Statistical prediction of the occurrence of maximum magnitude earthquakes

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Abstract
This paper intends (a) to improve the early results for statistical prediction of the occurrence of maximum magnitude earthquakes obtained by Yegulalp and Kuo by including all of the seismicity data of both Gutenberg and Richter, and Rothé covering the period 1904 to 1965 and (b) to show the predictability of the regional occurrence of maximum magnitude earthquakes for the period 1953 to 1965 by using the seismicity data for 1904 to 1952. Of 51 regions, as classified by Gutenberg and Richter for the world, data for 46 have been analyzed and tested for their goodness-of-fit to the theoretical extremal distributions. The parameters of the asymptotic extremal distributions have been estimated by the method of least squares. Results show that the regional occurrence of maximum magnitude earthquakes definitely favors the third type asymptotic distribution over the first type. The existence of a finite upper bound for the third type asymptotic distribution is physically consistent with the fact that the strength of the solid Earth is finite. Among all of the regions, the curves for the northern and western circum-Pacific belt are generally the highest; those for the eastern circum-Pacific belt are the second highest: those for Eurasia, i.e., the Alpide belt and its adjacent regions, are the third highest; and those for the oceans and stable continental masses are the lowest. The predictability of the regional occurrence of maximum magnitude earthquakes has been tested by predicting the magnitudes corresponding to the return periods of 2, 3, 5, and 13 years for the period 1953 to 1965 and comparing the corresponding number of exceedances with the observed number of exceedances for these magnitudes. Except for the regions with inadequate data, agreement has been remarkably good for most of the regions: thus, the validity and the usefulness of the present results are established. Apparently, the two sets of the seismicity data of Gutenberg and Richter (1954) and Richter (1958) and that of Rothé (1972) are statistically stable. On the basis of the present complete data for 1904 to 1965, predicted maximum magnitudes in each of 46 regions for the return periods of 20, 50, and 100 years are given.

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