Abstract
Assessing seismic risk in low-to-moderate seismic activity areas like French mainland is a challenge. In these areas, the estimation of large earthquake hazard calls for models driven by sparse observation data and interpretative seismic knowledge. This leads models used in probabilistic seismic hazard assessment (PSHA) and declustering algorithms to large epistemic uncertainties that are overrepresented due to the large amount of parameters used in it. To concentrate epistemic uncertainties into one single method, we intend to limit the number of parameters under consideration by using the non-parametric inter-event time method. This method is empirical and needs a lot of data to be accurate. In the context of sparse large earthquake data, this paper proposes an implementation of the inter-event time method that ensures the stability of main shock proportions for sparse seismic data. We call this implementation magnitude of inferred main shock proportion (MIMP). This method is applied to the historical French seismic catalogue. We use a Monte Carlo Markov Chain to sample the whole space of magnitude uncertainties contained in this catalogue. We produce a set of equiprobable main shock proportion–magnitude and frequency–magnitude distributions. Results are discussed in the light of reference works published in the literature.
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References
Aki K (1965) Maximum likelihood estimate of b in the formula log N= a-bM and its confidence limits. Bulletin of the Earthquake Research Institute 43:237–239
Azak TE, Kalafat D, Şeşetyan K, Demircioğlu MB (2017) Effects of seismic declustering on seismic hazard assessment: a sensitivity study using the Turkish earthquake catalogue. Bulletin of Earthquake Engineering 16:3339–3366. https://doi.org/10.1007/s10518-017-0174-y
Bak P, Christensen K, Danon L, Scanlon T (2002) Unified scaling law for earthquakes. Physical Review Letters 88:178501. https://doi.org/10.1103/PhysRevLett.88.178501
Båth M (1965) Lateral inhomogeneities of the upper mantle. Tectonophysics 2:483–514. https://doi.org/10.1016/0040-1951(65)90003-X
Baumont D, Manchuel K, Traversa P, Durouchoux C, Nayman E, Ameri G (2018) Intensity predictive attenuation models calibrated in Mw for metropolitan France. Bulletin of Earthquake Engineering 16:2285–2310. https://doi.org/10.1007/s10518-018-0344-6
Bottiglieri M, Lippiello E, Godano C, de Arcangelis L (2009) Identification and spatiotemporal organization of aftershocks. Journal of Geophysical Research 114:B03303. https://doi.org/10.1029/2008JB005941
Burkhard M, Grünthal G (2009) Seismic source zone characterization for the seismic hazard assessment project PEGASOS by the Expert Group 2 (EG1b). Swiss Journal of Geosciences 102:149–188. https://doi.org/10.1007/s00015-009-1307-3
Cara M, Cansi Y, Schlupp A, Arroucau P, Béthoux N, Beucler E, Bruno S, Calvet M, Chevrot S, Deboissy A (2015) SI-Hex: a new catalogue of instrumental seismicity for metropolitan France. Bulletin de la Société Géologique de France 186:3–19. https://doi.org/10.2113/gssgfbull.186.1.3
Castellaro S, Mulargia F, Kagan YY (2006) Regression problems for magnitudes. Geophysical Journal International 165:913–930. https://doi.org/10.1111/j.1365-246X.2006.02955.x
Corral Á (2004) Long-term clustering, scaling, and universality in the temporal occurrence of earthquakes. Physical Review Letters 92:108501. https://doi.org/10.1103/PhysRevLett.92.108501
Drouet S, Ameri G, Le Dortz K, Secanell R, Senfaute G (2020) A probabilistic seismic hazard map for the metropolitan France. Bulletin of Earthquake Engineering 18:1865–1898. https://doi.org/10.1007/s10518-020-00790-7
Frohlich C, Davis S (1985) Identification of aftershocks of deep earthquakes by a new ratios method. Geophysical Research Letters 12:713–716
Galina NA, Bykova VV, Vakarchuk RN, Tatevosian RE (2019) Effect of earthquake catalog declustering on seismic hazard assessment. Seismic Instruments 55:59–69. https://doi.org/10.3103/S0747923919010079
Gardner JK, Knopoff L (1974) Is sequence of earthquakes in Southern California, with aftershocks removed, Poissonian? Bulletin of the Seismological Society of America 64:1363–1367
Godano C (2015) A new expression for the earthquake interevent time distribution. Geophysical Journal International 202:219–223. https://doi.org/10.1093/gji/ggv135
Gouache C, Bonneau F, Tinard P (2019) Regional and exhaustive French seismic catalogues. 20th Annual Conference IAMG. State College, Pennsylvania, USA.
