Seismograms at small epicentral distances, usually, show higher harmonics, which appear as the waves superposed on the lower frequency waves and disappear with the increasing of epicentral distance. The investigations of these harmonics and their travel times make us possible to estimate the source spectrum.
If we count peaks (or troughs) of seismic waves as many as possible, we can define the apparent highest frequency
fmas
n/τ, where
n is the number of peaks (or troughs) in the time interval τ. Using some of the seismograms of the earthquakes occurred off the east coast of Hokkaido, we have the relation log
fm=
K0-
b log
tm, where
K0 and
b are constants and
tm is the travel time at the beginning of τ. Since this relation may be concerned with source spectrum, it will be obtained from this in combination with theoretical formulae. It will be a reasonable assumption that
fm is equal to the frequency of the sinusoidal wave of which amplitude is the smallest in those composing the seismogram. The obtained source spectrum is
S(
f)=
Gf-p/bexp (
Cf(
b-1)/
b), where
G,
p and
C are constants.
p is concerned with geometrical expansion and
C may be related to dissipation of waves.
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