IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v143y2021ics0960077920310134.html
   My bibliography  Save this article

κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes

Author

Listed:
  • da Silva, Sérgio Luiz E.F.

Abstract

The earthquakes statistical analysis are essential for understanding the seismic activity of a region and consequently, in seismic hazard studies. Nowadays, the statistics that describe the relationship between the earthquake magnitude and the total number of quakes in a given region has been dominated by the Gutenberg–Richter (GR) power-law. However, the GR law is only valid from a threshold magnitude (local scale invariance). To mitigate this limitation, we introduce in this work a statistical mechanics approach to appropriately describe the earthquakes in a wide range of magnitudes. In this way, we formulate a generalisation of the GR law based on a κ-probability function, which is a distribution linked to Kaniadakis statistics (or κ-statistics). We have tested the viability of our proposal using real data sets recorded in 6 different regions of the Earth by considering more than 150,000 earthquakes. The results show that the κ-generalised GR law describes appropriately enough the energy distribution in an ample range of magnitudes, especially for low magnitude earthquakes where the standard GR law fails. Besides, the entropic index of the Kaniadakis entropy is a universal parameter with a value close to 1. Furthermore, the results reveal the fractal nature of the fragments filling the space between tectonic plates. They also show the self-similarity of earthquakes regardless of their magnitude.

