Skip to main content
SpringerLink
Log in

A probabilistic model of seismicity: Kamchatka earthquakes

  • Published:
Journal of Volcanology and Seismology Aims and scope Submit manuscript

Abstract

The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, \( \tilde F \) P}. Each earthquake is treated as an outcome ω i in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events. In turn, ω i is characterized by a system of random variables, viz., energy class ki, latitude φ i , longitude λ i , and depth h i . The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set \( \tilde F \) and are defined by multivariate distributions, either by the distribution function \( \tilde F \) (φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of a power law for probability density f(k), where the initial value of the distribution function f(k 0) is the basic data [Bogdanov, 2006] rather than the seismic activity A 0, we proceed to show that for different intervals of coordinates and time the distribution f elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f full(k), which corresponds to the full catalog. It follows from our calculations that f 0(k) takes on nearly identical numeral values for different initial values of energy class k 0 (8 ≤ k 0 ≤ 12) f(k 0). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k 0) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function with the initial value f(k 0) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for several periods

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bogdanov, V.V., A Probabilistic Interpretation of the Earthquake Recurrence Relation: The Kamchatka Region, Dokl. RAN, 2006, vol. 408, no. 3, pp. 393–397.

    Google Scholar 

  • Bogdanov, V.V., Geppener, V.V., and Mandrikova, O.V., Modelirovanie nestatsionarnykh vremennykh ryadov geofizicheskikh parametrov so slozhnoi strukturoi (Modeling of Nonstationary Time Series of Complex-Structured Geophysical Parameters), St. Petersburg: LETI, 2006.

    Google Scholar 

  • Bogdanov, V.V. and Pavlov, A.V., A Program for Calculating the Probabilities of Seismic Events, Moscow: VNTITs, 2007 (Inventor’s Certificate no. 50200702092, Certificate of Industry Development no. 9093 as of October 10, 2007).

    Google Scholar 

  • Boldyrev, S.A., The Reflection of Lithosphere Structure and Properties in the Seismic Field of the Kamchatka Region, Fizika Zemli, 2002, no. 6, pp. 5–28.

  • Venttsel’, E.S., Teoriya veroyatnosti (Probability Theory), Moscow: GIFML, 1962.

    Google Scholar 

  • Gaiskii, V.N., Statisticheskie issledovaniya seismicheskogo rezhima (Statistical Studies in Seismicity), Moscow: Nauka, 1970.

    Google Scholar 

  • Golitsyn, G.S., Pisarenko, V.F., Rodkin, M.V., and Yaroshevich, M.I., The Statistical Characteristics of Tropical Cyclones and Risk Assessment, Izv. RAN, Fizika Atmosfery i Okeana, 1999, vol. 35, no. 6, pp. 734–741.

    Google Scholar 

  • Dobrovol’skii, I.P., Teoriya podgotovki tektonicheskogo zemletryaseniya (A Theory of the Preparation of a Tectonic Earthquake), Moscow: IFZ RAN, 1991.

    Google Scholar 

  • Keilis-Borok, V.I. and Kosobokov, V.G., Periods of High Probability of Occurrence of the World’s Strongest Earthquakes, in Mathematical Methods in Seismology and Geodynamics, New York: Allerton Press Inc., 1987, pp. 45–53.

    Google Scholar 

  • Kolmogorov, A.N., Osnovnye ponyatiya teorii veroyatnostei (The Basic Concepts of Probability Theory), Moscow: Nauka, 1974.

    Google Scholar 

  • Matvienko, Yu.D., The Application of the M8 Method to Kamchatka: A Successful Advance Forecast of the December 5, 1997 Earthquake, Vulkanol. Seismol., 1998, no. 6, pp. 27–36.

  • Molchan, G.M. and Dmitrieva, O.E., The Objective Function Approach to Aftershock Identification, in Seismichnost’ i seismicheskoe raionirovanie Severnoi Evrazii (The Seismicity and Seismic Zonation of North Eurasia), Moscow: IFZ RAN, 1993, pp. 62–69.

    Google Scholar 

  • V.F. Pisarenko, F.M. Pruchkina, and M.G. Shnirman, Stochastic Model of Evolution of a System with Defects, in Vychislitel’naya seismologiya (Computational Seismology, vol. 17), Mathematical Modeling and Interpretation of Geophysical Data, II, 1984, pp. 24–27 (Translated by Allerton Press in 1985).

  • Pyt’ev, Yu.A., Vozmozhnost’. Elementy teorii i primenenie (Possibility. Principles of the Theory and Applications), Moscow: Editorial URSS, 2000.

    Google Scholar 

  • Riznichenko, Yu.V., Problemy seismologii (Problems in Seismology), Moscow: Nauka, 1985.

    Google Scholar 

  • Sadovskii, M.A., Golubeva, T.V., Pisarenko, V.F., and Shnirman, M.G., Typical Rock Sizes and the Hierarchical Properties of Seismicity, Fizika Zemli, 1984, no. 2, pp. 2–15.

  • Smirnov, V.B., Earthquake Catalogs: Evaluation of Data Completeness, Vulkanol. Seismol., 1997, no. 4, pp. 93–105 [Volcanology and Seismology, 1998, vol. 19, no. 4, pp. 497–510].

  • Sobolev, G.A., Osnovy prognoza zemletryasenii (Principles of Earthquake Prediction), Moscow: Nauka, 1993.

    Google Scholar 

  • Sobolev, G.A., Precursory Periods of Large Kamchatka Earthquakes, Vulkanol. Seismol., 1999, no. 4/5, pp. 63–72.

  • Stakhovskii, I.R., The Expansion of the f(α-Spectra of Seismic Fields in the Precursory Volumes of Large Earthquakes, Fizika Zemli, 2002, no. 2, pp. 74–78.

  • Fedotov, S.A., Chernyshev, S.D., Matvienko, Yu.D., and Zharinov, N.A., The Forecast of the December 5, 1997, Magnitude 7.8–7.9 Kronotskii Earthquake, Kamchatka, and Its M≥ 6 Aftershocks, Vulkanol. Seismol., 1998, no. 6, pp. 3–16 [Volcanology and Seismology, Gordon and Breach, cover-to-cover translation, 1999, vol. 20, no. 6, pp. 597–613).

  • Fedotov, S.A., Shumilina, L.S., and Chernysheva, G.V., The Seismicity of Kamchatka and the Commander Islands Based on Data of Detailed Investigations, Vulkanol. Seismol., 1987, no. 6, pp. 29–60.

Download references

Author information

Authors and Affiliations

  1. Institute of Space Physics Research and Radio Wave Propagation, Far East Division, Russian Academy of Sciences, Kamchatskii Krai, Paratunka, 684034, Russia

    V. V. Bogdanov, A. V. Pavlov & A. L. Polyukhova

Authors
  1. V. V. Bogdanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Pavlov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. L. Polyukhova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Bogdanov.

Additional information

Original Russian Text © V.V. Bogdanov, A.V. Pavlov, A.L. Polyukhova, 2010, published in Vulkanologiya i Seismologiya, 2010, No. 6, pp. 52–64.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogdanov, V.V., Pavlov, A.V. & Polyukhova, A.L. A probabilistic model of seismicity: Kamchatka earthquakes. J. Volcanolog. Seismol. 4, 412–422 (2010). https://doi.org/10.1134/S0742046310060059

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0742046310060059

Keywords

Search

Navigation