IDEAS home Printed from https://ideas.repec.org/a/spr/nathaz/v110y2022i3d10.1007_s11069-021-05012-0.html
   My bibliography  Save this article

Bayesian estimation of b-value in Gutenberg–Richter relationship: a sample size reduction approach

Author

Listed:
  • Saman Yaghmaei-Sabegh

    (University of Tabriz)

  • Gholamreza Ostadi-Asl

    (University of Tabriz)

Abstract

One of the most widely used relationships for prediction of b-value is the Aki–Utsu relationship, which is based on the maximum likelihood estimating. This method has some limitations that can lead to inaccurate estimations of b-value. The need for an accurate estimate of mean earthquake magnitude for the whole seismic catalog samples is one of them. Given that the data in seismic catalogs are usually incomplete, the obtained mean value is far from the actual value, and consequently, the value of the parameter b estimated from the Aki–Utsu relationship will not be reliable enough. In this paper, a Bayesian approach is proposed for b-value estimation to reduce the minimum required sample size. To evaluate the accuracy of the proposed method, catalogs with mostly less than 200 sample sizes were simulated with Monte Carlo method. For each of the catalogs, the b-values were estimated and errors were found and compared to those of the classic methods. The results show a considerable reduction in b-value estimation error, and significant decrease in the minimum sample size required for a reliable estimation.

Suggested Citation

  • Saman Yaghmaei-Sabegh & Gholamreza Ostadi-Asl, 2022. "Bayesian estimation of b-value in Gutenberg–Richter relationship: a sample size reduction approach," 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. 110(3), pages 1783-1797, February.
    • Handle: RePEc:spr:nathaz:v:110:y:2022:i:3:d:10.1007_s11069-021-05012-0
    DOI: 10.1007/s11069-021-05012-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11069-021-05012-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11069-021-05012-0?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. repec:dau:papers:123456789/1906 is not listed on IDEAS
    2. Danijel Schorlemmer & Stefan Wiemer & Max Wyss, 2005. "Variations in earthquake-size distribution across different stress regimes," Nature, Nature, vol. 437(7058), pages 539-542, September.
    3. M. Goldstein & S. Morris & G. Yen, 2004. "Problems with fitting to the power-law distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(2), pages 255-258, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mendy Bengoubou-Valérius & Dominique Gibert, 2013. "Bootstrap determination of the reliability of b-values: an assessment of statistical estimators with synthetic magnitude series," 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. 65(1), pages 443-459, January.
    2. Fenner, Trevor & Levene, Mark & Loizou, George, 2010. "Predicting the long tail of book sales: Unearthing the power-law exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2416-2421.
    3. Rezvanian, Alireza & Meybodi, Mohammad Reza, 2015. "Sampling social networks using shortest paths," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 424(C), pages 254-268.
    4. Rafael González-Val, 2012. "A Nonparametric Estimation of the Local Zipf Exponent for all US Cities," Environment and Planning B, , vol. 39(6), pages 1119-1130, December.
    5. Rafael González-Val, 2021. "The Probability Distribution of Worldwide Forest Areas," Sustainability, MDPI, vol. 13(3), pages 1-19, January.
    6. Rafael González‐Val, 2019. "Historical urban growth in Europe (1300–1800)," Papers in Regional Science, Wiley Blackwell, vol. 98(2), pages 1115-1136, April.
    7. Marcus Berliant & Hiroki Watanabe, 2015. "Explaining the size distribution of cities: Extreme economies," Quantitative Economics, Econometric Society, vol. 6(1), pages 153-187, March.
    8. Klabunde, Anna, 2014. "Computational Economic Modeling of Migration," Ruhr Economic Papers 471, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    9. Fenner, Trevor & Levene, Mark & Loizou, George, 2005. "A stochastic evolutionary model exhibiting power-law behaviour with an exponential cutoff," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(2), pages 641-656.
    10. Peltonen, Tuomas A. & Scheicher, Martin & Vuillemey, Guillaume, 2014. "The network structure of the CDS market and its determinants," Journal of Financial Stability, Elsevier, vol. 13(C), pages 118-133.
    11. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    12. Politi, Mauro & Scalas, Enrico, 2008. "Fitting the empirical distribution of intertrade durations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2025-2034.
    13. Fan Jiang & Niancai Liu, 2018. "The hierarchical status of international academic awards in social sciences," Scientometrics, Springer;Akadémiai Kiadó, vol. 117(3), pages 2091-2115, December.
    14. A. Singh & Indrajit Roy & Santosh Kumar & J. Kayal, 2015. "Seismic source characteristics in Kachchh and Saurashtra regions of Western India: b-value and fractal dimension mapping of aftershock sequences," 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. 77(1), pages 33-49, May.
    15. Bar-Ilan, Judit, 2008. "Informetrics at the beginning of the 21st century—A review," Journal of Informetrics, Elsevier, vol. 2(1), pages 1-52.
    16. Davide Provenzano, 2014. "Power laws and the market structure of tourism industry," Empirical Economics, Springer, vol. 47(3), pages 1055-1066, November.
    17. Aaron Clauset & Maxwell Young & Kristian Skrede Gleditsch, 2007. "On the Frequency of Severe Terrorist Events," Journal of Conflict Resolution, Peace Science Society (International), vol. 51(1), pages 58-87, February.
    18. Morales, R.V. & da Cunha, C.R. & Rambo, C.R., 2014. "A complex network approach for the growth of aerogels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 131-138.
    19. Mauro Politi & Nicolas Millot & Anirban Chakraborti, 2011. "The near-extreme density of intraday log-returns," Papers 1106.0039, arXiv.org.
    20. Ausloos, Marcel & Cerqueti, Roy & Lupi, Claudio, 2017. "Long-range properties and data validity for hydrogeological time series: The case of the Paglia river," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 39-50.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:nathaz:v:110:y:2022:i:3:d:10.1007_s11069-021-05012-0. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.