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

Article

Received:

Revised:

Accepted:

## Abstract

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)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)For the value of the maximum earthquake magnitude, which is exceeded with probability
*P*in*T*-years period,*M*_{ PT }$$M_{PT} = \frac{{ln(A_2 .T)}}{{A_3 }} - \frac{{ln[A_1 .T - ln(1 - P)]}}{{A_3 }}.$$ - 3)For the probability of occurrence of an earthquake of magnitude
*M*in a*T*-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## Preview

Unable to display preview. Download preview PDF.

## References

- 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 - Epstein, B. andLomnitz, C. (1966).
*A model for the occurrence of large earthquakes*, Nature*211*, 954–956.Google Scholar - Gumbel, E. J. (1966),
*Statistics of Extremes*. (Columbia Univ. Press, New York), 375 pp.Google Scholar - Gutenberg, B. andRichter, C. F. (1944),
*Frequency of earthquakes in California*, Bull. Seism. Soc. Am.*24*, 185–188.Google Scholar - Latousakis, J. (1985),
*Proposal for a modification of the cumulative frequency-magnitude relationship*, Ph.D. Thesis, Athens University, pp. 1–167.Google Scholar - Latousakis, J. andDrakopoulos, J. (1987),
*A modified formula for frequency-magnitude distribution*, PAGEOPH*125*, this issue.Google Scholar - 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 - 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 - 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