The writer tried to find out whether any secular variations occur in the value of β in the expression of relation between the number
N of earthquakes and their magnitude logΔ, log
N=α-βlogΔ, using, in place of magnitude
M, the value logΔ, a common logarithm of the maximum felt distance, Δ (km), of the earthquake.
The areas investigated in the present paper are Regions E, F, G, and H shown in Fig. 1. The values of Δ were sorted out for the years from 1920 to 1967 and divided into four groups: Δ=180km(100km≤Δ<250km), 320km (250km≤Δ<400km), 500km (400km≤Δ<600km), and 800km (600km≤Δ<1000km). With regard to the number
N of earthquakes during the period of every five years (for Regions E and F) or every ten years (for Regions G and H), the coefficients α and β in each region and each period were determined by the method of least squares.
The obtained values of α and β are shown in Tables 1 to 4, together with their probable errors, and the variations of the value of β are shown in Figs. 2 to 5, respectively. In each region, it is certain that the value of β shows secular variation. At the top of each figure, the total energy released by the earthquakes during the statistical period is described. It is noticeable that release of great seismic energy took place when the value of β was becoming minimum. The relationship between the seismic energy (erg) per 10
4km
2 per year and the values of β is, as shown in Fig. 6, expressed by the form, log
E=23.97-1.07β. If we in this expression let β→0, we find that
E≈10
24erg/10
4km
2, and it means that the maximum energy released by a earthquake is about 10
24erg. This estimated value may be reasonable.
In Region E, the value of β for the aftershocks of '68 Tokachi-Oki Earthquake was obviously greater than the value of β for the earthquakes during five years just before the Earthquake.
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