Suggested Citation

  • da Silva, Sérgio Luiz E.F., 2021. "κ-generalised Gutenberg–Richter law and the self-similarity of earthquakes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920310134
    DOI: 10.1016/j.chaos.2020.110622
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920310134
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110622?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. Ioannis, Koutalonis & Filippos, Vallianatos, 2020. "Observational evidence of non-extensive behavior of seismic coda waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 550(C).
    2. da Silva, Sérgio Luiz Eduardo Ferreira & dos Santos Lima, Gustavo Zampier & de Araújo, João Medeiros & Corso, Gilberto, 2021. "Extensive and nonextensive statistics in seismic inversion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    3. Clementi, F. & Di Matteo, T. & Gallegati, M. & Kaniadakis, G., 2008. "The κ-generalized distribution: A new descriptive model for the size distribution of incomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3201-3208.
    4. Darooneh, Amir H. & Mehri, Ali, 2010. "A nonextensive modification of the Gutenberg–Richter law: q-stretched exponential form," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 509-514.
    5. Abreu, Everton M.C. & Ananias Neto, Jorge & Mendes, Albert C.R. & de Paula, Rodrigo M., 2019. "Loop quantum gravity Immirzi parameter and the Kaniadakis statistics," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 307-310.
    6. Vallejos, Adams & Ormazábal, Ignacio & Borotto, Félix A. & Astudillo, Hernán F., 2019. "A new κ-deformed parametric model for the size distribution of wealth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 819-829.
    7. Carpinteri, A. & Lacidogna, G. & Niccolini, G., 2009. "Fractal analysis of damage detected in concrete structural elements under loading," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2047-2056.
    8. Abe, Sumiyoshi & Suzuki, Norikazu, 2005. "Scale-free statistics of time interval between successive earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 588-596.
    9. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    10. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    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. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    2. Yuri Biondi & Simone Righi, 2019. "Inequality, mobility and the financial accumulation process: a computational economic analysis," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 93-119, March.
    3. Ferreira, Douglas S.R. & Papa, Andrés R.R. & Menezes, Ronaldo, 2014. "Small world picture of worldwide seismic events," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 170-180.
    4. Fabio CLEMENTI & Mauro GALLEGATI, 2017. "NEW ECONOMIC WINDOWS ON INCOME AND WEALTH: THE k-GENERALIZED FAMILY OF DISTRIBUTIONS," Journal of Social and Economic Statistics, Bucharest University of Economic Studies, vol. 6(1), pages 1-15, JULY.
    5. Scherrer, T.M. & França, G.S. & Silva, R. & de Freitas, D.B. & Vilar, C.S., 2015. "Nonextensivity at the Circum-Pacific subduction zones—Preliminary studies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 426(C), pages 63-71.
    6. José María Sarabia & Vanesa Jordá & Lorena Remuzgo, 2017. "The Theil Indices in Parametric Families of Income Distributions—A Short Review," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(4), pages 867-880, December.
    7. da Silva, Sérgio Luiz E.F. & Silva, R. & dos Santos Lima, Gustavo Z. & de Araújo, João M. & Corso, Gilberto, 2022. "An outlier-resistant κ-generalized approach for robust physical parameter estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    8. Ferreira, Douglas S.R. & Ribeiro, Jennifer & Oliveira, Paulo S.L. & Pimenta, André R. & Freitas, Renato P. & Papa, Andrés R.R., 2020. "Long-range correlation studies in deep earthquakes global series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    9. repec:prg:jnlcfu:v:2022:y:2022:i:1:id:572 is not listed on IDEAS
    10. Chang, Andrew C. & Hanson, Tyler J., 2016. "The accuracy of forecasts prepared for the Federal Open Market Committee," Journal of Economics and Business, Elsevier, vol. 83(C), pages 23-43.
    11. Ling Tang & Chengyuan Zhang & Tingfei Li & Ling Li, 2021. "A novel BEMD-based method for forecasting tourist volume with search engine data," Tourism Economics, , vol. 27(5), pages 1015-1038, August.
    12. Hewamalage, Hansika & Bergmeir, Christoph & Bandara, Kasun, 2021. "Recurrent Neural Networks for Time Series Forecasting: Current status and future directions," International Journal of Forecasting, Elsevier, vol. 37(1), pages 388-427.
    13. Michael Vössing & Niklas Kühl & Matteo Lind & Gerhard Satzger, 2022. "Designing Transparency for Effective Human-AI Collaboration," Information Systems Frontiers, Springer, vol. 24(3), pages 877-895, June.
    14. Frank, Johannes, 2023. "Forecasting realized volatility in turbulent times using temporal fusion transformers," FAU Discussion Papers in Economics 03/2023, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    15. Kourentzes, Nikolaos & Petropoulos, Fotios & Trapero, Juan R., 2014. "Improving forecasting by estimating time series structural components across multiple frequencies," International Journal of Forecasting, Elsevier, vol. 30(2), pages 291-302.
    16. Jeon, Yunho & Seong, Sihyeon, 2022. "Robust recurrent network model for intermittent time-series forecasting," International Journal of Forecasting, Elsevier, vol. 38(4), pages 1415-1425.
    17. Snyder, Ralph D. & Ord, J. Keith & Koehler, Anne B. & McLaren, Keith R. & Beaumont, Adrian N., 2017. "Forecasting compositional time series: A state space approach," International Journal of Forecasting, Elsevier, vol. 33(2), pages 502-512.
    18. Paulo Júlio & Pedro M. Esperança, 2012. "Evaluating the forecast quality of GDP components: An application to G7," GEE Papers 0047, Gabinete de Estratégia e Estudos, Ministério da Economia, revised Apr 2012.
    19. Rivera, Nilza & Guzmán, Juan Ignacio & Jara, José Joaquín & Lagos, Gustavo, 2021. "Evaluation of econometric models of secondary refined copper supply," Resources Policy, Elsevier, vol. 73(C).
    20. Cameron Roach & Rob Hyndman & Souhaib Ben Taieb, 2021. "Non‐linear mixed‐effects models for time series forecasting of smart meter demand," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(6), pages 1118-1130, September.
    21. Massimo Guidolin & Manuela Pedio, 2019. "Forecasting and Trading Monetary Policy Effects on the Riskless Yield Curve with Regime Switching Nelson†Siegel Models," Working Papers 639, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.

    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:eee:chsofr:v:143:y:2021:i:c:s0960077920310134. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.