principles and applications of microearthquake networks

34 2. Instrumentation Systems
1 0 7 ~ I I I 1 I I I I I I I I\ I 1 I I
i
I I l l I I I / I I I l l I I I I
0.01 0.1 1 10 100
FREQUENCY (Hz)
Fig. 13. Smoothed amplitude response of the seismic system used in the USGS Central
California Microearthquake Network as determined by Bakun and Dratler ( 1976) using a
Fourier transform technique.
vidual components as well) could be adequately approximated by
where w is the frequency in radians per second, al are the poles of the
function F(w), Cj are real constants associated with each pole, 1 is the
power of the low-frequency roll-off, n - 1 is the power of the highfrequency
roll-off in the amplitude response, and Aj are amplitude factors
representing the sensitivity or gain of individual components within the
system.
Because the physical system represented by F( w) is real and causal, all
the poles lie in the upper half of the complex plane. They are located
either on the imaginary axis or off the axis as matched pairs (i,e,, mirror
images through the imaginary axis). Those that lie on the imaginary axis
are single poles and have the form -aj/( w - aj), or the form w/( w - af),
where aj = iwo, and wo is the frequency in radians per second. Those poles
that occur as matched pairs are double poles and have the form aJaL/( w -
cq)(w - ak) or w2/(o - q )(w- ak), where