地殻変動の継続期間と地震の規模との関係について

抄録

If the earthquake is the result of the accumulation of strain energy in the crust and the upper mantle, it might be expected that the necessary period of energy storage will be related to the scale of the resulting earthquake. For shallow earthquakes, it is expected that the crustal deformation accompanied by the strain accumulation may be observed by frequent surveys of geodetic nets in the area concerned. Although it is quite difficult at the present stage to find geodetic data which clarified the period of duration of the preseismic crustal deformation, the writer looked for following three examples which might have the possibility of suggesting the preseismic duration.Name Year and Mag. Assumed duration T Nankaido Earthquake 1946 M 8.1 92 years Kitamino Earthquake 1961 M 7.0 12 years Omi Earthquake 1967 M 5.0 0.3 years Considering that these three data show a linear relation between M and log T, the writer calculated the coefficient of log T = bM+a by using method of least squares as follows;log T = bM+a = 0.79 M-4.44. (1)Further he checked this equation by applying it to some examples which suggest the durations of preseismic deformations in somewhat insufficient features comparing the above mentioned data, and found considerable consistency (Table I and Fig. 5). If the earthquake may occur when the linear strain per unit length of the rock of the earth's upper layer attained to some limiting value and Eq. (1) is concluded, then we may have the following equation;eT = const. (2)where e is the velocity of strain accumulation per unit length per year. This shows that the small earthquake will be caused by quicker accumulation of strain than large one, which is favourable condition for the purpose of earthquake prediction. From Eq. (1), the duration of crustal deformation of the earthquake of M8.6 (which may be the maximum to be expected) is about 220 years. If we assume that, in the volume surrounding the epicentral region which stores most part of seismic energy, the average strain per unit length will be about 5 x 10-5 immediately before the earthquake, then Eq. (2) becomeseT≈5 x 10-5, (3)and for the earthquake of M8.6e≈2.2 x 10-7 per year.Let us assume furthermore that the horizontal average diameter of this seismic volume be about 200 km, then the crustal movement of the circumference of this area will be about 4.5 cm/year, which nearly corresponds to the value suggested by the theory of continental drift and ocean bottom spreading. The writer assumed the time interval To and the block (described as a seismic province in the following) which covers so-called a seismic cycle and contains one complete sequence of earthquakes including one earthquake of maximum scale. Let the number of earth-quakes of almost same magnitude per year be N, and T be the period of preparation which might be considered as duration of progressive strain accumulation, then in one seismic province the following equation might be obtained, assuming statistically the sequential collation of duration periods for earthquakes of nearly the same magnitude, ToNT = To, as ToN is the number of earthquakes in To years. Then NT =1. (4)After Gutenberg and Richter log N = β M+α. (5)From Eqs. (1), (4) and (5), b = - β and α = - a. (6)According to the estimation by Gutenberg and Richter, the coefficients 3 and a for Japan area β=-0.80 and α=+5.5. (7)Comparing (1) with (7), the first condition of (7) is almost satisfied and the second may also hold, if we assume about ten seismic provinces for Japan. To confirm the reality of these relations, more data and investigations are expected.