principles and applications of microearthquake networks

2.2. Central Calfornicr i2Iic.roeiirthyrrulie Netwvrk 35
00 = 27TfO
and p can be interpreted as a damping coefficient.
For example, if Eq. (2.8) is taken as the frequency response of the
complete seismic system, then the impulse response in the time domain is
I (2.10) f(t) = (2 ~TT)-I F( w ) exdiwt) do
--r
When this integral is evaluated, the residue at thejth pole is found to be
bj(aj) exp(iaJt), where
b,( ar) means bj evaluated at o = ai, and the factors Ai have been ignored.
The impulse response for the complete seismic system is written as
(2.12)
Expressions similar in form to Eq. (2.12) were derived by Healy and
O'Neill(l977) for the time domain representation of the amplifier step test
and the seismometer release test.
Starting with the expression for the time domain form of the amplifier
step test, Healy and O'Neill (1977) applied a least-squares method to
calculate the locations of the poles a,. Trial values of the ai and fixed
values of I and n were determined from calibration of various components
of the system-for the step test this is the amplifier, VCO, and the discriminator.
Refined values for the poles ai were computed by least
squares, and these were substituted into Eq. (2.9) to computefo and p.
The refined values also were substituted into Eq. (2.81, and a theoretical
response was computed for the amplifier-VCO-discriminator combination.
The agreement between the calculated response and that determined
by calibration in the laboratory was very good.
Stewart and O'Neill (1980) used Eq. (2.8) to calculate the ,frequency
response for various combinations of units used in the USGS Central
California Microearthquake Network. We shall illustrate their method by
calculating the response of the complete seismic system from seismometer
to the viewing screen used for the 16-mm Develocorder films.
Before the system response can be calculated from Eq. (2.8), the constants
I, n, Ci, ai, and Ai must be determined. It is convenient to divide the
complete system into four units and to determine these constants sepa-