1) Gutenberg and Richter studied frequencies and magnitudes of earthquakes and obtained the following relation establishing a relationship between magnitude and energy released annually by earthquake waves (NE),
log
NE=18.7+0.9
M. (1)
This relation shows that “
NE” becomes greater as
M becmes bigger. And they concluded that smaller shocks almost never were sufficiently frequent to approximate the energy, released in larger shocks. This conclusion is, of course, not wrong, so far as the Richter's Magnitude-scale is concerned. But if
E is adopted instead of
M, the above formula is transformed into the following one,
log
NE=cont.-0.5log
E. (2)
This shows that the energy released annually by larger shocks is smaller than that by minor shocks. This seeming contradiction between (1) and (2) is due to how the magnitude is measured, by
M or by
E.
2) Kawasumi's results on energies and frequencies of earthquakes derived from the data of earthquakes in and near Japan fairly agree with those by Gutenberg and Richter.
3) The Ishimoto-lida's formula,
n(
a)
da=
ka-
mda, can be changed into a formula, log
N=cost.-b
M, under some suitable assumptions. If m is 1.9, the value of b is 0.9.
4) The energy of the smallest micro-earthquakes observed by the present authors is of the order of 10
10 erg. which is about 1/100 of that of the minimum earthquake observed by Richter and Nordquist. The Ishimoto-Iida's formula holds good even for such small earthquakes.
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