pure and applied geophysics

, Volume 125, Issue 5, pp 765–775 | Cite as

Reoccurrence formulas for the largest earthquake magnitudes based on the modified cumulative frequency-magnitude relationship

  • J. Latousakis
  • J. Drakopoulos


A modified formula of the cumulative frequency-magnitude relation has been formulated and tested in a previous paper by the authors of this study.

Based on the modified relationship, the following reoccurrence formulas have been obtained.
  1. 1)
    For the ‘T-years period’ larger earthquake magnitude,M T
    $$M_T = \frac{1}{{A_3 }}ln\frac{{A_2 }}{{(1/T) + A_1 }}.$$
  2. 2)
    For the value of the maximum earthquake magnitude, which is exceeded with probabilityP inT-years period,M PT
    $$M_{PT} = \frac{{ln(A_2 .T)}}{{A_3 }} - \frac{{ln[A_1 .T - ln(1 - P)]}}{{A_3 }}.$$
  3. 3)
    For the probability of occurrence of an earthquake of magnitudeM in aT-years period,P MT
    $$P_{MT} = 1 - \exp [ - T[ - A_1 + A_2 \exp ( - A_3 M)]].$$

The above formulas provide estimates of the probability of reoccurrence of the largest earthquake events which are significantly more realistic than those based on the Gutenberg-Richter relationships; at least for numerous tested earthquake samples from the major area of Greece.

Key words

Reoccurrence formulas hazard assessment 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Drakopoulos, J. andMakropoulos, C. (1983),Seismicity and hazard analysis studies in the area of Greece. (Seism. Lab. Athens Univ., Publ. no. 1,) pp. 1–126.Google Scholar
  2. Epstein, B. andLomnitz, C. (1966).A model for the occurrence of large earthquakes, Nature211, 954–956.Google Scholar
  3. Gumbel, E. J. (1966),Statistics of Extremes. (Columbia Univ. Press, New York), 375 pp.Google Scholar
  4. Gutenberg, B. andRichter, C. F. (1944),Frequency of earthquakes in California, Bull. Seism. Soc. Am.24, 185–188.Google Scholar
  5. Latousakis, J. (1985),Proposal for a modification of the cumulative frequency-magnitude relationship, Ph.D. Thesis, Athens University, pp. 1–167.Google Scholar
  6. Latousakis, J. andDrakopoulos, J. (1987),A modified formula for frequency-magnitude distribution, PAGEOPH125, this issue.Google Scholar
  7. Makropoulos, C. (1978),The statistics of large earthquake magnitude and an evaluation of Greek seismicity, Ph.D. Thesis, University of Edinburgh, pp. 1–178.Google Scholar
  8. Makropoulos, K., Drakopoulos, J. andLatousakis, J. (1986),A revised earthquake catalogue for Greece since 1900. (Geoph. Dep. of Athens Univ., Publ. no. 2), pp. 1–94.Google Scholar
  9. Papazachos, B. C. andComninakis, P. E. (1982),A catalogue of historical earthquakes in Greece and the surrounding area. (Geoph. Lab. Thessaloniki Univ., Publ. no. 5,) pp. 1–71.Google Scholar

Copyright information

© Birkhäuser Verlag 1987

Authors and Affiliations

  • J. Latousakis
    • 1
  • J. Drakopoulos
    • 1
  1. 1.Seismological InstituteNational Observatory of AthensAthensGreece

Personalised recommendations