Grünthal G (1985) The up-dated earthquake catalogue for the German democratic Republic and adjacent areas–statistical data characteristics and conclusions for hazard assessment. 3rd International Symposium on the Analysis of Seismicity and Seismic Risk. Liblice Castle, Czechoslovakia.
Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bulletin of the Seismological Society of America 34:185–188
Hainzl S, Scherbaum F, Beauval C (2006) Estimating background activity based on interevent-time distribution. Bulletin of the Seismological Society of America 96:313–320. https://doi.org/10.1785/0120050053
Luen B, Stark PB (2012) Poisson tests of declustered catalogues: Poisson tests. Geophysical Journal International 189:691–700. https://doi.org/10.1111/j.1365-246X.2012.05400.x
Manchuel K, Traversa P, Baumont D, Cara M, Nayman E, Durouchoux C (2017) The French seismic CATalogue (FCAT-17). Bulletin of Earthquake Engineering 16:2227–2251. https://doi.org/10.1007/s10518-017-0236-1
Marsan D, Lengline O (2008) Extending earthquakes’ reach through cascading. Science 319:1076–1079. https://doi.org/10.1126/science.1148783
Martin C, Ameri G, Baumont D, Carbon D, Senfaute G, Thiry JM, Faccioli E, Savy J (2018) Probabilistic seismic hazard assessment for South-Eastern France. Bulletin of Earthquake Engineering 16:2477–2511. https://doi.org/10.1007/s10518-017-0249-9
Martin Ch, Combes Ph, Secanell R, Lignon G, Fioravanti A, Carbon D, Monge O, Grellet B (2002) Révision du zonage sismique de la France, Etude probabiliste. GTR/MATE/0701-150, MATE, Paris (in French).
Marzocchi W, Spassiani I, Stallone A, Taroni M (2019) How to be fooled searching for significant variations of the b-value. Geophysical Journal International 220:1845–1856. https://doi.org/10.1093/gji/ggz541
McGuire RK (2004) Seismic hazard and risk analysis. Earthquake Engineering Research Institute, Oakland
Michas G, Vallianatos F (2018) Stochastic modeling of nonstationary earthquake time series with long-term clustering effects. Physical Review E 98:042107. https://doi.org/10.1103/PhysRevE.98.042107
Molchan G (2005) Interevent time distribution in seismicity: a theoretical approach. Pure and Applied Geophysics 162:1135–1150. https://doi.org/10.1007/s00024-004-2664-5
Musson RMW (2012) The effect of magnitude uncertainty on earthquake activity rates. Bulletin of the Seismological Society of America 102:2771–2775. https://doi.org/10.1785/0120110224
Page R (1968) Aftershocks and microaftershocks of the great Alaska earthquake of 1964. Bulletin of the Seismological Society of America 58:1131–1168
Pasari S (2018) Stochastic modelling of earthquake interoccurrence times in Northwest Himalaya and adjoining regions. Geomatics, Natural Hazards and Risk 9:568–588. https://doi.org/10.1080/19475705.2018.1466730
Pecker A, Faccioli E, Gurpinar A, Martin C, Renault P (2017) An overview of the SIGMA research project. Springer, Berlin. https://doi.org/10.1007/978-3-319-58154-5
Petersen MD, Moschetti MP, Powers PM, Mueller CS, Haller KM, Frankel AD, Zeng Y, Rezaeian S, Harmsen SC, Boyd OS (2015) The 2014 United States national seismic hazard model. Earthquake Spectra 31:S1–S30. https://doi.org/10.1193/120814EQS210M
Reasenberg P (1985) Second-order moment of central California seismicity, 1969-1982. Journal of Geophysical Research: Solid Earth 90:5479–5495. https://doi.org/10.1029/JB090iB07p05479
