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

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## 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

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### References

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© Birkhäuser Verlag 1987