Absolute Calibration by nikeborome

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```									        International Training Course, Potsdam
ORFEUS Workshop, Vienna
IRIS Metadata Workshop, Kuala Lumpur 2007
Title
International Training Course, Heredia 2008

E. Wielandt:
Absolute (mechanical) calibration of seismometers
Systematics
Absolute Calibration
Except for geophone-type sensors, absolute calibration
requires a mechanical motion of the whole instrument
(„frame input“). It is normally obtained from a shake
table.
Shake tables are precise only in a frequency band around
1 Hz that does not cover the full bandwidth of broadband
sensors. So the frequency response must be measured
electrically (over the calibration coil). The absolute
calibration then determines the last unknown instrumental
parameter, the generator constant or responsivity. It is
most easily measured in the middle of the passband.
Passive electromagnetic sensors:

When the motion of the seismic mass is linear and its size is
known, then the generator constant can be determined
electrically, without moving the frame of the instrument. See
the old MSOP or the manual of the Sensonics MkIII seismo-
meter for a parameter determination based on the transient
response („ringdown“) following the interruption a known
current through the signal coil. Another method is suggested
in the next slide.
The generator constant can also be determined from
the numerical damping at different damping resistors.
Rd is sum of coil resistance and load resistance.
Comparison with a reference instrument

An unknown seismometer B can be absolutely calibrated by comparison with a well-
calibrated reference instrument A. For broad-band instruments, marine microseisms
provide a convenient test signal.
It is however a prerequisite that the components of A and B have the same orientation
in space. This may be inconvenient to achieve mechanically – it would require iterative
adjustments of the 3-d orientation until the best coherency is observed, which might not
occur for all three components at the same time. It is much easier to produce, from the
output signals of A, synthetic traces of ground motion that have the same orientation as
the components of B. The mathematical problem is to find a coefficient matrix G such
that, in a least-squares sense,

 Bx     gxx gxy         gxz     Ax 
 By    gyx gyy         gyz    Ay 
                                
 Bz 
        gzx gzy
                 gzz 
    Az 
 

This matrix equation can be solved with the LINCOMB3 software, or with MATLAB.
The gain of Bx relative to A is then (gxx2+gxy2+gxz2 )1/2, etc. We may also use the
reverse formulation (with A and B interchanged) and thus directly obtain a calibrated
three-component output signal from sensor B.
Systematics
Swing

Why horizontal shake tables are not useful at long periods: Tilt couples
gravity into the horizontal components of motion. We illustrate this with
a ball sitting on a swing. The ball (representing the seismic mass) would
not indicate any motion because the swing is an inertial system.
milling machine

The table of a milling machine
can provide a well-defined,
steplike frame input in three
axes. The only auxiliary device
is a stop for the handwheel,
here realized with a wooden

The DISPCAL software
evaluates only the start and
final positions of the sensor,
and is unsensitive to the time-
history of the motion. The
generator constant is obtained
with a precision of 1%.
plot

Calibration of an old STS1 (20s) on a milling machine.
Top: output signal; center: restored frame velocity; bottom: restored
frame displacement. Since the true displacement is known, we can
determine the generator constant of the sensor.
plot

The method works also with short-period seismometers
(here a Sensonics Mk III). However, in this case the free
period and damping of the sensor must be known with some
precision, so an electrical calibration should be made while
the sensor is installed on the milling machine. Top trace:
output signal, bottom: restored frame displacement.
balance

An ordinary packet balance can serve as an unexpensive vertical
step table. It may be necessary to suppress the wobbling horizontal
motion with steel ribbons (red) clamped to a fixed block (blue).
Further hints are given in the NMSOP (see last slide).
Calibrating an STS2 on a packet balance.
plot

Calibration of a 10 Hz geophone on a packet balance. Top: output
signal; traces 2 and 4: restored frame velocity; trace 5: a zoom of the
„quiet“ sections of trace 4; bottom: restored frame displacement.
For seismometers up
to 600 kg this
centesimal balance is
a perfect step table

(OVSICORI-UNA,
Heredia, Costa Rica)
tilt lever

Horizontal sensors or sensor components can be calibrated with tilt
steps. Broadband seismometers may go offscale when the tilt exceeds
a few parts in 10 000, but this takes some time. So one can use larger
tilts and keep the output within scale by reversing the tilt. The output
signal is analyzed with the TILTCAL3 software that is similar to
DISPCAL3 but identifies and measures steps of acceleration.
plot

A calibration by tilt steps. Top: output signal; trace 2: restored frame
velocity; trace 3 and 4: automatic identification of steps; bottom:
restored frame acceleration (the transitions have been blanked out).
Why seismometers should be calibrated in
situ:

some things can be wrong, or go wrong
during the installation in a vault, that
might not be detected in the lab.

We have seen:
and: undocumented or forgotten damping resistors,
dividers, even preamps ...
A portable step table for in
situ absolute calibration.

No need to disconnect and
reconnect cables.
The basic design element is an
elastic frame that permits only a
parallel motion of its sides. Four
of these frames connect the top
and bottom base-plates (in red) of
the table.

(side view as in the next slide)
close-up
A reduction lever for use with high-gain sensors

• IASPEI New Manual of Seismological Observatory
Practice, ed. P. Bormann, ISBN 3-9808780-0-7,
GeoForschungsZentrum Potsdam 2002: chapter 5

• IASPEI International Handbook of Earthquake and
Engineering Seismology Part A, ed. W. H. Lee et al.,
ISBN 0-12-440652-1, Elsevier 2003: chapter 18