Rhoades DA (1996) Estimation of the Gutenberg-Richter relation allowing for individual earthquake magnitude uncertainties. Tectonophysics 258:71–83. https://doi.org/10.1016/0040-1951(95)00182-4
Richter CF (1958) Elementaty seismology. W.F. Freeman and Company; Bailey Bros. & Swinfen Ltd., San Francisco and London
Sokolov V, Zahran HM, Youssef S, El-Hadidy M, Alraddadi WW (2016) Probabilistic seismic hazard assessment for Saudi Arabia using spatially smoothed seismicity and analysis of hazard uncertainty. Bulletin of Earthquake Engineering 15:2695–2735. https://doi.org/10.1007/s10518-016-0075-5
Tinti S, Mulargia F (1985) Effects of magnitude uncertainties on estimating the parameters in the Gutenberg-Richter frequency-magnitude law. Bulletin of the Seismological Society of America 75:1681–1697
Traversa P, Baumont D, Manchuel K, Nayman E, Durouchoux C (2017) Exploration tree approach to estimate historical earthquakes Mw and depth, test cases from the French past seismicity. Bulletin of Earthquake Engineering 16:2169–2193. https://doi.org/10.1007/s10518-017-0178-7
Uhrhammer RA (1986) Characteristics of northern and central California seismicity. Earthquake Notes 57:21
Utsu T (1966) A statistical significance test of the difference in b-value between two earthquake groups. Journal of Physics of the Earth 14:37–40
van Stiphout T, Zhuang J, Marsan D (2012) Seismicity declustering. Community Online Resource for Statistical Seismicity Analysis. https://doi.org/10.5078/corssa-52382934
Veneziano D, Van Dyck J (1985) Seismic hazard methodology for nuclear facilities in the Eastern United States. P101-29, EPRI Research Project Report.
Weichert DH (1980) Estimation of the earthquake recurrence parameters for unequal observation periods for different magnitudes. Bulletin of the Seismological Society of America 70:1337–1346
Wiemer S, Wyss M (2000) Minimum magnitude of completeness in earthquake catalogs: examples from Alaska, the Western United States, and Japan. Bulletin of the Seismological Society of America 90:859–869. https://doi.org/10.1785/0119990114
Woessner J, Laurentiu D, Giardini D, Crowley H, Cotton F, Grünthal G, Valensise G, Arvidsson R, Basili R, Demircioglu MB, Hiemer S, Meletti C, Musson RW, Rovida AN, Sesetyan K, Stucchi M (2015) The 2013 European Seismic Hazard Model: key components and results. Bulletin of Earthquake Engineering 13:3553–3596. https://doi.org/10.1007/s10518-015-9795-1
Zhuang J, Ogata Y, Vere-Jones D (2002) Stochastic declustering of space-time earthquake occurrences. Journal of the American Statistical Association 97:369–380. https://doi.org/10.1198/016214502760046925
Acknowledgments
This work was performed in the frame of the RING project (http://ring.georessources.univ-lorraine.fr/) at Université de Lorraine. We would like to thank for their support the Caisse Centrale de Réassurance and every industrial and academic sponsors of the RING-GOCAD Consortium managed by ASGA. We sincerely thank Gloria Senfaute for her careful review of our paper.
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Gouache, C., Bonneau, F., Tinard, P. et al. Estimation of main shock frequency–magnitude distributions by adapting the inter-event time method for low-to-moderate seismicity areas: application to French mainland. J Seismol 25, 771–782 (2021). https://doi.org/10.1007/s10950-021-10001-8
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DOI: https://doi.org/10.1007/s10950-021-10001-8