Clustering in Time and Periodicity of Strong Earthquakes in Tokyo Masami OKADA Kobe Marine Observatory (Received on March 30, 1977) The clustering in time and periodicity of earthquake occurrence are investigated statistically by the use of historical data of strong earthquakes in Tokyo. In order to discuss the periodicity of main shocks, the author examines the homogeneity of historical materials and the distributions of the intervals between any two earthquakes and between two successive earthquakes. It is found that one third to one fourth of events can be regarded as fore- and aftershocks in a wide sense. By the use of Monte Calro method, it is tested statistically whether the occurrence of main shocks is represented by a stationary random process or a periodic process. As a result, the 69-year periodicity, which is the highest peak in the periodgram calculated from Kawasumis table, is not statistically significant at a 95% confidence level, but becomes significant if we lower the confidence level down to 80%. From the table of Usami and Hisamoto, the 36-year periodicity, which is the most predominant in their table, is found to be insignificant even at the 80% confidence level.

Tabel 1. Frequency of strong earthquakes and meteorogical disasters. The figures in parentheses are the ratio of yearly frequency to the 5th period. *: before 1900. Fig. 1. Time series of strong earthquakes in Tokyo tabulated by Kawasumi (case K). Intensity is denoted by JMA scale. Circles show the crests of the 69-year periodicity.

(a) Fig. 2. Power spectrum of the strong earthquake occurrence in Tokyo. Broken line shows y(w) and solid line denotes Y(w). (a) case K, (b) case U (tabulated by USAMI & HISAMOTO).

Fig. 3. V, VS and Vc+Cs. and Vc VS are variances of cos 2irftj-c and sin 2irftj-s, respectively.

Fig. 4. Frequency of time intervals between any two earthquakes in the 5-th period. Broken line shows the case for a randow process. Fig. 5. Frequency of time intervals between two successive earthquakes in the 5-th period.

Fig. 6. Distribution of mean and maximum powers of random cases with a stationary process (no aftershock model). Oblique lines and numbers show the ratio of maximum/mean power. Cross shows the values for case K. The maximum power for solid circles is larger than the one for case K.

Fig. 7. Distribution of mean and maximum powers (seven-aftershock model). Nk denotes the number of main shocks accompanied by k aftershocks. Fig. 8. Distribution of mean and maximum powers (eleven-aftershock model).

Fig. 9. Distribution of mean and maximum powers with a periodic process f(t)dt= a (1.0+0.85 sin wot)dt (nine-aftershock model). Solid circles show that the power for wo is maximum power. When they disagree with each other, the power for Oo is denoted with open circle and maximum power is shown by a cross. Square is the values of case K.

VERE-JONES D. and R. B. DAVIES, 1966, A Statistical Survey of Earthquakes in the Main Seismic Region of New Zealand, Part 2, -Time Series Analyses, N. Z. J. Geol. Geophys., 9, 251-284.