1) The formulas have been deduced by the method of least squares by which to determine the magnitude
M of a distant shallow-focus earthquake from surface wave data obtained at Matsushiro Seismological Observatory. These are
M=log
A+1.32logΔ+4.11(for 30sec period) (2) and
M=log
A+1.31logΔ+4.28(for 20sec period), (3)
where
A is the surface wave ground amplitude expressed in micron, Δ the epicentral distance in 1, 000km and log is the common logarithm.
If, instead of the amplitude
A, we use (
A/
T) which is proportional to the ground velocity, we get from the equations (2) and (3),
M=log(
A/30)+1.32logΔ+5.58 (4) and
M=log(
A/20)+1.31log Δ+5.58 (5)
which are almost exactly the same. We may write
M=log(
A/
T)+1.31logΔ+5.58. (6)
2) The energy
E′ of RAYLEIGH waves has been calculated for each of 16 selected shallow earthquakes, using seismograms obtained with the Galitzin and the Long Period seismographs working at Matsushiro. The magnitudes of the earthquakes range from 5.4 to 8.1. The energy
E′ and the magnitude
M have been found to be connected as follows
log
E′=(1.98±0.074)
M+(6.65±0.48). (9)
If the total energy
E of an earthquake is assumed to be twice the energy of RAYLEIGH waves, then follows the relation:
log
E=1.98
M+6.95. (10)
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