Global Distribution of Maximum Earthquake Magnitude M_c Based on a Modified G-R Model of Magnitude-Frequency Distribution

Abstract

We expect the existence of upper limit in the size of earthquakes, which may vary from region to region under the influence of the tectonic environment, stress distribution, structural heterogeneity and so on. In this paper, we investigated the possibility of estimating the maximum possible magnitude M* based on a modified G-R model of frequency distribution of earthquake magnitude.
The modified G-R model we used was proposed by Utsu (1971) as
logn (M) =a-bM+log (M_c-M),
where M_c is the maximum magnitude estimated from the magnitude-frequency distribution model. We estimated M_c by using 9734 globally distributed earthquakes with moment magnitude equal to or larger than 5.5 that are listed in the Harvard Centroid Moment Tensor Catalogue for the last 25 years.
We estimated three model parameters a, b and M_c by the maximum likelihood method. The error in M_c was also estimated by taking the maximum range of 1σ error ellipsoid on the assumption that the error of maximum likelihood estimates follows a bivariate normal distribution. We estimated M_c=8.61±0.12 for all the data. Dividing the whole data into data subsets by focal depths and seismic regions, we found depth dependence and remarkable regional dependence for shallow earthquakes (h≤60km) in the M_c value. The comparison with the earthquake catalogue for the past about 100 years showed that M_c estimated from the data of 25 years can predict the maximum magnitude in the longer period with an uncertainty of ±1-2. These results indicate that there exists a strong regionality in M_c M_c may be used, to some extent, for estimating the maximum earthquake magnitude inherent to the region.