IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v49y2006i3p377-401.html
   My bibliography  Save this article

Power law distribution of seismic rates: theory and data analysis

Author

Listed:
  • A. Saichev
  • D. Sornette

Abstract

We report an empirical determination of the probability density functions P data (r) (and its cumulative version) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 ×5 km 2 , 20 ×20 km 2 and 50 ×50 km 2 and time intervals $\tau =10,~100$ and 1000 days. The data can be represented by asymptotic power law tails together with several cross-overs. These observations are explained by a simple stochastic branching process previously studied by many authors, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (“aftershocks”). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. We develop the full theory in terms of generating functions for describing the space-time organization of earthquake sequences and develop several approximations to solve the equations. The calibration of the theory to the empirical observations shows that it is essential to augment the ETAS model by taking account of the pre-existing frozen heterogeneity of spontaneous earthquake sources. This seems natural in view of the complex multi-scale nature of fault networks, on which earthquakes nucleate. Our extended theory is able to account for the empirical observation but some discrepancies, especially for the shorter time windows, point to limits of both our theoretical approach and of the ETAS model. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Suggested Citation

  • A. Saichev & D. Sornette, 2006. "Power law distribution of seismic rates: theory and data analysis," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(3), pages 377-401, February.
    • Handle: RePEc:spr:eurphb:v:49:y:2006:i:3:p:377-401
    DOI: 10.1140/epjb/e2006-00075-3
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2006-00075-3
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1140/epjb/e2006-00075-3?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    2. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    3. Holliday, James R. & Turcotte, Donald L. & Rundle, John B., 2008. "Self-similar branching of aftershock sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 933-943.

    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:eurphb:v:49:y:2006:i:3:p:377-401. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.