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Journal of Seismology

, Volume 19, Issue 1, pp 27–40 | Cite as

Completeness assessment of earthquake catalogues under uncertain knowledge

  • Jorge L. AlamillaEmail author
  • Rossana Vai
  • Luis Esteva
Original Article

Abstract

A probabilistic model is proposed to quantify the completeness levels of earthquake catalogues used for the estimation of the activity of seismic sources. This variable, related to the probability that an event of a given magnitude is recorded in the earthquake catalogue, reflects both aleatory and epistemic uncertainties about the catalogue information. Two alternative approaches are presented for the estimation of the completeness levels: one is related to a catalogue suspected to be incomplete throughout the magnitude range of interest because the monitoring network is not capable of detecting the occurrence of all seismic events and the other is related to an earthquake catalogue considered to be almost complete above a given threshold magnitude. The completeness probabilities for given magnitudes are described by explicit completeness functions whose parameters are treated as random variables described by their posterior joint probability density function based on a Bayesian estimation. Two case studies are presented: The first one extends throughout the Gulf of Mexico with a seismic catalogue suspected or known to be incomplete and the second one corresponds to a seismic source covering a segment along the southwest coast of Mexico, with an earthquake catalogue known to be almost complete.

Keywords

Catalogue completeness Bayesian estimation Epistemic and aleatory uncertainties Completeness level 

References

  1. Alamilla JL, Vai R, Esteva L (2014a) Estimating seismic-source rate parameters associated with incomplete catalogues and superimposed poisson-renewal generating processes. J Seismology SubmittedGoogle Scholar
  2. Alamilla JL, Vai R, Esteva L (2014b) Seismicity assessment using earthquake catalogues with uncertain and incomplete data: Probabilistic formulation. J Seismology AcceptedGoogle Scholar
  3. Box GEP, Tiao GC (1973) Bayesian inference in statistical analysis, vol 40. WileyGoogle Scholar
  4. Cornell CA, Vanmarcke E (1969) The major influences on seismic risk. In: 4th World Conference on Earthquake Engineering, Santiago de Chile, 15-19 JanuaryGoogle Scholar
  5. D’Alessandro A, Ruppert NA (2012) Evaluation of location performance and magnitude of completeness of the Alaska regional seismic network by the SNES method. Bull Seis Soc Am 102:2098–2115CrossRefGoogle Scholar
  6. Frohlich C (1982) Seismicity of the central Gulf of Mexico. Geology 10:103–106CrossRefGoogle Scholar
  7. Gangopadhyay A, Sen MK (2008) A possible mechanism for the spatial distribution of seismicity in northern Gulf of Mexico. Geophys J Int 175:1141–1153CrossRefGoogle Scholar
  8. Gutenberg B, Richter CF (1944) Frequency of earthquakes in California. Bull Seis Soc Am 34(4):185–188Google Scholar
  9. Hakimhashemi AH, Grünthal G (2012) A statistical method for estimating catalog completeness applicable to long-term nonstationary seismicity data. Bull Seis Soc Am 102(6):2530–2546CrossRefGoogle Scholar
  10. Mignan A (2012) Functional shape of the earthquake frequency-magnitude distribution and completeness magnitude. J Geophys Res 117 (B08302)Google Scholar
  11. Mignan A, Woessner J (2012) Estimating the magnitude of completeness for earthquake catalogs. Community Online Resource for Statistical Seismicity AnalysisGoogle Scholar
  12. Ogata Y, Katsura K (1993) Analysis of temporal and spatial heterogeneity of magnitude frequency distribution inferred from earthquake catalogs. Geophys J Int 113:727–738CrossRefGoogle Scholar
  13. Ogata Y, Katsura K (2006) Immediate and updated forecasting of aftershock hazard. Geophys Res Lett 33(10)Google Scholar
  14. Omi T, Ogata Y, Hirata Y, Aihara K (2013) Forecasting large aftershocks within one day after the main shock. Scientific Reports 3Google Scholar
  15. Pardo M, Suárez G (1995) Shape of the subduced Rivera and Cocos plates in southern Mexico: seismic and tectonic implications. J Geophys Res 100(12):357–373Google Scholar
  16. Press SJ (2003) Subjective and objective Bayesian statistics. Wiley InterscienceGoogle Scholar
  17. Ringdal F (1975) On the estimation of seismic detection thresholds. Bull Seis Soc Am 65(6):1631–1642Google Scholar
  18. Rotondi R, Garavaglia E (2002) Statistical analysis of the completeness of a seismic catalogue. Nat Hazards 25:245–258CrossRefGoogle Scholar
  19. Schorlemmer D, Woessner J (2008) Probability of detecting an earthquake. Bull Seis Soc Am 98(5):2103–2117CrossRefGoogle Scholar
  20. Singh SK, Rodríguez M, Esteva L (1983) Statistics of small earthquakes and frequency of occurrence of large earthquakes along the Mexican subduction zone. Bull Seis Soc Am 73(6):1779–1796Google Scholar
  21. Singh SK, Rodríguez M, Espindola JM (1984) A catalog of shallow earthquakes of Mexico from 1900 to 1981. Bull Seis Soc Am 74(1):267–279Google Scholar
  22. Woessner J, Wiemer S (2005) Assessing the quality of earthquake catalogues: estimating the magnitude of completeness and its uncertainty. Bull Seis Soc Am 95 (2):684–698CrossRefGoogle Scholar
  23. Yamamoto J, Jimenez Z (2009) The May 23th 2007 Gulf of Mexico earthquake. In: American Geophysical Union, Fall Meeting, S31A-1692, San FranciscoGoogle Scholar
  24. Zuñiga FR, Guzmán-Speziale M (1997) Seismogenic sources zones of Mexico. In: Technical report, IPGH, Seismic Hazard Project, Instituto de Geofsica, UNAM, MexicoGoogle Scholar
  25. Zuñiga FR, Reyes MA, Valdés C (2000) A general overview of the catalog of recent seismicity compiled by the Mexican seismological survey. Geophys J Int 39:161–170Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.IMP Mexican Institute of PetroleumMexicoMexico
  2. 2.UNAM National University of MexicoMexicoMexico

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