A magnitude-frequency relation for the lognormal distribution of earthquake magnitude

SummaryThe paper discusses the magnitude-frequency relation, logN(M)=a+b logM-c(logM)2, for the lognormal distribution of earthquake magnitude in a given series. Bothb andc coefficients are usually determined by the method of least squares. Being given an estimation method for this coefficient values, there is obtained: $$b = \frac{{\log e\log \gamma }}{{\sigma ^2 \log }},c = \frac{{\log e}}{{2\sigma ^2 \log }}$$ where log λ and σlog2 are the mean and the variance of the variable, logM, respectively. Some aspects of this magnitude-frequency relation are also discussed for the earthquake series where the lognormality assumption is accepted.