principles and applications of microearthquake networks

22 2. Ins tru inen ta t ion Systems
placement spectra that would be recorded by the instrumental system is
shown in Fig. 6. These are obtained by adding the logarithmic instrumental
response curve to each of the logarithmic theoretical ground displacement
curves. The locations of the theoretical corner frequencies for earthquakes
from magnitude 0 to 6 are shown by arrows in this figure. All the
response curves are stylized; each is represented by a small number of
linear segments. This is sufficient for the present discussion and is an
accepted way to diagram frequency response (Willmore, 1961). The theoretical
ground displacement curves in Fig. 4 do not include the effects of
the radiation pattern at the source, absorption and scattering along the
transmission path, and conditions at the recording site. These effects are
discussed in Thatcher and Hanks (1973).
Some interesting relations can be inferred from the combined displacement
response curves (Fig. 6). For earthquakes in the magnitude range
slightly greater than 1 to about 4, the peak of the combined displacement
response curve or, equivalently, the frequency of the maximum amplitude
that would be seen on the seismogram, varies with the magnitude of the
earthquake. For the assumed source model this frequency corresponds
to the corner frequencyfo.
I
21
1
-6 1 / '\
1 ,-t
i
i-.r__-
1 0 1
0.01 01
1 10 100
FREQUENCY (Hz)
Fig. 6. Theoretical combined displacement response as a function of frequency for
earthquakes ranging in magnitude from 0 to 6. Corner frequencies of these earthquakes are
shown by arrows, and magnitude of each earthquake is indicated by an integer to the left of
each curve.