estimation of the B-value and its uncertainty. Ann Geophys 46:1271–1282
Musson RMW (1999) Determination of design earthquakes in seismic hazard analysis through Monte Carlo simulation. J Earthq Eng 3:463–474
Musson RMW (2000) The use of Monte Carlo simulations for seismic hazard assessment in the UK. Ann Geophys 43:1–9
Page R (1968) Aftershocks and microaftershocks of the Great Alaska Earthquake of 1964. Bull Seismol Soc Am 58:1131–1168
Petersen M, Frankel A, Harmsen S, Mueller C, Haller K, Wheeler R, Wesson R, Zeng Y, Boyd O, Perkins D, Luco N, Field E, Wills C, Rukstales K (2008). Documentation for the 2008 update of the United States National Seismic Hazard Maps: U.S. Geological Survey Open-File Report 2008–1128, 61 p
Utsu T (1965) A method for determining the value of b in a formula log n = a – bM showing the magnitude-frequency relation for earthquakes. Geophys Bull Hokkaido Univ Hokkaido Jpn 13:99–103 (in Japanese)
Weichert DH (1980) Estimation of the earthquake recurrence parameters for unequal observation periods for different Magnitudes. Bull Seismol Soc Am 70:1337–1346
Whittle RM, Yarwood J (1973) Experimental physics for students. Chapman and Hall, London, 370p
Acknowledgments
This work was supported by the National Sciences and Engineering Research Council of Canada. We thank two anonymous reviewers for their constructive comments. It was one of those reviewers who suggested trying a centroid-based method.
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Mohammed, T., Atkinson, G.M. & Assatourians, K. Uncertainty in recurrence rates of large magnitude events due to short historic catalogs. J Seismol 18, 565–573 (2014). https://doi.org/10.1007/s10950-014-9428-1
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DOI: https://doi.org/10.1007/s10950-014-9428-1