Guralp Systems CMG-6T - Manual (Page 21)

Operator's Guide
3.2 Poles and zeroes
Most users of seismometers find it convenient to consider the sensor
as a “black box”, which produces an output signal V from a measured
input x. So long as the relationship between V and x is known, the
details of the internal mechanics and electronics can be disregarded.
This relationship, given in terms of the Laplace variable s, takes the
form
[V / x](s) = G A H(s)
In this equation
•
G is the output sensitivity (gain constant) of the instrument.
This relates the actual output to the desired input over the flat
portion of the frequency response.
•
A is a constant which is evaluated so that A H(s) is
dimensionless and has a value of 1 over the flat portion of the
frequency response. In practice, it is possible to design a system
transfer function with a very wide-range flat frequency
response.
The normalising constant A is calculated at a normalising
frequency value fm = 1 Hz, with s = j fm, where j = √–1.
•
H(s) is the transfer function of the sensor, which can be
expressed in factored form:
In this equation z
n
are the roots of the numerator polynomial,
giving the zeros of the transfer function, and p
m
are the roots of
the denominator polynomial giving the poles of the transfer
function.
In the calibration pack, G is the sensitivity given for each component
on the first page, whilst the roots z
n
and p
m
, together with the
normalising factor A, are given in the Poles and Zeros table. The poles
and zeros given are measured directly at Güralp Systems' factory using
a spectrum analyser. Transfer functions for the vertical and horizontal
sensors may be provided separately.
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