principles and applications of microearthquake networks

2.2. C'errtrcil C'alifornicr Microecit-thqmke Netirwk 37
rately for each unit (Table I). These units are (1) the seismometer and
L-pad, (2) the seismic amplifier and voltage-controlled oscillator, (3) the
discriminator at the central recording site, and (4) the 16-mm film recorder
and film viewer.
For the seismometer and L-pad, the constants I = 3 , = ~ 2, and Ci =
Cj = 1 are determined by comparing Eq. (2.8) with the Fourier transform
of the response of an electromagnetic seismometer to a delta function
(Healy and O'Neill, 1977)
(2.13) V(O) = G~w~/(w - aj)(w - C Y ~ )
where V(w) is the Fourier transform of the output voltage u(t), G is the
effective motor constant of the seismometer and L-pad combination, and
w, aj, and cxk have the same meaning as in Eq. (2.8). The constants cq and
ak are computed from Eq. (2.9) using the USGS standard values& = 1.0
Hz, and /3 = 0.8. The constant A, = G = 1.0 V cm-' sec is the USGS
standard value for the effective motor constant (Fig. 7). These values are
all given in the first line of Table I.
For the remaining three units, the amplitude factors Aj are standard
values specified by the USGS (Table I), and other response parameters
are determined by calibration in the laboratory. For each of the three units
the measured frequency response curves were compared to sets of master
response curves calculated for certain values of I, n, Cj and, where appropriate,
@. A visual fit of the laboratory calibration curves to the master
curves provided the values offo and /3 for each instrumental unit. From
these values aj and ak were determined from Eq. (2.9).
Table I contains all the data required by Eq. (2.8) to calculate the
system amplitude response. If complex arithmetic is used to calculate
F(w), then the system amplitude response is the absolute value of the
complex expression Eq. (2.8). The amplitude response for the system
specified by Table I is shown in Fig. 14.
Bakun and Dratler (1976) summarized the relative merits of the Fourier
transform and least-squares techniques. They pointed out that these two
approaches are complementary, and each has its applications in calibrating
microearthquake networks. The Fourier transform technique may be
used routinely to verify that the system is operating within specifications
with no unexpected sources of noise. It may also be used to correct
seismic data for system response at lower frequencies, as required by
some seismological studies. The least-squares approach may be used in
studies that require an analytical expression for the response function. It
may also be used to extend the system response to higher frequencies than
those computed from the Fourier transform technique.