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Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case

Author

Listed:
  • Jan Beirlant

    (KU Leuven
    University of the Free State)

  • Andrzej Kijko

    (University of Pretoria Natural Hazard Centre)

  • Tom Reynkens

    (KU Leuven)

  • John H. J. Einmahl

    (Tilburg University)

Abstract

The area-characteristic, maximum possible earthquake magnitude $$T_M$$ T M is required by the earthquake engineering community, disaster management agencies and the insurance industry. The Gutenberg–Richter law predicts that earthquake magnitudes M follow a truncated exponential distribution. In the geophysical literature, several estimation procedures were proposed, see for instance, Kijko and Singh (Acta Geophys 59(4):674–700, 2011) and the references therein. Estimation of $$T_M$$ T M is of course an extreme value problem to which the classical methods for endpoint estimation could be applied. We argue that recent methods on truncated tails at high levels (Beirlant et al. Extremes 19(3):429–462, 2016; Electron J Stat 11:2026–2065, 2017) constitute a more appropriate setting for this estimation problem. We present upper confidence bounds to quantify uncertainty of the point estimates. We also compare methods from the extreme value and geophysical literature through simulations. Finally, the different methods are applied to the magnitude data for the earthquakes induced by gas extraction in the Groningen province of the Netherlands.

Suggested Citation

  • Jan Beirlant & Andrzej Kijko & Tom Reynkens & John H. J. Einmahl, 2019. "Estimating the maximum possible earthquake magnitude using extreme value methodology: the Groningen case," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 98(3), pages 1091-1113, September.
    • Handle: RePEc:spr:nathaz:v:98:y:2019:i:3:d:10.1007_s11069-017-3162-2
    DOI: 10.1007/s11069-017-3162-2
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    1. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    2. Aban, Inmaculada B. & Meerschaert, Mark M. & Panorska, Anna K., 2006. "Parameter Estimation for the Truncated Pareto Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 270-277, March.
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    2. Minakshi Mishra & Abhishek & R. B. S. Yadav & Manisha Sandhu, 2021. "Probabilistic assessment of earthquake hazard in the Andaman–Nicobar–Sumatra region," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 105(1), pages 313-338, January.

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